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Any replacements are listed farther down

[2678] **viXra:1804.0225 [pdf]**
*submitted on 2018-04-16 07:54:40*

**Authors:** Edgar Valdebenito

**Comments:** 4 Pages.

This note presents continued radicals and trigonometric formulas for the argument 2npi/13, n=1,2,3,4,5,6.

**Category:** General Mathematics

[2677] **viXra:1804.0195 [pdf]**
*submitted on 2018-04-14 11:41:48*

**Authors:** Claude Michael Cassano

**Comments:** 10 Pages.

This linear algebra technique provides a useful method of obtaining exact solutions to homogeneous linear ordinary differential equations. The Bessel half integer solutions, being long well known, have been used here to verify with confidence the above linear independence technique for solving ordinary differential equations. The Bessel second order LHODE has been used, here, as an example application of this vector space transformation technique. Clearly, it may be used on other non-general elementary second order LHODE, such as the Legendre, Laguerre, Hermite and other second order LHODE's. Using the two linearly independent solutions of a second order linear homogeneous ordinary differential equations insures that the two functions are linearly independent. However, any two linearly independent functions may be used, and the two resulting differential equations need not be the same, as was the case for the Bessel's above. In fact, clearly, the technique may also be used for higher order LHODE's, since there are N linearly independent solutions of an N-th order LHODE there would be an equal number of transformation equations.

**Category:** General Mathematics

[2676] **viXra:1804.0173 [pdf]**
*submitted on 2018-04-12 14:33:36*

**Authors:** Yeray Cachón Santana

**Comments:** 11 Pages.

As far as I know, there is no a study on fractals on non euclidean metrics.This paper proposes a first approach method about generating fractals on a non-euclidean metric. The idea is to extend the calculus of fractals on non-euclidean metrics. Using the Riemann metric, there will be defined a non-euclidean modulo of a complex number in order to check the divergence of the series generated by the Mandelbrot set. It also shown that the
fractals are not invariant versus rotations. The study will be extended to the quaternions, where is shown that the study of fractals might not be extended to quaternions with a general metric because of the high divergence of the series (a condition in order to generate a fractal is selecting bounded operators). Finally, a Java program will be found as example to show those kind of fractals, where any metric can be defined, so it will be helpful to study those properties.

**Category:** General Mathematics

[2675] **viXra:1804.0171 [pdf]**
*submitted on 2018-04-12 14:59:06*

**Authors:** Allen C. Conti

**Comments:** 1 Page. (c) Allen C. Conti 2015-2018

Possible solution to the Fermat Conjecture regarding other exponents satisfying the Pythagorus relationship. Solution uses algebraic substitution, logical deduction and modulus verification.

**Category:** General Mathematics

[2674] **viXra:1804.0073 [pdf]**
*submitted on 2018-04-04 08:06:18*

**Authors:** Christophe Chalons

**Comments:** 8 Pages.

Papier décrivant des procédés usant abusivement du mot science et qui met en garde

**Category:** General Mathematics

[2673] **viXra:1804.0066 [pdf]**
*submitted on 2018-04-04 15:53:11*

**Authors:** Franco Sabino Stoianoff Lindstron

**Comments:** 3 Pages.

This paper shows, for the first time, that the explicit and exact solution to the Troesch nonlinear twopoint
boundary value problem may be computed in a direct and straightforward fashion from the
general solution obtained by a generalized Sundman transformation for the related differential
equation, which appeared to be a special case of a more general equation. As a result, various initial
and boundary value problems may be solved explicitly and exactly.

**Category:** General Mathematics

[2672] **viXra:1804.0015 [pdf]**
*submitted on 2018-04-02 07:53:08*

**Authors:** Edgar Valdebenito

**Comments:** 3 Pages.

This note presents some formulas of pi in terms of sum of arctangents.

**Category:** General Mathematics

[2671] **viXra:1804.0001 [pdf]**
*submitted on 2018-04-01 07:28:16*

**Authors:** Koji KOBAYASHI

**Comments:** 18 Pages.

This paper describes about relation between circuit complexity and accept inputs structure in Hamming space by using almost all monotone circuit that emulate deterministic Turing machine(DTM).
Circuit family that emulate DTM are almost all monotone circuit family except some NOT-gate which connect input variables (like negation normal form (NNF)). Therefore, we can analyze DTM limitation by using this NNF Circuit family. NNF circuit family cannot compute sandwich structure effectively. Sandwich structure is two accept inputs that sandwich reject inputs in Hamming space. So NNF circuit have to use unique AND-gate to identify each different vector of sandwich structure. That is, we can measure problem complexity by counting different vectors.
Some dicision problem have caracteristic in sandwich structure. Different vectors of Negate HornSAT problem are at most constant length because we can delete constant part of each negative literal in Horn clauses by using definite clauses. Therefore, number of these different vector is at most polynomial size. The other hand, Negate CNFSAT problem have different vector which number is over polynomial size.

**Category:** General Mathematics

[2670] **viXra:1803.0735 [pdf]**
*submitted on 2018-03-30 15:55:52*

**Authors:** Huda E. Khalid, Ahmed K. Essa, A. A. Salama

**Comments:** 115 Pages.

ان التحليل النيوتروسوفكي يعد تعميما لتحليل المجموعة ، والتي بدورها تعد تعميما لتحليل الفترة ، ان الحسبان النيوتروسوفكي التمهيدي يشير الى قيم ثابتة للاتعيين ، بينما حسبان التفاضل والتكامل النيوتروسوفكي يمكن اعتبارها رياضيات ذات لاتعيين متغير ، مبادئ حساب التفاضل والتكامل النيوتروسوفي وحساب التفاضل والتكامل النيوتروسوفكي يمكن تطويرهما بطرق عديدة ، وذلك بالاعتماد على انواع اللاتعيين التي تملكها المسألة كذلك بالاعتماد على الطرق المستخدمة في التعامل معها . قدمنا في هذا الكتاب بعض الامثلة عن اللاتعيينات الخاصة ، لكن يوجد الكثير من اللاتعيينات في حياتنا اليومية ، يجب علينا دراستها واعادة حلها باستخدام طرق مشابهة او طرق مختلفة عن التي ذكرناها . لذلك نحن بحاجة الى مزيد من الابحاث العلمية في حقل النيوتروسوفك . يمكن مستقبلا دراسة حسبان التفاضل والتكامل النيوتروسوفكي الجزئي من خلال ابحاث متقدمة في هذا المضمار . قدم المؤلف في هذا الكتاب ولاول مرة افكار لكل من شبه الغاية النيوتروسوفية ، وشبة الاستمرارية النيوتروسوفكية بطرق مختلفة عن شبه – الاستمرارية التقليدية, وشبه المشتقة النيوتروسوفكية, وشبه التكامل النيوتروسوفكي بطرق تختلف عن حسبان التفاضل والتكامل الجزئي الاعتيادي ، بالاضافة الى التعاريف التقليدية للغاية والاستمرارية والمشتقة والتكامل تباعا.

**Category:** General Mathematics

[2669] **viXra:1803.0633 [pdf]**
*submitted on 2018-03-24 00:41:03*

**Authors:** Koji KOBAYASHI

**Comments:** 8 Pages.

This paper describes about "Almost all monotone circuit family" and introduce its interesting advantages to measuring problem complexity.
Explained in Michael Sipser "Introduction to the Theory of COMPUTATION", circuit family that emulate Deterministic Turing machine (DTM) are almost all monotone circuit family except some NOT-gate that connect input variables (like negation normal form (NNF)).
This "NNF Circuit family" have good characteristic which present each accept input exclusivity and symmetry. Each input make some INPUT-gate and NOT-gate output 1 which set is different from another input, and meet these output in OR-gate and finally connect (specified) OUTPUT-gate. That is, NNF circuit start accept input that exclusive each other, and meet each input as symmetry input step by step and finally goal same output. Especially, some accept input which sandwitch reject inputs correspond with unique gate. That is, we can measure problem complexity by using NNF circuit and sandwitch inputs. For examples, such sandwitch inputs include DNF tautorogy problem.

**Category:** General Mathematics

[2668] **viXra:1803.0622 [pdf]**
*submitted on 2018-03-23 07:18:35*

**Authors:** Kalyan Mondal, Surapati Pramanik, Bibhas C. Giri, Florentin Smarandache

**Comments:** 15 Pages.

A neutrosophic number (a + bI) is a significant mathematical tool to deal with indeterminate and incomplete information which exists generally in real-world problems, where a and bI denote the determinate component and indeterminate component, respectively. We define score functions and accuracy functions for ranking neutrosophic numbers.

**Category:** General Mathematics

[2667] **viXra:1803.0621 [pdf]**
*submitted on 2018-03-23 07:19:38*

**Authors:** P.V. Sudeep, P. Palanisamy, Chandrasekharan Kesavadas, Jeny Rajan

**Comments:** 10 Pages.

The presence of noise results in quality deterioration of magnetic resonance (MR) images and thus limits the visual inspection and influence the quantitative measurements from the data.

**Category:** General Mathematics

[2666] **viXra:1803.0620 [pdf]**
*submitted on 2018-03-23 07:20:51*

**Authors:** Nabeela Ishfaq, Sidra Sayed, Muhammad Akram, Florentin Smarandache

**Comments:** 19 Pages.

Graph theory has numerous applications in various disciplines, including computer networks, neural networks, expert systems, cluster analysis, and image capturing. Rough neutrosophic set (NS) theory is a hybrid tool for handling uncertain information that exists in real life.

**Category:** General Mathematics

[2665] **viXra:1803.0619 [pdf]**
*submitted on 2018-03-23 07:21:50*

**Authors:** Mehmet Serhat CAN, Ömerül Faruk ÖZGÜVEN

**Comments:** 12 Pages.

Bu çalışmada, giriş değişkenlerinin nötrosofik küme teorisindeki doğru (T), belirsiz (I) ve yanlış (F) üyelik fonksiyonları kullanılarak, evrensel küme üzerindeki dağılımlarının gruplandırıldığı nötrosofik üyelik değerli bulanık mantık-PID (NBMD-PID) denetleyici ile geleneksel bulanık mantık-PID denetleyicinin (BMD-PID) gerçek zamanlı karşılaştırılması yapılmıştır.

**Category:** General Mathematics

[2664] **viXra:1803.0617 [pdf]**
*submitted on 2018-03-23 07:36:28*

**Authors:** Shawkat Alkhazaleh, Ayman A. Hazaymeh

**Comments:** 8 Pages.

In this work we use the concept of a ’n’-valued refined neutrosophic soft sets and its
properties to solve decision making problems, Also a similarity measure between two ’n’-
valued refined neutrosophic soft sets are proposed. A medical diagnosis (MD) method is
established for ’n’-valued refined neutrosophic soft set setting using similarity measures.
Lastly a numerical example is given to demonstrate the possible application of similarity measures in medical diagnosis (MD).

**Category:** General Mathematics

[2663] **viXra:1803.0616 [pdf]**
*submitted on 2018-03-23 07:37:21*

**Authors:** J. Malarvizhi, G.Divya

**Comments:** 8 Pages.

In this paper we define Antipodal single valued neutrosophic graph and some Isomorphic properties of Antipodal single valued neutrosophic graph are discussed.

**Category:** General Mathematics

[2662] **viXra:1803.0615 [pdf]**
*submitted on 2018-03-23 07:38:55*

**Authors:** Sudip Bhattacharyya, Bikas Koli Roy, Pinaki Majumdar

**Comments:** 21 Pages.

An Interval Neutrosophic set (INS) is an instance of a Neutrosophic set and also an emerging tool
for uncertain data processing in real scientific and engineering applications. In this paper, several distance and similarity measures between two Interval Neutrosophic sets have been discussed.

**Category:** General Mathematics

[2661] **viXra:1803.0614 [pdf]**
*submitted on 2018-03-23 07:40:23*

**Authors:** Jianwen Yang, Xiangguang Chen, Huaiping Jin

**Comments:** 8 Pages.

Fermentative production of chlortetracycline is a complex fed-batch bioprocess. It generally takes over 90 h for cultivation and is often contaminated by undesired microorganisms.

**Category:** General Mathematics

[2660] **viXra:1803.0613 [pdf]**
*submitted on 2018-03-23 07:41:10*

**Authors:** Süleyman ŞENYURT, Gülşah KAYA

**Comments:** 10 Pages.

In this paper, we defined the neutrosophic continuous function, neutrosophic open function, neutrosophic closed function and neutrosophic homeomorphism on neutrosophic topological spaces. Then, we give some characteristics of these functions; neutrosophic closed function is a neutrosophic continuous function, neutrosophic open function is a neutrosophic continuous function.

**Category:** General Mathematics

[2659] **viXra:1803.0612 [pdf]**
*submitted on 2018-03-23 07:42:46*

**Authors:** Tuhin Bera, Nirmal Kumar Mahapatra

**Comments:** 21 Pages.

In this paper, the notion of neutrosophic soft metric space (NSMS) is introduced in terms of neutrosophic soft points and several related properties, structural characteristics have been investigated. Then the convergence of sequence in neutrosophic soft metric space is defined and illustrated by examples. Further, the concept of Cauchy sequence in NSMS is developed and some related theorems have been established, too.

**Category:** General Mathematics

[2658] **viXra:1803.0611 [pdf]**
*submitted on 2018-03-23 07:43:45*

**Authors:** P. Thirunavukarasu, R. Suresh

**Comments:** 8 Pages.

In this paper, we introduced a new concept of complex neutrosophic graphs called regular complex neutrosophic graph with degree for complex neutrosophic graphs and studied some properties of this new concept. The concept of regular complex
neutrosophic graph is an extension of complex neutrosophic fuzzy graphs of type.

**Category:** General Mathematics

[2657] **viXra:1803.0610 [pdf]**
*submitted on 2018-03-23 07:44:40*

**Authors:** Yan-Ling Bao, Hai-Long Yang

**Comments:** 14 Pages.

Neutrosophic set (NS) theory was originally established by Smarandache for handling indeterminate and inconsistent information. In this paper, we introduce single valued neutrosophic refined rough sets by combining single valued neutrosophic refined sets with rough sets and further study the hybrid model from two perspectives—constructive viewpoint and axiomatic viewpoint.

**Category:** General Mathematics

[2656] **viXra:1803.0609 [pdf]**
*submitted on 2018-03-23 07:46:20*

**Authors:** J. Montero, H. Bustince, C. Franco, J.T. Rodríguez, D. Gómez, M. Pagola, J. Fernández, E. Barrenechea

**Comments:** 9 Pages.

In this position paper we propose a consistent and unifying view to all those basic knowledge representa- tion models that are based on the existence of two somehow opposite fuzzy concepts.

**Category:** General Mathematics

[2655] **viXra:1803.0608 [pdf]**
*submitted on 2018-03-23 07:48:21*

**Authors:** E. Turunen, M.Öztürk, A.Tsoukiás

**Comments:** 15 Pages.

The root of this work is on the one hand in Belnap’s four valued paraconsistent logic,and on the other hand on Pavelka’s papers further developed by Turunen.

**Category:** General Mathematics

[2654] **viXra:1803.0607 [pdf]**
*submitted on 2018-03-23 07:49:30*

**Authors:** Omar Bouattane, Bouchaib Cherradi, Mohamed Youssfi, Mohamed O. Bensalah

**Comments:** 14 Pages.

In this paper, we propose a parallel algorithm for data classification, and its application for
Magnetic Resonance Images (MRI) segmentation. The studied classification method is the well-known c-means method.

**Category:** General Mathematics

[2653] **viXra:1803.0606 [pdf]**
*submitted on 2018-03-23 07:50:46*

**Authors:** makingPeide Liu, Junlin Liu, José M. Merigó

**Comments:** 28 Pages.

Heronian mean (HM) operator has the advantages of considering the interrelationships between parame-ters, and linguistic intuitionistic fuzzy number (LIFN), in which the membership and non-membership areexpressed by linguistic terms, can more easily describe the uncertain and the vague information existingin the real world.

**Category:** General Mathematics

[2652] **viXra:1803.0605 [pdf]**
*submitted on 2018-03-23 07:51:48*

**Authors:** Hong Hu, Liang Pang, Dongping Tian, Zhongzhi Shi

**Comments:** 13 Pages.

In the past decade, granular computing (GrC) has been an active topic of research in machine learning and computer vision. However, the granularity division is itself an open and complex problem.

**Category:** General Mathematics

[2651] **viXra:1803.0603 [pdf]**
*submitted on 2018-03-23 07:53:48*

**Authors:** Samah Ibrahim Abdel Aal, Mahmoud M. A. Abd Ellatif, Mohamed Monir Hassan

**Comments:** 14 Pages.

One of the most important reasons for information systems failure is lack of quality. Information Systems Quality (ISQ) evaluation is important to prevent the lack of quality. ISQ evaluation is one of the most important Multi-Criteria Decision Making (MCDM) problems.

**Category:** General Mathematics

[2650] **viXra:1803.0601 [pdf]**
*submitted on 2018-03-23 07:55:53*

**Authors:** Abteen Ijadi Maghsoodi, Gelayol Abouhamzeh, Mohammad Khalilzadeh, Edmundas Kazimieras Zavadskas

**Comments:** 21 Pages.

The selection process of appropriate Performance Appraisal (PA) methods for organizations in today’s dynamic and agile environments along with its funding scales is a complex problem.

**Category:** General Mathematics

[2649] **viXra:1803.0600 [pdf]**
*submitted on 2018-03-23 07:57:56*

**Authors:** Célia da Costa Pereira, Andrea G.B.Tettamanzi

**Comments:** 19 Pages.

This article is a first step in the direction of extending possibilistic planning to account for incomplete and imprecise knowledge of the worlds tate.

