This paper deals with the algorithm for computing outer inverse with prescribed range and null space, based on the choice of an appropriate matrix G and Gauss–Jordan elimination of the augmented matrix [G | I]. The advantage of such algorithms is the fact that one can compute various generalized inverses using the same procedure, for different input matrices. In particular, we derive representa...

A bstract We formulate a ? k -parafermionization/bosonization scheme for one-dimensional lattice models and field theories on torus, starting from generalized Jordan-Wigner transformation lattice, which extends the Majorana-Ising duality at = 2. The -parafermionization enables us to investigate critical of parafermionic chains whose fundamental degrees freedom are parafermionic, we find that th...

A new approach to formal solutions of (first order systems of) linear differential equations stressing as much as possible the similarity with systems of linear equations. This approach leads to a fine structure of formal solutions, comparable to [1] but from a different point of view. A quick introduction to characteristic classes (cf. [3]) will be given. 1 Linear algebra; recalling Jordan dec...

Let G be a Jordan domain and K C G be relatively closed with Area(K) = 0. Let A2(G\K) and A2 (G) be the Bergman spaces on G\K, respectively G and define N = A2(G\K) e A2 (G). In this paper we show that with a mild restriction on K, every function in N has an analytic continuation across the analytic arcs of 8G that do not intersect K. This result will be used to discuss the Fredholm theory of t...

We calculate Jordan–Kronecker invariants for semidirect sums of Lie algebras sl(n) and gl(n) with k copies ℝn respect to their standard representation cases where > n or is a multiple k.

In this paper, motivated by the study of the wide diameter and the Rabin number of graphs, we define the generalized k-diameter of k-connected graphs, and show that every k-regular k-connected graph on n vertices has the generalized k-diameter at most n/2 and this upper bound cannot be improved when n = 4k − 6 + i(2k − 4).

We consider a key case in the fundamental and substantial problem of the possible Jordan canonical forms of A, B,C ∈Mn(F ) when C = AB. If A ∈ M2k(F ) (respectively B, C ∈ M2k(F ) ) is diagonalizable with two distinct eigenvalues a1, a2 (respectively b1, b2, and c1, c2), each with multiplicity k, and when C = AB, all possibilities for a1, a2, b1, b2, c1, c2 are characterized. The possibilities ...