Physical Sciences and Mathematics Commons^™

A Quadratic Volterra Integral Equation And Its Solution For Various Kernels, Merlynd K. Nestell, Mostafa Ghandehari

Mathematics Technical Papers

Consider the Volterra integral equation [see pdf for notation], ^ is a parameter Solutions of this equation are discussed for separable and difference kernels using Laplace transform and differential equation techniques. Existence and uniqueness questions are explored for various assumptions on the kernel.

Steiner Trees Over Generalized Checkerboards, Meta M. Voelker '97

Honors Projects

To minimize the length of a planar network, we can build a Steiner minimal tree that is, a tree consisting of the original network points, as well as additional, strategically-placed (Steiner) points. Chung, Gardner and Graham [2] investigated building Steiner trees over grids of unit squares. We generalize their ideas to grids of rhombuses, and show that two near-optimal Steiner trees exist for each grid, one built from Steiner trees over rhombuses and one built from Steiner trees over isosceles triangles. Further, we conjecture that for grids with an odd number of layers, only the small angle of the rhombus …

Irreducible K-To-1 Maps Onto Grids, Susan M. Parker

Honors Theses

In this paper we explore the existence of exactly k-to-1 continuous functions between graphs, and more specifically 2-to-1 continuous function between graphs that are irreducibly 2-to-1, meaning that no restriction of the function to a subgraph is 2-to-l. We show how to construct such functions in some general cases, and then more specifically onto rectangular grids. We have in mind an application to distributed networks and signal verification.

An Introduction To Topological Quantum Field Theories, Michael Atiyah

Turkish Journal of Mathematics

No abstract provided.

Augmented Graded Rings, Mashhoor Refai

Turkish Journal of Mathematics

In this paper we study the augmented graded rings and give the ralationship between these rings and stronger properties of graded rings.

On Some Bounds For The Solutions Of The Semi-Discretized Time-Dependent Ginzburg-Landau Equations, Erhan Coşkun

Turkish Journal of Mathematics

We study the two-dimensional system of Time-Dependent Ginzburg-Landau Equations (TDGL) for modeling a thin film of superconductor subject to a uniform magnetic field. We discretize the TDGL for the space variables using bond variables and staggered grid partitioning technique. By investigating the temporal evolution of semi-discrete Helmholtz enery functional and that of Semi-discretized TDGL, we provide bounds for some observable physical quantities of interest such as superelectron density, supercurrent density, charge density, electric field, and induced magnetic field.

A Lower Bound Of The First Eigenvalue Of Certain Self-Adjoint Elliptic Operators On Manifolds Containing Long Necks, Weimin Chen

Turkish Journal of Mathematics

In this note, under certain regularity and transversality conditions we obtain a sharp lower bound of the first eigenvalue for certain self-adjoint elliptic operators on manifolds with long necks. This result is used in the gluing construction of 3-dimensional Seiberg-Witten moduli spaces along T^2. See [C1], [C2].

Kirby Calculus In Manifolds With Boundary, Justin Roberts

Turkish Journal of Mathematics

Suppose there are two framed links in a compact, connected 3-manifold (possibly with boundary, or non-orientable) such that the associated 3-manifolds obtained by surgery are homeomorphic (relative to their common boundary, if there is one.) How are the links related? Kirby's theorem gives the answer when the manifold is S^3, and Fenn and Rourke extended it to the case of any closed orientable 3-manifold, or S^1 \tilde{\times} S^2. The purpose of this note is to give the answer in the general case, using only minor modifications of Kirby's original proof.

The Rank And The Crank Modulo 5, A. Bülent Eki̇n

Turkish Journal of Mathematics

Let p(n) denote the number of partitions of n . Ramanujan's partition congruences are p(5n + 4) , p(7n + 5) and p(11n + 6) = mod 5, 7, and 11, respectively. These have been proved in number of ways. Atkin and Swinnerton-Dyer proved the congruences and some more relations about partition İn the case of mod5 and 7 in terms of rank, Garvan proved them in three cases in terms of crank. In this study, we give an another proof of their results in the case of mod5 by using the theory of modular forms. Although our method is …

On The Stability Results For Third Order Differential-Operator Equations, Varga Kalantarov, Aydın Ti̇ryaki̇

Turkish Journal of Mathematics

Sufficient conditions for the stability and the global asymptotic stability of the zero solution of third order linear differential- operator equations are established.

The Spectra And Fine Spectra For P-Cesáro Operators, Cafer Coşkun

Turkish Journal of Mathematics

In [6], Rhaly computed the spectrum of p-Cesaro operator on the Hilbert space l_2 = {x = (x_k): \Sigma_k IX_kl^2 < infinite}. In the present paper, we study the spectrum and fine spectrum for p-Cesáro operators acting on C_o, the space of null sequences.

