In this paper, a nonlinear Volterra-Fredholm integral equation of the first kind is solved by using the homotopy analysis method (HAM). In this case, the first kind integral equation can be reduced to the second kind integral equation which can be solved by HAM. The approximate solution of this equation is calculated in the form of a series which its components are computed easily. The accuracy...

In this paper we perform quantitative reconstruction of the electric susceptibility and the Grüneisen parameter of a non-magnetic linear dielectric medium using measurement of a multi-modal photoacoustic and optical coherence tomography system. We consider the mathematical model presented in [11], where a Fredholm integral equation of the first kind for the Grüneisen parameter was derived. For ...

This paper develops a modification of the dressing method based on inhomogeneous linear integral equation with integral operator having nonempty kernel. Method allows one to construct the systems of multidimensional Partial Differential Equations (PDEs) having differential polynomial structure in any dimension n. Associated solution space is not full, although it is parametrized by certain numb...

It is shown that under a certain condition on a semimartingale and a time-change, any stochastic integral driven by the time-changed semimartingale is a time-changed stochastic integral driven by the original semimartingale. As a direct consequence, a specialized form of the Itô formula is derived. When a standard Brownian motion is the original semimartingale, classical Itô stochastic differen...

The main result of the paper is an upper bound for oscillation of spatial curves around geodesic subspaces of the ambient space in terms of the integral geodesic curvatures of the curves. Let Mn be the Euclidean space Rn, projective space Pn or the sphere Sn equipped with the Riemannian metric of Gaussian curvature c(M) = 0, 1 or r−n > 0 respectively, and Γ ⊂ M be a smooth curve parameterized b...

A b s t r a c t Starting from the QCD Lagrangian we derive the effective action for massive quark and antiquark at large distances, corresponding to the minimal area low of the Wilson loop. The path integral method is used to quantize the system and the spectrum is obtained with asymptotically linear Regge trajec-tories. Two dynamical regimes distinguished by the string energy–momentum distribu...

Integral equation techniques are often used to extract models of integrated circuit structures. This extraction involves solving a dense system of linear equations, and using direct solution methods is prohibitive for large problems. In this paper, we present IES (pronounced \ice cube"), a fast Integral Equation Solver for three-dimensional problems with arbitrary kernels. Extraction methods ba...

Analytical solutions of precise equations that describe the rf-coupling of two cavities through a co-axial cylindrical hole are given for various limited cases. For their derivation we have used the method of solution of an infinite set of linear algebraic equations, based on its transformation into dual integral equations.