We derive a new expression for the diagonal matrix elements of irreducible representations of the symmetric group. We obtain this new expression using Cherednik’s fusion procedure. However, instead of splitting Young diagrams into their rows or columns, we consider their principal hooks. This minimises the number of auxiliary parameters needed in the fusion procedure.

Auxiliary systems for matrix nonisospectral equations, including coupled NLS with external potential and KdV with variable coefficients, were introduced. Explicit solutions of nonisospectral equations were constructed using the GBDT version of the Bäcklund-Darboux transformation. PACS numbers: 02.30.Ik, 02.30Yy, 03.65.Ge

We derive a new expression for the diagonal matrix elements of irreducible representations of the symmetric group. We obtain this new expression using Cherednik’s fusion procedure. However, instead of rows or columns, we consider the hooks of Young diagrams. This minimises the number of auxiliary parameters needed in the fusion procedure.

This paper presents a direct proof of the recursive formulae for the generalized LMinverse of a matrix augmented by a column vector. The recursive relations are proved by direct verification of the four conditions of the generalized LM-inverse. Several auxiliary results pertaining to generalized inverses are also provided. 2006 Elsevier Inc. All rights reserved.

Newton’s inequalities cn ≥ cn−1cn+1 are shown to hold for the normalized coefficients cn of the characteristic polynomial of any Mor inverse M-matrix. They are derived by establishing first an auxiliary set of inequalities also valid for both of these classes. They are also used to derive some new necessary conditions on the eigenvalues of nonnegative matrices.

We compute the Poisson bracket relations for the monodromy matrix of the auxiliary linear problem. If the basic Poisson brackets of the model contain derivatives, this computation leads to a peculiar kind of symmetry breaking which accounts for a 'spontaneous quantiza-tion' of the underlying global gauge group. A classification of possible patterns of symmetry breaking is outlined.

In practical localization system design, researchers need to consider several aspects to make the positioning efficiently and effectively, e.g., the available auxiliary information, sensing devices, equipment deployment and the environment. Then, these practical concerns turn out to be the technical problems, e.g., the sequential position state propagation, the target-anchor geometry effect, th...

An algorithm for orthogonal 4-tap integer multiwavelet transforms is proposed. We compute the singular value decomposition SVD of block recursive matrices of transform matrix, and then transform matrix can be rewritten in a product of two block diagonal matrices and a permutation matrix. Furthermore, we factorize the block matrix of block diagonal matrices into triangular elementary reversible ...