General Mathematics

La Formation Des Nombres Premiers

Authors: Denise DIDIER
Comments: 7 Pages. FRANCAIS

LA FORMATION DES NOMBRES PREMIERS
Category: General Mathematics

Fe, Fi, Fo, Folium: a Discourse on DESCARTES’ Mathematical Curiosity

Authors: Richard L. Amoroso
Comments: 7 Pages.

A brief history and biography of Descartes and his scientific work is given followed by some of the mathematical details of a mathematical curiosity called the Folium of Descartes which he discovered in an attempt to challenge Fermat’s extremum-finding techniques.
Category: General Mathematics

The Undergraduate Scientific Research Communication Platform of Applied Mathematics——Mathematical Modeling and Application Association

Authors: Zhang Huiming
Comments: 10 Pages. In Chinese

Mathematical modeling and application association (Shumo association) is a undergraduate scientific research communication platform face to whole students in CCNU under the leadership of the university Youth League committee and relying on the school Youth League committee of department of mathematics and statistics.
Category: General Mathematics

Applications of Dynamical Systems in Engineering

Authors: Yousuf Ibrahim Khan
Comments: 32 Pages.

This paper presents the current possible applications of Dynamical Systems in Engineering. The applications of chaos, fractals have proven to be an exciting and fruitful endeavor. These applications are highly diverse ranging over such fields as Electrical, Electronics and Computer Engineering. Dynamical Systems theory describes general patterns found in the solution of systems of nonlinear equations. The theory focuses upon those equations representing the change of processes in time. This paper offers the issue of applying dynamical systems methods to a wider circle of Engineering problems. There are three components to our approach: ongoing and possible applications of Fractals, Chaos Theory and Dynamical Systems. Some basic and useful computer simulation of Dynamical System related problems have been shown also.
Category: General Mathematics

Selected Problems in the Navier-Stokes Equation

Authors: Cheng Tianren
Comments: 12 Pages.

we select the problems we mentioned in reference [2] and [3] to talk about,and we give a summary about these problems and relate them in a correctable way.
Category: General Mathematics

On A Property of Pascal's Triangle II

Authors: Germán Paz
Comments: 4 Pages.

Based on the paper viXra:1303.0163 (vixra.org/abs/1303.0163), we show a few more properties of Pascal's Triangle.
Category: General Mathematics

Borel Resummation and the Solution of Integral Equations

Authors: Jose Javier garcia Moreta
Comments: 11 Pages.

ABSTRACT: In this paper we study the methods of Borel resummation applied to the solution of integral equation with symmetric Kernels K(XS) and to the study of the Riesz criterion , which is important to the Riemann Hypothesis
Category: General Mathematics

On A Property of Pascal's Triangle

Authors: Germán Paz
Comments: 6 Pages. Draft version.

In this simple Math exercise we show a property of Pascal's Triangle. More precisely, we show that if $a$ is any positive odd integer, then $\binom{a}{1}-\binom{a}{2}+\binom{a}{3}-\binom{a}{4}+\dots+\binom{a}{a}=1$. Moreover, we prove that if $b$ is any positive even integer, then $\binom{b}{1}-\binom{b}{2}+\binom{b}{3}-\binom{b}{4}+\dots+\binom{b}{b-1}-\binom{b}{b}=1$.
Category: General Mathematics

Syntactic - Semantic Axiomatic Theories in Mathematics

Authors: Elemer E Rosinger
Comments: 17 Pages.

A more careful consideration of the recently introduced "Grossone Theory" of Yaroslav Sergeev, [1], leads to a considerable enlargement of what can constitute possible legitimate mathematical theories by the introduction here of what we may call the {\it Syntactic - Semantic Axiomatic Theories in Mathematics}. The usual theories of mathematics, ever since the ancient times of Euclid, are in fact axiomatic, [1,2], which means that they are {\it syntactic} logical consequences of certain assumed axioms. In these usual mathematical theories {\it semantics} can only play an {\it indirect} role which is restricted to the inspiration and motivation that may lead to the formulation of axioms, definitions, and of the proofs of theorems. In a significant contradistinction to that, and as manifestly inspired and motivated by the mentioned Grossone Theory, here a {\it direct} involvement of {\it semantics} in the construction of axiomatic mathematical theories is presented, an involvement which gives semantics the possibility to act explicitly, effectively, and altogether directly upon the usual syntactic process of constructing the logical consequences of axioms. Two immediate objections to what appears to be an unprecedented and massive expansion of what may now become legitimate mathematical theories given by the {\it syntactic - semantic axiomatic theories} introduced here can be the following : the mentioned direct role of semantics may, willingly or not, introduce in mathematical theories one, or both of the "eternal taboo-s" of {\it inconsistency} and {\it self-reference}. Fortunately however, such concerns can be alleviated due to recent developments in both inconsistent and self-referential mathematics, [1,2]. Grateful recognition is acknowledged here for long and most useful ongoing related disccussions with Yaroslav Sergeev.
Category: General Mathematics

Five Departures in Logic, Mathematics, and Thus Either We Like It, or not in Physics as Well ...