**Category:** General Mathematics

[2648] **viXra:1803.0599 [pdf]**
*submitted on 2018-03-23 07:58:48*

**Authors:** Sindhu Saranya, V. Ellappan

**Comments:** 10 Pages.

Segmenting blood vessel from the retinal image is important for detecting many retinal vascular disorders. Diseases which are all affecting the blood vessels of the eye are known as Retinal vascular disorders.

**Category:** General Mathematics

[2647] **viXra:1803.0598 [pdf]**
*submitted on 2018-03-23 07:59:39*

**Authors:** M.Kaviyarasu, K.Indhira

**Comments:** 8 Pages.

The aim of the paper is to investigate the relationship between BCK/BCIalgebras
and other algebras namely d-algebras, Q-algebras-BCH-algebras- TM-algebras-INK-algebras and we introduce some algebraic system.

**Category:** General Mathematics

[2646] **viXra:1803.0597 [pdf]**
*submitted on 2018-03-23 08:00:55*

**Authors:** Sidra Sayed, Nabeela Ishfaq, Muhammad Akram, Florentin Smarandache

**Comments:** 20 Pages.

A rough neutrosophic set model is a hybrid model which deals with vagueness by using the lower and upper approximation spaces. In this research paper, we apply the concept of rough
neutrosophic sets to graphs.

**Category:** General Mathematics

[2645] **viXra:1803.0596 [pdf]**
*submitted on 2018-03-23 08:02:44*

**Authors:** Hüseyin Kamacı, Akın Osman Atagün, Abdullah Sönmezoglu

**Comments:** 23 Pages.

In this paper, we firstly introduce row-products of the soft matrices and investigate their properties and algebraic structures in detail. We aim to show that these row-products can be used in handling decision making problems.

**Category:** General Mathematics

[2644] **viXra:1803.0595 [pdf]**
*submitted on 2018-03-23 08:03:53*

**Authors:** Mumtaz Ali, Le Hoang Son, Mohsin Khan, Nguyen Thanh Tung

**Comments:** 8 Pages.

Over the last few decades, the advance of new technologies in computer equipment, cameras and med- ical devices became a starting point for the shape of medical imaging systems.

**Category:** General Mathematics

[2643] **viXra:1803.0593 [pdf]**
*submitted on 2018-03-23 08:08:13*

**Authors:** V.Krishnaraj, R.Vikramaprasad, R.Dhavaseelan

**Comments:** 8 Pages.

In this paper, we introduce the concepts of length, distance, eccentricity, radius, diameter, status, total status, median and central vertex of a single valued neutrosophic graph. We present the concept of self-centered single valued neutrosophic graph. We investigated some properties of self-centered single valued neutrosophic graphs.

**Category:** General Mathematics

[2642] **viXra:1803.0590 [pdf]**
*submitted on 2018-03-23 08:10:11*

**Authors:** Said Broumi, Mohamed Talea, Florentin Smarandache, Kishore Kumar P.K.

**Comments:** 6 Pages.

single valued neutrosophic graph is a generalized
structure of fuzzy graph, intuitionistic fuzzy graph that gives more precision, flexibility and compatibility to a system when compared with systems that are designed using fuzzy graphs
and intuitionistic fuzzy graphs.

**Category:** General Mathematics

[2641] **viXra:1803.0587 [pdf]**
*submitted on 2018-03-23 08:12:55*

**Authors:** Jun Ye

**Comments:** 6 Pages.

single valued neutrosophic set (SVNS) is an instance of a neutrosophic set, which give us
an additional possibility to represent uncertainty, imprecise, incomplete, and inconsistent information which exist in real world.

**Category:** General Mathematics

[2640] **viXra:1803.0584 [pdf]**
*submitted on 2018-03-23 08:16:05*

**Authors:** J.Dhivya, B.Sridevi

**Comments:** 9 Pages.

Neutrosophic set (NS) is very useful to express incomplete, uncertainty, and inconsistent information in a more general way. In the
modern medical technologies, each element can be expressed as NS having different truth – membership, indeterminacy – membership, and
falsity – membership degrees.

**Category:** General Mathematics

[2639] **viXra:1803.0583 [pdf]**
*submitted on 2018-03-23 08:17:19*

**Authors:** Xin Li, Xiaohong Zhang

**Comments:** 15 Pages.

This paper aims at developing new methods for multi-attribute decision making (MADM) under a single-valued neutrosophic hesitant fuzzy environment, in which each element has sets of
possible values designed by truth, indeterminacy, and falsity membership hesitant functions.

**Category:** General Mathematics

[2638] **viXra:1803.0579 [pdf]**
*submitted on 2018-03-23 08:21:24*

**Authors:** A. Borumand Saeid, A. Ahadpanah, L. Torkzadeh

**Comments:** 9 Pages.

In this paper we define the Smarandache BL-algebra, Q -Smarandache ideal and Q -
Smarandache implicative ideal, we obtain some related results. After that by considering
the notions of these ideals we determine relationships between ideals in BL-algebra
and Q -Smarandache (implicative) ideals of BL-algebra. Finally we construct quotient of
Smarandache BL-algebras via MV-algebra and prove some theorems.

**Category:** General Mathematics

[2637] **viXra:1803.0578 [pdf]**
*submitted on 2018-03-23 08:23:24*

**Authors:** Mervat Elzawy

**Comments:** 4 Pages.

The purpose of this paper is to study Smarandache curves in the 4-dimensional Euclidean space E 4 , and to obtain the Frenet–Serret and Bishop invariants for the Smarandache curves in E 4 . The first, the second and the third curvatures of Smarandache curves are calculated. These values depending upon the first, the second and the third curvature of the given curve.

**Category:** General Mathematics

[2636] **viXra:1803.0577 [pdf]**
*submitted on 2018-03-23 08:24:24*

**Authors:** M. Elzawy, S. Mosa

**Comments:** 4 Pages.

In this paper, we study Smarandache curves in the 4-dimensional Galilean space G 4 . We obtain Frenet- Serret invariants for the Smarandache curve in G 4 . The first, second and third curvature of Smarandache curve are calculated. These values depending upon the first, second and third curvature of the given curve. Examples will be illustrated.

**Category:** General Mathematics

[2635] **viXra:1803.0570 [pdf]**
*submitted on 2018-03-23 08:33:11*

**Authors:** J.A. Morente-Molinera, G. Kou, R. González-Crespo, J.M. Corchado, E. Herrera-Viedma

**Comments:** 11 Pages.

Classic multi-criteria group decision making models that have a high amount of alternatives are unman- ageable for the experts.

**Category:** General Mathematics

[2634] **viXra:1803.0569 [pdf]**
*submitted on 2018-03-23 08:34:24*

**Authors:** Harish Garg &Nancy

**Comments:** 18 Pages.

Neutrosophic sets (NS) contain the three ranges: truth, indeterminacy, and falsity membership degrees,and are very useful for describing and handling the uncertainties in the real life problem.

**Category:** General Mathematics

[2633] **viXra:1803.0565 [pdf]**
*submitted on 2018-03-23 08:40:16*

**Authors:** Said Broumi, Assia Bakali, Mohamed Talea, Florentin Smarandache, Arindam Dey, Le Hoang Son

**Comments:** 10 Pages.

Neutrosophic set and neutrosophic logic theory are renowned theories to deal with complex, not clearly explained and uncertain real life problems, in which classical fuzzy sets/models may fail to model properly.

**Category:** General Mathematics

[2632] **viXra:1803.0564 [pdf]**
*submitted on 2018-03-23 08:41:13*

**Authors:** E.M. Solouma

**Comments:** 7 Pages.

A regular non-null curve in Minkowski space-time, whose posi- tion vector is composed by Frenet frame vectors on another regular curve, is called a Smarandache curve.

**Category:** General Mathematics

[2631] **viXra:1803.0563 [pdf]**
*submitted on 2018-03-23 08:42:30*

**Authors:** E. M. Solouma

**Comments:** 16 Pages.

In Smarandache geometry, a regular non-null curve in Minkowski 3-space, whose position vector is collected by the Frenet frame vectors of other regular non-null curve, is said to be
Smarandache curve.

**Category:** General Mathematics

[2630] **viXra:1803.0562 [pdf]**
*submitted on 2018-03-23 08:43:57*

**Authors:** Said Broumi, Assia Bakali, Seema Mehra, Mohamed Talea, Florentin Smarandache, Manjeet Singh

**Comments:** 9 Pages.

The concept of single valued neutrosophic graphs (SVNGs) generalizes the concept of fuzzy graphs and intuitionistic fuzzy graphs. The purpose of this research paper is to define different types of strong degrees in SVNGs and introduce novel concepts, such as the vertex truth-membership, vertex indeterminacy-membership and falsity-membership sequence in SVNG with proof and numerical illustrations.

**Category:** General Mathematics

[2629] **viXra:1803.0561 [pdf]**
*submitted on 2018-03-23 08:45:12*

**Authors:** Florentin Smarandache, Jun Ye

**Comments:** 4 Pages.

Over a period of seven months (August 2017–February 2018), the Special Issue dedicated to
“Neutrosophic Information Theory and Applications” by the “Information” journal (ISSN 2078-2489),
located in Basel, Switzerland, was a success.

**Category:** General Mathematics

[2628] **viXra:1803.0560 [pdf]**
*submitted on 2018-03-23 08:46:35*

**Authors:** Edmundas Kazimieras Zavadskas, Jurgita Antucheviciene, Tatjana Vilutiene, Hojjat Adeli

**Comments:** 21 Pages.

Sustainable decision-making in civil engineering, construction and building technology can be supported by fundamental scientific achievements and multiple-criteria decision-making (MCDM) theories.

**Category:** General Mathematics

[2627] **viXra:1803.0559 [pdf]**
*submitted on 2018-03-23 08:47:57*

**Authors:** Didier Dubois, Siegfried Gottwald, Petr Hajek, Janusz Kacprzyk, Henri Prade

**Comments:** 7 Pages.

This note points out a terminological clash between Atanassov’s “intuitionistic fuzzy sets” and what is currently understood as intuitionistic logic. They differ both by their motivations and their underlying mathematical structure.

**Category:** General Mathematics

[2626] **viXra:1803.0558 [pdf]**
*submitted on 2018-03-23 08:51:29*

**Authors:** Marie Truelove, Maria Vasardani, Stephan Winter

**Comments:** 13 Pages.

This paper demonstrates a framework of processes for identifying potential witnesses of events from evidence they post to social media.

**Category:** General Mathematics

[2625] **viXra:1803.0557 [pdf]**
*submitted on 2018-03-23 08:52:43*

**Authors:** Ashraf Al-Quran, Nasruddin Hassan

**Comments:** 14 Pages.

This paper presents a novel complex neutrosophic soft expert set (CNSES) concept. The range of values of CNSES is extended to the unit circle in the complex plane by adding an additional term called the phase term which describes
CNSES’s elements in terms of the time aspect.

**Category:** General Mathematics

[2624] **viXra:1803.0556 [pdf]**
*submitted on 2018-03-23 08:54:08*

**Authors:** Victor Vladareanu, Radu I. Munteanu, Ali Mumtaz, Florentin Smarandache, Luige Vladareanu

**Comments:** 8 Pages.

The paper presents a VIPRO versatile, intelligent and mobile platform for robots, using an original virtual projection method
which involves the representation of modern mobile robots in a 3D virtual environment using a strong robotic simulator, an open
architecture system and adaptive networks over the classical control system of the robot, developing intelligent control interfaces
The advanced control technologies adapted to the robot environment such as neutrosophic control, robot Extenics control and
robot haptic control are used. The obtained results lead to the conclusion that the VIPRO platform is to be integrated on the IT
market as a new component alongside the existing ones, allowing a correct evaluation of robot behaviours in hazardous or
challenging environments and high level real-time simulation in order to correctly model interactions among the robots and
between the robots and the environment.

**Category:** General Mathematics

[2623] **viXra:1803.0554 [pdf]**
*submitted on 2018-03-23 08:56:25*

**Authors:** Dragisa STANUJKIC, Edmundas Kazimieras ZAVADSKAS, Darjan KARABASEVIC, Florentin SMARANDACHE, Zenonas TURSKIS

**Comments:** 18 Pages.

The weights of evaluation criteria could have a significant impact on the results obtained by
applying multiple criteria decision-making methods.

**Category:** General Mathematics

[2622] **viXra:1803.0553 [pdf]**
*submitted on 2018-03-23 08:57:29*

**Authors:** Andrei-Lucian Drăgoi

**Comments:** 32 Pages.

This article proposes a synthesized classification of some Goldbach-like conjectures, including those which are “stronger” than the Binary Goldbach’s Conjecture (BGC) and launches a new generalization of BGC briefly called “the Vertical Binary Goldbach’s Conjecture” (VBGC), which is essentially a metaconjecture, as VBGC states an infinite number of conjectures stronger than BGC, which all apply on
“iterative” primes with recursive prime indexes (i-primeths).

**Category:** General Mathematics

[2621] **viXra:1803.0551 [pdf]**
*submitted on 2018-03-23 08:59:08*

**Authors:** Lavinia Corina Ciungu

**Comments:** 21 Pages.

In this paper we introduce the very true operators on pseudo-BCK algebras and we study their properties. We prove that the composition of two very true operators is a very true operator if and only if they commute.

**Category:** General Mathematics

[2620] **viXra:1803.0548 [pdf]**
*submitted on 2018-03-23 09:02:07*

**Authors:** Victor Christianto, Florentin Smarandache

**Comments:** 11 Pages.

In recent years, the Big Bang as described by the Lambda CDM-Standard Model Cosmology has become widely accepted by majority of physics and cosmology communities.

**Category:** General Mathematics

[2619] **viXra:1803.0547 [pdf]**
*submitted on 2018-03-23 09:03:20*

**Authors:** Hua Ma, Haibin Zhu, Zhigang Hu, Wensheng Tang

**Comments:** 19 Pages.

The imprecise quality of service (QoS) evaluations from consumers may lead to the inappropriate pre- diction for the trustworthiness of cloud services in an uncertain cloud environment.

**Category:** General Mathematics

[2618] **viXra:1803.0543 [pdf]**
*submitted on 2018-03-23 06:11:35*

**Authors:** Mariya A. Sodenkamp, Madjid Tavana, Debora Di Caprio

**Comments:** 16 Pages.

We propose a novel meta-approach to support collaborative multi-objective supplier selection and order allocation (SSOA) decisions by integrating multi-criteria decision analysis and linear programming (LP).

**Category:** General Mathematics

[2617] **viXra:1803.0542 [pdf]**
*submitted on 2018-03-23 06:12:38*

**Authors:** Victor Christianto, Florentin Smarandache

**Comments:** 2 Pages.

Although virus is widely known to significantly affect many biological form of life, its physical model is quite rare. In this regard, experiments on the acoustic vibrations of elastic nanostructures in fluid media have been used to study the mechanical properties of materials, as well as for mechanical and biological sensing.

**Category:** General Mathematics

[2616] **viXra:1803.0541 [pdf]**
*submitted on 2018-03-23 06:14:05*

**Authors:** JieWang, Xiyue Tang, Guiwu Wei

**Comments:** 15 Pages.

In this article, we expand the dual generalized weighted BM (DGWBM) and dual generalized weighted geometric Bonferroni mean (DGWGBM) operator with single valued neutrosophic numbers (SVNNs) to propose the dual generalized single-valued neutrosophic number WBM (DGSVNNWBM) operator and dual generalized single-valued neutrosophic numbers WGBM
(DGSVNNWGBM) operator. Then, the multiple attribute decision making (MADM) methods are
proposed with these operators. In the end, we utilize an applicable example for strategic suppliers selection to prove the proposed methods.

**Category:** General Mathematics

[2615] **viXra:1803.0540 [pdf]**
*submitted on 2018-03-23 06:15:13*

**Authors:** Gehad Ismail Sayed, Aboul Ella Hassanien

**Comments:** 12 Pages.

This paper presents an automatic mitosis detection
approach of histopathology slide imaging based on
using neutrosophic sets (NS) and moth-flame optimization (MFO).

**Category:** General Mathematics

[2614] **viXra:1803.0538 [pdf]**
*submitted on 2018-03-23 06:17:58*

**Authors:** Juan-juan Peng, Jian-qiang Wang, Jun-hua Hu, Chao Tian

**Comments:** 14 Pages.

Multi-valued neutrosophic sets (MVNSs) have recently become a subject of great interest for researchers, and have been applied widely to multi-criteria decision-making (MCDM) problems. In this paper, the multi-valued neutrosophic geometric weighted Choquet integral Heronian mean (MVNGWCIHM) operator, which is based on the Heronian mean and Choquet integral, is proposed, and some special cases and the corresponding properties of the operator are discussed.

**Category:** General Mathematics

[2613] **viXra:1803.0537 [pdf]**
*submitted on 2018-03-23 06:19:00*

**Authors:** Irem Otay, Basar Oztaysi, Sezi Cevik Onar, Cengiz Kahraman

**Comments:** 17 Pages.

Healthcare management and healthcare industry have been one of the popular and complex topics that many researchers and professionals have focused on.

**Category:** General Mathematics

[2612] **viXra:1803.0535 [pdf]**
*submitted on 2018-03-23 06:21:20*

**Authors:** Jun Ye

**Comments:** 10 Pages.

The normal distribution is a usual one of various distributions in the real world. A normal
neutrosophic set (NNS) is composed of both a normal fuzzy number and a neutrosophic number,
which a significant tool for describing the incompleteness, indeterminacy, and inconsistency of the decision-making information.

