Mathematics Commons^™

On Well-Posedness, Stability, And Bifurcation For The Axisymmetric Surface Diffusion Flow, Jeremy Lecrone, Gieri Simonett

Department of Math & Statistics Faculty Publications

We study the axisymmetric surface diffusion (ASD) flow, a fourth-order geometric evolution law. In particular, we prove that ASD generates a real analytic semiflow in the space of (2+α)-little-Holder regular surfaces of revolution embedded in R3 and satisfying periodic boundary conditions. Further, we investigate the geometric properties of solutions to ASD. Utilizing a connection to axisymmetric surfaces with constant mean curvature, we characterize the equilibria of ASD. Then, focusing on the family of cylinders, we establish results regarding stability, instability, and bifurcation behavior, with the radius acting as a bifurcation parameter.

Truncated Toeplitz Operators And Boundary Values In Nearly Invariant Subspaces, William T. Ross, Andreas Hartmann

Department of Math & Statistics Faculty Publications

We consider truncated Toeplitz operator on nearly invariant subspaces of the Hardy space H². Of some importance in this context is the boundary behavior of the functions in these spaces which we will discuss in some detail.

On A Theorem Of Livsic, William T. Ross, Alexandru Aleman, R. T. W. Martin

Department of Math & Statistics Faculty Publications

The theory of symmetric, non-selfadjoint operators has several deep applications to the complex function theory of certain reproducing kernel Hilbert spaces of analytic functions, as well as to the study of ordinary differential operators such as Schrodinger operators in mathematical physics. Examples of simple symmetric operators include multiplication operators on various spaces of analytic functions such as model subspaces of Hardy spaces, deBranges-Rovnyak spaces and Herglotz spaces, ordinary differential operators (including Schrodinger operators from quantum mechanics), Toeplitz operators, and infinite Jacobi matrices.

In this paper we develop a general representation theory of simple symmetric operators with equal deficiency indices, and …

Recent Progress On Truncated Toeplitz Operators, William T. Ross, Stephan Ramon Garcia

Department of Math & Statistics Faculty Publications

This paper is a survey on the emerging theory of truncated Toeplitz operators. We begin with a brief introduction to the subject and then highlight the many recent developments in the field since Sarason’s seminal paper [88] from 2007.

Reverse Carleson Embeddings For Model Spaces, William T. Ross, Alain Blandigneres, Emmanuel Fricain, Frederic Gaunard, Andreas Hartmann

Department of Math & Statistics Faculty Publications

The classical embedding theorem of Carleson deals with finite positive Borel measures μ on the closed unit disk for which there exists a positive constant c such that for all f∈H², the Hardy space of the unit disk. Lefèvre et al. examined measures μ for which there exists a positive constant c such that for all f∈H². The first type of inequality above was explored with H² replaced by one of the model spaces (Θ H²)^⊥ by Aleksandrov, Baranov, Cohn, Treil, and Vol'berg. In this paper, we discuss …

An Extremal Problem For Characteristic Functions, William T. Ross, Isabelle Chalendar, Stephan Ramon Garcia, Dan Timotin

Department of Math & Statistics Faculty Publications

Suppose E is a subset of the unit circle T and H^∞C L^∞ is the Hardy subalgebra. We examine the problem of Finding the distance from the characteristic function of E to zⁿ H^∞. This admits an alternate description as a dual extremal problem. Precise solutions are given in several important cases. The techniques used involve the theory of Toeplitz and Hankel operators as well as the construction of certain conformal mappings.

A Single-Parameter Model Of The Immune Response To Bacterial Invasion, Lester Caudill

Department of Math & Statistics Faculty Publications

The human immune response to bacterial pathogens is a remarkably complex process, involving many different cell types, chemical signals, and extensive lines of communication. Mathematical models of this system have become increasingly high-dimensional and complicated, as researchers seek to capture many of the major dynamics. In this paper, we argue that, in some important instances, preference should be given to low-dimensional models of immune response, as opposed to their high-dimensional counterparts. One such model is analyzed and shown to reflect many of the key phenomenological properties of the immune response in humans. Notably, this model includes a single parameter values, …

Characterizations Of Exponentiated Distributions, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

Various characterizations of the class of exponentiated distributions are presented. These characterizations are based on a simple relationship between two truncated moments and based on functions of the nth order statistic. The results are applied to certain well-known members of this class.

Some Remarks On Arslan’S 2011 Paper, Gholamhossein Hamedani, Hans Volkmer

Mathematics, Statistics and Computer Science Faculty Research and Publications

It is shown that the main theorem of Arslan’s paper (Theorem 2, 2011), as stated, is incorrect. Under additional conditions, we present a short proof of the corrected version of the theorem. We also give a proof of a theorem of Rao and Shanbhag (1991), employed by Arslan, without the use of the Kolmogorov Consistency Theorem.

Probability Inequalities For The Sum Of Random Variables When Sampling Without Replacement, Jeremy Becnel, Kent Riggs, Dean Young

Faculty Publications

Exponential-type upper bounds are formulated for the probability that the maximum of the partial sample sums of discrete random variables having finite equispaced support exceeds or differs from the population mean by a specified positive constant. The new inequalities extend the work of Serfling (1974). An example of the results are given to demonstrate their efficacy.

