Let Md(k) denote the space of d×d-matrices with coefficients in an algebraically closed field k. Let X be an orbit closure in the product [Md(k)] t equipped with the action of the general linear group GLd(k) by simultaneous conjugation. We show that X is regular at any point y such that the orbit of y has codimension one in X. The proof uses mainly the representation theory of associative algeb...

The main goal of this paper is to introduce and study fuzzy multiset regular grammar to show that fuzzy multiset finite automata and fuzzy multiset regular grammars are equivalent. We also study fuzzy multiset linear grammars and fuzzy multiset regular grammars in normal form. Furthermore, we show the equivalence of fuzzy multiset regular grammars, fuzzy multiset left linear grammars, fuzzy mul...

In this note we characterize polynomial numerical hulls of matrices $A in M_n$ such that$A^2$ is Hermitian. Also, we consider normal matrices $A in M_n$ whose $k^{th}$ power are semidefinite. For such matriceswe show that $V^k(A)=sigma(A)$.

defined by a four-dimensional "triangular" matrix jamnkjjj (m, n, k, I = 1, 2, 3, ...; amnkl = O for k > m or I > n or both) of real or complex numbers. We showed (Theorem 2 of I) that if (A) is regular for bounded sequences, it is in general regular also for a large class of unbounded sequences. Special interest attaches to the type of transformation (A) for which we have amnklz = amk anl (m, ...

A matrix of discrimination measures (discrimination probabilities, numerical estimates of dissimilarity, etc.) satisfies Regular Minimality (RM) if every row and every column of the matrix contains a single minimal entry, and an entry minimal in its row is minimal in its column. We derive a formula for the proportion of RM-compliant matrices among all square matrices of a given size and with no...

We find a relationship between regular embeddings of G, an elementary abelian p-group of order p, into unipotent upper triangular matrices with entries in Fp and commutative dimension n degree 2 polynomial formal groups with nilpotent upper triangular structure matrices. We classify the latter when n = 3 up to linear isomorphism, and use that classification to determine the number of Hopf Galoi...

Let A be a finite matrix with rational entries. We say that A is doubly image partition regular if whenever the set N of positive integers is finitely coloured, there exists ~x such that the entries of A~x are all the same colour (or monochromatic) and also, the entries of ~x are monochromatic. Which matrices are doubly image partition regular? More generally, we say that a pair of matrices (A,...

This survey paper deals with upper and lower bounds on the number of k-matchings in regular graphs on N vertices. For the upper bounds we recall the upper matching conjecture which is known to hold for perfect matchings. For the lower bounds we first survey the known results for bipartite graphs, and their continuous versions as the van der Waerden and Tverberg permanent conjectures and its var...

The class of the s-transitive (resp. w-transitive) fuzzy matrices contains properly the class of the max-min transitive fuzzy matrices for which reduction models are already known. It is shown that some basic properties of these models remain valid also for s-transitive (resp. w-transitive)fuzzy matrices.

In this paper, we investigate the algebraic properties of intuitionistic fuzzy matrices under the new operations and . The properties of intuitionistic fuzzy matrices are also obtained in the case where these new operations are combined with the well known operations of intuitionistic fuzzy matrices.