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[54] viXra:1411.0599 [pdf] submitted on 2014-11-30 14:23:39
Authors: Horatio Sanchez
Comments: 3 Pages.
In this paper we prove that math is a democracy.
Category: General Mathematics
[53] viXra:1411.0593 [pdf] replaced on 2018-01-20 13:00:49
Authors: Peter Waaben
Comments: 32 Pages.
It is a popular belief supported by proof: that nothing further can be achieved by an additional completion of the Real number system.Here I reconstruct the reals from a particular implementation of the reals ,(using the Cantorian method of partitioning convergent sequences), producing a surprising result. A coupled infinitesmial point structure with a completed interior. This gives rise to a natural interpretation of Color as an intrinsic feature of geometry. As apposed to a mere method of labeling.
In a sense then: I simply open further discussions here on the properties of geometry, and ask now:
What really then is geometric-color ?
Category: General Mathematics
[52] viXra:1411.0513 [pdf] submitted on 2014-11-21 01:45:59
Authors: Xin-de Li, Jin-dong Pan, Jean Dezert
Comments: 8 Pages.
In this paper we propose a new method for solving
the Automatic Aircraft Recognition (AAR) problem from a sequence of images of an unknown observed aircraft. Our method exploits the knowledge extracted from a training image data set
(a set of binary images of different aircrafts observed under three different poses) with the fusion of information of multiple features
drawn from the image sequence using Dezert-Smarandache Theory (DSmT) coupled with Hidden Markov Models (HMM).
Category: General Mathematics
[51] viXra:1411.0512 [pdf] submitted on 2014-11-21 01:47:42
Authors: Luige Vladareanu, Alexandru Gal, Hongnian Yu, Mincong Deng
Comments: 6 Pages.
This paper presents an innovative algorithm for improvement of the walking robot dynamic stability, using the Desert Smarandache Theory (DSmT) and the neutrosophic logic set. Starting from the hybrid force-position control, by applying the Robot Neutrosophic Control (RNC) method we extend the fuzzy control for walking robot stability motion on uneven terrain and in unstructured environments. Results analysis through virtual experimentation for motion control of a mobile walking robot proves that the neutrosophic logic leads to performance improvement of real time control through robustness, adaptation to robot's environment, efficient control and fast and clear identification of robot states.
Category: General Mathematics
[50] viXra:1411.0511 [pdf] submitted on 2014-11-21 01:49:12
Authors: Shobha Jose
Comments: 5 Pages.
Feature extraction is an important part in Content-based image retrieval (CBIR).It is an active research area over the past
few decades. In this paper texture feature extraction of mammogram images are done. Biorthogonal wavelet filter via lifting scheme is
used for the extraction of texture features. Maximum likelihood estimator (MLE) is used for texture feature estimation. Here Digital
Database for Screening Mammography (DDSM) is used as the database. Here biorthogonal wavelets are used in the lifting scheme to get texture feature vectors of mammogram images. By using lifting scheme in all biorthogonal wavelets, predict and update filter coefficients are also got. These coefficients will be adapted later and thus we can find the optimal wavelet filter bank for increasing the retrieval performance of the retrieval system. By using lifting scheme methodology decomposition of images are done and thus got approximation and detail coefficients of image.
Category: General Mathematics
[49] viXra:1411.0479 [pdf] submitted on 2014-11-20 03:59:03
Authors: Muhammad Zulfiqar
Comments: 21 Pages.
The theory of fuzzy sets, which was initiated by Zadeh in his seminal paper [33] in 1965, was applied to generalize some of the basic concepts of
algebra. The fuzzy algebraic structures play a vital role in mathematics with wide applications in many other branches such as theoretical physics, computer sciences, control engineering, information sciences, coding theory, logic, set theory, real analysis, measure theory etc.
Category: General Mathematics
[48] viXra:1411.0478 [pdf] submitted on 2014-11-20 04:00:16
Authors: Gülnur Şaffak Atalay, Emin Kasap
Comments: 12 Pages.
In this paper, we analyzed the problem of consructing a family of surfaces from a given some special Smarandache curves in Euclidean 3-space. Using the Frenet frame of the curve in Euclidean 3-space, we express the family of surfaces as a linear combination of the components of this frame, and derive the necessary
and sufficient conditions for coefficents to satisfy both the asymptotic and isoparametric
requirements. Finally, examples are given to show the family of surfaces with common Smarandache curve.
