summing the Boltzmann factor over all spin configurations {si}. The enumeration of all configurations cannot be done for d ≥ 3, and although possible in d = 2 is extremely hard there as well (a problem solved by Onsager). We will use an approximate solution technique known as mean field theory. Last term we solved the problem of noninteracting spins in a magnetic field described by the Hamilton...

Results from analyzing the curvature of a surface can be used to improve the implementation, e ciency, and e ectiveness of manufacturing and visualization of sculptured surfaces. In this paper, we develop a robust method using hybrid symbolic and numeric operators to create trimmed surfaces each of which is solely convex, concave, or saddle and partitions the original surface. The same method i...

We introduce a new class of second-order cover inequalities whose members are generally stronger than the classical knapsack cover inequalities that are commonly used to enhance the performance of branch-and-cut methods for 0–1 integer programming problems. These inequalities result by focusing attention on a single knapsack constraint in addition to an inequality that bounds the sum of all var...

where F : T × R → CK(R) is a set-valued map and g : T × T → R is a single-valued continuous map (CK(R) denotes the set of nonempty, closed, and convex subsets of R). In Section 3 some general existence principles for inclusions (1.1) are derived by using fixed point theory discussed in [1]. In Section 4 we present a specific function g such that y is a solution of (1.1) if and only if y is a so...

Program synthesis is the automated construction of software from a specification. While program synthesis is undecidable in general, we show that synthesising finite-state programs is NEXPTIMEcomplete. We then present a fully automatic, sound and complete algorithm for synthesising C programs from a specification written in C. Our approach uses a combination of bounded model checking, explicit-...

We present a new class of second-order unification problems, which we have called linear. We deal with completely general second-order typed unification problems, but we restrict the set of unifiers under consideration: they instantiate free variables by linear terms, i.e. terms where any λ-abstractions bind one and only one occurrence of a bound variable. Linear second-order unification proper...

mathematical/logical text that is a central reference for all second order cyberneticians. The introduction is a wonderfully insightful essay. So are some of the appendices.] von Foerster H. (1995). The Cybernetics of Cybernetics, second edn. Minneapolis, MN: Future Systems Inc. 497 pp. [The book of the name: a collection of papers by distinguished cyberneticians with graphic commentaries and o...

The standard second-order matching algorithm by Huet may be expansive in matching a exible-rigid pair. On one hand, many fresh free variables may need to be introduced; on the other hand, attempts are made to match the heading free variable on the exible side with every \top layer" on the rigid side and every argument of the heading free variable with every subterm covered by the \top layer". W...