**Category:** General Mathematics

[2611] **viXra:1803.0534 [pdf]**
*submitted on 2018-03-23 06:22:25*

**Authors:** Özgür Kabak, Bilal Ervural

**Comments:** 18 Pages.

The research activities in group decision making have dramatically increased over the last decade. In particular, the application of multiple attribute decision-making methods to group decision-making problems occupies a vast area in the related literature. However, there is no systematic classification scheme for these researches.

**Category:** General Mathematics

[2610] **viXra:1803.0533 [pdf]**
*submitted on 2018-03-23 06:24:39*

**Authors:** Bao-lin Li, Juan-ru Wang, Li-hua Yang, Xue-tao Li

**Comments:** 32 Pages.

The neutrosophic set and linguistic term set are widely applied in recently years. Motivated
by the advantages of them, we combine the multi-valued neutrosophic set and linguistic set and define the concept of the mult i-valued neutrosophic linguistic set (MVNLS).

**Category:** General Mathematics

[2609] **viXra:1803.0532 [pdf]**
*submitted on 2018-03-23 06:26:00*

**Authors:** Victor Vladareanu, Rozica Moga, Paul Schiopu, Luige Vladareanu

**Comments:** 6 Pages.

The work presents the studies and research in order to implement new techniques concerning
semi-active control of the magneto rheological dissipaters dynamic systems with applications to the antivibration isolating systems and the reducing of structural vibrations of the power systems.

**Category:** General Mathematics

[2608] **viXra:1803.0531 [pdf]**
*submitted on 2018-03-23 06:27:56*

**Authors:** Hua Ma, Haibin Zhu, Zhigang Hu, Wensheng Tang, Pingping Dong

**Comments:** 14 Pages.

Aiming at the diversity of user features, the uncertainty and the variation characteristics of quality of service (QoS), by exploiting the continuous monitoring data of cloud services, this paper proposes a multivalued collaborative approach to predict the unknown QoS values via time series analysis for potential users.

**Category:** General Mathematics

[2607] **viXra:1803.0530 [pdf]**
*submitted on 2018-03-23 06:29:33*

**Authors:** Radu-Emil Precup, Marius-Csaba Sabau, Emil M. Petriu

**Comments:** 15 Pages.

This paper suggests a synergy of fuzzy logic and nature-inspired optimization in terms of the nature-inspired optimal tuning of the input membership functions of a class of Takagi-Sugeno-Kang (TSK) fuzzymodels dedicated to Anti-lock Braking Systems (ABSs).

**Category:** General Mathematics

[2606] **viXra:1803.0529 [pdf]**
*submitted on 2018-03-23 06:31:18*

**Authors:** Yanhui Guo, Abdulkadir Sengur

**Comments:** 15 Pages.

In this paper,a new clustering algorithm, neutrosophic c-means (NCM),is introduced for uncertain dataclustering, which is inspired from fuzzy c-means and the neutrosophic set framework.

**Category:** General Mathematics

[2605] **viXra:1803.0527 [pdf]**
*submitted on 2018-03-23 06:34:50*

**Authors:** Florentin Smarandache

**Comments:** 3 Pages.

În mod paradoxist, există pinguini la ecuator! Atât de mici în comparație cu cei din Antarctica...

**Category:** General Mathematics

[2604] **viXra:1803.0526 [pdf]**
*submitted on 2018-03-23 06:42:15*

**Authors:** A.Q. Ansari, Ranjit Biswas, Swati Aggarwal

**Comments:** 11 Pages.

Fuzzy classification has become of great interest because of its ability to utilize simple linguistically interpretable rules and has overcome the limitations of symbolic or crisp rule based classifiers.

**Category:** General Mathematics

[2603] **viXra:1803.0524 [pdf]**
*submitted on 2018-03-23 06:45:35*

**Authors:** Ümit Budak, Yanhui Guo, Abdulkadir Sengür, Florentin Smarandache

**Comments:** 12 Pages.

Hough transform (HT) is a useful tool for both pattern recognition and image processing
communities. In the view of pattern recognition, it can extract unique features for description of
various shapes, such as lines, circles, ellipses, and etc.

**Category:** General Mathematics

[2602] **viXra:1803.0523 [pdf]**
*submitted on 2018-03-23 06:46:34*

**Authors:** Bijan Davvaz, Samy M. Mostafa, Fatema F.Kareem

**Comments:** 10 Pages.

In this paper, the concept of a neutrosophic KU-algebra is introduced and some related
properties are investigated. Also, neutrosophic KU-ideals of a neutrosophic KU-algebra are
studied and a few properties are obtained. Furthermore, a few results of neutrosophic KU-ideals of a neutrosophic KU-algebra under homomorphism are discussed

**Category:** General Mathematics

[2601] **viXra:1803.0522 [pdf]**
*submitted on 2018-03-23 06:47:35*

**Authors:** Debabrata Mandal

**Comments:** 11 Pages.

Neutrosophic ideals of a semiring are introduced
and studied in the sense of Smarandache[14], along with some operations such as intersection, composition, cartesian product etc. on them. Among the other results/characterizations, it is
shown that all the operations are structure preserving.

**Category:** General Mathematics

[2600] **viXra:1803.0521 [pdf]**
*submitted on 2018-03-23 06:48:36*

**Authors:** Jun Ye

**Comments:** 10 Pages.

A neutrosophic number (NN) presented by Smarandache can express determinate and/or
indeterminate information in real life. NN (z = a + uI) consists of the determinate part a and the
indeterminate part uI for a, u 2 R (R is all real numbers) and indeterminacy I, and is very suitable for representing and handling problems with both determinate and indeterminate information.

**Category:** General Mathematics

[2599] **viXra:1803.0519 [pdf]**
*submitted on 2018-03-23 06:50:26*

**Authors:** Umberto Rivieccio

**Comments:** 9 Pages.

Neutrosophy has been introduced some years ago by Florentin Smarandache as a new branch of philosophy dealing with “the origin, nature and scope of neutralities, as well as their interactions with different ideational spectra”.

**Category:** General Mathematics

[2598] **viXra:1803.0517 [pdf]**
*submitted on 2018-03-23 06:52:20*

**Authors:** Madad Khan, Saima Anis, Florentin Smarandache, Young Bae Jun

**Comments:** 17 Pages.

The notion of neutrosophic N-structure is introduced, and applied it to semigroup. The notions of neutrosophic N-subsemigroup,
neutrosophic N-product and "-neutrosophic N-subsemigroup are introduced, and several properties are investigated.

**Category:** General Mathematics

[2597] **viXra:1803.0515 [pdf]**
*submitted on 2018-03-23 06:54:24*

**Authors:** Jun Ye, Wenhua Cuim Zhikang Lu

**Comments:** 10 Pages.

The possible optimal ranges of the decision variables and NN objective function are indicated when the indeterminacy I is considered for possible interval ranges in real situations.

**Category:** General Mathematics

[2596] **viXra:1803.0514 [pdf]**
*submitted on 2018-03-23 07:00:46*

**Authors:** K. Thirusangu, S. Poornavel, R. Vasuki

**Comments:** 11 Pages.

In this paper, the notion of neutrosophic Q- fuzzy left N-subgroups is introduced in a near ring and investigated some related properties. Characterization of neutrosophic Q- fuzzy left N-subgroups with respect to T-norm and S-norm are given. Few homomorphic image and its pre-image on neutrosophic Q- fuzzy are obtained.

**Category:** General Mathematics

[2595] **viXra:1803.0513 [pdf]**
*submitted on 2018-03-23 07:01:30*

**Authors:** K. Thirusangu, S. Poornavel, R. Vasuki

**Comments:** 6 Pages.

Goguen [1967] introduced L-fuzzy set. Murali [1991] analyzed lattice of fuzzy algebras and closure systems. Saibaba [2008] initiated fuzzy lattice ordered groups, and studied many properties on fuzzy lattice. Swamy and Raju [1991] gave a detailed findings on algebraic fuzzy system.

**Category:** General Mathematics

[2594] **viXra:1803.0512 [pdf]**
*submitted on 2018-03-23 07:02:26*

**Authors:** A.Edward Samuel, R.Narmadhagnanam

**Comments:** 7 Pages.

In this paper, a new approach (cosecant similarity measure) is proposed to construct the decision method for medical diagnosis by using neutrosophic refined set. Also, we develop a technique to diagnose which patient is suffering from what disease.

**Category:** General Mathematics

[2593] **viXra:1803.0511 [pdf]**
*submitted on 2018-03-23 07:03:32*

**Authors:** C. Antony Crispin Sweety, I. Arockiarani

**Comments:** 9 Pages.

A rough set is a formal approximation of a crisp set which gives lower and upper approximation of original set to deal with uncertainties. The concept of neutrosophic set is a mathematical tool for handling imprecise, indeterministic and inconsistent data. In this paper, we defne concepts of Rough Neutrosophic algebra and investigate some of their properties.

**Category:** General Mathematics

[2592] **viXra:1803.0509 [pdf]**
*submitted on 2018-03-23 07:06:01*

**Authors:** Muhammad Akram, Hafsa M. Malik, Sundas Shahzadi, Florentin Smarandache

**Comments:** 27 Pages.

Neutrosophic sets (NSs) handle uncertain information while fuzzy sets (FSs) and
intuitionistic fuzzy sets (IFs) fail to handle indeterminate information.

**Category:** General Mathematics

[2591] **viXra:1803.0507 [pdf]**
*submitted on 2018-03-23 07:08:16*

**Authors:** Mehmet Şahin, Abdullah Kargın

**Comments:** 8 Pages.

In this paper; new properties for neutrosophic
triplet groups are introduced. A notion of neutrosophic triplet metric space is given and properties of neutrosophic triplet metric spaces are studied.

**Category:** General Mathematics

[2590] **viXra:1803.0506 [pdf]**
*submitted on 2018-03-23 07:09:29*

**Authors:** A.Mary Margaret, M.Trinita Pricilla

**Comments:** 13 Pages.

The aim of this paper is to introduce and develop a new class of sets namely neutrosophic vague generalized pre-closed sets in neutrosophic vague topological space. Further we have analyse the properties of neutrosophic vague generalized pre-open sets.

**Category:** General Mathematics

[2589] **viXra:1803.0505 [pdf]**
*submitted on 2018-03-23 07:14:54*

**Authors:** Florentin Smarandache, Mirela Teodorescu, Daniela Gîfu

**Comments:** 4 Pages.

This paper describes the importance of Neutrosophy Theory in order to find a method that could solve the uncertainties arising on discursive analysis.

**Category:** General Mathematics

[2588] **viXra:1803.0504 [pdf]**
*submitted on 2018-03-23 07:15:46*

**Authors:** Jia Huang, Zhaojun Li, Hu-Chen Liu

**Comments:** 8 Pages.

As a proactive risk management instrument, failure mode and effect analysis (FMEA) has been broadly utilized to recognize, evaluate and eliminate failure modes of products, processes, systems and services. Nevertheless, the conventional FMEA method suffers from many important deficiencies when used in the real world.

**Category:** General Mathematics

[2587] **viXra:1803.0503 [pdf]**
*submitted on 2018-03-23 07:17:41*

**Authors:** Yanhui Guo, H.D.Cheng

**Comments:** 9 Pages.

Neutrosophic set (NS), a part of neutrosophy theory, studies the origin, nature and scope of neutralities, as well as their interactions with different ideational spectra.

**Category:** General Mathematics

[2586] **viXra:1803.0501 [pdf]**
*submitted on 2018-03-22 11:48:26*

**Authors:** Colin James III

**Comments:** 1 Page. © Copyright 2018 by Colin James III All rights reserved. info@cec-services dot com

Neutrosophic logic is defined as a five-valued logic on {-0, 0, 0<p<1, 1, 1+}.
We map this using Meth8/VL4 and find it not tautologous.
We next map the multiplication look up table of sub-indeterminacies and find it a vector space.
Neutrosophic logic is not suitable as a universal logic to map and confirm all other logic systems.

**Category:** General Mathematics

[2585] **viXra:1803.0499 [pdf]**
*submitted on 2018-03-22 19:18:51*

**Authors:** Colin James III

**Comments:** 1 Page. © Copyright 2018 by Colin James III All rights reserved. info@cec-services dot com

The Dezert-Smarandache theory arises from the following scenario with Alice and Bob as suspects.
That either Alice or Bob is not innocent or both Alice and Bob are not innocent is a tautology.
If cast with a probability, that either Alice or Bob is not innocent or both Alice and Bob are not innocent is ordinal one.
Neither scenario is tautologous in the Meth8/VL4 modal logic model checker.

**Category:** General Mathematics

[2584] **viXra:1803.0490 [pdf]**
*submitted on 2018-03-22 08:44:38*

**Authors:** Zhong-xing Wang, Jian Li

**Comments:** 18 Pages.

Correlation coefficient is one of the broadly use indexes in multi-criteria decision-making
(MCDM) processes. However, some important issues related to correlation coefficient utilization
within probabilistic hesitant fuzzy environments remain to be addressed.

**Category:** General Mathematics

[2583] **viXra:1803.0489 [pdf]**
*submitted on 2018-03-22 08:46:50*

**Authors:** Yun-Lai Zhou, Magd Abdel Wahab

**Comments:** 9 Pages.

Structural damage detection using vibration-based techniques and transmissibility is investigated and proposed with elaborating the mathematical interrelationship between modal assurance criterion (MAC) and cosine similarity measure.

**Category:** General Mathematics

[2582] **viXra:1803.0488 [pdf]**
*submitted on 2018-03-22 08:48:03*

**Authors:** Jian Liu, Hong-Kuan Zhao, Zhao-Bin Li, Si-Feng Liu

**Comments:** 7 Pages.

A new decision process is proposed to address the challenge that a large number criteria in the multicriteria decision making (MCDM) problem and the decision makers with heterogeneous risk preferences.

**Category:** General Mathematics

[2581] **viXra:1803.0486 [pdf]**
*submitted on 2018-03-22 08:48:57*

**Authors:** Gülcan Petriçli, Gül Gökay Emel

**Comments:** 30 Pages.

Supplier Selection is one of the most studied areas in management and decision sciences. However, it is still a highly problematic subject since decision-makers take an educated guess after a certain stage in real life practices.

**Category:** General Mathematics

[2580] **viXra:1803.0485 [pdf]**
*submitted on 2018-03-22 08:50:04*

**Authors:** Florentin Smarandache, Dmitri Rabounski

**Comments:** 1 Page.

“Angel particle” bearing properties of both particles and anti-particles, which was recently discovered by the Stanford team of experimental physicists, is usually associated
with Majorana fermions (predicted in 1937 by Ettore Majorana). In this message we point out that particles bearing properties of both matter and anti-matter were as well predicted without any connexion with particle physics, but on the basis of pure mathematics, namely — neutrosophic logic which is a generalization of fuzzy and intuitionistic fuzzy logics in mathematics.

**Category:** General Mathematics

[2579] **viXra:1803.0484 [pdf]**
*submitted on 2018-03-22 08:51:42*

**Authors:** Ion PATRASCU, Florentin SMARANDACHE

**Comments:** 3 Pages.

In acest articol rezolvam doua probleme de minim geometric.

**Category:** General Mathematics

[2578] **viXra:1803.0483 [pdf]**
*submitted on 2018-03-22 08:53:19*

**Authors:** Chuan Yue

**Comments:** 13 Pages.

The weights of decision makers play an important role in group decision-making problems. Entropy is avery important measure in information science.

**Category:** General Mathematics

[2577] **viXra:1803.0481 [pdf]**
*submitted on 2018-03-22 08:55:52*

**Authors:** Sergio Pastrana, Aikaterini Mitrokotsa, Agustin Orfila, Pedro Peris-Lopez

**Comments:** 19 Pages.

Mobile Ad hoc Networks (MANETs) are wireless networks without fixed infrastructure based on the
cooperation of independent mobile nodes.

**Category:** General Mathematics

[2576] **viXra:1803.0479 [pdf]**
*submitted on 2018-03-22 08:57:02*

**Authors:** Ruxia Liang, Jianqiang Wang, Hongyu Zhang

**Comments:** 16 Pages.

E-commerce website evaluation is recognized as a complex multi-criteria decision-making (MCDM) problem involving vast amounts of imprecise and inconsistent evaluation data. Single-valued trapezoidal neutrosophic numbers (SVTNNs), which are elements in single-valued trapezoidal neutrosophic sets (SVTNSs), have a strong capacity to model such complex evaluation information.

**Category:** General Mathematics

[2575] **viXra:1803.0478 [pdf]**
*submitted on 2018-03-22 08:58:19*

**Authors:** Xinde Li, Jean Dezert, Florentin Smarandache, Xinhan Huang

**Comments:** 18 Pages.

This paper presents a newmethod for reducing the number of sources of evidence to combine in order to reduce the complexity of the fusion processing. Such a complexity reduction is often required in many applications where the real-time constraint and limited computing resources are of prime importance.

**Category:** General Mathematics

[2574] **viXra:1803.0477 [pdf]**
*submitted on 2018-03-22 08:59:37*

**Authors:** Bingyi Kang, Yong Deng, Rehan Sadiq, Sankaran Mahadevan

**Comments:** 10 Pages.

In order to handle uncertain information, this paper proposes evidential cognitive maps (ECMs), similar to the fuzzy cognitive maps (FCMs). ECMs are uncertain-graph structures for representing causal reasoning through the combination of cognitive maps and Dempster Shafer evidence theory. The framework of ECMs is developed in detail and an application to socio-economic model is used to illustrate the application of the proposed methodology.

**Category:** General Mathematics

[2573] **viXra:1803.0476 [pdf]**
*submitted on 2018-03-22 09:00:22*

**Authors:** Chris Lucas

**Comments:** 7 Pages.

A deliberation upon the possibility of generating a comprehensive view of ‘mind as a whole’ by integrating biology, psychology and sociology, and considering ‘Mind’ as a dynamical interplay between values existing over many levels and
scales of complex systems.

