Mathematics Commons^™

A Fractal Example Of A Continuous Monotone Function With Vanishing Derivatives On A Dense Set And Infinite Derivatives On Another Dense Set, Bünyami̇n Demi̇r, Vakif Dzhafarov, Şahi̇n Koçak, Mehmet Üreyen

Turkish Journal of Mathematics

Inspired by the theory of analysis on fractals, we construct an example of a continuous, monotone function on an interval, which has vanishing derivatives on a dense set and infinite derivatives on another dense set. Although such examples could be constructed by classical means of probability and measure theory, this one is more elementary and emerges naturally as a byproduct of some new fractal constructions.

On Uniform Hermitian P-Normed Algebras, A. El-Kinani

Turkish Journal of Mathematics

We show that the completion of a uniform hermitian p-normed algebra is a commutative C^*-algebra.

On The Power Subgroups Of The Extended Modular Group \Overline{\Gamma} (Corrigendum - Turk. J. Math. 28,143-151, 2004), Recep Şahi̇n, Sebahatti̇n İki̇kardeş, Özden Koruoğlu

Turkish Journal of Mathematics

No abstract provided.

Pullbacks Of Crossed Modules And Cat^1- Commutative Algebras, Murat Alp

Turkish Journal of Mathematics

In this paper we first review the definitions of crossed module [10], pullback crossed module and cat^1-object in the category of commutative algebras. We then describe a certain pullback of cat^1- commutative algebras.

Connectedness In Isotonic Spaces, Eissa D. Habil, Khalid A. Elzenati

Turkish Journal of Mathematics

An isotonic space (X,cl) is a set X with isotonic operator cl:P(X) \to P(X) which satisfies cl(\emptyset) = \emptyset and cl(A)\subseteq cl(B) whenever A\subseteq B\subseteq X. Many properties which hold in topological spaces hold in isotonic spaces as well. The notion of connectedness that is familiar from topological spaces generalizes to isotonic spaces. We further extend the notions of Z-connectedness and strong connectedness to isotonic spaces, and we indicate the intimate relationship between these notions.

On Reduced And Semicommutative Modules, Muhi̇tti̇n Başer, Nazim Agayev

Turkish Journal of Mathematics

In this paper, various results of reduced and semicommutative rings are extended to reduced and semicommutative modules. In particular, we show: (1) For a principally quasi-Baer module, M_R is semicommutative if and only if M_R is reduced. (2) If M_R is a p.p.-module then M_R is nonsingular.

A Survey On The Distribution Of B-Free Numbers, Emre Alkan, Alexandru Zaharescu

Turkish Journal of Mathematics

In this paper we present a survey of recent progress on the distribution of B-free numbers in short intervals and some of its applications.

Existence Of Linear-Quadratic Regulator For Degenerate Diffusions, Md. Azizul Baten

Turkish Journal of Mathematics

This paper studies a linear regulatory quadratic control problem for degenerate Hamilton-Jacobi-Bellman (HJB) equation. We establish the existence of a unique viscosity and a classical solution of the degenerate HJB equation associated with this problem by the technique of viscosity solutions, and, hence, derive an optimal control from the optimality conditions in the HJB equation.

Two-Weight Norm Inequalities For Some Anisotropic Sublinear Operators, Yusuf Zeren, V. S. Guliyev

Turkish Journal of Mathematics

In this paper, we establish several general theorems for the boundedness of the anisotropic sublinear operators on a weighted Lebesgue space. Conditions of these theorems are satisfied by many important operators in analysis. We also give some applications the boundedness of the parabolic singular integral operators, and the maximal operators associated with them from one weighted Lebesgue space to another one. Using this results, we prove weighted embedding theorems for the anisotropic Sobolev spaces W_{\omega_0,\omega_1,...,\omega_n}^{l_1,...,l_n}(\Rn).

On Graded Weakly Prime Ideals, Shahabaddin Ebrahimi Atani

Turkish Journal of Mathematics

Let G be an arbitrary group with identity e, and let R be a G-graded commutative ring. Weakly prime ideals in a commutative ring with non-zero identity have been introduced and studied in [1]. Here we study the graded weakly prime ideals of a G-graded commutative ring. A number of results concerning graded weakly prime ideals are given. For example, we give some characterizations of graded weakly prime ideals and their homogeneous components.

Diagonal Lift In The Tangent Bundle Of Order Two And Its Applications, Fouzi Hathout, H. M. Dida

Turkish Journal of Mathematics

In this paper we define a diagonal lift ^{D}g of Riemannian metric g of manifold M_n to the tangent bundle of order two denoted by T^{2}M_n of M_n, we associate to ^{D}g its Levi-civita connection of T^2 M and we investigate applications of the diagonal lifts in the killing vectors and geodesics.

Note On Generalized Jordan Derivations Associate With Hochschild 2-Cocycles Of Rings, Atsushi Nakajima

Turkish Journal of Mathematics

We introduce a new type of generalized derivations associate with Hochschild 2-cocycles and prove that every generalized Jordan derivation of this type is a generalized derivation under certain conditions. This result contains the results of I. N. Herstein [6, Theorem 3.1] and M. Ashraf and N-U. Rehman [1, Theorem].

