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2010

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Articles 481 - 510 of 690

Full-Text Articles in Mathematics

Bitopological Duality For Distributive Lattices And Heyting Algebras, Guram Bezhanishvili, Nick Bezhanishvili, David Gabelaia, Alexander Kurz Jan 2010

Bitopological Duality For Distributive Lattices And Heyting Algebras, Guram Bezhanishvili, Nick Bezhanishvili, David Gabelaia, Alexander Kurz

Engineering Faculty Articles and Research

We introduce pairwise Stone spaces as a natural bitopological generalization of Stone spaces—the duals of Boolean algebras—and show that they are exactly the bitopological duals of bounded distributive lattices. The category PStone of pairwise Stone spaces is isomorphic to the category Spec of spectral spaces and to the category Pries of Priestley spaces. In fact, the isomorphism of Spec and Pries is most naturally seen through PStone by first establishing that Pries is isomorphic to PStone, and then showing that PStone is isomorphic to Spec. We provide the bitopological and spectral descriptions of many algebraic concepts important for the study …

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Algebraic Theories Over Nominal Sets, Alexander Kurz, Daniela Petrişan, Jiří Velebil Jan 2010

Algebraic Theories Over Nominal Sets, Alexander Kurz, Daniela Petrişan, Jiří Velebil

Engineering Faculty Articles and Research

We investigate the foundations of a theory of algebraic data types with variable binding inside classical universal algebra. In the first part, a category-theoretic study of monads over the nominal sets of Gabbay and Pitts leads us to introduce new notions of finitary based monads and uniform monads. In a second part we spell out these notions in the language of universal algebra, show how to recover the logics of Gabbay-Mathijssen and Clouston-Pitts, and apply classical results from universal algebra.

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Families Of Symmetries As Efficient Models Of Resource Binding, Vincenzo Ciancia, Alexander Kurz, Ugo Montanari Jan 2010

Families Of Symmetries As Efficient Models Of Resource Binding, Vincenzo Ciancia, Alexander Kurz, Ugo Montanari

Engineering Faculty Articles and Research

Calculi that feature resource-allocating constructs (e.g. the pi-calculus or the fusion calculus) require special kinds of models. The best-known ones are presheaves and nominal sets. But named sets have the advantage of being finite in a wide range of cases where the other two are infinite. The three models are equivalent. Finiteness of named sets is strictly related to the notion of finite support in nominal sets and the corresponding presheaves. We show that named sets are generalisd by the categorical model of families, that is, free coproduct completions, indexed by symmetries, and explain how locality of interfaces gives good …

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On Coalgebras Over Algebras, Adriana Balan, Alexander Kurz Jan 2010

On Coalgebras Over Algebras, Adriana Balan, Alexander Kurz

Engineering Faculty Articles and Research

We extend Barr’s well-known characterization of the final coalgebra of a Set-endofunctor as the completion of its initial algebra to the Eilenberg-Moore category of algebras for a Set-monad M for functors arising as liftings. As an application we introduce the notion of commuting pair of endofunctors with respect to the monad M and show that under reasonable assumptions, the final coalgebra of one of the endofunctors involved can be obtained as the free algebra generated by the initial algebra of the other endofunctor.

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Curvature Measures For Nonlinear Regression Models Using Continuous Designs With Applications To Optimal Design, Timothy O'Brien, Somsri Jamroenpinyo, Chinnaphong Bumrungsup Jan 2010

Curvature Measures For Nonlinear Regression Models Using Continuous Designs With Applications To Optimal Design, Timothy O'Brien, Somsri Jamroenpinyo, Chinnaphong Bumrungsup

Mathematics and Statistics: Faculty Publications and Other Works

We present and illustrate the methodology to calculate curvature measures for continuous designs, and extend design criteria to incorporate continuous designs. These design algorithms include quadratic design procedures, a subset design criterion, a second-order mean-square error design criterion, and a marginal curvature design methodology. A discussion of confidence intervals is also provided for continuous designs.

