Global solution to the incompressible viscous-multipolar material problem

In the paper we give a proof of the global existence of the weak solution to the initial-boundary-value problem describing an incompressible elasto-viscous-multipolar material in finite geometry. A brief introduction to the physical background of viscous-multipolar materials is given. We suggest the hypothesis% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaamaaxadabaGaeu4OdmfaleaacaWGPbGaaiilaGqaciaa-bcacaWG% QbGaa8hiaiabg2da9iaa-bcacaaIXaaabaGaaG4maaaakiaa-bcada% abdiqcaasaaOWaaSaaaKaaGeaacqGHciITcqqHOoqwcaGGOaGaamOr% aiaacYcacqaH4oqCcaGGPaaabaGaeyOaIyRaamOraOWaaSbaaSqaai% aadMgacaWGbbaabeaaaaqcaaIaa8hiaiaadAeakmaaBaaaleaacaWG% QbGaamyqaaqabaaajaaqcaGLhWUaayjcSdGaa8hiaiabgsMiJkaado% gakmaaBaaaleaacaWFVbaabeaakiaadwgacaGGOaGaamOraiaacYca% ieaacaGFGaGaeqiUdeNaaiykaiaa+bcacqGHRaWkcaGFGaGaam4yam% aaBaaaleaacaaIXaGaa4hiaiaacYcaaeqaaaaa!686E!\[\mathop \Sigma \limits_{i, j = 1}^3 \left| {\frac{{\partial \Psi (F,\theta )}}{{\partial F_{iA} }} F_{jA} } \right| \leqslant c_o e(F, \theta ) + c_{1 ,} \] which enables one to obtain a priori estimates.     

Photoelectric properties of linear oligoaniline derivatives

Dark conductivity and photoconductivity were measured on polycrystalline layers and single crystals of the arylamine type compounds. The photoconductivity process is largely affected by the effects of trapping of the charge carriers followed by their thermal releasing from traps. The activation energy of photoconductivity is determined by the depth of the traps, similarly to the activation energy of the dark conductivity at lower temperatures. At laboratory temperatures and higher ones the activation energy of the dark conductivity is determined by the position of the Fermi level.The author is indebted to Dr B.Sedláek and Dr J.Honzl for their interest, to Dr K.Ulbert for support, valuable discussion, and critical reading of the whole paper, to Dr K.Vacek for discussion and surveying the paper, to Dr M.Tlusáková for sample preparation, to Mr J.Obrda M. Sc. for assistance in measurements of the photoconductivity of single crystals, and to Mrs V.Berdychová and Mrs J.Vaková for technical assistance.     

Quantum entropy and special relativity

We consider a single free spin- 1 / 2 particle. The reduced density matrix for its spin is not covariant under Lorentz transformations. The spin entropy is not a relativistic scalar and has no invariant meaning.     

Counterexamples in chemical ring perception

Ring information is a large part of the structural topology used to identify and characterize molecular structures. It is hence of crucial importance to obtain this information for a variety of tasks in computational chemistry. Many different approaches for "ring perception", i.e., the extraction of cycles from a molecular graph, have been described. The chemistry literature on this topic, however, reports a surprisingly large number of incorrect statements about the properties of chemically relevant ring sets and, in particular, about the mutual relationships of different sets of cycles in a graph. In part these problems seem to have arisen from a sometimes rather idiosyncratic terminology for notions that are fairly standard in graph theory. In this contribution we translate the definitions of concepts such as the Smallest Set of Smallest Rings, Essential Set of Essential Rings, Extended Set of Smallest Rings, Set of Smallest Cycles at Edges, Set of Elementary Rings, K-rings, and beta-rings into a more widely used mathematical language. We then outline the basic properties of different cycle sets and provide numerous counterexamples to incorrect claims in the published literature. These counterexamples may have a serious practical impact because at least some of them are molecular graphs of well-known molecules. As a consequence, we propose a catalog of desirable properties for chemically useful sets of rings.     

Finite Paths are Universal

We prove that any countable (finite or infinite) partially ordered set may be represented by finite oriented paths ordered by the existence of homomorphism between them. This (what we believe a surprising result) solves several open problems. Such path-representations were previously known only for finite and infinite partial orders of dimension 2. Path-representation implies the universality of other classes of graphs (such as connected cubic planar graphs). It also implies that finite partially ordered sets are on-line representable by paths and their homomorphisms. This leads to new on-line dimensions. Mathematics Subject Classifications (2000) 06A06, 06A07, 05E99, 05C99.J. Nešetřil: Supported by a Grant LN00A56 of the Czech Ministry of Education. The first author was partially supported by EU network COMBSTRU at UPC Barcelona.     

Chiral induction effects in ruthenium(II) amino alcohol catalysed asymmetric transfer hydrogenation of ketones: an experimental and theoretical approach

The enantioselective outcome of transfer hydrogenation reactions that are catalysed by ruthenium(II) amino alcohol complexes was studied by means of a systematically varied series of ligands. It was found that both the substituent at the 1-position in the 2-amino-1-alcohol ligand and the substituent at the amine functionality influence the enantioselectivity of the reaction to a large extent: enantioselectivities (ee values) of up to 95% were obtained for the reduction of acetophenone. The catalytic cycle of ruthenium(II) amino alcohol catalysed transfer hydrogenation was examined at the density functional theory level. The formation of a hydrogen bond between the carbonyl functionality of the substrate and the amine proton of the ligand, as well as the formation of an intramolecular H...H bond and a planar H-Ru-N-H moiety are crucially important for the reaction mechanism. The enantioselective outcome of the reaction can be illustrated with the aid of molecular modelling by the visualisation of the steric interactions between the ketone and the ligand backbone in the ruthenium(II) catalysts.