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.     

Stochastic flows on the boundaries of SL(n,R)

Summary We study the asymptotic stability of the stochastic flows on a class of compact spaces induced by a diffusion process in SL(n, R) or GL(n, R). These compact spaces are called boundaries of SL(n, R), which include SO(n), the flag manifold, the sphereS ⁿ–1 and the Grassmannians. The one point motions of these flows are Brownian motions. For almost every, , we determine the set of stable points. This is a random open set whose complement has zero Lebesgue measure. The distance between any two points in the same component of this set tends to zero exponentially fast under the flow. The Lyapunov exponents at stable points are computed explicitly. We apply our results to a stochastic flow onS ⁿ–2 generated by a stochastic differential equation which exhibits some nice symmetry.Research supported in part by Hou Yin Dong Education Foundation of China On leave from Nankai University, Tianjin, China     

Dianion approach to chiral cyclopropene carboxylic acids

[reaction: see text] In this Letter, we describe a general method for preparing the dianions of cyclopropene carboxylic acids, and we show that their subsequent reactions with electrophiles provide a general means for selectively introducing diverse types of functional groups. This provides a general method for the synthesis of chiral 1,2-disubstituted cyclopropenes, and opens new avenues for the enantioselective preparation of cyclopropenes.     

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%.     

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.     

Additional peaks in the cluster size distribution of amphiphile + water systems: a clue for shape/phase transition or statistical uncertainty

In some works on the lattice Monte Carlo simulation of amphiphilic systems additional peaks in the cluster size distribution has been interpreted as a clue for the phase or shape transition of micellar aggregates. On the other hand, some other works showed that the additional peaks are a result of finite size of the lattice box. In this paper using calculating energy-auto-correlation function and statistical error in correlated data, it is shown that how these apparently contradictory results are the same. To do this, we have simulated a pure system containing amphiphile and water molecules. A simple model of potential containing the main feature for these systems (the hydrophobicity of surfactant molecules) that cause the aggregates to be formed is considered to avoid any synthetic results due to additional non-real parameters. To relax the initial configuration faster, configurational bias Monte Carlo move is used in addition to reptation move. Periodic boundary condition and self-avoiding walks are used as former published works in this field. It is shown that the additional peaks is a result of the statistical errors for averaged cluster size distribution and can not be interpreted as a clue for shape or phase transition.     

Kinetics of Oxidation of 4-Oxoacids by <Emphasis Type="Italic">N</Emphasis>-Chlorosaccharin in Aqueous Acetic Acid Medium

The oxidation kinetics of substituted and unsubstituted 4-oxoacids (S) by N-chlorosaccharin (NCSA) have been studied in aqueous acetic acid media. The reaction follows first-order kinetics in each of the 4-oxoacids, NCSA and H⁺. The effect of changes in the electronic nature of the substrate reveals that positive charge develops in the transition state. Based on the kinetic results and product analysis, a suitable mechanism has been proposed for the reaction of NCSA with 4-oxoacids.     

Copolymers and two-layered composites of poly(<Emphasis Type="Italic">o</Emphasis>-aminophenol) and polyaniline

Electroactive conducting copolymers of aniline (ANI) and o-aminophenol (OAP) and two-layered poly(o-aminophenol) (POAP)/polyaniline (PANI) composites were prepared in aqueous acidic solution by electrode potential cycling. Copolymerization was carried out at different feed concentrations of OAP and ANI on a gold electrode. A strong inhibition of electropolymerization was found at a high molar fraction of OAP in the feed. The copolymers showed good adherence on the electrode surface and gave a redox response up to pH=10.0. Two transitions were observed in the in situ conductivities of the copolymers (as with PANI), but the conductivities were lower by 2.5–3 orders of magnitude as compared to PANI. Electrosynthesis of PANI on POAP modified electrodes showed copolymer formation after reaction initiation and finally formation of a PANI layer at the copolymer/solution interface. The ‘memory effect’ of the bilayer structures of both polymers was discussed in terms of protonation/deprotonation and anion consumption taking place during redox processes of both polymers.