Other Mathematics Commons^™

Infinite Dimensional Laplacians On A Lévy-Gelfand Triple, Abdessatar Barhoumi, Hui-Hsiung Kuo, Habib Ouerdiane

Communications on Stochastic Analysis

No abstract provided.

Application Of White Noise Calculus In Evaluating The Path Integral In Relativistic Quantum Mechanics, C C Bernido, J B Bornales, M V Carpio-Bernido

Communications on Stochastic Analysis

No abstract provided.

Brownian Super-Exponents, Victor Goodman

Communications on Stochastic Analysis

No abstract provided.

Actors, Objects, Contextures, Morphograms, Rudolf Kaehr

Rudolf Kaehr

Systematic and historic overview and critics of actor and object oriented programming.

From Dialogues To Polylogues, Rudolf Kaehr

Rudolf Kaehr

No abstract provided.

Application Of Ansys In Seismic Response Analysis Of Constructing Of High Buildings, Yang Xiaojun

Xiao-Jun Yang

The dynamic feature of high buildings is discussed in the present study with the application of ANSYS，the large finite element analysis software，aimed at the analysis of dynamic response of high buildings．Based on the case of a 15一story-building，a model of beam and shell 3-D finite element structure is built and the frequency of structure and the mode of vibration are computed in the study；furthermore，the structural dynamic response is discussed under different seismic waves with the use of the history analysis method．The results show that the more intense the seismic wave is，the bigger is the dynamic response of the buildings．The information can …

Neutrality And Many-Valued Logics, Florentin Smarandache, Andrew Schumann

Branch Mathematics and Statistics Faculty and Staff Publications

ThisbookwrittenbyA. Schumann &F. Smarandache isdevotedtoadvances of non-Archimedean multiple-validity idea and its applications to logical reasoning. Leibnitz was the first who proposed Archimedes’ axiom to be rejected. He postulated infinitesimals (infinitely small numbers) of the unit interval [0,1] which are larger than zero, but smaller than each positive real number. Robinson applied this idea into modern mathematics in [117] and developed so-called non-standard analysis. In the framework of non-standard analysis there were obtained many interesting results examined in [37], [38], [74], [117].

There exists also a different version of mathematical analysis in that Archimedes’ axiom is rejected, namely, p-adic analysis (e.g., …

Special Fuzzy Matrices For Social Scientists, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral

Branch Mathematics and Statistics Faculty and Staff Publications

This book is a continuation of the book, "Elementary fuzzy matrix and fuzzy models for socio-scientists" by the same authors. This book is a little advanced because we introduce a multi-expert fuzzy and neutrosophic models. It mainly tries to help social scientists to analyze any problem in which they need multi-expert systems with multi-models. To cater to this need, we have introduced new classes of fuzzy and neutrosophic special matrices. The first chapter is essentially spent on introducing the new notion of different types of special fuzzy and neutrosophic matrices, and the simple operations on them which are needed in …

Neutrosophy In Arabic Philosophy, Florentin Smarandache, Salah Osman

Branch Mathematics and Statistics Faculty and Staff Publications

Is there an absolute reality? Yes, “God” is the only absolute reality. The three main religions: Judaism, Christianity and Islam have all claimed that God is a supreme reality, and that all other creatures are finite beings. Since they relatively continue and also relatively change, so they can not be absolute. The world is full of paradoxes, there is no absolute persistence, and also there is no change at a stretch. There is no absolute truth and there is no continuous falsehood. What exist are many faces or aspects between the two terms. Those faces are reduced to a neutral …

Techno-Art Of Selariu Supermathematics Functions, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this album we include the so called Super-Mathematics functions (SMF), which constitute the base for, most often, generating, technical, neo-geometrical objects, therefore less artistic. These functions are the results of 38 years of research, which began at University of Stuttgart in 1969. Since then, 42 related works have been published, written by over 19 authors, as shown in the References. The name was given by the regretted mathematician Professor Emeritus Doctor Engineer Gheorghe Silas who, at the presentation of the very first work in this domain, during the First National Conference of Vibrations in Machine Constructions, Timişoara, Romania, 1978, …

Lessons Learned From The 1918-1919 Influenza Pandemic In Minneapolis And St. Paul, Minnesota, Miles Q. Ott, Shelly F. Shaw, Richard N. Danila, Ruth Lynfield

Statistical and Data Sciences: Faculty Publications

No abstract provided.

