NOVIKOV SUPER-ALGEBRAS WITH ASSOCIATIVE NON-DEGENERATE SUPER-SYMMETRIC BILINEAR FORMS

Novikov super-algebras are related to quadratic conformal super-algebras which correspond to Hamiltonian pairs and play fundamental role in completely integrable systems. In this paper, we focus on quadratic Novikov super-algebras, which are Novikov super-algebras with associative non-degenerate super-symmetric bilinear forms. We show that quadratic Novikov super-algebras are associative and the associated Lie-super algebras of quadratic Novikov super-algebras are 2-step nilpotent. Moreover, we give some properties on quadratic Novikov super-algebras and classify the associated Lie-super algebras of quadratic Novikov super-algebras up to dimension 7.     

Bilinear Forms on Novikov Algebras

Novikov algebras were introduced in connection with the Poisson brackets of hydrodynamic type and Hamiltonian operators in the formal variational calculus. On the other hand, there can be geometry and Lagrangian mechanics on homogenous spaces related to Novikov algebras. The nondegenerate symmetric bilinear forms on Novikov algebras can be regarded as the pseudometrics, and some additional identities for these forms correspond to some conserved quantities. In particular, there is an important kind of conserved nondegenerate symmetric bilinear forms that correspond to the pseudo-Riemannian connections such that parallel translation preserves the bilinear form on the tangent spaces. Moreover, the fact that the left multiplication operators form a Lie algebra for a Novikov algebra is compatible with such a form. However, we show in this note that there are no such forms on most Novikov algebras in low dimensions.     

On the Classification of Admissible Representations of the Virasoro Algebra

For the Virasoro algebra, the problems of classifying bounded admissible representations, on the one hand, and finite-length extensions of highest weight modules, on the other hand, are wild: they are as complicated as the problem of classifying a pair of matrices. This follows from results by Martin and Piard and Feigin and Fuchs.     

Some Results on Novikov–Poisson Algebras

Novikov algebras were introduced in connection with the Poisson brackets of hydrodynamic type and Hamiltonian operators in the formal variational calculus. A Novikov–Poisson algebra is a Novikov algebra with a compatible commutative associative algebraic structure, which was introduced to construct the tensor product of two Novikov algebras. In this paper, we commence a study of finite-dimensional Novikov–Poisson algebras. We show the commutative associative operation in a Novikov–Poisson algebra is a compatible global deformation of the associated Novikov algebra. We also discuss how to classify Novikov–Poisson algebras. And as an example, we give the classification of 2-dimensional Novikov–Poisson algebras.     

A construction of N = 2 and centerless N = 4 superconformal fields via affine superalgebras

In this paper we give a new construction of the N = 2 superconformal algebra using currents of the affine superalgebra and free bosonic fields, and also the N = 4 supercomformal algebra without central charge in terms of currents of and free bosonic fields.     

THE FIRST COHOMOLOGY OF THE SUPERCONFORMAL ALGEBRA K(1|4)

The infinitesimal deformations of the embedding of the Lie superalgebra of contact vector fields on the supercircle S^1|4 into the Poisson superalgebra of symbols of pseudodifferential operators on S^1|2 are explicitly calculated.     

q-Deformation of the Krichever–Novikov Algebra

Using q-operator product expansions between U(1) current fields and the corresponding energy-momentum tensors, we furnish the q-analogues of the generalized Heisenberg algebra and the Krichever–Novikov algebra.     

