L^(p)-solutions of Multi-dimensional Oblique Reflected BSDEs and Optimal Switching Problem on Finite or Infinite Time Horizon

In this paper,we study mulit-dimensional oblique reflected backward stochastic differential equations(RBSDEs)in a more general framework over finite or infinite time horizon,corresponding to the pricing problem for a type of real option.We prove that the equation can be solved uniquely in L^(p)(1<p≤2)-space,when the generators are uniformly continuous but each component taking values independently.Furthermore,if the generator of this equation fulfills the infinite time version of Lipschitzian continuity,we can also conclude that the solution to the oblique RBSDE exists and is unique,despite the fact that the values of some generator components may affect one another.

A study on the surface overpressure distribution and formation of a double curvature liner under a two-point initiation

The formation mechanism of an EFP(explosively formed projectile)using a double curvature liner under the overpressure effect generated by a regular oblique reflection was investigated in this paper.Based on the detonation wave propagation theory,the change of the incident angle of the detonation wave collision at different positions and the distribution area of the overpressure on the surface of the liner were calculated.Three dimensional numerical simulations of the formation process of the EFP with tail.as well as the ability to penetrate 45#steel were performed using LS-DYNA software,and the EFP ve locity,the penetration ability,and the forming were assessed via experiments and x_ray photographs.The experimental results coincides with those of the simulations.Results indicate that the collision of the detonation wave was controlled to be a regular oblique reflection acting on the liner by setting the di-mensions of the unit charge and maintai ning the pressure at the collision point region at more than 2.4 times the CJ detonation when the incident angle approached the cnitical angle.The distance from the liner midline to the boundary of the area within which the pressure ratio of the regular oblique reflection pressure to the qJ detonation pressure was greater than 2.5,2,and 15was approximately 0.66 mm,132 mm,and 3.3 mm,respectively.Itis noted that pressure gradient caused the liner to turn inside out in the middle to form the head of the EFP and close the two tails of the EFP at approximately 120μs.The penetration depth of the EFP into a 45#steel target exceeded 30 mm,and there was radial expansion between the head and tail of the EFP,increasing the penetration resistance of the EFP.Therefore,the structural size of the unit charge and the liner can be further optimized to reduce resist ance to increase the penetration ability of the EFP.

NUMERICAL SIMULATION FOR DYNAMIC INITIAL SHOCK PARAMETERS OF COUPLING CHARGE ON BOREHOLE WALL UNDER THE ACTION OF HIGH EXPLOSIVES

According to detonation theory and hydrodynamic principle, a physical model has been set up in this paper. Based on the model a methodology for calculating dynamic initial shock parameters such as shock pressure pm shock wave velosity Dm etc. of coupling charge on borehole wall has ben developed. The shock parameters have been calculated when high explosives works on granite, limestone and marble respectively. The magnitude of every parameter on borehole wall has been obtained from ignited dot to the end of borehole along axial direction. Some important conclusions are also gained.

WEAK APPROXIMATION OF OBLIQUELY REFLECTED DIFFUSIONS IN TIME-DEPENDENT DOMAINS

In an earlier paper, we proved the existence of solutions to the Skorohod problem with oblique reflection in time-dependent domains and, subsequently, applied this result to the problem of constructing solutions, in time-dependent domains, to stochastic differential equations with oblique reflection. In this paper we use these results to construct weak approximations of solutions to stochastic differential equations with oblique reflection, in time-dependent domains in Rd, by means of a projected Euler scheme. We prove that the constructed method has, as is the case for normal reflection and time-independent domains, an order of convergence equal to 1/2 and we evaluate the method empirically by means of two numerical examples. Furthermore, using a well-known extension of the Feynman-Kac formula, to stochastic differential equations with reflection, our method gives, in addition, a Monte Carlo method for solving second order parabolic partial differential equations with Robin boundary conditions in time-dependent domains.

Parallel detection and quantitative analysis of specific binding of proteins by oblique-incidence reflectivity difference technique in label-free format

In this work,we parallelly detected the specific binding between microarray targets including 12 different kinds of proteins and the probe solution containing five corresponding antibodies and quantitatively analyzed the interactions between CDH13 and solution phase anti-CDH13 at six different probe concentrations by oblique-incidence reflectivity difference(OIRD)method in label-free format.The detection sensitivity reached 10 ng/mL.The experimental results indicate that the OIRD method is a promising and competing technique not only in research work but also in clinic.

Invariance for Stochastic Differential Systems with Time-dependent Constraining Sets

The first part of this article presents invarlance criteria Ior a sl;ocnasl;lC （lllier^n~x^l ~qu^luu whose state evolution is constrained by time-dependent security tubes. The key results of this section are derived by considering an equivalent problem where the square of distance function represents a viscosity solution to an adequately defined partial differential equation. The second part of the paper analyzes the broader context when solutions are constrained by more general time-dependent convex domains. The approach relies on forward stochastic variational inequalities with oblique reflection, the generalized subgradients acting as a reacting process that operates only when the solution reaches the boundary of the domain.