Irregular wavelet frames on L~2 (R~n)

In this paper, we present the conditions on dilation parameter {sj}j that ensure a discrete irregular wavelet system to be a frame on L2(Rn), and for the wavelet frame we consider the perturbations of translation parameter b and frame function ψ respectively.     

Berezin transforms on the 2×2 matrix space related to theU(2)×U(2)-action

In this paper we establish the spectral decomposition of the Berezin transforms on the space Mat(2,) of complex 2×2 matrices related to the two-sided action ofU(2)×U(2). The eigenspaces are described explicitly by means of the matrix elements of a certain representation ofGL(2,) and each eigenvalue is expressed as a finite sum involving the MeijerG-functions evaluated at 1 and the Hahn polynomials.     

Invariant Sp(1)-instantons on S 2 × S 2

In this paper all (anti)self-dual invariant connections on homogeneous quaternionic line bundles over S ² × S ² are calculated and described in terms of the isotropy homomorphism of the bundle using Wang's theorem. These are the canonical connections on bundles with an (anti)symmetric twist and an S ¹-parametrized family of flat structures on bundles with a simple twist.     

Arc-transitive cubic Cayley graphs on PSL(2,p)

For a prime p at least 5,let T=PSL(2,p).This paper gives a classification of the connected arc-transitive cubic Cayley graphs on T and a determination of the gener- ated pairs ((?),(?)) of T such that o((?))=2 and o((?))=3.     

Smooth Involutions on the 2k-dimensional Quaternionic Projective Space HP(2k)

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Cohomology of osp(2|2) acting on spaces of linear differential operators on the superspace ℝ1|2

We compute the first differential cohomology of the orthosymplectic Lie superalgebra osp(2|2) with coefficients in the superspace of linear differential operators acting on the space of weighted densities on the (1, 2)-dimensional real superspace. We also compute the same, but osp(1|2)-relative, cohomology. We explicitly give 1-cocycles spanning these cohomologies. This work is the simplest generalization of a result from [1].     

计数法(2)

(续上期 )3　算两次“算两次”的典型做法是选择一个适当的量 ,从两个方面去考虑它 ,“一方面… ,另一方面… ,综合起来可得… .”好像三步舞曲 ,这种舞曲在组合计数中常常用到 .例 8　n ,k∈Z ,S为平面上几个点的集合 ,对于S中任一点A ,S中至少有k个点到A的距离相等 .证明k <1     

Traces on an (AF)-Algebra

Let A= U A_n be an (AF)-algebra with identity e, where A_n = M(p(n)),p(n) = (p~(n)) ∈Z_(++)~(r(n)), A_n→A_(n+1), e∈A_n, n, τ(A) be the space of alltracial states on A,G(A) = lim (Z~(r(n)),φ_n) be the dimension group of A,φ_u(G) bethe state space of G(A), where u =φ_(n∞).(p(n)) is an ordered unit of G(A).     

A Note on Property(ω)

In this note we study the property(ω),a variant of Weyl's theorem introduced by Rakoevic,by means of the new spectrum.We establish for a bounded linear operator defined on a Banach space a necessary and sufficient condition for which both property(ω) and approximate Weyl's theorem hold.As a consequence of the main result,we study the property(ω) and approximate Weyl's theorem for a class of operators which we call the λ-weak-H(p) operators.     

A note on the crossed product R(A, α) associated with PSL_2(R)

Given the hyperbolic measure dxdy/y2 on the upper half plane H, the rational actions of PSL2(R) on H induces a continuous unitary representation α of this group on the Hilbert space L2(H, dxdy/y2). Supposing that A = {Mf : f ∈ L∞(H, dxdy/y2)}, we show that the crossed product R(A,α) is of type I. In fact, the crossed product R(A,α) is *-isomorphic to the von Neumann algebra B(L2(P,ν))■LK, where LK is the abelian group von Neumann algebra generated by the left regular representation of K.     

The integral points on elliptic curves y 2 = x 3 + (36n 2 − 9)x − 2(36n 2 − 5)

Let n be a positive odd integer. In this paper, combining some properties of quadratic and quartic diophantine equations with elementary analysis, we prove that if n > 1 and both 6n ² ? 1 and 12n ² + 1 are odd primes, then the general elliptic curve y ² = x ³+(36n ²?9)x?2(36n ²?5) has only the integral point (x, y) = (2, 0). By this result we can get that the above elliptic curve has only the trivial integral point for n = 3, 13, 17 etc. Thus it can be seen that the elliptic curve y ² = x ³ + 27x ? 62 really is an unusual elliptic curve which has large integral points.     

Orthogonal polynomials for Jacobi-exponential weights (1−x 2) ρ e −Q(x) on (−1,1)

This paper deals with orthogonal polynomials for Jacobi-exponential weights (1?x ²) ^ρ e ^?Q(x) on (?1,1) and gives bounds on orthogonal polynomials, zeros, and Christofel functions. In addition, restricted range inequalities are also obtained.     

A Dominated Theorem on 5L(2, R) and Its Application

In this paper, we give the following dominated theorem: Let φ(g) ∈ L1(G//K),φε(t)=ε> 0, and the least radical decreasing dominatedfunction φ(t) = sup |φ(y)| ∈L1(G//K). If shtφ(t) is monotonically decreasingon (0, ∞), then for any f∈L1loc(G//K) , the following inequality holds:sup |φε * f(x)| ≤ Cmf(x),where mf(x) is the Hardy-Littlewood maximal function of f, and C = ||φ||1.An application of this dominated theorem is also given.     

(a~(1/2))~2与(a~2)~(1/2)的异同

<正>学习二次根式时,经常要遇到与二次根式有关的两个重要式子:(a^(1/2))(1/2))²与(a2与(a²)2)^(1/2).这两个式子在形式上很相近,既有不同点又有相同点,因此一不小心就很容易把它们混淆了.一、不同点1.运算顺序不同(a(1/2).这两个式子在形式上很相近,既有不同点又有相同点,因此一不小心就很容易把它们混淆了.一、不同点1.运算顺序不同(a^(1/2))(1/2))²是对实数a先开方再平方,表示a的算术平方根的平方;(a2是对实数a先开方再平方,表示a的算术平方根的平方;(a²)2)^(1/2)是对实数a先平方再开方,表示a的平方的算术平方根.     

(a~(1/2))~2与(a~2)~(1/2)的辨析

(a~(1/2))2与(a~2)~(1/2)在二次根式中扮演着十分重要的角色,由于这两个二次根式的外表较相似,有些同学在运算中往往对它们产生了混淆,发生这样或那样的错误．下面谈谈这两个概念的区别与联系．     

On (4p~2q~(2b),2p~2q~(2b)-pq~b,p~2q~(2b)-pq~b) Menon Difference Sets

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(a~(1/2))~2和(a~2)~(1/2)告状记

(a~(1/2))~2和(a~2)~(1/2)兄妹俩,一来到花果山就受到众猴儿的青睐,争相和他俩交朋友,哪知有的小猴对他俩不礼貌,有时还受到了委屈,于是他俩就到猴王那里去告状,兄妹俩来到猴王面前,深深行了个鞠躬礼说:“报告猴王,小猴儿常把我俩张冠李戴,用我俩来解题时,     

正确理解并运用(a~2)~(1/2)

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