**Category:** General Mathematics

[2572] **viXra:1803.0474 [pdf]**
*submitted on 2018-03-22 09:02:25*

**Authors:** Le Wang, Hong-yu Zhang, Jian-qiang Wang

**Comments:** 16 Pages.

In this study, comprehensive multi-criteria
decision-making (MCDM) methods are investigated under bipolar neutrosophic environment. First, the operations of BNNs are redefined based on the Frank operations considering the extant operations of bipolar neutrosophic numbers (BNNs) lack flexibility and robustness.

**Category:** General Mathematics

[2571] **viXra:1803.0473 [pdf]**
*submitted on 2018-03-22 09:05:45*

**Authors:** Abdolreza Rashno, Behzad Nazari, Dara D. Koozekanani, Paul M. Drayna, Saeed Sadri, Hossein Rabbani, Keshab K. Parhi

**Comments:** 26 Pages.

A fully-automated method based on graph shortest path, graph cut and neutrosophic (NS) sets is presented for fluid segmentation in OCT volumes for exudative age related macular degeneration (EAMD) subjects.

**Category:** General Mathematics

[2570] **viXra:1803.0472 [pdf]**
*submitted on 2018-03-22 09:06:54*

**Authors:** P Veeresh, R Praveen Sam, C Shoba Bindu

**Comments:** 9 Pages.

In recent years, computational capability of mobile devices such as Laptops, mobile phones, PDAs, etc., are greatly improved. Implementation of SOA ("Service Oriented Architectures") in mobile ad hoc networks increases the flexibility of using mobile devices.

**Category:** General Mathematics

[2569] **viXra:1803.0471 [pdf]**
*submitted on 2018-03-22 09:08:06*

**Authors:** Ashraful Alam

**Comments:** 9 Pages.

Fuzzy Cognitive Maps (FCM) have been applied in many fields successfully to show the causes and effect relationship. In this research work, the relationship between risk factors band symptoms of Diabetes has been analyzed with the help of FCM. FCM is a fuzzy-graph modeling approach based on expert’s opinion.

**Category:** General Mathematics

[2568] **viXra:1803.0470 [pdf]**
*submitted on 2018-03-22 09:09:20*

**Authors:** Muhammad Nazir Muhammad, Nadire Cavus

**Comments:** 8 Pages.

Today, many common activities have been transformed to electronic and online based environments because of the increased usage
of technology and the Internet. Education is one of the sectors that is using computer technologies for training and delivering learning information to learners.

**Category:** General Mathematics

[2567] **viXra:1803.0466 [pdf]**
*submitted on 2018-03-22 09:16:21*

**Authors:** Seon Jeong Kim, Seok-Zun Song, Young Bae Jun

**Comments:** 16 Pages.

As a more general platform which extends the notions of the classical set, fuzzy set, interval valued fuzzy set, intuitionistic fuzzy set and interval valued intuitionistic fuzzy set, Smarandache developed the concept of neutrosophic set which consists of three member functions, so called truth membership function, indeterminacy membership function and falsity membership function.

**Category:** General Mathematics

[2566] **viXra:1803.0465 [pdf]**
*submitted on 2018-03-22 09:17:31*

**Authors:** Hai-Long Yang, Yan-Ling Bao, Zhi-Lian Guo

**Comments:** 23 Pages.

Neutrosophic set (NS) was originally proposed by Smarandache to handle indeterminate and
inconsistent information. It is a generalization of fuzzy sets and intuitionistic fuzzy sets. Wang and Smarandache proposed interval neutrosophic sets (INS) which is a special case of NSs and would be extensively applied to resolve practical issues.

**Category:** General Mathematics

[2565] **viXra:1803.0464 [pdf]**
*submitted on 2018-03-22 09:19:06*

**Authors:** R. Dhavaseelan, S. Jafari, C. Ozel, M. A. Al-Shumrani

**Comments:** 17 Pages.

In this paper, the concepts of generalized neutrosophic contra-continuous function, gen-
eralized neutrosophic contra-irresolute function and strongly generalized neutrosophic
contra-continuous function are introduced. Some interesting properties are also studied.

**Category:** General Mathematics

[2564] **viXra:1803.0460 [pdf]**
*submitted on 2018-03-22 09:25:44*

**Authors:** Muhammad Akram, Muzzamal Sitara, Florentin Smarandache

**Comments:** 20 Pages.

A bipolar single-valued neutrosophic (BSVN) graph structure is a generalization of a bipolar fuzzy graph. In this research paper, we present certain concepts of BSVN graph structures.We describe some operations on BSVN graph structures and elaborate on these with examples. Moreover, we investigate some related properties of these operations.

**Category:** General Mathematics

[2563] **viXra:1803.0459 [pdf]**
*submitted on 2018-03-22 09:27:06*

**Authors:** Sujit Das, Saurabh Kumar, Samarjit Kar, Tandra Pal

**Comments:** 20 Pages.

This article proposes an algorithmic approach for group decision making (GDM) problems using neutrosophic soft matrix (NSM) and relative weights of experts. NSM is the matrix representation of neutrosophic soft sets (NSSs), where NSS is the combination of neutrosophic set and soft set.

**Category:** General Mathematics

[2562] **viXra:1803.0458 [pdf]**
*submitted on 2018-03-22 09:28:01*

**Authors:** Octavian Melinte, Luige Vladareanu, Radu A. Munteanu, Hongnian Yu

**Comments:** 7 Pages.

This paper presents a Neural Network approach to compensate dynamic terms, friction force in particular, of a rescue walking
robot used in haptic interfaces. The impedance control through dynamic compensation of the friction force is studied, followed
by the implementation of neural intelligent networks in the feed-forward loop in order to eliminate the corresponding terms in the
dynamics, friction force in particular. The friction force model is analyzed using a general compensation method after which a
trained Multi-Layer Neural Network is introduced in order to obtain an accurate friction model so that the movement of the
walking robot feels free and unconstraint.

**Category:** General Mathematics

[2561] **viXra:1803.0457 [pdf]**
*submitted on 2018-03-22 09:29:14*

**Authors:** Victor Christianto, Florentin Smarandache

**Comments:** 2 Pages.

In their classic book, the art of thinking, Robert Bramson and Allen Harrison describe five thinking styles that one tends to adopt: pragmatist, analyst, realist, synthesist, and idealist. In this paper, we tell our story on
thinking modes we often use, and sometimes we took a synthesizer mode, i.e. to combine three or four of the above thinking styles. We present some examples too. We hope this retelling may be useful for young scientists and mathematicians in developing new theories either in theoretical physics and cosmology.

**Category:** General Mathematics

[2560] **viXra:1803.0456 [pdf]**
*submitted on 2018-03-22 09:30:28*

**Authors:** Mihaela Colhon, Stefan Vladutescu, Xenia Negrea

**Comments:** 14 Pages.

In the latest studies concerning the sentiment polarity of words, the authors mostly consider
the positive and negative constructions, without paying too much attention to the neutral words,
which can have, in fact, significant sentiment degrees.

**Category:** General Mathematics

[2559] **viXra:1803.0455 [pdf]**
*submitted on 2018-03-22 09:31:43*

**Authors:** Yohana Yunet Bakarbessy, Henry W. M. Patty, Elvinus R. Persulessy

**Comments:** 6 Pages.

Penelitian ini membahas identifikasi struktur-struktur tersebut melalui definisi dan teorema dengan tahapan sebagai berikut : mengidentifikasi struktur ring dan perkembangannya seperti lapangan, near-ring dan near-field, mengidentifikasi struktur dasar Smarandache near-ring yang dibangun oleh near-ring dengan himpunan bagian sejatinya near-field, mengidentifikasi struktur dasar Smarandache near-ring lainnya berdasarkan perkembangan struktur dasar Smarandache near-ring.

**Category:** General Mathematics

[2558] **viXra:1803.0454 [pdf]**
*submitted on 2018-03-22 09:33:52*

**Authors:** Jun Ye

**Comments:** 9 Pages.

In pattern recognition and medical diagnosis, similarity measure is an important mathematical
tool. To overcome some disadvantages of existing cosine similarity measures of simplified neutrosophic sets (SNSs) in vector space, this paper proposed improved cosine similarity measures of SNSs based on cosine function, including single valued neutrosophic cosine similarity measures and interval neutrosophic cosine similarity measures. Then, weighted cosine similarity measures of SNSs were introduced by taking into account the importance of each element. Further, a medical diagnosis method using the improved cosine similarity measures was proposed to solve medical diagnosis problems with simplified
neutrosophic information.

**Category:** General Mathematics

[2557] **viXra:1803.0453 [pdf]**
*submitted on 2018-03-22 09:35:20*

**Authors:** F. Naveed, B. Hu

**Comments:** 6 Pages.

The inability to detect the Emerald Ash Borer (EAB) at an early stage has led to the enumerable loss of different species of ash trees.
Due to the increasing risk being posed by the EAB, a robust and accurate method is needed for identifying Individual Tree Crowns (ITCs) that are at a risk of being infected or are already diseased.

**Category:** General Mathematics

[2556] **viXra:1803.0452 [pdf]**
*submitted on 2018-03-22 09:36:53*

**Authors:** Edjard de Souza Mota, Jacob M. Howe, Artur S. d'Avila Garcez

**Comments:** 12 Pages.

The learning of rules from examples is of continuing interest to machine learning since it allows generalization from fewer training examples. Inductive Logic Programming (ILP) generates hypothetical rules (clauses) from a knowledge base augmented with (positive and negative) examples.

**Category:** General Mathematics

[2555] **viXra:1803.0450 [pdf]**
*submitted on 2018-03-22 09:39:17*

**Authors:** A. Edward Samuel, R. Narmadhagnanam

**Comments:** 12 Pages.

The objective of the study was to find out the relationship between the disease and the symptoms seen within patients and diagnose
the disease that impacted the patient using n-valued interval neutrosophic sets. Neoteric methods were devised in n-valued interval
neutrosophic sets. Utilization of medical diagnosis was commenced with using prescribed procedures to identify a person suffering from
the disease for a considerable period. The result showed that the proposed methods were free from shortcomings that affect the existing
methods and found to be more accurate in diagnosing the diseases. It was concluded that the techniques adopted in this study were more
reliable and easier to handle medical diagnosis problems.

**Category:** General Mathematics

[2554] **viXra:1803.0448 [pdf]**
*submitted on 2018-03-22 09:50:12*

**Authors:** Arian Hafezalkotob, Ashkan Hafezalkotob

**Comments:** 13 Pages.

By considering target values for attributes in addition to beneficial and non-beneficial attributes, a traditional MADM technique is converted to a comprehensive form. In many machine selection problems, some attributes have given target values.

**Category:** General Mathematics

[2553] **viXra:1803.0447 [pdf]**
*submitted on 2018-03-22 09:51:19*

**Authors:** Muhammad Akram, Muzzamal Sitara

**Comments:** 25 Pages.

In this research article, we introduce certain notions of interval-valued neutrosophic graph structures.

**Category:** General Mathematics

[2552] **viXra:1803.0446 [pdf]**
*submitted on 2018-03-22 10:07:53*

**Authors:** Florentin SMARANDACHE

**Comments:** 4 Pages.

Image and video processing research has undergone enormous changes and development in recent decades. This is due to the rapid advancements of visual technologies and their use in portable devices, medical imaging, and video streaming, for applications in photography, social media, entertainment, security and health care, among others. As images and video have become main means of communication and verification, the creation, transfer, and storage of high-quality imagesand videos require special attention.

**Category:** General Mathematics

[2551] **viXra:1803.0445 [pdf]**
*submitted on 2018-03-22 10:09:15*

**Authors:** J. G. Lee, P. K. Lim, J. H. Kim, K. Hur

**Comments:** 21 Pages.

First of all, we dene an intuitionistic quotient mapping and obtain its some properties. Second, we dene some types continuities, open and closed mappings. And we investigate relationships among them and give some examples. Finally, we introduce the notions of an intuitionistic subspace and the heredity, and obtain some properties of each concept.

**Category:** General Mathematics

[2550] **viXra:1803.0444 [pdf]**
*submitted on 2018-03-22 10:10:12*

**Authors:** Vahid Khatibi, Gholam Ali Montazer

**Comments:** 10 Pages.

One of the toughest challenges in medical diagnosis is uncertainty handling.The detection of intestinal bacteria such as Salmonella and Shigella which cause typhoid fever and dysentery, respectively, is one such challenging problem for
microbiologists.

**Category:** General Mathematics

[2549] **viXra:1803.0443 [pdf]**
*submitted on 2018-03-22 10:11:35*

**Authors:** J. H. Kim, P. K. Lim, J. G. Lee, K. Hur

**Comments:** 18 Pages.

First of all, we list some concepts and results introduced by[10, 15]. Second, we give some examples related to intuitionistic topologies
and intuitionistic bases, and obtain two properties of an intuitionistic base and an intuitionistic subbase. And we dene intuitionistic intervals in R.Finally, we dene some types of intuitionistic closures and interiors, and
obtain their some properties.

**Category:** General Mathematics

[2548] **viXra:1803.0440 [pdf]**
*submitted on 2018-03-22 10:15:01*

**Authors:** Zhikang Lu, Jun Ye

**Comments:** 12 Pages.

Fault diagnosis is an important task for the normal operation and maintenance of equipment.
In many real situations, the diagnosis data cannot provide deterministic values and are usually
imprecise or uncertain.

**Category:** General Mathematics

[2547] **viXra:1803.0439 [pdf]**
*submitted on 2018-03-22 10:16:40*

**Authors:** Azeddine Elhassouny, Florentin Smarandache

**Comments:** 13 Pages.

The purpose of this paper is to present an e[xtension and alternative of the hybrid method based on Saaty’s Analytical Hierarchy Process and Technique for Order Preference by Similarity to Ideal Solution method (AHP-TOPSIS), that based on the AHP and its use of pairwise comparisons, to a new method called α -D MCDM-TOPSIS( α -Discounting Method for multicriteria decision making-TOPSIS).

**Category:** General Mathematics

[2546] **viXra:1803.0437 [pdf]**
*submitted on 2018-03-22 10:19:12*

**Authors:** Nguyen Xuan Thao, Le Hoang Son, Bui Cong Cuong, Mumtaz Ali, Luong Hong Lan

**Comments:** 9 Pages.

In this paper, we propose the concept of fuzzy equivalence on standard neutrosophic sets and rough standard neutrosophic sets. We also provide
some formulas for fuzzy equivalence on standard neutrosophic sets and rough standard neutrosophic sets. We also apply these formulas for cluster
analysis. Numerical examples are illustrated.

**Category:** General Mathematics

[2545] **viXra:1803.0436 [pdf]**
*submitted on 2018-03-22 10:20:28*

**Authors:** Edmundas Kazimieras Zavadskas, Romualdas Bausys, Birute Juodagalviene, Inga Garnyte-Sapranaviciene

**Comments:** 10 Pages.

This article aims to create a theoretical evaluation model based on decision support methods for the residential house construction materials and elements selection. The research and analyses of most of the scientists are invoked on individual elements and materials of the building, which have an impact on different aspects of
sustainability.

**Category:** General Mathematics

[2544] **viXra:1803.0435 [pdf]**
*submitted on 2018-03-22 10:22:21*

**Authors:** Jean-Claude Okaingni, Sié Ouattara, Adles Kouassi, Wognin J. Vangah, Aubin K. Koffi, Alain Clement

**Comments:** 17 Pages.

In this paper, the theory of plausible and paradoxical reasoning of Dezert-Smarandache (DSmT) is used to take into account the paradoxical character through the intersections of vegetation, aquatic and mineral surfaces. In order to do this, we developed a classification model of pixels by aggregating information
using the DSmT theory based on the PCR5 rule using the NDVI, MNDWI and NDBaI spectral indices obtained from the ASTER satellite images.

**Category:** General Mathematics

[2543] **viXra:1803.0431 [pdf]**
*submitted on 2018-03-22 07:33:12*

**Authors:** S. Shanmugam, J. Preethi

**Comments:** 13 Pages.

Arthritis is the most familiar element of disability in the World. At a rate of 20 million people in the US are suffering from Arthritis. It characterizes around 200 rheumatic diseases and conditions that influence joints. The tissues surround the joint, and other connective tissue.

**Category:** General Mathematics

[2542] **viXra:1803.0428 [pdf]**
*submitted on 2018-03-22 07:36:47*

**Authors:** Abbas Mardani, Mehrbakhsh Nilashi, Norhayati Zakuan, Nanthakumar Loganathan, Somayeh Soheilirad, Muhamad Zameri Mat Saman, Othman Ibrahim

**Comments:** 28 Pages.

The Multiple Criteria Decision Making (MCDM) utility determining approaches and fuzzy sets are considered to be new development approaches, which have been recently presented, extended, and used by some scholars in area of decision making.

**Category:** General Mathematics

[2541] **viXra:1803.0427 [pdf]**
*submitted on 2018-03-22 07:40:13*

**Authors:** H.D. Cheng, JuanShan, Wen Ju, Yanhui Guo, Ling Zhang

**Comments:** 19 Pages.

Breast cancer is the second leading cause of death for women all over the world. Since the cause of the disease remains unknown, early detection and diagnosis is the key for breast cancercontrol,and it can increase the success of treatment, save lives and reduce cost.

**Category:** General Mathematics

[2540] **viXra:1803.0423 [pdf]**
*submitted on 2018-03-22 07:44:29*

**Authors:** Arkajyoti Saha, Swagatam Das

**Comments:** 17 Pages.

For decades practitioners have been using the center-based partitional clustering algorithms
like Fuzzy C Means (FCM), which rely on minimizing an objective function, comprising of an appropriately weighted sum of distances of each data point from the cluster representatives.

