Mathematics Commons^™

A Borsuk-Ulak Theorem For Heisenberg Group Actions, Necdet Güner

Turkish Journal of Mathematics

Let $G=H_{2n+1}$ be a $(2n+1)$-dimensional Heisenberg Lie group acts on $M=C^m-\{0\}$ and $M^{'}=C^{m'}-\{0\}$ exponentially. By using Cohomological Index we proved the following theorem. If $f:M{\to}M^{'}$ is a $G$-equivariant map, then $m{\le}m'$.

On Conjugation In The Mod-P Steenrod Algebra, İsmet Karaca, İlkay Yaslan Karaca

Turkish Journal of Mathematics

In this paper we prove a formula involving the canonical anti-automorphism $\chi$ of the mod-$p$ Steenrod algebra.

On The Linearity Of Certain Mapping Class Groups, Mustafa Korkmaz

Turkish Journal of Mathematics

S. Bigelow proved that the braid groups are linear. That is, there is a faithful representation of the braid group into the general linear group of some field. Using this, we deduce from previously known results that the mapping class group of a sphere with punctures and hyperelliptic mapping class groups are linear. In particular, the mapping class group of a closed orientable surface of genus $2$ is linear.

On Subspaces Isomorphic To L^Q In Interpolation Of Quasi Banach Spaces, J. A. Lopez Molina

Turkish Journal of Mathematics

We show that every sequence $\{x_n\}_{n=1}^{\infty}$ in a real interpolation space $(E_0,E_1)_{\theta,q}$, $0 < \theta < 1$, $0 < q < \infty,$ of quasi Banach spaces $E_0,E_1,$ which is $0-$convergent in $E_0 + E_1$ but $\inf_n \;\ x_n\ _{(E_0,E_1)_{\theta,q}} > 0,$ has a subsequence which is equivalent to the standard unit basis of $\ell^q.$

The P-Stirling Numbers, Russel Merris

Turkish Journal of Mathematics

The purpose of this article is to introduce \( p \)-Stirling numbers of the first and second kinds.

Some Radius Problem For Certain Families Of Analytic Functions, Yaşar Polatoğlu, Meti̇n Bolcal

Turkish Journal of Mathematics

The aim of this paper is to give bounds of the radius of $\alpha $-convexity for certain families of analytic functions in the unit disc. The radius of $\alpha $-convexity is generalization of the radius of convexity and the radius of starlikeness, and introduced by S.S.Miller; P.T.Mocanu and M.O.Reade [3,4]

Nonstationary Panels, Cointegration In Panels And Dynamic Panels: A Survey, Badi H. Baltagi, Chihwa Kao

Center for Policy Research

This paper provides an overview of topics in nonstationary panels: panel unit root tests, panel cointegration tests, and estimation of panel cointegration models. In addition it surveys recent developments in dynamic panel data models.

Nonparametric Bayes Estimation Of Contamination Levels Using Observations From The Residual Distribution, Paul H. Kvam, Ram C. Tiwari, Jyoti N. Zalkikar

Department of Math & Statistics Faculty Publications

A nonparametric Bayes estimator of the survival function is derived for right censored data where additional observations from the residual distribution are available. The estimation is motivated by data on contamination concentrations for chromium from one of the EPA's toxic waste sites. The residual sample can be produced by hot spot sampling, where only samples above a given threshold value are collected. The Dirichlet process is used to formulate prior information about the chromium contamination, and we compare the Bayes estimator of the mean concentration level to other estimators currently considered by the EPA and other sources. The Bayes estimator …

About Non-Spherically Symmetric Deformations Of An Incompressible Neo-Hookean Sphere, Marek Elźanowski

Mathematics and Statistics Faculty Publications and Presentations

A class of non-spherically symmetric deformations of a neo-Hookean incompressible elastic ball is considered. It is shown that the only possible solution, the cavitated radially symmetric solution and the deformation of radial inflation and polar stretching. These are the same solutions as found by Polignone-Warne and Warne [6] for a smaller class of deformations. This fact shows once again that the radial deformations are the only deformations, at least within the class considered, which may support a formation of a cavity in the center of an incompressible, isotropic, elastic sphere.

Estimation Of A Monotone Mean Residual Life, Subhash C. Kochar, Hari Mukerjee, Francisco J. Samaniego

Mathematics and Statistics Faculty Publications and Presentations

In survival analysis and in the analysis of life tables an important biometric function of interest is the life expectancy at age x,M(x), defined by M(x)=E[X?x|X>x], where X is a lifetime. M is called the mean residual life function. In many applications it is reasonable to assume that M is decreasing (DMRL) or increasing (IMRL); we write decreasing (increasing) for nonincreasing (non-decreasing). There is some literature on empirical estimators of M and their properties. Although tests for a monotone M are discussed in the literature, we are not aware of any estimators of M under these order restrictions. In …

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.

