A quasi Riemann surface is defined to be a certain kind of complete metric space Q whose integral currents are analogous to the integral currents of a Riemann surface. In particular, they have properties sufficient to express Cauchy-Riemann equations on Q. The prototypes are the spaces D 0 (Σ)m of integral 0-currents of total mass m in a Riemann surface Σ (usually called the integral 0-cycles o...

How to get the original ideas” is the fundamental and critical issue for the researchers in science and technology. In this paper, the author writes his experiences concerning how he could encounter the interesting and original ideas of three research subjects, i.e., the accelerating medium effect, the guided-mode extracted integral equation and the surface plasmon gap waveguide. key words: ide...

the principal aim of this paper is to serve the numerical solution of an integral-algebraic equation (iae) by using the bernoulli polynomials and the residual correction method. after implementation of our scheme, the main problem would be transformed into a system of algebraic equations such that its solutions are the unknown bernoulli coefficients. thismethod gives an analytic solution when t...

in this article we decide to define a modified homotopy perturbation for solving non-linear integral equations. almost, all of the papers that was presented to solve non-linear problems by the homotopy method, they used from two non-linear and linear operators. but we convert a non-linear problem to two suitable non-linear operators also we use from appropriate bases functions such as legendre ...

a reproducing kernel hilbert space restricts the space of functions to smooth functions and has structure for function approximation and some aspects in learning theory. in this paper, the solution of an integral equation of the third kind is constructed analytically using a new method. the analytical solution is represented in the form of series in the reproducing kernel space. some numerical ...

‎the main purpose of this paper is to study the numerical solution of nonlinear volterra integral equations with constant delays, based on the multistep collocation method. these methods for approximating the solution in each subinterval are obtained by fixed number of previous steps and fixed number of collocation points in current and next subintervals. also, we analyze the convergence of the...

A new higher-order method of moment (MoM) technique is presented for volume-surface integral equations (VSIE) for electromagnetic modeling of composite metallic and dielectric objects. The higher-order MoM scheme comprises higher-order hierarchical Legendre basis functions and an accurate representation of the object by higher-order curvilinear elements. Due to the orthogonal nature of the basi...

in this paper the fixed point theorem of schauder is used to prove the existence of a continuous solution of the nonlinear fuzzy volterra integral equations. then using some conditions the uniqueness of the solution is investigated.