Physical Sciences and Mathematics Commons^™

Oscillation Criteria For Second Order Nonlinear Differential Equations With Damping, Aydin Ti̇ryaki̇, Ağacik Zafer

Turkish Journal of Mathematics

Oscillation criteria are given for second order nonlinear differential equations with damping of the form $$(a(t) \psi (x ) \dot x)\dot{}+ p(t) \dot x + q (t) f (x ) = 0,\quad t\geq t_0,$$ where $p$ and $q$ are allowed to change signs on $[t_0,\infty)$. We employ the averaging technique to obtain sufficient conditions for oscillation of solutions of the above equation. Our results generalize and extend some known oscillation criteria in the literature.

The K-Derivation Of A Gamma-Ring, Hati̇ce Kandamar

Turkish Journal of Mathematics

In this paper, the $k$-derivation is defined on a $\Gamma$-ring $M$ (that is, if $M$ is a $\Gamma$-ring, $d:M\to M$ and $k:\Gamma\to \Gamma$ are to additive maps such that $d(a\beta b )= d(a)\beta b + ak(\beta)b + a\beta d(b) $ for all $a,b\in M, \quad \beta \in \Gamma$, then $d$ is called a $k$-derivation of $M$) and the following results are proved. (1) Let $R$ be a ring of characteristic not equal to 2 such that if $xry=0$ for all $x, y\in R$ then $r=0$. If $d$ is a $k$-derivation of the $(R=)\Gamma$-ring $R$ with $k=d$, then $d$ is the …

Qr-Submanifolds And Almost Contact 3-Structure, Rifat Güneş, Bayram Şahi̇n, Sadik Keleş

Turkish Journal of Mathematics

In this paper,QR-submanifolds of quaternion Kaehlerian manifolds with $\dim \nu ^{\perp }=1$ has been considered. It is shown that each QR-submanifold of quaternion Kaehlerian manifold with $\dim \nu ^{\perp }=1$ is a manifold with an almost contact 3-structure. We apply geometric theory of almost contact 3-structure to the classification of QR-submanifolds (resp.Real hypersurfaces) of quaternion Kaehler manifolds (resp.$IR^{4m}$, $m>1$). Some results on integrability of an invariant distribution of a QR-submanifold and on the immersions of its leaves are also obtained.

A Remark On The Asymptotic Properties Of Positive Homogeneous Maps On Homogeneous Lattices, Alp Eden

Turkish Journal of Mathematics

An abstract version of Lyapunov exponents is defined for positive homogeneous maps on Homogeneous Lattices and a sufficient condition is given for the asymptotic stability of the map.

The Pitch And The Angle Of Pitch Of A Closed Nonnull Ruled Hypersurface Whose Generator Is Spacelike In R^{K+2}_1, Ayşe Altin, Aysel Turgut Vanli

Turkish Journal of Mathematics

In this paper, the pitch and the angle of pitch of a closed nonnull ruled hypersurface whose generators are spacelike are calculated in $R^{k+2}_1 $.

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 $\ell^q.$

Definitions, Solved And Unsolved Problems, Conjectures, And Theorems In Number Theory And Geometry, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Florentin Smarandache, an American mathematician of Romanian descent has generated a vast variety of mathematical problems. Some problems are easy, others medium, but many are interesting or unsolved and this is the reason why the present book appears. Here, of course, there are problems from various types. Solving these problems is addictive like eating pumpkin seed: having once started, one cannot help doing it over and over again.

On Simplicial Commutative Algebras With Vanishing André-Quillen Homology, James M. Turner

University Faculty Publications and Creative Works

In this paper, we study the André-Quillen homology of simplicial commutative ℓ-algebras, ℓ a field, having certain vanishing properties. When ℓ has non-zero characteristic, we obtain an algebraic version of a theorem of J.-P. Serre and Y. Umeda that characterizes such simplicial algebras having bounded homotopy groups. We further discuss how this theorem fails in the rational case and, as an application, indicate how the algebraic Serre theorem can be used to resolve a conjecture of D. Quillen for algebras of finite type over Noetherian rings, having non-zero characteristic.

An Extension Of Zermelo's Model For Ranking By Paired Comparisons, Christopher P. Grant, Gregory R. Conner

Faculty Publications

In 1929, Zermelo proposed a probabilistic model for ranking by paired comparisons and showed that this model produces a unique ranking of the objects under consideration when the outcome matrix is irreducible. When the matrix is reducible, the model may yield only a partial ordering of the objects. In this paper, we analyse a natural extension of Zermelo's model resulting from a singular perturbation. We show that this extension produces a ranking for arbitrary (nonnegative) outcome matrices and retains several of the desirable properties of the original model. In addition, we discuss computational techniques and provide examples of their use.

Visually Building Smale Flows In S3, Michael C. Sullivan

Articles and Preprints

A Smale flow is a structurally stable flow with one dimensional invariant sets. We use information from homology and template theory to construct, visualize and in some cases, classify, Smale flows in the 3-sphere.