C.P. Modules And Their Applications, Qiongling Liu, Jianlong Chen

Turkish Journal of Mathematics

Let R be a ring. A left R-module M is called a c.p. module if every cyclic submodule of M is projective. This notion is a generalization of left p.p. rings in the general module theoretic setting. The aim of this article is to investigate these modules. Some characterizations and properties are given. As applications, the connections among Baer rings, p.p. rings and von Neumann regular rings are studied.

A Nonlocal Parabolic Problem In An Annulus For The Heaviside Function In Ohmic Heating, Fei Liang, Hongjun Gao, Charles Bu

Turkish Journal of Mathematics

In this paper, we consider the nonlocal parabolic equation u_t=\Delta u+\frac{\lambda H(1-u)}{\big(\int_{A_{\rho, R}} H(1-u)dx\big)^2}, x\in A_{\rho, R} \subset R^2, t>0, with a homogeneous Dirichlet boundary condition, where \lambda is a positive parameter, H is the Heaviside function and A_{\rho, R} is an annulus. It is shown for the radial symmetric case that: there exist two critical values \lambda_* and \lambda^*, so that for 0

Braiding For Internal Categories In The Category Of Whiskered Groupoids And Simplicial Groups, Erdal Ulualan, Sedat Pak

Turkish Journal of Mathematics

In this work, we define the notion of `braiding' for an internal groupoid in the category of whiskered groupoids and we give a relation between this structure and simplicial groups by using higher order Peiffer elements in the Moore complex of a simplicial group.

Generalized Class Invariants With `Thetanullwerte\', Osmanbey Uzunkol

Turkish Journal of Mathematics

We introduce generalized class invariants as quotients of Thetanullwerte, which realize the computation of class polynomials more efficiently than as quotients of values of the Dedekind \eta-function. Furthermore, we prove that these invariants are units in the corresponding class field as most of their classical counterparts.

Generalized Derivations Of Prime Rings On Multilinear Polynomials With Annihilator Conditions, Nurcan Argaç, Çağri Demi̇r

Turkish Journal of Mathematics

Let K be a commutative ring with unity, R be a prime K-algebra with characteristic not 2, U be the right Utumi quotient ring of R, C the extended centroid of R, I a nonzero right ideal of R and a a fixed element of R. Let g be a generalized derivation of R and f(X_1,..., X_n) a multilinear polynomial over K. If ag(f(x_1,...,x_n))f(x_1,...,x_n)=0 for all x_1,...,x_n \in I, then one of the following holds: (1) aI=ag(I)=0; (2) g(x)=bx+[c,x] for all x\in R, where b,c\in U. In this case either [c,I]I=0=abI or aI=0=a(b+c)I; (3) [f(X_1,...,X_n),X_{n+1}]X_{n+2} is an identity for I.

Derived And Residual Sylvester-Hadamard Designs And The Smith Normal Form, İlhan Hacioğlu

Turkish Journal of Mathematics

We computed the Smith normal form of Sylvester-Hadamard designs and its complement, their derived and residual Sylvester-Hadamard designs and their complementary derived and residual Sylvester-Hadamard designs.

Growth And Distortion Theorems For Multivalent Janowski Close-To-Convex Harmonic Functions With Shear Construction Method, Yaşar Polatoğlu, Hati̇ce Esra Özkan, Emel Yavuz Duman

Turkish Journal of Mathematics

In this paper we introduce the class of m-valent Janowski close to convex harmonic functions. Growth and distortion theorems are obtained for this class. Our study is based on the harmonic shear methods for harmonic functions.

Half Inverse Problem For Sturm-Liouville Operators With Boundary Conditions Dependent On The Spectral Parameter, Yuping Wang, Chuan Fu Yang, Zhenyou Huang

Turkish Journal of Mathematics

In this paper, we discuss the half inverse problem for the Sturm-Liouville operator with boundary conditions dependent on the spectral parameter and show that if q(x) is prescribed on [\frac{\pi}{2},\pi], then one spectrum is sufficient to determine the potential q(x) on the whole interval [0,\pi] and coefficient function \frac{a_1\lambda+b_1}{c_1\lambda+d_1} of the boundary condition.

Blow-Up Phenomena For Nonlocal Inhomogeneous Diffusion Problems, Jianwen Sun, Feiying Yang

Turkish Journal of Mathematics

This paper is concerned with the blow-up of solutions to some nonlocal inhomogeneous dispersal equations subject to homogeneous Neumann boundary conditions. We establish conditions on nonlinearities sufficient to guarantee that solutions exist for all time as well as blow up at some finite time. Moreover, lower bounds for blow-up time of nonlocal problems are obtained.

Lie Groupoids And Generalized Almost Paracomplex Manifolds, Fulya Şahi̇n, Mustafa Habi̇l Gürsoy, İlhan İçen

Turkish Journal of Mathematics

In this paper, we show that there is a close relationship between generalized paracomplex manifolds and Lie groupoids. We obtain equivalent assertions among the integrability conditions of generalized almost paracomplex manifolds, the condition of compatibility of source and target maps of symplectic groupoids with symplectic form and generalized paraholomorphic maps.