Convolution semigroups and central limit theorem associated with a dual convolution structure

We consider hypergroups associated with Jacobi functions ⁽⁾ (x), (–1/2). We prove the existence of a dual convolution structure on [0,+[i(]0,s ₀]{{) =++1,s ₀=min(,–+1). Next we establish a Lévy-Khintchine type formula which permits to characterize the semigroup and the infinitely divisible probabilities associated with this dual convolution, finally we prove a central limit theorem.     

Characterization of measures by potentials

Let μ be a measure in a Banach spaceE, f be an even function onR. We consider the potentialg(a)=f _E f(‖x?a‖)dμ(x). The question is as follows: For whichf does the potentialg determine μ uniquely? In this article we give answers in the cases whereE=l _∞ ⁿ and wheref(t)=|t| ^p andE is a finite dimensional Banach space with symmetric analytic norm. Calculating the Fourier transform of the functionf(‖x‖ _∞) we give a new proof of the J. Misiewicz's result that the functionf(‖x‖ _∞) is positive definite only iff is a constant function.     

Three-Dimensional Modeling of the Turbulent Plasma Jet Impinging upon a Flat Plate and with Transverse Particle and Carrier-Gas Injection

Modeling results are presented concerning the turbulent thermal plasma jet impinging normally on a substrate and with transverse injection of feedstock particles and their carrier gas from a single injection tube. The k- two-equation model is employed to model the turbulence, and particle dispersion is studied considering the interaction between the moving particles and turbulent eddies and considering the effect on particle trajectories of the random variation of the turbulent fluctuating velocities in their magnitude and direction. A well-validated three-dimensional (3-D) computer code is used in the modeling. The 3-D effects due to the carrier gas injection on the jet flow field and thus on the particle trajectories and heating histories are shown to be appreciable. The radial location of the injection tube with respect to the plasma jet is shown to be a critical parameter for the study of 3-D effects, besides the carrier-gas/plasma stream mass flux ratio. Particle dispersion considerably widens the distribution of the particle trajectories and heating histories. In addition, although pertinent swirl number is often rather small, swirling may also affect the modeling results.     

A pseudoreceptor docking study of 4,5-α-epoxymorphinans with a range of dielectric constants

Summary Thirteen 4,5-epoxymorphinan agonists with established analgesic action were docked into an Asp-Lys-His-Phe pseudoreceptor complex under a range of distance-dependent dielectric conditions. The number of compounds with potential energies of the docked complexes that agreed in rank order with corresponding analgesic potencies was determined for each condition. Two dielectric conditions, n-decane (1.991) and ethanol (24.3), enabled the greatest number of compounds to relate to their pseudoreceptors with each having 9 and 8 successes respectively. Both of these conditions demonstrated unique influences on the types of structures that were successfully docked. For example, the morphine stereoisomer -isomorphine, the geometric isomer B/C trans-morphine, and the 8-position-substituted -isomorphine were successes in the n-decane condition, whereas the ethanol condition produced the substituted codeine derivatives dihydroco-deinone and dihydroxycodeinone. These findings emphasize the importance of dielectric influence when developing force-field modeled quantitative structure-activity relationships for a closely related homologous series.     

Solid-liquid equilibrium diagrams of common ion binary salt hydrate mixtures involving nitrates and chlorides of magnesium, cobalt, nickel, manganese, and iron(III)

The solid-liquid equilibrium diagrams of binary mixtures involving magnesium nitrate hexahydrate with cobalt nitrate hexahydrate, nickel nitrate hexahydrate (partly), manganese nitrate tetrahydrate, and iron(III) nitrate nonahydrate and of magnesium chloride hexahydrate with cobalt and nickel chlorides hexahydrates and manganese chloride tetrahydrate, and the of two manganese salts were determined. Those diagrams that showed a simple eutectic were fitted by the Ott equation and where the required BET parameters were available, the magnesium salt rich parts of the liquidus were modeled by means of this method.     

ansa-Zirconocenium catalysis of syndiospecific polymerization of propylene: Theory and experiment

The syndiospecific propylene polymerizations catalyzed by isopropylidene(cyclopentadienyl)(fluorenyl)- and (2,2-dimethylpropylidene)(cyclopentadienyl)(fluorenyl)-zirconocenium ( 1 ⁺ and 2 ⁺) have been investigated theoretically and compared with experimental observations. With the ab initio calculated structures for the transition state (TS) of 1 ⁺(M)P and 2 ⁺(M)P (M = propylene, P = 2-methylpentyl), their steric energies (E°) have been computed using MM2 force-field. The difference between steric energies E°(m) and E°(r) for the meso and racemic enchainment of propylene, respectively, is defined as the stereocontrol energy [δE°(m ? r)] for syndiotactic propagation. The δE°(m ? r) for the TS of 1 ⁺ (M)P is about 2.1 kcal/mol, the value is 1 kcal/mol greater for 2 ⁺(M)P. The observed steric pentad distributions of the syndiotactic poly(propylene) obtained by these catalysts are consistent with smaller effective stereocontrol energy, which is about two-third as large as δE°(m ? r) values calculated for the MM2 optimized structure. Syndiotactic enchainment is favored over isotactic enchainment for all combinations of site configurations in the catalyst. α-Agostic interaction seems to enhance syndioselectivity, whereas γ-agostic interaction changes the stereoselectivity to meso enchainment. The mirror plane symmetry of the syndiotactic propagating species renders the stereoselectivity of the polymerization insensitive to reaction conditions. These catalysts are also highly regiospecific. © 1995 John Wiley & Sons, Inc.     

