Many problems of computational electromagnetics [1,2], stationary heat transfer [3,4] and elasticity theory [5] can be naturally reduced to integral equations of the first kind (IEFK) with a weak singularity. So we shall name the equations with a logarithmic peculiarity in one-dimensional case and equation with a peculiarity of an aspect 1 0 rMM in two-dimensional case, where rMM 0 is distance ...

In the late afternoon of November 25, 2002 a gamma–ray burst (GRB) was detected in the partially coded field of view (about 7.3◦ from the centre) of the imager IBIS on board the INTEGRAL satellite. The instruments on-board INTEGRAL allowed, for the first time, the observation of the prompt gamma-ray emission over a broad energy band from 15 to 500 keV. GRB021125 lasted ∼ 24 s with a mean flux o...

This paper discusses about the solution of fuzzy Volterra integral equation of first-kind (F-VIE1) using spectral method. The parametric form of fuzzy driving term is applied for F-VIE1, then three classifications for (F-VIE1) are searched to solve them. These classifications are considered based on the interval sign of the kernel. The Gauss-Legendre points and Legendre weights for arithmetics ...

‎‎‎In this paper‎, we use the collocation method for to find an approximate solution of the problem by cubic B-spline basis.‎ The proposed method as a basic function led matrix systems, including band matrices and smoothness and capability to handle low calculative costly. ‎The absolute errors in the solution are compared to existing methods to verify the accuracy and convergent nature of propo...

 Abstract: In this paper homotopy perturbation is applied to system of linear Fredholm integral equations of the first kind .For these systems, degenerate kernels are considered and in order to avoid successive integrations ,an easy matrix computation is derived for approximating the solution of the problem.  

The Darbouxian theory of integrability allows to determine when a polynomial differential system in C2 has a first integral of the kind f λ1 1 · · ·f λp p exp(g/h) where fi , g and h are polynomials in C[x, y], and λi ∈ C for i = 1, . . . , p. The functions of this form are called Darbouxian functions. Here, we solve the inverse problem, i.e. we characterize the polynomial vector fields in C2 h...

An elliptic boundary value problem in the interior or exterior of a polygon is transformed into an equivalent rst kind boundary integral equation. Its Galerkin discretization with N degrees of freedom on the boundary with spline wavelets as basis functions is analyzed. A truncation strategy is presented which allows to reduce the number of nonzero elements in the stiiness matrix from O(N 2) to ...

The main objective of this article is to study the topology of the fibers of a generic rational function of the type F p Gq in the projective space of dimension two. We will prove that the action of the monodromy group on a single Lefschetz vanishing cycle δ generates the first homology group of a generic fiber of F p Gq . In particular, we will prove that for any two Lefschetz vanishing cycles...

We consider the local regularization problem for integral equations of the first kind, generalizing previous work which applied only to problems of Volterra type. Our approach allows for local control of the regularization process, allowing for resolution of fine/sharp features of solutions without having to resort to nondifferentiable optimization techniques. In addition we present examples il...

Given a foliation F in an algebraic surface having a rational first integral a genus formula for the general solution is obtained. In the case S = P2 some new counter-examples to the classic formulation of the Poincaré problem are presented. If S is a rational surface and F has singularities of type (1, 1) or (1,−1) we prove that the general solution is a non-singular curve.