Related papers: On the Riemann-Hilbert problem for hyperplane arra…

For the bi-orthogonal polynomials with the third degree polynomial potential functions, the 3 x 3 matrix Riemann-Hilbert problem is explicitly constructed. The developed approach admits an extension to the bi-orthogonal polynomials with…

Let $\mathcal A$ be a hyperplane arrangement in $\mathbb C^n$. We show that the number of decomposition factors as a perverse sheaf of the direct image $Rj_*\mathbb C_U $ of the constant sheaf on the complement $U$ to the arrangement is…

We present a Hilbert space perspective to homogenization of standard linear evolutionary boundary value problems in mathematical physics and provide a unified treatment for (non-)periodic homogenization problems in thermodynamics,…

Generalized Halphen systems are solved in terms of functions that uniformize genus zero Riemann surfaces, with automorphism groups that are commensurable with the modular group. Rational maps relating these functions imply subgroup…

An integrable generalization of the super Kaup-Newell(KN) isospectral problem is introduced and its corresponding generalized super KN soliton hierarchy are established based on a Lie super-algebra B(0,1) and super-trace identity in this…

We study a variant of the Whitney extension problem for the space $C^k\Lambda^m_{\omega}(R^n)$ of functions whose partial derivatives of order $k$ satisfy the generalized Zygmund condition. We identify $C^k\Lambda^m_{\omega}(R^n)$ with a…

Bundle methods have been intensively studied for solving both convex and nonconvex optimization problems. In most of the bundle methods developed thus far, at least one quadratic programming (QP) subproblem needs to be solved in each…

Given a Lie pseudo-group action, an equivariant moving frame exists in the neighborhood of a submanifold jet provided the action is free and regular. For local equivalence problems the freeness requirement cannot always be satisfied and in…

Conjectures of J. Igusa for p-adic local zeta functions and of J. Denef and F. Loeser for topological local zeta functions assert that (the real part of) the poles of these local zeta functions are roots of the Bernstein-Sato polynomials…

This paper is devoted to Riemann-Hilbert problems with constraints. We obtain results characterizing the existence of solutions as well as the dimension of the solution space in terms of certain indices. As an application, we show how such…

This paper is devoted to study the existence of a solution to Hilfer fractional differential equation with nonlocal boundary condition. We use the equivalent integral equation to study the considered Hilfer differential problem with…

We study the Hadamard product of the linear forms defining a hyperplane arrangement with those of its dual, which we view as generating an ideal in a certain polynomial ring. We use this ideal, which we call the ideal of pairs, to study…

The present paper is focused on the computation of the Lipschitz upper semicontinuity modulus of the feasible set mapping in the context of fully perturbed linear inequality systems; i.e., where all coefficients are allowed to be perturbed.…

This paper deals with the local existence and uniqueness results for the solution of fractional differential equations with Hilfer-Hadamrd fractional derivative. Using Picard's approximations and generalizing the restrictive conditions…

In this paper we study iterative algorithms for finding a common element of the set of fixed points of $\kappa$-strict pseudocontractions or finding a solution of a variational inequality problem for a monotone, Lipschitz continuous…

Dorff et al. [4], proved that the harmonic convolution of right half-plane mapping with dilatation -z and mapping f_\beta = h_\beta + \bar{g}_\beta, where f_\beta is obtained by shearing of analytic vertical strip mapping, with dilatation…

We prove a general existence theorem for nonlinear partial differential systems of any order in one complex variable. A special case of first order contains a well-known theorem of Nijenhuis and Woolf concerning local existence of…

This paper provides an overview of selected results and open problems in the theory of hyperplane arrangements, with an emphasis on computations and examples. We give an introduction to many of the essential tools used in the area, such as…

This paper improves the algorithms based on supporting halfspaces and quadratic programming for convex set intersection problems in our earlier paper in several directions. First, we give conditions so that much smaller quadratic programs…

This paper continues a series of investigations on converging representations for the Riemann Zeta function. We generalize some identities which involve Riemann's zeta function, and moreover we give new series and integrals for the zeta…