The Economics of Social Stratification in Premodern Societies

We present a microeconomic model of social stratification, which includes an endogenous fertility component. In the model, egalitarian and stratified societies coexist. The latter are divided into 2 hereditary classes: a warrior elite and a productive class. The model entails that the extra cost warriors must incur to train and equip their children for war determines the relative sizes of both classes and the degree of economic inequality. Higher costs of warrior children imply a greater economic advantage for warriors and a smaller ratio of warriors to producers. These results are consistent with the historical evidence. Finally, we explore conditions under which the social contributions of the warrior elite could discourage a revolution.     

ON OPTIMAL ENVIRONMENTAL TAXATION AND ENFORCEMENT: INFORMATION,MONITORING AND EFFICIENCY

ABSTRACT. The purpose of the paper is to contribute to the narrowing of the distance between formal theory and practical environmental policy design. We formulate a general and comprehensive theoretical model in order to take into account the different informational and technological problems which characterize the definition and implementation of environmental taxes in a second best world where there also are distortionary taxes. Having formalized these problems, we present a general model which allows us to discuss the existence of efficient and implementable environmental quality objectives and policy instruments, and to analyze many particular cases.     

Study of the solid-liquid-vapour phase equilibria of flexible chain molecules using Wertheim's thermodynamic perturbation theory

The phase diagram of flexible molecules formed by freely-jointed tangent spheres is studied using the first-order thermodynamic perturbation theory of Wertheim for both fluid and solid phases. A mean-field term is added to the free energy of the fluid and solid phase in order to account for attractive dispersion forces. The approach is used to determine the global (solid-liquid-vapour) phase diagrams and triple points of chain molecules of increasing chain length. It is found that the triple point temperature is not affected strongly by the length of the chain, whereas the gas-liquid critical temperature increases dramatically. The asymptotic limits of the phase diagram for infinitely long chains are discussed. The reduced critical temperature of infinitely long chains as given by the mean-field theory is 2/3, and the reduced triple point temperature is 0.048 56, so that an asymptotic value of T _t/T _c = 0.07284 for the ratio of the triple to critical point temperatures is obtained. This indicates that fully-flexible tangent chains present an enormous liquid range. The proposed theory, while being extremely simple, provides a useful insight into the phase behaviour of chain molecules, showing the existence of finite asymptotic limits for the triple and critical point temperatures. However, since n-alkanes present an asymptotic limit of about T _t/T _c, = 0.40, the agreement With experiment is not quantitative. This suggests that fully flexible models may not be appropriate to model the solid phases of real chain molecules.     

The Kepler problem in the Snyder space

In this paper the Kepler problem in the non-commutative Snyder scenario was studied. The deformations were characterized in the Poisson bracket algebra under a mimic procedure from quantum standard formulations by taking into account a general recipe to build the non-commutative phase space coordinates (in the sense of Poisson brackets). An expression for the deformed potential was obtained, and then the consequences in the precession of the orbit of Mercury were calculated. The result could be used for finding an estimated value for the non-commutative deformation parameter.     

A Theoretical and Experimental Analysis of Support-excited Non-linear Vibrations of the Extensible Pendulum

Using the Lagrangian formulation, the equations of motion areset up for a damped extensible pendulum subjected to supportexcitation. The well established perturbation technique knownas the Method of Multiple Scales is used to investigate steadystates, with the outstanding feature that the original non-autonomousproblem is reduced to an autonomous form, thus easing the analysisand the stability verification. The theory is thereafter correlatedwith an extensive experimental study.     

The basic reproduction ratio for a model of directly transmitted infections considering the virus charge and the immunological response

Correspondent author email: hyunyang{at}ime.unicamp.br In order to describe mathematically the transmission of microparasites,especially directly transmitted infections, it is usual to setup differential equations assuming the mass action law and ahomogeneously mixed population. In this paper we analyze sucha model taking into account heterogeneity with respect to theinfectivity, that is, the variability in the evolution of theinteraction between parasite and the human host during the infectiousperiod. The well established biological phenomenon of initialincrease in parasite abundance followed by its decrease, dueto the interaction between the host's immunological responseand the parasite, has thus been taken into account The variableamount of microparasites eliminated by an infectious individual,and the different (heterogeneous) immunological response buildup by the host when in interaction with parasite are presentin the model. The analytical expression for the basic reproductionratio is derived through stability analysis.     

