New perspectives on Kac ring models

It is proposed that the type of model first suggested by Kac in connection with problems of nonequilibrium statistical mechanics can be generalized and modified so that it can be directly applied to cellular automata. It is further noted that these same models can be used to illuminate some basic questions in the interpretation of quantum mechanics.The content of this paper shows more clearly than any words how much physics owes to the insight, vigor, and brilliance of Mark Kac. It cannot show the personal debt this author owes to him. Throughout his life he showed compassion, kindness, and consideration. Few days go by that I do not think of him, his work, his humanity.     

Scale-free random graphs and Potts model

We introduce a simple algorithm that constructs scale-free random graphs efficiently: each vertexi has a prescribed weight P_i ∝ i^-μ (0 < μ< 1) and an edge can connect verticesi andj with rateP _i P _j . Corresponding equilibrium ensemble is identified and the problem is solved by theq → 1 limit of the q-state Potts model with inhomogeneous interactions for all pairs of spins. The number of loops as well as the giant cluster size and the mean cluster size are obtained in the thermodynamic limit as a function of the edge density. Various critical exponents associated with the percolation transition are also obtained together with finite-size scaling forms. The process of forming the giant cluster is qualitatively different between the cases of λ > 3 and 2 < λ < 3, whereλ = 1 +μ ^-1 is the degree distribution exponent. While for the former, the giant cluster forms abruptly at the percolation transition, for the latter, however, the formation of the giant cluster is gradual and the mean cluster size for finiteN shows double peaks.     

Enzymatic Synthesis of a CCK-8 Tetrapeptide Fragment

The enzymatic synthesis of a tetrapeptide Phac-Met-Gly-Trp-Met-OEt is reported. It was synthesized by coupling Phac-Met-OEt with Gly-OMe. HCI, Trp-OMe and Met-OEt successively, catalyzed by α-chymotrypsin, papain and α-chymotrypsin respectively. The results of FAB-MS showed that the products had the correct molecular mass.     

Four Novel Hydropyranoindeno-Derivatives from Marine Fungus Aspergillus versicolor

In the previous report on bioactive secondary metabolites from the sponge-associated fungus Aspergillus versicolor (Vuill) Tirab, the bioassay guiding fractionation led to isolation of six new compounds with unusual skeleton based on chromone ring system from the inculated fungus which was isolated from fresh samples of marine sponge Xestospongia exigua, collected along coast line of Bali, Indonesia in 19971. In the continuation of our chemical investigation on the marine fungus, four compou…     

Novel Chromone Derivatives from Marine Fungus Aspergillus versicolor Isolated from the Sponge Xestospongia exigua

In the continuation of our research for the bioactive secondary metabolites from the sponge-associated fungi, the bioassay guiding fractionation led to the isolation of six new secondary metabolites with unusual skeleton based on chromone ring system from the inoculated fungus Aspergillus versicolor, that had been isolated from fresh samples of marine sponge Xestospongia exigua, collected along coast line of Bali, Indonesia in 1997. The basic skeleton of those compounds possessed an oxohexacy…     

Finite morphisms of projective and K■hler manifolds

In this paper we study finite morphisms of projective and compact K■hler manifolds, in particular,positivity properties of the associated vector bundle,deformation theory and ramified endomorphisms.     

CONVERGENCE OF ADAPTIVE EDGE ELEMENT METHODS FOR THE 3D EDDY CURRENTS EQUATIONS

We consider an Adaptive Edge Finite Element Method （AEFEM） for the 3D eddy currents equations with variable coefficients using a residual-type a posteriori error estimator. Both the components of the estimator and certain oscillation terms, due to the occurrence of the variable coefficients, have to be controlled properly within the adaptive loop which is taken care of by appropriate bulk criteria. Convergence of the AEFEM in terms of reductions of the energy norm of the discretization error and of the oscillations is shown. Numerical results are given to illustrate the performance of the AEFEM.     

Sums of heights of algebraic numbers

For , we consider the set . The polynomials are in , with only mild restrictions, and is the Weil height of . We show that this set is dense in for some effectively computable limit point .