Validity of the quantum regression theorem for resonance fluorescence in a photonic crystal

Correlation functions of a driven two‐level system embedded in a photonic crystal are analyzed. The spectral density of the photonic bands near a gap makes this system non‐Markovian. The equations of motion for two‐time correlations are derived by two different methods, the quantum regression theorem and the fluctuation dissipation theorem, and found to be the same.     

Free (open) boundary condition: some experiences with viscous flow simulations

The free (or open) boundary condition (FBC, OBC) was proposed by Papanastasiou et al. (A new outflow boundary condition, International Journal for Numerical Methods in Fluids, 1992; 14:587–608) to handle truncated domains with synthetic boundaries where the outflow conditions are unknown. In the present work, implementation of the FBC has been tested in several benchmark problems of viscous flow in fluid mechanics. The FEM is used to provide numerical results for both cases of planar and axisymmetric domains under laminar, isothermal or non‐isothermal, steady‐state conditions, for Newtonian fluids. The effects of inertia, gravity, compressibility, pressure dependence of the viscosity, slip at the wall, and surface tension are all considered individually in the extrudate‐swell benchmark problem for a wide range of the relevant parameters. The present results extend previous ones regarding the applicability of the FBC and show cases where the FBC is inappropriate, namely in the extrudate‐swell problem with gravity or surface‐tension effects. Particular emphasis has been given to the pressure at the outflow, which is the most sensitive quantity of the computations. In all cases where FBC is appropriate, excellent agreement has been found in comparisons with results from very long domains. The formulation for Picard‐type iterations is given in some detail, and the differences with the Newton–Raphson formulation are highlighted regarding some computational aspects. Copyright © 2011 John Wiley & Sons, Ltd.     

A weakly compressible MPS method for modeling of open‐boundary free‐surface flow

A mesh‐free particle method, based on the moving particle semi‐implicit (MPS) interaction model, has been developed for the simulation of two‐dimensional open‐boundary free‐surface flows. The incompressibility model in the original MPS has been replaced with a weakly incompressible model. The effect of this replacement on the efficiency and accuracy of the model has been investigated. The new inflow–outflow boundary conditions along with the particle recycling strategy proposed in this study extend the application of the model to open‐boundary problems. The final model is able to simulate open‐boundary free surface flow in cases of large deformation and fragmentation of free surface. The models and proposed algorithms have been validated and applied to sample problems. The results confirm the model's efficiency and accuracy. Copyright © 2009 John Wiley & Sons, Ltd.     

糖基亚苄基NaBH_3 CN-HCl选择性开环过程中乙酰基迁移现象的研究

用NaBH3CN HCl/Et2 O对 3 O 乙酰基 4,6 O 亚苄基 β D 吡喃半乳糖乙硫苷 (2 )进行还原开环 ,发现有乙酰基迁移至 2 位的产物生成 ;进一步的实验表明 ,室温条件下 ,NaBH3CN与 2的作用导致乙酰基的迁移     

Diffraction reflection of light on natural periodic inhomogeneities of a crystal with open surface of wave vectors

The forms of the surface of wave vectors for an extraordinary wave in the presence and absence of absorption are discussed. The normal transmission of light through a plane-parallel layer of a crystal with an open surface of wave vectors is considered. The diffraction reflection of light on natural periodic inhomogeneities of a crystal is studied. The frequency dependence of the reflection coefficient is calculated.     

The Study of Minimax Inequalities, Abstract Economics and Applications to Variational Inequalities and Nash Equilibria

In this survey, a new minimax inequality and one equivalent geometricform are proved. Next, a theorem concerning the existence of maximalelements for an LC-majorized correspondence is obtained.By the maximal element theorem, existence theorems of equilibrium point fora noncompact one-person game and for a noncompact qualitative game withLC-majorized correspondences are given. Using the lastresult and employing 'approximation approach', we prove theexistence of equilibria for abstract economies in which the constraintcorrespondence is lower (upper) semicontinuous instead of having lower(upper) open sections or open graphs in infinite-dimensional topologicalspaces. Then, as the applications, the existence theorems of solutions forthe quasi-variational inequalities and generalized quasi-variationalinequalities for noncompact cases are also proven. Finally, with theapplications of quasi-variational inequalities, the existence theorems ofNash equilibrium of constrained games with noncompact are given. Our resultsinclude many results in the literature as special cases.     

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.