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On Self-Clique Graphs., Ong Poh Hwa Jan 2010

On Self-Clique Graphs., Ong Poh Hwa

Student Works (2010-2019)

The clique graph of a graph G is the graph obtained by taking the cliques of G as vertices, and two vertices are adjacent if and only if the corresponding cliques have non-empty intersection. A graph G is self-clique if it is isomorphic to its clique graph. Clique graphs have been studied for some time. However, not much is known about self-clique graphs. Self-clique graphs were ¯rst introduced and studied by Escalante [Abh. Math. Sem. Univ. Hamburg 39 (1973) 59-68]. Since then, self-clique graphs have been characterized for some classes of graphs. Chia [Discrete Math. 212 (2000) 185-189] gave a …

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Diagonal Forms And The Rationality Of The Poincaré Series, Dibyajyoti Deb Jan 2010

Diagonal Forms And The Rationality Of The Poincaré Series, Dibyajyoti Deb

University of Kentucky Doctoral Dissertations

The Poincaré series, Py(f) of a polynomial f was first introduced by Borevich and Shafarevich in [BS66], where they conjectured, that the series is always rational. Denef and Igusa independently proved this conjecture. However it is still of interest to explicitly compute the Poincaré series in special cases. In this direction several people looked at diagonal polynomials with restrictions on the coefficients or the exponents and computed its Poincaré series. However in this dissertation we consider a general diagonal polynomial without any restrictions and explicitly compute its Poincaré series, thus extending results of Goldman, Wang and Han. In a separate …

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The Maximal Pure Spectrum Of An Abelian Group, Brendan Goldsmith, Ruediger Goebel Jan 2010

The Maximal Pure Spectrum Of An Abelian Group, Brendan Goldsmith, Ruediger Goebel

Articles

This paper introduces the notion of the maximal pure spectrum of an Abelian group - this is the set of isomorphism classes of maximal proper pure subgroups - and focuses on the situation in which this spectrum is small. The converse situation is also examined i.e. given a collection of isomorphism classes of groups, can one find an Abelian group having precisely this collection as its maximal pure spectrum. Finally, it is shown that in some familiar situations, the answers to these questions may be undecidable.

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From Permutahedron To Aassociahedron, Colum Watt, Thomas Brady Jan 2010

From Permutahedron To Aassociahedron, Colum Watt, Thomas Brady

Articles

For each finite real reflection group $W$, we identify a copy of the type-$W$ simplicial generalised associahedron inside the corresponding simplicial permutahedron. This defines a bijection between the facets of the generalised associahedron and the elements of the type $W$ non-crossing partition lattice which is more tractable than previous such bijections. We show that the simplicial fan determined by this associahedron coincides with the Cambrian fan for $W$.

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The Similarity Problem For Indefinite Sturm-Liouville Operators With Periodic Coefficients, Aleksey Kostenko Jan 2010

The Similarity Problem For Indefinite Sturm-Liouville Operators With Periodic Coefficients, Aleksey Kostenko

Articles

We investigate the problem of similarity to a self-adjoint operator for $J$-positive Sturm-Liouville operators $L=\frac{1}{\omega}(-\frac{d^2}{dx^2}+q)$ with $2\pi$-periodic coefficients $q$ and $\omega$. It is shown that if 0 is a critical point of the operator $L$, then it is a singular critical point. This gives us a new class of $J$-positive differential operators with the singular critical point 0. Also, we extend the Beals and Parfenov regularity conditions for the critical point $\infty$ to the case of operators with periodic coefficients.

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A Time Series Analysis Of The New Jersey Meadowlands Weather And Air Quality Data, Steven Spero Jan 2010

A Time Series Analysis Of The New Jersey Meadowlands Weather And Air Quality Data, Steven Spero

Theses, Dissertations and Culminating Projects

This research applies time series methods to determine relationships among a set of weather variables which are continually monitored in the Hackensack Meadowlands region of northern New Jersey. Weather data includes chemical and atmospheric factors. Chemical factors are Nitrogen Oxide, atmospheric Ozone, Carbon Monoxide, and Carbon Dioxide. Weather factors are wind speed, barometric pressure, air temperature, humidity, and solar radiation. Additionally, traffic density and time of week are brought in as categorical factors. This research attempts to (a) introduce the reader to various time series methodologies, (b) find a significant and efficient model for forecasting Nitrogen Oxide levels, and (c) …

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Categorical Approaches To Non-Commutative Fuzzy Logic, Lawrence Stout Jan 2010

Categorical Approaches To Non-Commutative Fuzzy Logic, Lawrence Stout

Scholarship

In this paper we consider what it means for a logic to be non-commutative, how to generate examples of structures with a non-commutative operation * which have enough nice properties to serve as the truth values for a logic. Inference in the propositional logic is gotten from the categorical properties (products, coproducts, monoidal and closed structures, adjoint functors) of the categories of truth values. We then show how to extend this view of propositional logic to a predicate logic using categories of propositions about a type A with functors giving change of type and adjoints giving quantifiers. In the case …

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On Orders And Types Of Dirichlet Series Of Slow Growth, Yinying Kong, Huilin Gan Jan 2010

On Orders And Types Of Dirichlet Series Of Slow Growth, Yinying Kong, Huilin Gan

Turkish Journal of Mathematics

The present paper has the object of showing some interesting relationship on the maximum modulus, the maximum term, the index of maximum term and the coefficients of entire functions defined by Dirichlet series of slow growth; some properties like Taylor entire functions are obtained.