**Category:** General Mathematics

[2539] **viXra:1803.0422 [pdf]**
*submitted on 2018-03-22 07:46:01*

**Authors:** S.F. Ghaderi, A. Azadeh, B. Pourvalikhan Nokhandan, E. Fathi

**Comments:** 12 Pages.

Simulation can be used in a wide range of applications in an electricity market. There are many reasons that market players and regulators are very interested in anticipating the behavior of the market. Behavior of a generation company (GENCO) in electricity market is an important factor that affects the market behavior. Several factors affect the behavior of a GENCO directly and indirectly.

**Category:** General Mathematics

[2538] **viXra:1803.0421 [pdf]**
*submitted on 2018-03-22 07:48:23*

**Authors:** Pawalai Kraipeerapun, Chun Che Fung

**Comments:** 12 Pages.

This paper presents an ensemble neural network and interval neutrosophic sets approach to the
problem of binary classification.

**Category:** General Mathematics

[2537] **viXra:1803.0419 [pdf]**
*submitted on 2018-03-22 07:50:43*

**Authors:** Mumtaz Ali, Le Hoang Son, Irfan Deli, Nguyen Dang Tien

**Comments:** 11 Pages.

Neutrosophic set, proposed by Smarandache considers a truth membership function, an indeterminacy membership function and a falsity membership function. Soft set, proposed by Molodtsov is a mathematical framework which has the ability of independency of parameterizations inadequacy, syndrome of fuzzy set, rough set, probability.

**Category:** General Mathematics

[2536] **viXra:1803.0418 [pdf]**
*submitted on 2018-03-22 07:51:46*

**Authors:** Ion PATRASCU, Florentin SMARANDACHE

**Comments:** 2 Pages.

In this Note, the authors present some properties of Apollonius circles of rank −1 associated to a triangle.

**Category:** General Mathematics

[2535] **viXra:1803.0415 [pdf]**
*submitted on 2018-03-22 07:56:02*

**Authors:** Abdulkadir Sengura, Yanhui Guo

**Comments:** 11 Pages.

Efficient and effective image segmentation is an important task in computer vision and pattern recognition. Since fully automatic image segmentation is usually very hard for natural images, interactive schemes with a few simple user inputs are good solutions.

**Category:** General Mathematics

[2534] **viXra:1803.0414 [pdf]**
*submitted on 2018-03-22 07:57:06*

**Authors:** Sangeeta K Siri, Mrityunjaya V. Latte

**Comments:** 9 Pages.

Many different diseases can occur in the liver, including infections such as hepatitis, cirrhosis, cancer and over effect of medication or toxins. The foremost stage for computer-aided diagnosis of liver is the identification of liver region.

**Category:** General Mathematics

[2533] **viXra:1803.0413 [pdf]**
*submitted on 2018-03-22 07:58:18*

**Authors:** Harmeet Kaur, Navdeep Singh

**Comments:** 8 Pages.

A group of defective cells that grow inside or around the brain referred as Barin Tumor. The number of Brain Tumor cases around the World is increasing day by day. So, it is significant to detect it at anearly stage. Segmentation of brain images holds thesignificant part for detection of Tumor brain.

**Category:** General Mathematics

[2532] **viXra:1803.0412 [pdf]**
*submitted on 2018-03-22 07:59:54*

**Authors:** Fu Yuhua

**Comments:** 9 Pages.

As No.4 of comparative physics series papers, this paper mainly discusses the comparative studies of various theories (or formulae) of force, and
on this basis, presents the concepts of generalized theory of force and generalized
theories clusters of force.

**Category:** General Mathematics

[2531] **viXra:1803.0411 [pdf]**
*submitted on 2018-03-22 08:01:12*

**Authors:** Linfan MAO

**Comments:** 20 Pages.

A complex system S consists of m components, maybe inconsistence with m ≥ 2 such as those of self-adaptive systems, particularly the biological systems and usually, a system with contradictions, i.e., there are no a classical mathematical subfield applicable. Then, how can we hold its global and local behaviors or true face?

**Category:** General Mathematics

[2530] **viXra:1803.0410 [pdf]**
*submitted on 2018-03-22 08:02:37*

**Authors:** Prem Kumar Singh

**Comments:** 9 Pages.

Recently, the calculus of concept lattice is extended from unipolar to bipolar fuzzy space for precise measurement of vagueness in the attributes based on their acceptation and rejection part. These ex- tensions still unable to highlight the uncertainty in vague attributes and measurement of fluctuation at given phase of time.

**Category:** General Mathematics

[2529] **viXra:1803.0409 [pdf]**
*submitted on 2018-03-22 08:03:28*

**Authors:** H.S. Abdel-Aziz, M. Khalifa Saad

**Comments:** 9 Pages.

In this paper, we study Smarandache curves according to Darboux frame in the three-dimensional Minkowski space E 3 1 . Using the usual transformation between Frenet and Darboux frames, we investi- gate some special Smarandache curves for a given timelike curve lying fully on a timelike surface. Finally, we defray a computational example to confirm our main results.

**Category:** General Mathematics

[2528] **viXra:1803.0408 [pdf]**
*submitted on 2018-03-22 08:07:29*

**Authors:** Deepika Koundal, Savita Gupta, Sukhwinder Singh

**Comments:** 14 Pages.

Thyroid nodule is one of the endocrine problem caused due to abnormal growth of cells. This survival rate can be enhanced by earlier detection of nodules. Thus, the accurate detection of nodule is of utmost importance in providing effective diagnosis to increase the survival rate. However, accuracy of nodule
detection from ultrasound images is suffered due to speckle noise. It considerably deteriorates the image quality and makes the differentiation of fine details quite difficult.

**Category:** General Mathematics

[2527] **viXra:1803.0407 [pdf]**
*submitted on 2018-03-22 08:15:56*

**Authors:** X), Said Broumi, Assia Bakali, Mohamed Talea, Florentin Smarandache, Rajkumar Verma

**Comments:** 5 Pages.

Interval valued bipolar neutrosophic sets is a new generalization of fuzzy set, bipolar fuzzy set, neutrosophic set and bipolar neutrosophic set so that it can handle uncertain information more flexibly in the process of decision making. In this paper, an algorithm for finding minimum spanning tree (MST) of an undirected neutrosophic weighted connected graph (UNWCG) in which the edge weights is represented by
a an interval valued bipolar neutrosophic number is presented.

**Category:** General Mathematics

[2526] **viXra:1803.0406 [pdf]**
*submitted on 2018-03-22 08:17:34*

**Authors:** M. Kavitha, P. Murugadas, S. Sriram

**Comments:** 15 Pages.

Uncertainty forms have a very important part in our daily life. During the time we handle real life problems involving uncertainty like Medical elds, Engineering, Industry and Economics and so on.

**Category:** General Mathematics

[2525] **viXra:1803.0405 [pdf]**
*submitted on 2018-03-22 08:18:26*

**Authors:** Xu Wu

**Comments:** 19 Pages.

Mobile cloud computing (MCC) has attracted extensive attention in recent years. With the prevalence of MCC, how to select trustworthy and high quality mobile cloud services becomes one of the most urgent problems.

**Category:** General Mathematics

[2524] **viXra:1803.0403 [pdf]**
*submitted on 2018-03-22 08:21:38*

**Authors:** Rıdvan Sahin, Peide Liu

**Comments:** 9 Pages.

As a combination of the hesitant fuzzy set
(HFS) and the single-valued neutrosophic set (SVNS), the single-valued neutrosophic hesitant fuzzy set (SVNHFS) is an important concept to handle uncertain and vague information existing in real life, which consists of three membership functions including hesitancy, as the truthhesitancy membership function, the indeterminacy-hesitancy membership function and the falsity-hesitancy membership function, and encompasses the fuzzy set, intuitionistic fuzzy set (IFS), HFS, dual hesitant fuzzy set (DHFS) and SVNS.

**Category:** General Mathematics

[2523] **viXra:1803.0401 [pdf]**
*submitted on 2018-03-21 20:09:35*

**Authors:** Colin James III

**Comments:** 1 Page. © Copyright 2018 by Colin James III All rights reserved. info@cec-services dot com

In neutrosophic logic, the designated values are ((1 or 0) or (less_than 1 and greater_than 0)) as three sets. As rendered, it is not tautologous, not bivalent, and hence refuted.
Note: This paper was uploaded to General Mathematics because of the deluge of neutrosophic papers mainly from PRC, but is more properly under the heading Set theory and logic where our other papers are regarding neutrosophic matters.

**Category:** General Mathematics

[2522] **viXra:1803.0392 [pdf]**
*submitted on 2018-03-21 10:09:07*

**Authors:** Yanhui Guo, Ümit Budak, Abdulkadir Sengür, Florentin Smarandache

**Comments:** 10 Pages.

A fundus image is an effective tool for ophthalmologists studying eye diseases.
Retinal vessel detection is a significant task in the identification of retinal disease regions. This study presents a retinal vessel detection approach using shearlet transform and indeterminacy filtering.

**Category:** General Mathematics

[2521] **viXra:1803.0391 [pdf]**
*submitted on 2018-03-21 10:11:09*

**Authors:** Abbas Mardania, Edmundas Kazimieras Zavadskas, Zainab Khalifah, Norhayati Zakuan, Ahmad Jusoh, Khalil Md Nor, Masoumeh Khoshnoudi

**Comments:** 41 Pages.

Energy management problems associated with rapid institutional, political, technical, ecological, social and economic development have been of critical concern to both national and local governments worldwide for many decades; thus, addressing such issues is a global priority.

**Category:** General Mathematics

[2520] **viXra:1803.0390 [pdf]**
*submitted on 2018-03-21 10:14:29*

**Authors:** XiaoWang, Jianhu Zhao, Bangyan Zhu, Tingchen Jiang, Tiantian Qin

**Comments:** 16 Pages.

To accurately achieve side scan sonar (SSS) image target detection, a novel target detection algorithm based on a neutrosophic set (NS) and diffusion maps (DMs) is proposed in this paper. Firstly, the neutrosophic subset images were obtained by transforming the input SSS image into the NS domain. Secondly, the shadowed areas of the SSS image were detected using the single gray value threshold method before the diffusion map was calculated.

**Category:** General Mathematics

[2519] **viXra:1803.0389 [pdf]**
*submitted on 2018-03-21 10:15:23*

**Authors:** Lei Cai, Dianjun Chen, Luyong Zhang

**Comments:** 6 Pages.

Decoupling characteristics of Software Defined Network(SDN) control plane and data plane provides us with a new idea to improve dynamic routing. SDN
controllers can easily obtain the global situation of the whole network. The network topology information and bandwidth data are applied to the classical Dijstra algorithm.

**Category:** General Mathematics

[2518] **viXra:1803.0377 [pdf]**
*submitted on 2018-03-21 06:15:57*

**Authors:** Min Xian, Yingtao Zhang, H. D. Cheng, Fei Xu, Kuan Huang, Boyu Zhang, Jianrui Ding, Chunping Ning, Ying Wang

**Comments:** 9 Pages.

Breast ultrasound (BUS) image segmentation is challenging and critical for BUS Computer-Aided Diagnosis (CAD) systems. Many BUS segmentation approaches have been proposed in the last two decades, but the performances of most approaches
have been assessed using relatively small private datasets with different quantitative metrics, which result in discrepancy in performance comparison.

**Category:** General Mathematics

[2517] **viXra:1803.0375 [pdf]**
*submitted on 2018-03-21 06:21:05*

**Authors:** Yoichi Hayashi, Kazuhiro Fukunaga

**Comments:** 13 Pages.

Although liver cancer is the second most common cause of death from cancer worldwide, because of the limited accuracy and interpretability of extracted classification rules, the diagnosis of liver disease remains difficult. In addition, hepatitis, which is inflammation of the liver, can progress to fibrosis, cirrhosis, or even liver cancer.

**Category:** General Mathematics

[2516] **viXra:1803.0374 [pdf]**
*submitted on 2018-03-21 06:30:21*

**Authors:** Soumyadip Dhara, Malay K. Kundu

**Comments:** 15 Pages.

tIn any image segmentation problem, there exist uncertainties. These uncertainties occur from gray leveland spatial ambiguities in an image.

**Category:** General Mathematics

[2515] **viXra:1803.0373 [pdf]**
*submitted on 2018-03-21 07:02:01*

**Authors:** Yilin Dong, Xinde Li, Yihai Liu

**Comments:** 25 Pages.

In many applications involving epistemic uncertainties usually modeled by belief functions, it is often necessary to approximate general (non-Bayesian) basic belief assignments (BBAs)
to subjective probabilities (called Bayesian BBAs).

**Category:** General Mathematics

[2514] **viXra:1803.0370 [pdf]**
*submitted on 2018-03-21 07:41:58*

**Authors:** Chaouki Khammassi, Saoussen Krichen

**Comments:** 23 Pages.

Intrusions constitute one of the main issues in computer network security. Through malicious
actions, hackers can have unauthorised access that compromises the integrity, the confidentiality, and the availability of resources or services. Intrusion detection systems (IDSs) have been developed to monitor and filter network activities by identifying attacks and alerting
network administrators.

**Category:** General Mathematics

[2513] **viXra:1803.0369 [pdf]**
*submitted on 2018-03-21 07:45:02*

**Authors:** Mutasem K. Alsmadi

**Comments:** 10 Pages.

It is really important to diagnose jaw tumor in its early stages to improve its prognosis. A
differential diagnosis could be performed using X-ray images; therefore, accurate and fully automatic jaw lesions image segmentation is a challenging and essential task. The aim of this work was to develop a novel, fully automatic and effective method for jaw lesions in panoramic X-ray image segmentation.

**Category:** General Mathematics

[2512] **viXra:1803.0368 [pdf]**
*submitted on 2018-03-21 07:46:04*

**Authors:** Prem Kumar Singh

**Comments:** 26 Pages.

The precise measurement of uncertainty exists in the complex fuzzy attributes and their graphical analytics is a mathematically expensive tasks for knowledge processing researchers. To deal with this problem recently, the calculus of complex neutrosophic sets are introduced to characterize the uncertainty in data based on its truth, indeterminacy, and falsity membership– value, independently.

**Category:** General Mathematics

[2511] **viXra:1803.0367 [pdf]**
*submitted on 2018-03-21 07:47:15*

**Authors:** Xindong Peng, Jingguo Dai

**Comments:** 27 Pages.

In this paper, we define a new axiomatic definition of interval neutrosophic similarity measure, which is presented by interval neutrosophic number (INN). Later, the objective weights of various attributes are determined via Shannon entropy theory; meanwhile, we develop the combined weights, which can show both subjective information and objective information.

**Category:** General Mathematics

[2510] **viXra:1803.0366 [pdf]**
*submitted on 2018-03-21 07:48:30*

**Authors:** Xindong Peng, Chong Liu

**Comments:** 14 Pages.

This paper presents three novel single-valued neutrosophic soft set (SVNSS) methods. First, we initiate a new axiomatic definition of single-valued neutrosophic similarity measure, which is expressed by single-valued neutrosophic number (SVNN) that will reduce the information loss and remain more original information. Then, the objective weights of various parameters are determined via grey system theory.

**Category:** General Mathematics

[2509] **viXra:1803.0365 [pdf]**
*submitted on 2018-03-21 07:49:51*

**Authors:** Run-yu Zhang, Mingyang Yu, Yan Gao

**Comments:** 6 Pages.

By co mbin ing neutrosophic sets and hesitant fuzzy sets, the definition of hesitant neutrosophic sets is presented. Based on the Euclidean distance and the cosine similarity formu la, the similarity formu la of neutrosophic sets is constructed. Then its similarity formu la is also provided. According to the similarity formu la of hesitant neutrosophic sets, a new mu lti-attribute VIKOR decision-making method for hesitant neutrosophic information is develop. At last an illustrative example is given to verify its practicality and effectiveness.

**Category:** General Mathematics

[2508] **viXra:1803.0361 [pdf]**
*submitted on 2018-03-21 07:56:24*

**Authors:** Serpil Altinirmak, Basil Okoth, Mustafa Ergun, Caglar Karamasa

**Comments:** 14 Pages.

Mobile banking, also known as m-banking, provides low cost, innovative and easily accessible services to customers with technological developments as compared to retail banking. In this context, m-banking quality factors of the banks are considered to be important issues for customers. The aim of this study is to analyze the m-banking quality factors and to rank banks offering this service in Turkey under incomplete, inconsistent and indeterminate information.

**Category:** General Mathematics

[2507] **viXra:1803.0360 [pdf]**
*submitted on 2018-03-21 07:58:11*

**Authors:** Süleyman ŞENYURT, Selin SİVAS

**Comments:** 15 Pages.

In this paper, Firstly we define NC-Smarandache curve, then we calculate the curvature and
torsion of NB and TNB- Smarandache curves together with NC-Smarandache curve. Here T, N and B are Frenet vectors of a curve α and vector C is unit Darboux vector.

**Category:** General Mathematics

[2506] **viXra:1803.0359 [pdf]**
*submitted on 2018-03-21 08:00:34*

**Authors:** Edgar Valdebenito

**Comments:** 3 Pages.

In this note we recall some formulas for pi. they express pi in terms of the Golden Ratio.

**Category:** General Mathematics

[2505] **viXra:1803.0358 [pdf]**
*submitted on 2018-03-21 07:59:46*

**Authors:** Mostafa El-Baz, Ibrahim El-Henawy

**Comments:** 5 Pages.

Cloud Computing has already changed the way that people think about and use the information technology services. Cloud data storage is one of such services in which data is stored, managed, remotely backed up and accessed by users over the Internet. when the organization need to depend on cloud computing solution as intelligent solution ,the first problem facing the organization is to choosing the appropriate provider between different providers available especially in the cases of confused portfolios which contain complex pricing models and different criteria's. for addressing this problem the thesis providing a multi-criteria algorithm which based on neutrosophic to help the organization to choose the best appropriate providers achieving high degree of security and privacy according their requirements map .

