[19] **viXra:1810.0434 [pdf]**
*submitted on 2018-10-25 06:29:22*

**Authors:** Agbo Felix Isaac

**Comments:** 17 Pages.

In this article, I propose a generalized method for obtaining a substitution for reducing a reducible linear ordinary differential equation with function coefficients (RLDEF) to a linear ordinary differential equation with constant coefficient (LDE). This proposed method was also used to obtain the already known substitutions for the Euler’s and Legendre’s homogeneous second order linear differential equation. The derived method is able to reduce quite a large number of RLDEF to LDE including the Euler’s and Legendre’s homogeneous second order linear differential equation. However, these RLDEF (homogeneous and inhomogeneous) must satisfy the condition for reducibility, which is also proposed before the substitution is derived. the condition for reducibility is based on the order of the differential equation. In this article, the condition for reducibility is presented for a second and third order LDEF. Keywords: reducibility, generalized, differential equations.

**Category:** General Mathematics

[18] **viXra:1810.0408 [pdf]**
*replaced on 2018-11-17 09:34:46*

**Authors:** Zaid Laadjal

**Comments:** 10 Pages.

In this paper, we describe the solution approaches based on Homotopy Analysis Method for the follwing Nonlinear Mixed Volterra-Fredholm integro-differential equation of fractional order $$^{C}D^{\alpha }u(t)=\varphi (t)+\lambda \int_{0}^{t}\int_{0}^{T}k(x,s)F\left( u(s\right) )dxds,$$ $$u^{(i)}(0)=c_{i},i=0,...,n-1,$$ where $t\in \Omega =\left[ 0;T\right] ,\ k:\Omega \times \Omega \longrightarrow \mathbb{R},$ $\varphi :\Omega \longrightarrow \mathbb{R},$ are known functions,\ $F:C\left(\Omega, \mathbb{R}\right) \longrightarrow \mathbb{R}$ is nonlinear function, $c_{i} (i=0,...,n-1),$ and $\lambda $ are constants, $^{C}D^{\alpha }$ is the Caputo derivative of order $\alpha $ with $n-1<\alpha \leq n.$ In addition some examples are used to illustrate the accuracy and validity of this approach.

**Category:** General Mathematics

[17] **viXra:1810.0407 [pdf]**
*submitted on 2018-10-24 15:31:00*

**Authors:** Colin James III

**Comments:** 2 Pages. © Copyright 2018 by Colin James III All rights reserved. Respond to the author by email at: info@ersatz-systems dot com.

Definitions of neutrosophy as further embellished with probability and (in)dependency share the same result as denied of tautology. This means neutrosophic logic as a general framework for unification of many existing logics, such as intuitionistic fuzzy logic) and paraconsistent logic, is refuted.

**Category:** General Mathematics

[16] **viXra:1810.0398 [pdf]**
*submitted on 2018-10-23 06:05:17*

**Authors:** Rebeca Escobar Jara, Maikel Leyva Vázquez, Cesar Ernesto Roldan Martínez

**Comments:** 13 Pages.

Objective. Social learning analytics is a subset of learning analysis as it attempts to demonstrate how new skills and ideas are not just individual achievements, but are developed, carried forward and transmitted through interaction and collaboration.

**Category:** General Mathematics

[15] **viXra:1810.0397 [pdf]**
*submitted on 2018-10-23 06:06:49*

**Authors:** Neilys González Benítez

**Comments:** 9 Pages.

The mental upsets are affections or psychic syndromes and conduct ales, opposed to the town of the individuals that enjoy good mental health. They are varied the causes of the mental illnesses. The biological factors are one of the more common causes. Of similar form a traumatic injury of the brain can conduct to a mental upset. The exposition of the mother during the embarrassments to virus or chemical toxics constitutes other causes, of similar form exist other factors capable of increase the risk of suffering of mental upsets, just as the use of illegal drugs or suffer a medical serious condition.

**Category:** General Mathematics

[14] **viXra:1810.0395 [pdf]**
*submitted on 2018-10-23 06:09:58*

**Authors:** Rodolfo González Ortega, Maikel Leyva Vázquez, João Alcione Sganderla Figueiredo

**Comments:** 14 Pages.

The Sinos River Basin is one of the most contaminated water basin in Bra-zil which leads to tremendous efforts for its recovery through adequate integral management. The management of water quality through the analysis of the interrelations between the different factors could be difficult. In this paper, the authors
present Fuzzy Cognitive Maps and Neutrosophic Cogntive Maps for a better choice of environmental management i by the Basin Management Committee of the Sino River. With this method it’s possible to use FCM/NCM to model the complex system of variables involved into the determination of water quality,
according to the water quality index (WQI).

