Solutions to a gradient-dependent integro-differential parabolic problem arising in the pricing of financial options in a Lévy market

We study an integro-differential parabolic problem modeling a process with jumps arising in financial mathematics. Under suitable conditions, we prove the existence of solutions in a general domain by proving a uniform bound on an iterative sequence of solutions and then applying the Arzelà–Ascoli theorem.     

Numerical Solutions for Option Pricing Models Including Transaction Costs and Stochastic Volatility

The option pricing problem when the asset is driven by a stochastic volatility process and in the presence of transaction costs leads to solving a nonlinear partial differential equation. The nonlinear term in the PDE reflects the presence of transaction costs. Under a particular market completion assumption we derive the nonlinear PDE whose solution may be used to find the price of options. In this paper under suitable conditions, we give an algorithmic scheme to obtain the solution of the problem by an iterative method and provide numerical solutions using the finite difference method.     

Large deformation extensional rheology of bread dough

The stress–strain curves of bread dough were derived under uniaxial compression, uniaxial tension and equi-biaxial tension loading conditions. In uniaxial compression, a lubricant was used to eliminate frictional effects between the loading platens and the sample. In uniaxial tension, cylindrical samples with thin flat discs at both ends (‘I’ samples) were tested. The discs at both ends were allowed to air-dry and were subsequently glued onto the loading platens. In equi-biaxial tension, a thin disc of dough was inflated into a bubble using pressurised air. The thickness at the top of the bubble was measured by shining a light through the walls of the bubble and recording the change in light intensity as the wall becomes thinner. All methods ensured that uniform deformation was obtained. Stress and strain were accurately evaluated using image analysis techniques. The tests were performed at various strain rates and speeds that defined the time dependence of the material. A non-linear viscoelastic model based on the Prony series and Van der Waals hyperelasticity was used to predict all test data. The model had a total of five material parameters and two time constants, which were set to represent the actual time scales of the experiments. A reasonable agreement between the experimental data and the chosen material model was observed.     

Antisymmetric tensor fields in a generalized Randall–Sundrum scenario

Bulk antisymmetric tensor fields of different ranks have been studied in the context of a generalized Randall–Sundrum model with a non-vanishing induced cosmological constant on the visible brane. It is shown that instead of the usual exponential suppression of the couplings of the zero modes of these bulk fields with the brane fermions in the original Randall–Sundrum model, here the couplings are proportional to the brane cosmological constant. Thus in an era of large cosmological constant these fields have significant role in physical phenomena because of their enhanced couplings with the visible brane fermions.     

Spinning test particle in Kalb-Ramond background

In this work we explore the geodesic deviations of spinning test particles in a string inspired Einstein-Kalb-Ramond background. Such a background is known to be equivalent to a spacetime geometry with torsion. We have shown here that the antisymmetric Kalb-Ramond field has a significant effect on the geodesic deviation of a spinning test particle. A search for observational evidence of such an effect in astrophysical experiments may lead to a better understanding of the geometry of the background spacetime.Received: 5 April 2005, Revised: 19 May 2005, Published online: 8 July 2005     

Does a Kalb–Ramond field make spacetime optically active?

A spacetime with torsion produced by a Kalb–Ramond field coupled gravitationally to the Maxwell field, in accordance with a recent proposal by two of us (PM and SS), is argued to lead to optical activity in synchrotron radiation from cosmologically distant radio sources. We show that this indicates a very small, but possibly observable rotation of the plane of polarization of the radiation, above and beyond the Faraday rotation due to magnetized galactic plasma. Implications for heterotic string theory are outlined. Received: 27 October 2001 / Published online: 25 January 2002     

Biaxial deformation of dough using the bubble inflation technique. I. Experimental