**Category:** General Mathematics

[2504] **viXra:1803.0357 [pdf]**
*submitted on 2018-03-21 08:02:10*

**Authors:** Mutasem K. Alsmadi

**Comments:** 11 Pages.

Content based image retrieval (CBIR) systems work by retrieving images which are related to the query image (QI) from huge databases. The available CBIR systems extract limited feature sets which confine the retrieval efficacy. In this work, extensive robust and important features were extracted from the images database and then stored in the feature repository.

**Category:** General Mathematics

[2503] **viXra:1803.0356 [pdf]**
*submitted on 2018-03-21 08:03:21*

**Authors:** B. Kavitha, S. Karthikeyan, P. Sheeba Maybell

**Comments:** 9 Pages.

In the real world it is a routine that one must deal with uncertainty when security is concerned. Intrusion detection systems offer a new challenge in handling uncertainty due to imprecise knowledge in classifying the normal or abnormal behaviour patterns

**Category:** General Mathematics

[2502] **viXra:1803.0355 [pdf]**
*submitted on 2018-03-21 08:06:02*

**Authors:** Ming Zhang, LingZhang, H.D.Cheng

**Comments:** 8 Pages.

Neutrosophy studies the origin, nature,scope of neutralities,and their interactions with
different ideational spectra.

**Category:** General Mathematics

[2501] **viXra:1803.0349 [pdf]**
*submitted on 2018-03-21 08:27:50*

**Authors:** Z. Hajighasemi, S. M. Mousavi

**Comments:** 23 Pages.

Failure modes and effects analysis (FMEA) is a well-known risk analysis approach that has been conducted to distinguish, analyze and mitigate serious failure modes.

**Category:** General Mathematics

[2500] **viXra:1803.0348 [pdf]**
*submitted on 2018-03-21 08:32:22*

**Authors:** Antigoni P. Anninou, Peter P. Groumpos, Panagiotis Poulios, Ioannis Gkliatis

**Comments:** 6 Pages.

A new approach of Dynamic Fuzzy Cognitive Knowledge Networks is presented. This
is an evolutionary type of Fuzzy Cognitive Maps (FCM) that arose from the need for updating
classic methodology in order to overcome its drawbacks, concerning the single calculation rule,
stability and real time problems and expands its use in a varity of applications.

**Category:** General Mathematics

[2499] **viXra:1803.0347 [pdf]**
*submitted on 2018-03-21 08:33:31*

**Authors:** Fangling Ren, Mingming Kong, Zheng Pei

**Comments:** 19 Pages.

Hesitant fuzzy linguistic decision making is a focus point in linguistic decision making,
in which the main method is based on preference ordering.

**Category:** General Mathematics

[2498] **viXra:1803.0346 [pdf]**
*submitted on 2018-03-21 08:35:08*

**Authors:** Mehdi Keshavarz Ghorabaee, Maghsoud Amiri, Edmundas Kazimieras Zavadskas, Zenonas Turskis, Jurgita Antucheviciene

**Comments:** 16 Pages.

Evaluation of airlines based on service quality criteria can help to improve the processes of airlines, and also can give guidance to travel agencies to provide better choices for passengers and tourists. In this study, a hybrid simulation-based assignment approach is proposed to deal with multi-criteria decision making problems with a group of decision-makers.

**Category:** General Mathematics

[2497] **viXra:1803.0345 [pdf]**
*submitted on 2018-03-21 08:42:59*

**Authors:** Groumpos P. Peter, Anninou P. Antogoni, Groumpos P. Vasileios

**Comments:** 6 Pages.

The aim of this paper is to present a new approach in modelling wine quality and quantity
using Fuzzy Cognitive Maps trained by non linear Hebbian learning algorithm. The methodology described extracts the knowledge from the experts and exploits their experience on wine production. Two case studies with data from real vineyards were examined. The results of this study show that software tools using Fuzzy Cognitive Maps could be explored further and problems that arise during the wine
production could be prevented by an efficient decision support system.

**Category:** General Mathematics

[2496] **viXra:1803.0344 [pdf]**
*submitted on 2018-03-21 08:46:50*

**Authors:** Eser Sert

**Comments:** 17 Pages.

Segmentation is paramount to 3D video systems employing multi-view video-plus-depth data (MVD) to implement free-viewpoint navigation and comfortable 3D viewing, modeling, and comprehension.

**Category:** General Mathematics

[2495] **viXra:1803.0343 [pdf]**
*submitted on 2018-03-21 08:49:49*

**Authors:** Mehdi Keshavarz Ghorabaee, Maghsoud Amiri, Edmundas Kazimieras Zavadskas, Zenonas Turskis, Jurgita Antucheviciene

**Comments:** 19 Pages.

Nowadays environmental performance of suppliers becomes more important because of competitive
conditions. Besides, the economic performance has been a significant factor for companies to choose their suppliers.

**Category:** General Mathematics

[2494] **viXra:1803.0342 [pdf]**
*submitted on 2018-03-21 08:50:57*

**Authors:** Victor Christianto, Florentin Smarandache

**Comments:** 4 Pages.

Some years ago, Matt Visser asked the following interesting questions: How much of modern cosmology is really cosmography? How much of modern cosmology is independent of the Einstein equations? (Independent of the Friedmann equations?)

**Category:** General Mathematics

[2493] **viXra:1803.0337 [pdf]**
*submitted on 2018-03-21 09:42:26*

**Authors:** Chao Zhang, Deyu Li, Yimin Mu, Dong Song

**Comments:** 12 Pages.

In the field of mechanical engineering, steam turbine fault diagnosis is a difficult task for mechanical engineers who are confronted with challenges in dealing with copious amounts of uncertain information.

**Category:** General Mathematics

[2492] **viXra:1803.0336 [pdf]**
*submitted on 2018-03-21 09:43:35*

**Authors:** Nadeem Akhtar, Mohammad Naved Qureshi, Mohd Vasim Ahamad

**Comments:** 13 Pages.

As a technique of Information Retrieval, we can consider clustering as an unsupervised learning problem in which we provide a structure to unlabeled and unknown data.

**Category:** General Mathematics

[2491] **viXra:1803.0335 [pdf]**
*submitted on 2018-03-21 09:45:00*

**Authors:** Eduardo H.M. Pena, Luiz F. Carvalho, Sylvio Barbon Jr.Joel J.P.C. Rodrigues, Mario Lemes Proença Jr.

**Comments:** 16 Pages.

This study presents the correlational paraconsistent machine (CPM), a tool for anomaly
detection that incorporates unsupervised models for traffic characterization and principles
of paraconsistency, to inspect irregularities at the network traffic flow level.

**Category:** General Mathematics

[2490] **viXra:1803.0331 [pdf]**
*submitted on 2018-03-21 09:50:34*

**Authors:** setYanhui Guo, Abdulkadir Sengür, Jia-Wei Tian

**Comments:** 11 Pages.

Breast ultrasound (BUS) image segmentation is a challenging task due to the speckle noise,poor quality of the ultrasound images and size and location of the breast lesions.

**Category:** General Mathematics

[2489] **viXra:1803.0329 [pdf]**
*submitted on 2018-03-21 09:54:30*

**Authors:** Baolin Li, Juanru Wang, Lihua Yang, Xuetao Li

**Comments:** 6 Pages.

In order to handle the indeterminate information and inconsistent information in some complex decision-making environment, some novel aggregation operators are firstly proposed based on Einstein operational
laws and generalized aggregation operators under simplified neutrosophic environment, where the truth-membership degree, indeterminacy-membership degree and
falsity-membership degree of each element are singleton subsets in [0,1] .

**Category:** General Mathematics

[2488] **viXra:1803.0328 [pdf]**
*submitted on 2018-03-21 09:56:11*

**Authors:** Fangjun Kuanga, Weihong Xua, Siyang Zhang

**Comments:** 7 Pages.

tA novel support vector machine (SVM) model combining kernel principal component analysis (KPCA)with genetic algorithm (GA) is proposed for intrusion detection.

**Category:** General Mathematics

[2487] **viXra:1803.0321 [pdf]**
*submitted on 2018-03-21 10:05:20*

**Authors:** Cengiz Kahraman, Selcuk Cebi, Sezi Cevik Onar, Basar Oztaysi

**Comments:** 16 Pages.

Information axiom is used to determine the best option among the potential alternatives. In case of uncertain parameters, information axiom has been extended to its ordinary fuzzy versions in the literature. In this paper, we developed a trapezoidal intuitionistic fuzzy information axiom model in order to handle the hesitancy of experts.

**Category:** General Mathematics

[2486] **viXra:1803.0320 [pdf]**
*submitted on 2018-03-21 10:06:35*

**Authors:** Harish Garg, Sukhveer Singh

**Comments:** 25 Pages.

The objective of this work is to present a triangular interval type-2 (TIT2) intuitionistic fuzzy sets and their corresponding aggregation operators, namely, TIT2 intuitionistic fuzzy weighted averaging, TIT2 intuitionistic
fuzzy ordered weighted averaging and TIT2 intuitionistic fuzzy hybrid averaging based on Frank norm operation laws.

**Category:** General Mathematics

[2485] **viXra:1803.0319 [pdf]**
*submitted on 2018-03-21 10:07:46*

**Authors:** Hai Wang, Zeshui Xu, Witold Pedrycz

**Comments:** 16 Pages.

In the era of big data, we are facing with an immense volume and high velocity of data with complex structures. Data can be produced by online and offline transactions, social networks, sensors and through our daily life activities.

**Category:** General Mathematics

[2484] **viXra:1803.0308 [pdf]**
*submitted on 2018-03-20 11:01:02*

**Authors:** Ling Shuwei

**Comments:** 11 Pages.

The Color Dimension Theorem is divided into two parts: The first part gives a constructive proof of the four-color theorem, and points out that the existence of the "one-dimensional-two-color, two-dimensional-four-color" relationship is not accidental; The second part discusses the upper limit of the dimensionality of the space. The method is: suppose the space above the N dimension exists, there must be a geometry. Considering the projection of this geometry on the plane, we will find that this projection image produces a paradox, which means N The space above the dimension does not exist

**Category:** General Mathematics

[2483] **viXra:1803.0294 [pdf]**
*submitted on 2018-03-20 23:22:34*

**Authors:** D Williams

**Comments:** 14 Pages.

A Mathematical Museum is described for INSPIRING students and the general public and provide an alternative to the soul-destroying 19th century institutionalised rote-learning (with subsequent near-instantaneous forgetting) of barely understood material in assembly-line schools/factories of "learning" by people who are thereby taught to HATE mathematics.

**Category:** General Mathematics

[2482] **viXra:1803.0158 [pdf]**
*submitted on 2018-03-11 07:58:47*

**Authors:** Yuly Shipilevsky

**Comments:** 4 Pages.

A class of converted target functions
preserving the set of minimizers

**Category:** General Mathematics

[2481] **viXra:1803.0130 [pdf]**
*submitted on 2018-03-09 05:41:53*

**Authors:** Suraj deshmukh

**Comments:** 1 Page.

It was just found luckily. It is a new method to get primes easily.
Just a rearrangement of numbers.

**Category:** General Mathematics

[2480] **viXra:1803.0111 [pdf]**
*submitted on 2018-03-08 06:41:04*

**Authors:** Edgar Valdebenito

**Comments:** 5 Pages.

This note presents eight series for pi.

**Category:** General Mathematics

[2479] **viXra:1803.0085 [pdf]**
*submitted on 2018-03-06 10:43:29*

**Authors:** Koji KOBAYASHI

**Comments:** 9 Pages.

This paper describes about complexity of PH problems by using
problem input independence, and provide new approach to solve P vs NP problem.
Circuit family that emulate Deterministic Turing machine (DTM) are almost monotone circuits except input variables (like negation normal form (NNF)). Therefore, we can find out DTM limitation by using this "NNF circuit family".
To clarify NNF circuit limitation, we pay attention to AND-gate and OR-gate of NNF circuit DAG network. Because each pair of positive and negative variables do not become 1 in same input, these pair join at OR-gate to output computation result as 1. If some accept inputs does not include another accept input between these input with Hamming distance, OR-gate which join "Neighbor input" as accept input have to meet AND-gate to exclude between "Boundary input" as reject input. This means that these different variables of neighbor input are finally meet AND-gate, and NNF circuit have to use unique AND-gate to differentiate such different variables and boundary input variables.
The other hand, we can make neighbor input problem "Neighbor Tautology DNF problem (NTD)" from DNF Tautology problem. NTD is in PH, and
NTD consist of neighbor input and number of these input is over polynomial size of input length. Therefore NNF circuit family that compute NTD are over polynomial size, and NTD that include PH is not in P.

**Category:** General Mathematics

[2478] **viXra:1802.0428 [pdf]**
*submitted on 2018-02-28 06:55:11*

**Authors:** Edgar Valdebenito

**Comments:** 7 Pages.

This note presents a collection of integral formulas.

**Category:** General Mathematics

[2477] **viXra:1802.0426 [pdf]**
*submitted on 2018-02-28 07:21:50*

**Authors:** Edgar Valdebenito

**Comments:** 9 Pages.

This note presents some formulas involving pi.

**Category:** General Mathematics

[2476] **viXra:1802.0392 [pdf]**
*submitted on 2018-02-27 01:06:36*

**Authors:** Surapati Pramanik, Shyamal Dalapati, Shariful Alam, Florentin Smarandache, Tapan Kumar Roy

**Comments:** 21 Pages.

A single-valued neutrosophic set has king power to express uncertainty characterized by
indeterminacy, inconsistency and incompleteness. Most of the existing single-valued neutrosophic cross entropy bears an asymmetrical behavior and produces an undefined phenomenon in some situations. In order to deal with these disadvantages, we propose a new cross entropy measure under a single-valued neutrosophic set (SVNS) environment, namely NS-cross entropy, and prove its basic properties.

**Category:** General Mathematics

[2475] **viXra:1802.0391 [pdf]**
*submitted on 2018-02-27 01:07:59*

**Authors:** Seok-Zun Song, Florentin Smarandache, Young Bae Jun

**Comments:** 9 Pages.

The notion of a neutrosophic commutative N-ideal in BCK-algebras is introduced, and several properties are investigated. Relations between a neutrosophic N-ideal and a neutrosophic
commutative N-ideal are discussed. Characterizations of a neutrosophic commutative N-ideal are considered.

**Category:** General Mathematics

[2474] **viXra:1802.0390 [pdf]**
*submitted on 2018-02-27 01:09:08*

**Authors:** Young Bae Jun, Florentin Smarandache, Hashem Bordbar

**Comments:** 12 Pages.

Neutrosophic N-structures with applications in BCK/BCI-algebras is discussed. The notions of a neutrosophic N-subalgebra and a (closed) neutrosophic N-ideal in a BCK/BCI-algebra are introduced, and several related properties are investigated. Characterizations of a neutrosophic N-subalgebra and a neutrosophic N-ideal are considered, and relations between a
neutrosophic N-subalgebra and a neutrosophic N-ideal are stated. Conditions for a neutrosophic
N-ideal to be a closed neutrosophic N-ideal are provided.

**Category:** General Mathematics

[2473] **viXra:1802.0389 [pdf]**
*submitted on 2018-02-27 01:10:35*

**Authors:** Florentin Smarandache, Jun Ye

**Comments:** 212 Pages.

The concept of Information is to disseminate scientific results achieved via experiments and theoretical results in depth. It is very important to enable researchers and practitioners to learn new technology and findings that enable development in the applied field.

**Category:** General Mathematics

[2472] **viXra:1802.0388 [pdf]**
*submitted on 2018-02-27 01:11:40*

**Authors:** Rui Wang, Yanlai Li

**Comments:** 19 Pages.

Single-valued neutrosophic hesitant fuzzy set (SVNHFS) is a combination of single-valued
neutrosophic set and hesitant fuzzy set, and its aggregation tools play an important role in the
multiple criteria decision-making (MCDM) process. This paper investigates the MCDM problems in
which the criteria under SVNHF environment are in different priority levels.

**Category:** General Mathematics

[2471] **viXra:1802.0387 [pdf]**
*submitted on 2018-02-27 01:12:36*

**Authors:** Harish Garg, Nancy

**Comments:** 20 Pages.

Single-valued neutrosophic sets (SVNSs) handling the uncertainties characterized by truth,
indeterminacy, and falsity membership degrees, are a more flexible way to capture uncertainty. In this paper, some new types of distance measures, overcoming the shortcomings of the existing measures, for SVNSs with two parameters are proposed along with their proofs.

**Category:** General Mathematics

[2470] **viXra:1802.0386 [pdf]**
*submitted on 2018-02-27 01:13:43*

**Authors:** Muhammad Akram, Muzzamal Sitara

**Comments:** 19 Pages.

A graph structure is a generalization of simple graphs. Graph structures are very useful tools
for the study of different domains of computational intelligence and computer science. In this research paper, we introduce certain notions of intuitionistic neutrosophic graph structures. We illustrate these
notions by several examples. We investigate some related properties of intuitionistic neutrosophic graph structures. We also present an application of intuitionistic neutrosophic graph structures.

