Shape and phase transitions in quantum-Hall skyrmions

The shape deformability of quantum-Hall skyrmions leads to a rich phase diagram in the –g space. We study the long-wavelength physics of a collection of interacting skyrmions using a nonlinear sigma model. At zero temperature the ground state is crystalline with generalized Nèel order. As a function of the filling factor , the skyrmion crystal undergoes a sequence of structural transitions driven by a change of shape of the individual skyrmions. Quantum effects lead to melting and orientational disordering transitions at high and low skyrmion densities, respectively. We show that moment of inertia of skyrmions also arises from the shape deformability of the skyrmions.     

Constrained games as complementary eigenvalue problems

A class of two-person nonzero sum games where the strategy choices are constrained in some form for each player is analyzed here to show the equivalent nonlinear programs which must be solved for the Cournot-Nash equilibrium. This equilibrium solution is shown in appropriate cases to lead to complementary eigenvalue problems, which have applications in normal solutions of stochastic LP models and optimal design problems in linear regression theory.     

Hartree-fock wave functions and oscillator strengths for the helium isoelectronic sequence

Oscillator strengths for 1¹S?n¹P transitions for some members of the helium isoelectronic sequence have been calculated by utilizing the dipole length, velocity and acceleration forms of the transition matrix element with coupled H.F. wave functions. Good agreement has been obtained between the values of the oscillator strengths. The quantities $\text{(?}{}_{\mathrm{A}}\text{??}{}_{\mathrm{L}}\text{)}$ and $\text{(?}{}_{\mathrm{A}}\text{??}{}_{\mathrm{V}}\text{)}$ decrease slowly with nuclear charge Z, whereas $\text{(?}{}_{\mathrm{L}}\text{-?}{}_{\mathrm{V}}\text{)}$ first increase to a maximum value and then decreases slowly.     

Charm production in 400 GeV/c proton-emulsion interactions: Bombay-Chandigarh-Delhi-Jammu Collaboration

5032 proton-emulsion interactions at 400 GeV/c momentum have been carefully scrutinized for production and decay of charged charm particles. In order to detect these decays, shower tracks from 3056 stars have been followed to a maximum length of 1 mm and those from 1976 stars up to 2 mm. A total of 23 three-prong charm-like candidates have been recorded in the forward cone. The background due to γ-overlap on a shower track, trident/pseudo-trident production and secondary interactions is estimated to be 15. Attributing the signal of 8 events to Λ_c⁺ and assuming the branching ratio of Λ_c⁺ → 3 prong to be 0.6 and τ_Λc to be 10^?13 sec we obtain the production cross section to be 106±39μb/nucleon. Out of these 8 events one example of semileptonic decay of Λ_c⁺ is seen.     

On the stability of solutions under recursive programming

Summary Recursive linear programming is defined by a sequence of linear programming problems in which a recursive relation is built into the system through either the coefficients of the objective function, the constraint matrix, or the right-hand side parameters. Here we consider the case where the right-hand side parameters are subject to a recursive time relation indicating how current period plans are related to past expectations and performance. Our object here is twofold: first, to analyze the stability properties of a linear recursive programming (LRP) model and second, to indicate some basic extensions of the LRP in the light of what is generally called the active approach of stochastic linear programming (SLP). Some simple theorems are developed in this connection and this is followed by a brief discussion of the possible lines of empirical applications.

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Zusammenfassung Rekursives lineares Programmieren wird als eine Aufeinanderfolge von linearen Programmproblemen definiert, bei denen eine rekursive Beziehung in das System eingebaut ist, und zwar entweder über die Koeffizienten der Zielfunktion, die Matrix der Beschränkungen oder die Parameter der rechten Seite. Wir betrachten hier den Fall, bei dem die Parameter der rechten Seite einer rekursiven Zeitrelation unterliegen, die den Zusammenhang zwischen den Plänen der gegenwärtigen Periode und früheren Erwartungen sowie deren Erfüllung angibt. Wir verfolgen zwei Ziele: Erstens wollen wir die Stabilitätseigenschaften eines linearen rekursiven Programm (LRP)-Modells analysieren, und zweitens wollen wir gewisse grundlegende Erweiterungen des LRP im Hinblick auf das sogenannte aktive Verhalten beim stochastischen Linearen Programmieren (SLP) angeben. Damit zusammenhängend werden einige einfache Theoreme entwickelt und eine kurze Diskussion der möglichen Richtungen empirischer Anwendungen angeschlossen.