Authors: Elemer E Rosinger
Comments: 36 Pages.

Physics depends on ”physical intuition”, much of which is formulated in terms of Mathematics. Mathematics itself depends on Logic. The paper presents three latest novelties in Logic which have major consequences in Mathematics. Further, it presents two possible significant departures in Mathematics itself. These five departures can have major implications in Physics. Some of them are indicated, among them in Quantum Mechanics and Relativity.
Category: General Mathematics

Notes on the Real Numbers

Authors: K. Raja Rama Gandhi
Comments: 23 Pages.

This is first part of eight parts of lecture notes on Real Analysis. This notes is well designed and useful to all Undergraduate, Graduate and postgraduate in their regular study. Apart from this, the problems discussed in exercise will increase the readability of readers and they love Number Theory as well as analysis without any doubts. Also, some problems presented in the exercises of this part as well as coming parts will create motivation towards research and development.
Category: General Mathematics

My Mathematical Work II

Authors: Jaivir Baweja
Comments: 2 Pages.

This is the second set of mathematical discoveries made by me, a 15-year old. The current system of mathematics education is failing me, as I am capable of much more as seen below, and yet I am still stuck in the ladder at Algebra II. However, even more potential great mathematicians are being failed too; and so far there is no solution that has been found. For now, the best thing we can do is eliminate the standard mathematics curriculum and replace it with modern mathematics through discovery, like the work in this paper.
Category: General Mathematics

Interesting Mathematics

Authors: Cheng Tianren
Comments: 15 Pages.

Lectures, in mathematics, worse still in abstract course such as algebra,analysis,often create boredom to some students,especially when the lectures are delivered in two continuous sessions.However interesting the lecture is,surely there must be some students who fall asleep. In this paper,we give suggestions on how to make lecture or teaching interesting.Two things that should be included are historical aspect of cencerts,and some applications of the concept in our daily life.
Category: General Mathematics

An Introduction of a New Number.

Authors: Vadim V. Nazarenko
Comments: 1 Page. An Introduction of a New Number.

प (poorna /purna) - is a number and the numerical digit.
Category: General Mathematics

My Ideas for Mathematics Education

Authors: Baweja Jaivir
Comments: 1 Page.

The current system of K-12 mathematics education is a curiosity killer by focusing on step-by-step instructions, tests, nonrelevant and ancient mathematics, arithmetic (even in calculus), and focusing on rules of manipulation that the students cannot play around with and realize the notions of modern mathematics. This note serves to give several ideas that can change this.
Category: General Mathematics

Some Properties on Convex Cone

Authors: Cheng Tianren
Comments: 19 Pages.

This paper proposes and compares several ways of measuring the degree of normality of a convex cone contained in a normed space. The dual concept of modulability is also considered. Other notion like solidity and sharpness are also analyzed from a point of view.
Category: General Mathematics

Zero Division

Authors: Robert S. Miller
Comments: 18 Pages.

In mathematics it has long been held that anything divided by zero is an undefined value. This is because the limits of any such ratio will approach infinity or the indeterminate form as the denominator approaches zero. This article will provide new theory to show the present understanding of zero division is inaccurate and that real number solutions do exist. The ultimate goal will be to complete our currently incomplete picture of division, and thereby multiplication at zero. It will also show why, despite the genius of earlier mathematicians this concept could likely not be understood till the modern era.
Category: General Mathematics

Discuss the Navier-Stokes Equation in Fluid (2)

Authors: Cheng Tianren
Comments: 27 Pages.

We show that solutions to the cauchy problem for the three dimensional navier-stokes equations are smooth.We study the cauchy problem for this type equations,and prove some regularity criteria involving the integrability of the pressure.We also study the isentropic compressible navier-stokes equations with radially symmetric data and non-negative initial density in an domain.
Category: General Mathematics

My Mathematical work I

Authors: Jaivir Baweja
Comments: 2 Pages.

These are a set of mathematical discoveries made by me, a 15-year old. The current system of mathematics education is failing me, as I am capable of much more as seen below, and yet I am still stuck in the ladder at Algebra II. However, even more potential great mathematicians are being failed too; and so far there is no solution that has been found. For now, the best thing we can do is eliminate the standard mathematics curriculum and replace it with modern mathematics through discovery, like the work in this paper.
Category: General Mathematics

Nonarchimedean Analysis-the Application of Symmetry Method

Authors: Cheng Tianren
Comments: 27 Pages.

This paper deal with the problem of existence multi-orthogonal bases in finite-dimensional normed spaces over, where is a nonArchimedean complete valued field.
Category: General Mathematics

Weak Fixed Point Property and Schauder Conjecture

Authors: Cheng Tianren
Comments: 27 Pages.

In this paper we introduce weak fixed point property and schauder conjecture. Firstly we investigate when various Banach algebras associated to a locally compact group C have the weak fixed point property for left reversible semigroups . Then we discuss the problem known as schauder conjecture.
Category: General Mathematics

What is Form?

Authors: Joerg Schiller
Comments: 19 Pages.

