平稳正态序列超过数点过程与部分和的渐近联合分布

{Xi}为平稳正态序列,具有EX1=0,EX12=1,ρn=EX1Xn 1.对于水平un= ,记在 的条件下,得到了Nn(B)与Sn的渐近联合分布,同时也给出了极值与Sn的渐近联合分布.     

环径比接近2的托卡马克堆芯等离子体特征

初步研究了环径比接近2的托卡马克堆芯等离子体的基本特征。这类位形具有非常好的使磁流体稳定的特性，可以基本排除等离子体破裂不稳定性。从H模约束要求和氘氚燃烧实验出发，讨论r相关的基本问题：比压极限和密度极限、基本等离子体参数间的凋整、氘氚自持燃烧条件等。参数选取的基本依据是ITER和ITER-FEAT的设计经验。     

Partial linearization for generalized fractional programming

An algorithm based on partial linearization is proposed to deal with generalized fractional programs. This algorithm is shown to be equivalent to the so called generalized Dinkelbach's algorithm applying to this problem. Hence we have another setting for this last algorithm.This research was supported by NSERC (grant A8312) and FCAR (grant 0899).     

Optimal quasi-static shape control for large aerospace antennae

In this paper, we propose an on-line control approach which will adjust the steady-state shape of a large antenna arbitrarily close to any achievable desired profile. The method makes use of distributed parameter system theory and allows refocusing using a limited number of control actuators and sensors.The controller gains are calculated by approximating the solution to an infinite-dimensional optimal quasi-static control problem. We prove a very general convergence result for such quasi-static controllers here and apply it to the antenna controller to show convergence using any Galerkin (finite-element) approximation method.This research was partially supported by the National Science Foundation, the National Aeronautics and Space Administration, and the Air Force Office of Scientific Research under Grants ECS-80-16173, NAG-1-171, and AFOSR-83-0124, respectively.     

A functional central limit theorem for ϱ-mixing sequences

In this note a functional central limit theorem for ?-mixing sequences of I. A. Ibragimov (Theory Probab. Appl.20 (1975), 135–141) is generalized to nonstationary sequences (X_n)_n ∈ $\text{N}$, satisfying some assumptions on the variances and the moment condition $\text{E |X}{}_{\mathrm{n}}\text{|}{}^{\mathrm{2\; +\; b}}\text{= O(n}{}^{\mathrm{<mtext>b</mtext><mtext>2</mtext><mtext>??</mtext>}}\text{)}$ for some b > 0, ? > 0.     

Melting and crystallization behavior of poly(vinylidene fluoride) produced isothermally in the intercrystalline spaces of poly(ethylene terephthalate) from its blends

The melting of isothermally crystallized poly(vinylidene fluoride) (PVF₂), produced in the intercrystalline spaces of poly(ethylene terephthalate) (PET) from its blends, showed a unique behavior: the melting temperature decreased with the increasing crystallinity of PVF₂ (i.e., with increasing crystallization time) for PVF₂ volume fractions of 0.64 and 0.51. The melting temperature of already crystallized PET also decreased as the PVF₂ crystallization progressed and the isothermal crystallization temperature of PVF₂ increased. Separate reasons were proposed to account for these behaviors. The equilibrium melting temperatures of PVF₂ in the blends, measured by the Hoffman–Weeks extrapolation procedure, were used to calculate the polymer–polymer interaction parameter (χ₂₁); only the noncrystallized portion of PET contributing to the mixed amorphous phase was considered. The χ₂₁value (−1.75) was lower than χ₁₂ (−0.14), calculated from the melting temperature depression of PET. However, when they were normalized to the unit volumes of the respective components, the two values were found to be the same. The crystallization rate of PVF₂ decreased with an increasing volume fraction of PET in the blend. The Avrami exponent increased for the volume fraction of PVF₂ (0.77) and then progressively decreased with an increasing volume fraction of PET. A gradual change in the nature of the regime transition from regime II/regime I to regime III/regime II with increasing PET concentration was observed. The value of the chain-extension factor of PVF₂ significantly increased with an increase in the PET concentration in the blends. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2215–2227, 2004     

Advanced supply chain planning with mixtures of backorders,lost sales,and lost contract

This paper investigates a supply chain system in which a supplier prepares for the selling season by building stock levels prior to the beginning of the season and shortages realized at the beginning of the season are represented as mixtures of backorders and lost sales. Backlogged items are replenished as soon as possible through an emergency procurement as opposed to waiting until the next scheduled delivery as in many continuous review scenarios, and the backorder rate is modeled as a piecewise linear function of the magnitude of the shortage. The often intangible cost associated with lost sales and customer goodwill is also quantified. In particular, the buyer and supplier are engaged in a contractual agreement and the loss of customer goodwill from the supplier’s perspective is represented as the expected cost associated with violating the conditions of the contract. The likelihood of contract cancellation is also represented as a function of the magnitude of shortage. The optimal solution is derived in closed form for the case of exponential demand distribution, and an example problem is illustrated with numerical data in order to demonstrate calculation of the optimal solution and corresponding sensitivity analysis for demand distributions in which the solution cannot be expressed in closed form.     

Explicit solution for Lamé and other PDE systems

We provide a general series form solution for second-order linear PDE system with constant coefficients and prove a convergence theorem. The equations of three dimensional elastic equilibrium are solved as an example. Another convergence theorem is proved for this particular system. We also consider a possibility to represent solutions in a finite form as partial sums of the series with terms depending on several complex variables.