The Existence of Pair Potential Corresponding to Specified Density and Pair Correlation

Given a potential of pair interaction and a value of activity, one can consider the Gibbs distribution in a finite domain $\Lambda \subset \mathbb{Z}^d$. It is well known that for small values of activity there exist the infinite volume ($\Lambda \to \mathbb{Z}^d$) limiting Gibbs distribution and the infinite volume correlation functions. In this paper we consider the converse problem - we show that given $\rho_1$ and $\rho_2(x)$, where $\rho_1$ is a constant and $\rho_2(x)$ is a function on $\mathbb{Z}^d$, which are sufficiently small, there exist a pair potential and a value of activity, for which $\rho_1$ is the density and $\rho_2(x)$ is the pair correlation function

Binary jumps in continuum. II. Non-equilibrium process and a Vlasov-type scaling limit

Let $\Gamma$ denote the space of all locally finite subsets (configurations) in $\mathbb R^d$. A stochastic dynamics of binary jumps in continuum is a Markov process on $\Gamma$ in which pairs of particles simultaneously hop over $\mathbb R^d$. We discuss a non-equilibrium dynamics of binary jumps. We prove the existence of an evolution of correlation functions on a finite time interval. We also show that a Vlasov-type mesoscopic scaling for such a dynamics leads to a generalized Boltzmann non-linear equation for the particle density

Tagged particle process in continuum with singular interactions

By using Dirichlet form techniques we construct the dynamics of a tagged particle in an infinite particle environment of interacting particles for a large class of interaction potentials. In particular, we can treat interaction potentials having a singularity at the origin, non-trivial negative part and infinite range, as e.g., the Lennard-Jones potential.Comment: 27 pages, proof for conservativity added, tightened presentatio

Outsiders in an Inside Game: The Effects of the Traditional Soviet Economy of Favors on Foreigners Doing Business in Contemporary Russia

Blat, or the exchange of favors among friends, played a key role in the Soviet Union. The ability to use connections to gain access to hard-to-find goods or services was practically indispensible in the shortage economy. But blat has also been important in the post-Soviet environment, particularly in business. People with powerful connections have achieved success, while those outside of the business networks have been left behind. Thus, the ability to establish and maintain connections determines who succeeds in Russian business today. I argue that this dynamic significantly disadvantages foreign businesses in Russia because it favors insiders, is difficult for foreigners to understand, and most importantly, leads foreign companies into ethically questionable practices that are unacceptable in international business. Using the case of IKEA’s experiences in the Russian market, I hope to investigate whether this theory can inform our understanding of foreign businesses’ experiences in Russia

The Political Economy of Federal Assistance: Demand-Side Determinants of New Awards in the 110th Congress

An extensive literature examines how distributive (i.e., “pork barrel”) spending is allocated among congressional districts. Much of this research finds evidence that intra-chamber factors like ideology, party, and committee membership are the primary determinants of various forms of distributive spending. However, we know much less about how extra-chamber factors such as district-level demand and the economy impact the distribution of federal outlays. In this study, I find that district-level demand and variation in economic factors, in particular, income and unemployment, significantly predict the distribution of new bureaucratic awards in the 110th Congress. The results support the contention that districts get what they need, and this raises questions about the ability of members of powerful committees to steer awards selectively to their districts. It also provides evidence for the economic “law of increasing state activity,” by which districts with higher income levels receive a larger share of federal assistance

The Transportation Program in Illinois School Districts

This field study, which is an examination of the transportation program in a local school district in Illinois, gives special attention to what is expected of a local district by the state of Illinois. Many of those expectations are found in the school code as regulations for the local school district in its transportation program. Though this field experience, which was done in the Shelbyville Community Unit Schools during the fall semester, 1979, is a summary of transportation practices in one school district, it does contain information of a general nature which may be of interest. Much of the information about the Shelbyville District was obtained through interviews of local district personnel, who provided details about rules and regulations for their bus riders, and also provided information relating to the bus routes. During the interview with a local bus driver, special requirements were discussed which qualified a person to become a driver. It was learned that these requirements had been recently strengthened. The Illinois General Assembly was observed as a group having a tremendous influence on the local school district transportation program. This came as no surprise, since this group was merely performing its duty of directing the state educational programs by amending the school code as the need arises. However as this study demonstrates, the impact is more widespread than a casual inspection would reveal. It was found that many of the spending practices in a local district were effected by the structure of the transportation formula. Rural residents were also observed as another group which may exert pressure on the local board and its transportation policies. Also noted was a slight increase in the percent of rural students in the Shelbyville District brought about by the clustering of people in subdivisions around Shelbyville. Private schools in the same general area were observed as yet another group which may influence the local school transportation program. Private schools were asking for free transportation under a proposal which was passed by the Illinois General Assembly but vetoed by Governor James Thompson. Another factor noted as having an effect on the transportation finances in a local school was the price and availability of gasoline. With the present world petroleum market and the projected increases in this area, the financial picture is glum. The voucher system was observed as another factor which has the potential of considerable impact on the local transportation program. Because of the uncertainties surrounding this topic, school personnel should keep themselves well informed about any proposals relating to it. Finally, the challenge of the future was observed as being in the area of conservation of energy because of the tremendous rise in costs in transportation. As a recommendation, school districts should be encouraged to implement conservation practices by the state through the transportation formula to help meet this challenge

Individual based model with competition in spatial ecology

We analyze an interacting particle system with a Markov evolution of birth-and-death type. We have shown that a local competition mechanism (realized via a density dependent mortality) leads to a globally regular behavior of the population in course of the stochastic evolution.Comment: 22 page

Tips : resources for teachers

This small booklet is designed as a ready reference for teachers who are confronted with a problem or engaged in a particular activitity in the primary school. All books which are listed are considered useful. However, those with annotations are considered more useful in the general classroom

The second law, Maxwell's daemon and work derivable from quantum heat engines

With a class of quantum heat engines which consists of two-energy-eigenstate systems undergoing, respectively, quantum adiabatic processes and energy exchanges with heat baths at different stages of a cycle, we are able to clarify some important aspects of the second law of thermodynamics. The quantum heat engines also offer a practical way, as an alternative to Szilard's engine, to physically realise Maxwell's daemon. While respecting the second law on the average, they are also capable of extracting more work from the heat baths than is otherwise possible in thermal equilibrium