Notion of the form of a set.
Category: General Mathematics

Linear Programming using NNLS

Authors: Dhananjay P. Mehendale
Comments: 7 Pages

We discuss a new simple method to solve linear programming (LP) problems, based on the so called duality theory and nonnegative least squares method. The success for this method as far efficiency is concerned depends upon the success one may achieve by further research in finding efficient method to obtain nonnegative solution for a system of linear equations. Thus, the suggested method points the need to devise better methods, if possible, of finding nonnegative solution for a system of linear equations. Because, it is shown here that the problem of linear programming reduces to finding nonnegative solution of certain system of linear equations, if and when it exists, and this system of equations consists of 1) the equation representing duality condition; 2) the equations representing the constraints imposed by the given primal problem; and 3) the equations representing the constraints imposed by its corresponding dual problem. In this paper we have made use of well known method of nonnegative least squares (NNLS), [1], as a primary start for finding nonnegative solution for a system of linear equations. Two simple MATLAB codes for testing method by implementing it to solving some simple problems are provided at the end.
Category: General Mathematics

An Outline of Problems with Our Mathematics Education System

Authors: Jaivir Baweja
Comments: 1 page. Latex.

This document outlines some of the key problems in American mathematics education. They are based on observations by a 15-year old aspiring mathematician inside a high school honors algebra class. The results are very shocking.
Category: General Mathematics

A Virtual Test Bed Implementation Using the Precision Model of Feed-Drive System for the Verification of Command Generators

Authors: Mohammad Mahdi Emami, Behrooz Arezoo
Comments: 7 Pages.

I this paper, a simulation model of CNC feed-drive's servo-control system, witch could be utilized to design and develop CNC controllers, is presented. A precise model of machine tools components and controller, which we may call virtual machine, is employed as an experimental aid to carry out practical and economical test for verifying command generation modules.
Category: General Mathematics

The Curriculum Vitae of Ren Shiquan by Nov 2012

Authors: Ren Shiquan
Comments: 4 Pages.

This is the Curriculum Vitae of Mr. Ren Shiquan, a new Master-graduate in mathematics.
Category: General Mathematics

Why the American Math Education Fails and How to Fix it

Authors: Jaivir B.
Comments: 3 Pages.

This paper provides an overview of the problems facing our mathematics education system today, their impacts on the future of mathematics, and how these problems can be resolved.
Category: General Mathematics

A New Conjecture Towards the Proof of the Hodge Conjecture

Authors: Jaivir S. Baweja
Comments: 3 Pages.

In this paper, we review important facts related to the Hodge conjecture. Also, we review Chow classes and their importance to the problem. At the end of this survey, we pose a new conjecture that would advance work on it if proven true, to further the development of the important Millennium prize problem
Category: General Mathematics

Proof of the SYZ Conjecture

Authors: Jaivir S.Baweja
Comments: 5 Pages.

In this short paper, we prove that the Strominger-Yau-Zaslow (SYZ) conjecture holds by showing that mirror symmetry is equivalent to T- duality under fibrations from Lagrangian tori. In order to do this, we use some recent developments on Ooguri- Vafa spaces to construct such fibers. Moreover, we show that this is only possible under the trivial vector bundle {0}, thus giving an equivalence between the triangulated categories D^b Fuk_0 (Y,ω) and D_0^b (Y ̌).
Category: General Mathematics

On the Affine Nonlinearity in Circuit Theory

Authors: Emanuel Gluskin
Comments: 34 Pages. This is the set of the slides for my first NDES 2012 lecture, which significantly extends the content of the associated proceedings article.

According to the definition of the linear operator, as accepted in system theory, an affine dependence is a nonlinear one. This implies the nonlinearity of Thevenin's 1-port, while the battery itself is a strongly nonlinear element that in the 1-port's "passive mode" (when the 1-port is fed by a "stronger" circuit) can be replaced by a hardlimiter. For the theory, not the actual creation of the equivalent 1-port, but the selection of one of the ports of a (linear) many-port for interpreting the circuit as a 1-port, is important. A practical example of the affine nonlinearity is given also in terms of waveforms of time functions. Emphasizing the importance of the affine nonlinearity, it is argued that even when straightening the curved characteristic of the solar cell, we retain the main part of the nonlinearity. Finally, the "fractal-potential" and "f-connection-analysis" of 1- ports, which are missed in classical theory, are mentioned.
Category: General Mathematics

Why Does Possibility Exist

Authors: Jonathan Anon
Comments: 80 Pages.

Why does possibility exist and where does it come from? These are questions not usually asked because possibility is so deeply woven into the fabric of the universe we take its existence completely for granted. By exploring a well known, but essentially unexamined absolute first principle, we describe why possibility exists, where it comes from and the form it takes in our universe. We describe the fundamental mechanism which enables possibility to exist and to resolve to choice in context, which means we also generate the existence of context and choice. We discuss a number of examples to demonstrate how this mechanism operates and what it means.

