Separable Banach spaces which admitl n ∞ approximations

In this paper we study a class of separable Banach spaces which can be approximated by certain special finite-dimensional subspaces. This class is characterized in Theorem 1.1, from which it follows that the space of continuous scalar-valued functions on a compact metric space always belongs to this class, and that every member of this class has a monotone basis. Supported in part by N.S.F. Grant 11-5020. Supported in part by N.S.F. Grant GP-3579.     

Reactions of the N,N-dialkylpyridylcarboxylic amides with lithium amides. Regioselective lithiation of N,N-diisopropylpyridylcarboxylic amides,a useful method for synthesis of 2,3- and 3,4-disubstituted pyridines

The behaviour of the N,N-dimethyl-, N,N-diethyl- and N,N-diisopropylpyridylcarboxylic amides in the reactions with Et₂NLi and iPr₂NLi, and a convenient way of synthesis of 2,3- and 3,4-disubstituted pyridines, by the direct lithiation of N,N-diisopropylamides leading subsequently to the ortho new CC bonds formation, are described.     

The influence of some fuzzy implication operators on the accuracy of a fuzzy model-part II

The influence of fuzzy implication operators and the connective Also on the accuracy of a fuzzy model of a d.c. series motor is considered. Some typical fuzzy implication operators are applied to the construction of a fuzzy model of a d.c. series motor. A root-mean-square error is used as the criterion of the fuzzy model's adequacy to the real system. A number of mathematical operations necessary for the implementation of the fuzzy model are used as the criterion by which the fuzzy model's applicability if estimated from the point of view of computing techniques. The best types of fuzzy relations, representing fuzzy models of a real system, are chosen in order to secure the least root-mean-square error with minimal number of mathematical operations necessary for computer implementation.     

Holomorphically projective structures II. The transgressed classes

There is proved that the transgressed classes are invariant under holomorphically projective transformations of connections.     

Control problems in fuzzy systems

This paper deals with some problems of the control of fuzzy systems described by means of a relational equation of the type: X_{κ + 1} = U_κ ° X_κ ° R. The basic aspects such as mutual identification and control, stabilization control, control with constraints, generation of control rules of a fuzzy logic controller, important from the theoretical and applicational point of view are discussed and illustrated by means of numerical examples.     

Adsorption from solutions on patchwise heterogeneous solids

An attempt is made to develop the expression for surface excess, in adsorption of binary ideal mixtures on patchwise heterogeneous surfaces. The distribution of adsorption energies is evaluated for an adsorption system, investigated experimentally and theoretically by Sircar and Mayers.     

Chiral corrections to the axion mass

The leading non analytic chiral corrections to the mass of the invisible axion and to the parameters describing its mixing with the pion and the eta are calculated. It is found that these corrections are much smaller than expected on the basis of order of magnitude estimates. The correction to the decay width into two photons is also found to be negligible.     

Concepts of lower semicontinuity and continuous selections for convex valued multifunctions

We discuss several concepts of continuity, weaker than lower semicontinuity, but still implying the existence of a continuous selection for a closed convex valued multifunction from a paracompact Hausdorff topological space into a Banach space. In this way, an extension of Michael's celebrated selection theorem is given. The behavior of -envelop approximations, as well as the localization of continuous selections, is also discussed.     

The role of the liquid interface agent in mechanical properties improvement of modified chalk filled polyolefins

On the basis of the experimental results described in detail in the following sections an explanation of the mechanism of liquid modifier in chalk filled PP action was proposed. After concluding that liquid modifier does not change the sample morphology and crystallinity it was stated that it facilitates filler particles translocation in polymer matrix during deformation. Such translocations are the necessary condition for saturation of volume increase of the sample due to void formation in the process of polymer filler separation preserving the sample from its premature fracture. The most important physicochemical parameter of liquid modifier seems to be its molecular weight. This parameter determines liquids ability to migrate in micropore structure arising under stress and thus to act as a cracking agent. The possibility of the importance of more efficient heat dissipation in the sample was shown indicating the role of better thermal contacts in the sample in the case of modified chalk used as a filler. Such picture of mechanism of liquid modifier action leads also to two important conclusions:

Due to polymer filler separation by means of liquid layer no further filler particles surface processing, as in some cases, is needed.

The method of modification can be easily generalized for other polymers especially other polyolefins [19], [20] as physicochemical requirements for liquid are known.