A Mathematical Model For Spatially Varying Extracellular Matrix, J. C. Dallon, J. A. Sherratt

Faculty Publications

Orientation of extracellular matrix fibers in the skin is a key ingredient of tissue appearance and function, and differences in fiber alignment are one of the main distinctions between scar tissue and normal skin. In this paper, the authors develop a mathematical model for alignment of collagen fibers and the fibroblast cells that remodel them; the model extends previous work in which spatial variation was excluded. Numerical simulations of the model are presented, which show spatial variations in alignment over long transients, but with spatially uniform behavior in the long term. This is investigated further via asymptotic analysis, using the …

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 …

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.

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 …

Notes On Coalgebras, Cofibrations And Concurrency, Alexander Kurz, Dirk Pattinson

Engineering Faculty Articles and Research

We consider categories of coalgebras as (co)-fibred over a base category of parameters and analyse categorical constructions in the total category of deterministic and non-deterministic coalgebras.

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.

Incentives To Settle Under Joint And Several Liability: An Empirical Analysis Of Superfund Litigation, Howard F. Chang, Hilary Sigman

All Faculty Scholarship

Congress may soon restrict joint and several liability for cleanup of contaminated sites under Superfund. We explore whether this change would discourage settlements and is therefore likely to increase the program 's already high litigation costs per site. Recent theoretical research by Kornhauser and Revesz finds that joint and several liability may either encourage or discourage settlement, depending on the correlation of outcomes at trial across defendants. We extend their two-defendant model to a richer framework with N defendants. This extension allows us to test the theoretical model empirically using data on Superfund litigation. We find that joint and several …

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 …

Boundary Quadrature Formulas And Their Applications, Tian-Xiao He

Tian-Xiao He

This chapter surveys the analytical approach for constructing multivariate numerical integration formulas that use only boundary points as evaluation points. The applications of boundary quadrature formulas to boundary value problems of partial differential equations are also discussed.

Interactive Real Analysis. / Glossary, Bert Wachsmuth

Bert Wachsmuth

No abstract provided.

C1 Quadratic Macroelements And C1 Orthogonal Multiresolution Analyses In 2d, Tian-Xiao He

Tian-Xiao He

Each triangle of an arbitrary regular triangulation Δ of a polygonal region in R² is subdivided into twelve subtriangles by using three connecting lines joining three arbitrarily chosen points on its edges, three connecting lines from an arbitrarily chosen interior point in the triangle to its three vertices, and three connecting lines joining the points on the edges and the interior point. In this refinement, C¹ quadratic finite elements can be constructed. In this paper, we will give explicit Bezier coefficients of elements in terms of the parameters that describe function and first partial derivative values at vertices …

Rhapsody In White: A Victory For Mathematics, J. Bruning, A. Cantrell, R. Longhurst, D. Schwalbe, Stan Wagon

Stan Wagon, Retired

No abstract provided.

Logic-Based Methods For Optimization: Combining Optimization And Constraint Satisfaction, John Hooker

John Hooker

No abstract provided.

A Brief Biography Of Professor L.C. Hsu (Lizhi Xu), Tian-Xiao He

Tian-Xiao He

No abstract provided.

Systems Of Difference Equations With Asymptotically Constant Solutions, William F. Trench

William F. Trench

No abstract provided.

Noncommutative Computer Algebra In The Control Of Singularly Perturbed Dynamical Systems, J. W. Helton, F. Dell Kronewitter, Mark Stankus

Mathematics

Most algebraic calculations which one sees in linear systems theory, for example in IEEE TAC, involve block matrices and so are highly noncommutative. Thus conventional commutative computer algebra packages, as in Mathematica and Maple, do not address them. Here we investigate the usefulness of noncommutative computer algebra in a particular area of control theory-singularly perturbed dynamic systems-where working with the noncommutative polynomials involved is especially tedious. Our conclusion is that they have considerable potential for helping practitioners with such computations. For example, the methods introduced here take the most standard textbook singular perturbation calculation, [KK086], one step further than had …

Grundlagenreflexionen Zur Thematik Anthropomorpher Schnittstellen, Rudolf Kaehr

Rudolf Kaehr

Report for the EMBASSI Project

Hopf Bifurcation In Models For Pertussis Epidemiology, Herbert W. Hethcote, Yi Li, Zhujun Jing

Yi Li

Pertussis (whooping cough) incidence in the United States has oscillated with a period of about four years since data was first collected in 1922. An infection with pertussis confers immunity for several years, but then the immunity wanes, so that reinfection is possible. A pertussis reinfection is mild after partial loss of immunity, but the reinfection can be severe after complete loss of immunity. Three pertussis transmission models with waning of immunity are examined for periodic solutions. Equilibria and their stability are determined. Hopf bifurcation of periodic solutions around the endemic equilibrium can occur for some parameter values in two …

Anneli Lax: In Memoriam, Elena Anne Corie Marchisotto

Humanistic Mathematics Network Journal

No abstract provided.

Teaching A Humanities Course: A Mathematician’S View, Bill Marion

Humanistic Mathematics Network Journal

No abstract provided.