In the late 19th Century, paradoxes revealed that no true universal set, no true set of all sets, can exist. Axiomatic set theory was developed as the solution to the problem this impossibility presented and the impossibility was treated as a failure of the naive conception of set theory and was set aside. We do not address set theory except in passing. Set theory assumes possibility exists to describe which sets are possible. We look instead directly at the meaning of the impossibility uncovered by the paradoxes to uncover why possibility itself can exist. This has never been done. We show that deriving without assumptions from this impossibility generates a specific structure which enables the existence of possibility, context and choice.

We begin by explaining the process by which we focused on this impossibility; we describe the process by which we can answer a question so obvious we take it for granted. We then derive the existence of possibility, context and choice and define the inherent structure we call the Choice Mechanism. To use a metaphor from the paper, we describe a box whose sides are absolute impossibility and which can be filled with all the possibility that can exist. By structure, we mean an actual structure in which possibility occurs and through which all resolution of possibility happens.

The rest of the paper consists of five discussion groups. We present in these a number of illustrative examples all of which cannot currently be explained. To be clear, we use the Choice Mechanism to provide the missing "why" for a number of otherwise unexplainable, fundamental phenomena, with each discussion group covering a major aspect of how this underlying structure for possibility appears and operates.

1. The first group explains how the Choice Mechanism calculates: we explain why numbers exist, meaning both Base 2 and Base 10, why the fundamental analytic constant e, the base of natural logarithms, exists and why functions exist. Again to be clear, we mean we derive the actual existence of numbers, of e and of function. We show in this and other sections how the universe actually calculates possibilities and how those become results.
2. The second group discusses physical examples which literally manifest the Choice Mechanism context structure; we explain why the logarithmic spiral occurs in nature and how the context structure of the Choice Mechanism completely explains certain fundamental behaviors of elementary particles.
3. The third group focuses on how the Choice Mechanism context structure operates, specifically on how coherent resolution to choice of context expresses as a force; we explain why natural selection and economic “markets” exist.
4. The fourth discusses fundamental aspects of how the Choice Mechanism acts on persistent structures, meaning how coherence interacts with things that have a past, present and future. This section contains too many examples to list.
5. The fifth discussion group describes how the Choice Mechanism functions at scale, meaning the effects of coherent resolution of context to choice at various scales of existence: we explain why the arrow of time exists and why the subjective experience of time exists. We also explain why and how constants of infinite depth can exist in a universe in which time exists.

Please understand this work completely agrees with established fact and theory, does not in any way rely on "hidden variables" or new particles or forces, and is not in any way mystical. We do not advance any new paradigms. We merely explain what we in essence already know: that possibilities exist and that somehow these come together to make our universe and all that happens in it. We provide the missing “why”. We understand this is difficult to believe. You have to read it. We can't otherwise persuade you.

The material is presented in a non-technical manner. The math is trivial.

No contact information is provided because we prefer to remain unknown.

The Axiomatic Method In Mathematics

Authors: Bertrand Wong
Comments: 2 Pages.

This paper highlights an evident inherent inconsistency or arbitrariness in the axiomatic method in mathematics.
Category: General Mathematics

Some Problems in Hungarian Mathematical Competition. Iv.

Authors: Fang Chen
Comments: 2 Pages.

In this work, we continue to @@ present some interesting problems in the Transylvanian Hungarian Mathematical Competition held in 2012.
Category: General Mathematics

A Simple Proof of Bernoulli's Inequality

Authors: Sanjeev Saxena
Comments: 2 Pages.

In this note an elementary proof of Bernoulli's inequality for rational exponent is described. The proof is only based on the fact that for any n non-negative numbers, geometric mean can not exceed arithmetic mean
Category: General Mathematics

Some Problems in Hungarian Mathematical Competition. III.

Authors: Fang Chen
Comments: 2 Pages.

@@In this work, we continue to present some interesting problems in the Transylvanian Hungarian Mathematical Competition held in 2012.
Category: General Mathematics

Some Problems in Hungarian Mathematical Competition. II.

Authors: Fang Chen
Comments: 2 Pages.

In this work, we continue to present some interesting problems in the Transylvanian Hungarian Mathematical Competition held in 2012.
Category: General Mathematics

Some Problems in Hungarian Mathematical Competition. I.

Authors: Fang Chen
Comments: 2 Pages.

In this work, we present some interesting problems in the Transylvanian Hungarian Mathematical Competition held in 2012.
Category: General Mathematics

Cellular Fight. Two Player Game

Authors: Martiros Khurshudyan, Amalya Khurshudyan
Comments: 7 Pages.

In this article we proposed a new Game called as 'Cellular Fights'. It takes a long time for giving such title to this game. Before and after publishing this letter, rules are not tested and are not classified, by other words they are given as they were born in our minds and we have not any idea about issues. Fight does not mean, that the game claims and propagates inhumanity. It is pure mathematical game where we need to develop moves and provide beautiful winning over opponent, which is big art not only in desk games but in everyday life. In physics, chemistry, biology as well as in our life fight exists continuously: our healthy biological cells struggle with ill cells, political parties are involved in very hot debuts etc. Other interesting example of the fight can be considered natural reaction occurring between two chemical elements during chemical reactions. Of course many examples can be given to readers, but it is reasonable to restrict ourselves and start our trip. All basic ideas of Cellular Automata are given. Then flat jump to main purpose is given: Rules, objects for the fight as well as an environment for the fight are presented. At the and of article some problems are given for future investigations.
Category: General Mathematics

Vertex-Only Bifurcation Diagrams Are Deceptively Simple

Authors: S Halayka
Comments: 7 Pages.

