Free boundary problem for a fully nonlinear and degenerate parabolic equation in an angular domain

This paper concerns with the problem of how to running an insurance company to maximize his total discounted expected dividends. In our model, the dividend rate is limited in $[0,M]$ and the company is allowed to transfer any proportion of risk by reinsuring. So there are two strategies which we call dividend strategy and reinsurance strategy. The objective function and the corresponding optimal two strategies are the solution and the two free boundaries of the following Barenblatt parabolic equation

$v_t?\underset{0\le a\le 1}{\max }?(\frac{1}{2}{a}^2{\sigma }^2{v}_{xx}+a\mu v_x)+cv?\underset{0\le l\le M}{\max }?[(1?v_x)l]=0$

under certain boundary conditions on an angular domain

$Q_T=\{(x,t)|0<x<Mt,0<t\le T\}.$

The main effort is to analyze the properties of the solution and the free boundaries to show the optimal decision for the insurance company.     

Asymptotic analysis for multi-objective sequential stochastic assignment problems

ABSTRACT

We provide an asymptotic analysis of multi-objective sequential stochastic assignment problems (MOSSAP). In MOSSAP, a fixed number of tasks arrive sequentially, with an n-dimensional value vector revealed upon arrival. Each task is assigned to one of a group of known workers immediately upon arrival, with the reward given by an n-dimensional product-form vector. The objective is to maximize each component of the expected reward vector. We provide expressions for the asymptotic expected reward per task for each component of the reward vector and compare the convergence rates for three classes of Pareto optimal policies.     

航空器供油问题中完全逆序类中的多项式时间可解类

航空器供油问题是一类非线性组合优化问题,其目标函数为分式形式,该问题目前不存在多项式时间算法,也未被证明是NP完全问题。一般可以用置换来刻画n架飞机的一个供油顺序。该问题中有一类实例被称为“完全逆序类”,“完全逆序类”用动态规划算法求解计算时间为O(n2ⁿ),具有指数时间复杂度。本文通过对该“完全逆序类”问题做进一步分析,发现在“完全逆序类”中也存在着多项式时间可解的情况。定理1研究一类一次可解的情况,若问题满足定理1的条件,则求解一次即可找到其最优解;定理2研究一类多项式时间可解的情况,当问题满足定理2的条件时,其最优解可在多项式时间内获得。     

Anti‐Pasch optimal packings with triples

It is shown that for , there exists an optimal packing with triples on points that contains no Pasch configurations. Furthermore, for all (mod 6), there exists a pairwise balanced design of order , whose blocks are all triples apart from a single quintuple, and that has no Pasch configurations amongst its triples.     

Regulation of shear stress on rolling behaviors of HL-60 cells on P-selectin

Circulating leukocytes in trafficking to the inflammatory sites, will be first tether to, and then roll on the vascular surface. This event is mediated through specific interaction of P-selectin and P-selectin glycoprotein ligand-1(PSGL-1), and regulated by hemodynamics. Poor data were reported in understanding P-selectin-mediated rolling. With the flow chamber technique, we herein observed HL-60 cell rolling on P-selectin with or without 3% Ficoll at various wall shear stresses from 0.05 to 0.4 dyn/cm2. The results demonstrated that force rather than transport regulated the rolling, similar to rolling on L- and E-selectin. The rolling was accelerated quickly by an increasing force below the optimal shear threshold of 0.15 dyn/cm2 first and then followed by a slowly decelerating phase starting at the optimum, showing a catch-slip transition and serving as a mechanism for the rolling. The catch-slip transition was completely reflected to the tether lifetime and other rolling parameters, such as the mean and fractional stop time. The narrow catch bond regime stabilized the rolling quickly, through steeply increasing fractional stop time to a plateau of about 0.85. Data presented here suggest that the low shear stress threshold serves as a mechanism for most cell rolling events through P-selectin.     

Control of Ionization in the Interaction of Strong Laser Fields with Dense Nanoplasmas

Different experimental methods to maximize the yield of highly charged ions in silver and xenon clusters interacting with intense and ultra‐short optical laser pulses are discussed. Theoretically, the interaction of strong laser fields with clusters is investigated within the nanoplasma model. The time evolution of the laser intensity has been parametrized. The free optimization of the parameters with a genetic algorithm is an effective but expensive tool to control the plasma dynamics. Comparison is given to the parametric control method in which pulse separation and relative intensity ratio of double‐pulses are varied. This method delivers in the case of silver and xenon clusters pulses quite close to the optimal pulse shape (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

STABILITY ANALYSIS OF A CAPACITIVE FGM MICRO-BEAM USING MODIFIED COUPLE STRESS THEORY

Based on the Modified Couple Stress Theory,a functionally graded micro-beam under electrostatic forces is studied.The FGM micro-beam is made of two materials and material properties vary continuously along the beam thickness according to a power-law.Dynamic and static pull-in voltages are obtained and it is shown that the static and dynamic pull-in voltages for some materials cannot be obtained using classic theories and components of couple stress must be taken into account.In addition,it is shown that the values of pull-in voltages depend on the variation through the thickness of the volume fractions of the two constituents.     

The first principles investigation of ferrite magnetic response with mismatch stress

The quasi-ferrite model is proposed and an appropriate PBE exchange functional with the spin density functional theory(SDFT) is selected for the calculation of the relation between magnetic moment and residual stress in ferrite using a quantum mechanics code. The relationship between ferrite magnetism and the carbon content is determined,and then a ferrite interstitial solid solution(ISS) model in a low carbon concentration state is replaced with an α- Fe model in the case of majority magnetic calculation. The band structure of the loaded-Fe is compared with that of the unloaded α-Fe. The comparison shows that the energy of Fe atomic 3d orbital changes a little,while the energy of electron orbital of iron core below 3d almost keeps unchanged. The relationship between the magnetic moment and the stress appears intermittent due to the Bragg total reflection. The change in the magnetic moment due to lattice mismatch is much larger than that caused by mechanical loading.