Mathematics Commons^™

Two Examples Concerning Extendable And Almost Continuous Functions, Krzysztof Ciesielski

Faculty & Staff Scholarship

The main purpose of this paper is to describe two examples. The first is that of an almost continuous, Baire class two, non-extendable function f:[0,1]-->[0,1] with a G_\delta graph. This answers a question of Gibson. The second example is that of a connectivity function F:R²-->R with dense graph such that F^-1(0) is contained in a countable union of straight lines. This easily implies the existence of an extendable function f:R-->R with dense graph such that f^-1(0) is countable.

We also give a sufficient condition for a Darboux …

International R&D Spillovers: An Application Of Estimation And Inference In Panel Cointegration, Chihwa Kao, Min-Hsien Chiang, Bangtian Chen

Center for Policy Research

In this paper, we apply the asymptotic theory of panel cointegration developed by Kao and Chiang (1997) to Coe and Helpman's (1995) international R&D spillovers regression. The OLS with bias-correction, the fully-modified (FM) and the dynamic OLS (DOLS) estimations produce different predictions about the impact of foreign R&D on total factor productivity (TFP), although all the estimations support the result that domestic R&D is related to TFP.

Totally Nonnegative Matrices, Shaun M. Fallat

Dissertations, Theses, and Masters Projects

An m-by-n matrix A is called totally nonnegative (resp. totally positive) if the determinant of every square submatrix (i.e., minor) of A is nonnegative (resp. positive). The class of totally nonnegative matrices has been studied considerably, and this class arises in a variety of applications such as differential equations, statistics, mathematical biology, approximation theory, integral equations and combinatorics. The main purpose of this thesis is to investigate several aspects of totally nonnegative matrices such as spectral problems, determinantal inequalities, factorizations and entry-wise products. It is well-known that the eigenvalues of a totally nonnegative matrix are nonnegative. However, there are many …

Some Results On Space-Like Line Congruences And Their Space-Like Parameter Ruled Surface, E. Özyilmaz

Turkish Journal of Mathematics

Using dual vectors, space-like ruled surfaces was introduced in [2]. In this paper, we define space-like line congruence and their space-like parameter ruled surfaces {\mathbf R_{11}(t)} and {\mathbf R_{21}(t)} of R_1^3. Then, by choosing space-like parameter ruled surfaces as space-like principle ruled surfaces, we obtain some relations among the magnitudes of space-like ruled surfaces {\mathbf R_1(t)}, {\mathbf R_{11}(t)}.

An Algorithm To Determine Non-Perfect Colorings That Arise From Plane Crystallographic Groups, Ma. Louise Antonette N. De Las Peñas

Mathematics Faculty Publications

This paper presents a computer algorithm that assists us in our research on non-perfect colorings of plane crystallographic patterns.

Asupra Unor Noi Functii În Teoria Numerelor, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Performantele matematicii actuale,ca si descoperirile din viitor isi au,desigur, inceputul in cea mai veche si mai aproape de filozofie ramura a matematicii, in teoria numerelor. Matematicienii din toate timpurile au fost, sunt si vor fi atrasi de frumusetea si varietatea problemelor specifice acestei ramuri a matematicii. Regina a matematicii, care la randul ei este regina a stiintelor, dupa cum spunea Gauss, teoria numerelor straluceste cu lumina si atractiile ei, fascinandu-ne si usurandu-ne drumul cunoasterii legitatilor ce guverneaza macrocosmosul si microcosmosul. De la etapa antichitatii, cand teoria numerelor era cuprinsa in aritmetica, la etapa aritmeticii superioare din perioada Renasterii, cand teoria …

Smarandache Type Functions Obtained By Duality, Florentin Smarandache, C Dumitrescu, N Varlan, St Zamfir, E Radescu, N Radescu

Branch Mathematics and Statistics Faculty and Staff Publications

we extend the Smarandache function from the set N* of positive integers to the set Q of rationals

Conjectures On Partitions Of Integers As Summations Of Primes, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this short note many conjectures on partitions of integers as summations of prime numbers are presented, which are extension of Goldbach conjecture.

Utilization Of Printer Resources Within A Computer Graphics Department: A Print Queue Analysis, Prentice Frazier

Theses and Dissertations

This paper examines print queue management for the graphics department of a financial services company. The current network configuration has proven to be sub-optimal. The IT department is currently undergoing testing of possible alternative network configurations. The objective is to improve performance by leveraging existing resources with new technology. In this paper, the effect of consolidating the queue into one primary queue manager is analyzed, along with prioritizing print jobs, and forecasting future printer needs. Analysis was performed using queuing theory concepts along with an analysis of both steady state and transient behavior using simulation modeling.

