On nonoscillatory solutions of differential inclusions

This paper introduces a nonoscillatory theory for differential inclusions based on fixed point theory for multivalued maps.

     

Representing the mean residual life in terms of the failure rate

In survival or reliability studies, the mean residual life or life expectancy is an important characteristic of the model. Whereas the failure rate can be expressed quite simply in terms of the mean residual life and its derivative, the inverse problem—namely that of expressing the mean residual life in terms of the failure rate—typically involves an integral of a complicated expression. In this paper, we obtain simple expressions for the mean residual life in terms of the failure rate for certain classes of distributions which subsume many of the standard cases. Several results in the literature can be obtained using our approach. Additionally, we develop an expansion for the mean residual life in terms of Gaussian probability functions for a broad class of ultimately increasing failure rate distributions. Some examples are provided to illustrate the procedure.     

Modes of vibrations due to (U-center + additive anion impurities) in KC1—II

Defect modes due to U-centers in potassium chloride containing additive anion impurities have been computed by Green's functions techniques. Local vibrations due to U-centers in alkali halides have cubic symmetry, but when one of the twelve nearest neighbour anions is replaced by an additive impurity, the site symmetry of the system reduces from O_h to C_2v and gives rise to new vibrational modes. The phonon Green's functions have been analysed according to the irreducible representation of the point group symmetry, pertaining to the substitutional impurity. We have considered the vibrations of the U-center, additive anion impurity and their nearest neighbours i.e. 36-dimensional defect space. Using group theory, symmetry coordinates were constructed and the 36 x 36 dimensional matrix was block diagonalised into various irreducible representations. The computed local mode frequencies have been conpared with the experimental measurements. Reasonably good agreement is found between them. The computed results for resonant mode frequencies are also displayed.     

Band structural properties of MoS2 (molybdenite)

Semiconductivity and superconductivity in MoS₂ (molybdenite) can be understood in terms of the band structure of MoS₂. We present here the band structural properties of MoS₂. The energy dependence of n_eff and ε_xeff is investigated. Using calculated values of n_eff and ε_xeff, the Penn gap has been determined. The value thus obtained is shown to be in good agreement with the reflectivity data and also with the value obtained from the band structure. The Ravindra and Srivastava formula has been shown to give values for the isobaric temperature gradient of $\text{E}{}_{\mathrm{G}}\text{[}\text{(?E}{}_{\mathrm{G}}\text{?T)}{}_{\mathrm{P}}\text{]}$, which are in agreement with the experimental data, and the contribution to $\text{(}\text{?E}{}_{\mathrm{G}}\text{?T)}{}_{\mathrm{P}}$ due to the electron lattice interaction has been evaluated. In addition, the electronic polarizability has been calculated using a modified Lorentz-Lorenz relation.     

An Incremental Algorithm for the Maximum Flow Problem

An incremental algorithm may yield an enormous computational time saving to solve a network flow problem. It updates the solution to an instance of a problem for a unit change in the input. In this paper we have proposed an efficient incremental implementation of maximum flow problem after inserting an edge in the network G. The algorithm has the time complexity of O((n)² m), where n is the number of affected vertices and m is the number of edges in the network. We have also discussed the incremental algorithm for deletion of an edge in the network G.     

Analysis of anharmonic and thermoelastic properties of non-centrosymmetric crystals

In the present paper an analytical potential form is used for overlap repulsive energy, derived by Harrison from quantum mechanical considerations, along with the composite effect of three-body forces and intersublattice displacement. The short-range overlap parameters in Harrison's potential form have direct correlation with the valence state energies for outermost electrons. The potential model is applied to calculate the third and fourth order elastic constants, first and second pressure derivatives of second order elastic constants, Grüneisen parameter and its volume dependence, Anderson parameter, and thermal expansion coefficient for three non-centrosymmetric crystals, viz. CaF₂, SrF₂ and BaF₂. The calculated values of various physical quantities are found to be in good agreement with experimental data.The authors are grateful to Dr. Mansour Khalef, the Head of Physics Department, TNRC, Tajura (Tripoli) for the facilities and encouragements.     

Electrical conductivity studies of cobalt-precipitation in RbCl crystals

The results of electrical conductivity measurements in heavily doped RbCl:CoCl₂ crystals with 2500 and 6000 ppm of cobalt are being reported in this paper. The different regions of the conductivity plots for the crystals with the two concentrations of cobalt have been explained and relevant energy parameters determined. The crystals with 6000 ppm of cobalt have been found to contain two types of precipitates one of these being of the same type as that existing in RbCl crystals with 2500 ppm of cobalt while the other being of a different composition. Further, it has been found that the crystals appear blackened after heating during measurements. The blackening has been attributed to the expulsion of cobalt from the bulk of the crystal which forms an oxide at the surface.     

On composition of some general fractional integral operators

In the present paper we derive three interesting expressions for the composition of two most general fractional integral oprators whose kernels involve the product of a general class of polynomials and a multivariableH-function. By suitably specializing the coefficients and the parameters in these functions we can get a large number of (new and known) interesting expressions for the composition of fractional integral operators involving classical orthogonal polynomials and simpler special functions (involving one or more variables) which occur rather frequently in problems of mathematical physics. We have mentioned here two special cases of the first composition formula. The first involves product of a general class of polynomials and the Fox’sH-functions and is of interest in itself. The findings of Buschman [1] and Erdélyi [4] follow as simple special cases of this composition formula. The second special case involves product of the Jacobi polynomials, the Hermite polynomials and the product of two multivariableH-functions. The present study unifies and extends a large number of results lying scattered in the lierature. Its findings are general and deep.