cut* 空间的拓扑性质

该文引入了 cut^*空间的概念,所谓的 cut^*空间是指去掉任意一点连通,去掉任意两点不连通的连通空间.通过对其性质的讨论,得到如下主要结论: 首先得到cut^*空间中每个点非开即闭,并且cut^*空间中有无限多个闭点;其次讨论了一类特殊的 cut^*空间,即去掉一点是COTS的 cut^* 空间.指出``$X$是 cut^*空间,任意 $x\inX,X\setminus\{x\}$是不可约cut空间'这样的空间类是不存在的.在文章的最后,讨论了去掉一点是LOTS的 cut^*空间的覆盖性质,得到这样的空间是紧空间或Lindel\"of空间的结论.     

非线性抛物椭圆方程组的正则解和奇异解

该文用单模方法在Lorentz空间研究了抛物椭圆方程组奇异解和正则解的存在性, 其中初值属于Lorentz空间L^{n/2,∞ ₍}Rⁿ), n≥ 3. 利用时间加权的Lorentz空间, 还得到了其正则解. 此外, 如果初值满足自相似结构, 也得到了自相似解的存在性.     

H+离子在固体中的电子俘获

在0.6, 0.9, 1.2, 1.6和1.8 MeV的能量下, 测量了H⁺离子在不同厚度的碳膜中产生的中性产物H和负离子产物H-的产额Φ(H)和Φ(H^-). 测量结果表明, 在相同的能量下Φ(H)和Φ(H^-)都是常数, 而且Φ(H)比Φ(H^-)大几个数量级. 分析了H⁺在固体中运行时不断地俘获和损失电子的电荷交换过程. 证明快离子在固体中确实存在这个过程, 并得到了电荷交换截面比的经验公式.     

积域上奇异积分算子的Lp有界性

用旋转法证明了对于Ω∈ L(log⁺L)² (Sⁿ-1×S^m-1),Ω(x′,y′)dσ(x′)= 0(y′∈S^m-1), Ω(x′,y′)dσy′)=0(x′∈Sⁿ-1),带核函数K(u,v)= Ω(u′,v′)|u|^-n|v|^-m的奇异积分算子T是L^p(Rⁿ×R^m)有界的,其中1<p<∞.     

H1中(次)临界的复Ginzburg-Landau

研究H¹ (Rⁿ)中临界的复Ginzburg-Landau方程的初值问题, 当空间维数n≥3时, 讨论了它的解在空间C(0, ∞; 1(Rⁿ) )∩L²(0, ∞;H ^{1, 2n/(n-2)} (Rⁿ) )的长时间衰减行为. 当空间维数n≥1时, 对非线性项在H¹(Rⁿ)中具有次临界的增长阶的情形也有类似的结果.     

拟共形映射Lp -可积指数的上确界

设 f 是R²中单位圆 B²上的K -拟共形映射, 该文证明了 $\sup_{0相似文献   

Hk流的微分Harnack 估计

对k>0,得到了在Rⁿ⁺¹中的H^k流的解的微分Harnack估计. 应用这个估计, 得到了关于H^k-流迁移孤立子的一些性质.     

Woronowicz C*代数交叉积的正则与协变表示

A是Woronowicz C^*代数, G是作用于其上的离散群, 主要证明了它们的交叉积代数A×_αG的正则表示和协变表示都对应于乘法酉算子,同时证明了正则协变的C^*代数也是一个对应乘法酉算子的Woronowicz C^*代数,最后给出了C(SU_q(2)×_αZ对应的乘法酉算子的一个明确表示.     

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定义了L^*-逆半群, 并引入了半群左圈积的概念. 证明了半群S是一个L^*-逆半群, 当且仅当S是一个型A半群Γ和一个左正则带B连同结构映射φ的左圈积B_âφ. 这一结果的一个直接推论是关于左逆半群结构的著名Yamada定理. 利用半群的左圈积, 给出了一个非平凡的L^*-逆半群的例子.     

算子代数的超滤积

研究了C^*代数和von Neumann代数的超滤积的一些基本问题，包括和C^*代数K理论的关系.特别地, 证明了在一定的条件下, C^*代数超滤积的K群同构于相应C^*代数K群的超滤积, 还证明了II₁型因子的超滤积是素的, 也就是说, 不同构于任意非平凡的张量积.     

Fourier Multipliers for Lp on Chebli-Trimeche Hypergroups

In this paper we consider Fourier multipliers for L^p (p>1)on Chébli-Trimèche hypergroups and establish aversion of Hörmander's multiplier theorem. As applicationswe give some results concerning the Riesz potentials and oscillatingmultipliers. 1991 Mathematics Subject Classification: 43A62,43A15, 43A32.     

