Über Automorphismengruppen lokal-kompakter Gruppen und Derivationen von Lie-Gruppen

Ohne ZusammenfassungResearch partially supported by NSF grants GP-8496, GP-6946, and GP-9444, resp. The first-named author also received support from Research Funds of the Graduate School of the University of Minnesota.     

On the structure of some abstract differential problems II

Summary Various notions of operator homotopy are examined and results are given describing situations such that homotopy of data implies homotopy of subordinate “boundary value” problems. Research supported in part by NSF grants GP-4575 and GP-7374. Entrata in Redazione il 9 aprile 1968.     

Über eine Charakterisierung der Determinante

Ohne ZusammenfassungDiese Arbeit wurde von NSF unter Grant GP-5870 gefördert.     

Super-reflexivity and the girth of spheres

It is shown that a Banach space is super-reflexive if and only if the girth of its unit ball is greater than 4. Consequently, “girth greater than 4” is a property preserved under isomorphisms and duality. This work was supported in part by NSF Grants GP-28578 and GP-28999, respectively.     

Countable models of ℵ1-categorical theories

Countable models of ℵ₁-categorical theories are classified. It is shown that such a theory has only a countable number of nonisomorphic countable models. The author was partially supported by NSF grants GP-1621 and GP-4257 during the period those results were obtained.     

Locally compact subgroups of the spectrum of the measure algebra III

The maximal ideal space of the measure algebra of a locally compact abelian (LCA) group has the structure of a compact commutative semitopological semigroup (separately continuous multiplication). Idempotents in the semigroup correspond to certain algebraic projections on the measure algebra. In this paper we study the maximal groups about certain idempotents. This research was partially supported by NSF contract number GP-19852 and GP-31483X.     

On homologies of finite projective planes

Study of finite projective planes which have a polarity preserved by many homologies. This research was supported in part by NSF Grant GP-33223.     

On the integration of Radon measures and set functions

A theory of integration is described which subsumes as special cases Bourbaki's integration of Radon measures and Caratheodory's integration of set functions.Supported partly by NSF Grant GP-20541     

An existence theorem for optimal controls

An existence theorem is given based on a criterion ensuring compactness of the controls in the metric corresponding to convergence in measure.This research was performed under NSF Grant No. GP-7372     

Every two elementarily equivalent models have isomorphic ultrapowers

We prove (without G.C.H.) that every two elementarily equivalent models have isomorphic ultrapowers, and some related results. The preparation of this paper was supported in Part by NSF Grant GP-22937.     

Approximation by functions having restricted ranges: Equality case

Summary In this paper an alternation theorem is developed for approximating with functions having restricted ranges where equality is allowed to occur between the restraining curves.Supported in part by NSF grant GP-7624.     

A note on solutions of orientor fields for periodic systems

It is shown that the orientor field problem can be solved for control problems governed by ordinary differential equations where periodic controls give periodic trajectories.This research was partially supported by NSF Grant No. GP-27973.     

Collective bargaining: A differential game

Earlier differential game models of collective bargaining deal only with the strike phase. The model proposed here allows for negotiations without and with a strike.This paper is based on research supported by NSF under Grant No. GP-24205.     

Inequalities forf-vectors of 4-polytopes

LetV, E, S andF be the number of vertices, edges, subfacets and facets, respectively, of a 4-dimensional convex polytope. In this paper we derive new upper and lower bounds forS in terms ofF andV. Research supported by NSF grants GP-27963 and GP-19221.     

A characteristic initial value problem for the Euler-Poisson-Darboux equation

Summary An explit solution is obtained for a charasteristic initial value problem for the Euler-Poisson-Darboux equation by Riesz method of analytic continuation of a generalized Riemann-Liouville integral. This work was supported by NSF research grant GP-11543. Entrata in Redazione il 18 ottobre 1969.     

Flat ideals II

This paper is concerned with the relationships that hold between finiteness and divisibility properties of flat ideals of integral domains. Brought out often is the role of the arithmetic of a ring in the finiteness of its flat ideals.Supported in part by NSF grant GP-33133X.     

A de bruijn-type formula for enumerating patterns of partitions

We develop a formula for enumerating the partitions of a set up to the action of a group. We give some special cases of this formula and illustrate its use with an example. Some comments are made relating the formula to an earlier formula.This work was supported in part by NSF Contract GP-43010.     

On the Cauchy problem for hyperbolic differential equations with multiple characteristics

A priori estimates leading to existence results for the Cauchy problem are obtained for a class of linear variable coefficient hyperbolic operators with multiple characteristics. These estimates provide an extension of the energy inequalities known for strictly hyperbolic operators. Supported by NSF Grant No. GP-7234.     

SeparableL 1 preduals are quotients ofC(Δ)

It is proved that every separable predual space of anL ₁ space is a quotient space ofC(Δ). Johnson's work was supported in part by NSF GP-33578.     

A minimum principle for a population equation

A minimum principle for the Verhulst-Pearl population equation is given in terms of the integral of the inverse of population. This principle is contrasted with one given earlier by Volterra in terms of the integral of population.This research was supported by NSF under Grant No. GP-2405.