Mathematics Commons^™

Geometric Programming Subject To System Of Fuzzy Relation Inequalities, Elyas Shivanian, Mahdi Keshtkar, Esmaile Khorram

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, an optimization model with geometric objective function is presented. Geometric programming is widely used; many objective functions in optimization problems can be analyzed by geometric programming. We often encounter these in resource allocation and structure optimization and technology management, etc. On the other hand, fuzzy relation equalities and inequalities are also used in many areas. We here present a geometric programming model with a monomial objective function subject to the fuzzy relation inequality constraints with maxproduct composition. Simplification operations have been given to accelerate the resolution of the problem by removing the components having no effect on …

Distal Fuzzy Dynamical Systems, Y. Sayyari, M. R. Molaei

Applications and Applied Mathematics: An International Journal (AAM)

In this paper the t-distal notion is extended for fuzzy dynamical systems on fuzzy metric spaces. A method for constructing fuzzy metric spaces is studied. The product of t-distal fuzzy dynamical systems is considered. It is proved that: a product of fuzzy dynamical systems is t- distal if and only if its components are t-distal. The persistence of the t-distal property up to a fuzzy factor map is proved.

A New Four Point Circular-Invariant Corner-Cutting Subdivision For Curve Design, Jian-Ao Lian

Applications and Applied Mathematics: An International Journal (AAM)

A 4-point nonlinear corner-cutting subdivision scheme is established. It is induced from a special C-shaped biarc circular spline structure. The scheme is circular-invariant and can be effectively applied to 2-dimensional (2D) data sets that are locally convex. The scheme is also extended adaptively to non-convex data. Explicit examples are demonstrated.

Q -Analogs Of Identities Involving Harmonic Numbers And Binomial Coefficients, Toufik Mansour, Mark Shattuck, Chunwei Song

Applications and Applied Mathematics: An International Journal (AAM)

Recently, McCarthy presented two algebraic identities involving binomial coefficients and harmonic numbers, one of which generalizes an identity used to prove the Apéry number supercongruence. In 2008, Prodinger provided human proofs of identities initially obtained by Osburn and Schneider using the computer program Sigma. In this paper, we establish q -analogs of a fair number of the identities appearing in McCarthy (Integers 11 (2011): A37) and Prodinger (Integers 8 (2008): A10) by making use of q -partial fractions.

Fractional Integrals And Derivatives For Sumudu Transform On Distribution Spaces, Deshna Loonker, P. K. Banerji

Applications and Applied Mathematics: An International Journal (AAM)

We propose, in the present paper, the investigation of the Sumudu transformation for certain distribution spaces with regard to the fractional integral and differential operators of the transform. This paper is organized in two sections, first of which gives an abriged text on fractional operators and the Sumudu transform (which is less discussed and reserached). Basic concept in analysing the investigation is initiated by the fact that the Riemann-Liouville fractional integral can be expressed as one of the appropriate forms of the Abel integral equation, which is the second section of this paper.

Numerical Solution Of Interval And Fuzzy System Of Linear Equations, Suparna Das, S. Chakraverty

Applications and Applied Mathematics: An International Journal (AAM)

A system of linear equations, in general is solved in open literature for crisp unknowns, but in actual case the parameters (coefficients) of the system of linear equations contain uncertainty and are less crisp. The uncertainties may be considered in term of interval or fuzzy number. In this paper, a detail of study of linear simultaneous equations with interval and fuzzy parameter (triangular and trapezoidal) has been performed. New methods have been proposed for solving such systems. First, the methods have been tested for known problems viz. a circuit analysis solved in the literature and the results are found to …

Two Numerical Algorithms For Solving A Partial Integro-Differential Equation With A Weakly Singular Kernel, Jeong-Mi Yoon, Shishen Xie, Volodymyr Hrynkiv

Applications and Applied Mathematics: An International Journal (AAM)

Two numerical algorithms based on variational iteration and decomposition methods are developed to solve a linear partial integro-differential equation with a weakly singular kernel arising from viscoelasticity. In addition, analytic solution is re-derived by using the variational iteration method and decomposition method.

Modeling Glacial Termination, Michael Murphy

Natural Resources Management and Environmental Sciences

Examines possible cause of the glacial termination or ice age cycle using a numerical model created by Tziperman et al. Also explores possible physical mechanisms causing the observed cycle of slow cooling followed by rapid warming.

