Reconstruction of f(R) Gravity with Ordinary and Entropy-Corrected (m,n)-Type Holographic Dark Energy Model

In this assignment we will present a reconstruction scheme between f(R) gravity with ordinary and entropy corrected (m, n)-type holographic dark energy. The correspondence is established and expressions for the reconstructed f(R) models are determined. To study the evolution of the reconstructed models plots are generated. The stability of the calculated models are also investigated using the squared speed of sound in the background of the reconstructed gravities.     

Nematic-isotropic phase transition in lyotropic liquid crystals

We propose a Landau-de Gennes phenomenological model to describe the nematic-isotropic phase transition in lyotropic liquid crystals. The possibility of a first or second order transition is explored by means of the variation of the concentration of surfactant. We show that a Landau point on the nematic-isotropic phase transition line can be achieved under certain conditions. The theoretical predictions are found to be in good qualitative agreement with available experimental results.     

Sharp bounds for singular values of fractional integral operators

From the results of Dostanic [M.R. Dostanic, Asymptotic behavior of the singular values of fractional integral operators, J. Math. Anal. Appl. 175 (1993) 380-391] and V? and Gorenflo [Kim Tuan V?, R. Gorenflo, Singular values of fractional and Volterra integral operators, in: Inverse Problems and Applications to Geophysics, Industry, Medicine and Technology, Ho Chi Minh City, 1995, Ho Chi Minh City Math. Soc., Ho Chi Minh City, 1995, pp. 174-185] it is known that the jth singular value of the fractional integral operator of order α>0 is approximately (πj)^−α for all large j. In this note we refine this result by obtaining sharp bounds for the singular values and use these bounds to show that the jth singular value is (πj)^−α[1+O(j⁻¹)].     

A Fast Algorithm for Two-Dimensional Elliptic Problems

In this paper, we extend the work of Daripa et al. [14–16,7] to a larger class of elliptic problems in a variety of domains. In particular, analysis-based fast algorithms to solve inhomogeneous elliptic equations of three different types in three different two-dimensional domains are derived. Dirichlet, Neumann and mixed boundary value problems are treated in all these cases. Three different domains considered are: (i) interior of a circle, (ii) exterior of a circle, and (iii) circular annulus. Three different types of elliptic problems considered are: (i) Poisson equation, (ii) Helmholtz equation (oscillatory case), and (iii) Helmholtz equation (monotone case). These algorithms are derived from an exact formula for the solution of a large class of elliptic equations (where the coefficients of the equation do not depend on the polar angle when written in polar coordinates) based on Fourier series expansion and a one-dimensional ordinary differential equation. The performance of these algorithms is illustrated for several of these problems. Numerical results are presented.     

Singular integral transforms and fast numerical algorithms

Fast algorithms for the accurate evaluation of some singular integral operators that arise in the context of solving certain partial differential equations within the unit circle in the complex plane are presented. These algorithms are generalizations and extensions of a fast algorithm of Daripa [11]. They are based on some recursive relations in Fourier space and the FFT (Fast Fourier Transform), and have theoretical computational complexity of the order O(N) per point, where N² is the total number of grid points. An application of these algorithms to quasiconformal mappings of doubly connected domains onto annuli is presented in a follow-up paper.     

Phototoxicity of Some Bromine-Substituted Rhodamine Dyes: Synthesis, Photophysical Properties and Application as Photosensitizers

Abstract— The synthesis of some bromine-substituted rhodamine derivatives viz. , 4,5-dibromorhodamine methyl ester (dye 2) and 4,5-dibromorhodamine n -butyl ester (dye 3) are reported. These dyes were synthesized to promote a more efficient cancer cell photosensitizer for potential use in in vitro bone marrow purging in preparation for autologous bone marrow transplantation. Spectroscopic and photo-physical characterization of these dyes together with rhodamine 123 (dye 1) are reported in water, methanol, eth-anol and also in a microheterogeneous system, sodium dodecyl sulfate. The possible mechanism of photosensi-tization is characterized in terms of singlet oxygen efficiency of these dyes. Singlet oxygen quantum yields for bromine-substituted dyes are in the range of 0.3-0.5 depending on the solvent. For dye 1 no singlet oxygen production is found. The photodynamic actions of these dyes in different cell lines are tested. It was found that dye 2 and dye 3 are efficient photosensitizers and mediate eradication of K562, EM2, myeloid cell lines (CML) and the SMF-AI rhabdomyosarcoma line.