Mathematics Commons^™

A Model For Radiation Interactions With Matter, Carrie Beck

Senior Honors Theses and Projects

The intent of this project is to derive a realistic mathematical model for radiation interactions with matter. The model may be solved analytically, but I will also employ two computational methods, a finite difference method and a stochastic (Monte Carlo) method to gain insight into the physical process and to test the numerical techniques. Radiation interactions with matter constitute a large number of important scientific, industrial, and medical applications. This project will derive a model for the interaction of radiation with matter, which might allow one to compare different designs for shielding. It is also applicable in atmospheric physics in …

Blowup And Dissipation In A Critical-Case Unstable Thin Film Equation, Thomas P. Witelski, Andrew J. Bernoff, Andrea L. Bertozzi

All HMC Faculty Publications and Research

We study the dynamics of dissipation and blow-up in a critical-case unstable thin film equation. The governing equation is a nonlinear fourth-order degenerate parabolic PDE derived from a generalized model for lubrication flows of thin viscous fluid layers on solid surfaces. There is a critical mass for blow-up and a rich set of dynamics including families of similarity solutions for finite-time blow-up and infinite-time spreading. The structure and stability of the steady-states and the compactly-supported similarity solutions is studied.

Semilinear Equations With Discrete Spectrum, Alfonso Castro

All HMC Faculty Publications and Research

This is an overview of the solvability of semilinear equations where the linear part has discrete spectrum. Semilinear elliptic and hyperbolic equations, as well as Hammerstein integral equations, are used as motivating examples. The presentation is intended to be accessible to non experts.

An Existence Result For A Class Of Sublinear Semipositone Systems, Alfonso Castro, C. Maya, Ratnasingham Shivaji

All HMC Faculty Publications and Research

We consider the existence of positive solutions for the system

-Δu_i = λ[f_i(u₁,u₂,...,u_m) - h_i]; Ω

u_i = 0; ∂Ω

where λ > 0 is a parameter, Δ is the Laplacian operator, Ω is a bounded domain in Rⁿ; n ≥ 1 with a smooth boundary ∂Ω, f_i are C¹ functions satisfying f₁(0,0,...,0) = 0, lim z→∞ f_i(z,z,...,z) = ∞ and lim z→∞ f_i(z,z,...,z)/z = 0, and h_i are nonnegative continuous functions in Ω for i = 1,2,...,m. …

Random Walks With Badly Approximable Numbers, Doug Hensley, Francis Su

All HMC Faculty Publications and Research

Using the discrepancy metric, we analyze the rate of convergence of a random walk on the circle generated by d rotations, and establish sharp rates that show that badly approximable d-tuples in Rd give rise to walks with the fastest convergence.

Book Review: Differential Equations And Mathematical Biology, D.S. Jones, B.D. Sleeman, In: Crc Mathematical Biology And Medicine Series. Chapman & Hall (2003), Hardback, 408 Pages, $79.95, Isbn: 1584882964, Christopher Kribs

Mathematics Faculty Publications - Archive

No abstract provided.

Effects Of Education, Vaccination And Treatment On Hiv Transmission In Homosexuals With Genetic Heterogeneity, Christopher Kribs, Sara Del Valle, Arlene Morales Evangelista, Maria Cristina Velasco, Shu-Fang Hsu Schmitz

Mathematics Faculty Publications - Archive

Genetic studies report the existence of a mutant allele Δ32 of CC R5 chemokine receptor gene at high allele frequencies ( 10%) in Caucasian populations. The presence of the allele is believed to provide partial or full resistance to HIV. In this study, we look at the impact of education, temporarily effective vaccines and therapies on the dynamics of HIV in homosexually active populations. In our model, it is assumed that some individuals possess one or two mutant alleles (like Δ32 of CCR5) that prevent the successful invasion or replication of HIV. Our model therefore differentiates by genetic and epidemiological …

Residues And Tame Symbols On Toroidal Varieties, Ivan Soprunov

Mathematics and Statistics Faculty Publications

We introduce a new approach to the study of a system of algebraic equations in (C) whose Newton polytopes have sufficiently general relative positions. Our method is based on the theory of Parshin’s residues and tame symbols on toroidal varieties. It provides a uniform algebraic explanation of the recent result of Khovanskii on the product of the roots of such systems and the Gel’fond–Khovanskii result on the sum of the values of a Laurent polynomial over the roots of such systems, and extends them to the case of an algebraically closed field of arbitrary characteristic.