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Sufficient Conditions For Univalence Obtained By Using Second Order Linear Strong Differential Subordinations, Georgia Irina Oros Jan 2010

Sufficient Conditions For Univalence Obtained By Using Second Order Linear Strong Differential Subordinations, Georgia Irina Oros

Turkish Journal of Mathematics

The concept of differential subordination was introduced in [3] by S.S. Miller and P.T. Mocanu and the concept of strong differential subordination was introduced in [1], [2] by J.A. Antonino and S. Romaguera. In [5] we have studied the strong differential subordinations in the general case and in [6] we have studied the first order linear strong differential subordinations. In this paper we study the second order linear strong differential subordinations. Our results may be applied to deduce sufficient conditions for univalence in the unit disc, such as starlikeness, convexity, alpha-convexity, close-to-convexity respectively.

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Nontrivial Periodic Solutions Of Nonlinear Functional Differential Systems With Feedback Control, Yingxin Guo Jan 2010

Nontrivial Periodic Solutions Of Nonlinear Functional Differential Systems With Feedback Control, Yingxin Guo

Turkish Journal of Mathematics

This paper examines the existence of nontrivial periodic solutions for the nonlinear functional differential system with feedback control: \{\aligned x'(t)=x(t)a(t)-\big[\sum_{i=1}^n a_i(t)\int_0^{+\infty} f(t, x(t-\theta)) d}\varphi_i(\theta) +\sum_{j=1}^m b_j(t) \int_0^{+\infty} f(t,x'(t-\theta))\,d}\phi_j(\theta)+\sum_{\mu=1}^p c_\mu(t) \int_0^{\infty} u(t-\theta)\,d}\delta_\mu(\theta)\big], u'(t)=-\rho(t)u(t)+\sum_{\nu=1}^q \beta_\nu(t) \int_0^{\infty} f(t, x(t-\theta))\,d}\psi_\nu(\theta).\endaligned Under certain growth conditions on the nonlinearity f, several sufficient conditions for the existence of nontrivial solution are obtained by using Leray-Schauder nonlinear alternative.

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Existence And Uniqueness Of Solutions To Neutral Stochastic Functional Differential Equations With Infinite Delay In L^P(\Omega,C_H), Haibo Bao Jan 2010

Existence And Uniqueness Of Solutions To Neutral Stochastic Functional Differential Equations With Infinite Delay In L^P(\Omega,C_H), Haibo Bao

Turkish Journal of Mathematics

In this paper, we shall consider the existence and uniqueness of solutions to neutral stochastic functional differential equations with infinite delay in L^p(\Omega,C_h) space: d[x(t)-G(x_t)]=f(t,x_t)dt+g(t,x_t)dB(t), where we assume f:R^+\times L^p(\Omega,C_h) \to L^p(\Omega,R^n), g:R^+\times L^p(\Omega,C_h) \to L^p(\Omega,L(R^m, R^n)), G: L^p(\Omega,C_h) \to L^p(\Omega,R^n), p>2,\, and B(t) is a given m-dimensional Brownian motion.

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On Maximum Principle And Existence Of Positive Weak Solutions For N\Times N Nonlinear Elliptic Systems Involving Degenerated P-Laplacian Operators, H. M. Serag, S. A. Khafagy Jan 2010

On Maximum Principle And Existence Of Positive Weak Solutions For N\Times N Nonlinear Elliptic Systems Involving Degenerated P-Laplacian Operators, H. M. Serag, S. A. Khafagy

Turkish Journal of Mathematics

We study the Maximum Principle and existence of positive weak solutions for the n \times n nonlinear elliptic system -\Delta_{P,p}u_i=\sum_{j=1}^na_{ij}(x) u_j ^{p-2}u_j+f_i(x,u_1,u_2, ... ,u_n) in \Omega, u_i=0,\ i=1,2,. n on \partial \Omega \} where the degenerated p-Laplacian defined as \Delta _{P,p}u=div [P(x) \nabla u ^{p-2}\nabla u] with p>1,p \neq 2 and P(x) is a weight function. We give some conditions for having the Maximum Principle for this system and then we prove the existence of positive weak solutions for the quasilinear system by using ``sub-super solutions method''.

