Derivation of the Bosonic Part of the Electroweak Chiral Lagrangian from a General Underlying Technicolor Theory

Bosonic part of SU(2)_L\otimes U(1)_Y effective chiral Lagrangian for electroweak symmetry breaking is derived from an underlying technicolor theory with no approximation. The underlying theory is assumed to be the most general gauge theory without fundamental scalars. A condensate is required to exist in the theory which breaks SU(2)_L\otimes U(1)_Y dynamically to U(1)_em and the anomaly of the theory caused by gauge interaction must be cancelled. The formulation offers general definitions in terms of underlying theory for the low energy constants in effective chiral Lagrangian.     

非定常可压等熵流非线性方程显式解析解的推导

本文对作者以前凭试凑、灵感、运气与经验得出的一系列非定常可压流动显式解析解,寻找线索,总结出其可能的推导途径,并以非定常可压等熵一维流为例,具体给出了四种新的求解方法。这些方法会对今后寻找工程热物理领域的非线性主控方程的解析解有所帮助。本文同时还给出了两个新的解析解。     

物理量单位的智能导出算法及其应用

推导物理量的单位是物理作业中不可缺少的重要环节。提出一种物理量单位的智能导出算法,即计算机根据物理量的运算式自动推导出待求物理量的单位。实验结果表明,物理量单位导出及换算算法的结果正确,对算术运算式中的物理量单位导出及换算的正确率为100%,且物理量数值的运算正确。     

Derivation of baroclinic Ertel–Rossby invariant-based thermally-coupled vorticity equation in moist flow

For the potential vorticity （PV） invariant, there is a PV-based complete-form vorticity equation, which we use heuris- tically in the present paper to answer the following question： for the Ertel-Rossby invariant （ERI）, is there a corresponding vorticity tendency equation？ Such an ERI-based thermally-coupled vorticity equation is derived and discussed in detail in this study. From the obtained new vorticity equation, the vertical vorticity change is constrained by the vertical velocity term, the term associated with the slope of the generalized momentum surface, the term related to the horizontal vorticity change, and the baroclinic or solenoid term. It explicitly includes both the dynamical and thermodynamic factors＇ influence on the vorticity change. For the ERI itself, besides the traditional PV term, the ERI also includes the moisture factor, which is excluded in dry ERI, and the term related to the gradients of pressure, kinetic energy, and potential energy that reflects the fast-manifold property. Therefore, it is more complete to describe the fast motions off the slow manifold for severe weather than the PV term. These advantages are naturally handed on and inherited by the ERI-based thermally-coupled vorticity equation. Then the ERI-based thermally-coupled vorticity equation is further transformed and compared with the traditional vorticity equation. The main difference between the two equations is the term which describes the contribution of the solenoid term to the vertical vorticity development. In a barotropic flow, the solenoid term disappears, then the ERI-based thermally-coupled vorticity equation can regress to the traditional vorticity equation.     

The reliability of measurements on electron energy distribution function in silane rf glow discharges

Electron energy distribution function (EEDF) is a key parameter of plasmas, which is directly proportional to the second derivative of the probe I-V characteristics. Because of an amplifying effect of unavoidable noises in the experimental probe I-V curves during the derivation process, the experimental I-V curves should be smoothed before performing the numerical derivation. This paper investigates the effect of adjustable factors used in the smoothing process on the deduced second derivative of the I-V curves, and an optimum group of the adjustable factors is selected to make the rms deviation of the smoothed I-V curves from the measured curves less than 1%. A simple differentiation circuit is designed and used to measure the EEDF parameter straightforwardly. It is the first time, so far as we know, to measure the EEDF parameters simultaneously by means of both numerical and circuit derivative methods under the same discharge conditions and on the same discharge equipment. The deviation between two groups of mean electron energy E and electron density n_e obtained by the above different methods is within about 7%. This apparently improves the reliability of the measurements of the EEDF parameters.     

基于小关联时间两相湍流色噪声的近似模型及数值模拟

从一般高斯型色噪声模型出发,通过泛函导数,应用小关联时间,近似计算多维色噪声,得到有效Fokker-Planck方程.将其应用到两相湍流中得到颗粒相的概率密度函数输运方程,从而得到颗粒相的二阶矩模型.将颗粒应力方程简化成代数方程,建立代数应力模型.将对流扩散方程的有限分析法运用到求解两相流模型中,对壁面两相射流进行数值模拟,并将求解结果与实验结果进行对比分析.     

The atomic and molecular reaction statics

This work presents a new science called atomic and molecular reaction statics (AMRS). There are four parts for AMRS, i.e. the group theoretical derivation of molecular electronic states, the principle of microscopic reversibility, the principle of microscopic transitivity and the optimum energy process rule. AMRS has been developed for about twenty years.     

Structure of Degenerate Block Algebras

Given a non-trivial torsion-free abelian group (A,+,Q), a field F of characteristic 0, and a non-degenerate bi-additive skew-symmetric map : A A F, we define a Lie algebra = (A, ) over F with basis {e_x | x A/{0}} and Lie product [e_x,e_y] = (x,y)e_x+y. We show that is endowed uniquely with a non-degenerate symmetric invariant bilinear form and the derivation algebra Der of is a complete Lie algebra. We describe the double extension D( , T) of by T, where T is spanned by the locally finite derivations of , and determine the second cohomology group H²(D( , T),F) using anti-derivations related to the form on D( , T). Finally, we compute the second Leibniz cohomology groups HL²( , F) and HL²(D( , T), F).2000 Mathematics Subject Classification: 17B05, 17B30This work was supported by the NNSF of China (19971044), the Doctoral Programme Foundation of Institution of Higher Education (97005511), and the Foundation of Jiangsu Educational Committee.     

von Neumann代数中套子代数上的Lie导子

本文对因子von Neumann代数中套子代数上的线性映射L:alg_Mβ→M满足L(AB—BA)=L(A)B-BL(A)+AL(B)-L(B)A( A,B∈alg_Mβ)进行了刻划,证明了存在线性函数h:alg_Mβ→C;且对任意A,B∈alg_Mβ,有h(AB—BA)=0和算子T∈M,使得对任意X∈alg_Mβ,都有L(X)=XT-TX+h(X)I.     

Obstructions to nonnegative curvature and rational homotopy theory

We establish a link between rational homotopy theory and the problem which vector bundles admit a complete Riemannian metric of nonnegative sectional curvature. As an application, we show for a large class of simply-connected nonnegatively curved manifolds that, if lies in the class and is a torus of positive dimension, then ``most' vector bundles over admit no complete nonnegatively curved metrics.