Weighted Norm Inequalities For A Class Of Rough Maximal Operators, Hussain Al-Qassem

Turkish Journal of Mathematics

We consider maximal singular integral operators arising from rough kernels satisfying an H^1-type condition on the unit (n-1)-sphere and prove weighted L^p estimates for certain radial weights. We also prove weighted L^p estimates with A_p-weights where in this case the H^1 -type condition is replaced by an L^q-type condition with q > 1. Some applications of these results are also obtained regarding singular integrals and Marcinkiewicz integrals. Our results are essential extensions and improvements of some known results.

A Note On Kaehlerian Manifolds, Nejmi̇ Cengi̇z, Ö. Tarakçi, A. A. Sali̇mov

Turkish Journal of Mathematics

The main purpose of the present paper is to study nearly Kaehlerian manifolds. We give the condition for an almost Hermitian manifold to be nearly Kaehlerian.

Problem Solving In The Fourth Grade Classroom, Lisa Lefevre

Senior Honors Theses and Projects

No abstract provided.

Enumerations Of The Kolmogorov Function, Richard Beigel, Harry Buhrman, Peter Fejer, Lance Fortnow, Piotr Grabowski, Luc Longpré, Andrej Muchnik, Frank Stephan, Leen Torenvliet

Computer Science Faculty Publication Series

A recursive enumerator for a function h is an algorithm f which enumerates for an input x finitely many elements including h(x). f is a k(n)-enumerator if for every input x of length n, h(x) is among the first k(n) elements enumerated by f. If there is a k(n)-enumerator for h then h is called k(n)-enumerable. We also consider enumerators which are only A-recursive for some oracle A.

We determine exactly how hard it is to enumerate the Kolmogorov function, which assigns to each string x its Kolmogorov complexity:

• For every underlying universal machine U, there is a constant a …

Universal Kernels, Charles A. Micchelli, Yuesheng Xu, Haizhang Zhang

Mathematics - All Scholarship

In this paper we investigate conditions on the features of a continuous kernel so that it may approximate an arbitrary continuous target function uniformly on any compact subset of the input space. A number of concrete examples are given of kernels with this universal approximating property.

Testing For Cointegrating Rank Via Model Selection: Evidence From 165 Data Sets, Badi H. Baltagi, Zijun Wang

Center for Policy Research

The model selection approach has been proposed as an alternative to the popular tests for cointegration such as the residual-based ADF test and the system-based trace test. Using information criteria, we conduct cointegration tests on 165 data sets used in published studies. The empirical results demonstrate the usefulness of the model selection approach for applied researchers.

Reliability Modeling In Spatially Distributed Logistics System, Ni Wang, Jye-Chyi Lu, Paul H. Kvam

Department of Math & Statistics Faculty Publications

This article proposes methods for modeling service reliability in a supply chain. The logistics system in a supply chain typically consists of thousands of retail stores along with multiple distribution centers (DC). Products are transported between DC & stores through multiple routes. The service reliability depends on DC location layouts, distances from DC to stores, time requirements for product replenishing at stores, DC's capability for supporting store demands, and the connectivity of transportation routes. Contingent events such as labor disputes, bad weather, road conditions, traffic situations, and even terrorist threats can have great impacts on a system's reliability. Given the …

A Logistic Regression/Markov Chain Model For Ncaa Basketball, Paul H. Kvam, Joel Sokol

Department of Math & Statistics Faculty Publications

Each year, more than $3 billion is wagered on the NCAA Division I men’s basketball tournament. Most of that money is wagered in pools where the object is to correctly predict winners of each game, with emphasis on the last four teams remaining (the Final Four). In this paper, we present a combined logistic regression/Markov chain model for predicting the outcome of NCAA tournament games given only basic input data. Over the past 6 years, our model has been significantly more successful than the other common methods such as tournament seedings, the AP and ESPN/USA Today polls, the RPI, and …

Statistical Reliability With Applications, Paul H. Kvam, Jye-Chyi Lu

Department of Math & Statistics Faculty Publications

This chapter reviews fundamental ideas in reliability theory and inference. The first part of the chapter accounts for lifetime distributions that are used in engineering reliability analyis, including general properties of reliability distributions that pertain to lifetime for manufactured products. Certain distributions are formulated on the basis of simple physical properties, and other are more or less empirical. The first part of the chapter ends with a description of graphical and analytical methods to find appropriate lifetime distributions for a set of failure data.

The second part of the chapter describes statistical methods for analyzing reliability data, including maximum likelihood …

Use Of Pen-Based Technology In Calculus Courses, John R. Hubbard

Department of Math & Statistics Faculty Publications

The author and his students used Tablet computers in Calculus I and Calculus II classes, providing students with dynamic digital transcripts that they could replay at their convenience. He and his students agreed that these graphic replays provide an effective alternative to the static explanations found in textbooks and in traditional course notes. Two specific examples are given in this paper.

