This paper is devoted to the analysis of the two-or three-dimensional elastic contact problem with Coulomb friction. quasi-static equilibrium, and small displacements. The classical approach is based on two minimum principles, or variational inequalities: the first for unilateral contact and the second for friction. In practical applications, this leads to an algorithm of alternately solving the two problems until convergence is achieved. A coupled approach using one principle or one inequality only is presented. This new approach, based on a model of material called implicit standard, allows for extension of the notion of a normality law to dissipative be

In this article, we propose a recursive equilibrium algorithm for the numerical simulation of nonoptimal dynamic economies. This algorithm builds upon a convergent operator over an expanded set of state variables. The fixed point of this operator defines the set of all Markovian equilibria. We study approximation properties of the operator. We also apply our recursive equilibrium algorithm to various models with heterogeneous agents, incomplete financial markets, endogenous and exogenous borrowing constraints, taxes, and money.

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The genetic structure of populations of the sea cucumber Stichopus (Apostichopus) japonicus was investigated using 10 microsatellite markers. In all, 152 individuals from five natural populations were collected from Aomori, Japan (JA and JR), Yosu, South Korea (KY), Dalian, China (CD) and Vladivostock, Russia (RV). A total of 145 alleles were found at 10 loci. The number of alleles per locus ranged from 9 at PSC03 to 20 at SCZ06, with an average of 14.5. Average Ho and He ranged from 0.260 (JR) to 0.434 (JA) and from 0.654 (RV) to 0.778 (KY), respectively. No significant differences at A, Ho and He were found, indicating similar genetic diversity in the five populations. A single allele was found at the PSC05 locus in the RV population. Of the 50 loci, 42 significantly deviated from Hardy–Weinberg equilibrium, all showing heterozygote deficiency. The genetic distances were all relatively great, ranging from 0.497 (between JA and KY) to 1.029 (between KY and JR). This suggests the five populations are genetically distinct. Cluster analysis indicated that JA, KY and CD form one branch and RV and JR another in the UPGMA tree. A hypothesis is proposed for the evolution of the Japanese red sea cucumbers and the genetic relationship among the populations.

In this paper, the formulation of complex anisotropic frictional models with orthotropic friction condition and non-associated sliding rule is discussed. The friction law is described by a superellipse, which allow to consider a wide range of convex friction condition by simply varying the roundness factor affecting the shape of the limit surface. The sliding potential is also a superellipse but with a different semi-axis ratio, which lead to a non-associated sliding rule. For bodies in contact, the Signorini conditions can be formulated in terms of velocities and combined with the sliding rule to give the frictional contact law describing interfacial interactions. Its is shown that the frictional contact law as well as its inverse can be derived from the same scalar valued function called bi-potential. Due to the non-associated nature of the law, this relation is implicit. The advantage of the present formulation lies in the existence of stationary points of a functional, called bi-functional, that depends on both the displacements and the stresses.