关于Noether对称性的两种理解

介绍了对Lagrange系统Noether对称性的两种理解，一种理解为Lagrange函数的不变性，另一种理解为作用量的不变性.研究表明，这两种理解是不同的.在一些条件下，Lagrange函数的不变性可以成为作用量的不变性，在另一些条件下，作用量的不变性可以成为Lagrange函数的不变性.将Noether对称性理解为作用量的不变性是合理的. 关键词： Lagrange系统 Noether对称性 作用量的不变性 Lagrange函数的不变性     

On functional central limit theorems for certain continuous time parameter stochastic processes

Weak invariance principles for certain continuous time parameter stochastic processes (including martingales and reverse martingales) are considered. Weak convergence in the sup-norm metric is also studied.     

环形振子与超对称性

采用量子力学中的超对称性和形不变性，讨论环形振子的波函数和能量本征值。     

Spin Statistics and CPT for Solitons

Conditions are analysed under which the statistics of soliton sectors of massive two-dimensional field theories can be properly defined. A soliton field algebra is defined as a crossed product with the group of soliton sectors. In this algebra, the nonlocal commutation relations are determined and weak locality, spin statistics and CPT theorems are proven. These theorems depart from their usual appearance due to the broken symmetry connecting the inequivalent vacua. An interpretation of these results in terms of modular theory is given. For the neutral subalgebra of the soliton algebra, the theorems hold in a familiar form, and twisted duality is derived.     

一种用于旋转不变分类识别的线性判别函数

提出利用线性判别函数，ｄ（ｘ）＝Ｗ＇ｘ，对轰炸机和战斗机两类目标进行旋转不变识别。每一目标有７２个旋转模式，其中９个为训练样本，６３个为测试样本，在每个目标的训练样本中随机取一个相减作为线性判别函数的系数（Ｗｉｊ）的初始值，然后利用误判的训练样本优化判别函数的权值以提高函数的正确识别率。为便于光电实现，线性判别函数的权值系数只有２、１、０、－１、－２五个值。计算机模拟表明利用此判别函数进行分类的正     

On the combinatorial invariance of Kazhdan-Lusztig polynomials

In this paper, we solve the conjecture about the combinatorial invariance of Kazhdan-Lusztig polynomials for the first open cases, showing that it is true for intervals of length 5 and 6 in the symmetric group. We also obtain explicit formulas for the R-polynomials and for the Kazhdan-Lusztig polynomials associated with any interval of length 5 in any Coxeter group, showing in particular what they look like in the symmetric group.     

ON BANDLIMITED SCALING FUNCTION

AbstractThis paper discuss band-limited scaling function, especially on the interval band case and three interval bands case, its relationship to oversampling property and weakly translation invariance are also studied. At the end, we propose an open problem.     

The First-Order Nonholonomic Connections with the Galilean Groups of Local Transformations. III

In the canonical smooth fiber bundles endowed with the metric tensor fields of relevant structure, we consider natural representations of the Galilean groups (1, n) and construct (1, n)-invariant generalized differential-geometric connections. In both regular and special cases of the representations of the considered groups (1, n), we find all affine nonholonomic , and _1,2-connections of the first order (see [1]–[3]) possessing the local Lie groups of transformations (1, n) and also describe the corresponding (1, n)invariant planar connections.     

Necessary and Sufficient Condition for the Functional Central Limit Theorem in Hölder Spaces

Let (X _i ) _i1 be an i.i.d. sequence of random elements in the Banach space B, S _n X ₁++X _n and _n be the random polygonal line with vertices (k/n,S _k ), k=0,1,...,n. Put (h)=h L(1/h), 0h1 with 0<1/2 and L slowly varying at infinity. Let H ⁰ (B) be the Hölder space of functions x:[0,1]B, such that x(t+h)–x(t)=o((h)), uniformly in t. We characterize the weak convergence in H ⁰ (B) of n ^–1/2 _n to a Brownian motion. In the special case where B= and (h)=h , our necessary and sufficient conditions for such convergence are E X ₁=0 and P(|X ₁|>t)=o(t ^–p()) where p()=1/(1/2–). This completes Lamperti (1962) invariance principle.     

Oscillating minimizers of a fourth-order problem invariant under scaling

By variational methods, we prove the inequality