On a stochastic hyperbolic integro-differential equation

In this paper we study an initial-boundary-value problem for a hyperbolic integro-differential equation with random memory and a random noise. We establish the existence, uniqueness and exponential stability of solutions. Our method consists of finite-dimensional approximation and energy estimates.     

A new VOF‐based numerical scheme for the simulation of fluid flow with free surface. Part II: application to the cavity filling and sloshing problems

Finite element analysis of fluid flow with moving free surface has been performed in 2‐D and 3‐D. The new VOF‐based numerical algorithm that has been proposed by the present authors (Int. J. Numer. Meth. Fluids, submitted) was applied to several 2‐D and 3‐D free surface flow problems. The proposed free surface tracking scheme is based on two numerical tools; the orientation vector to represent the free surface orientation in each cell and the baby‐cell to determine the fluid volume flux at each cell boundary. The proposed numerical algorithm has been applied to 2‐D and 3‐D cavity filling and sloshing problems in order to demonstrate the versatility and effectiveness of the scheme. The proposed numerical algorithm resolved successfully the free surfaces interacting with each other. The simulated results demonstrated applicability of the proposed numerical algorithm to the practical problems of large free surface motion. It has been also demonstrated that the proposed free surface tracking scheme can be easily implemented in any irregular non‐uniform grid systems and can be extended to 3‐D free surface flow problems without additional efforts. Copyright © 2003 John Wiley & Sons, Ltd.     

SEQUENTIAL QUADRATIC PROGRAMMING METHODS FOR OPTIMAL CONTROL PROBLEMS WITH STATE CONSTRAINTS

A Kind of direct methods is presented for the solution of optimal control problems with state constraints.These methods are sequential quadratic programming methods.At every iteration a quadratic programming which is obtained by quadratic approximation to Lagrangian function and Linear approximations to constraints is solved to get a search direction for a merit function.The merit function is formulated by augmenting the Lagrangian funetion with a penalty term.A line search is carried out along the search direction to determine a step length such that the merit function is decreased.The methods presented in this paper include continuous sequential quadratic programming methods and discreate sequential quadrade programming methods.     

Photon gluon fusion cross sections at HERA energy

We present cross sections for heavy flavour production through photon gluon fusion in electron proton collisions at HERA energy. The electron photon vertex is taken into account explicitly, and theQ ² of the exchanged photon ranges from nearly zero (almost real photon) to the kinematically allowed maximum. In our approach the scale is set by the mass of the produced quarks. Our formalism is also applicable to the production of light quarks as long as the invariant mass of the pair is sufficiently high, so we also give cross sections for \(u\bar u,d\bar d\) and \(s\bar s\) production.     

Asymmetric Diels-Alder reactions with 5-menthyloxy-2-(5H)-furanone

A new class of chiral dienophiles, 5-alkoxy-2(5H)-furanones, has been developed. Both enantiomers of 5-menthyloxy-2(5H)-ftiranone are readily available in enantiomerically pure form, starting from furfural and d- or l-menthol. Excellent diastereoselectivities (d.e. β99%) are obtained in thermal Diels-Alder reactions with several cyclic and acyclic dienes. The use of silyl dienol ethers has resulted in new routes to enantiomerically pure cyclohexanones in a highly regioselective manner.