地基与海洋建筑物相互作用——以最近西班牙海岸线建筑物内部损坏为例

海洋工程通常是一个细长的线。我们通常看到的仅仅是建筑物狭长的表面,而不分析支撑他们的大量水下材料。毋庸置疑,海底地基将承受来自于海洋的周期性和交替的静力以及变化的动力。外部和内部的海上工程均在复杂的环境中运行。固态颗粒(防波堤)可以吸入入射水流,并且通过颗粒之间的间距吸收海浪的能量。回流试图从固态颗粒中抽离物质,这样一个遵从太沙基原理的基于有效拉力和中性拉力之间的平衡建立起来。 在某些情况下,防护层的液化已经造成了防波堤崩溃(Sines,葡萄牙,1978年2月)。在其他情况下,虹吸作用或液化导致巨石(垂直的防波堤)毁坏或崩溃(新巴塞罗那港口,西班牙,2001年11月)。结合复合设计工具的地基-作用力——结构相互作用的过程是一个复杂的分析,关于其研究刚刚开始。 本文介绍了最近发生在西班牙的、由于地基失效导致的海上工程内部损坏的两个例子(马拉加,2004年7月,巴塞罗那,2007年1月),分析了其成因。     

A computer simulation study of racemic mixtures

A simple model for a chiral molecule is proposed. The model consists of a central atom bonded to four different atoms in tetrahedral coordination. Two different potentials were used to describe the pair potentials between atoms: the hard sphere potential and the Lennard-Jones potential. For both the hard sphere and the Lennard-Jones chiral models, computer simulations have been performed for the pure enantiomers and also for the racemic mixture. The racemic mixture consisted of an equimolar mixture of the two optically active enantiomers. It is found that the equations of state are the same, within statistical uncertainty, for the pure enantiomer fluid and for the racemic mixture. Only at high pressures does the racemic mixture seem to have a higher density, for a given pressure, than the pure enantiomer. Concering the structure, no difference is found in the site-site correlation functions between like and unlike molecules in the racemic mixture either at low or at high densities. However, small differences are found for the site-site correlations of the pure enantiomer and those of the racemic mixtures. In the Lennard-Jones model, similar conclusions are drawn. The extension of Wertheim's first-order perturbation theory, denoted bonded hard sphere theory (ARCHER, A. L., and JACKSON, G., 1991, Molec. Phys., 73, 881; AMOS, M. D., and JACKSON, G., 1992, J. chem. Phys., 96, 4604), successfully reproduces the simulation results for the hard chiral model. Virial coefficients of the hard chiral model up to the fourth have also been evaluated. Again, no differences are found between virial coefficients of the pure fluid and of the racemic mixture. All the results of this work illustrate the quasi-ideal behaviour of racemic mixtures in the fluid phase.     

Theoretical prediction of a linear isomer for NeBr2(X1Γg + an ab initio approach

A supermolecular approach is used to predict the stationary structures of the NeBr₂(X¹Γ_g ⁺) van der Waals cluster. The intermolecular potential is calculated using the single and double excitation coupled-cluster method with non-iterative perturbation treatment of triple excitations [CCSD(T)]. Relativistic effects are included for the Br atoms using effective core potentials (ECPs) and their efficiency is tested for Br₂ and NeBr₂ molecules. Our results for NeBr₂ show minima for both linear and T-shaped configurations, in accord with previous ab initio calculations for rare gas-Br₂ species. The dependence of the interaction potential, as a function of the Br-Br bond, is also presented. Finally, vibrational analysis is carried out to examine the stability of the two isomers including zero-point vibrational energy effects.