We investigate numerical valuation of cross-currency interest rate-based derivatives under Babbs' extended Vasicek-style model by numerical solution of the associated partial di erential equation (PDE) | in particular, we consider the terminable di erential (di ) swap. Firstly we precisely formulate, in terms of their cash ows, various types of single and cross-currency swaps and swaptions. We ...

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...

Deterministic di€erential equation models indicate that partnership concurrency and non-homogeneous mixing patterns play an important role in the spread of sexually transmitted infections. Stochastic discreteindividual simulation studies arrive at similar conclusions, but from a very di€erent modeling perspective. This paper presents a stochastic discrete-individual infection model that helps t...

This article shows how a (linear) scale-space representation can be de ned for discrete signals of arbitrary dimension. The treatment is based upon the assumptions that (i) the scale-space representation should be de ned by convolving the original signal with a one-parameter family of symmetric smoothing kernels possessing a semi-group property, and (ii) local extrema must not be enhanced when ...

in this paper, we prove the existence of the solution for boundary value prob-lem(bvp) of fractional dierential equations of order q 2 (2; 3]. the kras-noselskii's xed point theorem is applied to establish the results. in addition,we give an detailed example to demonstrate the main result.

A large number of di erential equation problems which admit traveling waves have very large (typically in nite) naturally de ned domains, with boundary conditions de ned at the domain boundary. To be able to numerically solve these problems in smaller subdomains of the original domain, arti cial boundary conditions must be de ned for these subdomains. One such arti cal boundaryconditionswhich c...

Mycobacterium smegmatis contains three chaperonin (cpn60) genes homologous to the Escherichia coli groEL gene. One of these (cpn60.1) is required for biofilm formation, but is nonessential, whereas a second (cpn60.2) is essential. Mycobacterium smegmatis is unique among Mycobacteria in having a third chaperonin gene, cpn60.3. The cpn60.1 gene has a gene upstream (cpn10) that is homologous to th...

Game theory is concerned with optimization problems involving several players with conicting interests. Di erential games are an interesting area inside this eld in which the problem is formulated by means of dynamical systems. In spite that the theoretical solution of di erential games is well known, faced with large-scale, complex systems, analytical or, even, numerical methods are not usuall...

This paper summarizes recent results on the number and characterization of di erential invariants of transformation groups Generalizations of theorems due to Ovsiannikov and to M Green are presented as well as a new approach to nding bounds on the number of independent di erential invariants Consider a group of transformations acting on a jet space coordinatized by the inde pendent variables th...

Herein, an averaging theory for the solutions to Cauchy initial value problems of arbitrary order, "-dependent parabolic partial di erential equations is developed. Indeed, by directly developing bounds between the derivatives of the fundamental solution to such an equation and derivatives of the fundamental solution of an \averaged" parabolic equation, we bring forth a novel approach to compar...