Dual equivalence puts a crystal-like structure on linear representations of the symmetric group that affords many nice combinatorial properties. In this talk, we extend this theory to type B, putting an analogous structure on projective representations of the symmetric group. On the level of generating functions, the type A theory gives a universal method for proving Schur positivity, and the t...

The weak Galerkin (WG) methods have been introduced in [11, 16] for solving the biharmonic equation. The purpose of this paper is to develop an algorithm to implement the WG methods effectively. This can be achieved by eliminating local unknowns to obtain a global system with significant reduction of size. In fact this reduced global system is equivalent to the Schur complements of the WG metho...

If a nonnegative selfadjoint linear relation A in Hilbert space and closed subspace S are assumed to satisfy that the domain of is invariant under orthogonal projector onto S, then admits particular matrix representation with respect decomposition S⊕S⊥. This used give explicit formulae for Schur complement on as well S-compression A.

we introduce and discuss the homotopy perturbation method, the adomian decomposition method and the variational iteration method for solving the stefan problem with kinetics. then, we give an example of the stefan problem with  kinetics and solve it by these methods.

In this paper, we propose a direct method based on the real Schur factorization for solving the projected Sylvester equation with relatively small size. The algebraic formula of the solution of the projected continuous-time Sylvester equation is presented. The computational cost of the direct method is estimated. Numerical experiments show that this direct method has high accuracy. Keywords—Pro...

The goal of this paper is to develop the theory Schur complementation in context operators acting on anti-dual pairs. As a byproduct, we obtain natural generalization parallel sum and difference, as well Lebesgue-type decomposition. To demonstrate how operator approach works application, derive corresponding results for rigged Hilbert spaces, representable functionals ⁎-algebras.

We provide direct proofs of product and coproduct formulae for Schur functions where the coefficients (Littlewood–Richardson coefficients) are defined as counting puzzles. The product formula includes a second alphabet for the Schur functions, allowing in particular to recover formulae of [Molev–Sagan ’99] and [Knutson–Tao ’03] for factorial Schur functions. The method is based on the quantum i...

Raviart-Thomas finite elements are very useful for problems posed in H(div) since they are H(div)-conforming. We introduce two domain decomposition methods for solving vector field problems posed in H(div) discretized by RaviartThomas finite elements. A two-level overlapping Schwarz method is developed. The coarse part of the preconditioner is based on energy-minimizing extensions and the local...

Structure-preserving numerical techniques for computation of eigenvalues and stable deflating subspaces of complex skew-Hamiltonian/Hamiltonian matrix pencils, with applications in control systems analysis and design, are presented. The techniques use specialized algorithms to exploit the structure of such matrix pencils: the skew-Hamiltonian/Hamiltonian Schur form decomposition and the periodi...

We prove an explicit formula for the tensor product with itself of an irreducible complex representation of the symmetric group defined by a rectangle of height two. We also describe part of the decomposition for the tensor product of representations defined by rectangles of heights two and four. Our results are deduced, through Schur-Weyl duality, from the observation that certain actions on t...