Mathematics Commons^™

Fuzzy Relational Maps And Neutrosophic Relational Maps, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

The aim of this book is two fold. At the outset the book gives most of the available literature about Fuzzy Relational Equations (FREs) and its properties for there is no book that solely caters to FREs and its applications. Though we have a comprehensive bibliography, we do not promise to give all the possible available literature about FRE and its applications. We have given only those papers which we could access and which interested us specially. We have taken those papers which in our opinion could be transformed for neutrosophic study. The second importance of this book is that …

Analysis Of A Multigrid Algorithm For Time Harmonic Maxwell Equations, Jay Gopalakrishnan, Joseph E. Pasciak, Leszek Demkowicz

Mathematics and Statistics Faculty Publications and Presentations

This paper considers a multigrid algorithm suitable for efficient solution of indefinite linear systems arising from finite element discretization of time harmonic Maxwell equations. In particular, a "backslash" multigrid cycle is proven to converge at rates independent of refinement level if certain indefinite block smoothers are used. The method of analysis involves comparing the multigrid error reduction operator with that of a related positive definite multigrid operator. This idea has previously been used in multigrid analysis of indefinite second order elliptic problems. However, the Maxwell application involves a nonelliptic indefinite operator. With the help of a few new estimates, the …

A Characterization Of Hybridized Mixed Methods For Second Order Elliptic Problems, Bernardo Cockburn, Jay Gopalakrishnan

Mathematics and Statistics Faculty Publications and Presentations

In this paper, we give a new characterization of the approximate solution given by hybridized mixed methods for second order self-adjoint elliptic problems. We apply this characterization to obtain an explicit formula for the entries of the matrix equation for the Lagrange multiplier unknowns resulting from hybridization. We also obtain necessary and sufficient conditions under which the multipliers of the Raviart–Thomas and the Brezzi–Douglas–Marini methods of similar order are identical.

Quasioptimality Of Some Spectral Mixed Methods, Jay Gopalakrishnan, Leszek Demkowicz

Mathematics and Statistics Faculty Publications and Presentations

In this paper, we construct a sequence of projectors into certain polynomial spaces satisfying a commuting diagram property with norm bounds independent of the polynomial degree. Using the projectors, we obtain quasioptimality of some spectralmixed methods, including the Raviart–Thomas method and mixed formulations of Maxwell equations. We also prove some discrete Friedrichs type inequalities involving curl.

Fair-Weather Fans: The Correlation Between Attendance And Winning Percentage, Darren B. Glass

Math Faculty Publications

In Rob Neyer's chapter on San Francisco in his Big Book of Baseball Lineups, he speculates that there aren't really good baseball cities, and that attendance more closely correlates with winning percentage than with any other factor. He also suggests that a statistically minded person look at this. I took the challenge and have been playing with a lot of data.

Assessing Left-Handedness With Exact And Approximate Confidence Intervals Appropriate For Samples Of Different Sizes, Virginia Gardner

Honors Capstones

Capstone submitted as a graduation requirement for the BSU Honors Program.

A Unifying Field In Logics: Neutrosophic Logic Neutrosophy, Neutrosophic Set, Neutrosophic Probability (In Traditional Chinese), Florentin Smarandache, Feng Liu

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

Fixed Points Of Holomorphic Mappings For Domains In Banach Spaces, Lawrence A. Harris

Mathematics Faculty Publications

We discuss the Earle-Hamilton fixed-point theorem and show how it can be applied when restrictions are known on the numerical range of a holomorphic function. In particular, we extend the Earle-Hamilton theorem to holomorphic functions with numerical range having real part strictly less than 1. We also extend the Lumer-Phillips theorem estimating resolvents to dissipative holomorphic functions.

Stochastic 2-D Navier-Stokes Equation, J. L. Menaldi, S. S. Sritharan

Mathematics Faculty Research Publications

In this paper we prove the existence and uniqueness of strong solutions for the stochastic Navier-Stokes equation in bounded and unbounded domains. These solutions are stochastic analogs of the classical Lions-Prodi solutions to the deterministic Navier-Stokes equation. Local monotonicity of the nonlinearity is exploited to obtain the solutions in a given probability space and this signi cantly improves the earlier techniques for obtaining strong solutions, which depended on pathwise solutions to the Navier-Stokes martingale problem where the probability space is also obtained as a part of the solution.

