Origin of superconductivity in layered centrosymmetric LaNiGa2

The following article appeared in Applied Physics Letters , Vol. 104, 022603 (2014) and may be found at: http://dx.doi.org/10.1063/1.4862329We have examined the origin of superconductivity in layered centrosymmetric LaNiGa2 by employing a linear response approach based on the density functional perturbation theory. Our results indicate that this material is a conventional electron-phonon superconductor with intermediate level of coupling strength, with the electron-phonon coupling parameter of 0.70, and the superconducting critical temperature of 1.90 K in excellent accordance with experimental value of 1.97 K. The largest contribution to the electron-phonon coupling comes from the La d and Ga p electrons near the Fermi energy and the B3g phonon branch resulting from vibrations of these atoms along the Γ-Z symmetry line in the Brillouin zone. © 2014 AIP Publishing LLC

Phonon anomalies and superconductivity in the Heusler compound YPd 2Sn

The following article appeared in Journal of Applied Physics, Vol. 116, 013907 (2014) and may be found at: http://dx.doi.org/10.1063/1.4887355We have studied the structural and electronic properties of YPd 2Sn in the Heusler structure using a generalized gradient approximation of the density functional theory and the ab initio pseudopotential method. The electronic results indicate that the density of states at the Fermi level is primarily derived from Pd d states, which hybridize with Y d and Sn p states. Using our structural and electronic results, phonons and electron-phonon interactions have been studied by employing a linear response approach based on the density functional theory. Phonon anomalies have been observed for transverse acoustic branches along the [110] direction. This anomalous dispersion is merely a consequence of the strong coupling. By integrating the Eliashberg spectral function, the average electron-phonon coupling parameter is found to be λ=0.99. Using this value, the superconducting critical temperature is calculated to be 4.12K, in good accordance with the recent experimental value of 4.7K. © 2014 AIP Publishing LLC

Certain subclasses of multivalent functions defined by new multiplier transformations

In the present paper the new multiplier transformations \mathrm{{\mathcal{J}% }}_{p}^{\delta }(\lambda ,\mu ,l) (\delta ,l\geq 0,\;\lambda \geq \mu \geq 0;\;p\in \mathrm{% }%\mathbb{N} )} of multivalent functions is defined. Making use of the operator $\mathrm{{\mathcal{J}}}_{p}^{\delta }(\lambda ,\mu ,l),$ two new subclasses $\mathcal{P}_{\lambda ,\mu ,l}^{\delta }(A,B;\sigma ,p)$ and $\widetilde{\mathcal{P}}_{\lambda ,\mu ,l}^{\delta }(A,B;\sigma ,p)$\textbf{\ }of multivalent analytic functions are introduced and investigated in the open unit disk. Some interesting relations and characteristics such as inclusion relationships, neighborhoods, partial sums, some applications of fractional calculus and quasi-convolution properties of functions belonging to each of these subclasses $\mathcal{P}_{\lambda ,\mu ,l}^{\delta }(A,B;\sigma ,p)$ and $\widetilde{\mathcal{P}}_{\lambda ,\mu ,l}^{\delta }(A,B;\sigma ,p)$ are investigated. Relevant connections of the definitions and results presented in this paper with those obtained in several earlier works on the subject are also pointed out

Exact Fourier expansion in cylindrical coordinates for the three-dimensional Helmholtz Green function

A new method is presented for Fourier decomposition of the Helmholtz Green Function in cylindrical coordinates, which is equivalent to obtaining the solution of the Helmholtz equation for a general ring source. The Fourier coefficients of the Helmholtz Green function are split into their half advanced+half retarded and half advanced-half retarded components. Closed form solutions are given for these components in terms of a Horn function and a Kampe de Feriet function, respectively. The systems of partial differential equations associated with these two-dimensional hypergeometric functions are used to construct a fourth-order ordinary differential equation which both components satisfy. A second fourth-order ordinary differential equation for the general Fourier coefficent is derived from an integral representation of the coefficient, and both differential equations are shown to be equivalent. Series solutions for the various Fourier coefficients are also given, mostly in terms of Legendre functions and Bessel/Hankel functions. These are derived from the closed form hypergeometric solutions or an integral representation, or both. Numerical calculations comparing different methods of calculating the Fourier coefficients are presented

Erlangen Programme at Large: An Overview

This is an overview of Erlangen Programme at Large. Study of objects and properties, which are invariant under a group action, is very fruitful far beyond the traditional geometry. In this paper we demonstrate this on the example of the group SL(2,R). Starting from the conformal geometry we develop analytic functions and apply these to functional calculus. Finally we link this to quantum mechanics and conclude by a list of open problems. Keywords: Special linear group, Hardy space, Clifford algebra, elliptic, parabolic, hyperbolic, complex numbers, dual numbers, double numbers, split-complex numbers, Cauchy-Riemann-Dirac operator, M\"obius transformations, functional calculus, spectrum, quantum mechanics, non-commutative geometryComment: 77 pages, AMS-LaTeX, 12 figures (29 EPS graphic files); v2: section on QM was extende

Interacting Kasner-type cosmologies

It is well known that Kasner-type cosmologies provide a useful framework for analyzing the three-dimensional anisotropic expansion because of the simplification of the anisotropic dynamics. In this paper relativistic multi-fluid Kasner-type scenarios are studied. We first consider the general case of a superposition of two ideal cosmic fluids, as well as the particular cases of non-interacting and interacting ones, by introducing a phenomenological coupling function $q(t)$. For two-fluid cosmological scenarios there exist only cosmological scaling solutions, while for three-fluid configurations there exist not only cosmological scaling ones, but also more general solutions. In the case of triply interacting cosmic fluids we can have energy transfer from two fluids to a third one, or energy transfer from one cosmic fluid to the other two. It is shown that by requiring the positivity of energy densities there always is a matter component which violates the dominant energy condition in this kind of anisotropic cosmological scenarios.Comment: Accepted for publication in Astrophysics &Space Science, 8 page