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51.
Let (X, ⫿) be a Polish ideal space and let T be any set. We show that under some conditions on a relation RT 2 × X it is possible to find a set AT such that R(A 2) is completely ⫿-nonmeasurable, i.e, it is ⫿-nonmeasurable in every positive Borel set. We also obtain such a set AT simultaneously for continuum many relations (Ra )a < 2w {({R_\alpha })_{\alpha < {2^\omega }}}. Our results generalize those from the papers of K. Ciesielski, H. Fejzić, C. Freiling and M. Kysiak.  相似文献   
52.
Assume that no cardinal κ < 2 ω is quasi-measurable (κ is quasi-measurable if there exists a κ-additive ideal $ \mathbb{I} $ \mathbb{I} of X contains uncountably many pairwise disjoint subfamilies $ \mathbb{I} $ \mathbb{I} -Bernstein unions ∪ $ \mathbb{I} $ \mathbb{I} -Bernstein if A and X \ A meet each Borel $ \mathbb{I} $ \mathbb{I} -positive subset BX). This result is a generalization of the Four Poles Theorem (see [1]) and results from [2] and [4].  相似文献   
53.
We prove that density preserving homeomorphisms form a Π 1 1 -complete subset in the Polish space ? of all increasing autohomeomorphisms of unit interval.  相似文献   
54.
We present a technique for reducing the order of polynomial-like iterative equations; in particular, we answer a question asked by Wenmeng Zhang and Weinian Zhang. Our method involves the asymptotic behaviour of the sequence of consecutive iterates of the unknown function at a given point. As an application we solve a generalized problem of Zoltán Boros posed during the 50th ISFE.  相似文献   
55.
E. Helly's theorem asserts that any bounded sequence of monotone real functions contains a pointwise convergent subsequence. We reprove this theorem in a generalized version in terms of monotone functions on linearly ordered sets. We show that the cardinal number responsible for this generalization is exactly the splitting number. We also show that a positive answer to a problem of S. Saks is obtained under the assumption of the splitting number being strictly greater than the first uncountable cardinal.

  相似文献   

56.
Effective homo-metathesis of a series of dichloro-substituted vinylsilanes H2C = C(H)SiCl2R (where R = Me, OSiMe3, C6H5, C6H4–Me-4, C6H4–CF3-4) in the presence of second generation Grubbs catalyst [Cl2(PCy3)(IMesH2)Ru(=CHPh)] (I) and Hoveyda–Grubbs catalyst (II) leads to selective formation of E-1,2-bis(silyl)ethenes and ethene. On the basis of the results of experiments with deuterium-labelled reagents, a metallacarbene mechanism has been suggested for these reactions.  相似文献   
57.
The present study assessed the genotoxicity, the possibility of inhibiting selected enzymes, and the microbial activity of lyophilisate from 3-year-old A. arborescens leaves obtained from controlled crops. The lyophilisate from 3-year-old A. arborescens leaves was standardized for aloin A and aloenin A content. Moreover, concentrations of polyphenolic compounds and phenolic acids were determined. The first stage of the research was to determine genotoxicity using the comet test, which confirmed the safety of A. arborescens. Assays of enzymatic inhibition were performed for hyaluronidase (IC50 = 713.24 ± 41.79 µg/mL), α-glucosidase (IC50 = 598.35 ± 12.58 µg/mL), acetylcholinesterase and butyrylcholinesterase (1.16 vs. 0.34 µM of eserine/g d.m., respectively). The next stage of the research was to determine the ability of the healing properties using the scratch test, which showed a positive response using the extract. Microbial activity was evaluated and obtained against Gram-negative and Gram-positive bacteria and yeasts. We concluded that A. arborescens leaf gel meets the important conditions for plant raw materials to obtain semi-solid forms of herbal medicinal products.  相似文献   
58.
Regular processes generalize the notion of diffusion processes. We observe them with the aid of a linear map in order to determine (or to predict) the final state. The main features of observability for such processes are the phenomenon of critical time and exceeding fragility for perturbations.  相似文献   
59.
We characterize upper semicontinuity of multifunctions in terms of upper Hausdorff semicontinuity, measure of non compactness and active boundary. The results are applicable in optimization, theory of best approximation and in metrizability theory.  相似文献   
60.
We present a unified approach to certain controllability and optimization questions such as approximate controllability with bounded sequences, necessary and sufficient conditions for lower stability, a problem of moments, penalty techniques. The control processes concerned are given by strongly continuous semigroups in Banach spaces, but the argument is led in the generality of continuous operators.  相似文献   
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