Orthogonal polynomials and continued fractions arising from contiguous relations and generalizations of Kummer and q-Kummer identities

The Ramanujan Journal - In this paper, we show formally how can we generate continued fractions starting from three-term contiguous relations. Then as examples, starting from certain contiguous...     

A Numerical Study of Traveling Wave Fronts for a Reaction-Diffusion-Advection Model

This paper concerns with the traveling wave solutions of a nonlinear reaction-diffusion-advection model for describing the spatiotemporal evolution of bacterial colony pattern. We use different methods for computing the traveling wave fronts of the model equations. One of the methods involves the traveling wave equations. Numerical solutions of these equations as an initial-value problem lead to accurate computations of the wave profiles and speeds. The second method is to construct the time-dependent solutions by solving an initial-moving boundary-value problem for the PDE system, showing an approximation for such wave fronts, in particular, the minimum speed traveling wave.     

Counting derangements, involutions and unimodal elements in the wreath product Cr ? Sn

We count derangements, involutions and unimodal elements in the wreath product C _r ≀ S _n by the numbers of excedances, fixed points and 2-cycles. Properties of the generating functions, including combinatorial formulas, recurrence relations and real-rootedness are studied. The results obtained specialize to those on the symmetric group S _n and on the hyperoctahedral group B _n when r = 1, 2, respectively.     

An extended slacks-based measure model for data envelopment analysis with negative data

Data envelopment analysis (DEA) is a non-parametric approach based on linear programming that has been widely applied for evaluating the relative efficiency of a set of homogeneous decision-making units (DMUs) with multiple inputs and outputs. The original DEA models use positive input and output variables that are measured on a ratio scale, but these models do not apply to the variables in which negative data can appear. However, with the widespread use of interval scale data and undesirable data, the emphasis has been directed towards the simultaneous consideration of the positive and negative data in DEA models. In this paper, using the slacks-based measure, we propose an extended model to evaluate the efficiency of DMUs, even if some variables are measured on an interval scale and some on a ratio scale. Moreover, the extended model allows for the presence of all interval-scale variables, which are capable of taking both negative and positive values.     

A Hybrid Particle Swarm Optimization Algorithm for the Redundancy Allocation Problem

The Redundancy Allocation Problem generally involves the selection of components with multiple choices and redundancy levels that produce maximum system reliability given various system level constraints as cost and weight. In this paper we investigate the series–parallel redundant reliability problems, when a mixing of components was considered. In this type of problem both the number of redundancy components and the corresponding component reliability in each subsystem are to be decided simultaneously so as to maximise the reliability of system. A hybrid algorithm is based on particle swarm optimization and local search algorithm. In addition, we propose an adaptive penalty function which encourages our algorithm to explore within the feasible region and near feasible region, and discourage search beyond that threshold. The effectiveness of our proposed hybrid PSO algorithm is proved on numerous variations of three different problems and compared to Tabu Search and Multiple Weighted Objectives solutions.     

Convergence analysis of perturbed hemivariational inequalities

We consider the rate of convergence for a class of perturbed hemivariational inequalities in reflexive Banach Spaces. Our results can be viewed as an extension and refinement of some previous known results in this area.     

Maximizing a Sum Related to Image Segmentation Evaluation

Consider the set S of points in the plane consisting of the ordered pairs (i, j ), where 1 \leqslant i \leqslant m1 \leqslant i \leqslant m and 1 \leqslant j \leqslant n1 \leqslant j \leqslant n. A problem related to the study of segmentation evaluation of visual images concerns finding a permutation σ of the points of S for which the sum

The commutation relation <Emphasis Type="Italic">xy</Emphasis>=<Emphasis Type="Italic">qyx</Emphasis>+<Emphasis Type="Italic">hf</Emphasis>(<Emphasis Type="Italic">y</Emphasis>) and Newton’s binomial formula

Let x and y be two variables satisfying the commutation relation xy=qyx+hf(y), where f(y) is a polynomial. In this paper, using Young diagrams and generating functions techniques, we study the binomial formula (x+y) ⁿ and we present an identity for x ^m y. The connection to Operator Calculus is discussed and several special cases are treated explicitly.     

Adjoint polynomials of bridge–path and bridge–cycle graphs and Chebyshev polynomials

The chromatic polynomial of a simple graph G with n>0 vertices is a polynomial of degree n, where α_k(G) is the number of k-independent partitions of G for all k. The adjoint polynomial of G is defined to be , where is the complement of G. We find explicit formulas for the adjoint polynomials of the bridge–path and bridge–cycle graphs. Consequence, we find the zeros of the adjoint polynomials of several families of graphs.