By plotting the polynomials corresponding to several iterations of the logistic map, it is found that the entropy of a branching path can be larger than what is intuitively expected.
Category: General Mathematics

Recognition and Resolution of “Comprehension Uncertainty” in ai

Authors: Sukanto Bhattacharya, Kuldeep Kumar
Comments: 12 Pages.

Handling uncertainty is an important component of most intelligent behaviour – so uncertainty resolution is a key step in the design of an artificially intelligent decision system (Clark, 1990). Like other aspects of intelligent systems design, the aspect of uncertainty resolution is also typically sought to be handled by emulating natural intelligence (Halpern, 2003; Ball and Christensen, 2009). A three-valued extension of classical (i.e. binary) fuzzy logic was proposed by Smarandache (2002) when he coined the term “neutrosophic logic” as a generalization of fuzzy logic to such situations where it is impossible to de-fuzzify the original fuzzy–valued variables via some tractable membership function into either of set T or its complement TC where both T and TC are considered crisp sets. In these cases one has to allow for the possibility of a third unresolved state intermediate between T and TC.
Category: General Mathematics

A Personal Proof of the Stokes' Theorem

Authors: Leonardo Rubino
Comments: 3 Pages.

In this paper you will find a personal, practical and direct demonstration of the Stokes’ Theorem.
Category: General Mathematics

Inelastic Spherical Caps with Defects

Authors: J. Lellep, E. Tungel, J. M. Consuelo
Comments: 6 Pages.

Limit analysis and minimum weight design of stepped spherical shells is studied. The caps have piece wise constant thickness and are subjected to the uniform external pressure. The shells are made of an inelastic material obeying an approximation of the Tresca yield surface. The aim of the paper is to develop a procedure for minimum weight design for given limit load. Necessary optimality conditions are derived with the aid of variational methods of the theory of optimal control. Numerical results are presented for a simply supported spherical cap.
Category: General Mathematics

Two Faces Myth Figure in Chess

Authors: Martiros Khurshudyan
Comments: 1 Page.

A new version of Chess game is proposed, where in general case a figure(or figures) has "two faces": white and black. Depending on the position of the figure on the board, it could change its color(face) and be used by opponent. Initially which of figures should have "two faces" as well as positions of the colored cells will be defined by players before game will start.
Category: General Mathematics

Mathematical Objects :Past, Present, Future.

Authors: Vyacheslav Telnin
Comments: 4 Pages. This paper also fit for Mathematical Physics

Abstract. There are three main mathematical operations : [1] – addition, [2] - multiplication, [3] – raising to the power. Also there are three kinds of operands : A – numbers, B – vectors, C – vector spaces. This paper shows how to define new kinds of operands : D, E, F, … and new operations : [4], [5], [6], … ; [0], [-1], [-2], [-3], … . The study of inverse operations for new operations can open new classes of operands like it was with the operations [1], [2], [3]. Also there is a way to description of field with spin = 1/3.
Category: General Mathematics

The Structure of Fourier Series

Authors: Valery P. Dmitriyev
Comments: 6 pages

Fourier series is constructed basing on the idea to model the elementary oscillation (–1,+1) by the exponential function with negative base, viz. (–1)ⁿ.

Key words: Fourier transform, exponent, negative base.
Category: General Mathematics

Reflections on the Structure of the Universal Number Continuum

Authors: Jeffrey Bryant Bishop
Comments: 34 pages.

I am not currently associated with any institution. My work is a result of private correspondence with Dr. Marie Louise von Franz, former director of the Jungian Institute in Zurich before her death in 1999. You see a problem is that a large bulk of the subjects of my studies are not taught in our traditional educational systems. My work is a result of independent study related to materials, the basis of which lies outside our standard curricula. The following document addresses the basis of what I had hoped to share and which I have been working on since 1988. It is shown through a novel method of generation that number corresponds to form as a "becoming continuum" indicating specific forms apply to the first ten integers and through the process of explication we are required to consider related issues including dimensionality and growth. The work describes the spatial nature of the "archetypal" characteristics of the natural integers, and it is concluded that there exists what may be understood as a "Universal Number Continuum," which is represented through a pure projective geometry in a fifth dimensional framework, incorporating a Hypercube or Tesseract and where the basis of the fifth dimension here corresponds precisely to the characteristics of the nature of the fifth dimension as it is explicated in the Kaluza-Klein theory of Relativity. The desire being to lend a mathematically sound basis for the the fifth dimension and the qualities it possesses supportive of the Kaluza-Klein theory is much desired in the scientific community. Please be aware this was written as a preliminary discussion concerning the proposed publication of a document which purports to explicate a new theory related to mathematical philosophy and where overwhelming evidence exists in favor of the proposition, but where remain yet unresolved aspects related to special dimensionality and complex symmetry seen as relational subjects.
Category: General Mathematics

A New Variant of the Board Game Chess: Chess With New Mindless Figure.

