On the Second Fundamental Theorem of Asset Pricing

Let $X^1,\ldots, X^d$ be sigma-martingales on $(\Omega,{\cal F}, P)$. We show that every bounded martingale (with respect to the underlying filtration) admits an integral representation w.r.t. $X^1,\ldots, X^d$ if and only if there is no equivalent probability measure (other than $P$) under which $X^1,\ldots,X^d$ are sigma-martingales. From this we deduce the second fundamental theorem of asset pricing- that completeness of a market is equivalent to uniqueness of Equivalent Sigma-Martingale Measure (ESMM)

Initial stages of cavitation damage and erosion on copper and brass tested in a rotating disk device

In view of the differences in flow and experimental conditions, there has been a continuing debate as to whether or not the ultrasonic method of producing cavitation damage is similar to the damage occurring in cavitating flow systems, namely, venturi and rotating disk devices. In this paper, the progress of cavitation damage during incubation periods on polycrystalline copper and brass tested in a rotating disk device is presented. The results indicate several similarities and differences in the damage mechanism encountered in a rotating disk device (which simulates field rotary devices) and a magnetostriction apparatus. The macroscopic erosion appears similar to that in the vibratory device except for nonuniform erosion and apparent plastic flow during the initial damage phase

Influence of Mo6+ on Dielectric properties of Copper Ferrites

Two series of copper ferrites are prepared using the chemical compositional formula Cu1.0-3y Fe2.0-2x Mox + yO4.0. They are calcinated at 750 C and sintered at 950C.When x =y = 0.0, the ε′ of the basic copper ferrite is probably due to electronic exchange interactions of copper and iron ions as Cu2+↔ Cu1+ and Fe3+↔ Fe2+. The observed value of dielectric constant (є′) decreases as a function of substituent concentration (x) up to x = 0.20 and for further values of ‘x’ it found to increase. In the case of ‘C’ (x = 0) series ferrites є′ decreases with substituent concentration (y) up to y = 0.04, later it found to increase. The dispersion of ac resistivity with frequency is observed indicating their strong dependence on frequency as in the case of dielectric behaviour. These results are explained with different possible mechanisms

A NOVEL VALIDATED UHPLC METHOD FOR ESTIMATION OF ASSAY AND ITS RELATED SUBSTANCES OF TRICHOSTATIN-A

Objective: The main objective of the research work is to develop and validate a rapid UHPLC method for the estimation of assay and its related substances of Trichostatin A (TSA) in pharmaceutical samples. Methods: The UHPLC method developed for chromatographic separation between TSA and its related compounds on Poroshell 120 SB C18(50×4.6) mm; 2.7 µm RRLC column using Agilent RRLC (UHPLC) system with linear gradient elution. Results: The developed UHPLC method has shown excellent chromatographic separation between TSA and its related compounds within 12 min run time, during validation experiments, specificity study revealed that the peak threshold was more than the peak purity and no purity flag was observed. Repeatability, intra, and inter-day precision results were well within the tolerable limits. Limits of detection concentrations were found between 0.075 to 0.077 ppm and the limit of quantitation is between 0.252 to 0.258 ppm for related compounds and TSA. The related substances method recoveries were found between 80 and 120 % and assay method recovery was found between 98.0 to 102.0%. Conclusion: The developed method capability was proven for the assay of TSA and its related compounds in pharmaceutical samples and the method shows eco-friendlier than routine, conventional HPLC methods in terms of analysis time, cost and HPLC effluent waste

Some experiences with the viscous-inviscid interaction approach

Methods for simulating compressible viscous flow using the viscid-inviscid interaction approach are described. The formulations presented range from the more familiar full-potential/boundary-layer interaction schemes to a method for coupling Euler/Navier-Stokes and boundary-layer algorithms. An effort is made to describe the advantages and disadvantages of each formulation. Sample results are presented which illustrate the applicability of the methods

Spin Decoherence from Hamiltonian dynamics in Quantum Dots

The dynamics of a spin-1/2 particle coupled to a nuclear spin bath through an isotropic Heisenberg interaction is studied, as a model for the spin decoherence in quantum dots. The time-dependent polarization of the central spin is calculated as a function of the bath-spin distribution and the polarizations of the initial bath state. For short times, the polarization of the central spin shows a gaussian decay, and at later times it revives displaying nonmonotonic time dependence. The decoherence time scale dep ends on moments of the bath-spin distribuition, and also on the polarization strengths in various bath-spin channels. The bath polarizations have a tendency to increase the decoherence time scale. The effective dynamics of the central spin polarization is shown to be describ ed by a master equation with non-markovian features.Comment: 11 pages, 6 figures Accepted for publication in Phys.Rev