In this article we analyze the relationship between the growth and stability properties of coercive polynomials. For coercive polynomials we introduce the degree of stable coercivity which measures how stable the coercivity is with respect to small perturbations by other polynomials. We link the degree of stable coercivity to the Łojasiewicz exponent at infinity and we show an explicit relation between them.
Mathematical modeling of fibre composite materials is very difficult because of their random values of the coefficient describing mechanical properties of their separate phases. For the computational reasons, the real materials, i.e. materials with non-periodic structure are replaced by ‘equivalent‘ structures having almost the same mechanical properties. To the implementation of this, the various algorithms were developed for generating an ‘equivalent‘ structures, which will be similar to the real one as much as possible. Therefore some simple methodology for a statistical comparing of different structures developed by different algorithms is needed. and Obsahuje seznam literatury
We study the regularizing effect of the noise on differential equations with irregular coefficients. We present existence and uniqueness theorems for stochastic differential equations with locally unbounded drift.
H. Silverman (1999) investigated the properties of functions defined in terms of the quotient of the analytic representations of convex and starlike functions. Many research workers have been working on analytic functions to be strongly starlike like Obradovi´c and Owa (1989), Takahashi and Nunokawa (2003), Lin (1993) etc. In this paper we obtain a sufficient condition for p-valent functions to be strongly starlike of order α.
By a regular act we mean an act such that all its cyclic subacts are projective. In this paper we introduce strong $(P)$-cyclic property of acts over monoids which is an extension of regularity and give a classification of monoids by this property of their right (Rees factor) acts.
In the paper we obtain several characteristics of pre-T2 of strongly preirresolute topological vector spaces and show that the extreme point of a convex subset of a strongly preirresolute topological vector space X lies on the boundary.
We use graph-algebraic results proved in [8] and some results of the graph theory to characterize all pairs ⟨L1, L2⟩ of lattices for which there is a finite partial unary algebra such that its weak and strong subalgebra lattices are isomorphic to L1 and L2, respectively. Next, we describe other pairs of subalgebra lattices (weak and relative, etc.) of a finite unary algebra. Finally, necessary and sufficient conditions are found for quadruples ⟨L1, L2, L3, L4⟩ of lattices for which there is a finite unary algebra having its weak, relative, strong subalgebra and initial segment lattices isomorphic to L1, L2, L3, L4, respectively.
One of the main aims of the present and the next part [15] is to show that the theory of graphs (its language and results) can be very useful in algebraic investigations. We characterize, in terms of isomorphisms of some digraphs, all pairs A, L, where A is a finite unary algebra and L a finite lattice such that the subalgebra lattice of A is isomorphic to L. Moreover, we find necessary and sufficient conditions for two arbitrary finite unary algebras to have isomorphic subalgebra lattices. We solve these two problems in the more general case of partial unary algebras. In the next part [15] we will use these results to describe connections between various kinds of lattices of (partial) subalgebras of a finite unary algebra.
We consider, for a positive integer k, induced subgraphs in which each component has order at most k. Such a subgraph is said to be k-divided. We show that finding large induced subgraphs with this property is NP-complete. We also consider a related graph-coloring problem: how many colors are required in a vertex coloring in which each color class induces a k-divided subgraph. We show that the problem of determining whether some given number of colors suffice is NP-complete, even for 2-coloring a planar trianglefree graph. Lastly, we consider Ramsey-type problems where graphs or their complements with large enough order must contain a large k-divided subgraph. We study the asymptotic behavior of ''k-divided Ramsey numbers''. We conclude by mentioning a number of open problems.
The concept of super hamiltonian semigroup is introduced. As a result, the structure theorems obtained by A. Cherubini and A. Varisco on quasi commutative semigroups and quasi hamiltonian semigroups respectively are extended to super hamiltonian semigroups.