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2014

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Articles 691 - 720 of 995

Full-Text Articles in Mathematics

Early Investigations In Conformal And Differential Geometry, Raymond T. Walter Jan 2014

Early Investigations In Conformal And Differential Geometry, Raymond T. Walter

Inquiry: The University of Arkansas Undergraduate Research Journal

The present article introduces fundamental notions of conformal and differential geometry, especially where such notions are useful in mathematical physics applications. Its primary achievement is a nontraditional proof of the classic result of Liouville that the only conformal transformations in Euclidean space of dimension greater than two are Möbius transformations. The proof is nontraditional in the sense that it uses the standard Dirac operator on Euclidean space and is based on a representation of Möbius transformations using 2x2 matrices over a Clifford algebra. Clifford algebras and the Dirac operator are important in other applications of pure mathematics and mathematical physics, …

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A Numerical Method For A Nonlinear Singularly Perturbed Interior Layer Problem Using An Approximate Layer Location, Jason Quinn Jan 2014

A Numerical Method For A Nonlinear Singularly Perturbed Interior Layer Problem Using An Approximate Layer Location, Jason Quinn

Articles

A class of nonlinear singularly perturbed interior layer problems is examined in this paper. Solutions exhibit an interior layer at an a priori unknown location. A numerical method is presented that uses a piecewise uniform mesh refined around approximations to the first two terms of the asymptotic expansion of the interior layer location. The first term in the expansion is used exactly in the construction of the approximation which restricts the range of problem data considered. The method is shown to converge point-wise to the true solution with a first order convergence rate (overlooking a logarithmic factor) for sufficiently small …

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Bergm: Bayesian Exponential Random Graphs In R, Alberto Caimo, Nial Friel Jan 2014

Bergm: Bayesian Exponential Random Graphs In R, Alberto Caimo, Nial Friel

Articles

In this paper we describe the main featuress of the Bergm package for the open-source R software which provides a comprehensive framework for Bayesian analysis for exponential random graph models: tools for parameter estimation, model selection and goodness-of-fit diagnostics. We illustrate the capabilities of this package describing the algorithms through a tutorial analysis of three network datasets.

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New Insights On Free Energies And Saint-Venant’S Principle In Viscoelasticity, L. Diseri, G. Gentili, John Murrough Golden Jan 2014

New Insights On Free Energies And Saint-Venant’S Principle In Viscoelasticity, L. Diseri, G. Gentili, John Murrough Golden

Articles

This work was conceived in 1999 and brought near completion by 2003. Giorgio Gentili was deeply involved in this research until his untimely death. He is greatly missed. Work pressures on the other authors forced a postponement of research on this topic, originally envisaged as lasting a few months but in the event it turned out to be nearly ten years. We now dedicate this work to the memory of Giorgio and to his Family.

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Observing, Reporting, And Deciding In Networks Of Sentences, H. Jerome Keisler, Jeffrey M. Keisler Jan 2014

Observing, Reporting, And Deciding In Networks Of Sentences, H. Jerome Keisler, Jeffrey M. Keisler

Management Science and Information Systems Faculty Publication Series

In prior work we considered networks of agents who prove facts from their knowledge bases and report them to their neighbors in their common languages in order to help a decider verify a single sentence. In report complete networks, the signatures of the agents and the links between agents are rich enough to verify any decider's sentence that can be proved from the combined knowledge base. This paper introduces a more general setting where new observations may be added to knowledge bases and the decider must choose a sentence from a set of alternatives. We consider the question of when …

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Moser-Trudinger And Adams Type Inequalities And Their Applications, Nguyen Lam Jan 2014

Moser-Trudinger And Adams Type Inequalities And Their Applications, Nguyen Lam

Wayne State University Dissertations

In this dissertation, we study some variants of the Moser-Trudinger inequalities and Adams inequalities. The proofs of these inequalities relied crucially on the symmetrization arguments in the literature. By proposing new arguments and approaches, we develop successfully the critical versions of these well-known inequalities in many different settings where the rearrangement arguments may not be existed. As applications of our results, we also study in this dissertation the elliptic equations that contain the exponential nonlinearities.