Category: General Mathematics
[47] viXra:1411.0433 [pdf] submitted on 2014-11-20 00:44:23
Authors: Xingsen Li, Haolan Zhang, Wei Deng
Comments: 4 Pages.
Clustering has been applied in many field of
management for better decision making with a lot of algorithms such as K-means. Based on Extenics, we found that most of algorithms calculate the similarity of elements in a certain set by distance to each other; they focus on the position
of each element and neglect their criteria. However, in the real world, there are usually exist criteria to score the elements.
Therefore, we present a new clustering method. In our method,we use distance in Extenics for similarity calculating based on criteria, and compared a simple case with traditional K-means
algorithm. The results show that our method is more practical and has much potential value for data mining and knowledge management.
Category: General Mathematics
[46] viXra:1411.0409 [pdf] submitted on 2014-11-20 02:56:00
Authors: Octavian Cira
Comments: 18 Pages.
In acest articol demonstram ca daca conjectura Legendre este adevarata si se verifica ipoteza lui Riemann atunci si conjectura lui Smarandache este adevarata.
Category: General Mathematics
[45] viXra:1411.0408 [pdf] submitted on 2014-11-20 02:57:52
Authors: Octavian Cira
Comments: 11 Pages.
Functia care asociaza fiecarui numar natural n pe cel mai mic numar natural m care are proprietatea ca m! este multiplu lui n a fostconsiderata de prima data de Lucas in anul 1883.
Category: General Mathematics
[44] viXra:1411.0407 [pdf] submitted on 2014-11-20 02:59:12
Authors: Tanju KAHRAMAN, Mehmet ÖNDER, H. Hüseyin UGURLU
Comments: 18 Pages.
In this paper, by considering dual geodesic trihedron (dual Darboux frame) we define dual
Smarandache curves lying fully on dual unit sphere.
Category: General Mathematics
[43] viXra:1411.0404 [pdf] submitted on 2014-11-20 03:02:53
Authors: Linfan Mao
Comments: 24 Pages.
As we known, an objective thing not moves with one’s volition, which implies that all contradictions, particularly, in these semiotic systems for things are artificial. In classical view, a contradictory system is meaningless, contrast to that of geometry on figures of things catched by eyes of human beings. The main objective of sciences is holding the global behav-
ior of things, which needs one knowing both of compatible and contradictory systems on things. Usually, a mathematical system included contradictions is said to be a Smarandache system.
Category: General Mathematics
[42] viXra:1411.0402 [pdf] submitted on 2014-11-20 03:06:20
Authors: Kostaq Hila, Bijan Davvaz
Comments: 14 Pages.
A Smarandache multi-space is a union of n dierent spaces equipped with some dierent structures for an integer n 2 which can be used both for discrete or connected spaces, particularly for geometries and spacetimes in theoretical physics. In this paper, applying the Smarandaches notion and combining this with hyperrings in hyperring theory, we introduce the notion of multi-hyperring space and initiate a study of
multi-hyperring theory. Some characterizations and properties of multi-hyperring spaces are investigated and obtained. Some open problems
are suggested for further study and investigation.
Category: General Mathematics
[41] viXra:1411.0401 [pdf] submitted on 2014-11-20 03:08:05
Authors: Mircea Eugen Selariu
Comments: 21 Pages.
Exis tă ! Există şi între parabolele centrice şi parabolele excentrice sau excentricele parabolice !
Category: General Mathematics
[40] viXra:1411.0392 [pdf] submitted on 2014-11-20 03:21:00
Authors: Kareem Abass Layith AL-Ghurabi
Comments: 5 Pages.
In 1905, L.E. Drckson began the study of a near ring and later in 1930; Wieland has investigated it [1]. In 1977, G.Pilz, introduced the notion of a prime ideal of near ring [1]. In 1988, N.G. Groenewald introduced of a completely prime ideal of a near ring [5]. In 2002, W.B. Vasanth Kandasamy study samaradache near ring, (samaradache ideal, of a near ring [7]. In 2012 H.H. Abbass and M.A.Mohommed introduced the notion of a completely prime ideal with respect to an element of a near ring [3].
In this work, we introduce a Samaradache completely prime ideal with respect to an element related to a near field of near ring as we mentioned in the abstract.
Category: General Mathematics
[39] viXra:1411.0389 [pdf] submitted on 2014-11-20 03:26:10
Authors: Ufuk Ozturk, Esra Betul Koc Ozturk
Comments: 13 Pages.
