The value function of a transportation problem

We investigate the value of an optimal transportation problem with the maximization objective as a function of costs and vectors of production and consumption. The value is concave in production. For generic costs, the numbers of linearity domains and peak points are independent of costs and consumption. The peak points are determined by an auxiliary assignment problem. The volumes of the linearity domains are independent of costs while their dependence on consumption can be expressed via the multinomial distribution.     

Formation of molten metal films during metal-on-metal slip under extreme interfacial conditions

The present paper describes results of plate-impact pressure-shear friction experiments conducted to study time-resolved growth of molten metal films during dry metal-on-metal slip under extreme interfacial conditions. By employing tribo-pairs comprising hard tool-steel against relatively low melt-point metals such as 7075-T6 aluminum alloys, interfacial friction stress ranging from 100 to and slip speeds of approximately have been generated. These relatively high levels of friction stress combined with high slip-speeds generate conditions conducive for interfacial temperatures to approach the melting point of the lower melt point metal (Al alloy) comprising the tribo-pair.A Lagrangian finite element code is developed to understand the evolution of the thermo-mechanical fields and their relationship to the observed slip response. The code accounts for dynamic effects, heat conduction, contact with friction, and full thermo-mechanical coupling. At temperatures below the melting point the material is described as an isotropic thermally softening elastic-viscoplastic solid. For material elements with temperatures in excess of the melt point a purely Newtonian fluid constitutive model is employed.The results of the hybrid experimental-computational study provides new insights into the thermoelastic-plastic interactions during high speed metal-on-metal slip under extreme interfacial conditions. During the early part of frictional slip the coefficient of kinetic friction is observed to decrease with increasing slip velocity. During the later part transition in interfacial slip occurs from dry metal-on-metal sliding to the formation of molten Al films at the tribo-pair interface. Under these conditions the interfacial resistance approaches the shear strength of the molten aluminum alloy under normal pressures of approximately 1- and shear strain rates of . The results of the study indicate that under these extreme conditions molten aluminum films maintain a shearing resistance as high as .Scanning electron microscopy of the slip surfaces reveal molten aluminum to be smeared on the tribo-pair interface. Knoop hardness measurements in 7075-T6 Al alloy at various depths from the slip interface indicate that the hardness increases approximately linearly with depth and reaches a plateau at approximately from the surface.     

EAST快速极紫外光谱仪绝对强度的原位标定

磁约束等离子体中杂质(特别是高Z杂质)的存在将大大增强等离子体辐射功率损失，破坏等离子体的约束性能。杂质行为的定量研究首先要求对杂质测量的光谱诊断系统进行绝对强度标定，获得灵敏度响应曲线。介绍了EAST托卡马克上的快速极紫外光谱仪系统绝对强度的原位标定方法。在波长范围20～150Å内，通过对比极紫外(EUV)波段连续轫致辐射强度的计算值和测量值得到光谱仪的绝对强度标定。在此过程中，首先由(523±1) nm范围内可见连续轫致辐射强度的绝对测量值计算出有效电荷数Z_eff，进而结合电子温度和密度分布计算EUV波段连续轫致辐射强度；EUV波段连续轫致辐射强度的测量值即为不同波长处探测器的连续本底计数扣除背景噪声计数值。对于较长波段范围130～280Å，通过对比等离子体中类锂杂质离子(Fe23+，Cr21+，Ar15+)和类钠杂质离子(Mo31+，Fe15+)发出的共振谱线对(跃迁分别为1s22s 2S_1/2-1s22p 2P_{1/2, 3/2}及2p63s 2S_1/2-2p63p 2P_{1/2, 3/2})强度比的理论和实验值进行相对强度标定。其中共振谱线对强度比的理论值由辐射碰撞模型计算得到，模型中处在各个能级的离子数主要由电子碰撞激发，去激发以及辐射衰变三个过程决定。两种方法相结合，实现了光谱仪20～280Å范围的绝对强度标定。考虑轫致辐射、电子温度及电子密度的测量误差，绝对标定误差约为30%。在绝对标定的基础上，我们对杂质特征谱线强度进行绝对测量，并将测量结果与杂质输运程序结合ADAS(Atomic Data and Analysis Structure)原子数据库计算得到的模拟值进行比较，进而估算等离子体中的杂质浓度。     

Unital affine semigroups

Affine semigroups are convex sets on which there exists an associative binary operation which is affine separately in either variable. They were introduced by Cohen and Collins in 1959. We look at examples of affine semigroups which are of interest to matrix and operator theory and we prove some new results on the extreme points and the absorbing elements of certain types of affine semigroups. Most notably we improve a result of Wendel that every invertible element in a compact affine semigroup is extreme by extending this result to linearly bounded affine semigroups.     

Geometric structure of b 2,2-orbihedra and interpolation of operators

We compute the normals to faces of b _2,2-orbihedra and apply the results to Operator Interpolation Theory.     

Multi-choice stochastic transportation problem involving extreme value distribution

In this paper a multi choice stochastic transportation problem is considered where the supply and demand parameters of the constraints follow extreme value distribution. Some of the cost coefficients of the objective function are multi-choice type. At first all the probabilistic constraints are transformed into deterministic constraints. Further using the binary variables, multi-choice type cost coefficients are handled. Then the transformed problem is considered as a deterministic multi-choice transportation problem. Finally, a numerical example is presented to illustrate the solution procedure.     

Asymptotic expansions of the moments of extremes from general error distribution

In this paper, we derive the asymptotic expansions of the moments of normalized partial maxima for general error distribution. A byproduct is to deduce the convergence rates of the moments of normalized maxima to the moments of the corresponding extreme value distribution.