Optimal Regularity and Fredholm Properties of Abstract Parabolic Operators in Lp Spaces on the Real Line

We study the operator Lu(t):= u'(t) – A(t) u(t) on L^p(R; X) for sectorial operators A(t), with t R, on a Banachspace X that are asymptotically hyperbolic, satisfy the Acquistapace–Terreniconditions, and have the property of maximal L^p-regularity.We establish optimal regularity on the time interval R showingthat L is closed on its minimal domain. We further give conditionsfor ensuring that L is a semi-Fredholm operator. The Fredholmproperty is shown to persist under A(t)-bounded perturbations,provided they are compact or have small A(t)-bounds. We applyour results to parabolic systems and to generalized Ornstein–Uhlenbeckoperators. 2000 Mathematics Subject Classification 35K20, 35K90,47A53.     

The largest prime factor of X3+2

The largest prime factor of X³+2 was investigated in 1978 byHooley, who gave a conditional proo that it is infinitely oftenat least as large as X¹+, with a certain positive constant .It is trivial to obtain such a result with =0. One may thinkof Hooley's result as an approximation to the conjecture thatX³+2 is infinitely often prime. The condition required by Hooley,his R^* conjecture, gives a non-trivial bound for short Ramanujan–Kloostermansums. The present paper gives an unconditional proof that thelargest prime factor of X³+2 is infinitely often at least aslarge as X¹⁺, though with a much smaller constant than thatobtained by Hooley. In order to do this we prove a non-trivialbound for short Ramanujan–Kloosterman sums with smoothmodulus. It is also necessary to modify the Chebychev method,as used by Hooley, so as to ensure that the sums that occurdo indeed have a sufficiently smooth modulus. 2000 MathematicsSubject Classification: 11N32.     

C1,1半定规划的二阶最优性条件

该文研究了一类非光滑半定规划问题,其中目标函数是C^1,1函数,约束是半定的. 借助于Peano广义梯度,给出了其二阶最优性必要条件和二阶最优性充分条件     

Uniform l1 behaviour for time discretization of a Volterra equation with completely monotonic kernel: I. stability

This paper is the first of two papers on the time discretizationof the equation u_t + ^t ₀ ß (t — s) Au (s) ds= 0, t > 0, u (0) = u₀, where A is a self-adjoint denselydefined linear operator on a Hilbert space H with a completeeigensystem {_m, _m}_{m = 1}, and ß (t) is completely monotonicand locally integrable, but not constant. The equation is discretizedin time using first-order differences in combination with order-oneconvolution quadrature. The stability properties of the timediscretization are derived in the l¹_t (0, ; H) norm.     

(n+1)重周期和准周期Riemann边值问题

该文首先考虑了Rⁿ⁺¹维欧氏空间中(n+1)重周期正则函数和(n+1)重准周期正则函数的一些性质, 然后分别讨论了n+1重周期和准周期Riemann边值问题, 分别给出了两种边值问题 解的显式表达式和可解条件.     

A hierarchical basis preconditioner for the biharmonic equation on the sphere

^** Email: jan.maes{at}cs.kuleuven.be In this paper, we propose a natural way to extend a bivariatePowell–Sabin (PS) B-spline basis on a planar polygonaldomain to a PS B-spline basis defined on a subset of the unitsphere in [graphic: see PDF] . The spherical basis inherits many properties of the bivariatebasis such as local support, the partition of unity propertyand stability. This allows us to construct a C¹ continuous hierarchicalbasis on the sphere that is suitable for preconditioning fourth-orderelliptic problems on the sphere. We show that the stiffnessmatrix relative to this hierarchical basis has a logarithmicallygrowing condition number, which is a suboptimal result comparedto standard multigrid methods. Nevertheless, this is a hugeimprovement over solving the discretized system without preconditioning,and its extreme simplicity contributes to its attractiveness.Furthermore, we briefly describe a way to stabilize the hierarchicalbasis with the aid of the lifting scheme. This yields a waveletbasis on the sphere for which we find a uniformly well-conditionedand (quasi-) sparse stiffness matrix.     

具有退化粘性的非齐次双曲守恒律方程的Cauchy问题

该文讨论了如下具有退化粘性的非齐次双曲守恒律方程的Cauchy问题$\left\{\begin{array}{l} u_t+f(u)_x=a^2t^\alpha u_{xx}+g(u),\ \ \ x\in{\bf R},\ \ \ t>0,\\u(x,0)=u_0(x) \in L^\infty({\bf R}).\end{array}\right.\eqno{({\rm I})}$其中$f(u), g(u)$是${\bf R}$上的光滑函数, $a>0, 0<\alpha<1$均为常数.在此条件下, 作者首先给出了Cauchy问题(I)的局部解的存在性, 再利用极值原理获得了解的$L^{\infty}$估计, 从而证明了Cauchy问题(I)整体光滑解的存在性.