Authors: Martiros Khurshudyan
Comments: 4 pages.

In this article we present a new variant of Chess Game. This work is not written for attempt to propogate the Chess Game or to present whole beauty of the Game. We know that figures from ordinary Chess are faithful by means given by the definition at 'A New figure of the game and its properties' section. The aim here is different, here we want to make a new Game by playing with faithfulness of the figures. Directed by that motivation, we introduce a New Type Game Figure: Mindless Figure. This figure has very interesting property, it can not remember its past and its future do not known. And such property gives such name to our figure. From the future writing, our New Figure can be considered as a mirrow, which can reflect the properties of the other figures. In the coming sections of the article the following are presented and discused: discription of the new figure, general rules are for manage the game and the figure, final proposition and mechanisms of deciding of a winner. As general, the subject of the Game is the same as for the original Chess Game: 'kill the King' of Your opponent [1]. At the end a Conclusion is given.
Category: General Mathematics

A Board Game for Two Players: MKCess

Authors: Martiros Khurshudyan
Comments: 3 pages.

In this paper we are going to describe a board game for two players. In this issue are presented basic rules and necessary conditions for describing a winner. Two type of boards are presented for the same rules for the game. In this issue have not presented analyses or winning strategies for the game. Possible generalization schemes of the game are presented at the end of article
Category: General Mathematics

Representations and Primordial Self-Similarity in the Hierarchy of Universal Lexicons

Authors: T. E. Raptis
Comments: 24 pages

A set of fundamental objects is presented that facilitates derivation of some new results with special interest in a variety of topics including Chu spaces, dynamical systems, symbolic dynamics and the theory of polynomials. Three alternative representations of the power set of binary patterns in their associated exponential intervals are presented in terms of polynomials and a natural conjecture on their fractal structure is deduced. Practical applications in Automata theory and Digital Signal Processing are proposed based on special functions defined on the new representation.
Category: General Mathematics

Problems with and Without ... Problems!

Authors: Florentin Smarandache
Comments: 136 pages, translated from French to English

This book is addressed to College honor students, researchers, and professors. It contains 136 original problems published by the author in various scientific journals around the world. The problems could be used to preparing for courses, exams, and Olympiads in mathematics. Many of these have a generalized form. For each problem we provide a detailed solution. I was a professeur coopérant between 1982-1984, teaching mathematics in French language at Lycée Sidi EL Hassan Lyoussi in Sefrou, Province de Fès, Morocco. I used many of these problems for selecting and training, together with other Moroccan professors, in Rabat city, of the Moroccan student team for the International Olympiad of Mathematics in Paris, France, 1983.
Category: General Mathematics

A Case Study on the Clay Millenium Prize Problems

Authors: Jorma Jormakka
Comments: 12 pages

This article is a case study investigating ... (see paper)
Category: General Mathematics

On Sergeyev's Grossone : How to Compute Effectively with Infinitesimal and Infinitely Large Numbers

Authors: Elemér E Rosinger
Comments: 18 pages

The recently proposed and partly developed "Grossone Theory" of Y D Sergeyev is analyzed and partly clarified.
Category: General Mathematics

PDEs and Symmetry : an Open Problem

Authors: Elemér E Rosinger
Comments: 7 pages

A simple and basic problem is formulated about symmetric partial differential operators. The symmetries considered here are other than Lie symmetries.
Category: General Mathematics

Four Comments on "The Road to Reality" by R Penrose

Authors: Elemér E Rosinger
Comments: 8 pages

Four comments are presented on the book of Roger Penrose entitled "The Road to Reality, A Complete Guide to the Laws of the Universe". The first comment answers a concern raised in the book. The last three point to important omissions in the book.
Category: General Mathematics

Subjective Questions and Answers for a Mathematics Instructor of Higher Education

Authors: Florentin Smarandache
Comments: 15 pages

This article of mathematical education reflects author's experience with job applications and teaching methods and procedures to employ in the American Higher Education. It is organized as a standard questionnaire.
Category: General Mathematics

Proposed Problems of Mathematics (Vol. II)

Authors: Florentin Smarandache
Comments: 74 pages, Mathematical problems for student competitions, translated from Romanian and French into English by the author.

The first book of "Problèmes avec et sans ... problèmes!" was published in Morocco in 1983. I collected these problems that I published in various Romanian or foreign magazines (amongst which: "Gazeta Matematica", magazine which formed me as problem solver, "American Mathematical Monthly", "Crux Mathematicorum" (Canada), "Elemente der Mathematik" (Switzerland), "Gaceta Matematica" (Spain), "Nieuw voor Archief" (Holland), etc. while others are new proposed problems in this second volume. These have been created in various periods: when I was working as mathematics professor in Romania (1984-1988), or co-operant professor in Morocco (1982-1984), or emigrant in the USA (1990-1997). I thank to the Algebra Department of the State University of Moldova for the publication of this book.
Category: General Mathematics

Problemes Avec et Sans... Problemes!

