Solving A Generalized Heron Problem By Means Of Convex Analysis,
2010
Wayne State University
Solving A Generalized Heron Problem By Means Of Convex Analysis, Boris S. Mordukhovich, Nguyen Mau Nam, Juan Salinas Jr
Mathematics Research Reports
The classical Heron problem states: on a given straight line in the plane, find a point C such that the sum of the distances from C to the given points A and B is minimal. This problem can be solved using standard geometry or differential calculus. In the light of modern convex analysis, we are able to investigate more general versions of this problem. In this paper we propose and solve the following problem: on a given nonempty closed convex subset of IR!, find a point such that the sum of the distances from that point to n given nonempty …
Positive Solutions Of Singular Complementary Lidstone Boundary Value Problems,
2010
Florida Institute of Technology
Positive Solutions Of Singular Complementary Lidstone Boundary Value Problems, Ravi P. Agarwal, Donal O'Regan, Svatoslav Staněk
Mathematics and System Engineering Faculty Publications
We investigate the existence of positive solutions of singular problem (-1)mx(2m+1) = f(t, x,⋯, x(2m)), x (0) = 0, x(2i-1) (0) = x(2i-1) (T) = 0, 1 ≤ i ≤ m. Here, m ≥ 1 and the Carathéodory function f (t, x0,⋯, x2m) may be singular in all its space variables x0,⋯, x2m. The results are proved by regularization and sequential techniques. In limit processes, the Vitali convergence theorem is used.
Burkholder Integrals, Morrey's Problem And Quasiconformal Mappings,
2010
University of Helsinki
Burkholder Integrals, Morrey's Problem And Quasiconformal Mappings, Kari Astala, Tadeusz Iwaniec, Istvan Prause, Eero Saksman
Mathematics - All Scholarship
Inspired by Morrey's Problem (on rank-one convex functionals) and the Burkholder integrals (of his martingale theory) we find that the Burkholder functionals Bp, p > 2, are quasiconcave, when tested on deformations of identity f in Id+Coinifinty (omega) with Bp (Df(x)) > 0 pointwise, or equivalently, deformations such that abs[Df]2 < (p/(p-2))Jf. In particular, this holds in explicit neighbourhoods of the identity map. Among the many immediate consequences, this gives the strongest possible Lp-estimates for the gradient of a principal solution to the Beltrami equation fz = mu(z)fz , for any p in …
Feedback Control Of A Bioinspired Plate-Beam System,
2010
Missouri University of Science and Technology
Feedback Control Of A Bioinspired Plate-Beam System, Cody W. Ray, Belinda A. Batten, John R. Singler
Mathematics and Statistics Faculty Research & Creative Works
In this paper we present a model for a plate-beam system to represent a bioinspired flexible wing. Using a Galerkin based finite element approximation to the system, we compute functional gains that can be used for sensor placement and show that a piezoceramic actuator on the beam can be used for camber control
Completeness Of Ordered Fields,
2010
California Polytechnic State University, San Luis Obispo
Completeness Of Ordered Fields, James Forsythe Hall
Mathematics
The main goal of this project is to prove the equivalency of several characterizations of completeness of Archimedean ordered fields; some of which appear in most modern literature as theorems following from the Dedekind completeness of the real numbers, while a couple are not as well known and have to do with other areas of mathematics, such as nonstandard analysis. Continuing, we study the completeness of non-Archimedean fields, and provide several examples of such fields with varying degrees of properties, using nonstandard analysis to produce some relatively "nice" (in particular, they are Cantor complete) final examples. As a small detour, …
The Gini Index And Measures Of Inequality,
2010
Santa Clara University
The Gini Index And Measures Of Inequality, Frank A. Farris
Mathematics and Computer Science
The Gini index is a summary statistic that measures how fairly a resource is distributed in a population; income is a primary example. In addition to a self-contained presentation of the Gini index, we give two equivalent ways to interpret this summary statistic: first in terms of the percentile level of the person who earns the average dollar, and second in terms of how the lower of two randomly chosen incomes compares, on average, to mean income.
Generalized Twisted Quantum Doubles And The Mckay Correspondence,
2010
University of the Pacific
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 …
Sums Of Evenly Spaced Binomial Coefficients,
2010
Harvey Mudd College
Sums Of Evenly Spaced Binomial Coefficients, Arthur T. Benjamin, Bob Chen '10, Kimberly Kindred
All HMC Faculty Publications and Research
We provide a combinatorial proof of a formula for the sum of evenly spaced binomial coefficients. This identity, along with a generalization, are proved by counting weighted walks on a graph.
Closed-Range Composition Operators On A2 And The Bloch Space,
2010
University of Arkansas
Closed-Range Composition Operators On A2 And The Bloch Space, John R. Akeroyd, Pratibha G. Ghatage, Maria Tjani
Mathematics and Statistics Faculty Publications
For any analytic self-map φ of {z : |z| < 1} we give four separate conditions, each of which is necessary and sufficient for the composition operator Cφ to be closed-range on the Bloch space B . Among these conditions are some that appear in the literature, where we provide new proofs. We further show that if Cφ is closed-range on the Bergman space A2 , then it is closed-range on B , but that the converse of this fails with a vengeance. Our analysis involves an extension of the Julia-Carathéodory Theorem.
On Some Fractional Integral Operators Involving Generalized Gauss Hypergeometric Functions,
2010
National Technical University of Ukraine “KPI
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.
A New Method For Fuzzy Critical Path Analysis In Project Networks With A New Representation Of Triangular Fuzzy Numbers,
2010
Thapar University
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.
Optimal Correction Of Infeasible System In Linear Equality Via Genetic Algorithm,
2010
University of Guilan
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.
Solutions Of Nonlinear Second Order Multi-Point Boundary Value Problems By Homotopy Perturbation Method,
2010
Banaras Hindu University
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,
2010
Banaras Hindu University
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.
Approximate Approach To The Das Model Of Fractional Logistic Population Growth,
2010
Banaras Hindu University
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.
On The Eigenvalue And Inertia Problems For Descriptor Systems,
2010
University of Guilan
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.
Markov Chains And Dynamical Systems: The Open System Point Of View,
2010
Louisiana State University
Markov Chains And Dynamical Systems: The Open System Point Of View, Stéphane Attal
Communications on Stochastic Analysis
No abstract provided.
Transformation Of Quantum Lévy Processes On Hopf Algebras,
2010
Louisiana State University
Transformation Of Quantum Lévy Processes On Hopf Algebras, Michael Schürmann, Michael Skeide, Silvia Volkwardt
Communications on Stochastic Analysis
No abstract provided.
Characterization Of Unitary Processes With Independent Increments,
2010
Louisiana State University
Characterization Of Unitary Processes With Independent Increments, Un Cig Ji, Lingaraj Sahu, Kalyan B Sinha
Communications on Stochastic Analysis
No abstract provided.
How To Differentiate A Quantum Stochastic Cocycle,
2010
Louisiana State University
How To Differentiate A Quantum Stochastic Cocycle, J Martin Lindsay
Communications on Stochastic Analysis
No abstract provided.