An Application Of Monodromy Groupoid, Osman Mucuk

Turkish Journal of Mathematics

The monodromy groupoid was first inlioduced by Pradines in [7] and developed by Mucuk in [6] In this paper we give an application of the monodromy groupoid.

On A Generalisation Of Lie Ideals In Prime Rings, Arif Kaya

Turkish Journal of Mathematics

Let R be a prime ring of characteristic 3, \sigma and \tau automorphisms of R, U a non zero ( \sigma, \tau) - Lie ideal of R, d a nonzero derivation of R such that \sigmad = d\sigma , \taud = d\tau,d(U) (bak) U, and d^2(U) (bak) Z, the center of R. Then we prove that U (bak) Z. This provides a proof of the Theorem in [4], when char R = 3.

On The Solution Of The E.P.D. Equation Using Finite Integral Transformations, Neşe Dernek

Turkish Journal of Mathematics

In this paper, a solution is given for the following initial boundary value problem: \Delta=u_{tt}+k/t+u_t+g(x, t) (t>0) u(0, t)=u(a, t)=0 u(x, 0)=f(x), u_t(x, 0)=0 where x, a \epsilon R^n, t is the time variable, k < 1, k ? -1, -2, -3, . . . is a real parameter, \Delta is the n dimensional Laplace operator, f and g real analytic functions. The equation in this problem is known as the nonhomogeneous Euler-Poisson-Darboux (E.P.D.) Equation. The solution is obtained using finite integral transformation technique and is the sum of two uniformly and absolutely convergent power series.

An Application Of Linear Topological Invariants, Bora Arslan, Mefharet Kocatepe

Turkish Journal of Mathematics

We consider a possible isomorphism of cartesian product of two Dragilev spaces of infinite type, and by making use of Zahariuta invariants and some structural properties, we show that if there is such an isomorphism, then any factor on the left is nearly isomorphic to the corresponding factor on the right. Key Words and Phrases: Linear topological invariants, Dragilev space, Dragilev function, rapidly increasing function.

Near Ultrafilters And Luc-Compactification Of Real Numbers, Mahmut Koçak

Turkish Journal of Mathematics

In this work we will investigate some of the topological properties of the Luc compactification of real numbers R in terms of the concept of near ultrafilters.

Casson's Invariant And Seiberg-Witten Gauge Theory, Weimin Chen

Turkish Journal of Mathematics

In this paper, the very first step is taken towards solving the recently proposed conjecture by Kronheimer and Mrowka [KM2] concerning the Casson's invariant of an oriented homology 3-sphere and its Seiberg-Witten Floer homology.

Pin-Structures On Surfaces And Quadratic Forms, A. Degtyarev, S. Finashin

Turkish Journal of Mathematics

A correspondence between various Pin-type structures on a compact surface and quadratic (Iinear) forms on its homology is constructed. Sum of structures is defined and expressed in terms of these quadratic forms and in terms of Whitney sum of Spin structures.

The Study Of The Level Zero Crossing Time Of A Semi-Markovian Random Walk With Delaying Screen, Tahir A. Khaniev, İhsan Ünver

Turkish Journal of Mathematics

In this study, a semi-Markovian random walk with delaying screen at (\beta > O and the first crossing time ('\gamma1) of the zero level of this process are constructed. Furthermore, the distribution function with its Laplace transform, expected value and variance of random variable (\gamma1) are calculated. In addition to these, a formula for the higher order moments of ('\gamma1) is given.

On Coincidence Points Of Densifying Mappings, M. S. Khan, Z. Q. Liu

Turkish Journal of Mathematics

A coincidence point theorem for anew class of densifying mappings is obtained. Our result generalizes many previously known theorems and can be regarded as an extension of Jungck's fixed point theorem for densifying mappings. Key words and phases: complete metric space, common fixed points, densifying mappings, commuting mappings.

Extension And Separation Of Vector Valued Functions, Zafer Ercan

Turkish Journal of Mathematics

It is proved that: If X is a paracompact Hausdorff space and E is a Frechet lattice then (X, E) has the separation property. This is employed to extend some varies of functions that are known for spaces of Banach lattice valued functions.

The Linear Mean Value Of The Remainder Term In The Problem Of Asymptotic Behavior Of Eigenfunctions Of The Automorphic Laplacian, Zernişan Emi̇rleroğlu

Turkish Journal of Mathematics

The purpose of this paper is to obtain the estimate for the average mean value of the remainder term of the asymptotic formula for the quadratic mean value of the Fourier coefficients of the eigenfunctions over the discrete spectrum of the automorphic Laplacian.

