Solutions to an 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 weak solutions to a more general integro-differential equation by using the Schaefer’s fixed point theorem and generalize the result to unbounded domains.     

A differential evolution-based regression framework for forecasting Bitcoin price

This research proposes a differential evolution-based regression framework for forecasting one day ahead price of Bitcoin. The maximal overlap discrete wavelet transformation first decomposes the original series into granular linear and nonlinear components. We then fit polynomial regression with interaction (PRI) and support vector regression (SVR) on linear and nonlinear components and obtain component-wise projections. The sum of these projections constitutes the final forecast. For accurate predictions, the PRI coefficients and tuning of the hyperparameters of SVR must be precisely estimated. Differential evolution, a metaheuristic optimization technique, helps to achieve these goals. We compare the forecast accuracy of the proposed regression framework with six advanced predictive modeling algorithms- multilayer perceptron neural network, random forest, adaptive neural fuzzy inference system, standalone SVR, multiple adaptive regression spline, and least absolute shrinkage and selection operator. Finally, we perform the numerical experimentation based on—(1) the daily closing prices of Bitcoin for January 10, 2013, to February 23, 2019, and (2) randomly generated surrogate time series through Monte Carlo analysis. The forecast accuracy of the proposed framework is higher than the other predictive modeling algorithms.

     

Harder–Narasimhan reduction for principal bundles over a compact Kähler manifold

Generalizing the Harder–Narasimhan filtration of a vector bundle it is shown that a principal G-bundle over a compact K?hler manifold admits a canonical reduction of its structure group to a parabolic subgroup of G. Here G is a complex connected reductive algebraic group; in the special case where , this reduction is the Harder–Narasimhan filtration of the vector bundle associated to by the standard representation of . The reduction of in question is determined by two conditions. If P denotes the parabolic subgroup, L its Levi factor and the canonical reduction, then the first condition says that the principal L-bundle obtained by extending the structure group of the P-bundle using the natural projection of P to L is semistable. Denoting by the Lie algebra of the unipotent radical of P, the second condition says that for any irreducible P-module V occurring in , the associated vector bundle is of positive degree; here is considered as a P-module using the adjoint action. The second condition has an equivalent reformulation which says that for any nontrivial character of P which can be expressed as a nonnegative integral combination of simple roots (with respect to any Borel subgroup contained in P), the line bundle associated to for is of positive degree. The equivalence of these two conditions is a consequence of a representation theoretic result proved here. Received: 10 November 1999 / Revised version: 31 October 2001 / Published online: 26 April 2002     

Spectroscopic studies on nanodispersions of CdS, HgS, their core-shells and composites prepared in micellar medium

CdS is a large band gap material compared to HgS. Both are interesting from academic and technological points of view. The nanodispersions (colloids) of CdS and HgS as well their core-shell products and composites (co-colloids) were prepared by varied modes of precursor addition in micellar solution of cationic surfactant cetyltrimethylammonium bromide (CTAB). The prepared dispersions were studied by spectroscopic and electron microscopic techniques.     

On some moduli spaces of stable vector bundles on cubic and quartic threefolds

We study certain moduli spaces of stable vector bundles of rank 2 on cubic and quartic threefolds. In many cases under consideration, it turns out that the moduli space is complete and irreducible and a general member has vanishing intermediate cohomology. In one case, all except one component of the moduli space has such vector bundles.     

THE PHOTODYNAMIC EFFECTS ONV–79 CHINESE HAMSTER CELLS

Abstract— Holding of acriflavine sensitizedV–79 cells in growth medium before visible light exposure decreases inactivation by visible light. The decrease depended upon the period of holding, indicating that there was release of cellular dye during this period. Exposures to visible light were done in two conditions: (a) with no dye in the medium during visible light exposure (washed) and (b) with dye in the medium during exposure (unwashed). Caffeine was found to slightly increase the sensitivity of the cells to visible light in the washed condition, whereas, in the unwashed condition no such effect was observed. Interaction studies with far UV did not reveal any correlation between photodynamic damage and UV damage. Visible light exposure of acriflavine sensitized cells was found to be mutagenic, as studied from the induction of 8-azaguanine resistant mutants. Inhibition of singlet oxygen production by sodium azide suppressed the induction of mutants. All these, taken together, have been discussed with respect to the relative importance of DNA and non-DNA damage in the photodynamic action of acriflavine.     

Polar modes with elastic restoring forces, “bose condensation” and the possibility of a metastable “ferroelectric” state

The system consists of an electric polarisation field coupled on the one hand to an elastic field and on the other to a thermal reservoir. When the polarisation modes are pumped, Bose condensation in the lowest mode occurs, for energy inflow above a certain critical amount. It is shown that elastic forces, called into play to stabilise the excitation of the polar modes, lowers the threshold for Bose condensation. With further increase in the pumping rate the possibility exists for the softening of the polarisation oscillations leading, in the presence of quartic self-interaction of the polarisation field (inserted for stability), to a metastable ferroelectric state. The work represents an attempt to develop a microscopic approach to the Fröhlich model for the dynamics of macromolecules (such as proteins and enzymes) of biological significance.     

Excitons and Bose–Einstein condensation in living systems

The problems connected with the transformations of energy in the living systems are reviewed. Possibility of Bose–Einstein condensation by input of radiant energy over a critical level is considered as a route for overcoming the barriers of activation energy under the conditions of a pump and a thermalizing environment. Molecular force fields constitute the pump. Under our scheme excitons constitute the major fraction of bosons to so condense. Instantaneous dipoles of London theory are then examined as excitons. Lastly an energy packet from a quantized dipolar field is suggested rather than the concept of “conformons.” Questions of charge and of other modes of energy transfer are briefly discussed.     

On the possibility of ‘Bose condensation’ in the excitation of coherent modes in biological systems

The phenomenon of Bose-Einstein condensation of phonons in biological structure, predicted by Fröhlich on the basis of rate equations, is approached here from a microscopic point of view. Rough estimates are compared with the recent experimental evidence of the action of coherent millimeter electromagnetic radiation on biological systems.     

Synthesis of Graphene and Its Applications: A Review

Graphene, one-atom-thick planar sheet of carbon atoms densely packed in a honeycomb crystal lattice, has grabbed appreciable attention due to its exceptional electronic and optoelectronic properties. The reported properties and applications of this two-dimensional form of carbon structure have opened up new opportunities for the future devices and systems. Although graphene is known as one of the best electronic materials, synthesizing single sheet of graphene has been less explored. This review article aims to present an overview of the advancement of research in graphene, in the area of synthesis, properties and applications, such as field emission, sensors, electronics, and energy. Wherever applicable, the limitations of present knowledgebase and future research directions have also been highlighted.