Specific Antibodies To Recombinant Allergens Of Aspergillus Fumigatus In Cystic Fibrosis Patients With Abpa, Viswanath P. Kurup, Alan P. Knutsen, Richard B. Moss, Naveen K. Bansal

Mathematics, Statistics and Computer Science Faculty Research and Publications

Background

Aspergillus fumigatus, a widely distributed fungus, has been implicated in causing life threatening infections as well as severe asthma and allergic diseases in man. Allergic affliction like allergic bronchopulmonary aspergillosis (ABPA) is a disabling lung disease frequently seen in patients with asthma and cystic fibrosis. Immunodiagnosis of the former is comparatively easier due to the availability of purified antigens and sensitive methods. However, this is not true with cystic fibrosis patients where the prevalence of ABPA is fairly high and the morbidity and mortality are significant.

Methods

In the present study, we have evaluated purified recombinant allergens from …

The Classical Dirichlet Space, William T. Ross

Department of Math & Statistics Faculty Publications

In this survey paper, we will present a selection of results concerning the class of analytic functions f on the open unit disk D := {z ϵ C : │z│ < 1} which have finite Dirichlet integral.

The Chang-Los-Suszko Theorem In A Topological Setting, Paul Bankston

Mathematics, Statistics and Computer Science Faculty Research and Publications

The Chang-Łoś-Suszko theorem of first-order model theory characterizes universal-existential classes of models as just those elementary classes that are closed under unions of chains. This theorem can then be used to equate two model-theoretic closure conditions for elementary classes; namely unions of chains and existential substructures. In the present paper we prove a topological analogue and indicate some applications.

A Solidification Phenomenon In Random Packings, L. Bowen, R. Lyons, C. Radin, P. Winkler

Dartmouth Scholarship

We prove that uniformly random packings of copies of a certain simply connected figure in the plane exhibit global connectedness at all sufficiently high densities, but not at low densities.

The Sonic Representation Of Mathematical Data, Charlie Cullen

Doctoral

Conveying data and information using non-speech audio is an ever growing field of research. Existing work has been performed investigating sonfication and its applications, and this research seeks to build upon these ideas while also suggesting new areas of potential. In this research, initial work focused on the sonification of DNA and RNA nucleotide base sequences for analysis. A case study was undertaken into the potential of rhythmic parsing of such data sequences, with test results indicating that a more effective method of representing data in a sonification was required. Sonification of complex data such as DNA and RNA was …

Continued Fractions And Generalizations With Many Limits: A Survey, Douglas Bowman, James Mclaughlin

Mathematics Faculty Publications

There are infinite processes (matrix products, continued fractions, (r, s)-matrix continued fractions, recurrence sequences) which, under certain circumstances, do not converge but instead diverge in a very predictable way. We give a survey of results in this area, focusing on recent results of the authors.

Further Combinatorial Identities Deriving From The N-Th Power Of A 2 X 2 Matrix, James Mclaughlin, Nancy Wyshinski

Mathematics Faculty Publications

In this paper we use a formula for the n-th power of a 2×2 matrix A (in terms of the entries in A) to derive various combinatorial identities. Three examples of our results follow. 1) We show that if m and n are positive integers and s ∈ {0, 1, 2, . . . , b(mn − 1)/2c}, then X i,j,k,t 2 1+2t−mn+n (−1)nk+i(n+1) 1 + δ(m−1)/2, i+k m − 1 − i i ! m − 1 − 2i k ! × n(m − 1 − 2(i + k)) 2j ! j t − n(i + k) ! n …

A Q-Continued Fraction, Douglas Bowman, James Mclaughlin, Nancy Wyshinksi

Mathematics Faculty Publications

Let a, b, c, d be complex numbers with d 6= 0 and |q| < 1. Define H1(a, b, c, d, q) := 1 1 + −abq + c (a + b)q + d + · · · + −abq2n+1 + cqn (a + b)q n+1 + d + · · · . We show that H1(a, b, c, d, q) converges and 1 H1(a, b, c, d, q) − 1 = c − abq d + aq P∞ j=0 (b/d) j (−c/bd)j q j(j+3)/2 (q)j (−aq2/d)j P∞ j=0 (b/d) j (−c/bd)j q j(j+1)/2 (q)j (−aq/d)j . We then use this result to deduce various corollaries, including the following: 1 1 − q 1 + q − q 3 1 + q 2 − q 5 1 + q 3 − · · · − q 2n−1 1 + q n − · · · = (q 2 ; q 3 )∞ (q; q 3)∞ , (−aq)∞ X∞ j=0 (bq) j (−c/b)j q j(j−1)/2 (q)j (−aq)j = (−bq)∞ X∞ j=0 (aq) j (−c/a)j q j(j−1)/2 (q)j (−bq)j , and the Rogers-Ramanujan identities, X∞ n=0 q n 2 (q; q)n = 1 (q; q 5)∞(q 4; q 5)∞ , X∞ n=0 q n 2+n (q; q)n = 1 (q 2; q 5)∞(q 3; q 5)∞.