Poincaré cycles and ergodic behavior of a linear diatomic chain

The ergodic behavior of a linear diatomic chain is shown to be analogous to that of a linear monatomic chain. Starting with the expressions for the time-relaxed correlation functions between any two particles in the chain, we show that the existence of Poincaré cycles is not inconsistent with the development of an equilibrium state. Also, we show that those dynamical variables that are ergodic for the linear monoatomic chain remain ergodic in the diatomic chain. It is shown that the autocorrelation functions for particles with equal or different masses decay in time ast ^–1/2 .This work was completed when the author was associated with the Institute for Fluid Dynamics and Applied Mathematics, University of Maryland and 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. AF18(600)1315.     

Preface to topics in data envelopment analysis

This paper serves as an introduction to a series of three papers which are directed to different aspects of DEA (Data Envelopment Analysis) as follows: (1) uses and extensions of window analyses' to study DEA efficiency measures with an illustrative applications to maintenance activities for U.S. Air Force fighter wings, (2) a comparison of DEA and regression approaches to identifying and estimating, sources of inefficiency by means of artificially generated data, and (3) an extension of ordinary (linear programming) sensitivity analyses to deal with special features that require attention in DEA. Background is supplied in this introductory paper with accompanying proofs and explanations to facilitate understanding of what DEA provides in the way of underpinning for the papers that follow. An attempt is made to bring readers abreast of recent progress in DEA research and uses. A synoptic history is presented along with brief references to related work, and problems requiring attention are also indicated and possible research approaches also suggested.This research was partly supported by the National Science Foundation and USARI Contract MDA 903-83-K0312, with the Center for Cybernetic Studies, the University of Texas at Austin. It was also partly supported by the IC² Institute at the University of Texas at Austin. Reproduction in whole or in part is permitted for any purpose of the U.S. Government.     

Simple regge pole model for the reactionπ − p →η’n

The most recently measured differential cross-section data forπ ⁻ p → η’n has been fitted by using a simple Regge pole model with phenomenological residue functions. It has also been observed that this inelastic process has the scaling property.     

Contour lines of the optical functions for solids

The well-known equations for the optical functions of reflectance, transmittance and phase changes on reflection and transmission for a solid material have been rearranged into the form of simple geometric figures in the u, v (n, k) plane. The curves for F_p show a singularity on the n-axis.     

An analysis of quantum chromodynamic structure function beyond leading order

We obtain approximate solutions of Altarelli-Parisi equations beyond leading logarithmic approximation. Our results suggest quantitative utility of higher order terms in the structure function analysis of deep inelastic scattering.     

角域上的调和函数与条件Brown运动

设中的角域．该文绘出了A上正调和函数的Martin表示，讨论了极小调和函数与条件Brown运动的一个0—1律之间的关系，并给出了A上极小调和函数的表现形式，     

Numerical algorithms for uniform Airy-type asymptotic expansions

Airy-type asymptotic representations of a class of special functions are considered from a numerical point of view. It is well known that the evaluation of the coefficients of the asymptotic series near the transition point is a difficult problem. We discuss two methods for computing the asymptotic series. One method is based on expanding the coefficients of the asymptotic series in Maclaurin series. In the second method we consider auxiliary functions that can be computed more efficiently than the coefficients in the first method, and we do not need the tabulation of many coefficients. The methods are quite general, but the paper concentrates on Bessel functions, in particular on the differential equation of the Bessel functions, which has a turning point character when order and argument of the Bessel functions are equal.     

A weak Brun—Titchmarsh theorem for multiplicative functions

An important theorem of Shiu gives a (precise) bound for the average of values of multiplicative functions, of a certain class, over ‘short’ intervals. Here we obtain, by simple means, the above result of same qualitative order.     

Info-quantifiers’ map-characterization revisited

We highlight the potentiality of a special Information Theory (IT) approach in order to unravel the intricacies of nonlinear dynamics, the methodology being illustrated with reference to the logistic map. A rather surprising dynamic feature→plane-topography map becomes available.     

Wavelet expansions and asymptotic behavior of distributions

We develop a distribution wavelet expansion theory for the space of highly time-frequency localized test functions over the real line S₀(R)⊂S(R) and its dual space , namely, the quotient of the space of tempered distributions modulo polynomials. We prove that the wavelet expansions of tempered distributions converge in . A characterization of boundedness and convergence in is obtained in terms of wavelet coefficients. Our results are then applied to study local and non-local asymptotic properties of Schwartz distributions via wavelet expansions. We provide Abelian and Tauberian type results relating the asymptotic behavior of tempered distributions with the asymptotics of wavelet coefficients.