The Fine Structure Of The Kasparov Groups Ii: Topologizing The Uct, Claude Schochet

Mathematics Faculty Research Publications

The Kasparov Groups KK∗(A,B) have a natural structure as pseudopolonais groups. In this paper we analyze how this topology interacts with the terms of the Universal Coefficient Theorem (UCT) and the splitting sof the UCT constructed by J. Rosenberg and the author, as well as its canonical three term decomposition which exists under bootstrap hypotheses. We show that the various topologies on [cursive]Ext^{1}_{ℤ}(K∗(A),K∗(B)) and other related groups mostly coincide. Then we focus attention on the Milnor sequence and the fine structure subgroup of KK∗(A,B). …

Separable Preference Orders, Jonathan K. Hodge

Dissertations

Whenever a decision-maker must express simultaneously his or her preferences on several possibly related issues, the existence of interdependence among these preferences can lead to collective decisions that are unsatisfactory or even paradoxical. Intuitively, an individual’s preferences are said to be separable on a subset of issues if they do not depend on the choice of alternatives for issues outside the subset. Here we explore from a mathematical standpoint the properties of separable and nonseparable preference orders. We begin by formulating a general model of multidimensional preferences and we formally introduce the notions of separability and noninfluentiality. We study the …

Limits Highlights From Over 2000 Years Of Developments In Calculus Limits, Lauri A. Nevalainen

Honors Capstones

Capstone submitted as a graduation requirement for the BSU Honors Program.

The Evolution Of Cell Colonies In Volvocacean Algae : Investigation By Theoretical Analysis And Computer Simulation., Frank Noe

Theses

This thesis presents a mathematical analysis and computational simulation which is used to investigate the evolution of cell colonies. The evolutionary transition from unicellular to cell colony form is a prerequesite for multicellular life as it exists abundantly on earth. This transition has occured numerous times independently so that we expect a high selective advantage to be associated with it. The photosynthetic green algae order Volvocaceae is an appropriate set of model organisms for the study of the evolution of cell colonies since it comprises living unicellular organisms, cell colonies, and multicellular organisms of different shapes, sizes and levels of …

A Construction Of Compactly-Supported Biorthogonal Scaling Vectors And Multiwavelets On $R^2$, Bruce Kessler

Mathematics Faculty Publications

In \cite{K}, a construction was given for a class of orthogonal compactly-supported scaling vectors on $\R^{2}$, called short scaling vectors, and their associated multiwavelets. The span of the translates of the scaling functions along a triangular lattice includes continuous piecewise linear functions on the lattice, although the scaling functions are fractal interpolation functions and possibly nondifferentiable. In this paper, a similar construction will be used to create biorthogonal scaling vectors and their associated multiwavelets. The additional freedom will allow for one of the dual spaces to consist entirely of the continuous piecewise linear functions on a uniform subdivision of the …

On The Evolution Of Probability-Weighting Function And Its Impact On Gambling, Steven Li, Yun Hsing Cheung

Research outputs pre 2011

It is well known that individuals treat losses and gains differently and there exists non-linearity in probability. The asymmetry between gains and losses is highlighted by the reflection effect. The non-linearity in probability is described by the curvature of the probability-weighting function. This paper studies the evolution of the probability-weighting function. It is assumed that the probability weighting for an individual follows a mean-reverting stochastic process. The Monte Carlo simulation technique is employed to study the evolution of the weighting function. The evolution of the probability- weighting function implies that an individual does not treat gains or losses consistently over …

Heckman's Methodology For Correcting Selectivity Bias : An Application To Road Crash Costs, Margaret Giles

Research outputs pre 2011

Aggregate road crash costs are traditionally determined using average costs applied to incidence figures found in Police-notified crash data. Such data only comprise a non-random sample of the true population of road crashes, the bias being due to the existence of crashes that are not notified to the Police. The traditional approach is to label the Police-notified sample as 'non-random' thereby casting a cloud over data analyses using this sample. Heckman however viewed similar problems as 'omitted variables' problems in that the exclusion of some observations in a systematic manner (so-called selectivity bias) has inadvertently introduced the need for an …

Algebra În Exercijii Şi Probleme Pentru Liceu, Florentin Smarandache, Ion Goian, Raisa Grigor, Vasila Marin

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

Mortar Estimates Independent Of Number Of Subdomains, Jay Gopalakrishnan

Mathematics and Statistics Faculty Publications and Presentations

The stability and error estimates for the mortar finite element method are well established. This work examines the dependence of constants in these estimates on shape and number of subdomains. By means of a Poincar´e inequality and some scaling arguments, these estimates are found not to deteriorate with increase in number of subdomains.

