In this paper the notions of uniformly upper and uniformly lower $\ell $-estimates for Banach function spaces are introduced. Further, the pair $(X,Y)$ of Banach function spaces is characterized, where $X$ and $Y$ satisfy uniformly a lower $\ell $-estimate and uniformly an upper $\ell $-estimate, respectively. The integral operator from $X$ into $Y$ of the form \[ K f(x)=\varphi (x) \int _0^x k(x,y)f(y)\psi (y)\mathrm{d}y \] is studied, where $k$, $\varphi $, $\psi $ are prescribed functions under some local integrability conditions, the kernel $k$ is non-negative and is assumed to satisfy certain additional conditions, notably one of monotone type.
Let $\frak m$ be an infinite cardinal. We denote by $C_\frak m$ the collection of all $\frak m$-representable Boolean algebras. Further, let $C_\frak m^0$ be the collection of all generalized Boolean algebras $B$ such that for each $b\in B$, the interval $[0,b]$ of $B$ belongs to $C_\frak m$. In this paper we prove that $C_\frak m^0$ is a radical class of generalized Boolean algebras. Further, we investigate some related questions concerning lattice ordered groups and generalized $MV$-algebras.
First we summarize some properties of the nonholonomic $r$-jets from the functorial point of view. In particular, we describe the basic properties of our original concept of nonholonomic $r$-jet category. Then we deduce certain properties of the Weil algebras associated with nonholonomic $r$-jets. Next we describe an algorithm for finding the nonholonomic $r$-jet categories. Finally we classify all special types of semiholonomic $3$-jets.
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.