In this paper, we introduce Smarandache curves according to the Lorentzian Darboux frame of a curve on spacelike surface in Minkowski 3-space R
3 1. Also, we obtain the Sabban frame and the geodesic curvature of the Smarandache curves
and give some characterizations on the curves when the curve is an asymptotic curve or a principal curve. And, we give an example to illustrate these curves.
Category: General Mathematics
[38] viXra:1411.0388 [pdf] submitted on 2014-11-20 03:27:39
Authors: Muhammed Cetin, Yilmaz Tuncer, Murat Kemal Karacan
Comments: 19 Pages.
In this paper, we investigate special Smarandache curves according to Bishop frame in Euclidean 3-space and we give some differential geometric
properties of Smarandache curves. Also we find the centers of the osculating spheres and curvature spheres of Smarandache curves.
Category: General Mathematics
[37] viXra:1411.0387 [pdf] submitted on 2014-11-20 03:28:48
Authors: Kemal Taskopru, Murat Tosun
Comments: 8 Pages.
In this paper, we introduce special Smarandache curves according to Sabban frame on S2 and we give some characterization of Smarandache curves.
Besides, we illustrate examples of our results
Category: General Mathematics
[36] viXra:1411.0384 [pdf] submitted on 2014-11-20 03:34:49
Authors: N. Kannappa, K. Suresh
Comments: 9 Pages.
In this paper, we have introduced smarandache - 2 - Algebraic structure of lattice namely smarandache lattice. A smarandache 2- algebraic structure on a set N means a weak algebraic structure Ao on N such that there exists a proper
subset M of N which is embedded with a stronger algebraic structure A1. Stronger algebraic structure means a structure which satises more axioms, by proper subset one can understand a subset dierent from the empty set, by the unit element if any, and from the whole set. We have dened smarandache lattice and obtained some of its characterization through Pseudo complemented .For the basic concept, we referred the PadilaRaul [4].
Category: General Mathematics
[35] viXra:1411.0383 [pdf] submitted on 2014-11-20 03:36:14
Authors: Arsham Borumand Saeid, Akbar Rezaei
Comments: 11 Pages.
The Smarandache algebraic structures theory was introduced in 1998 by Padilla [11]. In [6], Kandasamy studied of Smarandache groupoids, sub-groupoids, ideal of groupoids, seminormal sub groupoids, Smarandache Bol groupoids,
and strong Bol groupoids and obtained many interesting results about them.
Category: General Mathematics
[34] viXra:1411.0382 [pdf] submitted on 2014-11-20 03:38:06
Authors: N. Kannappa, P. Hirudayaraj
Comments: 6 Pages.
In this paper we introduced Smarandache - 2 - algebraic structure of R-Module namely Smarandache - R - Module. A Smarandache - 2 - algebraic structure on a set N means a weak algebraic structure A0 on N such that there exist a proper subset M of N, which is embedded with a stronger algebraic structure A1, stronger
algebraic structure means satisfying more axioms, by proper subset one understands a subset from the empty set, from the unit element if any , from the whole set. We dene Smarandache - R - Module and obtain some of its characterization through S - algebra and Morita context. For basic concept we refer to Raul Padilla.
Category: General Mathematics
[33] viXra:1411.0380 [pdf] submitted on 2014-11-20 03:40:39
Authors: Qianli Yang
Comments: 4 Pages.
The Smarandache function S(n) is dened as the minimal positive integer m suchthat njm!.
Category: General Mathematics
[32] viXra:1411.0379 [pdf] submitted on 2014-11-20 03:42:10
Authors: Dr.N.Kannappa, Mrs.P.Tamilvani
Comments: 6 Pages.
In this paper, we introduced Samarandache-2-algebraic structure of Boolean-near-
ring namely Smarandache-Boolean-near-ring.
Category: General Mathematics
[31] viXra:1411.0378 [pdf] submitted on 2014-11-20 03:44:14
Authors: E. Ilojide, T. G. Jaiyeola
Comments: 16 Pages.
In this work, two normal congruences are built on two quasigroups with underlining set Z2
n relative to the linear-bivariate polynomial P(x; y) = a + bx + cy that generates a quasigroup over the ring Zn. Four quasigroups are built using the normal congruences and these are shown to be homomorphic to the quasigroups with underlining set Z2 n. Some subquasigroups of the quasigroups with underlining set Z2 n are also found.
Category: General Mathematics
[30] viXra:1411.0377 [pdf] submitted on 2014-11-20 03:45:45
Authors: Julius Fergy T. Rabago
Comments: 4 Pages.