Pi-Calculus In Logical Form, Marcello M. Bonsangue, Alexander Kurz

Engineering Faculty Articles and Research

Abramsky’s logical formulation of domain theory is extended to encompass the domain theoretic model for picalculus processes of Stark and of Fiore, Moggi and Sangiorgi. This is done by defining a logical counterpart of categorical constructions including dynamic name allocation and name exponentiation, and showing that they are dual to standard constructs in functor categories. We show that initial algebras of functors defined in terms of these constructs give rise to a logic that is sound, complete, and characterises bisimilarity. The approach is modular, and we apply it to derive a logical formulation of pi-calculus. The resulting logic is a …

Carathéodory Functions In The Banach Space Setting, Daniel Alpay, Olga Timoshenko, Dan Volok

Mathematics, Physics, and Computer Science Faculty Articles and Research

We prove representation theorems for Carathéodory functions in the setting of Banach spaces.

The Abacus Of Universal Logics, Rudolf Kaehr

Rudolf Kaehr

No abstract provided.

On The Nondegeneracy Of Constant Mean Curvature Surfaces, Nick Korevaar, Robert Kusner, Jesse Ratzkin

Robert Kusner

We prove that many complete, noncompact, constant mean curvature (CMC) surfaces $f:\Sigma \to \R^3$ are nondegenerate; that is, the Jacobi operator Δf+|Af|2 has no L2 kernel. In fact, if Σ has genus zero and f(Σ) is contained in a half-space, then we find an explicit upper bound for the dimension of the L2 kernel in terms of the number of non-cylindrical ends. Our main tool is a conjugation operation on Jacobi fields which linearizes the conjugate cousin construction. Consequences include partial regularity for CMC moduli space, a larger class of CMC surfaces to use in gluing constructions, and a surprising …

François Viète, Between Analysis And Cryptanalysis, Marco Panza

MPP Published Research

François Viète is considered the father both of modern algebra and of modern cryptanalysis. The paper outlines Viète's major contributions in these two mathematical fields and argues that, despite an obvious parallel between them, there is an essential difference. Viète's 'new algebra' relies on his reform of the classical method of analysis and synthesis, in particular on a new conception of analysis and the introduction of a new formalism. The procedures he suggests to decrypt coded messages are particular forms of analysis based on the use of formal methods. However, Viète's algebraic analysis is not an analysis in the same …

Place-Valued Logics Around Cybernetic Ontology, The Bcl And Afosr, Rudolf Kaehr

Rudolf Kaehr

No abstract provided.

From Ruby To Rudy, Rudolf Kaehr

Rudolf Kaehr

No abstract provided.

The Chinese Challenge. Hallucinations For Other Futures, Rudolf Kaehr

Rudolf Kaehr

The main question is: What can we learn from China that China is not teaching us? It is proposed that a study of polycontextural logic and morphogrammatics could be helpful to discover this new kind of rationality.

The Dynamics Of Newton's Method On Cubic Polynomials, Shannon N. Miller

Theses, Dissertations and Capstones

The field of dynamics is itself a huge part of many branches of science, including the motion of the planets and galaxies, changing weather patterns, and the growth and decline of populations. Consider a function f and pick x0 in the domain of f . If we iterate this function around the point x0, then we will have the sequence x0, f (x0), f (f (x0)), f (f (f (x0))), ..., which becomes our dynamical system. We are essentially interested in the end behavior of this system. Do …

Fuzzy Interval Matrices, Neutrosophic Interval Matrices And Their Applications, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

The new concept of fuzzy interval matrices has been introduced in this book for the first time. The authors have not only introduced the notion of fuzzy interval matrices, interval neutrosophic matrices and fuzzy neutrosophic interval matrices but have also demonstrated some of its applications when the data under study is an unsupervised one and when several experts analyze the problem. Further, the authors have introduced in this book multiexpert models using these three new types of interval matrices. The new multi expert models dealt in this book are FCIMs, FRIMs, FCInMs, FRInMs, IBAMs, IBBAMs, nIBAMs, FAIMs, FAnIMS, etc. Illustrative …

Neutrosophic Rings, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book we define the new notion of neutrosophic rings. The motivation for this study is two-fold. Firstly, the classes of neutrosophic rings defined in this book are generalization of the two well-known classes of rings: group rings and semigroup rings. The study of these generalized neutrosophic rings will give more results for researchers interested in group rings and semigroup rings. Secondly, the notion of neutrosophic polynomial rings will cause a paradigm shift in the general polynomial rings. This study has to make several changes in case of neutrosophic polynomial rings. This would give solutions to polynomial equations for …

Coalgebras And Their Logics, Alexander Kurz

Engineering Faculty Articles and Research

"Transition systems pervade much of computer science. This article outlines the beginnings of a general theory of specification languages for transition systems. More specifically, transition systems are generalised to coalgebras. Specification languages together with their proof systems, in the following called (logical or modal) calculi, are presented by the associated classes of algebras (e.g., classical propositional logic by Boolean algebras). Stone duality will be used to relate the logics and their coalgebraic semantics."

