Bulletin of the Polish Academy of Sciences. Mathematics
In this paper we provide a relaxation result for control systems under both equality and inequality constraints involving the state and the control. In particular we show that the Mangasarian-Fromowitz constraint qualification allows to rewrite constrained systems as differential inclusions with locally Lipschitz right-hand side. Then Filippov-Ważewski relaxation theorem may be applied to show that...
In the paper a necessary and sufficient condition for the mean square stabilization of two-dimensional linear systems is obtained.
In this paper, from a construction of the standard embedding Lie algebras associated with triple systems, we derive the connection of our earlier work with the study of exceptional real simple Lie algebras of the second kind.
When one deals with normed linear space (n.l.s.), the natural question arises when a n.l.s. is an inner product space (i.p.s.)? What further conditions the norm has to satisfy so that the n.l.s. an inner product space? Numerous charakterizations are known [2, 1, 2, 4, 5, 6, 7]. In this paper we study i.p.s. from functional equations point of view and consider three functional equations (ME), (14)...
In the paper some equivalent conditions to pointwise reducibility of polynomials with holomorphic coefficients (in an arbitrary connected set) are given.
Here we study the birational structure of "exceptional" irreducible components of moduli schemes of rank 2 vector bundles on algebraic surfaces with negative Kodaira dimension. In particular for every rational surface X prove the existence of several such components which are rational.
In [5, 6] and [8], we proved that if a plane compactum X with dim X > 0 admits a continuum-wise expansive homeomorphism f, then X is not locally connected and it contains a sigma-chaotic continuum Z (sigma = s or u) of f such that Z is indecomposable and for each z [...] Z, the continuum-wise sigma-stable set V[sup sigma] (z, Z) coincides with the composant containing z. In this note, we generalize...
We prove that a compact set E of C satysfying the generalized Markov inequality (i.e. for each polynomial P (1) [max {absolute value P'(z) : z belongs to E} is less than or equal M (deg P)^m max{ absolute value P(z) : z belongs to E}], where [M is greater than or equal to 1] and m > 0 are some constants independent of P) is not polar. Moreover cap [(E) is greater than or equal to 1/Mdelta^m(diam...
Given a continuum X we denote by [2^x] and C(X) the hyperspace of all nonempty compact subsets and of all nonempty subcontinua of X. For any two continua X and Y and a mapping [f : X --> Y let 2^f] and C(f) stand for the induced mappings between corresponding hyperspaces. A mapping g between the hypespaces is inducible is there exists a mapping f such that [g = 2^f] or g = C(f), respectively. Necessary...
Let X be a connected normal complex space and let D be a non-zero Cartier divisor on X with the support [...]. We show that if D is a principal divisor then the group H[sub 1](X \ [absolute value of D],Z) cannot be a torsion group. In particular the group H[sub1](H \ [absolute value of D],Z)] must be infinite. As a corollary we prove that simple Cartier divisors D[sub 1],...,D[sub r] on a complex...
The dynamics of automorphisms of minimal flows are studied using a group which generalizes the Ellis group of the flow.
We prove the existence of compact Maltsev spaces that are not retracts of compact groups.
Sharp estimates of the Nullstellensatz exponent on analytic and algebraic sets are given.
In this paper, we prove some pinching theorems with respect to the scalar curvatures of 4-dimensional projectively flat (conharmonically flat) totally real minimal submanifolds in [QP^4(c)].
We extend the theory of semifractals to arbitrary metric spaces. We also show kow to construct semifractals on Polish spaces by a use of Markov operators and Markov chain.
We show the equivalence of the L[sub p] (0 < p [a is less than or equal to] 2) (quasi)-norms of square functions for the systems {2 [...], where f satisfies some decay condition. This implies the boundedness of the shift operator on the wavelet type unconditional basis on L[sub p], 1 < p < [infinity]. We prove also that such operator is unbounded on L[sub 1].
In 1960, Arhangel'skii gave a metrization theorem, showing that a space is metrizable if and only if it has a regular base. In the present paper, we prove two metrization theorems analogous tu Arhangel'skii's. For these two, we make use of regular k-networks and generalized regular bases, called HCP-regular bases, respectively. Next, we give a characterization of Lasnev spaces, using HCP-regular networks...
In terms of difference quotients it is established the existence of generalized derivative of the function.
We introduce a new class of hereditarily t-Baire spaces (defined by G. Koumoullis (1993) - see below) which need not to have the restricted Baire property in a compactification - as an example serves the space (O,omega[sup 1])^A for A uncountable. We use this and a modification of a construction of D. Fremlin (1987) to get, under the assumption that there is a measurable cardinal, an example of a...
We characterize second category P-filters on omega in terms of topological games. These characterizations use strong Choquet game gamma in the function space C[sub p](N[sub F]) associated with the filter F and a certain game delta played on the filter F. This complements earlier characterizations of hereditary Baire spaces C[sub p](N[sub F]), given by Gul'ko, Sokolov and Marciszewski.