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On A Tower Of Garcia And Stichtenoth, Seher Tutdere Jan 2014

On A Tower Of Garcia And Stichtenoth, Seher Tutdere

Turkish Journal of Mathematics

In 2003, Garcia and Stichtenoth constructed a recursive tower F = (F_n)_{n \geq 0} of algebraic function fields over the finite field F_q, where q = l^r with r \geq 1 and l > 2 is a power of the characteristic of F_q. They also gave a lower bound for the limit of this tower. In this paper, we compute the exact value of the genus of the algebraic function field F_n/F_q for each n \geq 0. Moreover, we prove that when q = 2^k, with k \geq 2, the limit of the tower F attains the lower bound given by …

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Two-Weighted Norm Inequality On Weighted Morrey Spaces, Xiaofeng Ye, Tengfei Wang Jan 2014

Two-Weighted Norm Inequality On Weighted Morrey Spaces, Xiaofeng Ye, Tengfei Wang

Turkish Journal of Mathematics

Let u and \omega be weight functions. We shall introduce the weighted Morrey spaces L^{p,\kappa} (\omega) and investigate the sufficient condition and necessary condition about the 2-weighted boundedness of the Hardy--Littlewood maximal operator.

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Homological Dimensions Of Complexes Related To Cotorsion Pairs, Chongqing Wei, Limin Wang, Husheng Qiao Jan 2014

Homological Dimensions Of Complexes Related To Cotorsion Pairs, Chongqing Wei, Limin Wang, Husheng Qiao

Turkish Journal of Mathematics

Let (A, B) be a cotorsion pair in R-Mod. We define and study notions of A dimension and B dimension of unbounded complexes, which is given by means of dg-projective resolution and dg-injective resolution, respectively. As an application, we extend the Gorenstein flat dimension of complexes, which was defined by Iacob. Gorenstein cotorsion, FP-projective, FP-injective, Ding projective, and Ding injective dimension are also extended from modules to complexes. Moreover, we characterize Noetherian rings, von Neumann regular rings, and QF rings by the FP-projective, FP-injective, and Ding projective (injective) dimension of complexes, respectively.

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Norden Structures Of Hessian Type, Arif Salimov, Aydin Gezer Jan 2014

Norden Structures Of Hessian Type, Arif Salimov, Aydin Gezer

Turkish Journal of Mathematics

In this paper, we show that Kähler (para-Kähler) manifolds admit a Norden--Hessian metric h = \nabla^2f if the function f is holomorphic (para-holomorphic), and we further consider the existence condition of para-Kähler structures for Norden--Hessian metrics.

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Adapted Basic Connections To A Certain Subfoliation On The Tangent Manifold Of A Finsler Space, Adelina Manea, Cristian Ida Jan 2014

Adapted Basic Connections To A Certain Subfoliation On The Tangent Manifold Of A Finsler Space, Adelina Manea, Cristian Ida

Turkish Journal of Mathematics

On the slit tangent manifold TM^0 of a Finsler space (M,F) there are given some natural foliations as vertical foliation and some other fundamental foliations produced by the vertical and horizontal Liouville vector fields, see [A. Bejancu, H. R. Farran, Finsler Geometry and Natural Foliations on the Tangent Bundle, Rep. Math. Physics 58, No. 1 (2006), 131--146]. In this paper we consider a (n,2n-1)-codimensional subfoliation (F_V,F_{\Gamma}) on TM^0 given by vertical foliation F_V and the line foliation spanned by vertical Liouville vector field \Gamma and we give a triplet of basic connections adapted to this subfoliation.

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Equivariant Structure Constants For Hamiltonian-T-Spaces, Ho Hon Leung Jan 2014

Equivariant Structure Constants For Hamiltonian-T-Spaces, Ho Hon Leung

Turkish Journal of Mathematics

If there exists a set of canonical classes on a compact Hamiltonian-T-space in the sense of R Goldin and S Tolman, we derive some formulas for certain equivariant structure constants in terms of other equivariant structure constants and the values of canonical classes restricted to some fixed points. These formulas can be regarded as a generalization of Tymoczko's results.