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Korovkin Type Approximation Theorem For Functions Of Two Variables In Statistical Sense, Fadi̇me Di̇ri̇k, Kami̇l Demi̇rci̇ Jan 2010

Korovkin Type Approximation Theorem For Functions Of Two Variables In Statistical Sense, Fadi̇me Di̇ri̇k, Kami̇l Demi̇rci̇

Turkish Journal of Mathematics

In this paper, using the concept of A-statistical convergence for double sequences, we investigate a Korovkin-type approximation theorem for sequences of positive linear operator on the space of all continuous real valued functions defined on any compact subset of the real two-dimensional space. Then we display an application which shows that our new result is stronger than its classical version. We also obtain a Voronovskaya-type theorem \ and some differential properties for sequences of positive linear operators constructed by means of the Bernstein polynomials of two variables.

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A Note On Dominant Contractions Of Jordan Algebras, Farrukh Mukhamedov, Seyi̇t Temi̇r, Hasan Akin Jan 2010

A Note On Dominant Contractions Of Jordan Algebras, Farrukh Mukhamedov, Seyi̇t Temi̇r, Hasan Akin

Turkish Journal of Mathematics

We consider two positive contractions T,S:L_1(A,\tau) \longrightarrow L_1(A,\tau) such that T\leq S, here (A, \tau) is a semi-finite JBW-algebra. If there is an n_0 \in N such that S^{n_0}-T^{n_0}

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The Equivalence Of Centro-Equiaffine Curves, Yasemi̇n Sağiroğlu, Ömer Pekşen Jan 2010

The Equivalence Of Centro-Equiaffine Curves, Yasemi̇n Sağiroğlu, Ömer Pekşen

Turkish Journal of Mathematics

The motivation of this paper is to find formulation of the SL(n,R)-equivalence of curves. The types for centro-equiaffine curves and for every type all invariant parametrizations for such curves are introduced. The problem of SL(n,R)-equivalence of centro-equiaffine curves is reduced to that of paths. The centro-equiaffine curvatures of path as a generating system of the differential ring of SL(n,R)-invariant differential polinomial functions of path are found. Global conditions of SL(n,R)-equivalence of curves are given in terms of the types and invariants. It is proved that the invariants are independent.

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A Gap Theorem For Complete Space-Like Hypersurface With Constant Scalar Curvature In Locally Symmetric Lorentz Spaces, Jiancheng Liu, Lin Wei Jan 2010

A Gap Theorem For Complete Space-Like Hypersurface With Constant Scalar Curvature In Locally Symmetric Lorentz Spaces, Jiancheng Liu, Lin Wei

Turkish Journal of Mathematics

Let M^n be a complete space-like hypersurface with constant scalar curvature in locally symmetric Lorentz space N^{n+1}_1, S be the squared norm of the second fundamental form of M^n in N^{n+1}_1. In this paper, we obtain a gap property of S: if nP\leq \sup S\leq D(n,P) for some constants P and D(n, P), then either \sup S=nP and M^n is totally umbilical, or \sup S=D(n, P) and M^n has two distinct principal curvatures.

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B.-Y. Chen Inequalities For Slant Submanifolds In Quaternionic Space Forms, Gabriel Eduard Vilcu Jan 2010

B.-Y. Chen Inequalities For Slant Submanifolds In Quaternionic Space Forms, Gabriel Eduard Vilcu

Turkish Journal of Mathematics

In this paper some B.-Y. Chen inequalities for slant submanifolds in quaternionic space forms are established.

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Extremal Lagrangian Submanifolds In A Complex Space Form N^N(4c), Shichang Shu, Annie Yi Han Jan 2010

Extremal Lagrangian Submanifolds In A Complex Space Form N^N(4c), Shichang Shu, Annie Yi Han

Turkish Journal of Mathematics

Let N^n(4c) be the complex space form of constant holomorphic sectional curvature 4c, \varphi: M \to N^n(4c) be an immersion of an n-dimensional Lagrangian manifold M in N^n(4c). Denote by S and H the square of the length of the second fundamental form and the mean curvature of M. Let \rho be the non-negative function on M defined by \rho^2=S-nH^2, Q be the function which assigns to each point of M the infimum of the Ricci curvature at the point. In this paper, we consider the variational problem for non-negative functional U(\varphi)=\int_M\rho^2dv=\int_M(S-nH^2)dv. We call the critical points of U(\varphi) the …