**Category:** General Mathematics

[2469] **viXra:1802.0385 [pdf]**
*submitted on 2018-02-27 01:14:55*

**Authors:** Surapati Pramanik, Shyamal Dalapati, Shariful Alam, Tapan Kumar Roy

**Comments:** 21 Pages.

A neutrosophic cubic set is the hybridization of the concept of a neutrosophic set and an
interval neutrosophic set. A neutrosophic cubic set has the capacity to express the hybrid information of both the interval neutrosophic set and the single valued neutrosophic set simultaneously. As newly defined, little research on the operations and applications of neutrosophic cubic sets has been reported in the current literature.

**Category:** General Mathematics

[2468] **viXra:1802.0384 [pdf]**
*submitted on 2018-02-27 01:15:53*

**Authors:** Yu-Han Huang, Gui-WuWei, Cun Wei

**Comments:** 10 Pages.

In this paper, we will extend the VIKOR (VIsekriterijumska optimizacija i KOmpromisno
Resenje) method to multiple attribute group decision-making (MAGDM) with interval neutrosophic
numbers (INNs). Firstly, the basic concepts of INNs are briefly presented.

**Category:** General Mathematics

[2467] **viXra:1802.0382 [pdf]**
*submitted on 2018-02-27 01:18:00*

**Authors:** Dong-Sheng Xu, Cun Wei, Gui-Wu Wei

**Comments:** 18 Pages.

Recently, the TODIM has been used to solve multiple attribute decision making (MADM)
problems. The single-valued neutrosophic sets (SVNSs) are useful tools to depict the uncertainty of the MADM. In this paper, we will extend the TODIM method to the MADM with the single-valued
neutrosophic numbers (SVNNs).

**Category:** General Mathematics

[2466] **viXra:1802.0374 [pdf]**
*submitted on 2018-02-26 01:32:51*

**Authors:** Huaning Liu

**Comments:** 13 Pages.

In this paper we give a survey on recent results on Smarandache function.

**Category:** General Mathematics

[2465] **viXra:1802.0373 [pdf]**
*submitted on 2018-02-26 01:33:31*

**Authors:** Huaning Liu

**Comments:** 9 Pages.

In this paper we give a survey on recent results on pseudo-Smarandache function.

**Category:** General Mathematics

[2464] **viXra:1802.0249 [pdf]**
*submitted on 2018-02-19 06:55:39*

**Authors:** Edgar Valdebenito

**Comments:** 5 Pages.

This note presents a definite integral for pi.

**Category:** General Mathematics

[2463] **viXra:1802.0248 [pdf]**
*submitted on 2018-02-19 06:58:12*

**Authors:** Edgar Valdebenito

**Comments:** 5 Pages.

This note presents some integrals involving pi.

**Category:** General Mathematics

[2462] **viXra:1802.0247 [pdf]**
*submitted on 2018-02-19 07:03:38*

**Authors:** Edgar Valdebenito

**Comments:** 8 Pages.

This note presents some formulas related with pi.

**Category:** General Mathematics

[2461] **viXra:1802.0228 [pdf]**
*submitted on 2018-02-18 04:54:39*

**Authors:** Said Broumi, Le Hoang Son, Assia Bakali, Mohamed Talea, Florentin Smarandache, Ganeshsree Selvachandran

**Comments:** 9 Pages.

Neutrosophic set is a generalization of classical set, fuzzy set, and intuitionistic fuzzy set by employing a degree of truth (T), a degree of indeterminacy (I), and a degree of falsehood (F) associated with an element of the dataset. One of the most essential problems is studying set-theoretic operators in order to be applied to practical applications.

**Category:** General Mathematics

[2460] **viXra:1802.0227 [pdf]**
*submitted on 2018-02-18 04:56:17*

**Authors:** Shyamal Dalapati, Surapati Pramanik, Shariful Alam, Florentin Smarandache, Tapan Kumar Roy

**Comments:** 15 Pages.

Cross entropy measure is one of the best way to calculate the divergence of any variable from the priori one variable. We define a new cross entropy measure under interval neutrosophic set (INS) environment, which we call IN-cross entropy measure and prove its basic properties. We also develop weighted IN-cross entropy measure and investigats its basic properties.

**Category:** General Mathematics

[2459] **viXra:1802.0226 [pdf]**
*submitted on 2018-02-18 04:58:01*

**Authors:** Seok-Zun Song, Madad Khan, Florentin Smarandache, Young Bae Jun

**Comments:** 11 Pages.

In this article, we apply the notion of interval neutrosophic sets to ideal theory in BCK/BCI-algebras.

**Category:** General Mathematics

[2458] **viXra:1802.0225 [pdf]**
*submitted on 2018-02-18 04:59:36*

**Authors:** Qays Hatem Imran, F. Smarandache, Riad K. Al-Hamido, R. Dhavaseelan

**Comments:** 6 Pages.

In this paper, we presented another concept of neutrosophic open sets called neutrosophic semi-alfa-open sets and studied their fundamental properties in neutrosophic topological spaces. We also present neutrosophic semi-alfa-interior and neutrosophic semi-alfa-closure and study some of their fundamental properties.

**Category:** General Mathematics

[2457] **viXra:1802.0224 [pdf]**
*submitted on 2018-02-18 05:01:24*

**Authors:** Gulfam Shahzadi, Muhammad Akram, Arsham Borumand Saeid

**Comments:** 9 Pages.

In this paper, we present the use of single-valued neutrosophic sets in medical diagnosis by using distance measures and similarity measures. Using interconnection between single-valued neutrosophic sets and symptoms of patient, we determine the type of disease. We define new distance formulas for single valued neutrosophic sets. We develop two new medical diagnosis algorithms under neutrosophic environment. We also solve a numerical example to illustrate the proposed algorithms and finally, we compare the obtained results.

**Category:** General Mathematics

[2456] **viXra:1802.0223 [pdf]**
*submitted on 2018-02-18 05:02:31*

**Authors:** Tuhin Bera, Nirmal Kumar Mahapatra

**Comments:** 13 Pages.

The motivation of this paper is to extend the concept of Neutrosophic soft matrix (NSM) theory. Some basic definitions of classical matrix theory in the parlance of neutrosophic soft set theory have been presented with proper examples. Then, a theoretical studies of some traditional operations of NSM have been developed. Finally, a decision making theory has been proposed by developing an appropriate solution algorithm, namely, score function algorithm and it has been illustrated by suitable examples.

**Category:** General Mathematics

[2455] **viXra:1802.0222 [pdf]**
*submitted on 2018-02-18 05:03:51*

**Authors:** R. Narmada Devi, R. Dhavaseelan, S. Jafari

**Comments:** 10 Pages.

In this paper we introduce the concept of a new class of an ordered neutrosophic bitopological spaces. Besides giving some interesting properties of these spaces. We also prove analogues of Uryshon’s lemma and Tietze extension theorem in an ordered neutrosophic bitopological spaces.

**Category:** General Mathematics

[2454] **viXra:1802.0221 [pdf]**
*submitted on 2018-02-18 05:05:48*

**Authors:** Dalbinder Kour, Kajla Basu

**Comments:** 13 Pages.

The paper presents selection of transportation companies and their mode of transportation for interval valued neutrosophic data. The paper focuses on the application of distance measures to select mode of transportation for transportation companies. The paper also presents the application of multi-criteria decision making method using weighted correlation coefficient and extended TOPSIS for transportation companies.

**Category:** General Mathematics

[2453] **viXra:1802.0124 [pdf]**
*submitted on 2018-02-10 08:53:59*

**Authors:** A. A. Logan

**Comments:** 7 pages, 15 figures, 1 table, preprint for IET Journal of Engineering Submission.

This paper investigates the characteristics of the power series representation of the Riemann Xi function. A detailed investigation of the behaviour of the zeros of the real part of the power series and the behaviour of the curve, combined with a substitution of polar coordinates in the power series and in the definition of the critical strip (leading to a critical area), and the relationship with the zeros of the imaginary part of the power series leads to the conclusion that the Riemann Xi function only has real zeros.

**Category:** General Mathematics

[2452] **viXra:1802.0108 [pdf]**
*submitted on 2018-02-09 06:26:11*

**Authors:** Edgar Valdebenito

**Comments:** 4 Pages.

This note presents a definite integral for pi.

**Category:** General Mathematics

[2451] **viXra:1802.0107 [pdf]**
*submitted on 2018-02-09 06:31:18*

**Authors:** Edgar Valdebenito

**Comments:** 6 Pages.

This note presents some integrals for lemniscate constants.

**Category:** General Mathematics

[2450] **viXra:1802.0048 [pdf]**
*submitted on 2018-02-05 06:58:27*

**Authors:** Edgar Valdebenito

**Comments:** 4 Pages.

This note presents a definite integral for pi

**Category:** General Mathematics

[2449] **viXra:1802.0037 [pdf]**
*submitted on 2018-02-03 12:50:42*

**Authors:** Jean BENICHOU

**Comments:** 1 Page.

The curves of x^n + y^n = z^n seem to be identical to a trig parametric form which for n>2 would exclude integer solutions.

**Category:** General Mathematics

[2448] **viXra:1802.0001 [pdf]**
*submitted on 2018-02-01 00:52:03*

**Authors:** Dave Ryan T. Cariño

**Comments:** 3 Pages.

This study is an algorithm of predicting the day of New Year’s Day for any given year
in Gregorian & Julian calendar using simplified formula. It consists of five algebraic 2 for
Julian expression, three of which are integer function by substituting the year. This formula
will calculate the modulo 7 which gives a number from 0 to 6, i.e., 0Saturday, 1Sunday, and
so on, that determines the exact day of New Year This algorithm has no condition even during
leap‐year and 400‐year cycle.

**Category:** General Mathematics

[2447] **viXra:1801.0408 [pdf]**
*submitted on 2018-01-31 06:15:32*

**Authors:** Dave Ryan T. Cariño

**Comments:** 4 Pages.

This study is an algorithm of calculating nth day of the Date in a Year for any given
Date in Gregorian & Julian calendar using simplified formula. It consists of ten algebraic 6 for
Julian expression, eight of which are integer function by substituting the year, month and day.
This formula will calculate the nth day which gives a number from 1 to 366 that determines the
exact nth day in a given Date. This algorithm has no condition even during leap‐year and 400‐
year cycle.

**Category:** General Mathematics

[2446] **viXra:1801.0303 [pdf]**
*submitted on 2018-01-23 07:02:21*

**Authors:** Hee Sik Kim, Young Hee Kim, J. Neggers

**Comments:** 12 Pages.

In this paper we indroduce the notion of a (pre)-Coxeter algebra and show that a Coxeter algebra is equivalent to an abelian group all of whose elements have order 2, i.e., Boolean group.

**Category:** General Mathematics

[2445] **viXra:1801.0302 [pdf]**
*submitted on 2018-01-23 07:03:24*

**Authors:** Hee Sik Kim, Hyo Jin Kim

**Comments:** 6 Pages.

In this paper we show that the class of PC-algebras and the class of B-Algebras with condition (D) are Smarandache disjoint.

**Category:** General Mathematics

[2444] **viXra:1801.0301 [pdf]**
*submitted on 2018-01-23 07:04:19*

**Authors:** P. J. Allen, H. S. Kim, J. Neggers

**Comments:** 15 Pages.

In this paper we define Smarandache algebras and show that every finite group can be found in some Smarandache algebra.

**Category:** General Mathematics

[2443] **viXra:1801.0300 [pdf]**
*submitted on 2018-01-23 07:05:14*

**Authors:** P. J. Allen, H. S. Kim, J. Neggers

**Comments:** 3 Pages.

In this paper we include several new families of Smarandache-type P-algebras and we study some of their properties in relation to the properties of previously defined Smarandache-types.

**Category:** General Mathematics

[2442] **viXra:1801.0299 [pdf]**
*submitted on 2018-01-23 07:06:04*

**Authors:** P. J. Allen, H. S. Kim, J. Neggers

**Comments:** 5 Pages.

In this paper we introduce the notion of Super Commutative D-Algebra.

**Category:** General Mathematics

[2441] **viXra:1801.0285 [pdf]**
*submitted on 2018-01-22 06:50:28*

**Authors:** Edgar Valdebenito

**Comments:** 2 Pages.

this note presents certain clases of integrals containing trigonometric and hyperbolic trigonometric functions in their integrands.

**Category:** General Mathematics

[2440] **viXra:1801.0283 [pdf]**
*submitted on 2018-01-22 06:53:20*

**Authors:** Edgar Valdebenito

**Comments:** 2 Pages.

This note presents some series for pi^2

**Category:** General Mathematics

[2439] **viXra:1801.0281 [pdf]**
*submitted on 2018-01-22 06:56:03*

**Authors:** Edgar Valdebenito

**Comments:** 1 Page.

This note presents a double integral for pi^2

**Category:** General Mathematics

[2438] **viXra:1801.0270 [pdf]**
*submitted on 2018-01-21 23:20:12*

**Authors:** Dave Ryan T. Cariño

**Comments:** 3 Pages.

This study is an algorithm of predicting the day of Christmas Day for any given year in Gregorian & Julian calendar using simplified formula. It consists of five algebraic (2 for Julian) expression, three of which are integer function by substituting the year. This formula will calculate the modulo 7 which gives a number from 0 to 6, i.e., 0=Saturday, 1=Sunday, and so on, that determines the exact day of Christmas. This algorithm has no condition even during leap-year and 400-year cycle.

**Category:** General Mathematics

[2437] **viXra:1801.0213 [pdf]**
*submitted on 2018-01-18 00:32:43*

**Authors:** Young Bae Jun

**Comments:** 8 Pages.

The notions of Smarandache BCC-algebras and Smarandache BCC-ideals are introduced. Conditions for a (special) subset to be a Smarandache BCC-ideal are given.

**Category:** General Mathematics

[2436] **viXra:1801.0212 [pdf]**
*submitted on 2018-01-18 00:42:37*

**Authors:** Young Bae Jun

**Comments:** 6 Pages.

The notion of Smarandache (positive implicative, commutative, implicative) BCI-algebras, Smarandache subalgebras and Smarandache ideals is introduced, examples are given, and related properties are investigated.

**Category:** General Mathematics

[2435] **viXra:1801.0211 [pdf]**
*submitted on 2018-01-18 00:45:08*

**Authors:** Young Bae Jun

**Comments:** 8 Pages.

The notion of Smarandache fresh and clean ideals is introduced, examples are given, and related properties are investigated. Relations between Q-Smarandache fresh ideals and Q-Smarandache clean ideals are given. Extension properties for Q-Smarandache fresh ideals and Q-Smarandache clean ideals are established.

**Category:** General Mathematics

[2434] **viXra:1801.0210 [pdf]**
*submitted on 2018-01-18 00:48:39*

**Authors:** Kyung Ho Kim, Young Bae Jun, Eun Hwan Roh, Habib Harizavi

**Comments:** 6 Pages.

We introduce the notion of a Smarandache hyper (∩,∈)-idealand Ω-reflexive in hyper K-algebra, and some related properties are given.

**Category:** General Mathematics

[2433] **viXra:1801.0209 [pdf]**
*submitted on 2018-01-18 00:51:08*

**Authors:** Young Bae Jun, Eun Hwan Roh

**Comments:** 6 Pages.

The notion of Smarandache hyper I-algebra and Smarandache hyper Kalgebra are introduced, and related properties are investigated.

**Category:** General Mathematics

[2432] **viXra:1801.0208 [pdf]**
*submitted on 2018-01-18 00:54:21*

**Authors:** Young Bae Jun, Eun Hwan Roh, Habiib Harizavi

**Comments:** 8 Pages.

We introduce the notio of an extention of hyper K-algebra and Smarandache hyper (∩, ∈)-ideals on Smarandache Hyper K-algebras, and investigate its properties.

**Category:** General Mathematics

[2431] **viXra:1801.0207 [pdf]**
*submitted on 2018-01-18 01:03:17*

**Authors:** Young Bae Jun, Seok Zun Song, Kyung Tae Kang

**Comments:** 8 Pages.

The notion of positive immplicative Smarandache BCC-ideals is indroduced, and related properties are investigated.

**Category:** General Mathematics

[2430] **viXra:1801.0206 [pdf]**
*submitted on 2018-01-18 01:27:50*

**Authors:** Young Bae Jun

**Comments:** 6 Pages.

The Smarandache Stuctures of Generalized BCK-Algebras are considered.

**Category:** General Mathematics

[2429] **viXra:1801.0195 [pdf]**
*submitted on 2018-01-16 06:51:43*

**Authors:** Edgar Valdebenito

**Comments:** 3 Pages.

This note presents some formulas related with the integral: I=int(coth(1+x^3))dx , x=0..1.

**Category:** General Mathematics

[2428] **viXra:1801.0194 [pdf]**
*submitted on 2018-01-16 06:55:03*

**Authors:** Edgar Valdebenito

**Comments:** 7 Pages.

This note presents some formulas related with pi

**Category:** General Mathematics

[2427] **viXra:1801.0177 [pdf]**
*submitted on 2018-01-15 05:49:07*

**Authors:** Dave Ryan T. Cariño

**Comments:** 3 Pages.

This study is an algorithm of calculating number of days passed since the introduction of Gregorian Calendar for any given date using simplified formula. It consists of nine algebraic expressions, five of which are integer function by substituting the year, month and day. This formula will calculate the n^th days which gives a number from 1 to ∞ (October 15, 1582 being the day one), that determines the exact number of days passed. This algorithm has no condition even during leap-year and 400-year cycle.

**Category:** General Mathematics

[2426] **viXra:1801.0154 [pdf]**
*submitted on 2018-01-14 00:17:25*

**Authors:** Dave Ryan T. Cariño

**Comments:** 2 Pages.

This study is an algorithm of calculating days difference between Gregorian & Julian calendar using simplified formula. It consists of two integer function by substituting the year. This formula will determine the exact number of days in any given Year as of December 31. This algorithm has no condition even during leap-year and 400-year rule.