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Characteristic Classes On Grassmannians, Jin Shi, Jianwei Zhou Jan 2014

Characteristic Classes On Grassmannians, Jin Shi, Jianwei Zhou

Turkish Journal of Mathematics

In this paper, we study the geometry and topology on the oriented Grassmann manifolds. In particular, we use characteristic classes and the Poincaré duality to study the homology groups of Grassmann manifolds. We show that for k=2 or n \leq 8, the cohomology groups H^*(G(k,n), R) are generated by the first Pontrjagin class, the Euler classes of the canonical vector bundles. In these cases, the Poincaré duality: H^q(G(k,n), R) \to H_{k(n-k)-q}(G(k,n), R) can be expressed explicitly.

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The Geometry Of The Projective Joint Spectrum And The Commutativity Of Self-Adjoint Operators, Isaak Chagouel Jan 2014

The Geometry Of The Projective Joint Spectrum And The Commutativity Of Self-Adjoint Operators, Isaak Chagouel

Legacy Theses & Dissertations (2009 - 2024)

The theory of single operators is by now a very mature subject, with the notion of spectrum playing a key role in the theory. However, multivariate operator theory is only in its very early stages of development. There is not even wide agreement about how "the joint spectrum" of an n-tuple A = (A1, · · · , An) of bounded linear operators on the same Hilbert space H should be defined.

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On An Extension Of Riordan Array And Its Application In The Construction Of Convolution-Type And Abel-Type Identities, Tian-Xiao He, Leetsch Hsu, Xing Ron Ma Jan 2014

On An Extension Of Riordan Array And Its Application In The Construction Of Convolution-Type And Abel-Type Identities, Tian-Xiao He, Leetsch Hsu, Xing Ron Ma

Scholarship

Using the basic fact that any formal power series over the real or complex number field can always be expressed in terms of given polynomials {pn(t)}{pn(t)}, where pn(t)pn(t) is of degree nn, we extend the ordinary Riordan array (resp. Riordan group) to a generalized Riordan array (resp. generalized Riordan group) associated with {pn(t)}{pn(t)}. As new application of the latter, a rather general Vandermonde-type convolution formula and certain of its particular forms are presented. The construction of the Abel type identities using the generalized Riordan arrays is also discussed.

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Hyperbolic Expressions Of Polynomial Sequences And Parametric Number Sequences Defined By Linear Recurrence Relations Of Order 2, Tian-Xiao He, Peter Shiue, Tsui-Wei Weng Jan 2014

Hyperbolic Expressions Of Polynomial Sequences And Parametric Number Sequences Defined By Linear Recurrence Relations Of Order 2, Tian-Xiao He, Peter Shiue, Tsui-Wei Weng

Scholarship

A sequence of polynomial {an(x)} is called a function sequence of order 2 if it satisfies the linear recurrence relation of order 2: an(x) = p(x)an-1(x) + q(x)an-2(x) with initial conditions a0(x) and a1(x). In this paper we derive a parametric form of an(x) in terms of eθ with q(x) = B constant, inspired by Askey's and Ismail's works shown in [2] [6], and [18], respectively. With this method, we give the hyperbolic expressions of Chebyshev polynomials and Gegenbauer-Humbert Polynomials. The applications of the method to construct corresponding hyperbolic form of several well-known identities are also discussed in this paper.

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Symmetries Of Embedded Complete Bipartite Graphs, Erica Flapan, Nicole Lehle, Blake Mellor, Matt Pittluck, Xan Vongsathorn Jan 2014

Symmetries Of Embedded Complete Bipartite Graphs, Erica Flapan, Nicole Lehle, Blake Mellor, Matt Pittluck, Xan Vongsathorn

Mathematics, Statistics and Data Science Faculty Works

We characterize which automorphisms of an arbitrary complete bipartite graph Kn,m can be induced by a homeomorphism of some embedding of the graph in S3.

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Monomial Ideals Of Linear Type, Monica La Barbiera, Paola Lea Stagliano' Jan 2014

Monomial Ideals Of Linear Type, Monica La Barbiera, Paola Lea Stagliano'

Turkish Journal of Mathematics

Let S=K[x_1,…,x_n;y_1,…,y_m] be the polynomial ring in 2 sets of variables over a field K. We investigate some classes of monomial ideals of S in order to classify ideals of the linear type.

