Regularity and intersections of bracket powers

Czechoslovak Mathematical Journal - Among reduced Noetherian prime characteristic commutative rings, we prove that a regular ring is precisely that where the finite intersection of ideals commutes...     

Interspike interval embedding of chaotic signals

According to a theorem of Takens [Lecture Notes in Mathematics (Springer-Verlag, Berlin, 1981), Vol. 898], dynamical state information can be reproduced from a time series of amplitude measurements. In this paper we investigate whether the same information can be reproduced from interspike interval (ISI) measurements. Assuming an integrate-and-fire model coupling the dynamical system to the spike train, there is a one-to-one correspondence between the system states and interspike interval vectors of sufficiently large dimension. The correspondence implies in particular that a data series of interspike intervals, formed in this manner, can be forecast from past history. This capability is demonstrated using a nonlinear prediction algorithm, and is found to be robust to noise. A set of interspike intervals measured from a simple neuronal circuit is studied for deterministic structure using a prediction error statistic. (c) 1995 American Institute of Physics.     

Lattice size estimates for Gabor decompositions

It is shown that the Gabor frame operator for frames with lattice such thatab=1/N for some integerN1 is continuous on the modulation spaces ([9], [20]) whenever the basic functiong is a Schwartz function and (g, a, b) generates a frame forL ² (R). From this a sufficient condition on the lattice is given which guarantees that one has a Banach frame for the modulation spaces of Feichtinger.This work was supported by NSF grant # DMS-8916968 while the author was visiting Yale University.     

Fractionally differenced models for water quality time series

This paper deals with the selection and evaluation of statistical techniques for use in the modeling and forecasting of water quality time series. The focus is on statistical concepts relevant to the analysis of flows and concentrations. A selection of time series procedures has been used for auditing water quality archival data, including the screening of data sets, correlation and spectrum calculations, and iterative model fitting. A summary is provided of experience with analyzing archival data on the Niagara River and the use of a fractionally differenced model.This paper is the result of a study performed for the International Joint Commission, United States and Canada. The authors gratefully acknowledge the direction and support provided by Dr. Joel L. Fisher.     

What Makes a Theory Testable, or Is Intelligent Design Less Scientific Than String Theory?

I compare the theory of intelligent design to string theory to see on what basis, if any, only the former can be justifiably excluded as being scientific.We shall see that the classic criterion of testability or falsifiability is sometimes not so straightforward, and that there are other criteria to help us make such a distinction.     

A Lie theoretic galois theory for the spectral curves of an integrable system: I

In the study of integrable systems of ODE's arising from a Lax pair with a parameter, the constants of the motion occur as spectral curves. The specific curves depend upon the representation of the Lie algebra. In this paper a Galois theory of spectral curves is given that classifies the spectral curves from an integrable system. The spectral curves correspond to conjugacy classes of certain subgroups of the Weyl group for the Lie algebra. The theory is illustrated with the periodic Toda lattice.Partially supported by a Louisiana Education Quality Support Fund grant LEQSF (87-89)-RD-A-8     

Simultaneous measurements of the p+d→(A=3)+π reactions

A stack of annular detectors made of high-purity germanium was used to measure simultaneously pd → ³H π⁺ and pd → ³He π⁰ differential cross sections at beam momenta of 750 MeV/c, 800 MeV/c, and 850 MeV/c over a large angular range. The extracted total cross sections for the pd → ³He π⁰ reactions bridge a gap between near threshold data and those in the resonance region. The ratio of the cross sections for the two reaction channels taken at the same η=p^cm_π/m_π yields 2.11±0.08 indicating that a deviation from isospin symmetry is very small.