This paper introduces and analyzes a class of directionally reinforced random walks The work is motivated by an elementary model for time and space correlations in ocean surface wave elds We develop some basic properties of these walks For instance we investigate recurrence properties and give conditions under which the limiting continuous versions of the walks are Gaussian di usion processes M...

Section C In this section we provide additional discussion and descriptive statistics on our sample of loan packages. Section D In this section we analyze the optimal loan contract if the lenders can commit to renegotiation behavior. Section E In this section we derive the competitive equilibrium contract when the bank share k is endogenous. Section F In this section we present an extension of ...

The k-dimensional skeleton of a d-polytope P is the set of all faces of the polytope of dimension at most k. The 1-skeleton of P is called the graph of P and denoted by G(P ). G(P ) can be regarded as an abstract graph whose vertices are the vertices of P , with two vertices adjacent if they form the endpoints of an edge of P . In this chapter, we will describe results and problems concerning g...

ion of the result of an expression, it is obvious that without result, a type for an expression is irrelevant. Obviously, there is more to heterogeneity than just the addition or modification of typing rules. It has a profound impact on the meaning of a type, hence on the meaning of expressions. In Section 5.3.6, we have seen that heterogeneity is one of the causes of update anomalies if not pr...

We begin in this section with a brief introduction to the field of property testing. Section 2 explains the famous example of “linearity testing.” Section 3 gives upper bounds for the canonical problem of “monotonicity testing,” and Section 4 shows how to derive property testing lower bounds from communication complexity lower bounds. These lower bounds will follow from our existing communicati...

This note discusses some results on the non-BPS excitations of D-branes. We show that the excitation spectrum of a bound state of D-strings changes character when the length of the wrapping circle becomes less than ∼ g−1L(S). We review the observed relation between the low energy absorption cross-section of D-branes and the low energy absorption cross-section for black holes. We discuss various...