Some physical properties of KCl+Pb2+ crystals

This paper presents the results of measurements of the mechanical and electrical properties of as-received pure and lead-doped crystals of potassium chloride. The critical resolved shear stress of the crystals obeys the Franks relationship in the whole concentration range. In addition, the correlation between ₀ and the Vickers hardness numberH was found and the equation is of the form ₀=k (H–H ₀). The solubility of Pb²⁺ in as-received KCl crystals was observed, from measurements of the electrical conductivity, to be low—the successive saturation of the solid solution started already in an environment of 5 mole ppm in agreement with data from the mechanical measurements. The density of cation vacancies and their mobility were represented by the following euqations ₁ T=6·25×10⁴ exp(–·75/kT) cm² K/volt. sec,n ₁=6·95×10²³ exp(–2·12/kT) vacancies/cm³ The value of 0sd46±0·02 eV was found as a rough estimate of the association energy.The authors wish to express their thanks to Professor Dr. J. Z.Damm and Ing. E.Mariani for their stimulating interest in the present work.     

The spectrum of the random environment and localization of noise

We consider random walk on a mildly random environment on finite transitive d-regular graphs of increasing girth. After scaling and centering, the analytic spectrum of the transition matrix converges in distribution to a Gaussian noise. An interesting phenomenon occurs at d = 2: as the limit graph changes from a regular tree to the integers, the noise becomes localized. The graphs of the noise covariance structure for d = 4, 3, 2.1 from above.     

An Ising model for the stress relaxation of solids

A kinetic theory of stress relaxation of solids as a cooperative process is proposed. The theory is based on a two-state model for the relaxation. It is shown that the conventional mean field approximation leads to an exponential dependence of the rate of stress relaxation on the stress while the multiplicative approximation of Vol'kenstein et al. leads to a power law. It is argued that the exponential law should be valid initially in the relaxation process while the power law is appropriate when the system is nearer equilibrium, which is in qualitative agreement with recent experimental findings.     

To the relation between energies of molecular soliton and extended states in chains

A standard statement is that in the interacting electron (exciton) — phonon systems in molecular chains and on the level of the standard quantum mechanics, the formation of localised solition states is energetically more advantageous than the formation of extended (plane--wave-like or polaron) states (see e.g. /1/ for a review). The question about validity of this statement is not yet finally settled /2/. We are going to question this assertion using trivial variational arguments here. For arbitrary localized standing-soliton state (having its energy lower than the states describing running solitons irrespective of technique used to derive them), we are able to prove the existence of an intermediate or large polaron state whose energy is still lower. Hence, the energy arguments are not sufficient to explain the anomalous soliton stability.     

Hyperfine Field and Isomer Shift Evolution in Hydrogenated Nd–Fe–B Alloy

RE₂Fe₁₄B (RE=rare earth) materials are capable of absorbing hydrogen to form a stable solid solution at room temperature. Hydrogenation produces a number of significant changes in the hyperfine interactions. In this work, ⁵⁷Fe Mössbauer effect spectroscopy and X-ray diffraction measurements were performed on Nd_14.01Hf_0.08Fe_78.91B_7.00 alloys submitted to thermal treatment in hydrogen atmosphere. A non-linear increase of the hyperfine fields and isomer shifts with hydrogen concentration was observed. The hyperfine parameters of the 8j₁ site exhibit a rather different evolution than those experienced by the other major sites (8j₂, 16k₁, 16k₂). The origin of the hyperfine field enhancement is analyzed in terms of volume expansion and H nearest neighbors to the Fe sites. A linear expression on these two effects to give account of isomer shift evolution for 8j₁ site is given.     

Variable metric bundle methods: From conceptual to implementable forms

To minimize a convex function, we combine Moreau-Yosida regularizations, quasi-Newton matrices and bundling mechanisms. First we develop conceptual forms using “reversal” quasi-Newton formulae and we state their global and local convergence. Then, to produce implementable versions, we incorporate a bundle strategy together with a “curve-search”. No convergence results are given for the implementable versions; however some numerical illustrations show their good behaviour even for large-scale problems.     

Quotients of partial abelian monoids

A hierarchy of partial abelian structures is considered. In an order of decreasing generality, these structures include partial abelian monoids (PAM), cancellative PAMs (CPAM), effect algebras (or D-posets), orthoalgebras, orthomodular posets (OMP) and orthomodular lattices (OML). If P is a PAM, the concepts of a congruence on P and a quotient P are defined. Similar definitions are given for quotients of higher level categories in the hierarchy. The notion of a Riesz ideal I on a CPAM P is defined and it is shown that I generates a congruence on P. The corresponding quotients P/I for categories in the hierarchy are studied. It is shown that a subset I of an OML is a Riesz ideal if and only if I is a p-ideal. Moreover, for effect algebras, we show that congruences generated by Riesz ideals are precisely those that are given by a perspectivity. The paper includes a large number of counterexamples and examples that illustrate various concepts. Received April 14, 1997; accepted in final form January 19, 1998.     

Interferometric measurement of plasma density in the range 1019–1022 m−3

A laser interferometer, operating at the wavelength =0·337 mm suitable for the plasma density measurements in the range 10¹⁹–10²² m^–3 as well as a simple construction of the HCN laser are described.The authors wish to thank Dr. P.unka for fruitful discussions and Dr. J.Musil for the design and construction of the detector.     

Measurements of γ-γ and γ-electron directional correlations in119Sb

The directional correlations ofγ-γ andγ-electron cascades in¹¹⁹Sb are measured, in the decay of^119mTe. Bothγ-γ andγ-electron directional correlation coefficients are determined for the cascades (energies in keV): 153.5-1212.7, 942.3-270.5, (976.2+979.3)-270.5, 1095.7-270.5 and 1136.8-270.5. For the cascades 912.6-1366.2, 2013.4-270.5 and 2089.9-270.5γ-γ directional correlations are measured. The mixing ratios evaluated are:δ(M2/E1, 153.5 keV)=0.0003±0.0023,δ(E2/M1, 270.5 keV)=-0.39±0.29,δ(E2/M1, 942.3 keV)= ?0.26±0.12,δ(E3/M2,1095.7 keV)=?0.01±0.07, andδ(M3/E2,1212.7 keV) =0.004±0.007. The result is compared with theoretical predictions.     

Contributions to the theory of stochastic programming

Two stochastic programming decision models are presented. In the first one, we use probabilistic constraints, and constraints involving conditional expectations further incorporate penalties into the objective. The probabilistic constraint prescribes a lower bound for the probability of simultaneous occurrence of events, the number of which can be infinite in which case stochastic processes are involved. The second one is a variant of the model: two-stage programming under uncertainty, where we require the solvability of the second stage problem only with a prescribed (high) probability. The theory presented in this paper is based to a large extent on recent results of the author concerning logarithmic concave measures.This work was supported in part by the Institute of Economic Planning, Budapest.This paper was presented at the 7th Mathematical Programming Symposium 1970, The Hague, The Netherlands, under the title Programming under probabilistic constraints and programming under constraints involving conditional expectations.