Some Landau's type inequalities for infinitesimal generators

Summary Lett T(t) be a strongly continuous contraction semigroup on a complex Banach space and letA be its infinitesimal generator. We prove that, forx D(A ³), the following inequalities hold true: Ax³ 243/8 x²A ³ x, A ² x 24 xA ³ x². Ift T(t) is a contraction group (resp. cosine function) we get the analogous but better inequalities with constants 9/8 and 3 (resp. 81/40 and 72/25) instead of 243/8 and 24. We consider also uniformly bounded semigroups, groups and cosine functions.     

Numerical solution of a singularly perturbed problem via exponential splines

It is proved that a spline difference scheme for a singularly perturbed self-adjoint problem, derived by using exponential cubic splines at mid-points, has second order uniform convergence in a small parameter . Numerical experiments are presented to confirm the theoretical predictions.     

Interlayer pairing in high temperature superconductors: effect of nonmagnetic impurities

The influence of impurity scattering is studied theoretically in a two-layer model for the high-T _c superconductor Y₁Ba₂Cu₃O_7– with intra- and inter-layer pairing. Two types of impurities are considered: (I) impurities which conserve the reflection symmetry of the two layers and (II) impurities which break it. Impurities of type (I) have no influence on the critical temperature. Type (II) impurities have strong influence onT _c as well as onH _c2 if there is a pairing interaction between carriers of different layers. The treatment of type (II) impurities is generalized to a periodic layer model appropriate for La_2–x Ba _x CuO₄. Available experiments on impurities in Y₁Ba₂Cu₃O_7– and La_2–x Ba _x CuO₄ are interpreted with our theory.     

Restoration of universality for the rod-to-coil transition scaling in the infinite-dimensionality limit: Exact results for directed walks

We derive scaling forms for the thermodynamic and correlation quantities for the turn-weighted fully and partially directed self-avoiding walks on the hypercubic lattices ind2. In the grand canonical (fixed fugacity per step) ensemble, the conformational rod-to-coil transition sets up in the regimew¯N=O(1), wherew is the weight of each 90° turn and¯N is the (fugacity-dependent) average number of steps. Contrary to the conventional critical phenomena wisdom, the scaling functions for the two different walk models, directed and partially directed, become universal only in the limitd.     

Conditioning of industrial waste in cement matrix

Results are presented of a series of experimental tests performed to determine the influence of matrix characteristics on the leaching mechanism of copper aluminium oxychloride immobilized into cement matrices. The objective of this research was to investigate the leaching mechanism of copper as a constituent of copper aluminium oxychloride (CAOX).     

Unified quantum logic

Unified quantum logic based on unified operations of implication is formulated as an axiomatic calculus. Soundness and completeness are demonstrated using standard algebraic techniques. An embedding of quantum logic into a new modal system is carried out and discussed.On leave of absence from Department of Mathematics, University of Zagreb, Pot. Pret. 165, YU-41001 Zagreb, Yugoslavia.     

1,3,6,9,12,14,17,20-octaethynyltetrabenz[a,b,f,j,k,o]-4,5,10,11,15,16,21,22- octadehydro[18]annulene: a carbon-rich hydrocarbon

Dodecaynes 1a-d have been prepared via a convergent strategy that employs Sonogashira couplings as the carbon-carbon bond-forming tool. Due to the steric bulk of the DMTS groups, 1c adopts a nonplanar conformation, the dynamics of which have been probed by VT-NMR. The cobalt-catalyzed isomerization of 1a,b produced the new conjugated phenylenes 2a,b and 3a,b, respectively. [structure: see text]     

Transition metal complexes with Girard reagent-based ligands

The ligand, salicylaldehyde Girard-T hydrazonium chloride, [H₂SalGT]Cl (1), and two complexes [Cu(HSalGT)X₂]·H₂O (X = Br(2); Cl(3)) were synthesized and their crystal structures were determined by single-crystal X-ray analysis. In the two isostructural complexes, the Cu(II) is located in a square-pyramidal environment, with the chelating ligand and one halogen atom in the basal plane and the second halogen in the apical position. The most apparent structural difference between the 1 and its complexes 2 and 3 is the orientation of the N(CH₃)₃ group: in 1, it is practically coplanar to the rest of the molecule, while in 2 and 3 it is oriented to the side of the axially bonded halogen, which can be explained by the C–H…X intramolecular interactions. The compounds were characterized by elemental analysis, molar conductivity, magnetic susceptibility and electronic absorption spectra.     

Sorption of chromium(VI) and chromium(III) on aluminium hydroxide

Factors that influence the sorption of Cr(VI) and Cr(III) on aluminium hydroxide were investigated. The sorption of chromates decreases as the pH of the suspension increases. The mechanism of CrO ₄ ^2– sorption was interpreted in terms of reactions between chromates and –OH and/or H₂O groups at the hydroxide/liquid interface. It has been shown that chromates are more tightly sorbed on aluminium hydroxide compared to other anions, e.g. chlorides. On the other hand, specifically absorbed anions, such as molybdates, compete strongly with chromates for the sorption sites. The sorption of chromium(III) increases with the pH of the suspension. Also, the sorption of chromium(III) is suppressed in the presence of citrate ions. The best conditions for the fixation of Cr(VI) and Cr(III) by aluminium hydroxide are presented.