Boundedness and periodicity of solutions of the generalized liénard equation

Summary The object of this paper is to investigate, for large values of t, the solutions of Liénard type equations. A periodicity theorem is proved and several conditions which imply boundedness are discovered. This research was supported by the United States Air Force through the Air Force Office of Scientific Research of the Air Research and Development Command under contract No. AF 18(600)-1108.     

Existence of a σ finite invariant measure for a Markov process on a locally compact space

A σ finite invariant measure is found, for a Markov process, on a locally compact space, which maps continuous functions to continuous functions. The research reported in this document has been sponsored by the Air Force Office of Scientific Research under Grant AF EOAR 66-18, through the European Office of Aerospace Research (OAR) United States Air Force.     

On a paper of A. Feldzamen

Results of A. Feldzamen on semi-similarity of operators are proved here using matrix methods. The use of these methods yields simpler proofs, the formulations of the theorems assume a more transparent form. The research reported in this document has been sponsored in part by the Air Force Office of Scientific Research of the Air Research and Development Command United States Air Force through its European Office.     

On banach spaces whose duals areL 1 spaces

A structure theorem for Banach spaces whose duals areL ₁ spaces, is proved. The research of the second named author has been sponsored by the Air Force Office of Scientific Research under Grant AF EOAR 66-18 through the European Office of Aerospace Research (OAR) United States Air Force.     

Problems and methods in partial differential equations

Summary Finite part and logarithmic part of some divergent integrals with applications to theCauchy problem. A Giovanni Sansone nel suo 70^mo compleanno. The research reported in this document has been sponsored in part by the Air Force Office of Scientific Research of the Air Research and Development Command, United States Air Force, through its European Office under Contract AF 61 (056)-86.     

Espaces de dirichlet

Sans résumé This research was partly supported by the United States Air Force through the Air Force Office of Scientific Research of the Air Research and Development Command under contract No. AF 18 (600)-1109. Reproduction in whole or in part is permitted for any purpose of the United States Government.     

On the existence of equivalent finite invariant measures

Summary Necessary and sufficient conditions are given for the existence of a finite measure which is equivalent to a given measure and invariant with respect to each transformation in a given commutative semigroup of measurable null-invariant point transformations. This result was already known for denumerably generated semigroups. A complementary result is proved which states that if one such equivalent measure exists, then there exists a unique equivalent measure which agrees with the original measure on the invariant sets.Research sponsored by the Air Force Office of Scientific Research, Office of Aerospace Research, United States Air Force, under Grant No. AFOSR-68-1394.     

Bemerkung zu einem Satz von H. Grauert und R. Remmert

Ohne ZusammenfassungUnterstützt durch Air Force Office of Scientific Research, through the European Office, Aerospace Research, United States Air Force, OAR 62–40.     

On series in linear topological spaces

The main result is that in every complete locally-bounded linear topological space there exist series which are unconditionally yet not absolutely convergent. Relations between absolute, unconditional and metric convergence of series are studied. The research reported in this document has been sponsored in part by the Air Force Office of Scientific Research, OAR through the European Office, Aerospace Research, United States Air Force.     

On a singular differential operator

Summary Study of the properties of a singular differential operator in one independent variable. Applications to ordinary and partial differential equations. To Giovanni Sansone on his 70^th birth day. This research was supported by the United States Air Force through the Air Force Office of Scientific Research of the Air Research and Development Command under Contract No. 49 (638)-228.     

Constrained duality via unconstrained duality in generalized geometric programming

A specialization of unconstrained duality (involving problems without explicit constraints) to constrained duality (involving problems with explicit constraints) provides an efficient mechanism for extending to the latter many important theorems that were previously established for the former.This research was sponsored by the Air Force Office of Scientific Research, Air Force Systems Command, USAF, under Grant No. AFOSR-73-2516.     

The kernel of the wreath product of semigroups

All wreath products, in the general sense, of two semigroups with completely simple kernels have completely simple kernels. Presented here are computational characterizations of the primitive idempotents of such a wreath and of the identities and inverses in subgroups of its kernel. Research sponsored by the Air Force Office of Scientific Research, Office of Aerospace Research, United States Air Force, under Grant AF AFOSR 924-67.     

The treatment of nonhomogeneous Dirichlet boundary conditions by thep-version of the finite element method

Summary The paper addresses the problem of the implementation of nonhomogeneous essential Dirichlet type boundary conditions in thep-version of the finite element method.Partially supported by the Office of Naval Research under Grant N-00014-85-K-0169Research partially supported by the Air Force Office of Scientific Research, Air Force Systems Command, USAF, under Grant Number AFOSR 85-0322     

Computational complexity of parametric linear programming

We establish that in the worst case, the computational effort required for solving a parametric linear program is not bounded above by a polynomial in the size of the problem.This research is partially supported by Air Force Office of Scientific Research, Air Force Number AFOSR-78-3646.     

Classes of biorthonormal systems

Summary The (A)-summability and mean-convergence of Fourier series in terms of certain biorthonormal systems have been investigated. The problem of completing a set of polynomials to a biothonormal system has been solved in the case of certain sets of type zero (Sheffer’s classification). The research reported in this document has been sponsored in part by the Air Force Office of Scientific Research of the Air Research and Development Command, United States air Force, through its European Office, under Contract N₀ AF 61 (052)-324.     

On superlinear convergence in univariate nonsmooth minimization

This note demonstrates a new result on superlinear convergence in nonsmooth univariate minimization. It also gives other concepts of rapid convergence for minimization of functions that may have discontinuous derivatives.Research sponsored by the Air Force Office of Scientific Research, Air Force Systems Command, USAF, under Grant Numbers AFOSR-83-0210 and AFOSR-88-0180.     

Continuity of Bessel potentials

It is shown that certain capacities associated with potentials of functions in Lebesgue classes are non-increasing under orthogonal projection of sets. This inequality is then used to discuss continuity of traces of potentials on subspaces of possibly low dimension. The case of principal interest is the Bessel potential. This research was partially sponsored by the Air Force Office of Scientific Research, Office of Aerospace Research, United States Air Force, under AFOSR Grant No. 883-67.     

On complemented subspaces ofm

It is proved that an infinite dimensional subspace ofm is complemented inm if and only if it is isomorphic tom. The research reported in this document has been sponsored by the Air Force Office of Scientific Research under Grant AF EOAR 66-18, through the European Office of Aerospace Research (OAR) United States Air Force.     

On extreme points inl 1

It is proved that every bounded closed and convex subset ofl ₁ is the closed convex hull of its extreme points. The research reported in this document has been sponsored by the Air Force Office of Scientific Research under Grant AF EOAR 66-18 through the European Office of Aerospace Research (OAR) United States Air Force.     

Spherical means in spaces of constant curvature

Summary Extension of theorems ofF. Riesz on subharmonic functions to spaces of constant curvature by the use of hyperbolic partial differential equations. To Enrico Bompiani on his scientific Jubiles This research was supported in part by the United States Air Force through the Air Force Office of Scientific Research of the Air Research and Development Command under ontract No. AF 49 (638)–228.