Free interpolation in some banach spaces of analytic functions

We state a series of results regarding the interpolation in the spaces of analytic functions being the Taylor coefficient of the expansion at O, and. One asserts that a sequence with one condensation point, having a structure similar to a geometric progression, is an interpolation sequence for these spaces, i.e., the restriction operator on these sets maps these spaces onto the corresponding collection of sequences. In this case the restriction operator has a continuous right inverse which is explicitly constructed. This note is a continuation of the author's paper. Ref. Zh. Mat. 1973, 4B164.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 56, pp. 186–187, 1976.     

Free energy for Brownian and geodesic homology

Summary Existence and analyticity of the free energies associated with the asymptotic homology of Brownian paths and geodesics are proved and a simple relation is found between them.     

Free group factors and factors with some decompositions

In this paper, we show that if type von Neumann factors have some decompositions introduced by Liming Ge and Sorin Popa, then these von Neumann factors are not isomorphic to free group factors . Thus we have proved the number defined by Ge and Popa bigger than 3 for all free group factors and we also extend some results of M. Stefan.

     

Free energy of the spherical mean field model

We compute at any temperature the free energy of the multi p-spin spherical model when only terms for p even are considered. Work partially supported by an NSF grant     

Free energy fluctuations for a mixture of directed polymers

We study the free energy fluctuations for a mixture of directed polymers, which was first introduced by Borodin et al. (2015) to investigate the limiting distribution of a stationary Kardar-Parisi-Zhang (KPZ) equation. The main results consist of both the law of large numbers and the asymptotic fluctuation for the free energy as the model size tends to infinity. In particular, we find the explicit values (which may depend on model parameters) of normalizing constants in the fluctuation. This shows that such a mixture model is in the KPZ university class.     

On the energy of some circulant graphs

We give an explicit construction of circulant graphs of very high energy. This construction is based on Gauss sums. We also show the Littlewood conjecture can be used to establish new result for a certain class of circulant graphs.     

Asymptotic behavior of solutions for some chemical reactions models

1.IntroductionInthispapertweareconcernedwiththeasymptoticbehaviorofglobalpositivesolutionstothefollowingsemilinearreaction-dictionsystemac--didn=--any bltv,(1.1)yi--daal=--any bZw,xEfi,t>0(1.2)ac--daal=any--bZw,(1.3)withhomogeneousNeumannboundaryconditionsonofof~~on--an=on,xeoff,t>o(1.4)andinitialvalueconditionsu(x,0)="o(x),v(x,0)=v000,w(x,0)=w000,xEn,(l.5)wherenCRNisaboundeddomainwithsmoothboundaloff,kdenotestheoutwardnormalderiVativeonoff,anddltd2,d3,a,hi,bZarepositiveconstallts.Problem(…