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.

Tight Bounds On The Algebraic Connectivity Of A Balanced Binary Tree, Jason J. Molitierno, Michael Neumann, Bryan L. Shader

Mathematics Faculty Publications

In this paper, quite tight lower and upper bounds are obtained on the algebraic connectivity, namely, the second-smallest eigenvalue of the Laplacian matrix, of an unweighted balanced binary tree with k levels and hence n = 2^k - 1 vertices. This is accomplished by considering the inverse of a matrix of order k - 1 readily obtained from the Laplacian matrix. It is shown that the algebraic connectivity is 1/(2^k - 2k + 3) + 0(1/2^2k).

Student Solutions Manual For Elementary Differential Equations And Elementary Differential Equations With Boundary Value Problems, William F. Trench

Faculty Authored and Edited Books & CDs

This book was published previously by Brooks/Cole Thomson Learning.

This book has been judged to meet the evaluation criteria set by the Editorial Board of theAmerican Institute ofMathematics in connection with the Institute’s Open Textbook Initiative. It may be copied, modified, redistributed, translated, and built upon subject to the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

Oif Spaces, Zoltan Balogh, Harold Bennett, Dennis Burke, Gary Gruenhage, David Lutzer, Joe D. Mashburn

Mathematics Faculty Publications

A base β of a space X is called an OIF base when every element of B is a subset of only a finite number of other elements of β. We will explore the fundamental properties of spaces having such bases. In particular, we will show that in T2 spaces, strong OIF bases are the same as uniform bases, and that in T3 spaces where all subspaces have OIF bases, compactness, countable compactness, or local compactness will give metrizability.

Countable Positive Solutions Of A Conjugate Boundary Value Problem, Paul W. Eloe, Johnny Henderson, Nickolai Kosmatov

Mathematics Faculty Publications

In this paper we consider the conjugate type nonlinear boundary value problem (-1) n-k u (n) (t)=f(u(t)), 0

Directed Graphs, Stephen B. Maurer , '67

Mathematics & Statistics Faculty Works

No abstract provided.

Wavelet-Based Testing For Serial Correlation Of Unknown Form In Panel Models, Chihwa Kao

Center for Policy Research

Wavelet analysis is a new mathematical tool developed as a unified field of science over the last decade. As spatially adaptive analytic tools, wavelets are useful for capturing serial correlation where the spectrum has peaks or kinks, as can arise from persistent/strong dependence, seasonality or use of seasonal data such as quarterly and monthly data, business cycles, and other kinds of periodicity. This paper proposes a new class of wavelet-based tests for serial correlation of unknown form in the estimated residuals of an error component model, where the error components can be one-way or two-way, the individual and time effects …

Testing For Structural Change Of A Time Trend Regression In Panel Data, Jamie Emerson, Chihwa Kao

Center for Policy Research

In this paper we propose two classes of test statistics for detecting a break at an unknown date in panel data models with time trend. The first one is the fluctuation test of Ploberger-Kramer-Kontrus (1989). The second one is based on the mean and exponential Wald statistics of Andrew and Ploberger (1994) and maximum Wald statistic of Andrew (1993). We derive the limiting distributions of the proposed test and tabulate the critical values. Asymptotic results were derived I(0), I(1) and nearly I(1) error terms. We also show that these tests have non-trivial local power only when the error terms are …

Separation Property Of Solutions For A Semilinear Elliptic Equation, Yi Liu, Yi Li, Yinbin Deng

Mathematics and Statistics Faculty Publications

In this paper, we study the following elliptic problem[formula]where K(x) is a given function in C^α(ⁿ\0) for some fixed α∈(0, 1), p>1 is a constant. Some existence, monotonicity and asymptotic expansion at infinity of solutions of (*) are discussed.

Alternative Empirical Distributions Based On Weigted Linear Combinations Of Order Statistics, Theodore P. Hill, James Mann

Research Scholars in Residence

A class of empirical distributions is introduced which are based on various weighted linear combinations of order statistics, and which have convergence properties the classical empirical distribution does not, or which stochastically or convexly dominate the classical empirical distribution

State-Based Reconstructability Modeling For Decision Analysis, Michael S. Johnson, Martin Zwick

