and Applied Analysis 3 where L x, y , I x, y denote logarithmic mean and identric exponential mean, respectively, G a, b √ ab. The Schur convexity of Sp,q a, b and Gp,q a, b on 0,∞ × 0,∞ with respect to a, b was investigated by Qi et al. 4 , Shi et al. 5 , Li and Shi 6 , and Chu and Zhang 7 . Until now, they have been perfectly solved by Chu and Zhang 7 , Wang and Zhang 8 , respectively. Recent...

in this paper, we consider the boundedness of the libera operator on dirichlet spaces in terms of the schur test. moreover, we get its point spectrum and norm.

This paper considers an algebraic preconditioning algorithm for hyperbolicelliptic fluid flow problems. The algorithm is based on a parallel non-overlapping Schur complement domain-decomposition technique for triangulated domains. In the Schur complement technique, the triangulation is first partitioned into a number of non-overlapping subdomains and interfaces. This suggests a reordering of tr...

This study examines the block lower-triangular preconditioner with element-wise Schur complement as the lower diagonal block applied on matrices arising from an application in geophysics. The element-wise Schur complement is a special approximation of the exact Schur complement that can be constructed in the finite element framework. The preconditioner, the exact Schur complement and the elemen...

Since every even power of the Vandermonde determinant is a symmetric polynomial, we want to understand its decomposition in terms of the basis of Schur functions. We investigate several combinatorial properties of the coefficients in the decomposition. In particular, I will give a recursive approach for computing the coefficient of the Schur function sμ in the decomposition of an even power of ...

It is well-known [D. Carlson, T. Markham, Schur complements of diagonally dominant matrices, Czech. Math. J. 29 (104) (1979) 246–251, [1]] that the Schur complement of a strictly diagonally dominant matrix is strictly diagonally dominant. Also, if a matrix is an H-matrix, then its Schur complement is an H-matrix, too [J. Liu, Y. Huang, Some properties on Schur complements of H-matrices and diag...

We present a non-overlapping spatial domain decomposition method for the solution of linear–quadratic parabolic optimal control problems. The spatial domain is decomposed into non-overlapping subdomains. The original parabolic optimal control problem is decomposed into smaller problems posed on space-time cylinder subdomains with auxiliary state and adjoint variables imposed as Dirichlet bounda...

This paper builds upon the work of Cline [C] and Donkin [D1] to describe explicit equivalences between some categories associated to the category of rational modules for a reductive group G and categories associated to the category of rational modules for a Levi subgroup H . As an application, we establish an Ext-transfer result from rational G-modules to rational H-modules. In case G = GLn, th...

This paper uses the theory of dual equivalence graphs to give explicit Schur expansions for several families of symmetric functions. We begin by giving a combinatorial definition of the modified Macdonald polynomials and modified HallLittlewood polynomials indexed by any diagram δ ⊂ Z × Z, written as H̃δ(X; q, t) and H̃δ(X; 0, t), respectively. We then give an explicit Schur expansion of H̃δ(X; 0,...

We present a simple technique to compute moments of derivatives of unitary characteristic polynomials. The first part of the technique relies on an idea of Bump and Gamburd: it uses orthonormality of Schur functions over unitary groups to compute matrix averages of characteristic polynomials. In order to consider derivatives of those polynomials, we here need the added strength of the Generaliz...