Differential and integral calculus on time scales allows to develop a theory of dynamic equations in order to unify and extend the usual differential equations and difference equations. For single variable differential and integral calculus on time scales, we refer the reader to the textbooks [4, 5] and the references given therein. Multivariable calculus on time scales was developed by the aut...

The boundary element methodology is applied to the analysis of non-linear viscoelastic solids. The adopted non-linear model uses the same relaxation moduli as the respective linear relations but with a time shift depending on the volumetric strain. Nonlinearity introduces an irreducible domain integral into the original integral equation derived for linear viscoelastic solids. This necessitates...

In this paper, we will compare a Homotopy perturbation algorithm and Taylor series expansin method for a system of second kind Fredholm integral equations. An application of He’s homotopy perturbation method is applied to solve the system of Fredholm integral equations. Taylor series expansin method reduce the system of integral equations to a linear system of ordinary differential equation.

The purpose of this work is to investigate the existence of fixed points of some mappings in fixed point theory by combining some important concepts which are F-weak contractions, multivalued mappings, integral transformations and α-admissible mappings. In fixed point theory, it is important to find fixed points of some classess under F- or F-weak contractions. Also multivalued mappings is the ...

In this paper, a reliable iterative approach, for solving a wide range of linear and nonlinear Volterra-Fredholm integral equations is established. First the approach considers a discretized form of the integral terms where considering some conditions on the kernel of the integral equation it is proved that solution of the discretized form converges to the exact solution of the problem. Then th...

Algebraic integral equations is a special category of Volterra integral equations system,  that has many applications in physics and engineering. The principal aim of this paper is to serve the numerical solution of an integral algebraic equation by using the Taylor expansion method. In this method, using the Taylor expansion of the unknown function, the algebraic integral equation system becom...

We study the 2-loop part of the rational Kontsevich integral of a knot in an integer homology sphere. We give a general formula which explains how the 2-loop part of the Kontsevich integral of a knot changes after surgery on a single clasper whose leaves are not linked to the knot. As an application, we relate this formula with a conjecture of L. Rozansky about integrality of the 2-loop polynom...

We present several well-posed, well-conditioned integral equation formulations for the solution of two-dimensional acoustic scattering problems with Neumann boundary conditions in domains with corners. We call these integral equations Direct Regularized Combined Field Integral Equations (DCFIE-R) formulations because (1) they consist of combinations of direct boundary integral equations of the ...

We present multiresidue integral formulae for partial sums in the basis of link patterns of the polynomial solution to the level 1 Uq(ŝl2) quantum Knizhnik–Zamolodchikov equation at generic values of the quantum parameter q. These allow for rewriting and generalizing a recent conjecture [Di Francesco ’06] connecting the above to generating polynomials for weighted Totally Symmetric Self-Complem...

Determination of the Rate Expression and Prediction of Reaction Progress for Irreversible Reactions 12 Integral Methods: Rates Dependent on a Single Constituent 12 Integral Methods: Rates Dependent on a Multiple Constituents 24 Differential Methods 30 Characteristic Reaction Times 32 Analysis of Multiple Simultaneous Reactions 36 Reversible Reactions 36 Reversibility of Reactions and its Relati...