Let (X,S) be an association scheme where X is a finite set and S is a partition of X × X. We say that (X,S) is symmetric if σs is symmetric for each s ∈ S where σs is the adjacency matrix of s, and integral if ⋃ s∈S ev(σs) ⊆ Z where ev(σs) is the set of all eigenvalues of σs. For an association scheme (X,T ) we say that (X,T ) is a fusion of (X,S) if each element of T is a union of elements of ...

Let E be the Hilbert space of symmetric matrices of the form diag(A,M), where A is n× n, and M is an l× l diagonal matrix, and the inner product 〈x, y〉 ≡ Trace(xy). Given x ∈ E, we write x ≥ 0 (x > 0) if it is positive semidefinite (positive definite). Let Q : E → E be a symmetric positive semidefinite linear operator, and μ = min{φ(x) = 0.5Trace(xQx) : ‖x‖ = 1, x ≥ 0}. The feasibility problem ...

in this paper for a given prescribed ritz values that satisfy in the some special conditions, we nd a symmetric nonnegative matrix, such that the given set be its ritz values.

The matrix equation X + AXA = Q arises in Green’s function calculations in nano research, where A is a real square matrix and Q is a real symmetric matrix dependent on a parameter and is usually indefinite. In practice one is mainly interested in those values of the parameter for which the matrix equation has no stabilizing solutions. The solution of interest in this case is a special weakly st...

We give a combinatorial formula for the non-symmetric Macdonald polynomials Eμ(x; q, t). The formula generalizes our previous combinatorial interpretation of the integral form symmetric Macdonald polynomials Jμ(x; q, t). We prove the new formula by verifying that it satisfies a recurrence, due to Knop and Sahi, that characterizes the non-symmetric Macdonald polynomials.

A real n × n symmetric matrix X = (x i j)n×n is called a bisymmetric matrix if x i j = xn+1− j,n+1−i . Based on the projection theorem, the canonical correlation decomposition and the generalized singular value decomposition, a method useful for finding the least-squares solutions of the matrix equation AXA= B over bisymmetric matrices is proposed. The expression of the least-squares solutions ...

We give a combinatorial formula for the non-symmetric Macdonald polynomials E µ (x; q, t). The formula generalizes our previous combinatorial interpretation of the integral form symmetric Macdonald polynomials J µ (x; q, t). We prove the new formula by verifying that it satisfies a recurrence, due to Knop, that characterizes the non-symmetric Macdonald polynomials.

We give a combinatorial formula for the non-symmetric Macdonald polynomials E µ (x; q, t). The formula generalizes our previous combinatorial interpretation of the integral form symmetric Macdonald polynomials J µ (x; q, t). We prove the new formula by verifying that it satisfies a recurrence, due to Knop and Sahi, that characterizes the non-symmetric Macdonald polynomials.

We give a combinatorial formula for the non-symmetric Macdonald polynomials E µ (x; q, t). The formula generalizes our previous combinatorial interpretation of the integral form symmetric Macdonald polynomials J µ (x; q, t). We prove the new formula by verifying that it satisfies a recurrence, due to Knop and Sahi, that characterizes the non-symmetric Macdonald polynomials.