**Category:** General Mathematics

[13] **viXra:1810.0394 [pdf]**
*submitted on 2018-10-23 06:11:20*

**Authors:** Maikel Leyva Vázquez, Florentin Smarandache

**Comments:** 7 Pages.

Recommendation models are useful in the decision-making process that allow the user a set of options that are expected to meet their expectations. Recommendation models are useful in the decision-making process that offer the user a set of options that are expected to meet their SVN expectations to express linguistic terms.

**Category:** General Mathematics

[12] **viXra:1810.0393 [pdf]**
*submitted on 2018-10-23 06:12:22*

**Authors:** Artemio Leyva-Aguilera, Adalys Ray Hayne

**Comments:** 7 Pages.

In the present work it is demonstrated that the construction of the media agenda is a process whose structure does not behave in a rigid manner, whose application foundations have a dialectical character, since it assumes the eventualities of coverage which demands a content management that corresponds.
Additionally, the possibilities of using neutrosophical cognitive maps in the construction of the media agenda are explored. It explores neutrosophical cognitive maps for the analysis of causality.

**Category:** General Mathematics

[11] **viXra:1810.0389 [pdf]**
*submitted on 2018-10-23 07:33:43*

**Authors:** Edgar Valdebenito

**Comments:** 3 Pages.

This note presents some definite integrals.

**Category:** General Mathematics

[10] **viXra:1810.0388 [pdf]**
*submitted on 2018-10-23 07:36:02*

**Authors:** Edgar Valdebenito

**Comments:** 5 Pages.

This note presents some integrals for pi^3.

**Category:** General Mathematics

[9] **viXra:1810.0363 [pdf]**
*submitted on 2018-10-22 23:44:04*

**Authors:** Boram Han

**Comments:** 7 Pages. This paper is my first paper in High School life.

In many places of life today, the use of mathematics is increasing. In particular, the use of mathematics in various fields such as science, economics, and biotechnology is becoming more and more popular as the natural science advances. This paper briefly grasps the essence of vectors and matrices that play a key role in mathematics, and explains the vector approach is effective for controlling the robot through how vector-based methods are used in recognizing and solving the problems of input and output of EV3 robots.
As a result of using vector analytical methods to overcome defects in hardware and software, many defects could be overcome in many areas. The result of using the concept of the vector which is able to conclude the recognized color of the color sensor with certainty was obtained satisfactory result, the program that controls the omni wheel can also overcome the hardware difficulties in a vector interpretive manner. Also, when attempting to use re-parameterization to create an unit speed curve to overcome the hardware defect of the motor, it was necessary to know the concept of the vector. Therefore, it can be said that the vector was used successfully to overcome the shortcomings and difficulties of EV3.
Nonetheless, the decline of the computation function could not be avoided by the vector approach, because it was a problem that was closer to engineering and physical part rather than mathematical part. Therefore, although it was able to achieve some degree of success in overcoming the disadvantages and difficulties of EV3, it came to the conclusion that it was impossible to overcome it completely. In addition, solving problems using vectors means being more dependent on mathematics, so it relies more heavily on the computation function of EV3. Thus, if the underlying computational function of the EV3, that is, the processing speed is not improved, the vector interpretation approach will show its limitations again.

**Category:** General Mathematics

[8] **viXra:1810.0333 [pdf]**
*replaced on 2018-10-23 12:19:41*

**Authors:** Waldemar Zieliński

**Comments:** 5 Pages.

We will derive the formulas for the N-th element of the union of two arithmetic progressions with rational and real common differences.

**Category:** General Mathematics

[7] **viXra:1810.0186 [pdf]**
*submitted on 2018-10-11 08:57:08*

**Authors:** John Smith

**Comments:** 6 Pages.

basic economics

**Category:** General Mathematics

[6] **viXra:1810.0152 [pdf]**
*submitted on 2018-10-09 07:46:04*

**Authors:** Edgar Valdebenito

**Comments:** 3 Pages.

En esta nota recordamos una serie trigonométrica que involucra a la constante de Catalan.

**Category:** General Mathematics

[5] **viXra:1810.0150 [pdf]**
*submitted on 2018-10-09 08:05:47*

**Authors:** Edgar Valdebenito

**Comments:** 15 Pages.

This note presents a collection of mathematical formulas.