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Some Notes On Nil-Semicommutative Rings, Yinchun Qu, Junchao Wei Jan 2014

Some Notes On Nil-Semicommutative Rings, Yinchun Qu, Junchao Wei

Turkish Journal of Mathematics

A ring R is defined to be nil-semicommutative if ab \in N(R) implies arb \in N(R) for a, b, r \in R, where N(R) stands for the set of nilpotents of R. Nil-semicommutative rings are generalization of NI rings. It is proved that (1) R is strongly regular if and only if R is von Neumann regular and nil-semicommutative; (2) Exchange nil-semicommutative rings are clean and have stable range 1; (3) If R is a nil-semicommutative right MC2 ring whose simple singular right modules are YJ-injective, then R is a reduced weakly regular ring; (4) Let R be a nil-semicommutative …

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Generalized Derivations Centralizing On Jordan Ideals Of Rings With Involution, Lahcen Oukhtite, Abdellah Mamouni Jan 2014

Generalized Derivations Centralizing On Jordan Ideals Of Rings With Involution, Lahcen Oukhtite, Abdellah Mamouni

Turkish Journal of Mathematics

A classical result of Posner states that the existence of a nonzero centralizing derivation on a prime ring forces the ring to be commutative. In this paper we extend Posner's result to generalized derivations centralizing on Jordan ideals of rings with involution and discuss the related results. Moreover, we provide examples to show that the assumed restriction cannot be relaxed.

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Generalized Derivations On Jordan Ideals In Prime Rings, Mahmoud El-Soufi, Ahmed Aboubakr Jan 2014

Generalized Derivations On Jordan Ideals In Prime Rings, Mahmoud El-Soufi, Ahmed Aboubakr

Turkish Journal of Mathematics

Let R be a 2-torsion free prime ring with center Z(R), J be a nonzero Jordan ideal also a subring of R, and F be a generalized derivation with associated derivation d. In the present paper, we shall show that J\subseteq Z(R) if any one of the following properties holds: (i) [F(u), u]\in Z(R), (ii) F(u)u = ud(u), (iii) d(u^2)=2F(u)u, (iv) F(u^2)-2uF(u) = d(u^2)-2ud(u), (v) F^2(u)+3d^2(u)=2Fd(u)+2dF(u), (vi) F(u^2) = 2uF(u) for all u \in J.

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On Nr^*-Subgroups Of Finite Groups, Xianggui Zhong Jan 2014

On Nr^*-Subgroups Of Finite Groups, Xianggui Zhong

Turkish Journal of Mathematics

Let G be a finite group and let H be a subgroup of G. H is said to be an NR^*-subgroup of G if there exists a normal subgroup T of G such that G = HT and if whenever K \lhd H and g \in G, then K^g \cap H \cap T\leq K. A number of new characterizations of a group G are given, under the assumption that all Sylow subgroups of certain subgroups of G are NR^*-subgroups.

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Hölder Regularity For Weak Solutions Of Diagonal Divergence Quasilinear Degenerate Elliptic Systems, Yan Dong, Xuewei Cui Jan 2014

Hölder Regularity For Weak Solutions Of Diagonal Divergence Quasilinear Degenerate Elliptic Systems, Yan Dong, Xuewei Cui

Turkish Journal of Mathematics

In this paper, we establish Hölder regularity for weak solutions of a class of diagonal divergence quasilinear degenerate elliptic systems of Hörmander's vector fields when the coefficients belong to the class of VMO_X functions with respect to x and uniformly with respect to u, and the lower order terms satisfy a natural growth condition.

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Asymptotic Analysis Of The 2-Dimensional Soliton Solutions For The Nizhnik--Veselov--Novikov Equations, Meti̇n Ünal Jan 2014

Asymptotic Analysis Of The 2-Dimensional Soliton Solutions For The Nizhnik--Veselov--Novikov Equations, Meti̇n Ünal

Turkish Journal of Mathematics

In this paper we present a direct approach to determining a class of solutions, the asymptotic analysis of the dromion solutions, and their asymptotic properties of the Nizhnik--Veselov--Novikov equations by means of Pfaffians. The form of the solution obtained allows a detailed asymptotic analysis of the dromion solutions and compact expression for the phase shifts and changes of amplitude as a result of interaction of the dromions to be determined.

