Catalytic Hydrogen Transfer over Magnesia, xv. Preliminary Studies of Active Centers of Catalysts

Reduction of 7-tridecanone and 1-phenyl-1-hexanone by 2-propanol at 573-673 K in the presence of MgO has been studied. Acidic as well as strong and weak basic sites of MgO surface have been blocked in the reaction of the oxide with triethylamine, phenol or benzoic acid (1000 mol/g of catalyst), respectively. Retention of activity of MgO treated with triethylamine or phenol in ketones reduction by 2-propanol has been observed. Only residual activity of MgO poisoned by benzoic acid has been noted. The exclusive participation of moderate basic centers of MgO in catalytic reduction of ketones by 2-propanol has been ascertained.     

Weak and strong vibronic coupling limits in molecules and their correlation

An exactly solvable vibronic coupling model is used to improve existing definitions of strong and weak vibronic coupling limits in molecules and to derive a unique correlation between the corresponding energy levels.     

Structural Study of C-undecylcalix[4]resorcinarene Solvate with Dioxane

The crystal structure of the molecular complex of C-undecylcalix[4]resorcinarene with dioxane has been determined by X-ray analysis. The asymmetric unit contains one host and four guest molecules. The calix[4]resorcinarene moiety adopts a bowl conformation with C_4v symmetry. Four undecyl chains are axially oriented. Calix molecules are packed in a bowl-to-bowl fashion with alternating hydrophilic and hydrophobic layers. One of the hydrophilic dioxane molecules is located at the rim of the calix moiety and is hydrogen bonded to the other one. There is no interaction to attract, or direct the dioxane molecule into the interior of the cavity. There is an exo complex formed. The dioxane molecules – located in the hydrophobic part – are highly disordered.     

On relatively short and long sides of convex pentagons

By the relative distance of pointsa andb of a convex bodyC we mean the ratio of the Euclidean distance ofa andb to the half of the Euclidean distance ofa, b C such thatab is a longest chord ofC parallel to the segmentab. We say that a sideab of a convexn-gon is relatively short (respectively: relatively long) if the relative distance ofa andb is at most (respectively: at least) the relative distance of two consecutive vertices of the regularn-gon. We show that every convexn-gon, wheren 5, has a relatively short side and a relatively long side, and that it is affine-regular if and only if all its sides are of equal relative lengths.Research supported in part by Komitet Bada Naukowych (Committee of Scientific Research), grant number 2 2005 92 03.     

Pion multiplicity in nuclear collisions

Data on the mean multiplicity of ^- produced in minimum bias proton-proton, proton-neutron and proton-nucleus interactions as well as central nucleus-nucleus collisions at momenta of 1.4–400 GeV/c per nucleon have been compiled and studied. The results for neutron-neutron and nucleon-nucleon interactions were then constructed. The dependence of the mean pion multiplicity in proton-nucleus interactions and central collisions of identical nuclei are studied as a function of the collision energy and the nucleus mass number. The number of produced pions per participant nucleon in central collisions of identical nuclei is found to be independent of the number of participants at a fixed incident momentum per nucleon. The mean multiplicity of negatively charged hadrons per participant nucleon for central nucleus-nucleus collisions is lower by about 0.12 than the corresponding multiplicity for nucleon-nucleon interactions atp _LAB 15 A·GeV/c, whereas the result at 200 A·GeV/c is above the corresponding nucleon-nucleon multiplicity. This may indicate change of the collision dynamics at high energy.     

The maximal monotonicity of the subdifferentials of convex functions: Simons' problem

In the paper we deal with the problem when the graph of the subdifferential operator of a convex lower semicontinuous function has a common point with the product of two convex nonempty weak and weak^* compact sets, i.e. when graph (Q × Q ^*) 0. The results obtained partially solve the problem posed by Simons as well as generalize the Rockafellar Maximal Monotonicity Theorem.     

Pathwise global attractors for stationary random dynamical systems

Summary The asymptotic behaviour of random dynamical systems in Polish spaces is considered. Under the assumption of existence of a random compact absorbing set, assumption supposed to hold path by path, a candidate pathwise attractorA() is defined. The goal of the paper is to show that, in the case of stationary dynamical systems,A() attracts bounded sets, is measurable with respect to the -algebra of invariant sets, and is independent of when the system is ergodic. An application to a general class of Navier-Stokes type equations perturbed by a multiplicative ergodic real noise is discussed in detail.     

Synthesis of arylboronates by the palladium catalysed cross-coupling reaction in ionic liquids

The palladium catalysed cross-coupling reaction of aryl iodides and bromides with pinacolborane in 1,3-dialkylimidazolium tetrafluoroborates and hexafluorophosphates producing arylboronates is described.