Mathematics Commons^™

The Cohomology Of Modules Over A Complete Intersection Ring, Jesse Burke

Department of Mathematics: Dissertations, Theses, and Student Research

We investigate the cohomology of modules over commutative complete intersection rings. The first main result is that if M is an arbitrary module over a complete intersection ring R, and if one even self-extension module of M vanishes then M has finite projective dimension. The second main result gives a new proof of the fact that the support variety of a Cohen-Macaulay module whose completion is indecomposable is projectively connected.

Rademacher-Type Formulas For Restricted Partition And Overpartition Functions, Andrew Sills

Mathematical Sciences: Faculty Publications

A collection of Hardy-Ramanujan-Rademacher type formulas for restricted partition and overpartition functions is presented, framed by several biographical anecdotes.

On Some Fractional Integral Operators Involving Generalized Gauss Hypergeometric Functions, N. Virchenko, O. Lisetska, S. L. Kalla

Applications and Applied Mathematics: An International Journal (AAM)

The object of this paper is to give a generalization of Gauss hypergeometric function, and to investigate its basic properties. Further, we define some fractional integral operators and their inverses in terms of the Mellin transform. Several well known integral operators, including Saigo operators can be derived from the results established here.

Exact Solutions Of The Generalized- Zakharov (Gz) Equation By The Infinite Series Method, N. Taghizadeh, M. Mirzazadeh, F. Farahrooz

Applications and Applied Mathematics: An International Journal (AAM)

The infinite series method is an efficient method for obtaining exact solutions of some nonlinear partial differential equations. This method can be applied to nonintegrable equations as well as to integrable ones. In this paper, the direct algebraic method is used to construct new exact solutions of generalized- Zakharov equation.

A New Method For Fuzzy Critical Path Analysis In Project Networks With A New Representation Of Triangular Fuzzy Numbers, Amit Kumar, Parmpreet Kaur

Applications and Applied Mathematics: An International Journal (AAM)

The method for finding fuzzy optimal solution of fully fuzzy critical path (FFCP) problems i.e., critical path problems in which all the parameters are represented by fuzzy numbers, is at best scant; possibly non-existent. In this paper, a method is proposed to find the fuzzy optimal solution of FFCP problems, together with a new representation of triangular fuzzy numbers. This paper will show the advantages of using, the proposed representation over the existing representations of triangular fuzzy numbers and will present with great clarity the proposed method and illustrate its application to FFCP problems occurring in real life situations.

An Analytical Technique For Solving Nonlinear Heat Transfer Equations, Hossein Aminikhah, Milad Hemmatnezhad

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, an analytic technique, namely the New Homotopy Perturbation Method (NHPM) is applied for solving the nonlinear differential equations arising in the field of heat transfer. In this method, the solution is considered as an infinite series expansion where converges rapidly to the exact solution. The nonlinear convective–radioactive cooling equation and nonlinear equation of conduction heat transfer with the variable physical properties are chosen as illustrative examples and the exact solutions have been found for each case.

Duality In Fuzzy Linear Programming With Symmetric Trapezoidal Numbers, S. H. Nasseri, E. Ebrahimnejad, S. Mizuno

Applications and Applied Mathematics: An International Journal (AAM)

Linear programming problems with trapezoidal fuzzy numbers have recently attracted much interest. Various methods have been developed for solving these types of problems. Here, following the work of Ganesan and Veeramani and using the recent approach of Mahdavi-Amiri and Nasseri, we introduce the dual of the linear programming problem with symmetric trapezoidal fuzzy numbers and establish some duality results. The results will be useful for post optimality analysis.

Approximate Approach To The Das Model Of Fractional Logistic Population Growth, S. Das, P. K. Gupta, K. Vishal

Applications and Applied Mathematics: An International Journal (AAM)

In this article, the analytical method, Homotopy perturbation method (HPM) has been successfully implemented for solving nonlinear logistic model of fractional order. The fractional derivatives are described in the Caputo sense. Using initial value, the explicit solutions of population size for different particular cases have been derived. Numerical results show that the method is extremely efficient to solve this complicated biological model.

Optimal Correction Of Infeasible System In Linear Equality Via Genetic Algorithm, S. Ketabchi, H. Moosaei, S. Fallahi

Applications and Applied Mathematics: An International Journal (AAM)

This work is focused on the optimal correction of infeasible system of linear equality. In this paper, for correcting this system, we will make the changes just in the coefficient matrix by using l 􀬶 norm and show that solving this problem is equivalent to solving a fractional quadratic problem. To solve this problem, we use the genetic algorithm. Some examples are provided to illustrate the efficiency and validity of the proposed method.

Slider-Pinning Rigidity: A Maxwell-Laman-Type Theorem, Ileana Streinu, Louis Theran

Computer Science: Faculty Publications

We define and study slider-pinning rigidity, giving a complete combinatorial characterization. This is done via direction-slider networks, which are a generalization of Whiteley’s direction networks.

Solutions Of Nonlinear Second Order Multi-Point Boundary Value Problems By Homotopy Perturbation Method, S. Das, Sunil Kumar, O. P. Singh

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we present an algorithm for the numerical solution of the second order multi- point boundary value problem with suitable multi boundary conditions. The algorithm is based on the homotopy perturbation approach and the solutions are calculated in the form of a rapid convergent series. It is observed that the method gives more realistic series solutions that converge very rapidly in physical problems. Illustrative numerical examples are provided to demonstrate the efficiency and simplicity of the proposed method in solving this type of multipoint boundary value problems.

