The transformation which assigns to a linear operator L the recurrence satis ed by coe cient se quences of the polynomial series in its kernel is shown to be an isomorphism of the corresponding operator algebras We use this fact to help factoring q di erence and recurrence operators and to nd nice power series solutions of linear di erential equations In particular we characterize generalized h...

The Poisson-Boltzmann (PB) equation describes the electrostatic potential of a biomolecular system composed by a molecule in a solvent. The electrostatic potential is involved in biomolecular models which are used in molecular simulation. In consequence, nding an e cient method to simulate the numerical solution of PB equation is very useful. As a rst step, we establish in this paper a probabil...

A q-di erence analog of the sixth Painlev e equation is presented. It arises as the condition for preserving the connection matrix of linear q-di erence equations, in close analogy with the monodromy preserving deformation of linear di erential equations. The continuous limit and special solutions in terms of q-hypergeometric functions are also discussed. Mathematical Subject Classi cations (19...

In this paper we consider the pair di usion process in more than two spatial dimensions. In this case we are able to prove just a local existence result, since it is not possible to deduce global a priori estimates for the equations as it can be done in the two dimensional case. The model includes a nonlinear system of reaction{ drift{di usion equations, a nonlinear ordinary di erential equatio...

in this work, we have applied elzaki transform and he's homotopy perturbation method to solvepartial dierential equation (pdes) with time-fractional derivative. with help he's homotopy per-turbation, we can handle the nonlinear terms. further, we have applied this suggested he's homotopyperturbation method in order to reformulate initial value problem. some illustrative examples...

Three schemes for linearizing the transconductance of the basic di erential pair in subthreshold CMOS are examined: 1) multiple asymmetric di erential pairs, 2) source degeneration via symmetric di usors, and 3) source degeneration via a single di usor. Using a maximally at optimizing criterion, the linear range of the basic di erential pair can be increased by four-to-eight times.

An action system framework is a predicate transformer based method for modelling and analysing distributed and reactive systems. The actions are statements in Dijkstra's guarded command language, and their semantics is given by predicate transformers. We extend conventional action systems with a di erential action consisting of a di erential equation and an evolution guard. The semantics is giv...

We study parallel two-level overlapping Schwarz algorithms for solving nonlinear nite element problems, in particular, for the full potential equation of aerodynamics discretized in two dimensions with bilinear elements. The overall algorithm, Newton-Krylov-Schwarz (NKS), employs an inexact nite-di erence Newton method and a Krylov space iterative method, with a two-level overlapping Schwarz me...

We introduce and study the Koszul complex for a Hecke R-matrix. Its cohomologies, called the Berezinian, are used to de ne quantum superdeterminant for a Hecke R-matrix. Their behaviour with respect to Hecke sum of R-matrices is studied. Given a Hecke R-matrix in n-dimensional vector space, we construct a Hecke R-matrix in 2n-dimensional vector space commuting with a di erential. The notion of ...

The `volatility smile' is one of the well-known biases of Black-Scholes models for pricing options. In this paper, we introduce a robust method of reducing this bias by pricing subject to a deterministic functional volatility = (S; t). This instantaneous volatility is chosen as a spline whose weights are determined by a regularised numerical strategy that approximately minimises the di erence b...