搜索结果: 121-135 共查到“知识库 实变函数论”相关记录168条 . 查询时间(1.953 秒)
On the Algebraic Properties of Convex Bodies and Some Applications
(differences of) convex bodies Minkowski operations quasilinear spaces (differences of) support functions
2009/1/13
We extend the set of convex bodies up to differences (factorized pairs) of convex bodies; thereby (Minkowski) multiplication by real scalar is extended in a natural way. We show that differences of co...
Regular Maximal Monotone Operators and the Sum Theorem
Maximal Monotone Operators Sum Theorem
2009/1/13
In this note, which is a continuation of [17], we study two classes of maximal monotone operators on general Banach spaces which we call ${\cal C}_0$ (resp. ${\cal C}_1$)-{\mit regular}. All maximal m...
Harmonic Sum and Duality
conjugate function convex sets duality gauge harmonic sum inverse sum normal cone shady set star-shaped set
2009/1/13
We consider an operation on subsets of a topological vector space which is closely related to what has been called the inverse addition by R.T. Rockafellar. Applied to closed convex sets, it appears a...
Piecewise Affine Selections for Piecewise Polyhedral Multifunctions and Metric Projections
Piecewise Affine Selections Piecewise Polyhedral Multifunctions Metric Projections
2009/1/13
Piecewise polyhedral multifunctions are the set-valued version of piecewise affine functions. We investigate selections of piecewise polyhedral multifunctions, in particular, the least norm selection ...
Epi-Distance Convergence of Parametrised Sums of Convex Functions in Non-Reflexive Spaces
Epi-Distance Convergence Parametrised Sums Convex Functions Non-Reflexive Spaces
2009/1/13
A weakened set of conditions is established for the epi-distance convergence of a sum $\{f_v+g_v\}_{v\in W}$ of parametrised closed convex functions $\{f_v\}_{v\in W}$ and $\{g_v\}_{v\in W}$ for $v\to...
Rank-One Connections at Infinity and Quasiconvex Hulls
Rank-One Infinity Quasiconvex Hulls
2009/1/13
We define $p$-rank-one connections at infinity for an unbounded set $K$ in $M^{N\times n}$ and show that the quasiconvex hull $Q_p(K)$ may be bigger than $K$ if $K$ has a $p$-rank-one connection, wher...
Optimality Conditions for Constrained Convex Parabolic Control Problems via Duality
Optimality Conditions Constrained Convex Parabolic Control via Duality
2009/1/13
The optimality system is given for a phase-constrained control problem governed by a linear parabolic equation. The control may act on the boundary and the cost function may depend on the boundary val...
加权K-NN分类器及其应用
K-NN分类器 权函数 加权K-NN分类器
2008/12/24
本文介绍了加权K-NN分类器的基本原理,并给出了相应的算法,着重对权函数的形式
进行了讨论,提出了两种新的权函数定义公式.将加权K-NN分类器用在白血球自动分类
系统中,分类精度比K-NN分类器有明显提高.
一类NMIFS吸引子
NMIFS吸引子 平衡向量测度 矩
2008/7/17
本文给出了NMIFS (Nonlinear Markov Iterated FunctionSystem)理论与构造NMIFS吸引子的方法,讨论了一类NMIFS吸引子的平衡向量测度和``矩''的递归计算，分析了NMIFS吸引子的结构特征.研究结果表明:对于MIFS,可以通过递归方法来计算矩$\hat{M}^{(i)}(i = 1,2, \ldots )$;而对于NMIFS,因$\hat{M...
本文研究了Oppenheim展式中一类例外关系集的Hausdorff维数。作为其应用，我们得到了L\"{u}roth级数展式中一些集合的Hausdorff维数的确切值，并给出了这些确切值的一个估计式.
一类反应扩散方程波前解的存在性
反应扩散方程 行波解 波前解的存在性
2008/7/14
本文讨论一类反应扩散方程满足各种条件的单调波前解及振荡波前解的存在性; 得到了一系列保证波前解存在的充分条件.
有关Gamma函数的一个双不等式
双边不等式 $\Gamma$函数 Stirling公式
2008/7/3
本文将文献[1]中的双边不等式从自然数推广至实数,证明了下面不等式成立: $$(\frac{x}{e})^x\sqrt {2\pi x} (1+\frac{1}{12x})<\Gamma (x+1)<(\frac{x}{e})^x\sqrt {2\pi x} (1+\frac{1}{12x-0.5}),$$ 其中$x\ge 1$.
实二次城$Q\sqrt{1+4k^2n}{a^2}$类数的可除性
2007/12/13
设d是无平方因子正整数,h(d)是实二次域$Q(\sqrt{d})$的类数.本文证明了:如果$da^2=1+4k^{2n}$,a、k、n是正整数,k>1,n>1,n的奇素因子p和k的素因子q都适合gcd(p,(q-1)q)=1,而且$2k^n+a\sqrt{d}$是Pell方程$u'^2-dv'^2=-1$的基本解,则除了(a,d,k,n)=(5,41,2,4)以及n=2,$k=P_mP_{m+1...
本文主要讨论Ｍ－连续格到Ｈｉｌｂｅｒｔ方体的嵌入问题．我们建立了Ｍ－连续格的次直积表示理论，推广并统一了Ｒａｎｅｙ，Ｂｒｕｎｓ，Ｌａｗｓｏｎ，Ｂａｎｄｅｌｔ和Ｅｒｎｅ等人的相应工作．Ｒｅｎａｙ与Ｂｒｕｎｓ的经典方法是建立在对相应的弱辅助关系的极大完备链作深入分析之上的，富于技巧性，且有局限性．与之相比，本文所使用的方体则相当朴素而自然，但却能处理更为广泛的情形．