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Existence And Multiplicity Of Positive Solutions For Discrete Anisotropic Equations, Marek Galewski, Renata Wieteska Jan 2014

Existence And Multiplicity Of Positive Solutions For Discrete Anisotropic Equations, Marek Galewski, Renata Wieteska

Turkish Journal of Mathematics

In this paper we consider the Dirichlet problem for a discrete anisotropic equation with some function \alpha , a nonlinear term f, and a numerical parameter \lambda :\Delta (\alpha (k) \Delta u(k-1) ^{p(k-1)-2}\Delta u(k-1)) + \lambda f(k,u(k))=0, k\in [1,T] . We derive the intervals of a numerical parameter \lambda for which the considered BVP has at least 1, exactly 1, or at least 2 positive solutions. Some useful discrete inequalities are also derived.

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A Reproducing Kernel For A Hilbert Space Related To Harmonic Bergman Space On A Domain Outside Compact Set, Alem Memic Jan 2014

A Reproducing Kernel For A Hilbert Space Related To Harmonic Bergman Space On A Domain Outside Compact Set, Alem Memic

Turkish Journal of Mathematics

In this paper for 1\leq p

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Pullback Diagram Of H^*-Algebras, Mahnaz Khanehgir, Maryam Amyari, Marzieh Moradian Khibary Jan 2014

Pullback Diagram Of H^*-Algebras, Mahnaz Khanehgir, Maryam Amyari, Marzieh Moradian Khibary

Turkish Journal of Mathematics

In this paper we obtain some properties for the pullback diagram of H^*-algebras. More precisely, we prove that the commutative diagram of H^*-algebras and morphisms A_1 @>\varphi_1>> B_1 @VV\psi_1V @VV\psi_2V A_2 @>\varphi_2>> B_2 is pullback and \psi_1 is an injection if and only if \psi_1 is a surjection, \psi_2 is an injection, and \ker \varphi_1 \cap \ker \psi_1 = \{0\}.

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Semi-Cotangent Bundle And Problems Of Lifts, Furkan Yildirim, Arif Salimov Jan 2014

Semi-Cotangent Bundle And Problems Of Lifts, Furkan Yildirim, Arif Salimov

Turkish Journal of Mathematics

Using the fiber bundle M over a manifold B, we define a semi-cotangent (pull-back) bundle t^{\ast}B, which has a degenerate symplectic structure. We consider lifting problem of projectable geometric objects on M to the semi-cotangent bundle. Relations between lifted objects and a degenerate symplectic structure are also presented.

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On Generalized Robertson--Walker Spacetimes Satisfying Some Curvature Condition, Kadri̇ Arslan, Ryszard Deszcz, Ridvan Ezentaş, Marian Hotlos, Cengi̇zhan Murathan Jan 2014

On Generalized Robertson--Walker Spacetimes Satisfying Some Curvature Condition, Kadri̇ Arslan, Ryszard Deszcz, Ridvan Ezentaş, Marian Hotlos, Cengi̇zhan Murathan

Turkish Journal of Mathematics

We give necessary and sufficient conditions for warped product manifolds (M,g), of dimension \geqslant 4, with 1-dimensional base, and in particular, for generalized Robertson--Walker spacetimes, to satisfy some generalized Einstein metric condition. Namely, the difference tensor R . C - C . R, formed from the curvature tensor R and the Weyl conformal curvature tensor C, is expressed by the Tachibana tensor Q(S,R) formed from the Ricci tensor S and R. We also construct suitable examples of such manifolds. They are quasi-Einstein, i.e. at every point of M rank (S - \alpha g) \leqslant 1, for some \alpha \in R, …

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Counting Pseudo-Anosov Mapping Classes On The 3-Punctured Projective Plane, Blazej Szepietowski Jan 2014

Counting Pseudo-Anosov Mapping Classes On The 3-Punctured Projective Plane, Blazej Szepietowski

Turkish Journal of Mathematics

We prove that in the pure mapping class group of the 3-punctured projective plane equipped with the word metric induced by certain generating set, the ratio of the number of pseudo-Anosov elements to the number of all elements in a ball centered at the identity tends to one, as the radius of the ball tends to infinity. We also compute growth functions of the sets of reducible and pseudo-Anosov elements.

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