On The Estimation And Inference Of A Cointegrated Regression In Panel Data, Chihwa Kao

Center for Policy Research

The main contribution of this paper is to add to the literature by suggesting a dynamic OLS (DOLS) estimator and providing a serious comparison of the finite sample properties of the OLS, fully modified OLS (FMOLS), and DOLS estimators in panel cointegrated regression models. Monte Carlo results illustrate the sampling behavior of the proposed estimators and show that (1) the OLS estimator has a non-negligible bias in finite samples, (2) the FMOLS estimator does not improve over the OLS estimator in general, and (3) the DOLS outperforms both the OLS and FMOLS estimators.

On The Estimation Of A Linear Time Trend Regression With A One-Way Error Component Model In The Presence Of Serially Correlated Errors, Chihwa Kao, Jamie Emerson

Center for Policy Research

In this paper we study the limiting distributions for ordinary least squares (OLS), fixed effects (FE), first difference (FD), and generalized least squares (GLS) estimators in a linear time trend regression with a one-way error component model in the presence of serially correlated errors. We show that when the error term is I(0), the FE is asymptotically equivalent to the GLS. However, when the error term is I(1) the GLS could be less efficient than the FD or FE estimators, and the FD is the most efficient estimator. However, when the intercept is included in the model and the error …

Geometrical Models For Grain Dynamics, Giovani L. Vasconcelos, J. J. P. Veerman

Mathematics and Statistics Faculty Publications and Presentations

We study models for the gravity-driven, dissipative motion of a single grain on an inclined rough surface. Imposing some conditions on the momentum loss due to the collisions between the particle and the surface, we arrive at a class of models in which the grain dynamics is described by one-dimensional maps. The dynamics of these maps is studied in detail. We prove the existence of various dynamical phases and show that the presence of these phases is independent of the restitution law (within the class considered).

Computational Geometry Column 35, Joseph O'Rourke

Computer Science: Faculty Publications

The subquadratic algorithm of Kapoor for finding shortest paths on a polyhedron is described.

Locked And Unlocked Polygonal Chains In 3d, Therese Biedl, Erik D. Demaine, Martin L. Demaine, Sylvain Lazard, Anna Lubiw, Joseph O'Rourke, Mark Overmars, Steve Robbins, Ileana Streinu, Godfried Toussaint, Sue Whitesides

Computer Science: Faculty Publications

In this paper, we study movements of simple polygonal chains in 3D. We say that an open, simple polygonal chain can be straightened if it can be continuously reconfigured to a straight sequence of segments in such a manner that both the length of each link and the simplicity of the chain are maintained throughout the movement. The analogous concept for closed chains is convexification: reconfiguration to a planar convex polygon. Chains that cannot be straightened or convexified are called locked. While there are open chains in 3D that are locked, we show that if an open chain has a …

A Program To Search For Homotopy 3-Spheres, Michael Greene, Colin Rouke

Turkish Journal of Mathematics

No abstract provided.

Canonical Framings For 3 -Manifolds, Rob Kirby, Paul Melvin

Turkish Journal of Mathematics

No abstract provided.

Seiberg-Witten Invariants Of Mapping Tori,Symplectic Fixed Points, And Lefschetz Numbers, Dietmar A. Salamon

Turkish Journal of Mathematics

No abstract provided.

Simply Connected Symplectic 4-Manifolds Withpositive Signature, Andras I. Stipsicz

Turkish Journal of Mathematics

No abstract provided.

On Symplectic Fillings Of 3-Manifolds, Paola Lisca

Turkish Journal of Mathematics

No abstract provided.

A Fake Cusp And A Fishtail, Selman Akbulut

Turkish Journal of Mathematics

No abstract provided.

Countable Dense Homogeneous Bıtopologıcal Spaces, Abdalla Tallafha, Adnan Al-Bsoul, Ali̇ Ahmad Fora

Turkish Journal of Mathematics

In this paper we shall introduce the concept of being countable dense homogeneous bitopological spaces and define several kinds of this concept. We shall give some results concerning these bitopological spaces and their relations. Also, we shall prove that all of these bitopological spaces satisfying the axioms p-T_0 and p-T_1.

Left Adjoint Of Pullback Cat^1 -Groups, Murat Alp

Turkish Journal of Mathematics

In [1] we define the pullback Cat^1-groups and showed that the category of pullback Cat^1-groups is equivalent to the category of pullback crossed modules. In this paper we proved that the pullback Cat^1-group has a left adjoint which is the induced Cat^1-group. We also give the left adjoint construction.