Approximation For The Expectation Of A Function Of The Sample Mean, Rasul A. Khan

Mathematics and Statistics Faculty Publications

Let X¯ n be the mean of a random sample of size n from a distribution with mean μ and variance σ2. Under some conditions it is shown that Ef(X¯ n ) = f(μ) + (σ2/2n) f″(μ) + O(n −2), and var(f(X¯ n )) = (σ2/n) (f′(μ))2 + O(n −2), where f is a continuous function with a suitable growth condition. This complements a result of Lehmann [(1991). Theory of Point Estimation. Wadsworth, California] and Cramér [(1946). Mathematical Methods of Statistics. Princeton University Press, Princeton, N.J.] for wider application. An illustrative example is given to show an application where the …

A Furi-Pera Theorem In Hausdorff Topological Spaces For Acyclic Maps, Ravi P. Agarwal, Donal O'Regan, Jewgeni H. Dshalalow

Mathematics and System Engineering Faculty Publications

We present new Furi-Pera theorems for acyclic maps between topological spaces.

Preface, Thomas Hildebrandt, Alexander Kurz

Engineering Faculty Articles and Research

No abstract provided.

Practical Approach To Incorporating Maple Into The Finite Mathematics Course: 3 Modules And 8 Case Studies, Jonica Helene Craft-Mcbride

Masters Theses

No abstract provided.

Cyclic Rings, Warren K. Buck

Masters Theses

No abstract provided.

Quantization With Knowledge Base Applied To Geometrical Nesting Problem, Grzegorz Chmaj, Leszek Koszalka

Electrical & Computer Engineering Faculty Research

Nesting algorithms deal with placing two-dimensional shapes on the given canvas. In this paper a binary way of solving the nesting problem is proposed. Geometric shapes are quantized into binary form, which is used to operate on them. After finishing nesting they are converted back into original geometrical form. Investigations showed, that there is a big influence of quantization accuracy for the nesting effect. However, greater accuracy results with longer time of computation. The proposed knowledge base system is able to strongly reduce the computational time.

Pencils Of Quadratic Forms Over Finite Fields, Robert W. Fitzgerald, Joseph L. Yucas

Articles and Preprints

A formula for the number of common zeros of a non-degenerate pencil of quadratic forms is given. This is applied to pencils which count binary strings with an even number of 1's prescribed distances apart.

The Linking Homomorphism Of One-Dimensional Minimal Sets, Alex Clark, Michael C. Sullivan

Articles and Preprints

We introduce a way of characterizing the linking of one-dimensional minimal sets in three-dimensional flows and carry out the characterization for some minimal sets within flows modeled by templates, with an emphasis on the linking of Denjoy continua. We also show that any aperiodic minimal subshift of minimal block growth has a suspension which is homeomorphic to a Denjoy continuum.

Fixed Point Theorems For Infinite Dimensional Holomorphic Functions, Lawrence A. Harris

Mathematics Faculty Publications

This talk discusses conditions on the numerical range of a holomorphic function defined on a bounded convex domain in a complex Banach space that imply that the function has a unique fixed point. In particular, extensions of the Earle-Hamilton Theorem are given for such domains. The theorems are applied to obtain a quantitative version of the inverse function theorem for holomorphic functions and a distortion form of Cartan's uniqueness theorem.

Conjugacy Classes Of Finite Subgroups Of Certain Mapping Class Groups, Michal Stukow

Turkish Journal of Mathematics

We give a complete description of conjugacy classes of finite subgroups of the mapping class group of the sphere with r marked points. As a corollary we obtain a description of conjugacy classes of maximal finite subgroups of the hyperelliptic mapping class group. In particular, we prove that, for a fixed genus g, there are at most five such classes.

Moments Equalities For Nonnegative Integer-Valued Random Variables, Mohamed I. Riffi

Turkish Journal of Mathematics

We present and prove two theorems about equalities for the nth moment of nonnegative integer-valued random variables. These equalities generalize the well known equality for the first moment of a nonnegative integer-valued random variable X in terms of its cumulative distribution function, or in terms of its tail distribution.

The Theory Of Jacobi Systems And Their Abelian Representations, M. Shahryari, Y. Zamani

Turkish Journal of Mathematics

In this article we introduce a new generalization of the concept of Lie ring which we call Jacobi system and we investigate some elementary properties of these systems and their Abelian representations.

On \Theta-Euclidean L-Fuzzy Ideals Of Rings, Ayten Koç, Erol Balkanay

Turkish Journal of Mathematics

In this paper we define a \theta-Euclidean level subset and a \theta-Euclidean level ideal. We also give some properties of a \theta-Euclidean level subset.

On The Power Subgroups Of The Extended Modular Group \Gamma, Recep Şahi̇n, Sebahatti̇n İki̇kardeş, Özden Koruoğlu

Turkish Journal of Mathematics

In this paper we describe the group structure of power subgroups \Gamma^m of the extended modular group \Gamma and the quotients to them. Then we give some relations between the power subgroups \Gamma^m, the commutator subgroups \Gamma^{\prime} and \Gamma^{\prime \prime} and also the information of interest about free normal subgroups of the extended modular group \Gamma.

