Annealing of electron irradiated GaP studied by positron lifetime technique

GaP single crystals were irradiated by 3 MeV electrons at 20 K to a dose of 4 × 10¹⁸ e/cm². An isochronal annealing in temperature region 77 ÷ 650 K followed the irradiation. Positron lifetime measurement indicated the presence of irradiation-induced vacancies in Ga sublattice. The vacancies disappeared at two stages observed at temperatures 200 ÷ 300 K and 450 ÷ 550 K.     

Multivariate Liouville distributions

A random vector (X₁, …, X_n), with positive components, has a Liouville distribution if its joint probability density function is of the formf(x₁ + … + x_n)x₁^a₁.1 … x_n^a_n.1 with thea_i all positive. Examples of these are the Dirichlet and inverted Dirichlet distributions. In this paper, a comprehensive treatment of the Liouville distributions is provided. The results pertain to stochastic representations, transformation properties, complete neutrality, marginal and conditional distributions, regression functions, and total positivity and reverse rule properties. Further, these topics are utilized in various characterizations of the Dirichlet and inverted Dirichlet distributions. Matrix analogs of the Liouville distributions are also treated, and many of the results obtained in the vector setting are extended appropriately.     

A multiplicative Gauss-Newton minimization algorithm:Theory and application to exponential functions

Multiplicative calculus(MUC) measures the rate of change of function in terms of ratios, which makes the exponential functions significantly linear in the framework of MUC.Therefore, a generally non-linear optimization problem containing exponential functions becomes a linear problem in MUC. Taking this as motivation, this paper lays mathematical foundation of well-known classical Gauss-Newton minimization(CGNM) algorithm in the framework of MUC. This paper formulates the mathematical derivation of proposed method named as multiplicative Gauss-Newton minimization(MGNM) method along with its convergence properties.The proposed method is generalized for n number of variables, and all its theoretical concepts are authenticated by simulation results. Two case studies have been conducted incorporating multiplicatively-linear and non-linear exponential functions. From simulation results, it has been observed that proposed MGNM method converges for 12972 points, out of 19600 points considered while optimizing multiplicatively-linear exponential function, whereas CGNM and multiplicative Newton minimization methods converge for only 2111 and 9922 points, respectively. Furthermore, for a given set of initial value, the proposed MGNM converges only after 2 iterations as compared to 5 iterations taken by other methods. A similar pattern is observed for multiplicatively-non-linear exponential function. Therefore, it can be said that proposed method converges faster and for large range of initial values as compared to conventional methods.     

Loss of collectivity in 79Rb

High-spin states in ⁷⁹Rb were populated in the reaction at E(beam) = 60 MeV. The lifetimes of the excited states of the positive-parity yrast band and of the negative-parity band in ⁷⁹Rb were measured by the Doppler Shift Attenuation Method. The deduced transition quadrupole moments Q_t are found to have a decreasing trend with rotational frequency for both the bands, consistent with those found experimentally in neighbouring nuclei. An erratum to this article is available at .     

Biological activity of aldose reductase and lipophilicity of pyrrolyl-acetic acid derivatives

Quantitative Structure-Activity Relationship modeling is a powerful approach for correlating an organic compound to its lipophilicity. In this paper QSAR models are established for estimation of correlation of the lipophilicity of a series of pyrrolyl-acetic acid derivatives, inhibitors of the aldose reductase enzyme, in the n-octanol-water system with biological activity of aldose reductase. Lipophilicity, expressed by the logarithm of n-octnol-water partition coefficient log P and biological activity of aldose reductase inhibitory activity by log it. Result obtained by QSAR modeling of compound series reveal a definite trend in biological activity and a further improvement in quantitative relationships are established if, beside log P, Hammett electronic constant σ and connectivity index chi-3 (³ χ) term included in the regression equation.     

Calibration of a stochastic health evolution model using NHIS data

This paper presents and calibrates an individual’s stochastic health evolution model. In this health evolution model, the uncertainty of health incidents is described by a stochastic process with a finite number of possible outcomes. We construct a comprehensive health status index (HSI) to describe an individual’s health status, as well as a health risk factor system (RFS) to classify individuals into different risk groups. Based on the maximum likelihood estimation (MLE) method and the method of nonlinear least squares fitting, model calibration is formulated in terms of two mixed-integer nonlinear optimization problems. Using the National Health Interview Survey (NHIS) data, the model is calibrated for specific risk groups. Longitudinal data from the Health and Retirement Study (HRS) is used to validate the calibrated model, which displays good validation properties. The end goal of this paper is to provide a model and methodology, whose output can serve as a crucial component of decision support for strategic planning of health related financing and risk management.     

An improved approximation algorithm for requirement cut

This note presents improved approximation guarantees for the requirement cut problem: given an n-vertex edge-weighted graph G=(V,E), and g groups of vertices X₁,…,X_g⊆V with each group X_i having a requirement r_i between 0 and |X_i|, the goal is to find a minimum cost set of edges whose removal separates each group X_i into at least r_i disconnected components. We give a tight Θ(logg) approximation ratio for this problem when the underlying graph is a tree, and show how this implies an O(logk⋅logg) approximation ratio for general graphs, where .     

A Fourier transform speckle method to determine the change in angle of illumination

It is analytically shown that the position of the Fourier transform of the speckle pattern produced by a coherently illuminated, diffusely reflecting surface depends upon its angle of illumination. A method is proposed to measure small changes in this angle by doubly exposing the photographic plate with the original and laterally displaced Fourier transforms of the object speckle. The method is well suited for accurate measurements of the wedge angle and tilt of optical surfaces and to determine variations in refractive index or temperature of axially symmetric phase objects.