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

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

Electronic phase separation in the rare earth manganates, (La1-xLnx)0.7Ca0.3MnO3 (Ln = Nd, Gd and Y)

All the three series of manganates showsaturation magnetization characteristic of ferromagnetism, with the ferromagnetic Tc decreasing with increasing in x up to a critical value of x, xc (xc = 0.6, 0.3, 0.2 respectively for Nd, Gd, Y). For x > xc, the magnetic moments are considerably smaller showing a small increase around TM, the value of TM decreasing slightly with increase in x or decrease in . The ferromagnetic compositions (x xc) show insulator-metal (IM) transitions, while the compositions with x > xc are insulating. The magnetic and electrical resistivity behavior of these manganates is consistent with the occurrence of phase separation in the compositions around xc, corresponding to a critical average radius of the A-site cation, , of 1.18 A. Both Tc and TIM increase linearly when < rA > > or x xc as expected of a homogenous ferromagnetic phase. Both Tc and TM decrease linearly with the A-site cation size disorder at the A-site as measured by the variance s2. Thus, an increase in s2 favors the insulating AFM state. Percolative conduction is observed in the compositions with > < rAc >. Electron transport properties in the insulating regime for x > xc conforms to the variable range hopping mechanism. More interestingly, when x > xc, the real part of dielectric constant (e') reaches a high value (104-106) at ordinary temperatures dropping to a very small (~500) value below a certain temperature, the value of which decreases with decreasing frequency.Comment: 27 pages; 11 figures, Submitted to J.Phys:Condens Matte

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&nbsp;(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