Maximum probability dominance and portfolio theory

The concept of probability dominance and some of its parametric and nonparametric aspects are explored here in comparing two or more competing portfolios of returns. These aspects deal with the theory of stochastic dominance and that of mean-variance efficiency, which have been applied frequently in portfolio literature. Some illustrative applications are also developed here for evaluating the performance of mutual fund portfolios.Grateful thanks are due to P. L. Yu and the anonymous referee for their many constructive suggestions.     

Homogeneous deformation theory for noncentrosymmetric ionic crystals in quadratic response regime: Antipiezoelectricity

We derive expressions for the third-order elastic, piezoelectric, and dielectric constants, in terms of the interaction potential, and show that in fluorite structure, equal and opposite dipole moments under homogeneous strain develop. The presence of such latent polarisation is reflected in the dielectric response of the strained crystal.     

A new 2-form for connections on surfaces with boundary

A natural gauge-invariant 2-form is introduced on the space of connections over a compact oriented surface with boundary. It is shown that this 2-form descends to the moduli space of flat connections, under a group of based gauge transformations. An explicit expression (in terms of holonomy variations) is given for the resulting 2-form, and it is related to the symplectic structure of the extended moduli space introduced by L. C. Jeffrey.     

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.