in this paper, the concept of k-regular fuzzy matrix as a general- ization of regular matrix is introduced and some basic properties of a k-regular fuzzy matrix are derived. this leads to the characterization of a matrix for which the regularity index and the index are identical. further the relation between regular, k-regular and regularity of powers of fuzzy matrices are dis- cussed.

In this paper, the concept of k-regular fuzzy matrix as a general- ization of regular matrix is introduced and some basic properties of a k-regular fuzzy matrix are derived. This leads to the characterization of a matrix for which the regularity index and the index are identical. Further the relation between regular, k-regular and regularity of powers of fuzzy matrices are dis- cussed.

Functional MSO transductions, deterministic two-way transducers, as well as streaming string transducers are all equivalent models for regular functions. In this paper, we show that every regular function, either on finite words or on infinite words, captured by a deterministic two-way transducer, can be described with a regular transducer expression (RTE). For infinite words, the transducer us...

We study the disturbance decoupling problem for linear time invariant descriptor systems. We give necessary and suucient conditions for the existence of a solution to the disturbance decoupling problem with/without stability via a proportional and/or derivative feedback that also makes the resulting closed-loop system regular and/or of index at most one. All results are proved constructively ba...

If u, v ∈ N, A is a u × v matrix with entries from Q, and ~b ∈ Q, then (A,~b ) determines an affine transformation from Q to Q by ~x 7→ A~x + ~b. In 1933 and 1943 Richard Rado determined precisely when such transformations are kernel partition regular over N, Z, or Q, meaning that whenever the nonzero elements of the relevant set are partitioned into finitely many cells, there is some element o...

The following two important problems are considered in the paper: constructing a low density parity check code on a bipartite graph and rapid encoding of this code. For a given constituent code, the first problem solving is reduced to constructing and investigation of parameters of the matrix describing connections of two vertex subsets of a regular bipartite graph (biadjacency matrix). It is c...