A Novel Algorithm To Forecast Enrollment Based On Fuzzy Time Series, Haneen T. Jasim, Abdul G. Jasim Salim, Kais I. Ibraheem

Applications and Applied Mathematics: An International Journal (AAM)

In this paper we propose a new method to forecast enrollments based on fuzzy time series. The proposed method belongs to the first order and time-variant methods. Historical enrollments of the University of Alabama from year 1948 to 2009 are used in this study to illustrate the forecasting process. By comparing the proposed method with other methods we will show that the proposed method has a higher accuracy rate for forecasting enrollments than the existing methods.

Variations On A Graph Coloring Theme, Bryan Phinezy

Dissertations

Historically, the subject of graph colorings has been the most popular research area in graph theory. There are many problems in mathematics and in real life that can be represented by a graph and whose solution involves finding a specific coloring of this graph. Our research consists of two parts: (1) combinatorial problems and vertex colorings and (2) distance-defined colorings. In this research, we show that certain combinatorial puzzles and problems can be placed in a graph coloring setting and graph colorings can be defined in terms of distance in graphs that are useful in applications.

Two vertices u and …

Estimation And Testing For Spatially Indexed Curves With Application To Ionospheric And Magnetic Field Trends, Oleksandr Gromenko, Piotr Kokoszka, Lie Zhu, Jan Josef Sojka

All Physics Faculty Publications

We develop methodology for the estimation of the functional mean and the functional principal components when the functions form a spatial process. The data consist of curves X(sk;t), t∈[0, T], observed at spatial locations s1,s2, . . . ,sN. We propose several methods, and evaluate them by means of a simulation study. Next, we develop a significance test for the correlation of two such functional spatial fields. After validating the finite sample performance of this test by means of a simulation study, we apply it to determine if there is correlation between long-term trends in the so-called critical ionospheric frequency …

Cyclic Matching Sequencibility Of Graphs, Richard A. Brualdi, Kathleen P. Kiernan, Seth A. Meyer, Michael W. Schroeder

Mathematics Faculty Research

We define the cyclic matching sequencibility of a graph to be the largest integer d such that there exists a cyclic ordering of its edges so that every d consecutive edges in the cyclic ordering form a matching. We show that the cyclic matching sequencibility of K_2m and K_2m+1 equals m − 1.

A Guide To Rbf-Generated Finite Differences For Nonlinear Transport: Shallow Water Simulations On A Sphere, Natasha Flyer, Erik Lehto, Sébastien Blaise, Grady Wright, Amik St-Cyr

Mathematics Faculty Publications and Presentations

The current paper establishes the computational efficiency and accuracy of the RBF-FD method for large-scale geoscience modeling with comparisons to state-of-the-art methods as high-order discontinuous Galerkin and spherical harmonics, the latter using expansions with close to 300,000 bases. The test cases are demanding fluid flow problems on the sphere that exhibit numerical challenges, such as Gibbs phenomena, sharp gradients, and complex vortical dynamics with rapid energy transfer from large to small scales over short time periods. The computations were possible as well as very competitive due to the implementation of hyperviscosity on large RBF stencil sizes (corresponding roughly to 6th …

Scattered Data Interpolation On Embedded Submanifolds With Restricted Positive Definite Kernels: Sobolev Error Estimates, Edward J. Fuselier, Grady Wright

Mathematics Faculty Publications and Presentations

In this paper we present error estimates for kernel interpolation at scattered sites on manifolds. The kernels we consider will be obtained by the restriction of positive definite kernels on R^d, such as radial basis functions, to a smooth, compact embedded submanifold M ⊂ R^d with no boundary. For restricted kernels having finite smoothness, we provide a complete characterization of the native space on M. After this and some preliminary setup, we present Sobolev-type error estimates for the interpolation problem for smooth and non-smooth kernels. In the case of non-smooth kernels, we provide error estimates for target …

Renormalized Square Of White Noise Quantum Time Shift, Luigi Accardi, Habib Ouerdiane, Habib Rebei

Communications on Stochastic Analysis

No abstract provided.

Integral Representations Of Some Functionals Of Fractional Brownian Motion, Heikki Tikanmäki

Communications on Stochastic Analysis

No abstract provided.

Construction Of The Paths Of Brownian Motions On Star Graphs I, Vadim Kostrykin, Jürgen Potthoff, Robert Schrader

Communications on Stochastic Analysis

No abstract provided.

Limiting Distributions Of Galton-Watson Branching Processes With Immigration, Yoshinori Uchimura, Kimiaki Saitô

Communications on Stochastic Analysis

No abstract provided.

Wick Product And Clark-Ocone Formula In Abstract Wiener Space, Fariborz Asadian

Communications on Stochastic Analysis

No abstract provided.

Generalised Clark-Ocone Formulae For Differential Forms, Y Yang

Communications on Stochastic Analysis

No abstract provided.