Diamagnetic anisotropy of molecular complexes of 1,3,5-trinitrobenzene with anthracene and carbazole

The anisotropy of the diamagnetic properties of 1 : 1 EDA complex crystals of 1,3,5-trinitrobenzene with anthracene (A—TNB) and carbazole (C—TNB) has been measured as a function of temperature in the range 100–293 K. The results for 293 K are found to be in good agreement with the values calculated according to the rule of additivity for molecular susceptibilities. The temperature dependence of the diamagnetic anisotropy for both A—TNB and C—TNB crystals, is discussed in the context of possible phase transitions in the crystals. The influence of thermal motions on the diamagnetic properties is described     

The h-p version of the finite element method for parabolic equations. Part I. The p-version in time

The paper is the first in the series addressing the h-p version of the finite element method for parabolic equations. The h-p version is applied to both time and space variables. The present paper addresses the case when in time the p-version with one single time element is used. Error estimation is given and numerical computations are presented.     

Influence of potassium on the properties of steam reforming catalysts

The influence of K₂O on the amounts of chemisorbed hydrogen on a Ni catalyst, the catalyst activity and its resistance to coking were measured. Introducing potassium into the commercial catalyst (not into the support) appeared to enhance its resistance to coking. The best catalytic characteristics was noticed for a system containing ~0.5 wt. % K₂O. The investigations show a good agreement between the resistance to coking obtained by the temperature-programmed reaction (TPReaction) method and by the traditional thermogravimetric method. This revised version was published online in August 2006 with corrections to the Cover Date.     

Functional Calculus for Infinitesimal Generators of Holomorphic Semigroups

We give a functional calculus formula for infinitesimal generators of holomorphic semigroups of operators on Banach spaces, which involves the Bochner–Riesz kernels of such generators. The rate of smoothness of operating functions is related to the exponent of the growth on vertical lines of the operator norm of the semigroup. The strength of the formula is tested on Poisson and Gauss semigroups inL¹(Rⁿ) andL¹(G), for a stratified Lie groupG. We give also a self-contained theory of smooth absolutely continuous functions on the half line [0, ∞).     

Grain size and grain shape effect of zing sulphide structure and of oxidizing process conditions

The results in this paper give information about the influence of the zinc sulphide structure and the oxidation conditions on the shape of the crystallites in the oxide phase. Zinc sulphide has regular and hexagonal structures. The cross-sections of the samples have been observed before and after the oxidation at 1223 K.The reaction products are dependent of the temperature, the flow-rate of gases and the oxygen pressure. Showing these dependences the shape of zinc oxide crystallites has been investigated when the oxidation of' regular zinc sulphide was already finished. It was also taken into consideration that the growth of the grain of the sulphide may change the rate of oxidation. The results obtained agree with all the mentioned parameters of the shape of zinc oxide crystallites allowing to interpret the kinetic curves.     

Flotation-spectrophotometric determination of ruthenium in the Ru(IV)-chloride-rhodamine 6G-toluene system

Summary Flotation-Spectrophotometric Determination of Ruthenium in the Ru(lV)-Chloride-Rhodamine 6G-Toluene System The reduction of RuO₄ in hydrochloric acid has been examined. A sensitive flotation-spectrophotometric method of the determination of ruthenium based on the ion associate formed by the anionic chloride complex of ruthenium RuCl₆ ^2– with the basic dye Rhodamine 6G (R6G) has been developed. The solution of the ion associate obeys Beer's law up to the concentration of 0.25g Ru/ml. The ion associate precipitates when the aqueous solution is shaken with toluene. The separated compound is dissolved in acetone. The molar absorptivity () at 530 nm is 5.1×10⁵ 1·mole^–1-cm^–1. The relative standard deviation is 3–7%. The mole ratio of RuR6G in the complex is 15. Osmium reacts similarly. The determination of ruthenium can be selective after the preliminary separation of osmium as OsO₄. The method was applied to the determination of microgram amounts of ruthenium in crucible platinum.     

Significance of the second dip in the ultra-high energy cosmic ray spectrum

A new feature in the spectrum of ultra high energy cosmic rays (UHECR) has been announced in the paper by Berezinsky, Gazizov and Kachelrieβ. The ratio of the solution of the exact transport equation to its solution in the continuous energy loss limit shows intriguing features which, according to the Authors, are related to the very nature of the energy loss processes of UHECR: the very sharp second dip predicted at 6.3 × 10¹⁹ eV can be used as an energy calibration point and also as the UHECR mass indicator for big future cosmic ray experiments. In the present paper we would like to advocate that this statement is an overinterpretation. The second dip is a result of an inappropriate approximation used, and thus it cannot help to understand the nature of UHECR in any way.      

Relationship between substituent effect and aromaticity – Part III: naphthalene as a transmitting moiety for substituent effect

Molecular geometry of 10 isomeric nitronaphtholate ions (excluding peri‐ and ortho‐type substituted systems), 1‐ and 2‐naphtholate ions, 1‐ and 2‐nitronaphthalene, meta‐ and para‐nitrophenolate, phenolate, and nitrobenzene were optimized at B3LYP/6‐311G** level of approximation. Substituent effect stabilization energy (SESE), geometry‐based aromaticity index HOMA, magnetism‐based indices NICS, NICS(1), NICS(1)_zz, and parameters characterizing Bond Critical Points (BCP) (ρ, ?²ρ, ellipticity, ion/cov) of the Bader AIM theory were used to characterize transmitting properties for substituent effect through the naphthalene moiety. It results from our study that the studied systems could be clearly divided into two groups, (i) a para‐type group, where the intramolecular charge transfer between the π‐electron donating and π‐electron accepting substituents can be described by canonical forms with charge separation (as in the case of para‐nitrophenolate) and (ii) a meta‐type group, where this transfer requires using canonical forms with double charge separation (as in the case of meta‐nitrophenolate). Copyright © 2007 John Wiley & Sons, Ltd.     

Covering properties of ideals

Elekes proved that any infinite-fold cover of a σ-finite measure space by a sequence of measurable sets has a subsequence with the same property such that the set of indices of this subsequence has density zero. Applying this theorem he gave a new proof for the random-indestructibility of the density zero ideal. He asked about other variants of this theorem concerning I-almost everywhere infinite-fold covers of Polish spaces where I is a σ-ideal on the space and the set of indices of the required subsequence should be in a fixed ideal ${{\mathcal{J}}}$ on ω. We introduce the notion of the ${{\mathcal{J}}}$ -covering property of a pair ${({\mathcal{A}}, I)}$ where ${{\mathcal{A}}}$ is a σ-algebra on a set X and ${{I \subseteq \mathcal{P}(X)}}$ is an ideal. We present some counterexamples, discuss the category case and the Fubini product of the null ideal ${\mathcal{N}}$ and the meager ideal ${\mathcal{M}}$ . We investigate connections between this property and forcing-indestructibility of ideals. We show that the family of all Borel ideals ${{\mathcal{J}}}$ on ω such that ${\mathcal{M}}$ has the ${{\mathcal{J}}}$ -covering property consists exactly of non weak Q-ideals. We also study the existence of smallest elements, with respect to Katětov–Blass order, in the family of those ideals ${\mathcal{J}}$ on ω such that ${\mathcal{N}}$ or ${\mathcal{M}}$ has the ${\mathcal{J}}$ -covering property. Furthermore, we prove a general result about the cases when the covering property “strongly” fails.