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.     

A geometric method in nonlinear programming

A differential geometric approach to the constrained function maximization problem is presented. The continuous analogue of the Newton-Raphson method due to Branin for solving a system of nonlinear equations is extended to the case where the system is under-determined. The method is combined with the continuous analogue of the gradient-projection method to obtain a constrained maximization method with enforced constraint restoration. Detailed analysis of the global behavior of both methods is provided. It is shown that the conjugate-gradient algorithm can take advantage of the sparse structure of the problem in the computation of a vector field, which constitutes the main computational task in the methods.This is part of a paper issued as Stanford University, Computer Science Department Report No. STAN-CS-77-643 (Ref. 45), which was presented at the Gatlinburg VII Conference, Asilomar, California, 1977. This work was supported in part by NSF Grant No. NAT BUR OF ECON RES/PO No. 4369 and by Department of Energy Contract No. EY-76-C-02-0016.The main part of this work was presented at the Japan-France Seminar on Functional Analysis and Numerical Analysis, Tokyo, Japan, 1976. The paper was prepared in part while the author was a visitor at the Department of Mathematics, North Carolina State University, Raleigh, North Carolina, 1976–77, and was completed while he was a visitor at the Computer Science Department, Stanford University, Stanford, California, 1977. He acknowledges the hospitality and stimulating environment provided by Professor G. H. Golub, Stanford University, and Professors N. J. Rose and C. D. Meyer, North Carolina State University.     

Colloid chemical studies of polystyrene latices polymerized without any surface-active agents

Summary The influence of secondary minimum for the stability of spherical colloid has been studied using a series of soap-free polystyrene latices from 350 m to 1400 m in diameter.The critical flocculation concentration (c. f. c.) and the zeta-potential at the c. f. c. for each latex were determined with several salts of different ionic valencies. The values of c. f. c. varied with the particle size, reaching a maximum value at 750 m and then decreasing gradually with the diameter.Another phenomenon detected in the experiment was the complete reversibility of coagulation which was observed only in the cases of large size latices, i. e., the coagulates of large size particles were fully redispersed in the solution by stirring. The time-dependence of their sedimentation curves was reproducible.These experimental results could not be explained by the simple theoretical consideration for stability of suspension. The satisfactory explanation is given only using the term of secondary minimum of interaction potential, i. e., the origin of coagulation was shifted from the ordinary primary minimum to the shallow secondary minimum at about 750 m of the particle diameter.

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Zusammenfassung Der Einfluß des Sekundär-Minimum auf die Stabilität von Kolloiden wurde an seifenfreien Polystyrol-Latex-Suspensionen mit einem Durchmesser von 350 m bis 1400 m untersucht. Die kritische Flockungskonzentration (c. f. c.) und das Zeta-Potential bei c. f. c. wurde mit verschiedenen Salzen bestimmt.Der Wert von c. f. c. ändert sich mit der Teilchengröße.Ein weiterer wichtiger experimenteller Befund ist die vollständige Reversibilität der Flockung bei größeren Latices.Derartige Versuchsergebnisse können durch das Sekundär-Minimum befriedigend erklärt werden.

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With 7 figures in 10 details and 2 tables     

Helical gold nanotube synthesized at 150 K

Gold nanowires were synthesized at 150 K by electron beam thinning of a gold thin foil in an UHV electron microscope. The gold nanowires were found to have a helical multishell structure (HMS). One particular nanowire, which was thinner than the 7-1 HMS nanowire, was found to have a tubular structure. The gold single wall nanotube is composed of five atomic rows that coil about the tube axis. The diameter was 0.4 nm and the pitch was 11 nm. The stability of the (5,3) nanotube was discussed in terms of the shear deformation of the triangular network of gold atoms.