The scattering of electromagnetic wave at oblique incidence in a homogeneous chiral medium

We consider the scattering of a time-harmonic electromagnetic wave by a perfectly and imperfectly conducting infinite cylinder at oblique incidence respectively. We assume that the cylinder is embedded in a homogeneous chiral medium and the cylinder is parallel to the z axis. Since the x components and y components of electric field and magnetic field can be expressed in terms of their z components, we can derive from Maxwell's equations and corresponding boundary conditions that the scattering problem is modeled as a boundary value problem for the z components of electric field and magnetic field. By using Rellich's lemma and variational approach, the uniqueness and the existence of solutions are justified.     

Reflected Backward Stochastic Differential Equations,Convex Risk Measures and American Options

We use convex risk measures to assess unhedged risks for American-style contingent claims in a continuous-time non-Markovian economy using reflected backward stochastic differential equations (RBSDEs). A two-stage approach is adopted to evaluate the risk. We formulate the evaluation problem as an optimal stopping-control problem and discuss the problem using reflected BSDEs. The convex risk measures are represented as solutions of RBSDEs. In the Markov case, we relate the RBSDE solutions to the unique viscosity solutions of related obstacle problems for parabolic partial differential equations.     

Doppler as a new dimension for multiple access in LEO satellite systems

The problem of flow control for little LEO satellite communications systems is studied. In these systems the satellite functions as a ‘bent pipe’ transponder for messaging between small terminals and a command and data acquisition (CDA) earth station. A novel scheme for averting traffic overflow on the inbound channel (from terminal to CDA), which we call ‘Doppler-based multiple access’ (DBMA), is introduced. In DBMA the CDA specifies a subset of the visibility footprint as a region of eligibility (ROE). Only terminals located in the ROE are permitted to transmit. By varying the size and location of the ROE, effective flow control on the inbound channel is achieved. The ROEs are specified in terms of parameters of the Doppler frequency shift versus time curve observed at terminals on the outbound downlink channel (from satellite to terminal). The effectiveness and elegance of the DBMA protocol are illustrated through computer simulation. © 1997 John Wiley & Sons, Ltd.     

State constraints in the linear regulator problem: Case study

In this paper, we consider the problem of minimum-norm control of the double integrator with bilateral inequality constraints for the output. We approximate the constraints by piecewise linear functions and prove that the Langrange multipliers associated with the state constraints of the approximating problem are discrete measures, concentrated in at most two points in every interval of discretization. This allows us to reduce the problem to a convex finite-dimensional optimization problem. An algorithm based on this reduction is proposed and its convergence is examined. Numerical examples illustrate our approach. We also discuss regularity properties of the optimal control for a higher-dimensional state-constrained linear regulator problem.The first author was supported by the National Science Foundation, Grant No. DMS-9404431. The second author was supported by a François-Xavier Bagnoud Doctoral Fellowship and by NSF Grants DMS-9404431 and MSS-9114630.     

基于群智能和冲突规避策略的基因-基因交互作用检测方法

针对当前检测基因-基因交互作用方法中存在的一些缺陷,提出一种基于群智能和冲突规避策略的基因-基因交互作用检测方法（DEIBSC）.以SNP（single nucleotide polymorphism）为研究对象,从大量SNP中选出具有显著基因-基因交互作用的SNP组.初始化多个SNP组作为初值,同时产生多条搜索路径,利用得分单调递增原则寻找问题的解,通过冲突规避策略和群智能动态调整搜索路径的方向,使得到的解更能反映基因-基因交互作用在基因组范围内分布的情况.在仿真数据和真实数据上的实验证实,本文方法在统计能力上可以和SNPHarvester方法相比,在效率上有明显优势,得到的结果能够更广泛地代表基因-基因交互作用在基因组的分布.     

Strategy-indifferent games of best choice

The game of best choice (or “secretary problem”) is a model for making an irrevocable decision among a fixed number of candidate choices that are presented sequentially in random order, one at a time. Because the classically optimal solution is known to reject an initial sequence of candidates, a paradox emerges from the fact that candidates have an incentive to position themselves immediately after this cutoff which challenges the assumption that candidates arrive in uniformly random order.One way to resolve this is to consider games for which every (reasonable) strategy results in the same probability of success. In this work, we classify these “strategy-indifferent” games of best choice. It turns out that the probability of winning such a game is essentially the reciprocal of the expected number of left-to-right maxima in the full collection of candidate rank orderings. We present some examples of these games based on avoiding permutation patterns of size 3, which involves computing the distribution of left-to-right maxima in each of these pattern classes.     

分期付款购房模型及其抛物障碍问题

考虑常数利率条件下的分期付款购房模型,若风险资产市场价格服从几何布朗运动,则合约可以运用美式期权定价方法给出合理的价格.该文给出了分期付款购房合约定价的偏微分方程方法,得到一个一维抛物障碍问题,同时给出了贷款合约价格函数所联系的自由边界,并讨论了自由边界的单调性与有界性.     

A question on partial CAP-subgroups of finite groups

A subgroup H of a finite group G is a partial CAP-subgroup of G if there is a chief series of G such that H either covers or avoids every chief factor of the series.The structural impact of the partial cover and avoidance property of some distinguished subgroups of a group has been studied by many authors.However,there are still some open questions which deserve an answer.The purpose of the present paper is to give a complete answer to one of these questions.     

A multigrid method for the Cahn-Hilliard equation with obstacle potential

We present a multigrid finite element method for the deep quench obstacle Cahn-Hilliard equation. The non-smooth nature of this highly nonlinear fourth order partial differential equation make this problem particularly challenging. The method exhibits mesh-independent convergence properties in practice for arbitrary time step sizes. In addition, numerical evidence shows that this behaviour extends to small values of the interfacial parameter γ. Several numerical examples are given, including comparisons with existing alternative solution methods for the Cahn-Hilliard equation.