手性氮磷配体与钌的配位过程的研究—原位变温 31P核磁及分子模拟计算

用原位变温 ³¹P NMR和分子模拟研究了手性氮磷配体与金属钌的配位过程。首先确定了配体及其与金属的配合物的化学位移信号分别在δ=-13.0ppm和δ=48.2ppm。配位过程在293～343K温度范围内,相继生成四配位和五配位中间体。四配位体在 ³¹P NMR上对应于30.8ppm和-15.0ppm的两个信号;五配位中间体对应于35.1ppm和-16.5ppm的两个信号;最后在343K,产物中只有六配位的配合物存在,其信号出现在48.2ppm。为了得到各种中间体的结构,用分子模拟方法进行了结构优化计算,并比较了它们的构象能。计算结果表明,四配位中间体有两种构象,能量相差9kcal·mol^-1,它们可能同时存在于平衡状态。而五配位中间体只有一种绝对优势构象,尚有一个磷原子未参与配位。六配位的钌金属配合物的结构优化结果显示,两个氯原子分别位于PNNP原子所构成平面的两侧。其构象能为162.0kcal·mol^-1,其中键角能的贡献是112.5kcal·mol^-1,而非键静电作用是-41.4kcal·mol^-1,这表明分子内的静电吸引力对于形成完全配位产物是十分有利的,但是收敛的配体分子却承受了较大的键角张力。     

Particle dynamics and particle heat and mass transfer in thermal plasmas. Part III. Thermal plasma jet reactors and multiparticle injection

Thermal plasma processing involves complex interactions of particulates with plasmas. In previous studies (see Parts I and II of this series), an assessment of different effects has been made considering the dynamics and heat and mass transfer of a single particle immersed into a thermal plasma. The last paper of this sequence is concerned with the simulation of thermal plasma jet reactors and the effects caused by multiparticle injection.A mathematical model is proposed for the simulation of thermal plasma jet reactors, including the mixing phenomena between the jet and the surrounding gases by generalizing the governing equations for simple mixing flows. Also included is the density fluctuation effect by extending the K- model to a four-equation turbulence model combined with a probability density function. This model is internally consistent covering additional physical phenomena which are not covered by existing models. Unfortunately, its expected higher accuracy cannot be proven because of the present uncertainties associated with the input.For multiparticle injection, the simulation repeats calculations for single-particle injection, but with different initial conditions correcting the solutions by considering the coupling effects between particles and the plasma.The results indicate that (i) thermal plasmas show different mixing behavior in different gases; (ii) the density fluctuation effect is important since it causes large differences between the mass-weighted and unweighted time-averaged temperatures of thermal plasma jets; (iii) coupling effects become important when the particle loading rate exceeds half of the plasma mass flow rate; (iv) there are 16 constraints imposed on the modeling work which have to be considered for establishing a base for comparison with future experimental studies.     

A comparative study of various computational approaches in calculating the structure of pyridoxal 5'-phosphate (PLP)-dependent beta-lyase protein. The importance of protein environment

Various computational approaches, using molecular mechanics (Amber), semiempirical (AM1), density functional (B3LYP), and various ONIOM methods, have been comparatively investigated for the structure of Escherichia coli NifS CsdB protein. The structure of the entire monomer containing 407 amino acid residues and 579 surrounding water molecules has been optimized. The full geometry optimization in the "active site-only" approach (including only active site atoms) has been found to give the largest root-mean-square (RMS) deviation from the X-ray structure; a much better agreement has been achieved by keeping the atoms leading to the backbones of some amino acids frozen in their positions in the X-ray structure. The best agreement has been attained by including the surrounding protein in the calculations using the two-layer ONIOM (B3LYP:Amber) approach. The results presented in this study conclusively demonstrate the importance of the protein/active-site interaction on the active-site structure of the enzyme. The present theoretical study represents the largest system studied at the ONIOM level to date, containing 7992 atoms, including 84 atoms in the QM region and rest in the MM region.     

Vapor pressure of R227ea + ethanol at 343.13 K by molecular simulation

A new molecular model for 1,1,1,2,3,3,3-heptafluoropropane (R227ea) was developed on the basis of quantum chemical calculations and optimized using experimental vapor pressure and bubble density data. In combination with an existing model for ethanol, a molecular model for the binary mixture R227ea + ethanol was defined, using the Lorentz–Berthelot combining rule. It was validated at 283.17 K, where, considering the statistical uncertainties, it agrees to the experimental vapor pressure. The vapor–liquid equilibrium, comprising both bubble line and dew line data, was predicted at 343.13 K by molecular simulation. The Peng–Robinson equation of state fails for this system.