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Articles 1 - 12 of 12
Full-Text Articles in Education
Homological Dimensions And Regular Rings, Alina Iacob, Srikanth B. Iyengar
Homological Dimensions And Regular Rings, Alina Iacob, Srikanth B. Iyengar
Department of Mathematical Sciences Faculty Publications
A question of Avramov and Foxby concerning injective dimension of complexes is settled in the affirmative for the class of noetherian rings. A key step in the proof is to recast the problem on hand into one about the homotopy category of complexes of injective modules. Analogous results for flat dimension and projective dimension are also established.
Interior-Point Algorithms For A Class Of Convex Optimization Problems, Goran Lesaja, Verlynda Slaughter
Interior-Point Algorithms For A Class Of Convex Optimization Problems, Goran Lesaja, Verlynda Slaughter
Department of Mathematical Sciences Faculty Publications
In this paper we consider interior-point methods (IPM) for the nonlinear, convex optimization problem where the objective function is a weighted sum of reciprocals of variables subject to linear constraints (SOR). This problem appears often in various applications such as statistical stratified sampling and entropy problems, to mention just few examples. The SOR is solved using two IPMs. First, a homogeneous IPM is used to solve the Karush-Kuhn-Tucker conditions of the problem which is a standard approach. Second, a homogeneous conic quadratic IPM is used to solve the SOR as a reformulated conic quadratic problem. As far as we are …
Lifting Bailey Pairs To Wp-Bailey Pairs, James Mclaughlin, Andrew Sills, Peter Zimmer
Lifting Bailey Pairs To Wp-Bailey Pairs, James Mclaughlin, Andrew Sills, Peter Zimmer
Department of Mathematical Sciences Faculty Publications
A pair of sequences (αn(a,k,q),βn(a,k,q)) such that α0(a,k,q)=1 and βn(a,k,q)=∑nj=0 (k/a;q)n−j (k;q)n+j / (q;q)n−j (aq;q)n+j αj (a,k,q) is termed a WP-Bailey Pair. Upon setting k=0 in such a pair we obtain a Bailey pair.
In the present paper we consider the problem of “lifting” a Bailey pair to a WP-Bailey pair, and use some …
Rogers-Ramanujan Computer Searches, James Mclaughlin, Andrew Sills, Peter Zimmer
Rogers-Ramanujan Computer Searches, James Mclaughlin, Andrew Sills, Peter Zimmer
Department of Mathematical Sciences Faculty Publications
We describe three computer searches (in PARI/GP, Maple, and Mathematica, respectively) which led to the discovery of a number of identities of Rogers–Ramanujan type and identities of false theta functions.
Some More Identities Of Rogers-Ramanujan Type, Douglas Bowman, James Mclaughlin, Andrew Sills
Some More Identities Of Rogers-Ramanujan Type, Douglas Bowman, James Mclaughlin, Andrew Sills
Department of Mathematical Sciences Faculty Publications
In this we paper we prove several new identities of the Rogers-Ramanujan-Slater type. These identities were found as the result of computer searches. The proofs involve a variety of techniques, including series-series identities, Bailey pairs, a theorem of Watson on basic hypergeometric series, generating functions and miscellaneous methods.
Interpolation Theorems For Self-Adjoint Operators, Shijun Zheng
Interpolation Theorems For Self-Adjoint Operators, Shijun Zheng
Department of Mathematical Sciences Faculty Publications
We prove a complex and a real interpolation theorems on Besov spaces and Triebel-Lizorkin spaces associated with a self adjoint operator L, without assuming the gradient estimate for its spectral kernel. The result applies to the cases where L is a uniformly elliptic operator or a Schrödinger operator with electro-magnetic potential.
On Fourier Parabolic And Wave Equation, Mekki Terbeche, Broderick O. Oluyede
On Fourier Parabolic And Wave Equation, Mekki Terbeche, Broderick O. Oluyede
Department of Mathematical Sciences Faculty Publications
This paper is devoted to a diffusion (heat) and wave equations for the function of two independent variables. We establish a criterion for existence and uniqueness of the solution of Fourier parabolic equation using Taylor series. A formal solution for a wave equation is investigated.
Gorenstein Flat Dimension Of Complexes, Alina Iacob
Gorenstein Flat Dimension Of Complexes, Alina Iacob
Department of Mathematical Sciences Faculty Publications
We define a notion of Gorenstein flat dimension for unbounded complexes over left GF-closed rings. Over Gorenstein rings we introduce a notion of Gorenstein cohomology for complexes; we also define a generalized Tate cohomology for complexes over Gorenstein rings, and we show that there is a close connection between the absolute, the Gorenstein and the generalized Tate cohomology.
Introducing Interior-Point Methods For Introductory Operations Research Courses And/Or Linear Programming Courses, Goran Lesaja
Introducing Interior-Point Methods For Introductory Operations Research Courses And/Or Linear Programming Courses, Goran Lesaja
Department of Mathematical Sciences Faculty Publications
In recent years the introduction and development of Interior-Point Methods has had a profound impact on optimization theory as well as practice, influencing the field of Operations Research and related areas. Development of these methods has quickly led to the design of new and efficient optimization codes particularly for Linear Programming. Consequently, there has been an increasing need to introduce theory and methods of this new area in optimization into the appropriate undergraduate and first year graduate courses such as introductory Operations Research and/or Linear Programming courses, Industrial Engineering courses and Math Modeling courses. The objective of this paper is …
Establishment Of Weak Conditions For Darboux-Goursat-Beudon Theorem, Mekki Terbeche, Broderick O. Oluyede
Establishment Of Weak Conditions For Darboux-Goursat-Beudon Theorem, Mekki Terbeche, Broderick O. Oluyede
Department of Mathematical Sciences Faculty Publications
This paper is devoted to the establishment of weak conditions for Darboux-Goursat-Beudon (DGB) theorem in order to improve analogous results in [1, 7]. By adapting a technique proposed by [7] in another setting [8] via majorant method, we obtain the generalization of DGB theorem.
Combinatorics Of Ramanujan-Slater Type Identities, James Mclaughlin, Andrew Sills
Combinatorics Of Ramanujan-Slater Type Identities, James Mclaughlin, Andrew Sills
Department of Mathematical Sciences Faculty Publications
We provide the missing member of a family of four q-series identities related to the modulus 36, the other members having been found by Ramanujan and Slater. We examine combinatorial implications of the identities in this family, and of some of the identities we considered in Identities of the Ramanujan-Slater type related to the moduli 18 and 24.
On Some Differential Equations, Mekki Terbeche, Broderick O. Oluyede
On Some Differential Equations, Mekki Terbeche, Broderick O. Oluyede
Department of Mathematical Sciences Faculty Publications
This paper investigates Cauchy and Goursat problems for partial differential operators. Successive approximation techniques for partial differential equations and the estimated results are employed to obtain the existence and the uniqueness of the solutions of such problems. An extended Darboux-Goursat-Beudon problem is studied.