Conditioned Diffusions which are Brownian Bridges

Let X _t be a one-dimensional diffusion of the form dX _t=dB _t+(X _t)dt. Let Tbe a fixed positive number and let be the diffusion process which is X _t conditioned so that X ₀=X _T=x. If the drift is constant, i.e., , then the conditioned diffusion process is a Brownian bridge. In this paper, we show the converse is false. There is a two parameter family of nonlinear drifts with this property.     

Distances between classes in $$W^{1,1}(\Omega ;{\mathbb {S}}^{1})$$

We introduce an equivalence relation on the space \(W^{1,1}(\Omega ;{\mathbb {S}}^1)\) which classifies maps according to their “topological singularities”. We establish sharp bounds for the distances (in the usual sense and in the Hausdorff sense) between the equivalence classes. Similar questions are examined for the space \(W^{1,p}(\Omega ;{\mathbb {S}}^1)\) when \(p>1\).     

Optimal control applied to water flow using second order adjoint method

This paper presents an optimal control applied to water flow using the first and second order adjoint equations. The gradient of the performance function with respect to control variables is analytically obtained by the first order adjoint equation. It is not necessary to compute the Hessian matrix directly using the second order adjoint equation. Two numerical studies have been performed to show the adaptability of the present method. The performance of the second order adjoint method is compared with that of the weighted gradient method, Broyden–Fletcher–Goldfarb–Shanno method and Lanczos method. The precise forms of the adjoint equations and the gradient to use for the minimisation algorithm are derived. The computation by the Lanczos method is shown as superior to those of the other methods discussed in this paper. The message passing interface library is used for the communication of parallel computing.     

KPZ in One Dimensional Random Geometry of Multiplicative Cascades

We prove a formula relating the Hausdorff dimension of a subset of the unit interval and the Hausdorff dimension of the same set with respect to a random path matric on the interval, which is generated using a multiplicative cascade. When the random variables generating the cascade are exponentials of Gaussians, the well known KPZ formula of Knizhnik, Polyakov and Zamolodchikov from quantum gravity [KPZ88] appears. This note was inspired by the recent work of Duplantier and Sheffield [DS08] proving a somewhat different version of the KPZ formula for Liouville gravity. In contrast with the Liouville gravity setting, the one dimensional multiplicative cascade framework facilitates the determination of the Hausdorff dimension, rather than some expected box count dimension.     

Mössbauer spectroscopic study of photo-sensitive organic–inorganic hybrid system, (SP)[Fe(II)Fe(III)(dto)3](dto = C2O2S2, SP = spiropyran)

A photo-sensitive organic–inorganic hybrid system (SP)[Fe^IIFe^III(dto)₃] (SP = spiropyran, dto = C₂O₂S₂), has recently been developed, where the photo-isomerization of the intercalated spiropyran in solid state triggers the change of the magnetic properties, including the ferromagnetic transition temperature from 5 to 22 K. We performed ⁵⁷Fe Mössbauer measurement in order to probe the microscopic states of iron ions in (SP)[Fe^IIFe^III(dto)₃] and have investigated the photo-induced effect on them. The sample without UV-irradiation shows the charge transfer phase transition between 200 and 70 K and the higher and lower temperature phases coexist below 70 K, whereas the UV-irradiated sample does not undergo the charge transfer phase transition and the higher temperature phase is stable between 200 and 6 K.     

Nucleophilic addition reaction of 2-trimethylsilyloxyfuran to N-gulosyl-C-alkoxymethylnitrones: synthetic approach to polyoxin C

[reaction: see text] The stereoselectivity of nucleophilic addition of 2-trimethylsilyloxyfuran to N-gulosyl-C-alkoxymethylnitrones was investigated. It was found that the selectivity was highly dependent on the bulkiness of the C-substituent of the nitrone. The major adducts were elaborated into the key intermediate of polyoxin C.     

Generalized actions in Zp lattice gauge theory

In Z_p lattice gauge theory we generalize the Wilson action to include all group representations. We review the implications of duality for these models. With Monte Carlo methods, we find a rich phase structure for the cases p = 4 and 5.     

Synthesis and evaluation of 6-nitro-7-(1-piperazino)quinazolines: dual-acting compounds with inhibitory activities toward both tumor necrosis factor-alpha (TNF-alpha) production and T cell proliferation

We investigated the chemical modifications of the nitroquinazoline derivative (1) through the replacement of the NH group at the C(4)-position with several N-alkyl groups to increase the lipophilicity at the C(4)-position. Among them, we found that the N-methyl analogue (5a) showed a 2-fold loss in the inhibitory activity toward tumor necrosis factor-alpha (TNF-alpha) production in vitro as compared with the NH analogue (1); however, 5a exhibited an oral inhibitory activity on TNF-alpha production with an ED50 value of 26 mg/kg, whereas 1 did not. Moreover, the oral bioavailability of 5a was higher than that of 1 (1, F=1%; 5a, F=21%), and the calculated ClogP value for 5a was higher than that for 1. These results suggest that the improved lipophilicity of 5a compared with that of 1 reflects its greater inhibitory activity on TNF-alpha production in vivo as well as oral bioavailability.     

5-[4-(1-Hydroxyethyl)phenyl]-10,15,20-triphenylporphyrin as a probe of the transition-state conformation in hydrolase-catalyzed enantioselective transesterifications

5-[4-(1-Hydroxyethyl)phenyl]-10,15,20-triphenylporphyrin (1a) and zinc porphyrin 1b were designed and synthesized to experimentally examine the validity of the transition-state model previously proposed for the lipase-catalyzed kinetic resolution of secondary alcohols. The lipases from Pseudomonas cepacia (lipase PS), Candida antarctica (CHIRAZYME L-2), Rhizomucor miehei (CHIRAZYME L-9), and Pseudomonas aeruginosa (lipase LIP) exhibited excellent enantioselectivity (E >100 at 30 degrees C). Subtilisin Carlsberg from Bacillus licheniformis (ChiroCLEC-BL) also showed high enantioselectivity for 1a (E = 140 at 30 degrees C), and the thermodynamic parameters were determined: DeltaDeltaH = -6.8 +/- 0.8 kcal mol(-1), DeltaDeltaS = -13 +/- 3 cal mol(-1) K(-1). Lipases and subtilisin showed R- and S-preference for 1, respectively. The mechanisms underlying the experimental observations are explained in terms of the transition-state models. The large secondary alcohol 1 is a powerful tool for investigating the conformation of the transition state of the enzyme-catalyzed reactions. The fact that 1 was resolved with high enantioselectivity strongly suggests that the gauche conformation, but not the anti conformation, is taken in the transition state, in agreement with the transition-state models involving the stereoelectronic effect.