Second-order Nonlinear Optical Properties of a Series of Azulene Derivatives

The first hyperpolarizabilities of a series of novel azulenic-barbituric acid chromophores have been studied by using 12 excitation wavelengths, ranging from 900 to 1907 nm. The dispersion relation of the first hyperpolarizabilities of chromophores holds the same tendency as the experimental results. In addition, the static first hyperpolarizability β0 of molecules was calculated by means of the Sum-Over-States (SOS) expression and the two-level formula respectively. The results show that these molecules possess large static first hyperpolarizabilities and the, β0 value increases as the donor or acceptor strength enhances; the distorted degree of molecules has also an important influence on the β0 value.     

Generic Well-Posedness of Constrained Variational Problems Without Convexity Assumptions

In our previous work, a generic well-posedness result (with respect to variations of the integrand of the integral functional) without the convexity condition was established for a class of optimal control problems satisfying the Cesari growth condition. In this paper, we extend this generic well-posedness result to classes of constrained variational problems in which the values at the endpoints and constraint maps are also subject to variations.     

The canonical solution operator of $ {\bar \partial } $ on weighted spaces with holomorphic coefficients

On weighted spaces with strictly plurisubharmonic weightfunctions the canonical solution operator of and the ‐Neumann operator are bounded. In this paper we find a class of strictly plurisubharmonic weightfunctions with certain growth conditions, so that they are Hilbert‐Schmidt operators between weighted spaces with different weightfunctions, if they are restricted to forms with holomorphic coefficients. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

剖析博彩弹子机的赢钱原理

介绍了博彩弹子机 ,运用数学建模法剖析了它的赢钱原理 ,强调了一般博彩业主永远是赢家的道理     

On the group extension of the transformation associated to non-archimedean continued fractions

Summary Let F_q be a finite field with q elements. We consider formal Laurent series of F_q -coefficients with their continued fraction expansions by F_q -polynomials. We prove some arithmetic properties for almost every formal Laurent series with respect to the Haar measure. We construct a group extension of the non-archimedean continued fraction transformation and show its ergodicity. Then we get some results as an application of the individual ergodic theorem. We also discuss the convergence rate for limit behaviors.     

Observable signals of gauge-mediated supersymmetry breaking

The observable consequences of gauge-mediated supersymmetry breaking (GMSB) are reviewed here. Implications of scenarios both with a neutralino and a slepton as the next lightest supersymmetric particle (NLSP) are surveyed in relation to hadronic ande ⁺ e ^- colliders. We also discuss the phenomenological consequences of the NLSP decaying slowly, giving rise to delayed events in the detectors.The importance of distinguishing signals of GMSB models from those of the commonly discussed supergravity-type theories is emphasized.     

完备可分度量群上的齐次Levy过程的复合Poisson逼近

该文利用算子半群的方法给出了取值于具有左不变度量的完备可分群的齐次Levy过程是复合Poisson过程的弱极限这一结论．     

层次分析中广义最小偏差法的性质

广义最小偏差法（GLDM）是层次分析中一种重要的排序方法．本文讨论了广义最小偏差法的性质和灵敏度分析问题．     

逆（反）对策问题与“奇门遁甲”预测理论（术）

本文首先提出逆（反）对策这一新问题，给出了数学模型；探讨了“奇门遁甲”预测理论（术）中的数学问题；通过系统分析“专门遁甲”预测过程，可知它的预测过程隐含着一个特殊的逆（反）对策问题；最后指出逆（反）对策问题的广泛存在并给出案例分析．     

Prederivations of Lie Algebras and Isometries of Bi-invariant Lie Group

Lie groups with bi-invariant semi-Riemannian metrics are considered. We study the decomposition of the algebra of prederivations of a direct sum of Lie algebras and derive some results on the isotropy group of a bi-invariant product Lie group. We also give necessary and sufficient conditions to ensure that all isometries of a complex Lie group, endowed with a bi-invariant Norden metric, are holomorphic.