Murthy introduced the concept of the Smarandache Cyclic Determinant Natural Sequence, the Smarandache Cyclic Arithmetic Determinant Sequence, the Smarandache Bisymmetric Determinant Natural Sequence, and the Smarandache Bisymmetric Arithmetic Determinant Sequence and in [2], Majumdar derived the n-th terms of these four sequences. In this paper, we present some of the results found by Majumdar in [2] but of different approach..
Category: General Mathematics
[29] viXra:1411.0376 [pdf] submitted on 2014-11-20 03:47:03
Authors: Mahdieh Abbaslo, Arsham Borumand Saeid
Comments: 19 Pages.
A Smarandache structure on a set A means a weak structureW on A such that there exists
a proper subset B of A which is embedded with a strong structure S.
Category: General Mathematics
[28] viXra:1411.0291 [pdf] submitted on 2014-11-19 00:07:16
Authors: Girish.V.R., P.Usha
Comments: 7 Pages.
A dominating set of a graph n(G), is a total lict dominating set if the dominating set does not contain any isolates. The total lict dominating number t(n(G)) of G is a minimum cardinality of total lict dominating set of G. The current paper studies total lict domination in graph from an algorithmic point of view. In particular we had obtained the algorithm for a total lict domination number of any graph. Also we had obtained the time complexity of a proposed algorithm. Further we discuss the NP-Completeness of a total lict domination number of the split graph, bipartite graph and chordal graph.
Category: General Mathematics
[27] viXra:1411.0290 [pdf] submitted on 2014-11-19 00:08:56
Authors: M.Kamal Kumar
Comments: 12 Pages.
Representation of a set of vertices in a graph by means of a matrix was introduced by Sampath Kumar.
Category: General Mathematics
[26] viXra:1411.0289 [pdf] submitted on 2014-11-19 00:11:11
Authors: Nagesh.H.M, R.Chandrasekha
Comments: 6 Pages.
In this paper we introduce the concept of pathos adjacency blict graph PBn(T)of a tree T and present the characterization of graphs whose pathos adjacency blict graphs are planar, outerplanar, minimally non-outerplanar and Eulerian.
Category: General Mathematics
[25] viXra:1411.0288 [pdf] submitted on 2014-11-19 00:12:58
Authors: Rodrigo De Castro, Jose L. Ramırez
Comments: 6 Pages.
In this paper, we introduce a new family of generalized colored Motzkin paths,where horizontal steps are colored by means of Fk,l colors, where Fk,l is the l-th k-Fibonacci number. We study the enumeration of this family according to the length. For this, we use infinite weighted automata.
Category: General Mathematics
[24] viXra:1411.0287 [pdf] submitted on 2014-11-19 00:14:47
Authors: Pradeep G.Bhat, Devadas Nayak C
Comments: 15 Pages.
We begin with simple, finite, connected and undirected graph G = (V,E). Here elements of set
V and E are known as vertices and edges respectively. For all other terminologies and notations we follow Harary.
Category: General Mathematics
[23] viXra:1411.0286 [pdf] submitted on 2014-11-19 00:20:03
Authors: Rong-Xia Hao, Wenmao Cairen, Haoyang Liu
Comments: 9 Pages.
The folded hypercube FQn is a variance of the hypercube network and is superior to Qn in some properties[IEEE Trans.
Category: General Mathematics
[22] viXra:1411.0285 [pdf] submitted on 2014-11-19 00:22:11
Authors: S.Suganthi, V.Swaminathan, A.P.Pushpalatha, G.Jothilakshmi
Comments: 20 Pages.
In the case of finite dimensional vector spaces, every ordered basis induces a scalar coding of the
vectors where the scalars are from the base field. While finite dimensional vector spaces have
rich structures, graphs have only one structure namely adjacency. If a graph is connected, the
adjacency gives rise to a metric. This metric can be used to define a code for the vertices.
Category: General Mathematics
[21] viXra:1411.0284 [pdf] submitted on 2014-11-19 00:23:30
Authors: M.Murugan
Comments: 8 Pages.
In this paper, we consider special class of trees called uniform k-distant trees,which have many interesting properties. We show that they have an edge-magic total labeling, a super edge-magic total labeling, a (a, d)-edge-antimagic vertex labeling, an (a, d)-edge-antimagic total labeling, a super (a, d)- edge-antimagic total labeling. Also we introduce anew labeling called edge bi-magic vertex labeling and prove that every uniform k-distant
tree has edge bi-magic vertex labeling.