Multigrid For The Mortar Finite Element Method, Jay Gopalakrishnan, Joseph E. Pasciak

Mathematics and Statistics Faculty Publications and Presentations

A multigrid technique for uniformly preconditioning linear systems arising from a mortar finite element discretization of second order elliptic boundary value problems is described and analyzed. These problems are posed on domains partitioned into subdomains, each of which is independently triangulated in a multilevel fashion. The multilevel mortar finite element spaces based on such triangulations (which need not align across subdomain interfaces) are in general not nested. Suitable grid transfer operators and smoothers are developed which lead to a variable Vcycle preconditioner resulting in a uniformly preconditioned algebraic system. Computational results illustrating the theory are also presented.

Invariant Measure For Diffusions With Jumps, Jose-Luis Menaldi, Maurice Robin

Mathematics Faculty Research Publications

Our purpose is to study an ergodic linear equation associated to diffusion processes with jumps in the whole space. This integro-differential equation plays a fundamental role in ergodic control problems of second order Markov processes. The key result is to prove the existence and uniqueness of an invariant density function for a jump diffusion, whose lower order coefficients are only Borel measurable. Based on this invariant probability, existence and uniqueness (up to an additive constant) of solutions to the ergodic linear equation are established.

Elementary Inversion Of The Laplace Transform, Kurt M. Bryan

Mathematical Sciences Technical Reports (MSTR)

This paper provides an elementary derivation of a very simple "closed-form"

inversion formula for the Laplace Transform.

Asupra Unor Noi Functii În Teoria Numerelor, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Performantele matematicii actuale,ca si descoperirile din viitor isi au,desigur, inceputul in cea mai veche si mai aproape de filozofie ramura a matematicii, in teoria numerelor. Matematicienii din toate timpurile au fost, sunt si vor fi atrasi de frumusetea si varietatea problemelor specifice acestei ramuri a matematicii. Regina a matematicii, care la randul ei este regina a stiintelor, dupa cum spunea Gauss, teoria numerelor straluceste cu lumina si atractiile ei, fascinandu-ne si usurandu-ne drumul cunoasterii legitatilor ce guverneaza macrocosmosul si microcosmosul. De la etapa antichitatii, cand teoria numerelor era cuprinsa in aritmetica, la etapa aritmeticii superioare din perioada Renasterii, cand teoria …

Subiecte Posibile Pentru Examenul De Admitere În Liceu Şi Examenul De Capacitate (In Romanian), Florentin Smarandache, Constantin Coanda, Gheorghe Duta

Branch Mathematics and Statistics Faculty and Staff Publications

Prezenta lucrare" încearcă să pună la dispoziţia elevilor şi profesorilor instrumente de evaluare a cunoştinţelor la toate capitolele din actuala programă de matematică. " În evoluţia adolescenţi/or din ţara noastră etapa admiterii în liceu mobilizează eforturi şi emoţii cu totul speciale. 'Actuala lucrare se doreşte a fi un sfljtuitor permanent În perioada fierbinte dintre e.;wmenul de capacitate şi admiterea În liceu. Testele cuprinse in această culegere au un caracter complementar faţă de multe materiale scrise În vederea sprijinirii celor ce se pregătesc pentru astfel de examene şi se referă la intreaga materie cuprinsă În programele analitice de aritmetică, algebră şi …

Infinite-Dimensional Hamilton-Jacobi-Bellman Equations In Gauss-Sobolev Spaces, Pao-Liu Chow, Jose-Luis Menaldi

Mathematics Faculty Research Publications

We consider the strong solution of a semi linear HJB equation associated with a stochastic optimal control in a Hilbert space H: By strong solution we mean a solution in a L²(μ,H)-Sobolev space setting. Within this framework, the present problem can be treated in a similar fashion to that of a finite-dimensional case. Of independent interest, a related linear problem with unbounded coefficient is studied and an application to the stochastic control of a reaction-diffusion equation will be given.

Diagonal Operators, S-Numbers, And Bernstein Pairs, Asuman Güven Aksoy, Grzegorz Lewicki

CMC Faculty Publications and Research

Replacing the nested sequence of ''finite" dimensional subspaces by the nested sequence of "closed" subspaces in the classical Bernstein lethargy theorem, we obtain a version of this theorem for the space B(X , Y) of all bounded linear maps. Using this result and some properties of diagonal operators, we investigate conditions under which a suitable pair of Banach spaces form an exact Bernstein pair.We also show that many "classical" Banach spaces, including the couple (L_p [O, 1] , L_q[O, 1]) form a Bernstein pair with respect to any sequence of s-numbers (s_n) ,for 1 < p < ∞ and 1 ≤ q < ∞ …