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A Note On The Lyapunov Exponent In Continued Fraction Expansions, Jianzhong Cheng, Lu-Ming Shen Jan 2010

A Note On The Lyapunov Exponent In Continued Fraction Expansions, Jianzhong Cheng, Lu-Ming Shen

Turkish Journal of Mathematics

Let T:[0,1) \to [0,1) be the Gauss transformation. For any irrational x \in [0,1), the Lyapunov exponent \alpha(x) of x is defined as \alpha(x)=\lim_{n\to\infty}\frac{1}{n} \log (T^n)'(x) . By Birkoff Average Theorem, one knows that \alpha(x) exists almost surely. However, in this paper, we will see that the non-typical set \{x\in [0,1):\lim_{n\to\infty}\frac{1}{n} \log (T^n)'(x) does not exist\} carries full Hausdorff dimension.

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New Inequalities Similar To Hardy-Hilbert's Inequality, Namita Das, Srinibas Sahoo Jan 2010

New Inequalities Similar To Hardy-Hilbert's Inequality, Namita Das, Srinibas Sahoo

Turkish Journal of Mathematics

In this paper, we establish a new inequality similar to Hardy-Hilbert's inequality. As applications, some particular results and the equivalent form are derived. The integral analogues of the main results are also given.

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The Riemann Hilbert Problem For Generalized Q-Holomorphic Functions, Sezayi̇ Hizliyel, Mehmet Çağliyan Jan 2010

The Riemann Hilbert Problem For Generalized Q-Holomorphic Functions, Sezayi̇ Hizliyel, Mehmet Çağliyan

Turkish Journal of Mathematics

In this work, the classical Riemann Hilbert boundary value problem is extended to generalized Q-holomorphic functions.

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Trace Formulae For Schrödinger Systems On Graphs, Chuan-Fu Yang, Zhen-You Huang, Xiao-Ping Yang Jan 2010

Trace Formulae For Schrödinger Systems On Graphs, Chuan-Fu Yang, Zhen-You Huang, Xiao-Ping Yang

Turkish Journal of Mathematics

For Schrödinger systems on metric graphs with \delta'-type conditions at the central vertex, firstly, we obtain precise description for the square root of the large eigenvalue up to the o(1/n)-term. Secondly, the regularized trace formulae for Schrödinger systems are calculated with some techniques in classical analysis. Finally, these formulae are used to obtain a result of inverse problem in the spirit of Ambarzumyan.

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The Principal Eigencurves For A Nonselfadjoint Elliptic Operator, Aomar Anane, Omar Chakrone, Abdellah Zerouali Jan 2010

The Principal Eigencurves For A Nonselfadjoint Elliptic Operator, Aomar Anane, Omar Chakrone, Abdellah Zerouali

Turkish Journal of Mathematics

In this paper we study the existence of the principal eigencurves for a nonselfadjoint elliptic operator. We obtain their variational formulation. We establish also the continuity and the differentiability of the principal eigencurves.

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Structural Properties Of Bilateral Grand Lebesque Spaces, E. Liflyand, E. Ostrovsky, L. Sirota Jan 2010

Structural Properties Of Bilateral Grand Lebesque Spaces, E. Liflyand, E. Ostrovsky, L. Sirota

Turkish Journal of Mathematics

In this paper we study the multiplicative, tensor, Sobolev and convolution inequalities in certain Banach spaces, the so-called Bilateral Grand Lebesque Spaces. We also give examples to show the sharpness of these inequalities when possible.

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Direct And Inverse Theorems For The Bézier Variant Of Certain Summation-Integral Type Operators, Asha Ram Gairola, P. N. Agrawal Jan 2010

Direct And Inverse Theorems For The Bézier Variant Of Certain Summation-Integral Type Operators, Asha Ram Gairola, P. N. Agrawal

Turkish Journal of Mathematics

Recently, the Bézier variant of some well known operators were introduced (cf. [8]-[9]) and their rates of convergence for bounded variation functions have been investigated (cf. [2], [10]). In this paper we establish direct and inverse theorems for the Bézier variant of the operators M_n introduced in [5] in terms of Ditzian-Totik modulus of smoothness \omega_{\varphi^\lambda}(f,t) (0 \leqslant \lambda \leqslant1 ). These operators include the well known Baskakov-Durrmeyer and Szász-Durrmeyer type operators as special cases.

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