Complex Systems Faculty Publications and Presentations

Reconstructability analysis (RA) is a method for detecting and analyzing the structure of multivariate categorical data. Jones and his colleagues extended the original variable-based formulation of RA to encompass models defined in terms of system states (Jones 1982; Jones 1985; Jones 1985; Jones 1986; Jones 1989). In this paper, we demonstrate that Jones’ previous work comprises two separable ideas: the “g to k” transformation and state-based modeling. We relate the concept of state-based modeling to established variable-based RA methods (Klir 1985; Krippendorff 1986), and demonstrate that statebased modeling, when applied to event and decision tree models, is a valuable adjunct …

Small Combinatorial Cardinal Characteristics And Theorems Of Egorov And Blumberg, Krzysztof Ciesielski

Faculty & Staff Scholarship

We will show that the following set theoretical assumption

• \continuum=\omega₂, the dominating number d equals to \omega₁, and there exists an \omega₁-generated Ramsey ultrafilter on \omega

(which is consistent with ZFC) implies that for an arbitrary sequence f_n:R-->R of uniformly bounded functions there is a subset P of R of cardinality continuum and an infinite subset W of \omega such that {f_n|_P: n in W} is a monotone uniformly convergent sequence of uniformly continuous functions. Moreover, if functions f_n are measurable or have the …

Distribution Of Petrogenic Hydrocarbons In Water, Sediment And Cockles (Anadara Granosa) From Kuala Sungai Sepetang And Kuala Sungai Selangor, Mohd Hilmi Jaafar

Student Works (2000-2009)

In order to assess the level of oil pollution in the cockle culture areas along the Straits of Malacca, water, sediment and cockle samples were collected from the culture beds of Kuala Sepetang and Kuala Selangor, two of the largest cockle producing areas of Malaysia. The samples were analysed for petrogenic hydrocarbons by employing a spectrofluorometric technique which measures the content of polycyclic aromatic hydrocarbons (PAH) in oil. The content of aliphatic straight chain hydrocarbons were measured by using gas chromatography􀀐mass spectrometry (GCMS) which also allowed for the estimation of carbon preference indices and hence providing a means of estimating …

Cyclic Dehn Surgery And The A-Polynomial, Patrick Shanahan

Mathematics, Statistics and Data Science Faculty Works

We present a necessary condition for Dehn surgery on a knot in double-struck S sign3 to be cyclic which is based on the A-polynomial of the knot. The condition involves a width of the Newton polygon of the A-polynomial, and provides a simple method of computing a list of possible cyclic surgery slopes. The width produces a list of at most three slopes for a hyperbolic knot which contains no closed essential surface in its complement (in agreement with the Cyclic Surgery Theorem). We conclude with an application to cyclic surgeries along non-boundary slopes of hyperbolic mutant knots.

Finite Type Link Concordance Invariants, Blake Mellor

Mathematics, Statistics and Data Science Faculty Works

This paper is a generalization of the author's previous work on link homotopy to link concordance. We show that the only real-valued finite type link concordance invariants are the linking numbers of the components.

Finite Type Link Homotopy Invariants Ii: Milnor's Invariants, Blake Mellor

Mathematics, Statistics and Data Science Faculty Works

We define a notion of finite type invariants for links with a fixed linking matrix. We show that Milnor's triple link homotopy invariant is a finite type invariant, of type 1, in this sense. We also generalize the approach to Milnor's higher order homotopy invariants and show that they are also, in a sense, of finite type. Finally, we compare our approach to another approach for defining finite type invariants within linking classes.

The Intersection Graph Conjecture For Loop Diagrams, Blake Mellor

Mathematics, Statistics and Data Science Faculty Works

Vassiliev invariants can be studied by studying the spaces of chord diagrams associated with singular knots. To these chord diagrams are associated the intersection graphs of the chords. We extend results of Chmutov, Duzhin and Lando to show that these graphs determine the chord diagram if the graph has at most one loop. We also compute the size of the subalgebra generated by these "loop diagrams."

Codes And Curves, Judy L. Walker

Department of Mathematics: Faculty Publications

When information is transmitted, errors are likely to occur. Coding theory examines effi cient ways of packaging data so that these errors can be detected, or even corrected. The traditional tools of coding theory have come from combinatorics and group theory. Lately, however, coding theorists have added techniques from algebraic geometry to their toolboxes. In particular, by re-interpreting the Reed- Solomon codes, one can see how to defi ne new codes based on divisors on algebraic curves. For instance, using modular curves over fi nite fi elds, Tsfasman, Vladut, and Zink showed that one can defi ne a sequence of …

Efficient Presentations For Some Direct Products Of Groups, Bi̇lal Vatansever, David M. Gill

Turkish Journal of Mathematics

In this paper we give efficient presentations for $A_4\times D_n$, where n is odd number, or n is even number and (n,3)=1. We also give efficient presentations for $A_5\times D_n$ where n is an even or odd number.