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This work forms a part of a research project started originally at Iowa State University under the U.S. National Science Foundation Project NR 420-04-70 and continued presently by the authors. Some of the theoretical aspects closely related to this paper may be found in the following references: Sengupta, J. K., G. Tintner andC. Millham: On some theorems of stochastic linear programming with applications. Management Science, Vol. 10, October 1963, pp. 143–159. Sengupta, J. K., G. Tintner andB. Morrison: Stochastic linear programming with applications to economic models. Economica, August 1963, pp. 262–276. Sengupta, J. K.: Recursive constraints and stochastic linear programming. Accepted for publication Metrika. Sengupta, J. K., C. Millham andG. Tintner: On the stability of solutions under error in stochastic linear programming. Metrika No. 3, 1964. Sengupta, J. K. andT. Kumar: An application of sensitivity analysis to a linear programming problem. Unternehmungsforschung, Vol. 9, 1965, pp. 18–36. Sengupta, J. K.: On the stability of truncated solutions of stochastic linear programming. Mimeographed, December 20, 1963. Department of Economics, Iowa State University. (Sent for publication.) Sengupta, J. K., G. Tintner andC. Millham: A weak duality theorem for stochastic linear programming. Unternehmensforschung, Vol. 7, 1963, pp. 1–8.     

Infrared laser spectra of HF and DF

The six lowest states, dissociating into the $\text{(}{}^2\text{P)}\text{Al}\text{(}{}^4\text{S)}\text{N}$ and $\text{(}{}^2\text{P)}\text{Al}\text{(}{}^2\text{D)}\text{N}$ atomic states, are calculated using a nonempirical pseudopotential for the representation of the atomic cores and an extensive CI. The ground state is assigned as ³Π, but the ¹Σ⁺ and ³Σ^? minima are less than 0.5 eV higher. The results are compared with the few experimental data.     

Two-dimensional time-dependent simulation of contaminant transport from a landfill

A numerical model to simulate solute transport in flowing groundwater is developed using finite-difference solutions to the groundwater flow equation and the solute transport equation.The use of the model is illustrated by its application to a problem of groundwater contamination in a waste-disposal area in Miami, Florida. The model integrates the effects of several factors that controlled changes in iron concentrations, and successfully reproduced the record of contamination observed during a one-year period.The model was found to be insensitive to chemical parameters, but sensitive to an aquifer dispersion coefficient and the groundwater flow velocity. This implies that there can be sites where the chemical attenuation can be approximated without a significant impact on results.     

Magneto-elastic stresses of an infinite anisotropic medium with cylindrical hole

The paper is concerned with the derivation of a two dimensional theory of magneto-elasticity of anisotropic solids with cylindrical hole. The theory has been developed in complex variable formalism and illustrated by considering a particular type of magnetic field.Lastly, the authors are grateful to the Referee for his useful suggestions for the improvement of the paper.     

Interactions of 10.6 GeV/nucleon gold nuclei in nuclear emulsion

Stacks of nuclear emulsion were exposed at the Brookhaven AGS to a 10.6 GeV/n beam of gold nuclei in the BNL 868 experiment. A preliminary analysis of the main features of the interactions of these nuclei is reported here and compared with those observed previously at lower energies,E<1 GeV/n. The multiplicity and pseudo-rapidity distributions of the singly charged particles emitted both in central and in minimum bias samples of interactions have been analyzed in order to look for any non random effects indicative of the nuclear state during the interactions. The fragmentation characteristics of the gold projectiles appear to be different at 10.6 GeV/n from those at ≦1 GeV/n incident energy. Fission of the gold projectiles, which was relatively frequent at low energy, is almost entirely suppressed. Some of alpha particles from the projectile are emitted with very large transverse momenta. In gold-emulsion interactions the residual target nuclei are significantly smaller than in oxygen and sulfur interactions in emulsion.