Galois coverings of selfinjective algebras by repetitive algebras

In the representation theory of selfinjective artin algebras an important role is played by selfinjective algebras of the form where is the repetitive algebra of an artin algebra and is an admissible group of automorphisms of . If is of finite global dimension, then the stable module category of finitely generated -modules is equivalent to the derived category of bounded complexes of finitely generated -modules. For a selfinjective artin algebra , an ideal and , we establish a criterion for to admit a Galois covering with an infinite cyclic Galois group . As an application we prove that all selfinjective artin algebras whose Auslander-Reiten quiver has a non-periodic generalized standard translation subquiver closed under successors in are socle equivalent to the algebras , where is a representation-infinite tilted algebra and is an infinite cyclic group of automorphisms of .

     

A variational principle for the Navier-Stokes equation

Motivated from Arnold's variational characterization of the Euler equation in terms of geodesic families of diffeomorphisms, a variational principle for the motion of incompressible viscous fluids is presented. A volume preserving diffusion process with drift velocity field subject to the Navier-Stokes equation is shown to extremize the energy functional of the fluid under a certain class of stochastic variations.     

Vibrational frequencies,infrared absorption intensities and energy differences between rotational isomers of propyl halides

Infrared absorption intensities of fundamental bands of propyl halides n-C₃ H₇ Cl, n-C₃H₇ Br and n-C₃H₇I were measured in the pure liquid state. In order to obtain L matrix data necessary for the intensity computation, normal frequencies of the rotational isomers were calculated, and LSFF force constants were determined by the least squares method so as to attain the best fit between the observed and calculated frequencies. By applying the absolute intensity method, energy differences between the rotational isomers were evaluated, which are in quite good agreement with values obtained by the temperature variation method.     

Stochastic quantization: A review

The present status of the work on the application of the stochastic quantization procedure is reviewed. A compact mathematical introduction to the basic notions of random processes such as Markov processes, Martingales and Fokker-Planck equations is presented. The stochastic quantization procedure is explained in much detail and it is found to possess remarkable features which can not be achieved within the conventional framework of quantum theory. This admits us to give systematic analyses of irreversible quantum dynamics of dissipative systems and the vacuum tunneling phenomena in non-Abelian gauge theory     

Photolysis of tris(trimethylsilyl)-phenylsilane in alcohols: A consecutive generation of sililene species

Photolysis of tris(trimethylsilyl)phenylsilane, in alcohols yielded 1-aikoxy-1-phenyl-2, 2,2-trimethyldisilane, dialkoxyphenylsilane, hexamethyldistlane, and trimethylstlane as major products. The formation of the products was explained by a mechanssm which included the consecutive generatinn of phenyltrimethylsilylsilyleses and alkoxyphenylsilylenes.