A close relationship between the class of totally positive matrices and anti-Monge matrices is used for suggesting a new direction for investigating totally positive matrices. Some questions are posed and a partial answer in the case of Vandermonde-like matrices is given., Miroslav Fiedler., and Obsahuje seznam literatury
Relations introduced by Conrad, Drazin, Hartwig, Mitsch and Nambooripad are discussed on general, regular, completely semisimple and completely regular semigroups. Special properties of these relations as well as possible coincidence of some of them are investigated in some detail. The properties considered are mainly those of being a partial order or compatibility with multiplication. Coincidences of some of these relations are studied mainly on regular and completely regular semigroups.
Commutative semigroups satisfying the equation $2x+y=2x$ and having only two $G$-invariant congruences for an automorphism group $G$ are considered. Some classes of these semigroups are characterized and some other examples are constructed.
A semigroup S is called a generalized F-semigroup if there exists a group congruence on S such that the identity class contains a greatest element with respect to the natural partial order ≤S of S. Using the concept of an anticone, all partially ordered groups which are epimorphic images of a semigroup (S, ·, ≤S) are determined. It is shown that a semigroup S is a generalized F-semigroup if and only if S contains an anticone, which is a principal order ideal of (S, ≤S). Also a characterization by means of the structure of the set of idempotents or by the existence of a particular element in S is given. The generalized Fsemigroups in the following classes are described: monoids, semigroups with zero, trivially ordered semigroups, regular semigroups, bands, inverse semigroups, Clifford semigroups, inflations of semigroups, and strong semilattices of monoids.
In this paper, the concepts of indecomposable matrices and fully indecomposable matrices over a distributive lattice $L$ are introduced, and some algebraic properties of them are obtained. Also, some characterizations of the set $F_n(L)$ of all $n\times n$ fully indecomposable matrices as a subsemigroup of the semigroup $H_n(L)$ of all $n\times n$ Hall matrices over the lattice $L$ are given.
We study the problem of existence of orbits connecting stationary points for the nonlinear heat and strongly damped wave equations being at resonance at infinity. The main difficulty lies in the fact that the problems may have no solutions for general nonlinearity. To address this question we introduce geometrical assumptions for the nonlinear term and use them to prove index formulas expressing the Conley index of associated semiflows. We also prove that the geometrical assumptions are generalizations of the well known Landesman-Lazer and strong resonance conditions. Obtained index formulas are used to derive criteria determining the existence of orbits connecting stationary points.
Let X be a Banach space of analytic functions on the open unit disk and Γ a subset of linear isometries on X. Sufficient conditions are given for non-supercyclicity of Γ. In particular, we show that the semigroup of linear isometries on the spaces S^{p} (p>1), the little Bloch space, and the group of surjective linear isometries on the big Bloch space are not supercyclic. Also, we observe that the groups of all surjective linear isometries on the Hardy space H^{p} or the Bergman space L_{a}^{p} (1< p< ∞,p\neq 2) are not supercyclic., Abbas Moradi, Karim Hedayatian, Bahram Khani Robati, Mohammad Ansari., and Obsahuje seznam literatury
Let $S$ be a semigroup. For $a,x\in S$ such that $a=axa$, we say that $x$ is an associate of $a$. A subgroup $G$ of $S$ which contains exactly one associate of each element of $S$ is called an associate subgroup of $S$. It induces a unary operation in an obvious way, and we speak of a unary semigroup satisfying three simple axioms. A normal cryptogroup $S$ is a completely regular semigroup whose $\mathcal H$-relation is a congruence and $S/\mathcal H$ is a normal band. Using the representation of $S$ as a strong semilattice of Rees matrix semigroups, in a previous communication we characterized those that have an associate subgroup. In this paper, we use that result to find three more representations of this semigroup. The main one has a form akin to the one of semigroups in which the identity element of the associate subgroup is medial.
We characterize finitely generated abelian semigroups such that every completely positive definite function (a function all of whose shifts are positive definite) is an integral of nonnegative miltiplicative real-valued functions (called nonnegative characters).
We obtain a presentation for the singular part of the Brauer monoid with respect to an irreducible system of generators consisting of idempotents. As an application of this result we get a new construction of the symmetric group via connected sequences of subsets. Another application describes the lengths of elements in the singular part of the Brauer monoid with respect to the system of generators mentioned above.