Category: General Mathematics
[20] viXra:1411.0283 [pdf] submitted on 2014-11-19 00:24:30
Authors: Linfan Mao
Comments: 34 Pages.
A classical system of mathematics is homogenous without contradictions. But it is a little ambiguous for modern mathematics, for instance, the Smarandache geometry.
Category: General Mathematics
[19] viXra:1411.0282 [pdf] submitted on 2014-11-19 00:26:34
Authors: Teena Liza John, Mathew Varkey T.K
Comments: 7 Pages.
A graph that admits a Smarandachely near mean m-labeling is called Smarandachely near m-mean graph.
Category: General Mathematics
[18] viXra:1411.0281 [pdf] submitted on 2014-11-19 00:27:51
Authors: Lekha Bijukumar
Comments: 8 Pages.
In this paper we initiate a study on some new families of odd sequential graphs generated by some graph operations on some standard graphs.
Category: General Mathematics
[17] viXra:1411.0280 [pdf] submitted on 2014-11-19 00:29:30
Authors: V.Ramachandran, C C.Sekar
Comments: 11 Pages.
In this paper we prove that the arbitrary supersubdivisions of paths, disconnected paths, cycles and stars are one modulo N graceful for all positive integers N.
Category: General Mathematics
[16] viXra:1411.0279 [pdf] submitted on 2014-11-19 00:30:53
Authors: Nagesh.H.M, R.Chandrasekhar
Comments: 7 Pages.
In this paper the concept of pathos adjacency cut vertex jump graph PJC(T) of a tree T is introduced. We also present a characterization of graphs whose pathos adjacency cut vertex jump graphs are planar, outerplanar, minimally non-outerplanar, Eulerian and
Hamiltonian.
Category: General Mathematics
[15] viXra:1411.0278 [pdf] submitted on 2014-11-19 00:32:47
Authors: R.Ponraj, S.Sathish Narayanan, R.Kala
Comments: 8 Pages.
In this paper we find the radio mean number of some graphs which are related to complete bipartite graph and cycles.
Category: General Mathematics
[14] viXra:1411.0277 [pdf] submitted on 2014-11-19 00:34:31
Authors: B.O.Onasanya, S.A.Ilori
Comments: 5 Pages.
This paper is to further investigate some properties of an anti fuzzy subgroup of a group in relation to pseudo coset.
Category: General Mathematics
[13] viXra:1411.0276 [pdf] submitted on 2014-11-19 00:36:43
Authors: D.A.Mojdeh, H.Abdollahzadeh Ahangar, F.Choopani, F.Zeinali
Comments: 9 Pages.
Let u and v be adjacent vertices in G. If we assign colors to N[v] and N[u] such that the assignment colors to N[v] are different with the assignment colors to N[u], then this colorings is said to be vertex star colorings. In this paper we initiate the study of the star chromatic number and star defining number.
Category: General Mathematics
[12] viXra:1411.0275 [pdf] submitted on 2014-11-19 00:37:55
Authors: Linfan Mao
Comments: 9 Pages.
An ecologically industrial system is such an industrial system in harmony with its environment, especially the natural environment. The main purpose of this paper is to show how to establish a mathematical model for such systems by combinatorics, and find its topological characteristics, which are useful in industrial ecology and the environment protection.
Category: General Mathematics
[11] viXra:1411.0274 [pdf] submitted on 2014-11-19 00:39:12
Authors: Girish.V.R., P.Usha
Comments: 9 Pages.
In this paper many bounds on t(n(G)) are obtained and its exact values for some standard graphs are
found in terms of parameters of G. Also its relationship with other domination parameters
is investigated
Category: General Mathematics
[10] viXra:1411.0273 [pdf] submitted on 2014-11-19 00:43:49
Authors: A.Vijayalekshmi
Comments: 6 Pages.
Let G be a graph without isolated vertices. A total dominator coloring of a graph G is a proper coloring of G with the extra property that every vertex in G properly dominates a color class.
Category: General Mathematics
[9] viXra:1411.0272 [pdf] submitted on 2014-11-19 00:45:21
Authors: Ali Mohammed Sahal, Veena Mathad
Comments: 7 Pages.
By a graph G = (V,E) we mean a finite, undirected graph with neither loops nor multiple edges. The order and size of G are denoted by n and m, respectively. For graph theoretic terminology we refer to Chartrand and Lesnaik.
