We give the matrix characterizations from Nakano vector-valued sequence space (X,p) and Fr (X,p) into the sequence spaces Er , ∞, ∞(q), bs, and cs, where p = (pk) and q = (qk) are bounded sequences of positive real numbers such that pk > 1 for all k∈N and r ≥ 0. 2000 Mathematics Subject Classification. 46A45.

Let A= (ank) be an infinite matrix with all ank ≥ 0 and P a bounded, positive real sequence. For normed spaces E and Ek the matrix A generates paranormed sequence spaces such as [A,P]∞((Ek)), [A,P]0((Ek)), and [A,P](E) which generalize almost all the existing sequence spaces, such as l∞, c0, c, lp, wp , and several others. In this paper, conditions under which these three paranormed spaces are ...

We give several equivalent combinatorial descriptions of the space of states for the box-ball systems, and connect certain partition functions for these models with the q-weight multiplicities of the tensor product of the fundamental representations of the Lie algebra gl(n). As an application, we give an elementary proof of the special case t = 1 of the Haglund–Haiman–Loehr formula. Also, we pr...

In this paper, we mainly discuss solving the following problems. Problem I. Given matrices A ∈ Cm×n and B ∈ Cm×m, find X ∈ HRSn×n such that AXA∗ = B, where HRSn×n = {X ∈ Hn×n|RXR = X, for given R ∈ Cn×n satisfying R = R∗ = R−1 = In}. Problem II. Given a matrix X̃ ∈ Cn×n, find X̂ ∈ SE such that ‖X̃ − X̂‖F = inf X∈SE ‖X̃ − X‖F , where ‖ · ‖ is the Frobenius norm, and SE is the solution set of Problem ...

Counting periodic orbits of endomorphisms on the 2-torus is considered, with special focus on the relation between global and local aspects and between the dynamical zeta function on the torus and its analogue on finite lattices. The situation on the lattices, up to local conjugacy, is completely determined by the determinant, the trace and a third invariant of the matrix defining the toral end...

We investigate the perturbation of the palindromic eigenvalue problem for the matrix quadratic P(λ)= λ2 A?1 + λA0 + A1 with A0, A1 ∈ C n×n and A?0 = A0 (where ?= T or H ). The perturbation of eigenvalues in the context of general matrix polynomials, palindromic pencils, (semi-Schur) anti-triangular canonical forms and differentiation is discussed. 2000 Mathematics subject classification: primar...

The two-point boundary value problem is considered for the system of nonlinear generalized ordinary differential equations with singularities on a non-closed interval. Singularity is understood in a sense of the vector-function corresponding to the system which belongs to the local Carathéodory class with respect to the matrix-function corresponding to the system. The general sufficient conditi...