On unit time open shops with additional restrictions

We consider open shop problems with unit processing times,n jobs have to be processed onm machines. The order in which a given job is processed on the machines is not fixed. For each job a release time or a due date may be given. Additional, we consider the restriction that every machine must perform all corresponding operations without any delay time. Unit time open shop problems with release times to minimize total completion time were unsolved up to now for both allowed and forbidden delay times. We will solve these problems in the case of two and three machines. Furthermore we will give polynomial algorithms for several no-delay-problems with due dates.     

Characterization of limits of Bayes procedures

For the problem of estimating the natural parameter of a p-dimensional exponential family, a characterization of regular limits of Bayes procedures is obtained which generalizes results of Sacks [14], Brown [3], and Berger and Srinivasan [1]. The form is deduced under regularity conditions for the loss function which are more general than squared error. As a corollary it is then stated that the class of procedures with this form is a complete class. The parameter space may be open, and when it is closed, the limits of Bayes procedures are generalized Bayes.     

Nonstationary Theory of Perturbations for Open-Shell Atoms in the Hartree–Fock Approximation

For a multielectron open-shell system exposed to an external time-dependent perturbation, the Hartree–Fock nonstationary equations are obtained in terms of density operators. Using them as a basis, equations of nonstationary coupled perturbation theory are suggested in orbital representation within the framework of the two-operator variant of the Roothaan method for an open shell. The perturbation theory corrections to the orbitals have been found in the form of expansions in unperturbed orbitals which are assumed to be calculated in the LCAO approximation in the basis of Slater-type atomic orbitals. The dynamic polarizability of open-shell atoms of substances from Li to F and Sc has been calculated as an even-power series of the frequency of incident radiation.     

Equivalence of positive Hausdorff measure and the open set condition for self-conformal sets

A compact set is self-conformal if it is a finite union of its images by conformal contractions. It is well known that if the conformal contractions satisfy the ``open set condition' (OSC), then has positive -dimensional Hausdorff measure, where is the solution of Bowen's pressure equation. We prove that the OSC, the strong OSC, and positivity of the -dimensional Hausdorff measure are equivalent for conformal contractions; this answers a question of R. D. Mauldin. In the self-similar case, when the contractions are linear, this equivalence was proved by Schief (1994), who used a result of Bandt and Graf (1992), but the proofs in these papers do not extend to the nonlinear setting.

     

Factorization in generalized power series

The field of generalized power series with real coefficients and exponents in an ordered abelian divisible group is a classical tool in the study of real closed fields. We prove the existence of irreducible elements in the ring consisting of the generalized power series with non-positive exponents. The following candidate for such an irreducible series was given by Conway (1976): . Gonshor (1986) studied the question of the existence of irreducible elements and obtained necessary conditions for a series to be irreducible. We show that Conway's series is indeed irreducible. Our results are based on a new kind of valuation taking ordinal numbers as values. If we can give the following test for irreducibility based only on the order type of the support of the series: if the order type is either or of the form and the series is not divisible by any monomial, then it is irreducible. To handle the general case we use a suggestion of
M.-H. Mourgues, based on an idea of Gonshor, which allows us to reduce to the special case . In the final part of the paper we study the irreducibility of series with finite support.

     

可积开边界条件下的q形变玻色子模型

利用代数Bethe Ansatz方法在可积开边界条件下推广了q形变玻色子模型，得到可积开边界条件下此模型的哈密顿量及其本征方程.该工作可为在更小尺度下研究具有相互作用的玻色子系统提供有效的理论基础. 关键词： 代数Bethe Ansatz q形变玻色子模型')" href="#">q形变玻色子模型 开边界 可积系统     

聚心火焰在共振腔作用下引发爆轰的数值研究

 基于带化学反应的二维轴对称Euler方程，利用带有Superbee限制函数的波传播算法，对共振腔中的氢气-空气预混气的聚心燃烧进行了数值模拟，讨论了共振腔不同抛物面对起爆的影响。数值结果表明，在开始阶段，燃烧诱导的激波在轴心、火焰和固壁的反射，使火焰失稳，随后共振腔中的抛物壁面上产生一定频率和强度的反射激波，不断穿越火焰，使火焰进一步失稳，加剧了燃烧速度，最终导致爆轰的形成。同时，火焰在与激波的作用过程中，形状扭曲变形，呈封闭端小敞口端大的扁平头部蘑菇云。共振腔抛物面的不同形状引起激波聚焦位置的变化，会影响激波和火焰的相互作用，使起爆提前或推迟，甚至不起爆。     

Single-photon all-optical switching using coupled microring resonators

We study the nonlinear phase response of a microring resonator coupled to a bus waveguide and the use of this nonlinear phase shift to store information in the microring resonator and enhance the switching characteristics of a Mach-Zehnder interferometer (MZI). By introducing coupling between adjacent microring resonators, the switching characteristics of the MZI can be exponentially enhanced as a function of the number of microring resonators, when compared to the linear enhancement for uncoupled resonators. With only a few moderate-finesse microring resonators, the switching power can be reduced to attowatt level, allowing for photonic switching devices that operate at single-photon level in ordinary optical waveguides.      

1.444 mm Nd:YAG激光器的实验研究

 在理论分析的基础上设计了直腔结构1.444 mm Nd:YAG激光器，并进行了实验研究。获得了1.444 mm激光输出，当泵浦能量为55 J时，其最高静态激光输出310 mJ。电-光转换效率为0.56%，斜效率为0.81%。并实现了1.444 mm调Q输出，脉冲输出能量18 mJ，脉宽150 ns。