Authors: Florentin Smarandache
Comments: 175 Pages. In French

Problems with and without... problems!
Category: General Mathematics

La Formation Des Nombres Premiers

Authors: Denise DIDIER
Comments: 7 Pages.

Cette étude montre comment se forment les nombres premiers à travers les bases. Et donne les nombres premiers (deuxième terme de chaque base) dans l'ordre croissant à l'infini. Cette étude ne respecte peut être pas l'écriture conventionnelle mathématique mais la méthode fonctionne.
Category: General Mathematics

On A Property of Pascal's Triangle

Authors: Germán Paz
Comments: 6 Pages. Draft version.

In this simple Math exercise we show a property of Pascal's Triangle. More precisely, we show that if $a$ is any positive odd integer, then $\binom{a}{1}-\binom{a}{2}+\binom{a}{3}-\binom{a}{4}+\dots+\binom{a}{a}=1$. Moreover, we prove that if $b$ is any positive even integer, then $\binom{b}{1}-\binom{b}{2}+\binom{b}{3}-\binom{b}{4}+\dots+\binom{b}{b-1}-\binom{b}{b}=1$.
Category: General Mathematics

Notes on Real Numbers

Authors: K. Raja Rama Gandhi
Comments: 24 Pages.

This is first part of eight parts of lecture notes on Real Analysis. This notes is well designed and useful to all Undergraduate, Graduate and postgraduate in their regular study. Apart from this, the problems discussed in exercise will increase the readability of readers and they love Number Theory as well as analysis without any doubts. Also, some problems presented in the exercises of this part as well as coming parts will create motivation towards research and development.
Category: General Mathematics

An Introduction of a New Number.

Authors: Vadim V Nazarenko
Comments: 1 Page.

प (poorna /purna) - is a number and the numerical digit.
Category: General Mathematics

An Introduction of a New Number.

Authors: Vadim V Nazarenko
Comments: 1 Page.

प (poorna /purna) - is a number and the numerical digit.
Category: General Mathematics

An Introduction of a New Number.

Authors: Vadim V Nazarenko
Comments: 1 Page.

प (poorna /purna) - is a number and the numerical digit.
Category: General Mathematics

Zero Division

Authors: Robert S. Miller
Comments: 19 Pages. This is the second version of this paper. It includes corrected notation for 3-space equations in z = f(x , y) format, and a more complete solution for the negative radical with a graphic representation.

In mathematics it has long been held that anything divided by zero is an undefined value. This is because the limits of any such ratio will approach infinity or the indeterminate form as the denominator approaches zero. This article will provide new theory to show the present understanding of zero division is inaccurate and that real number solutions do exist. The ultimate goal will be to complete our currently incomplete picture of division, and thereby multiplication at zero. It will also show why, despite the genius of earlier mathematicians this concept could likely not be understood till the modern era.
Category: General Mathematics

Nonarchimedean Analysis-the Application of Symmetry Method

Authors: Cheng Tianren
Comments: 27 Pages.

This paper deal with the problem of existence multi-orthogonal bases in finite-dimensional normed spaces over, where is a nonArchimedean complete valued field.
Category: General Mathematics

Weak Fixed Point Property and Schauder Conjecture

Authors: Cheng Tianren
Comments: 27 Pages.

In this paper we introduce weak fixed point property and schauder conjecture. Firstly we investigate when various Banach algebras associated to a locally compact group C have the weak fixed point property for left reversible semigroups . Then we discuss the problem known as schauder conjecture.
Category: General Mathematics

Interesting Mathematics

Authors: Cheng Tianren
Comments: 15 Pages.

Lectures, in mathematics, worse still in abstract course such as algebra,analysis,often create boredom to some students,especially when the lectures are delivered in two continuous sessions.However interesting the lecture is,surely there must be some students who fall asleep. In this paper,we give suggestions on how to make lecture or teaching interesting.Two things that should be included are historical aspect of cencerts,and some applications of the concept in our daily life.
Category: General Mathematics

The Axiomatic Method In Mathematics

Authors: Bertrand Wong
Comments: 2 Pages.

This paper highlights an evident inherent inconsistency or arbitrariness in the axiomatic method in mathematics.
Category: General Mathematics

Mathematical Objects :Past, Present, Future.

Authors: Vyacheslav Telnin
Comments: 4 Pages.

Abstract. There are three main mathematical operations : [1] – addition, [2] - multiplication, [3] – raising to the power. Also there are three kinds of operands : A – numbers, B – vectors, C – vector spaces. This paper shows how to define new kinds of operands : D, E, F, … and new operations : [4], [5], [6], … ; [0], [-1], [-2], [-3], … . The study of inverse operations for new operations can open new classes of operands like it was with the operations [1], [2], [3]. Also there is a way to description of field with spin = 1/3.
Category: General Mathematics

Reflections on the Structure of the Universal Number Continuum

Authors: Jeffrey Bryant Bishop
Comments: 42 pages.