New Special Curves And Developable Surfaces, Shyuichi Izumiya, Nobuko Takeuchi

Turkish Journal of Mathematics

We define new special curves in Euclidean 3-space which we call slant helices and conical geodesic curves. Those notions are generalizations of the notion of cylindrical helices. One of the results in this paper gives a classification of special developable surfaces under the condition of the existence of such a special curve as a geodesic. As a result, we consider geometric invariants of space curves. By using these invariants, we can estimate the order of contact with those special curves for general space curves. All arguments in this paper are straight forward and classical. However, there have been no papers …

Modules Supplemented Relative To A Torsion Theory, M. Tamer Koşan, Abdullah Harmanci

Turkish Journal of Mathematics

This article introduces the concept of a \tau-supplemented module as follows: Given a hereditary torsion theory in Mod R with associated torsion functor \tau, we say that a module M is \tau-supplemented when for every submodule N of M there exists a direct summand K of M such that K\leq N and N/K is \tau-torsion module. We present here some fundamental properties of this class of modules and study the decompositions of \tau-supplemented modules under certain conditions on modules. The question of which direct sum of \tau-supplemented R-modules are \tau-supplemented is treated here.

Groups With Rank Restrictions On Non-Subnormal Subgroups, Leonid Andreevich Kurdachenko, Howard Smith

Turkish Journal of Mathematics

Let G be a group in which every non-subnormal subgroup has finite rank. This paper considers the question as to which extra conditions on such a group G ensure that G has all subgroups subnormal. For example, if G is torsion-free and locally soluble-by-finite then either G has finite 0-rank or G is nilpotent. Several results are obtained on soluble (respectively, locally soluble-by-finite) groups satisfying the stated hypothesis on subgroups.

On Orthogonal Generalized Derivations Of Semiprime Rings, Nurcan Argaç, Atsushi Nakajima, Emi̇ne Albaş

Turkish Journal of Mathematics

In this paper, we present some results concerning two generalized derivations on a semiprime ring. These results are a generalization of results of M. Bre\u{s}ar and J. Vukman in [2], which are related to a theorem of E. Posner for the product of derivations on a prime ring.

On Near-Rings With Two-Sided \Alpha-Derivations, Nurcan Argaç

Turkish Journal of Mathematics

In this paper, we introduce the notion of two-sided \alpha-derivation of a near-ring and give some generalizations of [1]. Let N be a near ring. An additive mapping f: N\rightarrow N is called an { \it (\alpha, \beta)-derivation } if there exist functions \alpha,\beta : N\rightarrow N such that f(xy)=f(x)\alpha(y)+\beta (x)f(y) for all x,y\in N. An additive mapping d:N\rightarrow N is called a two-sided \alpha-derivation if d is an (\alpha,1)-derivation as well as a (1,\alpha)-derivation. The purpose of this paper is to prove the following two assertions: (i) Let N be a semiprime near-ring, I be a subset of N …

Ideal Theory In Topological Algebras, A. Najmi

Turkish Journal of Mathematics

Given a simplicial topologically non radical algebra A, we characterize its topological radical, radA. If furthermore A is advertive, then radA coincides with the Jacobson radical RadA. On the other hand, it is shown that every two-sided invertive simplicial topological Gelfand-Mazur algebra has a functional spectrum and for every topologically nonradical simplicial Gelfand-Mazur amits the set \mathcal{X}(A), of all continuous multiplicative linear functionals, is not empty.

On Simultaneous Approximation By A Linear Combination Of A New Sequence Of Linear Positive Operators, P. N. Agrawal, Ali J. Mohammad

Turkish Journal of Mathematics

In [1] we introduced a new sequence of linear positive operators M_{n} to approximate unbounded continuous functions of exponential growth on [0,\infty). As this sequence is saturated with O(n^{-1}), to accelerate the rate of convergence we applied the technique of linear combination introduced by May [3] and Rathore et al. [4] to these operators. The object of the present paper is to study the phenomena of simultaneous approximation (approximation of derivatives of functions by the corresponding order derivatives of operators) by the linear combination M_{n} ( . , k, x) of M_{n}. First, we establish a Voronovskaja-type asymptotic formula and …

Coisotropic Submanifolds Of A Semi-Riemannian Manifold, Erol Kiliç, Bayram Şahi̇n, H. B. Karadağ, R. Güneş

Turkish Journal of Mathematics

In this paper, we study coisotropic submanifolds of a semi-Riemannian manifold. We investigate the integrability condition of the screen distribution and give a necessary and sufficient condition on Ricci tensor of a coisotropic submanifold to be symmetric. Finally, we present some new theorems and results about totally umbilical coisotropic submanifolds of a semi-Riemannian manifold