**Category:** General Mathematics

[2425] **viXra:1801.0135 [pdf]**
*submitted on 2018-01-11 14:43:16*

**Authors:** Mark Burgin

**Comments:** 15 Pages.

Different thinkers suggested varied images and descriptions of mathematics. Platonists believe that mathematical objects exist as Platonic Ideas and mathematicians only discover them. Nominalists think that mathematics is the contents of mathematical manuscripts, books, papers and lectures, with the increasingly growing net of theorems, definitions, proofs, constructions, and conjectures. Pragmatists assume that mathematics exists in mentality of people and when mathematicians introduce new objects they invent and then build them. An interesting peculiarity of the situation is that all these opinions and some others are true but … incomplete. The goal of this work is to explain this peculiarity presenting a complete vision of mathematics as an interconnected Whole.

**Category:** General Mathematics

[2424] **viXra:1801.0132 [pdf]**
*submitted on 2018-01-11 05:28:14*

**Authors:** Dave Ryan T. Cariño

**Comments:** 3 Pages.

This study is an algorithm of calculating the number of days in any given Year in Gregorian & Julian calendar using simplified formula. It consists of seven algebraic (3 for Julian) expression, six of it are integer function by substituting the year. This formula will calculate the number of days which gives a number from 365 to 366 that determines the exact number of days in a given Year. This algorithm has no condition even during leap-year and 400-year rule.

**Category:** General Mathematics

[118] **viXra:1804.0001 [pdf]**
*replaced on 2018-04-16 19:32:29*

**Authors:** Koji KOBAYASHI

**Comments:** 15 Pages.

This paper describes about relation between circuit complexity and accept inputs structure in Hamming space by using almost all monotone circuit that emulate deterministic Turing machine(DTM).
Circuit family that emulate DTM are almost all monotone circuit family except some NOT-gate which connect input variables (like negation normal form (NNF)). Therefore, we can analyze DTM limitation by using this NNF Circuit family. NNF circuit family cannot compute sandwich structure effectively (Sandwich structure is two accept inputs that sandwich reject inputs in Hamming space). So NNF circuit have to use unique AND-gate to identify each different vector of sandwich structure. That is, we can measure problem complexity by counting different vectors.
Some dicision problem have characteristic in sandwich structure. Different vectors of Negate HornSAT prob- lem are at most constant length because we can delete constant part of each negative literal in Horn clauses by using definite clauses. Therefore, number of these different vector is at most polynomial size. The other hand, we can design problem with coding theory. For the example, we design new problem by using linear coding which expand vector space.

**Category:** General Mathematics

[117] **viXra:1804.0001 [pdf]**
*replaced on 2018-04-15 01:56:01*

**Authors:** Koji KOBAYASHI

**Comments:** 14 Pages.

This paper describes about relation between circuit complexity and accept inputs structure in Hamming space by using almost all monotone circuit that emulate deterministic Turing machine(DTM).
Circuit family that emulate DTM are almost all monotone circuit family except some NOT-gate which connect input variables (like negation normal form (NNF)). Therefore, we can analyze DTM limitation by using this NNF Circuit family. NNF circuit family cannot compute sandwich structure effectively (Sandwich structure is two accept inputs that sandwich reject inputs in Hamming space). So NNF circuit have to use unique AND-gate to identify each different vector of sandwich structure. That is, we can measure problem complexity by counting different vectors.
Some dicision problem have characteristic in sandwich structure. Different vectors of Negate HornSAT prob- lem are at most constant length because we can delete constant part of each negative literal in Horn clauses by using definite clauses. Therefore, number of these different vector is at most polynomial size. The other hand, we can design problem with coding theory. For the example, we design new problem by using linear coding which expand vector space.

**Category:** General Mathematics

[116] **viXra:1804.0001 [pdf]**
*replaced on 2018-04-05 06:23:29*

**Authors:** Koji KOBAYASHI

**Comments:** 19 Pages.

This paper describes about relation between circuit complexity and accept inputs structure in Hamming space by using almost all monotone circuit that emulate deterministic Turing machine(DTM).
Circuit family that emulate DTM are almost all monotone circuit family except some NOT-gate which connect input variables (like negation normal form (NNF)). Therefore, we can analyze DTM limitation by using this NNF Circuit family. NNF circuit family cannot compute sandwich structure effectively. Sandwich structure is two accept inputs that sandwich reject inputs in Hamming space. So NNF circuit have to use unique AND-gate to identify each different vector of sandwich structure. That is, we can measure problem complexity by counting different vectors.
Some dicision problem have caracteristic in sandwich structure. Different vectors of Negate HornSAT problem are at most constant length because we can delete constant part of each negative literal in Horn clauses by using definite clauses. Therefore, number of these different vector is at most polynomial size. The other hand, special subset of Negate CNFSAT problem have different vector which number is over polynomial size.

**Category:** General Mathematics

[115] **viXra:1803.0633 [pdf]**
*replaced on 2018-03-26 06:48:03*

**Authors:** Koji KOBAYASHI

**Comments:** 12 Pages.

This paper describes about "Almost all monotone circuit family" and introduce its interesting advantages to measuring problem complexity.
Explained in Michael Sipser "Introduction to the Theory of COMPUTATION", circuit family that emulate Deterministic Turing machine (DTM) are almost all monotone circuit family except some NOT-gate that connect input variables (like negation normal form (NNF)).
This "NNF Circuit family" have good characteristic which present each accept input exclusivity and symmetry. Each input make some INPUT-gate and NOT-gate output 1 which set is different from another input, and meet these output in OR-gate and finally connect (specified) OUTPUT-gate. That is, NNF circuit start accept input that exclusive each other, and meet each input as symmetry input step by step and finally goal same output. Especially, some different variables which sandwich reject inputs correspond to unique AND-gate. That is, we can measure problem complexity by using different variables of accept inputs. For examples, such number of different variables type of negation HornSAT is at most polynomial size. This is one of reason that we can compute P problem easily.

**Category:** General Mathematics

[114] **viXra:1803.0633 [pdf]**
*replaced on 2018-03-25 05:56:51*

**Authors:** Koji KOBAYASHI

**Comments:** 9 Pages.

This paper describes about "Almost all monotone circuit family" and introduce its interesting advantages to measuring problem complexity.
Explained in Michael Sipser "Introduction to the Theory of COMPUTATION", circuit family that emulate Deterministic Turing machine (DTM) are almost all monotone circuit family except some NOT-gate that connect input variables (like negation normal form (NNF)).
This "NNF Circuit family" have good characteristic which present each accept input exclusivity and symmetry. Each input make some INPUT-gate and NOT-gate output 1 which set is different from another input, and meet these output in OR-gate and finally connect (specified) OUTPUT-gate. That is, NNF circuit start accept input that exclusive each other, and meet each input as symmetry input step by step and finally goal same output. Especially, some accept input which sandwich reject inputs correspond to unique gate. That is, we can measure problem complexity by using NNF circuit and sandwich inputs. For examples, such sandwich inputs include DNF tautology problem, and Horn DNF tautology problem.

**Category:** General Mathematics

[113] **viXra:1803.0085 [pdf]**
*replaced on 2018-03-27 08:31:42*

**Authors:** Koji KOBAYASHI

**Comments:** 18 Pages.

This paper describes about complexity of PH problems by using "Almost all monotone circuit family" and "Accept input pair that sandwich reject inputs".
Explained in Michael Sipser "Introduction to the Theory of COMPUTATION", circuit family that emulate Deterministic Turing machine (DTM) are almost all monotone circuit family except some NOT-gate that connect input variables (like negation normal form (NNF)). Therefore, we can find out DTM limitation by using this "NNF Circuit family".
To clarify NNF circuit family limitation, we pay attention to AND-gate and OR-gate relation. If two accept "Neighbor input" pair that sandwich reject "Boundary input" in Hamming distance, NNF circuit have to meet these different variables of neighbor inputs in AND-gate to differentiate boundary inputs. NNF circuit have to use unique AND-gate to identify such neighbor input.
The other hand, we can make neighbor input problem "Neighbor Tautology DNF problem (NTD)" in PH. NTD is subset of tautology DNF that do not become tautology if proper subset of one variable permutate positive / negative. NTD include many different variables which number is over polynomial size of input length. Therefore NNF circuit family that compute NTD are over polynomial size of length, and NTD that include PH is not in P.

**Category:** General Mathematics

[112] **viXra:1803.0085 [pdf]**
*replaced on 2018-03-24 00:38:31*

**Authors:** Koji KOBAYASHI

**Comments:** 13 Pages.

This paper describes about complexity of PH problems by using "Almost all monotone circuit family" and "Accept input pair that sandwich reject inputs".
Explained in Michael Sipser "Introduction to the Theory of COMPUTATION", circuit family that emulate Deterministic Turing machine (DTM) are almost all monotone circuit family except some NOT-gate that connect input variables (like negation normal form (NNF)). Therefore, we can find out DTM limitation by using this "NNF Circuit family".
To clarify NNF circuit family limitation, we pay attention to AND-gate and OR-gate relation. If two accept "Neighbor input" pair that sandwich reject "Boundary input" in Hamming distance, NNF circuit have to meet these different values of neighbor inputs in AND-gate to differentiate boundary inputs. NNF circuit have to use unique AND-gate to identify such neighbor input.
The other hand, we can make neighbor input problem "Neighbor Tautology DNF problem (NTD)" in PH. NTD is subset of tautology DNF that do not become tautology if proper subset of one variable permutate positive / negative. NTD include neighbor input pair which number is over polynomial size of input length. Therefore NNF circuit family that compute NTD are over polynomial size of length, and NTD that include PH is not in P.

**Category:** General Mathematics

[111] **viXra:1803.0085 [pdf]**
*replaced on 2018-03-17 11:32:08*

**Authors:** Koji KOBAYASHI

**Comments:** 12 Pages.

This paper describes about complexity of PH problems by using "Almost all monotone circuit family" and "Accept input pair that sandwich reject inputs".
Explained in Michael Sipser "Introduction to the Theory of COMPUTATION", circuit family that emulate Deterministic Turing machine (DTM) are almost all monotone circuit family except some NOT-gate that connect input variables (like negation normal form (NNF)). Therefore, we can find out DTM limitation by using this "NNF Circuit family".
To clarify NNF circuit family limitation, we pay attention to AND-gate and OR-gate relation. If two accept "Neighbor input" pair that sandwich reject "Boundary input" in Hamming distance, NNF circuit have to meet these different values of neighbor inputs in AND-gate to differentiate boundary inputs. NNF circuit have to use unique AND-gate to identify such neighbor input.
The other hand, we can make neighbor input problem "Neighbor Tautology DNF problem (NTD)" in PH. NTD is subset of tautology DNF that do not become tautology if proper subset of one variable permutate positive / negative. NTD include neighbor input pair which number is over polynomial size of input length. Therefore NNF circuit family that compute NTD are over polynomial size of length, and NTD that include PH is not in P.

**Category:** General Mathematics

[110] **viXra:1803.0085 [pdf]**
*replaced on 2018-03-13 11:14:01*

**Authors:** Koji KOBAYASHI

**Comments:** 12 Pages.

This paper describes about complexity of PH problems by using “Almost all monotone circuit family” and “Accept input pair that sandwich reject inputs”.
Explained in Michael Sipser "Introduction to the Theory of COMPUTATION", circuit family that emulate Deterministic Turing machine (DTM) are almost all monotone circuit family except some NOT-gate that connect input variables (like negation normal form (NNF)). Therefore, we can find out DTM limitation by using this "NNF Circuit family".
Abstract. To clarify NNF circuit family limitation, we pay attention to AND-gate and OR-gate relation. If two accept "Neighbor input" pair that sandwich reject "Boundary input" in Hamming distance, NNF circuit have to meet these different values of neighbor inputs in AND-gate to differentiate boundary inputs. NNF circuit have to use unique AND-gate to identify such neighbor input.
The other hand, we can make neighbor input problem "Neighbor Tautology DNF problem (NTD)" in PH. NTD is subset of tautology DNF that do not become toutology if proper subset of one variable permutate positive / negative. NTD include neighbor input pair which number is over polynomial size of input length. Therefore NNF circuit family that compute NTD are over polynomial size of length, and NTD that include PH is not in P.

**Category:** General Mathematics

[109] **viXra:1803.0085 [pdf]**
*replaced on 2018-03-09 23:22:52*

**Authors:** Koji KOBAYASHI

**Comments:** 10 Pages.

This paper describes about complexity of PH problems by using problem input independence, and provide new approach to solve P vs NP problem.
Abstract. Circuit family that emulate Deterministic Turing machine (DTM) are almost monotone circuits except input variables (like negation normal form (NNF)). Therefore, we can find out DTM limitation by using this "NNF circuit family".
Abstract. To clarify NNF circuit limitation, we pay attention to AND-gate and OR-gate of NNF circuit DAG network. Because each pair of positive and negative variables do not become 1 in same input, these pair join at OR-gate to output computation result as 1. If some accept inputs does not include another accept input between these input with Hamming distance, OR-gate which join "Neighbor input" as accept input have to meet AND-gate to exclude between "Boundary input" as reject input. This means that these different variables of neighbor input are finally meet AND-gate, and NNF circuit have to use unique AND-gate to differentiate such different variables and boundary input variables.
Abstract. The other hand, we can make neighbor input problem "Neighbor Tautology DNF problem (NTD)" from DNF Tautology problem. NTD is in PH, and NTD consist of neighbor input and number of these input is over polynomial size of input length. Therefore NNF circuit family that compute NTD are over polynomial size, and NTD that include PH is not in P.

**Category:** General Mathematics

[108] **viXra:1802.0224 [pdf]**
*replaced on 2018-02-19 04:36:12*

**Authors:** Gulfam Shahzadi, Muhammad Akram, Arsham Borumand Saeid

**Comments:** 9 Pages.

In this paper, we present the use of single-valued neutrosophic sets in medical diagnosis by using distance measures and similarity measures. Using interconnection between single-valued neutrosophic sets and symptoms of patient, we determine the type of disease. We define new distance formulas for single valued neutrosophic sets. We develop two new medical diagnosis algorithms under neutrosophic environment. We also solve a numerical example to illustrate the proposed algorithms and finally, we compare the obtained results.

**Category:** General Mathematics

[107] **viXra:1802.0124 [pdf]**
*replaced on 2018-03-20 18:44:12*

**Authors:** A. A. Logan

**Comments:** 7 pages, 14 figures, 1 table, preprint for IET Journal of Engineering submission (revised with improved structure, clearer explanation and more straightforward argument)

This paper investigates the characteristics of the power series representation of the Riemann Xi function. A detailed investigation of the behaviour of the zeros of the real part of the power series and the behaviour of the curve, combined with a substitution of polar coordinates in the power series and in the definition of the critical strip (leading to a critical area), and the relationship with the zeros of the imaginary part of the power series leads to the conclusion that the Riemann Xi function only has real zeros.

**Category:** General Mathematics

[106] **viXra:1801.0257 [pdf]**
*replaced on 2018-02-06 10:22:40*

**Authors:** Timothy W. Jones

**Comments:** 13 Pages. Further derivations added.

This article seeks to give a clear and motivated proof of Euler's formula for zeta(2n) using known proofs.

**Category:** General Mathematics

[105] **viXra:1801.0257 [pdf]**
*replaced on 2018-01-28 10:41:50*

**Authors:** Timothy W. Jones

**Comments:** 8 Pages. There are many texts that give this result, but they tend to be dated.

This article seeks to give a clear and motivated proof of Euler's formula for zeta(2n) using known proofs.

**Category:** General Mathematics

[104] **viXra:1801.0177 [pdf]**
*replaced on 2018-01-23 23:28:12*

**Authors:** Dave Ryan T. Cariño

**Comments:** 3 Pages.

This study is an algorithm of calculating number of days passed since the introduction of Gregorian Calendar for any given date using simplified formula. It consists of nine algebraic expressions, five of which are integer function by substituting the year, month and day. This formula will calculate the n^th days which gives a number from 1 to ∞ (October 15, 1582 being the day one), that determines the exact number of days passed. This algorithm has no condition even during leap-year and 400-year cycle.

**Category:** General Mathematics

[103] **viXra:1801.0154 [pdf]**
*replaced on 2018-01-22 22:25:10*

**Authors:** Dave Ryan T. Cariño

**Comments:** 2 Pages.

This study is an algorithm of calculating days difference between Gregorian & Julian
calendar using simplified formula. It consists of two integer function by substituting the year.
This formula will determine the exact number of days in any given Year as of December 31.
This algorithm has no condition even during leap‐year and 400‐year cycle.

**Category:** General Mathematics

[102] **viXra:1801.0132 [pdf]**
*replaced on 2018-01-30 23:58:46*

**Authors:** Dave Ryan T. Cariño

**Comments:** 3 Pages.

This study is an algorithm of calculating the number of days in any given Year in Gregorian & Julian calendar using simplified formula. It consists of seven algebraic 3 for Julian expression, six of it are integer function by substituting the year. This formula will calculate the number of days which gives a number from 365 to 366 that determines the exact number of days in a given Year. This algorithm has no condition even during leap‐year and 400‐year cycle.

**Category:** General Mathematics

[101] **viXra:1801.0132 [pdf]**
*replaced on 2018-01-22 00:44:48*

**Authors:** Dave Ryan T. Cariño

**Comments:** 3 Pages.

This study is an algorithm of calculating the number of days in any given Year in
Gregorian & Julian calendar using simplified formula. It consists of seven algebraic 3 for
Julian expression, six of it are integer function by substituting the year. This formula will
calculate the number of days which gives a number from 365 to 366 that determines the exact
number of days in a given Year. This algorithm has no condition even during leap‐year and
400‐year cycle.

**Category:** General Mathematics