Interdependency Of Pharmacokinetic Parameters: A Chicken-And-Egg Problem? Not!, Reza Mehvar

Pharmacy Faculty Articles and Research

Pharmacokinetic (PK) software packages are widely used by scientists in different disciplines to estimate PK parameters. However, their use without a clear understanding of physiological parameters affecting the PK parameters and how different PK parameters are related to each other may result in erroneous interpretation of data. Often, mathematical relationships used for the estimation of PK parameters obscure the true physiological relationships among these parameters, prompting a discussion of which parameter came first and giving the appearance of the-chicken-and-the-egg dilemma. In this article, the author attempts to show how different PK parameters are related to physiological parameters and each other …

Matrix-J-Unitary Non-Commutative Rational Formal Power Series, Daniel Alpay, D. S. Kalyuzhnyi-Verbovetzkii

Mathematics, Physics, and Computer Science Faculty Articles and Research

Formal power series in N non-commuting indeterminates can be considered as a counterpart of functions of one variable holomorphic at 0, and some of their properties are described in terms of coefficients. However, really fruitful analysis begins when one considers for them evaluations on N-tuples of n × n matrices (with n = 1, 2, . . .) or operators on an infinite-dimensional separable Hilbert space. Moreover, such evaluations appear in control, optimization and stabilization problems of modern system engineering.

In this paper, a theory of realization and minimal factorization of rational matrix-valued functions which are J-unitary on the imaginary …

A Mathematical Journey Through The Land Of The Maya, Philip Scalisi, Paul Fairbanks

Bridgewater Review

No abstract provided.

When A Mechanical Model Goes Nonlinear, Lisa D. Humphreys, P. J. Mckenna

Faculty Publications

This paper had its origin in a curious discovery by the first author in research performed with an undergraduate student. The following odd fact was noticed: when a mechanical model of a suspension bridge (linear near equilibrium but allowed to slacken at large distance in one direction) is shaken with a low-frequency periodic force, several different periodic responses can result, many with high-frequency components.

Dependence, Dispersiveness, And Multivariate Hazard Rate Ordering, Baha-Eldin Khaledi, Subhash C. Kochar

Mathematics and Statistics Faculty Publications and Presentations

To compare two multivariate random vectors of the same dimension, we define a new stochastic order called upper orthant dispersive ordering and study its properties. We study its relationship with positive dependence and multivariate hazard rate ordering as defined by Hu, Khaledi, and Shaked (Journal of Multivariate Analysis, 2002). It is shown that if two random vectors have a common copula and if their marginal distributions are ordered according to dispersive ordering in the same direction, then the two random vectors are ordered according to this new upper orthant dispersive ordering. Also, it is shown that the marginal distributions of …

Book Review: Across The Board: The Mathematics Of Chessboard Problems By John J. Watkins, Arthur T. Benjamin

All HMC Faculty Publications and Research

I think I became a mathematician because I loved to play games as a child. I learned about probability and expectation by playing games like backgammon, bridge, and Risk. But I experienced the greater thrill of careful deductive reasoning through games like Mastermind and chess. In fact, for many years I took the game of chess quite seriously and played in many tournaments. But I gave up the game when I started college and turned my attention to more serious pursuits, like learning real mathematics.

Some Sober Conceptions Of Mathematical Truth, Marco Panza

MPP Published Research

It is not sufficient to supply an instance of Tarski’s schema, ⌈“p” is true if and only if p⌉ for a certain statement in order to get a definition of truth for this statement and thus fix a truth-condition for it. A definition of the truth of a statement x of a language L is a bi-conditional whose two members are two statements of a meta-language L’. Tarski’s schema simply suggests that a definition of truth for a certain segment x of a language L consists in a statement of the form: ⌈v(x) is true if and only if τ(x)⌉, …