We study certain generalized Cauchy integral formulas for gradients of solutions to second order divergence form elliptic systems, which appeared in recent work by P. Auscher and A. Rosén. These are constructed through functional calculus and are in general beyond the scope of singular integrals. More precisely, we establish such Cauchy formulas for solutions u with gradient in weighted L2(R 1+...

This paper studies complex cobordisms between compact, three dimensional, strictly pseudoconvex Cauchy-Riemann manifolds. Suppose the complex cobordism is given by a complex 2-manifold X with one pseudoconvex and one pseudoconcave end. We answer the following questions. To what extent is X determined by the pseudoconvex end? What is the relation between the embeddability of the pseudoconvex end...

in this paper, operational matrices of riemann-liouville fractional integration and caputo fractional differentiation for shifted jacobi polynomials are considered. using the given initial conditions, we transform the fractional differential equation (fde) into a modified fractional differential equation with zero initial conditions. next, all the existing functions in modified differential equ...

This paper presents a new approach to constructing a meromorphic bundle map between flat vector bundles over a compact Riemann surface having a prescribed Weil divisor (i.e. having prescribed zeros and poles with directional as well as multiplicity information included in the vector case). This new formalism unifies the earlier approach of Ball-Clancey (in the setting of trivial bundles over an...

Abstract. We investigate wether three statements in analysis, that can be proved classically, are realizable in the realizability model of extensional continuous functionals induced by Kleene’s second model K2. We prove that a formulation of the Riemann Permutation Theorem as well as the statement that all partially Cauchy sequences are Cauchy cannot be realized in this model, while the stateme...

In this paper we study the Cauchy–Riemann equation in complex projective spaces. Specifically, we use the modified weight function method to study the ∂̄-Neumann problem on pseudoconvex domains in these spaces. The solutions are used to study function theory on pseudoconvex domains via the ∂̄-Cauchy problem. We apply our results to prove nonexistence of Lipschitz Levi-flat hypersurfaces in comple...

In present paper, a numerical approach for solving Cauchy type singular integral equations is discussed. Lagrange interpolation with Gauss Legendre quadrature nodes and Taylor series expansion are utilized to reduce the computation of integral equations into some algebraic equations. Finally, five examples with exact solution are given to show efficiency and applicability of the method. Also, w...

We survey some topics involving the Whitham equations, concentrating on the role of ψψ∗ (or square eigenfunctions) in averaging and in producing Cauchy kernels and differentials on Riemann surfaces.