Novel perturbation expansion for the Langevin equation

We discuss the randomly driven systemdx/dt= -W(x) +f(t), wheref(t) is a Gaussian random function or stirring force withf(t)f(t)=2(t–t), andW(x) is of the formgx ¹⁺². The parameter is a measure of the nonlinearity of the equation. We show how to obtain the correlation functionsx(t)f(t)···x(t( n)) _f as a power series in. We obtain three terms in the expansion and show how to use Padé approximants to analytically continue the answer in the variable. By using scaling relations, we show how to get a uniform approximation to the equal-time correlation functions valid for allg and.     

Rapidly decaying solutions of the nonlinear Schrödinger equation

We consider global solutions of the nonlinear Schrödinger equation

Re4(CO)12[μ3-InRe(CO)5]4 und Re2(CO)8[μ-InRe(CO)5]2-cluster aus dem reaktionssystem In/Re2(CO)10 in xylol

The thermally stable solids Re₂(CO)₈[μ-InRe(CO)₅]₂ and Re₄(CO)₁₂[μ₃-InRe(CO)₅]₄ could be obtained by treatment of In with Re₂(CO)₁₀ in a bomb tube. A mechanism of the formation of the latter cluster from the first one is proposed. Compared with Re₂(CO)₈[μ-InRe(CO)₅]₂, Re₄(CO)₁₂[μ₃_InRe(CO)₅]₄ shows in polar solvents an unusual high stability, which can be explained by the higher coordination number of In with rhenium carbonyl ligands. Re₄(CO)₁₂-[μ₃-InRe(CO)₅]₄ dissolves monomerically in acetone, where as Re₂(CO)₈[μ-InRe(CO)₅]₂ dissociates yielding Re(CO)₅^? anions. Single-crystal X-ray analyses of Re₄(CO)₁₂[μ₃-InRe(CO)₅]₄ establish the metal skeleton. The central molecular fragment Re₄(CO)₁₂ contains a tetrahedral arrangement of four bonded Re atoms [ReRe 302.8 (5) pm]. The triangles of this fragment are capped with a μ₃-InRe(CO)₅ group each [InRe(terminal) 273.5 (7) pm; InRe (polyhedral) 281.8 (7) pm]. The bridging type of In atoms with the Re₄ tetrahedron and the metal skeleton was realized for the first time. By treating Re₄(CO)₁₂[μ₃-InRe(CO)₅]₄ with Br₂ the existence of Re(CO)₅ ligands could be proved by isolating BrRe(CO)₅.     

The effects of gamma irradiation on the microbiological, physical and sensory qualities of diced tomatoes

Diced Roma tomatoes were treated with gamma irradiation and evaluated for changes in microbial, physical, chemical and sensory properties. Dosages for Trial 1 were 0.0, 0.39, 0.56 and 1.82 kGy and in Trial 2, 0.0, 0.50, 1.24 and 3.70 kGy. Irradiation at 3.70 kGy resulted in no aerobic populations through day 12 and significantly fewer colonies through day 15 whereas yeast and mold populations experienced a 2 log reduction through day 12. Color, titratable acidity, and °Brix were not significantly affected by irradiation. Tissue firmness decreased with increasing dose but not with storage time. Treatment with 3.7 kGy decreased firmness by 50% and 20% with 0.5 kGy, however, the reduced firmness induced by 0.50 kGy was undetected by a 9 member trained sensory panel. A significant (p0.05) inverse correlation between changes in texture and water-soluble pectin (WSP) was determined while total pectin remained relatively constant and oxalate soluble pectin content decreased slightly with irradiation dose. The significant inverse correlation between the loss of firmness and WSP indicates that the changes in WSP play an important role in the tissue softening of tomatoes, This study indicates that irradiation at 0.5 kGy can reduce microbial counts substantially to improve microbial shelf life without adverse effects on sensory qualities.     

The combi-CLEA approach: enzymatic cascade synthesis of enantiomerically pure (S)-mandelic acid

Enantiomerically pure (S)-mandelic acid was synthesised from benzaldehyde by sequential hydrocyanation and hydrolysis in a bienzymatic cascade at starting concentrations up to 0.25 M. A cross-linked enzyme aggregate (CLEA) composed of the (S)-selective oxynitrilase from Manihot esculenta and the non-selective nitrilase from Pseudomonas fluorescens EBC 191 was employed as the biocatalyst. The nitrilase produces approx. equal amounts of (S)-mandelic acid and (S)-mandelic amide from (S)-mandelonitrile under standard conditions, but we surprisingly found that high (up to 0.5 M) concentrations of HCN induced a marked drift towards amide production. By including the amidase from Rhodococcus erythopolis in the CLEA we obtained (S)-mandelic acid as the sole product in 90% yield and >99% enantiomeric purity.     

Cationic Quaternary Polyelectrolytes—A Literature Review

This paper is a literature survey of quaternary ammonium, sulfonium, and phosphonium polymers.     

A non-Gaussian Ornstein–Uhlenbeck model for pricing wind power futures

The recent introduction of wind power futures written on the German wind power production index has brought with it new interesting challenges in terms of modelling and pricing. Some particularities of this product are the strong seasonal component embedded in the underlying, the fact that the wind index is bounded from both above and below and also that the futures are settled against a synthetically generated spot index. Here, we consider the non-Gaussian Ornstein–Uhlenbeck type processes proposed by Barndorff-Nielsen and Shephard in the context of modelling the wind power production index. We discuss the properties of the model and estimation of the model parameters. Further, the model allows for an analytical formula for pricing wind power futures. We provide an empirical study, where the model is calibrated to 37 years of German wind power production index that is synthetically generated assuming a constant level of installed capacity. Also, based on 1 year of observed prices for wind power futures with different delivery periods, we study the market price of risk. Generally, we find a negative risk premium whose magnitude decreases as the length of the delivery period increases. To further demonstrate the benefits of our proposed model, we address the pricing of European options written on wind power futures, which can be achieved through Fourier techniques.     

Hlder Norm Estimate for a Hilbert Transform in Hermitean Clifford Analysis

A Hilbert transform for Hlder continuous circulant (2 × 2) matrix functions, on the d-summable (or fractal) boundary Γ of a Jordan domain Ω in R2n , has recently been introduced within the framework of Hermitean Clifford analysis. The main goal of the present paper is to estimate the Hlder norm of this Hermitean Hilbert transform. The expression for the upper bound of this norm is given in terms of the Hlder exponents, the diameter of Γ and a specific d-sum (d d) of the Whitney decomposition of Ω. The result is shown to include the case of a more standard Hilbert transform for domains with left Ahlfors-David regular boundary.