Category: General Mathematics
[8] viXra:1411.0268 [pdf] submitted on 2014-11-19 01:13:28
Authors: Florentin Smarandache
Comments: 23 Pages.
Bu makalede, Saaty’nin Analitik Hiyerarşi Sürecine (AHP) alternatif olan ve onu genişleten Çok Kriterli Karar Verme için Alfa İndirgeme Yöntemi (α-İ ÇKKV) olarak adlandırdığımız yeni bir yaklaşımı sunmaktayız. Yöntem, homojen lineer eşitlikler sistemine dönüştürülebilen herhangi bir tercihler kümesi için işe yarar. Karar verme probleminin tutarlılık derecesi (ve dolaylı olarak da tutarsızlık derecesi) tanımlanmaktadır. α-İ ÇKKV, lineer ve/veya lineer olmayan homojen ve/veya homojen olmayan eşitlikler ve/veya eşitsizlikler sistemine dönüştürülebilen bir tercihler kümesine genelleştirilmiştir. Makalede birçok tutarlı, zayıf tutarsız ve güçlü tutarsız örnekler verilmektedir.
Category: General Mathematics
[7] viXra:1411.0266 [pdf] submitted on 2014-11-19 01:15:53
Authors: Marian Nitu
Comments: 10 Pages.
The main goal of this paper is to present new transformations, previously non-existent in traditional mathematics, that we call centric mathematics (CM) but that became possible due to the new born eccentric mathematics, and, implicitly, to the supermathematics (SM).
Category: General Mathematics
[6] viXra:1411.0261 [pdf] submitted on 2014-11-19 01:37:09
Authors: Florentin Smarandache
Comments: 8 Pages.
This paper is an extension of our previous work on α-Discounting Method for MCDM ([1], [2], [3]) from crisp numbers to intervals.
Category: General Mathematics
[5] viXra:1411.0257 [pdf] submitted on 2014-11-19 01:42:31
Authors: Catalin Barbu, Florentin Smarandache
Comments: 6 Pages.
Hyperbolic geometry appeared in the …rst half of the 19th century as an attempt to understand Euclids axiomatic basis of geometry. It is also known as a type of non-euclidean geometry, being in many respects similar to euclidean geometry. Hyperbolic geometry includes similar concepts as distance and angle.
Category: General Mathematics
[4] viXra:1411.0251 [pdf] submitted on 2014-11-19 02:13:34
Authors: Mukhesh Kumar, Rajesh Singh, Florentin Smarandache
Comments: 5 Pages.
This paper addresses the problem of estimating population mean using auxiliaary information in the presence of measurement errors.
Category: General Mathematics
[3] viXra:1411.0162 [pdf] submitted on 2014-11-15 15:31:03
Authors: Florentin Smarandache
Comments: 122 Pages.
Since childhood I got accustomed to study with a pen in my hand.
I extracted theorems and formulas, together with the definitions, from my textbooks.
It was easier, later, for me, to prepare for the tests, especially for the final exams at the end of each semester.
I kept (and still do today) small notebooks where I collected not only mathematical but any idea I read from various domains.
These two volumes reflect my 1973-1974 high school studies in mathematics at the Pedagogical High School of Rm. Vâlcea, Romania.
Besides the textbooks I added information I collected from various mathematical books of solved problems I was studying at that time.
The first volume contains: Arithmetic, Plane Geometry, and Space Geometry.
(The Author)
Category: General Mathematics
[2] viXra:1411.0161 [pdf] submitted on 2014-11-15 15:32:07
Authors: Florentin Smarandache
Comments: 112 Pages.
Since childhood I got accustomed to study with a pen in my hand.
I extracted theorems and formulas, together with the definitions, from my textbooks.
It was easier, later, for me, to prepare for the tests, especially for the final exams at the end of each semester.
I kept (and still do today) small notebooks where I collected not only mathematical but any idea I read from various domains.
These two volumes reflect my 1973-1974 high school studies in mathematics at the Pedagogical High School of Rm. Vâlcea, Romania.
Besides the textbooks I added information I collected from various mathematical books of solved problems I was studying at that time.
The second volume contains: Algebra (9th to 12th grades), and Trigonometry.
(The Author)
Category: General Mathematics
[1] viXra:1411.0052 [pdf] submitted on 2014-11-07 05:52:40
Authors: Ricardo Alvira
Comments: 7 Pages.
Includes analysis of correlations/deviations between revised aggregation formulas, for several hierarchy types.
Category: General Mathematics
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