The bubble inflation test has been used to determine the equi-biaxial stress-strain curve of flour/water dough. This was achieved by undertaking experimental measurements of strain, wall thickness and radius of curvature at the top of the bubble as well as applied pressure. It was observed that the bubble was spherical initially but changed to an elliptical shape at large strains. The analysis derived by Bloksma (1957) was also used to calculate stress and strain at the top of the inflated bubble from gauge pressure and bubble volume data. It was found that the analysis led to accurate bubble heights at moderate strains only, a consequence of the non-spherical bubble shape. In addition, at the top of the bubble, the analytical strain was larger and the thickness was much smaller than the experimental values. The bubble wall thickness distribution was more uniform than the analytical predictions. The discrepancies in bubble height, radius of curvature, strain and thickness had a major effect in the analytical stress-strain curve, as both stress and strain were overestimated, the stress being in error by a factor of four at large strains. Therefore, it is concluded that when the bubble inflation test is used, it is necessary that experimental readings of strain, thickness and radius of curvature as well as pressure should be made to ensure accurate stress-strain curves.     

Polyaniline Langmuir-Blodgett film based cholesterol biosensor

Cholesterol oxidase (ChOx) has been covalently linked to Langmuir-Blodgett (LB) monolayers of polyaniline (PANI)-stearic acid (SA) prepared onto indium-tin-oxide (ITO) coated glass plates via glutaraldehyde (Glu) chemistry. These ChOx/Glu/PANI-SA LB film/ITO electrodes have been characterized by FT-IR, cyclic voltammetry, and scanning electron microscopy, respectively. The results of response measurements carried out on these bioelectrodes using linear sweep voltammetry (LSV) reveal linearity from 25 to 400 mg/dL of cholesterol concentration with sensitivity of 88.9 nA mg(-1) dL. The linear regression analysis of bioelectrode reveals standard deviation and correlation coefficient of 0.737 microA and 0.9988, respectively. The low value of the Michaelis-Menten constant of these bioelectrodes obtained as 1.21 mM for the immobilized enzyme indicates increased interaction between ChOx and cholesterol in the PANI-SA LB film.     

Cold hydrogen-hydrogen scattering using CCA model

Cold hydrogen-hydrogen scattering has been investigated using close coupling approximation (CCA) model. The total wave function of the system is expanded in terms of atomic expansion basis. The effect of electron exchange and coupling to the continuum of both the atoms are taken into account. Singlet and triplet partial wave elastic and total cross-sections are presented and compared with existing theoretical predictions. Thermally averaged total cross-sections with respect to temperature are also provided along with their earlier results.     

Unprecedented π···π interaction between an aromatic ring and a pseudo-aromatic ring formed through intramolecular H-bonding in a bidentate Schiff base ligand: crystal structure and DFT calculations

A combination of a single crystal X-ray diffraction study and density functional theory calculations has been applied to a bidentate Schiff base compound to elucidate different cooperative non-covalent interactions involved in the stabilization of the keto form over the enol one in the solid state. The single crystal X-ray structure reveals a remarkable supramolecular assembly of the keto form through a cyclic hydrogen bonded dimeric motif. The most interesting feature in the supramolecular assembly is the formation of a 'dimer of dimer' motif by π···π, CH···π and N···O/O···O interactions in which the π···π interaction involving the aromatic phenyl ring and the intramolecularly hydrogen bonded pseudo-aromatic ring of the keto form lying just above or below the phenyl ring of the other dimer seems to be unprecedented. The optimized geometry of the hydrogen bonded dimeric motif of the keto form of the organic molecule has been obtained by DFT calculations and agrees very well with that found within the crystalline state. The X-ray crystallographic geometry of the 'dimer of dimer' has also been computed, which shows that in the HOMO, the π electrons are localized in the phenyl rings away from each other, while in the LUMO, there is a strong π-π interaction between the phenyl ring of one dimer with the pseudo-aromatic ring of another dimer with an energy estimated to be 7.95 kJ mol(-1). Therefore, on HOMO → LUMO excitation there is localization of π electrons in the central part of the complex moiety which plays a stabilizing role of the dimer of dimer motif in the solid state.