Immersions Preserved Under Rotations With Totally Reducible Focal Set, Rıdvan Ezentaş

Turkish Journal of Mathematics

In [1] Carter and the author introduced the idea of an immersion f : Mm-+ Rn with totally reducible focal set (TRFS). Such an immersion has the property that, for all p E M, the focal set with base p is a union of hyperplanes in the normal plane to f(M) at f(p) . Here we show that if we take two immersions with TRFS then we can construct new immersions with TRFS. In particular, rotating an immersion with TRFS about an axis gives anew immersion with TRFS.

On Univalent Functions With Three Preassigend Values, Y. Avci, E. Zlotkiewicz

Turkish Journal of Mathematics

In this paper, univalent functions with three preassigend values are studied. The sharp bounds for the first coefficient are obtained. Moreover, the coefficient problem for a subclass of such functions is completely solved.

On Ideals Of Prime Rings With (\Sigma, \Tau)- Derivations, Q. Deng, M. Ş. Yeni̇gül, N. Argaç

Turkish Journal of Mathematics

Let R be a prime ring. Let \sigma , \tau be two homomorphisms and d be a (\sigma,\tau)-derivation of R. The purpose of this paper is to prove two results: (i) If char R \neq 2, U is a non-zero ideal of R, \sigma is subjective such that \sigma (U) \neq 0, \tau is an automorphism and [d(U), d(U)]_{\sigma,\tau} = 0, then \sigma^2 = \tau^2 and \sigma \tau = \tau \sigma. (ii) Under the assumptions that either char R = 0 or char R > max {2,n}, U is a non-zero right ideal, and \sigma, \tau are automorphisms of R, suppose …

Discrete-Time Linear And Nonlinear Aerodynamic Impulse Responses For Efficient Cfd Analyses, Walter A. Silva

Dissertations, Theses, and Masters Projects

This dissertation discusses the mathematical existence and the numerical identification of linear and nonlinear aerodynamic impulse response functions. Differences between continuous-time and discrete-time system theories, which permit the identification and efficient use of these functions, will be detailed. Important input/output definitions and the concept of linear and nonlinear systems with memory will also be discussed. It will be shown that indicial (step or steady) responses (such as Wagner's function), forced harmonic responses (such as Theodorsen's function or those from doublet lattice theory), and responses to random inputs (such as gusts) can all be obtained from an aerodynamic impulse response function. …

Scattering From Stellar Acoustic-Gravity Potentials: Ii. Phase Shifts Via The First Born Approximation, J. A. Adam, I. Mckaig

Mathematics & Statistics Faculty Publications

Using the first Born approximation, properties of the scattering phase shift are investigated for waves that are scattered by a schematic representation of a large-scale “stellar potential,” i.e., one for which the star itself is viewed as the potential inducing a phase shift in an incoming wave. In particular, the phase shift properties are examined as functions of the relative wavenumber (α) and the azimuthal wavenumber (l), high l-values being of interest in helioseismology.

The Dynamics Of Phase Farming: A Mathematical Model Of Economic Aspects Of Switching Between Cropping And Land Rehabilitation, Tuyet Tran

Theses : Honours

In this thesis we consider the following problem: Suppose that a farmer wishes to determine the best course of action to maximise returns from his I her land which has undergone some form of degradation. In order to rehabilitate the land, the farmer may have to change to a different farming practice for some time until the previous practice becomes profitable again. Switching from cropping to rehabilitation Of from rehabilitation to cropping incurs costs. From an economical point of view, the question then arises: When is the optimal time to switch from cropping· to rehabilitation and when is it optimal …

Global Attractors From The Explosion Of Singular Cycles, Carlos Arnoldo Morales, Maria José Pacífico, Enrique Ramiro Pujals

Publications and Research

Abstract:

In this paper we announce recent results on the existence and bifurcations of hyperbolic systems leading to non-hyperbolic global attractors.

Résumé:

Nous présentons dans cette Note des résultats récents concernant l’existence et les bifurcations d’un nouvel attracteur global chaotique.

Characterizing Derivatives By Preimages Of Sets, Krzysztof Ciesielski

Faculty & Staff Scholarship

In this note we will show that many classes F of real functions f : R → R can be characterized by preimages of sets in a sense that there exist families A and D of subsets of R such that F = C(D, A), where C(D, A) = {f ∈ R R : f −1 (A) ∈ D for every A ∈ A}. In particular, we will show that there exists a Bernstein B ⊂ R such that the family ∆ of all derivatives can be represented as ∆ = C(D, A), where A = S c∈R {(−∞, c),(c, …