清华大学物理系原子核物理研究的新进展

在清华大学物理系成立80周年之际,对近年来清华大学物理系原子核物理研究的主要进展情况作一介绍,包括原子核高自旋态的实验研究,原子核结构的理论研究,高能核物理的理论研究.在高自旋态研究方面,内容包括在A～100丰中子核区核的集体振动转动带结构、新的准粒子带特性、新手征二重带等特性研究;在A～140丰中子核区核的八极形变及八级关联等特性研究;在A～130缺中子核区核的形状驱动效应,包括扁椭形变带、形状共存等特性研究.在原子核结构理论研究方面,内容包括用相互作用玻色子模型、推转壳模型、投影壳模型以及相对论平均场对原子核特性的研究;对原子核结构或其他量子系统的各种对称性和代数方法的研究,如动力学对称性、超对称性、势代数方法等;与对称性紧密联系的普通李代数和非线性李代数的表示,如普通李代数、李超代数、平方根型非线性李代数、多项式型非线性李代数等.在高能核物理研究方面,内容主要包括量子色动力学（QCD）在高温高密条件下的相变以及在相对论重离子碰撞中相变信号的研究.     

半平面中调和函数的积分表示

本文对于半平面中的调和函数u(z),证明了正部u (z)满足某些限制增长条件,用半平面边界上的积分表示,它的负部u-(z)也被类似的增长条件所控制.得到了半平面中负的调和函数的经典结果.     

Triangular Matrix Representations of Rings of Generalized Power Series

Let R be a ring and S a cancellative and torsion-free monoid and 〈 a strict order on S. If either （S,≤） satisfies the condition that 0 ≤ s for all s ∈ S, or R is reduced, then the ring [[R^S,≤]] of the generalized power series with coefficients in R and exponents in S has the same triangulating dimension as R. Furthermore, if R is a PWP ring, then so is [[R^S,≤]].     

On <Emphasis Type="Italic">τ</Emphasis>-adic representations of integers

Elliptic curve cryptosystems (ECCs) have become increasingly popular due to their efficiency and the small size of the keys they use. Particularly, the anomalous curves introduced by Koblitz allow a complex representation of the keys, denoted τNAF, that make the computations over these curves more efficient. In this article, we propose an efficient method for randomizing a τNAF to produce different equivalent representations of the same key to the same complex base τ. We prove that the average Hamming density of the resulting representations is 0.5. We identify the pattern of the τNAFs yielding the maximum number of representations and the formula governing this number. We also present deterministic methods to compute the average and the exact number of possible representations of a τNAF.      

THE INDUCED REPRESENTATION OF C^＊-GROUPOID DYNAMIC SYSTEMS

1.IntroductionandDefinitionsTheinducedrepresentationofgroupC*-algebrasfirstwasalgebraicallyintroducedbyfueffelin[3].P.Greenin[6]similiaxlyintroducedtheoneforcovariantdynamicsystem.TheinducedrepresentationofcrossedproductsbycoactionswasintroducedbyK.Mansfieldin[9].Using[8]wecanobtaintheinducedrepresentationofgrollpoidC*-algebrasin[1Ol.TherichapplicationofthesecanbefoundamongmanypapersrelativetotheC*-analysisofgroupoidandgroup.TheC*-groupoiddynamicsystemanditsreducedcrossedprod-uctwereintro…     

Soap films spanning rectangular prisms

In this paper, we consider soap films spanning rectangular prisms with regular n-gon bases. As the number of edges n varies, we show that there are significant changes in the qualitative properties of the spanning soap films as well as a change in the number of spanning soap films whose existence we can prove: We can find two nontrivial soap films for n = 3, 4, 5 but only one for n ≥ 6. We also prove some results concerning the interval of aspect ratios through which the soap films exist: The interval is finite if n = 3, 4, 5 and infinite if n ≥ 6. Furthermore, for n > 6, we have that the spanning soap film converges to a soap film spanning the vertical lines through the vertices of a regular n-gon as the aspect ratio goes to infinity. We can also make sense of the case n = ∞. Here, we discover some interesting singly and triply periodic soap films spanning singly and doubly periodic sets of vertical lines or spanning singly periodic sets of vertical line segments connected by pairs of parallel, horizontal lines. Finally, for n = 3, 4, 5, 6, we can derive parameterizations for the spanning soap films, and these parameterizations are explicit up to knowing the aspect ratio.      

On a class of stopping times for M-estimators

For a given score function ψ = ψ(x, θ), let θ_n be Huber's M-estimator for an unknown population parameter θ. Under some mild smoothness assumptions it is known that $\text{n}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(θ}{}_{\mathrm{n}}\text{? θ)}$ is asymptotically normal. In this paper the stopping times $\text{τ}{}_{\mathrm{c}}\text{(m) =}\text{inf}\text{{n ≥ m: n}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{|θ}{}_{\mathrm{n}}\text{? θ | > c }}$ associated with the sequence of confidence intervals for θ are investigated. A useful representation of M-estimators is derived, which is also appropriate for proving laws of the iterated logarithm and Donskertype invariance principles for (π_n)_n.     

Irreducible * representations of realC*-algebras

In this paper, we show that a topologically irreducible * representation of a realC*-algebra is also algebraically irreducible. Moreover, the properties of pure real states on a realC*-algebra and their left kernels are discussed.Partially supported by the National Natural Science Foundation of China.     

Equivariant cobordism of Grassmann and flag manifolds

We consider certain natural (ℤ₂)ⁿ actions on real Grassmann and flag manifolds andS ¹ actions on complex Grassmann manifolds with finite stationary point sets and determine completely which of them bound equivariantly.     

SEMI-LINEAR SYSTEMS OF BACKWARD STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS IN $R^n$

This paper explores the diffeomorphism of a backward stochastic ordinary differential equation (BSDE) to a system of semi-linear backward stochastic partial differential equations (BSPDEs), under the inverse of a stochastic flow generated by an ordinary stochastic differential equation (SDE). The author develops a new approach to BSPDEs and also provides some new results. The adapted solution of BSPDEs in terms of those of SDEs and BSDEs is constructed. This brings a new insight on BSPDEs, and leads to a probabilistic approach. As a consequence, the existence, uniqueness, and regularity results are obtained for the (classical, Sobolev, and distributional) solution of BSPDEs.The dimension of the space variable x is allowed to be arbitrary n, and BSPDEs are allowed to be nonlinear in both unknown variables, which implies that the BSPDEs may be nonlinear in the gradient. Due to the limitation of space, however, this paper concerns only classical solution of BSPDEs under some more restricted assumptions.