Topological representation of posets

There is a canonical imbedding of a poset into a complete Boolean lattice and hence into a Boolean lattice. This gives it a representation as a collection of clopen sets of a Boolean space. There are reflective functions from a category of distributive posets to the subcategories of distributive and Boolean lattices and consequently a topological dual equivalence that extends the Stone duality of Boolean lattices.Presented by B. Jonsson.     

A unified quantum theory of mechanics and thermodynamics. Part IIb. Stable equilibrium states

Part IIb presents some of the most important theorems for stable equilibrium states that can be deduced from the four postulates of the unified theory presented in Part I. It is shown for the first time that the canonical and grand canonical distributions are the only distributions that are stable. Moreover, it is shown that reversible adiabatic processes exist which cannot be described by the dynamical equation of quantum mechanics. A number of conditions are discussed that must be satisfied by the general equation of motion which is yet to be discovered.Part I of this paper appeared inFound. Phys. 6(1), 15 (1976). Part IIa appeared inFound. Phys. 6(2), 127 (1976). The numbering of the sections, equations, and references in this part of the paper continues from those in Part IIa.     

Toeplitz operators on weighted Bergman spaces

In [2], Axler, Conway and McDonald, discuss the essential spectrum of Toeplitz operator, with continuous symbol, on the unweighted Bergman space. This paper extends their results to the weighted Bergman space, where the weight and its logarithm are assumed to be locally integrable.This paper represents part of the author's Ph.D. thesis, written at Indiana University under the direction of Professor John B. Conway.     

Existence theorems for lagrange control problems with unbounded time domain

Existence theorems are proved for usual Lagrange control systems, in which the time domain is unbounded. As usual in Lagrange problems, the cost functional is an improper integral, the state equation is a system of ordinary differential equations, with assigned boundary conditions, and constraints may be imposed on the values of the state and control variables. It is shown that the boundary conditions at infinity require a particular analysis. Problems of this form can be found in econometrics (e.g., infinite-horizon economic models) and operations research (e.g., search problems).The author wishes to thank Professor L. Cesari for his many helpful comments and assistance in the preparation of this paper. This work was sponsored by the United States Air Force under Grants Nos. AF-AFOSR-69-1767-A and AFOSR-69-1662.     

Direct synthesis of pyran-lactones related to naphthoquinoneantibiotics

Simple benzopyrans with a fused γ-lactone unit are prepared from an o-disubstituted arene by direct intramolecular alkoxycarbonylation/lactonization promoted by palladium diacetate; the process gives high yields and moderate stereoselectivity, favoring the $\text{cis}$ lactone over $\text{trans}$ by a factor of 5:1.