On metrizable non-Archimedean LF-spaces

It is known that no non-Archimedean LB-space (and no strict non-Archimedean LF-space) is metrizable. We show that there exist many metrizable (or even normable) non-Archimedean LF-spaces. We prove that every non-normable polar non-Archimedean Fréchet space (and every non-Archimedean Banach space with an infinite basis (x_α)) contains a dense subspace which is an LF-space.     

Mathematical modelling of heat conduction in certain functionally graded composites

The aim of contribution is to formulate a certain extended version of the tolerance modelling technique for functionally graded composites. For the sake of simplicity, the considerations are restricted to the bidirectionally graded heat conductors. It is shown that the proposed approach enables to determine an entire class of mathematical models for which applications can be found in various specific problems. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Structure of 1,4-dihydro-1-ethyl-4-iminecinnoline-3-carboxylic acids, classical isosters of quinolone antibacterials: Crystal structures of hydrochlorides of 7-chloro and 7-methyl derivatives

Crystal structures of hydrochlorides of 7-chloro- and 7-methyl-4-iminecinnoline analogs of antibacterial quinolones have been determined by X-ray diffraction methods. The cell parameters for the 7-chloro (1) analog in the space group P2₁/c are a = 9.061(1), b = 19.062(1), c = 7.310(1)Å, = 104.92(1)°, Z = 4, and D _calc = 1.569 g/cm³ and for the 7-methyl (2) analog in the space group P are a = 7.277(5), b = 9.080(5), c = 10.058(5) Å, = 106.10(1), = 102.38(1), = 90.18(1)°, Z = 2, and D _calc = 1.429 g/cm³. Despite geometrical equivalency of methyl and chlorine and some resemblance of their packings, the crystal structures are not isostructural. Each compound forms a strong intramolecular hydrogen bond between protonated 4-imine (a donor) and 3-carboxylic (an acceptor) groups. Compounds with a similar bond, but with reversed functionality and orientation of the 3-carboxylic group, form common quinolones, being mostly 4-oxoquinoline-3-carboxylic acids. The difference should exclude chemical affinity of 4-imine analogs to the guanine base of a bacterial DNA in DNA-gyrase complex, as proposed by Shen et al. ² for 4-oxoquinoline-3-carboxylic acids showing antibacterial activity. Also the free acidic function of a carboxyl group may significantly lower permeability of 4-imine-3-carboxylic analogs of quinolones. Surprisingly, they have demonstrated antibacterial activity comparable with that of nalidixic acid.     

Mechanistic and synthetic aspects of the reaction of gamma-halogeno-alpha,beta-unsaturated ketones and esters with simple trialkyl phosphites

Phosphorylation of different gamma-halogeno-alpha,beta-unsaturated ketones, ketoesters and diesters 11a-h with simple trialkyl phosphites gives 1,3-dienylphosphates 14, cyclopropylphosphonates 15, ketovinylphosphonates 17 and other products depending on the nature and number of activating groups and halogen atoms in the substrate. Most likely the reaction proceeds via oxaphospholene 23 which is in equilibrium with pseudorotamer 24 and an open, dipolar form 22. Dipolar form 33 is a likely intermediate when two activating groups are present.     

Differentiable functions defined in closed sets. A problem of Whitney

In 1934, Whitney raised the question of how to recognize whether a function f defined on a closed subset X of ℝ ⁿ is the restriction of a function of class 𝒞 ^p . A necessary and sufficient criterion was given in the case n=1 by Whitney, using limits of finite differences, and in the case p=1 by Glaeser (1958), using limits of secants. We introduce a necessary geometric criterion, for general n and p, involving limits of finite differences, that we conjecture is sufficient at least if X has a “tame topology”. We prove that, if X is a compact subanalytic set, then there exists q=q _X (p) such that the criterion of order q implies that f is 𝒞 ^p . The result gives a new approach to higher-order tangent bundles (or bundles of differential operators) on singular spaces. Oblatum 21-XI-2001 & 3-VII-2002?Published online: 8 November 2002 RID="*" ID="*"Research partially supported by the following grants: E.B. – NSERC OGP0009070, P.M. – NSERC OGP0008949 and the Killam Foundation, W.P. – KBN 5 PO3A 005 21.     

Relativistic and correlation corrections to electron affinities of alkali and halogen atoms

Electron affinities (EAs) of alkali and halogen atoms have been calculated using Hartree-Fock and Dirac-Hartree-Fock methods. Comparing the results with the experimental values, relativistic and correlation corrections to EAs have been estimated. In the case of alkalines correlation correction constitute 110%–120% of the experimental EA values. In the case of halogens the corresponding numbers are 30%–60%. Relativistic effects are negligibly small for alkalines but significant for halogens (40% of the experimental value for At).     

An attempt to improve the pozzolanic activity of waste aluminosilicate catalyst

The so-called pozzolanic activity of waste catalysts from fluidised cracking was investigated. For this purpose a series of cement mixtures with this waste material were prepared and subsequently the pastes and mortars were produced. Waste aluminosilicate catalyst was used both in raw form and after grinding in a ball mill for 60 min. The hydrating mixtures were subjected to the calorimetric measurements in a non-isothermal/non-adiabatic calorimeter. After an appointed time of curing the hydrating materials were studied by thermal analysis methods (TG, DTG, DTA). The pozzolanic activity factors were determined, basing on the compressive strength data. The increased activity of cement — ground pozzolana systems has been thus proved. An accelerated Ca(OH)₂ consumption as well as higher strength were found for materials containing ground waste catalyst, as compared to those, mixed with the raw one. Thus grinding was also proved to result in mechanical activation in the case of the waste catalyst from fluidised cracking. This revised version was published online in July 2006 with corrections to the Cover Date.     

Heat evolution in alkali activated synthetic slag–metakaolin mixtures

In this study the calorimeter was applied to follow the early hydration of mixtures produced using three different synthetic slag vitreous materials, differing with alumina to silica ratio and mixed or not with synthetic two different metakaolin additions (kaolin heated with sodium containing admixture or without admixture). These mixtures were processed with sodium/potassium hydroxide solutions and placed inside the chamber of calorimeter. The kinetics of hydration process was thus characterized and the hydraulic properties of slag–metakaolin mixtures were very well assessed. Substantial heat evolution was found in the presence of activators, in many cases exceeding 100 J g^–1 for 24 h process; heat evolved on hydration with water only was very poor, below 20 J g^–1 after 24 h. The rate of heat evolution vs. time plots showed specific shape, more or less similar to the typical heat evolution curves reported for cements. Finally, some conclusions were drawn and the amount/concentration of activators was selected for further studies.     

Nonlinear dielectric effect near the critical point of binary mixtures

The nonlinear dielectric effect (NDE) was measured in two binary systems near the critical point. The effect of independent of specific dipole-dipole interactions in contrast with previous conceptions. Its singular part is proportional to (T ? T_c)^{?$\text{1}\text{2}$} in agreement with Snider's theory as applied to NDE.