On The Boundedness Of Integral Operators, İsmai̇l Eki̇nci̇oğlu, Isroil A. Ikromov

Turkish Journal of Mathematics

In this paper, we consider integal operators defined by kernel functions. It is well known the boundedness of such kind of operators as Shur Lemma type statements. But, the norm of operators was estimated by two integrals of kernel function. We obtain estimation of operators norm by one integral of kernel function.

Some Asymptotic Estimates For The Instability Intervals Of Hill's Equation, Haskiz Coşkun

Turkish Journal of Mathematics

In this study, some asymptotic estimates for the length of the instability intervals of Hill's equation, y''(t)+(\lambda -q(t))y(t)=0, are derived by means of an auxiliary eigenvalue problem under various assumptions on the Fourier coefficients of the potential q.

Geodesics In A Tensor Bundle, Abdullah Kopuzlu, Ari̇f A. Salimov

Turkish Journal of Mathematics

The main purpose of the present paper is to study geodesics in a tensor bundle T^{p}_q(M_n) with respect to the horizontal lift ^H\nabla of an affine connection \nabla .

A Stone's Representation Theorem And Some Applications, Eissa D. Habil

Turkish Journal of Mathematics

In this paper, we prove the following form of Stone's representation theorem: Let \sum be a \sigma-algebra of subsets of a set X. Then there exists a totally disconnected compact Hausdorff space {\cal K} for which (\sum, \cup, \cap) and ({\cal C}({\cal K}), \cup ,\cap), where {\cal C}({\cal K}) denotes the set of all clopen subsets of {\cal K}, are isomorphic as Boolean algebras. Furthermore, by defining appropriate joins and meets of countable families in {\cal C}({\cal K}), we show that such an isomorphism preserves \sigma-completeness. Then, as a consequence of this result, we obtain the result that if ba(X,\sum) …

Univalent Harmonic Mappings Onto Half Planes, Meti̇n Öztürk

Turkish Journal of Mathematics

We consider the class S_H(D,\Omega ) of complex functions f which are univalent, harmonic, sense preserving on a simple connected domain D\neq {\Bbb C} \ containing the origin, satisfy f(0)=a_0, f_{\bar z}(0)=0a,\ a\in {\Bbb R}\}. In particularly, we describe the closure \overline{S_H(D,\Omega )} of S_H(D,\Omega ) and characterize its extreme points, as well as sharp estimates for coefficients and distortion theorems.

Cycloidal Normal Subgroups Of Hecke Groups Of Finite Index, İsmai̇l Naci̇ Cangül, Osman Bi̇zi̇m

Turkish Journal of Mathematics

Cycloidal normal subgroups, that is, subgroups with only one cusp, of finite index of Hecke groups, which have been introduced by E. Hecke, and can be thought of as some kind of generalisation of the well-known modular group, are studied. It is shown that they correspond to cyclic quotients of Hecke groups and therefore have non-compact associated Riemann surfaces with a cusp. Finally, their total number have been formulated.

Augmented Noetherian Graded Modules, Mashhoor Refai̇

Turkish Journal of Mathematics

Let $G$ be a multiplicative group with identity $e$, and let $R$ be an associative $G$-graded ring with unity 1. In this paper we study the augmented graded Noetherian modules and try to give some relationships between the Noetherian modules in the category $R-Agr$ and the Noetherian modules in the category $R_e-gr$.

Generalized Solutions Of A Class Of Linear And Quasi-Linear Degenerated Hyperbolic Equations, Rossitza Semerdjieva

Turkish Journal of Mathematics

The equation $L(u):=k(y)u_{xx}-\partial_y(\ell(y)u_y)+r(x,y)u=f(x,y,u),$ where $k(y)>0, \ell(y)>0$ for $y>0,k(0)=\ell(0)=0$ and $lim_{y\rightarrow 0}k(y)/\ell(y)$ exists, is strictly hyperbolic for $y>0$ and its order degenerates on the line $y=0$. We consider the boundary value problem $Lu=f(x,y,u)$ in $G, u\mid_{AC}=0$, where $G$ is a simply connected domain in $R^2$ with piecewise smooth boundary $\partial G=AB\cup AC\cup BC; AB=\{(x,0): 0\leq x\leq 1\}, AC : x=F(y) =\int_0^y(k(t)/\ell (t))^{1/2}dt$ and $BC: x=1-F(y)$ are characteristic curves. The existence and uniqueness of a generalized solution to this problem are proved in the linear case (where $f=f(x,y));$ the nonlinear case is treated by using the Schauder Fixed …