高阶Bernoulli多项式和高阶Euler多项式的关系

利用发生函数的方法，讨论了高阶Bernoulli数和高阶Euler数，高阶Bernoulli多项式和高阶Euler多项式之间的关系，得到了经典Bernoulli数和Euler数，经典Bernoulli多项式和Euler多项式之间的新型关系。     

S3上阿诺德弦猜想中的变分方法

本文使用变分方法证明了三维标准切触球的标准勒让德扭结，至少存在一个弦连结适应于标准切触结构的任何选定切触形式，这部分证明了著名的阿诺德弦猜想。     

Solitary wave solutions of nonlinear financial markets :data-modeling-concept-practicing

This paper seeks to solve the difficult nonlinear problem in financial markets on the complex system theory and the nonlinear dynamics principle, with the data-model-concept-practice issue-oriented reconstruction of the phase space by the high frequency trade data. In theory, we have achieved the differentiable manifold geometry configuration, discovered the Yang-Mills functional in financial markets, obtained a meaningful conserved quantity through corresponding space-time non-Abel localization gauge symmetry transformation, and derived the financial solitons, which shows that there is a strict symmetry between manifold fiber bundle and guage field in financial markets. In practical applications of financial markets, we have repeatedly carried out experimental tests in a fluctuant evolvement, directly simulating and validating the existence of solitons by researching the price fluctuations (society phenomena) using the same methods and criterion as in natural science and in actual trade to test the stock Guangzhou Proprietary and the futures Fuel Oil in China. The results demonstrate that the financial solitons discovered indicates that there is a kind of new substance and form of energy existing in financial trade markets, which likely indicates a new science paradigm in the economy and society domains beyond physics.      

Modulation of Spin Distribution and Spin Transport by a Magnetic Field in a Quasi-One-Dimensional System with Spin--Orbit Coupling

The distributions of spin and currents modulated by magnetic field in a transverse parabolic confined two-dimensional electronic system with a Rashba spin--orbit coupling have been studied numerically. It is shown that the spin accumulation and the spin related current are generated by magnetic field if the spin--orbit coupling is presented. The distributions of charge and spin currents are antisymmetrical along the cross-section of confined system. A transversely applied electric field does not influence the characteristic behaviour of charge- and spin-dependent properties.     

Mode equation and its solution for dielectric waveguide with parabolic cross-section

The mode equation for the dielectric waveguide with parabolic cross-section is derived using both the effective index method and WKB theory, and the expression of the mode propagation constant or effective index is solved directly from this mode equation, so that the mode-propagation properties of this kind of waveguide can be analysed conveniently with comparative accuracy.     

Bayes估计的进一步研究及其Pitman最优性

对线性模型参数,讨论了Bayes估计的Pitman最优性,将已有结果进行了改进,去掉了附加条件,证明了在Pitman准则下,Bayes估计一致优于最小二乘估计(LSE),在此基础上,提出了一种基于先验信息的方差分量估计,通过和基于LSE的方差分量估计作比较,证明了新估计是无偏估计且有更小的均方误差．最后,证明了在Pitman准则下生长曲线模型参数的Bayes估计优于最佳线性无偏估计．     

Dynamical Running Mass of Quark in the Dyson-Schwinger Equation Approach

Based on the Dyson-Schwinger equations of QCD in the "rainbow" approximation, the fully dressed quarkpropagator Sf(p) is investigated, and then an algebraic parametrization form of the propagator is obtained as a solutionof the equations. The dressed quark amplitudes Af and Bf built up the fully dressed quark propagator and the dynamicalrunning masses Mf defined by Af and Bf for light quarks u, d and s are calculated, respectively. Using the predictedrunning masses Mf, quark condensates <0|q(0)q(0)|0> = -(0.255 GeV)a for u, d quarks, and <0|s s|0> = 0.8<0|q(0)q(0)]0)for s quark, and experimental pion decay constant fπ = 0.093 GeV, the masses of Goldstone bosons K, π, and η are alsoevaluated. The numerical results show that the masses of quarks are dependent on their momentum p2. The fully dressedquark amplitudes Af and Bf have correct behaviors which can be used for many purposes in our future researches onnonperturbative QCD.     

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在常温常压下采用新型旋转电极等离子体反应器，对辉光等离子体作用下的甲烷偶联反应制C2烃进行了研究。结果表明，甲烷偶联反应的主要产物为C2H2，占C2烃的80%以上，能量效率在5.6%～11.2%之间；增加H2含量可以提高CH4转化率和C2烃收率；在500～2200kJ•mol−1的能量密度范围内，CH4转化率随能量密度的增大而线性增加，C2烃收率随着能量密度的增加呈峰形变化趋势。