共查询到20条相似文献,搜索用时 171 毫秒
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1.通过一个平面凸区域的一个边界点而把这个凸区域包含在内部的圆周叫做这凸区域在这个边界点的支持圆周.假如把直线看做半径是无限大的圆周的话,那末支持直线正是支持圆周的特别情形,因此一个平面凸区域一定在它的每个边界点都有支持圆周。现在我们要来证明下面这个 相似文献
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在L-拓扑空间中提出α-远域族和α-拟一致结构的概念,讨论它的一些基本性质。在此基础上证明了每一个α-拟一致结构都可以诱导出一个α-层拓扑,每个α-层拓扑空间都可以α-拟一致化。由此,进一步分析α-拟一致连续与层连续之间的关系。 相似文献
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用α和η关于第一分量是仿射的且是斜对称的条件代替条件C,得到如下结论:(1)如果一个函数的梯度是(严格)αη-伪单调的,则该函数是(严格)伪αη-不变凸的;(2)如果一个函数的梯度是拟αη-单调的,则该函数是拟αη-不变凸的. 相似文献
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广义度量S-KKM映射的性质及其对变分不等式的应用 总被引:3,自引:0,他引:3
文开庭 《纯粹数学与应用数学》2009,25(1):152-156
引入了超S-γ-广义拟凸(凹)函数,建立了广义度量S-KKM映射与超S-γ-广义拟凸(凹)函数的关系.作为应用,获得了超凸度量空间中的新的KyFan极大极小不等式和鞍点定理. 相似文献
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G -凸空间中的广义对策和广义矢量拟平衡问题组 总被引:2,自引:0,他引:2
丁协平 《数学物理学报(A辑)》2006,26(4):506-515
该文在广义G -凸空间中引入并研究了一类新的广义矢量拟平衡问题组(SGVQEP).利用作者的一族集值映象的极大元存在定理,证明了广义对策的一个新的平衡存在定理.作为应用,在非紧乘积G -凸空间中证明了SGVQEP解的一些新的存在定理. 相似文献
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郭坤宇 《数学年刊A辑(中文版)》1996,(3)
在具有光滑边界的强拟凸域Ω上(n>1).用方程可解性的技巧,证明了多复变Hardy(Bergman)空间上符号属于H∞+C的FredholmToeplitz算子的指标为零.同时,结合B-D-F定理研究了Bergman空间上由全体Toeplitz算子生成的C-代数.在Bergman空间上,回答了M.Englis的一个问题。 相似文献
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V. B. Philippov N. Ya. Kirpichnikova S. N. Kirpichnikov 《Journal of Mathematical Sciences》2000,102(4):4321-4327
The problem of diffraction of a creeping wave propagating in a domain near the convex part of the boundary and overrunning
a point where the convex boundary transforms to the concave one is studied. The tangent to the boundary is continuous at this
point, but the derivative of the tangent has the jump. The Green's function to the right of the point of jump of curvature
is a superposition of whispering gallery waves. The Dirichlet, Neumann, and impedance boundary conditions are considered.
The formulas for the boundary current and for the diffraction coefficients related to the problem are obtained. Bibliography:
3 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 250, 1998, pp. 288–299.
