Ont ∞ quasi-similarity of linear systems

Summary Conti defined t similarity of systems (1)x=tA(t)xand (2)y=B(t)y, and showed that it is an equivalence relation which preserves uniform and strict stability. Here the definition is weakened by imposing less stringent integrability conditions, some in terms of perhaps conditionally convergent improper integrals, on the matrix function relating A and B. The extended relation, t quasi-similarity, is not symmetric or transitive; however, it is shown that if (2) is t quasi-similar to (1)and (1)is uniformly, uniformly asymptotically, or strictly stable, then so is (2).Results are also given concerning linear asymptotic equilibrium of (2)in the case where (1)is stricly stable or has linear asymptotic equilibrium.     

The physics of detecting torsion and placing limits on its effects

We present the essential principles of torsion-detection physics and evaluate several conceivable types of experiments and observations for actually detecting torsion fields, reemphasizing also the evident impossibility of successfully searching for its manifestations among cosmological relics. In particular, a polarized body, with net intrinsic (fundamental-particle) spin, is essential for detecting a torsion field. One which possesses only orbital angular momentum—rotation—or an unpolarized intrinsic spin density will not feel torsion. The fundamental problem in searching for such fields is the extremely small basic unit of the coupling or interaction energy between the torsion field and spin,(8G/c ²)( ²/4). The best way of maximizing the total interaction energy is to increase the spin density of the source _s, and, at the same time the spin numberS _D of the detector.This essay was awarded an honorable mention in 1984 by the Gravity Research Foundation—Ed.     

Liouville's theorem and the method of the inverse problem

An approach to the investigation of the Zakharov-Shabat equations is developed. This approach is based on a classical theorem of Liouville and is the synthesis of finite-zone integration, the matrix Riemann problem method and the theory of isomonodromy deformations of differential equations. The effectiveness of the proposed scheme is demonstrated by developing dressing procedures for the Bullough-Dodd equation.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 133, pp. 113–125, 1984.     

Largep T double photon production in hadronic collisions-beyond leading logarithm QCD calculation

We calculateO(α _s ) corrections to largep _T double photon production in hadronic collisions. We find that these corrections to the basic \(q\bar q \to \gamma \gamma \) subprocess are important, preventing to describe double photon production on the basis of the leading logarithm approximation only. We give a phenomenological discussion of the results obtained at SPS, ISR and \(Sp\bar pS\) energies. In particular, we investigate how the effect of the intrinsic parton <K _T> may be disentangled from the perturbative contribution. We also calculate the aplanarity distribution characteristic of 3 jet events.     

Crossover critical correlation function

The anomalous dimension index assumes its critical value for small momenta and vanishes for large momenta. We provide, in the form of a quadrature, a momentum dependent (k) which interpolates between the above limits. High- and low-momentum expansions for the spectral function are obtained, leading to a Padé approximant from which (k) is determined, thereby giving a crossover critical correlation function.Dedicated to B. Mühlschlegel on the occasion of his 60th birthday     

Single and double passage AFP NMR/ON studies of54MnNi

High resolution conventional AFP NMR/ON studies provide evidence for very small efg's of predominantly negative sign at the nucleus of the nominal S-state ion⁵⁴Mn in single crystal nickel when the applied field is paralled to the 111 direction. The form of the mid passage signals for opposing sweep directions indicates a unique efg super-imposed upon a random component of comparable magnitude. The advantages of a second analyzing sweep performed during spin lattice relaxation of a conventional post-passage AFP NMR/ON sweep are demonstrated.     

Calculation of excited molecular states taking account of partial relaxation of the core

Effects of electron-core relaxation in the excitation of atomic systems are considered. A new approach to the consideration of relaxation is proposed, and the corresponding equations are obtained. In the -electron approximation, the first excited states of some organic molecules are calculated by the V^(N–1)-potential method, the Morokuma-Iwata method, and a method proposed in the present work.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 55–59, October, 1985.