高精度高分辨率迎风格式应用于不同速度范围内粘性流动

提出了一种适合于不同速度范围的高精度高分辨率的迎风有限差分格式，并基于此数植模型发展了适应于速度范围极宽的非定常粘性流动通用软件，不仅适用于超音速下捕捉强间断面，跨音速及高亚音速下捕捉弱间断面和滑移面，还可以精确地模拟低速情况下的粘性流动。此软件可分别用于研究内流和外流的流动特性以及预估其粘性损失。     

二维氢原子的相对论修正

求解了二维氢原子的Ｄｉｒａｃ方程,得到了精确的相对论能级与波函数,并详细讨论了非相对论极限。     

Role of the external surfaces on the superconducting properties of superconductor/normal metal trilayers

Superconducting proximity effect is studied in superconductor/normal metal trilayers. The dependences of the superconducting transition temperature _Tc$T_c$ versus Nb thickness in Cu/Nb/Cu systems and versus Cu thickness in Nb/Cu/Nb ones are described by different values of the microscopical parameters. We attribute this difference to the influence of the external surfaces of the Nb/Cu/Nb hybrids on the superconducting properties of the system.     

低电阻测量中的接触电阻

本采用两种实验方法对比测量可知通常的导线连接其接触点的电阻,并由此进行分析,阐述在双电桥测量低电阻实验中四端扭接法的必要性。     

低温低密度等离子体密度及分布函数测量

一、引言 近来,尽管等离子体诊断技术有了很大发展,古老的朗缪尔探针由于结构简单,使用方便且有较好的时间空间分辨,至今仍作为基本诊断工具而广泛使用。但是,简单的朗缪尔探针理论只适用于中等密度(L》r》λD,L是平均自由程,r是探针半径,λD是德拜长度),对于低密度等离子体(r≤λD),朗缪尔探针理论复杂得失去了实用价值。本文将给出两个适合于低密度情况下的简单公式,并介绍一种实验中所用的静电能量分析器。     

Poisson brackets,Novikov-Leibniz structures and integrable Riemann hydrodynamic systems

A general differential-algebraic approach is devised for constructing multi-component Hamiltonian operators as differentiations on suitably constructed loop Lie algebras. The related Novikov-Leibniz algebraic structures are presented and a new non-associative “Riemann” algebra is constructed, which is closely related to the infinite multi-component Riemann integrable hierarchies. A close relationship to the standard symplectic analysis techniques is also discussed.     

HL—1装置的低q放电实验

装置获得的最低qL值是衡最托卡马克磁流体不稳定性的控制水平的重要品质参数.通过精细调节补充送气和电流上升率的方法控制电流密度分布,使用钛吸气方法控制边缘等离子体参数,HL-1装置获得了最低qL值为1.8的稳定等离子体。实验结果表明,若电流上升率与密度上升率之比为(23—40)×10~(-19)kA·m~3的范围内,最利于获得低MHD增长率的稳定放电。预计这与中心q(0)<1峰化的电流密度分布有关。     

光折变聚合物中的小振幅空间光孤子(英文)

给出了稳态条件下光折变聚合物中的小振幅空间孤子的演化方程,得到了方程的暗、亮孤子解析解,并且给出了小振幅聚合孤子的宽度表达式。结果表明,光折变聚合物中存在着双曲正切形式的小振幅暗空间孤子和双曲正割形式的小振幅亮空间孤子,小振幅聚合孤子的宽度与外加电场成反比关系。     

A Lie algebraic approach to the Kondo problem

The Kondo problem is approached using the unitary Lie algebra of spin-singlet fermion bilinears. In the limit when the number of values of the spin N goes to infinity the theory approaches a classical limit, which still requires a renormalization. We determine the ground state of this renormalized theory. Then we construct a quantum theory around this classical limit, which amounts to recovering the case of finite N.     

The Einstein–Podolsky–Rosen State Maximally Violates Bell's Inequalities

In their well-known argument against the completeness of quantum theory, Einstein, Podolsky, and Rosen (EPR) made use of a state that strictly correlates the positions and momenta of two particles. We prove the existence and uniqueness of the EPR state as a normalized, positive linear functional of the Weyl algebra for two degrees of freedom. We then show that the EPR state maximally violates Bell's inequalities.     

金属低温杂质散射电阻率

用弛豫时间近似讨论了金属低温下杂质散射电阻率与温度的关系，给出了近自由电子系统的电阻率的温度平方项系数。并对其它情况进行了讨论。