Some Theorems on Generalized Basic Hypergeometric Series

In an earlier paper the author has established two theorems on generalized hypergeometric functions. In each theorem a numerator differs from a denominator by a positive integer. These theorems were further used to prove some theorems on the sums of Kampe de Feriet functions. Here, we have established the theorems which are the basic analogues of the theorems proved in the earlier paper

Some Theorems on Generalized Hypergeometric Function and Kampe De Feriet Function

Two theorems on the sums of generalized hypergeometric functions have been established. The theorems have further been employed to prove some theorems on the sums of Kampe de Feriet functions

Fermi Surface Topology and Rashba-Edelstein Charge-Spin Conversion in Lead-Halide Perovskites

The conversion of charge current into spin current by the Rashba-Edelstein effect enables the reciprocal control of electron charge and magnetization in magnetoelectric and magneto-optical devices. The fundamentals of this effect are described in 3D lead-halide perovskites: due to spin-momentum locking, a strong charge-spin conversion, widely tunable by the injected charge density, is envisaged. The analysis highlights the close relationship between charge-spin conversion and the topological transition occurring from the low-density, torus-shaped Fermi surface (genus 1) to the high-density, simply connected Fermi surfaces (genus 0). At room temperature, spin-polarizations as large as approximate to 10% are obtained for input charge currents in the approximate to 102 to 106 Acm(-2) range; at low temperature, almost full spin-polarization can be achieved, owed to the large, impurity scattering-limited mobilities. The results qualify lead-halide perovskites as suitable materials for spin-orbitronic applications

Trace element distributions in Yamato-793605, a chip off the "martian lherzolite" block

In situ ion microprobe analyses of various phases in Yamato-793605 (Y79) confirm that it is very similar to the other two lherzolitic shergottites, ALHA77005 and LEW88516. Differences in absolute REE abundances between bulk samples of these meteorites can be largely accounted for by sample heterogeneity. The three lherzolites were formed by essentially identical processes and they may even have originated from the same lithological unit on Mars. Preservation of major element zonation in olivines of Y79 indicates that it is less equilibrated than the other lherzolitic shergottites, and may have crystallized at shallower depth. The parent magmas of lherzolitic shergottites, like those of other shergottites, were derived by partial melting of a partly depleted martian mantle

Toric Calabi-Yau supermanifolds and mirror symmetry

We study mirror symmetry of supermanifolds constructed as fermionic extensions of compact toric varieties. We mainly discuss the case where the linear sigma A-model contains as many fermionic fields as there are U(1) factors in the gauge group. In the mirror super-Landau-Ginzburg B-model, focus is on the bosonic structure obtained after integrating out all the fermions. Our key observation is that there is a relation between the super-Calabi-Yau conditions of the A-model and quasi-homogeneity of the B-model, and that the degree of the associated superpotential in the B-model is given in terms of the determinant of the fermion charge matrix of the A-model.Comment: 20 pages, v2: references adde

Open Business Models and Venture Capital Finance

We investigate the differences in venture capital (VC) governance of investee firms with Open Business Models, specifically Open Source Software (OSS), versus closed business models. Due to OSS’s pronounced complexity and uncertainty, we conjecture that VC-backed OSS firms are more frequently staged and syndicated. We present robust empirical evidence from the United States that OSS ventures have more financing rounds and are more likely to be syndicated, and mixed evidence that OSS ventures have a larger number of syndicated investors

Bulk Viscosity of Magnetized Neutron Star Matter

We study the effect of magnetic field on the bulk viscosity of nuclear matter in neutron stars. We employ the framework of relativistic mean field theory to observe the dense nuclear matter in neutron stars. The effects are first studied for the case when the magnetic field does not exceed the critical value to confine the electrons to the lowest Landau levels. We then consider the case of intense magnetic field to evaluate viscosity for the URCA processes and show that the inequality $p_{F}(e)+p_{F}(p)\geq p_{F}(n)$ is no longer required to be satisfied for the URCA processes to proceed.Comment: Latex 2e file with four postscripts figure