Physical Sciences and Mathematics Commons^™

A Two-Stage Postnikov System Where E₂ ≠ E∞ In The Eilenberg-Moore Spectral Sequence, Claude Schochet

Mathematics Faculty Research Publications

Let ΩB → PB → B be the path fibration over the simply-connected space B, let ΩB → E → X be the induced fibration via the map ƒ : X → B, and let X and B be generalized Eilenberg-Mac Lane spaces. G. Hirsch has conjectured that H*E is additively isomorphic to Τοτ_H*B(Z₂,H*X), where cohomology is with Z₂ coefficients. Since the Elienberg-Moore spectral sequence which converges to H*E has E₂ = Τοτ_H*B(Z₂,H …

Fourier Transforms Of Unbounded Measures, Loren Argabright, Jesus De La Lamadrid

Department of Mathematics: Faculty Publications

Let G be a locally compact abelian group. For a (generally unbounded) measure μ on G we shall say that μ is transformable if there is a measure μˆ on the character group Γ of G such that, for every ƒЄK(G), the space of continuous functions with compact support on G,ƒЄL₂(μ) and (1) ∫_Gƒ^**ƒ(x) dμ(x) = ∫_r|∫(γ^-1)|²dμ(γ). The resulting "Fourier transformation” μ→μˆ contains the classical theory and leads to generalizations of a variety of classical results, including the Plancherel theorem and the Poisson summation …

Existence And Uniqueness For Nonlinear Neutral-Differential Equations, L. J. Grimm

Mathematics and Statistics Faculty Research & Creative Works

Fixed point theorems are used to prove existence and uniqueness of the C1 solution of the initial-value problem for a functional-differential equation of neutral type. © 1971, American Mathematical Society. All Rights Reserved.

On Completeness In Quasi-Uniform Spaces, John W. Carlson, Troy L. Hicks

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.

Existence And Continuous Dependence For A Class Of Nonlinear Neutraldifferential Equations, L. J. Grimm

Mathematics and Statistics Faculty Research & Creative Works

This paper presents existence, uniqueness, and continuous dependence theorems for solutions of initial-value problems for neutral-differential equations of the form (equation omited), where f, g, and h are continuous functions with g(0, x0)=h(0, x0) = 0. The existence of a continuous solution of the functional equation z(t) =f(t, z(h(t))) is proved as a corollary. © 1971 American Mathematical Society.

The Impulse And Doublet, Richard C. Heyser

Unpublished Writings

The basic problem to which this paper is directed is that of characterization of the acoustic field perceived by an observer and due to a loudspeaker situation in a room. Before immediately jumping into an apparent solution and presenting the results of a set of measurements it is essential to present the considerations leading to that measurment...First, there are at least two ways of characterizing the same acoustic signal if we restrict our attention to a well defined set of parameters...Secondly, since both characterizations define the same thing it must be possible to translate information without loss from one domain …

Toeplitz Operators On Locally Compact Abelian Groups, Henry A. Krieger, C.A. Schaffner

All HMC Faculty Publications and Research

The problem of global optimization of M incoherent phase signals in N complex dimensions is formulated. Then, by using the geometric approach of Landau and Slepian, conditions for optimality are established for $N = 2$, and the optimal signal sets are determined for $M = 2,3,4,6$ and 12.

The method is the following: The signals are assumed to be equally probable and to have equal energy, and thus are represented by points ${\bf s}_j $, $j = 1,2, \cdots ,M$, on the unit sphere $S_1 $ in $C^N $. If $W_{jk} $ is the half space determined by ${\bf s}_j …

The Global Optimization Of Incoherent-Phase Signals, Henry A. Krieger, Charles Albert Schaffner

All HMC Faculty Publications and Research

No abstract provided.

The Influence On A Finite Group Of The Cofactors And Subcofactors Of Its Subgroups, Larry R. Nyhoff

University Faculty Publications and Creative Works

The effect on a finite group G of imposing a condition 6 on its proper subgroups has been studied by Schmidt, Iwasawa, ltd, Huppert, and others. In this paper, the effect on G of imposing 6 on only the cofactor H/corGHor more generally, the subcofactor ///scorGH) of certain subgroups H of G is investigated, where corGH (scorGH) is the largest G-normal (07-subnormal) subgroup of H. It is shown, for example, that if (a) ///scorGH is p-nilpotent for all self-normalizing H> G, or if (b) ///scorGH is />-nilpotent for all abnormal H> G and p is odd or the p-Sylows …