Hyperfine structure and isotope shift studies of rhenium by laser optogalvanic spectroscopy

Doppler-limited high resolution laser optogalvanic spectra of six transitions of rhenium lying in the range 560–620 nm have been recorded. Isotope shifts between the two natural isotopes of rhenium,¹⁸⁵Re and¹⁸⁷Re, have been calculated in all the six transitions. Hyperfine coupling constants for eight levels belonging to the configurations 5d ⁵6s ², 5d ⁶6s, 5d ⁴6s ²6p and 5d ⁵6s6p are reported. Wherever possible our constants are compared with those given by others.     

Electrical properties of the Ag2SO4-Na2SO4 binary system

A systematic investigation of the Ag₂SO₄-Na₂SO₄ binary system which forms a complete solid solution in the entire compositional range reveals the mobility of Ag⁺ as well as Na⁺. This is concluded on the basis of the appearance of two overlapping semicircles in the complex impedance plane. Transport number measurements using Tubandt and dc polarisation methods support the mobility of both ions. Further, the maximum conductivity for 30 Ag₂SO₄-70 Na₂SO₄ is due to optimum percolating paths resulting from lattice expansion. The decrease in conductivity beyond this, is caused by the increased interaction of Ag⁺ and Na⁺.     

Certain fractional derivative formulae involving the product of a general class of polynomials and the multivariableH-function

In the present paper, we obtain three unified fractional derivative formulae (FDF). The first involves the product of a general class of polynomials and the multivariableH-function. The second involves the product of a general class of polynomials and two multivariableH-functions and has been obtained with the help of the generalized Leibniz rule for fractional derivatives. The last FDF also involves the product of a general class of polynomials and the multivariableH-function but it is obtained by the application of the first FDF twice and it involves two independent variables instead of one. The polynomials and the functions involved in all our fractional derivative formulae as well as their arguments which are of the typex ^ρ Π _i=1 ^s (x ^t _i +α _i ) ^σ _i are quite general in nature. These formulae, besides being of very general character have been put in a compact form avoiding the occurrence of infinite series and thus making them useful in applications. Our findings provide interesting unifications and extensions of a number of (new and known) results. For the sake of illustration, we give here exact references to the results (in essence) of five research papers [2, 3,10, 12, 13] that follow as particular cases of our findings. In the end, we record a new fractional derivative formula involving the product of the Hermite polynomials, the Laguerre polynomials and the product ofr different Whittaker functions as a simple special case of our first formula.     

Hermitian quark matrices

Assuming a relation between the quark mass matrices of the two sectors a unique solution can be obtained for the CKM flavor mixing matrix. A numerical example is worked out which is in excellent agreement with experimental data.     

Studies on (non) energetic compounds

Five salts of dichloroanilinium bromide (DCABr) were prepared and characterized by elemental and spectral studies. The thermal decomposition of DCABr was studied by using TG-DTG-DTA techniques and the results are discussed here. Kinetic parameters with the help of model fitting and isoconversional methods have been evaluated critically. A mechanism of decomposition has also been suggested.     

A note on mixed summation-integral-type operators

Very recently Deo, in the paper “Simultaneous approximation by Lupas operators with weighted function of Szasz operators” [J. Inequal. Pure Appl. Math., 5, No. 4 (2004)] claimed to introduce the integral modifications of Lupas operators. These operators were first introduced in 1993 by Gupta and Srivastava. They estimated the simultaneous approximation for these operators and called them Baskakov-Szasz operators. There are several misprints in the paper by Deo. This motivated us to perform subsequent investigations in this direction. We extend the study and estimate a saturation result in simultaneous approximation for the linear combinations of these summation-integral-type operators. Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 8, pp. 1135–1139, August, 2007.     

Equation of state of finite-size hadrons: thermodynamical consistency

A method is presented to derive hadronic gas equation of state incorporating the effect of finite size of baryons in a thermodynamically consistent way. The model contains a more realistic picture of incorporating the effect of excluded volume unlike earlier methods. The results obtained by our calculation and those by the thermodynamically inconsistent methods used in many earlier works are compared.     

Effect of hadronic hard-core radius on the phase transition to an interacting quark-gluon plasma

The effect of volume corrections on the equations of state for the hadron gas by treating nucleons and antinucleons as hard-core particles or bags is studied. Its consequences on the critical values of temperatureT and chemical potential μ _B of the phase transition from a gas of finite sized hadrons to an interacting quark matter are explored.     

LMI approach to the global robust stability of a larger class of neural networks with delay

Sufficient conditions in the form of linear matrix inequality for the uniqueness and global asymptotic stability of the equilibrium point of a large class of uncertain neural networks with delay are presented. The conditions are based on norm-bounded uncertainties. An example is given to show the effectiveness of the obtained results. A comparison is made between the present approach and an earlier approach due to Lu, Rong and Chen. An error is corrected in an earlier publication.