Influence of momentum-dependent interactions on balance energy and mass dependence⋆

We aim to understand the role of momentum-dependent interactions in transverse flow as well as in its disappearance. For the present study, central collisions involving masses between 24 and 394 are considered. We find that the momentum-dependent interactions have different impact in lighter colliding nuclei compared to heavier colliding nuclei. In lighter nuclei, the contribution of the mean field towards flow is smaller compared to heavier nuclei where binary nucleon-nucleon collisions dominate the scene. The inclusion of momentum-dependent interactions also explains the energy of the vanishing flow in the ¹²C + ¹²C reaction which otherwise was not possible with the static hard equation of state. An excellent agreement of our theoretical attempt is found for balance energy with experimental data throughout the periodic table.     

Weak invariance of the multidimensional rank statistic for nonstationary absolutely regular processes

In this paper, we study the weak invariance of the multidimensional rank statistic when the underlying random variables are nonstationary absolutely regular.     

Differential pulse polarographic determination of uranium(VI) in complex materials after adsorption of its trifluoroethylxanthate cetyltrimethylammonium ion-associated complex on naphthalene adsorbent.

Uranium(VI) is adsorbed as a uranium trifluoroethylxanthate (TFEX)-cetyltrimethylammonium (CTMA) ion-pair complex on microcrystalline naphthalene quantitatively in the pH range 4.2 - 7.0. Without cetyltrimethylammonium as the counter ion, the adsorption is hardly 70%. The metal has been desorbed with HCI and determined with a differential pulse polarograph. Uranium can alternatively be quantitatively adsorbed on TFEX-CTMA-naphthalene adsorbent packed in a column at a flow rate of 1 - 5 ml/min and determined similarly. A well-defined peak has been obtained in this medium at -0.20 V versus a saturated calomel electrode. Cyclic voltammetry, differential pulse polarography and D.C. polarography studies indicate that uranium has been reduced irreversibly under these conditions. The detection limit is 0.30 microg/ml at the minimum instrumental settings (signal-to-noise ratio of 2) (with a preconcentration factor of 10, the detection limit would be 30 ng/ml for uranium when the volume in the cell is 15 ml). However if the volume in the cell is 5 ml, it would have been 10 ng/ml with a preconcentration factor of 30. Linearity is maintained in a concentration range of 0.5 - 19.0 microg/ml (2.1 - 79.83 x 10(-9) M) with a correlation factor of 0.9994 and a relative standard deviation of +/-1.1% (in this case 7.5 microg may be concentrated from 150 ml of the aqueous sample where its concentration is as low as 50 ng/ml). Various parameters, such as the effect of the pH, volume of the aqueous phase, flow rate and the interference of a large number of metal ions and anions on the determination of uranium, have been studied in detail to optimize the conditions for its trace determination in various complex materials, like alloys, coal fly ash, biological, synthetic, and waste-water samples.     

A numerical method for computing radially symmetric solutions of a dissipative nonlinear modified Klein‐Gordon equation

In this article we develop a finite‐difference scheme to approximate radially symmetric solutions of a dissipative nonlinear modified Klein‐Gordon equation subject to smooth initial conditions ? and ψ in an open sphere D around the origin, with constant internal and external damping coefficients—β and γ, respectively—, and nonlinear term of the form G′(w) = w^p, with p > 1 an odd number. The functions ? and ψ are radially symmetric in D, and ?, ψ, r?, and rψ are assumed to be small at infinity. We prove that our scheme is consistent order ??(Δt²) + ??(Δr²) for G′ identically equal to zero and provide a necessary condition for it to be stable order n. Part of our study will be devoted to compare the physical effects of β and γ. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005     

Maximum and minimum weighted diagonal sums of certain non-negative matrices

This paper extends the notion of diagonal sums of a square matrix to “weighted diagonal sums”. Using simple probabilistic arguments, most of the results of Wang [5] concerning the maximum and minimum diagonal sums of doubly stochastic matrices are extended to maximum and minimum weighted diagonal sums of stochastic matrices (Sec. 3). Two stronger versions of one of Wang's conjectures are also proven (Theorems 4.1 and 5.1), of which the latter easily generalizes to the case of non-negative matrices (Theorem 5.2). The paper ends with a few open questions and counter-examples.     

Some regularities within the Stark widths and shifts of resonance ion lines from Li to Ca

A periodic dependence of the Stark widths and shifts of resonance lines, for singly- and doubly-ionized elements, has been found on nuclear charge number Z. These periodicities were found for Griem's theoretical values of the Stark parameters of resonance lines of some singly charged ions from Li to Ca; for other singly- and doubly- charged ions, this parameter was calculated from Griem's semiempirical formula. The dependence of the Stark parameters of the resonance lines on atomic polarizability X has been determined and used to estimate Stark widths and shifts for other singly-charged ions. These values are compared with estimates derived form Griem's semiempirical formula for the Gaunt factor g = 0.2.     

Mixed Ligand Complexes of Chromium (III) Ethylenediamine Tartrate: A Polarographic Study

Polarographic techniques have been used to investigate the complexing behaviour of chromium (III)-ethylenediamine-tartrate in aqueous solution. These complexes are reduced irreversibly at the dropping mercury electrode. The stability constants have been calculated by the method of Sundaresan and Sundaram. The values of the kinetic parameters; standard rate constant (K_s), transfer coefficient (α) and activation energy (Q) have also been calculated in each case.     

Asymptotically distribution-free aligned rank order tests for composite hypotheses for general multivariate linear models

For general multivariate linear models, a composite hypothesis does not usually induce invariance of the joint distribution under appropriate groups of transformations, so that genuinely distribution-free tests do not usually exist. For this purpose, some aligned rank order statistics are incorporated in the proposal and study of a class of asymptotically distribution-free tests. Tests for the parallelism of several multiple regression surfaces are also considered. Finally the optimal properties of these tests are discussed.Work supported by the Air Force Office of Scientific Research, AFSC, USAF, Contract Nos: AFOSR-74-2736 and AFOSR-76-2927. Reproduction in whole or part is permitted for any purpose of the U.S. Government