**Category:** General Mathematics

[4] **viXra:1810.0122 [pdf]**
*submitted on 2018-10-08 22:09:22*

**Authors:** Wendong Wang, Feng Zhang, Jianjun Wang

**Comments:** 10 Pages.

In this paper, we theoretically investigate the low-rank matrix recovery problem in the context of the unconstrained regularized nuclear norm minimization (RNNM) framework. Our theoretical findings show that, one can robustly recover any matrix X from its few noisy measurements b=A(X)+n with a bounded constraint ||n||_{2}<ε via the RNNM, if the linear map A satisfies restricted isometry property (RIP) with δ_{tk}<√(t-1)/t for certain fixed t>1. Recently, this condition with t≥4/3 has been proved by Cai and Zhang (2014) to be sharp for exactly recovering any rank-k matrices via the constrained nuclear norm minimization (NNM). To the best of our knowledge, our work first extends nontrivially this recovery condition for the constrained NNM to that for its unconstrained counterpart. Furthermore, it will be shown that similar recovery condition also holds for regularized l_{1}-norm minimization, which sometimes is also called Basis Pursuit DeNoising (BPDN).

**Category:** General Mathematics

[3] **viXra:1810.0121 [pdf]**
*replaced on 2018-11-22 03:02:24*

**Authors:** Feng Zhang, Wendong Wang, Jianwen Huang, Jianjun Wang

**Comments:** 25 Pages.

The essential task of multi-dimensional data analysis focuses on the tensor decomposition and the corresponding notion of rank. However, most tensor ranks are not well defined with a tight convex relaxation. In this paper, by introducing the notion of tensor singular value decomposition (t-SVD), we establish a regularized tensor nuclear norm minimization (RTNNM) model for low tubal rank tensor recovery. In addition, the tensor nuclear norm within the unit ball of the tensor spectral norm here has been shown to be a convex envelop of tensor average rank. On the other hand, many variants of the restricted isometry property (RIP) have proven to be crucial frameworks and analysis tools for recovery of sparse vectors and low-rank tensors. So, we initiatively define a novel tensor restrict isometry property (t-RIP) based on t-SVD. Besides, our theoretical results show that any third-order tensor X∈R^{n_{1}× n_{2}× n_{3}} whose tubal rank is at most r can stably be recovered from its as few as measurements y = M(X)+w with a bounded noise constraint ||w||_{2}≤ε via the RTNNM model, if the linear map M obeys t-RIP with δ_{tr}^{M}<√（t-1）/(n_{3}^{2}+t-1) for certain fixed t>1. Surprisingly, when n_{3}=1, our conditions coincide with T. Cai and A. Zhang's sharp work in 2013 for low-rank matrix recovery via the constrained nuclear norm minimization. We note that, as far as the authors are aware, such kind of result has not previously been reported in the literature.

**Category:** General Mathematics

[2] **viXra:1810.0023 [pdf]**
*replaced on 2019-04-10 09:47:15*

**Authors:** Peter J. Nolan, Shane D. Ross

**Comments:** 42 Pages. This manuscript has been submitted for publication.

Lagrangian diagnostics, such as the finite-time Lyapunov exponent and Lagrangian coherent structures, have become popular tools for analyzing unsteady fluid flows. These diagnostics can help illuminate regions where particles transported by a flow will converge to and diverge from, even in a divergence-free flow. Unfortunately, calculating Lagrangian diagnostics can be time consuming and computationally expensive. Recently, new Eulerian diagnostics have been developed which provide similar insights into the Lagrangian transport properties of fluid flows. These new diagnostics are faster and less expensive to compute than their Lagrangian counterparts. Because Eulerian diagnostics of Lagrangian transport structure are relatively new, there is still much about their connection to Lagrangian diagnostics that is unknown. This paper provides a mathematical bridge between Lagrangian and Eulerian diagnostics. It rigorously explores the mathematical relationship that exists between invariants of the right Cauchy-Green deformation tensor and the Rivlin-Ericksen tensors, primarily the Eulerian rate-of-strain tensor, in the infinitesimal integration time limit. Additionally, this paper develops the infinitesimal-time Lagrangian coherent structures (iLCSs) and demonstrates their efficacy in predicting the Lagrangian transport of particles even in realistic geophysical fluid flows generated by numerical models.

**Category:** General Mathematics

[1] **viXra:1810.0018 [pdf]**
*submitted on 2018-10-02 16:30:39*

**Authors:** Surapati Pramanik, Rama Mallick

**Comments:** 13 Pages.

VIseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) is a popular strategy for multi- attribute decision making (MADM). We extend the VIKOR strategy for multi- attribute group decision making (MAGDM) problems in trapezoidal neutrosophic number environment. In decision making situation, the attribute values are expressed in terms of single-valued trapezoidal neutrosophic numbers. Then we develop an extended VIKOR strategy to deal with MAGDM with single-valued trapezoidal neutrosophic numbers. The influence of decision-making mechanism coefficient is presented. To illustrate and validate the proposed VIKOR strategy, we solve an illustrative numerical example of MAGDM problem in trapezoidal fuzzy neutrosophic number environment.

**Category:** General Mathematics