Translated by N. Ya. Kirpichnikova 相似文献
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J. Haslinger T. Kozubek R. Kučera G. Peichl 《Numerical Linear Algebra with Applications》2007,14(9):713-739
This paper deals with a fast method for solving large‐scale algebraic saddle‐point systems arising from fictitious domain formulations of elliptic boundary value problems. A new variant of the fictitious domain approach is analyzed. Boundary conditions are enforced by control variables introduced on an auxiliary boundary located outside the original domain. This approach has a significantly higher convergence rate; however, the algebraic systems resulting from finite element discretizations are typically non‐symmetric. The presented method is based on the Schur complement reduction. If the stiffness matrix is singular, the reduced system can be formulated again as another saddle‐point problem. Its modification by orthogonal projectors leads to an equation that can be efficiently solved using a projected Krylov subspace method for non‐symmetric operators. For this purpose, the projected variant of the BiCGSTAB algorithm is derived from the non‐projected one. The behavior of the method is illustrated by examples, in which the BiCGSTAB iterations are accelerated by a multigrid strategy. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
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Andrzej Palczewski 《Mathematical Methods in the Applied Sciences》1992,15(6):375-393
The paper deals with the stationary Boltzmann equation in a bounded convex domain Ω. The boundary ?Ω is assumed to be a piecewise algebraic variety of the C2-class that fulfils Liapunov's conditions. On the boundary we impose the so-called Maxwell boundary conditions, that is a convex combination of specular and diffusive reflections. The non-linear Boltzmann equation is considered with additional volume and boundary source terms and it has been proved that for sufficiently small sources the problem possesses a unique solution in a properly chosen subspace of C(Ω × ?3). The proof is a refined version of the proof delivered by Guiraud for purely diffusive reflection. 相似文献
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Jaewoong Kim 《Journal of Mathematical Analysis and Applications》2010,371(1):184-189
In this paper it is shown that if an operator T satisfies ‖p(T)‖?‖p‖σ(T) for every polynomial p and the polynomially convex hull of σ(T) is a Carathéodory region whose accessible boundary points lie in rectifiable Jordan arcs on its boundary, then T has a nontrivial invariant subspace. As a corollary, it is also shown that if T is a hyponormal operator and the outer boundary of σ(T) has at most finitely many prime ends corresponding to singular points on ∂D and has a tangent at almost every point on each Jordan arc, then T has a nontrivial invariant subspace. 相似文献
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In this paper, we first show that for every mapping $f$ from a metric space $Ω$ to itself which is continuous off a countable subset of $Ω,$ there exists a nonempty
closed separable subspace $S ⊂ Ω$ so that $f|_S$ is again a self mapping on $S.$ Therefore,
both the fixed point property and the weak fixed point property of a nonempty closed
convex set in a Banach space are separably determined. We then prove that every
separable subspace of $c_0(\Gamma)$ (for any set $\Gamma$) is again lying in $c_0.$ Making use of these
results, we finally presents a simple proof of the famous result: Every non-expansive
self-mapping defined on a nonempty weakly compact convex set of $c_0(\Gamma)$ has a fixed
point. 相似文献
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The problem of the diffraction of creeping waves on a point of transition of the convex boundary to the straight boundary
of a domain is investigated. It is assumed that at the point of jump of curvature, the tangent to the boundary is continuous
and its derivative has a jump. An expression for the edge wave is obtained and investigated. Bibliography: 4 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 250, 1998, pp. 274–287.
Translated by N. Ya. Kirpichnikova. 相似文献
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Robert R. Miner 《Journal of Geometric Analysis》1999,9(1):143-160
A chain is the intersection of a complex totally geodesic subspace in complex hyperbolic 2-space with the boundary. The boundary
admits a canonical contact structure, and chains are distiguished curves transverse to this structure. The space of chains
is analyzed both as a quotient of the contact bundle, and as a subset of ℂP2. The space of chains admits a canonical, indefinite Hermitian metric, and curves in the space of chains with null tangent
vectors are shown to correspond to a path of chains tangent to a curve in the boundary transverse to the contact structure.
A family of local differential chain curvature operators are introduced which exactly characterize when a transverse curve
is a chain. In particular, operators that are invariant under the stabilizer of a point in the interior of complex hyperbolic
space, or a point on the boundary, are developed in detail. Finally, these chain curvature operators are used to prove a generalization
of Louiville's theorem: a sufficiently smooth mapping from the boundary of complex hyperbolic 2-space to itself which preserves
chains must be the restriction of a global automorphism. 相似文献
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《复变函数与椭圆型方程》2012,57(11):969-979
It is shown that a domain in C N with piecewise smooth boundary (and also of some more general shape) is a domain of holomorphy, provided the Levi form at every regular point is positively semidefinite and the tangent cone is convex at every point outside a boundary subset of zero Hausdorff (2N-2)-dimensional measure. 相似文献
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E. B. Kuznetsov 《Computational Mathematics and Mathematical Physics》2008,48(12):2162-2171
The numerical solution to a system of nonlinear algebraic or transcendental equations with several parameters is examined in the framework of the parametric continuation method. Necessary and sufficient conditions are proved for choosing the best parameters, which provide the best condition number for the system of linear continuation equations. Such parameters have to be sought in the subspace tangent to the solution space of the system of nonlinear equations. This subspace is obtained if the original system of nonlinear equations is solved at the various parameter values from a given set. The parametric approximation of curves and surfaces is considered. 相似文献
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基于代数等价变换和在KMM算法的框架基础上,在原始-对偶内点方法的牛顿方程里嵌入一种自调节功能.从而对凸二次规划提出了一种新的迭代方向的不可行内点算法,并证明了算法的全局收敛性. 相似文献