Approximate Analytical Solutions For Fractional Space- And Time- Partial Differential Equations Using Homotopy Analysis Method, Subir, Das, R. Kumar, P. K. Gupta, Hossein Jafari

Applications and Applied Mathematics: An International Journal (AAM)

This article presents the approximate analytical solutions of first order linear partial differential equations (PDEs) with fractional time- and space- derivatives. With the aid of initial values, the explicit solutions of the equations are solved making use of reliable algorithm like homotopy analysis method (HAM). The speed of convergence of the method is based on a rapidly convergent series with easily computable components. The fractional derivatives are described in Caputo sense. Numerical results show that the HAM is easy to implement and accurate when applied to space- time- fractional PDEs.

On The Eigenvalue And Inertia Problems For Descriptor Systems, Asadollah Aasaraai, Kameleh N. Pirbazari

Applications and Applied Mathematics: An International Journal (AAM)

The present study is intended to demonstrate that for a descriptor system with matrix pencil there exists a matrix such that matrix and matrix pencil have the same positive and negative eigenvalues. It is also shown that matrix can be calculated as a contour integral. On the other hand, different representations for matrix are introduced.

Structures On A K3 Surface, Nathan P. Rowe

UNLV Theses, Dissertations, Professional Papers, and Capstones

In the first part of this paper, we examine properties of K3 surfaces of the form:

(x2 + 1)(y2 + 1)(z2 + 1) + Axyz − 2 = 0

We show the surface has Picard number q " 12 by finding 12 curves whose equivalence classes are linearly independent. These curves have self intersection −2. We find the lattice representations of the single-coordinate swapping automorphisms in x, y, and z. We show that we have enough of the Lattice to make accurate predictions of polynomial degree growth under the automorphisms. We describe these automorphisms in terms of operations on elliptic …

Generalized Twisted Quantum Doubles And The Mckay Correspondence, Christopher D. Goff, Geoffrey Mason

College of the Pacific Faculty Articles

We consider a class of quasiHopf algebras which we call generalized twisted quantum doubles. They are abelian extensions H=C[G¯]∗⋈C[G] (G is a finite group, G¯ a homomorphic image, and * denotes the dual algebra), possibly twisted by a 3-cocycle, and are a natural generalization of the twisted quantum double construction of Dijkgraaf, Pasquier and Roche. We show that if G is a subgroup of SU₂(C) then H exhibits an orbifold McKay Correspondence: certain fusion rules of H define a graph with connected components indexed by conjugacy classes of G¯, each connected component being an extended affine Diagram of …

Invariant And Coinvariant Spaces For The Algebra Of Symmetric Polynomials In Non-Commuting Variables, Francois Bergeron, Aaron Lauve

Mathematics and Statistics: Faculty Publications and Other Works

We analyze the structure of the algebra K⟨x⟩Sn of symmetric polynomials in non-commuting variables in so far as it relates to K[x]Sn, its commutative counterpart. Using the "place-action" of the symmetric group, we are able to realize the latter as the invariant polynomials inside the former. We discover a tensor product decomposition of K⟨x⟩Sn analogous to the classical theorems of Chevalley, Shephard-Todd on finite reflection groups.

Résumé. Nous analysons la structure de l'algèbre K⟨x⟩Sn des polynômes symétriques en des variables non-commutatives pour obtenir des analogues des résultats classiques concernant la structure de l'anneau K[x]Sn des polynômes symétriques en des variables …

The Hopf-Laplace Equation, Jan Cristina, Tadeusz Iwaniec, Leonid V. Kovalev, Jani Onninen

Mathematics - All Scholarship

The central theme in this paper is the Hopf-Laplace equation, which represents stationary solutions with respect to the inner variation of the Dirichlet integral. Among such solutions are harmonic maps. Nevertheless, minimization of the Dirichlet energy among homeomorphisms often leads to nonharmonic solutions. We investigate the Hopf-Laplace equation for a certain class of topologically well behaved mappings which are almost homeomorphisms, called Hopf deformations. We establish Lipschitz continuity of Hopf deformations, the best possible regularity one can get. Thus in particular we show that the minimal-energy deformations are Lipschitz continuous, a result of considerable interest in the theory of minimal …

Building Graphs From Colored Trees, Rachel M. Esselstein, Peter Winkler

Dartmouth Scholarship

We will explore the computational complexity of satisfying certain sets of neighborhood conditions in graphs with various properties. More precisely, fix a radius $\rho$ and let $N(G)$ be the set of isomorphism classes of $\rho$-neighborhoods of vertices of $G$ where $G$ is a graph whose vertices are colored (not necessarily properly) by colors from a fixed finite palette. The root of the neighborhood will be the unique vertex at the "center" of the graph. Given a set S of colored graphs with a unique root, when is there a graph G with N (G) = S? Or N (G) ⊂ …

Fixed Point Theorems For Ws-Compact Mappings In Banach Spaces, Ravi P. Agarwal, Donal O'Regan, Mohamed-Aziz Taoudi

Mathematics and System Engineering Faculty Publications

We present new fixed point theorems for ws-compact operators. Our fixed point results are obtained under Sadovskii, Leray-Schauder, Rothe, Altman, Petryshyn, and Furi-Pera type conditions. An example is given to show the usefulness and the applicability of our results.

On The Construction Of Explicit Solutions To The Matrix Equation X2ax = Axa, Aihua Li, Edward Mosteig

Department of Mathematics Faculty Scholarship and Creative Works

In a previous article by Aihua Li and Duane Randall, the existence of solutions to certain matrix equations is demonstrated via nonconstructive methods. A recurring example appears in that work, namely the matrix equation AXA = X2AX, where A is a fixed, square matrix with real entries and X is an unknown square matrix. In this paper, the solution space is explicitly constructed for all 2×2 complex matrices using Gröbner basis techniques. When A is a 2×2 matrix, the equation AXA = X2AX is equivalent to a system of four polynomial equations. The solution space then is the variety defined …