Standard<Emphasis Type="Italic">SU</Emphasis>(5) supergravity grand unification model and predictions

A review is given of the StandardSU(5) supergravity model. This model has passed an important check regarding unification of the electro-weak and the strong couplings using high precision LEP data. It is shown that for a significant domain of the parameter space the model also satisfies constraints on the SUSY spectrum from CDF and LEP, as well as proton stability and cosmological relic density constraints.     

Rigorous results on the thermodynamics of the dilute Hopfield model

We study the Hopfield model of an autoassociative memory on a random graph onN vertices where the probability of two vertices being joined by a link isp(N). Assuming thatp(N) goes to zero more slowly thanO(1/N), we prove the following results: (1) If the number of stored patternsm(N) is small enough such thatm(N)/Np(N) 0, asN, then the free energy of this model converges, upon proper rescaling, to that of the standard Curie-Weiss model, for almost all choices of the random graph and the random patterns. (2) If in additionm(N) < ln N/ln 2, we prove that there exists, forT< 1, a Gibbs measure associated to each original pattern, whereas for higher temperatures the Gibbs measure is unique. The basic technical result in the proofs is a uniform bound on the difference between the Hamiltonian on a random graph and its mean value.     

Internal dynamics of flexible molecules: Cyclohexane

Summary The international motions of a single cyclohexane molecule are studied by molecular dynamics calculations. Classical trajectories are calculated by integrating Newton's equation of motion. The potential functions used are essentially the same as in Allinger's MM2 program which is widely applied for calculations on conformational energies of organic molecules.Geometries and relative energies are reported for all stable low energy conformers and some transition states of cyclohexane. Vibrational frequencies of classical oscillations of individual bonds — computed for ethane as reference system — are close to the experimental values.Two trajectories of the molecular dynamics of cyclohexane were simulated. In the first we were able to follow the process of ring inversion: chair twisted forms inverted chair. The reaction path is analysed in detail and compared with static approaches. The second trajectory shows the correlated reorientation of the possible twisted forms alone. This process is known as pseudorotation.Dedicated to Prof. Dr. Karl Schlögl     

Computing the Fukui function from ab initio quantum chemistry: approaches based on the extended Koopmans’ theorem

The extended Koopmans’ theorem is related to Fukui function, which measures the change in electron density that accompanies electron attachment and removal. Two approaches are used, one based on the extended Koopmans’ theorem differential equation and the other based directly on the expression of the ionized wave function from the extended Koopmans’ theorem. It is observed that the Fukui function for electron removal can be modeled as the square of the first Dyson orbital, plus corrections. The possibility of useful generalizations to the extended Koopmans’ theorem is considered; some of these extensions give approximations, or even exact expressions, for the Fukui function for electron attachment.     

Repeat Space Theory Applied to Carbon Nanotubes and Related Molecular Networks. I

The present article is the first part of a series devoted to extending the Repeat Space Theory (RST) to apply to carbon nanotubes and related molecular networks. Four key problems are formulated whose affirmative solutions imply the formation of the initial investigative bridge between the research field of nanotubes and that of the additivity and other network problems studied and solved by using the RST. All of these four problems are solved affirmatively by using tools from the RST. The Piecewise Monotone Lemmas (PMLs) are cornerstones of the proof of the Fukui conjecture concerning the additivity problems of hydrocarbons. The solution of the fourth problem gives a generalized analytical formula of the pi-electron energy band curves of nanotube (a, b), with two new complex parameters c and d. These two parameters bring forth a broad class of analytic curves to which the PMLs and associated theoretical devices apply. Based on the above affirmative solutions of the problems, a central theorem in the RST, called the asymptotic linearity theorem (ALT) has been applied to nanotubes and monocyclic polyenes. Analytical formulae derived in this application of the ALT illuminate in a new global context (i) the conductivity of nanotubes and (ii) the aromaticity of monocyclic polyenes; moreover an analytical formula obtained by using the ALT provides a fresh insight into Hückel’s (4n+2) rule. The present article forms a foundation of the forthcoming articles in this series. The present series of articles is closely associated with the series of articles entitled ‘Proof of the Fukui conjecture via resolution of singularities and related methods’ published in the JOMC.     

A simple and very sensitive spectrophotometric method for the direct determination of copper ions

A sensitive spectrophotometric method for the direct determination of copper in aqueous samples without a preconcentration step has been developed. It is based on the formation of a yellow complex with the chromogenic reagent di-2-pyridyl ketone benzoylhydrazone (dPKBH) in an alkaline medium. The complex stoichiometry was 1:2 (Cu:dPKBH) and presents maximum absorbance at 370 nm. The influence of chemical variables affecting the behaviour of the system such as pH, concentration of dPKBH, buffer solution and ethanol, order of addition of the reagents and stability of the complex, were evaluated. The molar absorptivity (epsilon) was 3.92x10(4) L mol(-1) cm(-1), and Beer's law was obeyed up to 3 mg L(-1) of copper. The relative standard deviation was 0.46% (n=11) for a sample containing 1 mg L(-1) Cu(II). The limit of detection was 2.5 micro g L(-1) and was therefore more sensitive than the direct methods reported previously. Finally, the method was successfully validated by analysing several real samples with different matrices, such as tap water, natural water or copper alloys, with an average relative error of 2.46%.     

Synthesis and absolute configuration of clemastine and its isomers (author's transl)]

Synthesis and Absolute Configuration of Clemastine and its Isomers. Condensation of 4-chloro-α-methylbenzhydrylalkohol ( 1 ) with 2-(2-chloroethyl)-1-methylpyrrolidine ( 2 ) gave an isomeric mixture of 2-[2-(p-chloro-α-methyl-=-phenylbenzyloxy)ethyl]-1-methylpyrrolidine ( 3 ) and 4-(p-chloro-=-phenylbenzyloxy)-1-methyl-hexahydroazepin ( 4 ). The separation of the four possible optically active isomers of 3 is described and their absolute configuration established by degradation to (R)- and (S)-1-methyl-2-pyrrolidineethanol ( 6 ), respectively, and by an X-ray cristallographic analysis of the quarternary methiodide of the isomer 3-A . Clemastine (3-A) is (+)-(2R)-2-[2-((αR)-(p-chloro-α-methyl-α-phenylbenzyloxy)ethyl)]-1-methylpyrrolidine.     

Enantioselective Alternating Terpolymerization of Styrene and Ethene with Carbon Monoxide. Preliminary communication

In spite of the higher reactivity of styrene with respect to ethene for the alternating copolymerization with carbon monoxide, catalyzed by chiral (dihydrooxazole)(phosphino)palladium complexes, ethene is preferentially (and randomly) enchained in terpolymerization experiments; enantioface selection for styrene is comparably high in both copolymerization and terpolymerization processes.     

Thermal and mechanical-induced phase transformations during YAG and alumina–YAG syntheses

The preparation of pure Y₃Al₅O₁₂ (YAG) and 50 vol% Al₂O₃–YAG composite powders by a wet chemical route is presented. The role of the synthesis temperature during reverse-strike precipitation has been investigated, showing its relevant effect on the purity and homogeneity of YAG powder. The composite material was prepared by comparing two different synthesis routes. A composite powder was synthesized via reverse-strike temperature-controlled co-precipitation. In the latter case, a pure-alumina precursor was firstly reverse-strike precipitated and then doped with an yttrium salt solution. For both syntheses, the role of thermal and mechanical pre-treatments on the phase development was demonstrated.