I am not currently associated with any institution. My work is a result of private correspondence with Dr. Marie Louise von Franz, former director of the Jungian Institute in Zurich before her death in 1999. You see a problem is that a large bulk of the subjects of my studies are not taught in our traditional educational systems. My work is a result of independent study related to materials, the basis of which lies outside our standard curricula. The following document addresses the basis of what I had hoped to share and which I have been working on since 1988. It is shown through a novel method of generation that number corresponds to form as a "becoming continuum" indicating specific forms apply to the first ten integers and through the process of explication we are required to consider related issues including dimensionality and growth. The work describes the spatial nature of the "archetypal" characteristics of the natural integers, and it is concluded that there exists what may be understood as a "Universal Number Continuum," which is represented through a pure projective geometry in a fifth dimensional framework, incorporating one view of a Hypercube or Tesseract and where the basis of the fifth dimension here corresponds precisely to the characteristics of the nature of the fifth dimension as it is explicated in the Kaluza-Klein theory of Relativity. The desire being to lend a mathematically sound basis for the fifth dimension and the qualities it possesses supportive of the Kaluza-Klein theory which is much desired in the scientific community. Please be aware this was written as a preliminary discussion concerning the proposed publication of a document which purports to explicate a new theory related to mathematical philosophy and where overwhelming evidence exists in favor of the proposition, but where remain yet unresolved aspects related to special dimensionality and complex symmetry seen as relational subjects.
Category: General Mathematics

Reflections on the Structure of the Universal Number Continuum

Authors: Jeffrey Bryant Bishop
Comments: 44 pages.

I am not currently associated with any institution. My work is a result of private correspondence with Dr. Marie Louise von Franz, former director of the Jungian Institute in Zurich before her death in 1999. You see a problem is that a large bulk of the subjects of my studies are not taught in our traditional educational systems. My work is a result of independent study related to materials, the basis of which lies outside our standard curricula. The following document addresses the basis of what I had hoped to share and which I have been working on since 1988. It is shown through a novel method of generation that number corresponds to form as a "becoming continuum" indicating specific forms apply to the first ten integers and through the process of explication we are required to consider related issues including dimensionality and growth. The work describes the spatial nature of the "archetypal" characteristics of the natural integers, and it is concluded that there exists what may be understood as a "Universal Number Continuum," which is represented through a pure projective geometry in a fifth dimensional framework, incorporating one view of a Hypercube or Tesseract and where the basis of the fifth dimension here corresponds precisely to the characteristics of the nature of the fifth dimension as it is explicated in the Kaluza-Klein theory of Relativity. The desire being to lend a mathematically sound basis for the fifth dimension and the qualities it possesses supportive of the Kaluza-Klein theory which is much desired in the scientific community. Please be aware this was written as a preliminary discussion concerning the proposed publication of a document which purports to explicate a new theory related to mathematical philosophy and where overwhelming evidence exists in favor of the proposition, but where remain yet unresolved aspects related to special dimensionality and complex symmetry seen as relational subjects.
Category: General Mathematics

Polynomial Representations and Primordial Self-Similarity in the Hierarchy of Universal Lexicons

Authors: T. E. Raptis
Comments: 30 pages. submitted in "Chaos, Solitons & Fractals"

A set of fundamental objects is presented that facilitates derivation of some new results with special interest in a variety of topics including Chu spaces, dynamical systems, symbolic dynamics and the theory of polynomials. Three alternative representations of the power set of binary patterns in their associated exponential intervals are presented in terms of polynomials and a natural conjecture on their fractal structure is deduced. Practical applications in Automata theory and Digital Signal Processing are proposed based on special functions defined on the new representation.
Category: General Mathematics

Polynomial Representations and Primordial Self-Similarity in the Hierarchy of Universal Lexicons

Authors: T. E. Raptis
Comments: 29 pages. This is an important update.

A set of fundamental objects is presented that facilitates derivation of some new results with special interest in a variety of topics including Chu spaces, dynamical systems, symbolic dynamics and the theory of polynomials. Three alternative representations of the power set of binary patterns in their associated exponential intervals are presented in terms of polynomials and a natural conjecture on their fractal structure is deduced. Practical applications in Automata theory and Digital Signal Processing are proposed based on special functions defined on the new representation.
Category: General Mathematics

A Case Study on the Clay Millenium Prize Problems

Authors: Jorma Jormakka
Comments: 12 pages

This article is a case study investigating the following issues: how well general purpose problem solving methods work on hard mathematical problems, how much time is required in order to learn enough from the fields in order to attack such hard problems, are there easy formulations and treatments of the Clay millennium prize problems, and what is the sociological response from the mathemacical community and media to proposed solutions to hard mathematical problems.
Category: General Mathematics

Four Comments on "The Road to Reality" by R Penrose

Authors: Elemér E Rosinger
Comments: 8 pages

Four comments are presented on the book of Roger Penrose entitled "The Road to Reality, A Complete Guide to the Laws of the Universe". The first comment answers a concern raised in the book. The last three point to important omissions in the book.
Category: General Mathematics