共查询到20条相似文献,搜索用时 31 毫秒
1.
Atsushi Shiho 《Selecta Mathematica, New Series》2011,17(4):833-854
Let
X \hookrightarrow[`(X)]{X \hookrightarrow \overline{X}} be an open immersion of smooth varieties over a field of characteristic p > 0 such that the complement is a simple normal crossing divisor and [`(Z)] í Z í [`(X)]{\overline{Z}\subseteq Z \subseteq \overline{X}} closed subschemes of codimension at least 2. In this paper, we prove that the canonical restriction functor between the categories
of overconvergent F-isocrystals F-Isocf(X,[`(X)]) ? F-Isocf(X\Z,[`(X)]\[`(Z)]){F-{\rm Isoc}^\dagger(X,\overline{X}) \longrightarrow F-{\rm Isoc}^\dagger(X{\setminus}Z, \overline{X}{\setminus}\overline{Z})} is an equivalence of categories. We also give an application of our result to the equivalence of certain categories. 相似文献
2.
Carlo Alberto De Bernardi 《Archiv der Mathematik》2009,93(4):369-378
A selection theorem concerning support points of convex sets in a Banach space is proved. As a corollary we obtain the following result. Denote by ${\mathcal{BCC}(X)}A selection theorem concerning support points of convex sets in a Banach space is proved. As a corollary we obtain the following
result. Denote by BCC(X){\mathcal{BCC}(X)} the metric space of all nonempty bounded closed convex sets in a Banach space X. Then there exists a continuous mapping S : BCC(X) ? X{S : \mathcal{BCC}(X) \rightarrow X} such that S(K) is a support point of K for each K ? BCC(X){K \in \mathcal{BCC}(X)}. Moreover, it is possible to prescribe the values of S on a closed discrete subset of BCC(X){\mathcal{BCC}(X)}. 相似文献
3.
Jean Saint Raymond 《Mediterranean Journal of Mathematics》2013,10(2):927-940
We prove that if X is a Banach space and ${f : X \rightarrow \mathbb{R} \cup \{+\infty\}}$ is a proper function such that f ? ? attains its minimum for every ? ε X *, then the sublevels of f are all relatively weakly compact in X. As a consequence we show that a Banach space X where there exists a function ${f : X \rightarrow \mathbb{R}}$ such that f ? ? attains its minimum for every ? ε X * is reflexive. We also prove that if ${f : X \rightarrow \mathbb{R} \cup \{+\infty\}}$ is a weakly lower semicontinuous function on the Banach space X and if for every continuous linear functional ? on X the set where the function f ? ? attains its minimum is convex and non-empty then f is convex. 相似文献
4.
Let A and X be nonempty, bounded and closed subsets of a geodesic metric space (E, d). The minimization (resp. maximization) problem denoted by min(A, X) (resp. max(A, X)) consists in finding ${(a_0,x_0) \in A \times X}$ such that ${d(a_0,x_0) = \inf\left\{d(a,x) : a \in A, x \in X\right\}}$ (resp. ${d(a_0,x_0) = \sup\left\{d(a,x) : a \in A, x \in X\right\}}$ ). We give generic results on the well-posedness of these problems in different geodesic spaces and under different conditions considering the set A fixed. Besides, we analyze the situations when one set or both sets are compact and prove some specific results for CAT(0) spaces. We also prove a variant of the Drop Theorem in Busemann convex geodesic spaces and apply it to obtain an optimization result for convex functions. 相似文献
5.
Daniela Roşu 《NoDEA : Nonlinear Differential Equations and Applications》2010,17(4):479-496
In this paper we consider a nonlinear evolution reaction–diffusion system governed by multi-valued perturbations of m-dissipative operators, generators of nonlinear semigroups of contractions. Let X and Y be real Banach spaces, ${\mathcal{K}}In this paper we consider a nonlinear evolution reaction–diffusion system governed by multi-valued perturbations of m-dissipative operators, generators of nonlinear semigroups of contractions. Let X and Y be real Banach spaces, K{\mathcal{K}} be a nonempty and locally closed subset in
\mathbbR ×X×Y, A:D(A) í X\rightsquigarrow X, B:D(B) í Y\rightsquigarrow Y{\mathbb{R} \times X\times Y,\, A:D(A)\subseteq X\rightsquigarrow X, B:D(B)\subseteq Y\rightsquigarrow Y} two m-dissipative operators, F:K ? X{F:\mathcal{K} \rightarrow X} a continuous function and
G:K \rightsquigarrow Y{G:\mathcal{K} \rightsquigarrow Y} a nonempty, convex and closed valued, strongly-weakly upper semi-continuous (u.s.c.) multi-function. We prove a necessary
and a sufficient condition in order that for each (t,x,h) ? K{(\tau,\xi,\eta)\in \mathcal{K}}, the next system
{ lc u¢(t) ? Au(t)+F(t,u(t),v(t)) t 3 tv¢(t) ? Bv(t)+G(t,u(t),v(t)) t 3 tu(t)=x, v(t)=h, \left\{ \begin{array}{lc} u'(t)\in Au(t)+F(t,u(t),v(t))\quad t\geq\tau \\ v'(t)\in Bv(t)+G(t,u(t),v(t))\quad t\geq\tau \\ u(\tau)=\xi,\quad v(\tau)=\eta, \end{array} \right. 相似文献
6.
Farthest points of sets in uniformly convex banach spaces 总被引:4,自引:0,他引:4
Michael Edelstein 《Israel Journal of Mathematics》1966,4(3):171-176
LetS be a closed and bounded set in a uniformly convex Banach spaceX. It is shown that the set of all points inX which have a farthest point inS is dense. Letb(S) denote the set of all farthest points ofS, then a sufficient condition for
to hold is thatX have the following property (I): Every closed and bounded convex set is the intersection of a family of closed balls. 相似文献
7.
The main result is that, for any projective compact analytic subset Y of dimension q > 0 in a reduced complex space X, there is a neighborhood Ω of Y such that, for any covering space ${\Upsilon\colon\widehat X\to X}
8.
Let X be a Banach space with a separable dual X*. Let ${Y\subset X}
9.
10.
On Well-posed Mutually Nearest and
Mutually Furthest Point Problems in Banach Spaces 总被引:3,自引:0,他引:3
ChongLI RenXingNI 《数学学报(英文版)》2004,20(1):147-156
Let G be a non-empty closed(resp.bounded closed)boundedly relatively weakly compact subset in a strictly convex Kadec Banach space X.Let K(X)denote the space of all non-empty compact convex subsets of X endowed with the Hausdorff distance.Moreover,let KG(X)denote the closure of the set {A∈K(x):A∩G=0}.We prove that the set of all A∈KG(X)(resp.A∈K(X)),such that the minimization (resp.maximization)problem min(A,G)(resp.max(A,G))is well posed,contains a dense Gδ-subset of KG(X)(resp.K(X)).thus extending the recent results due to Blasi,Myjak and Papini and Li. 相似文献
11.
J. Gandini 《Transformation Groups》2011,16(1):109-136
Let G be a simply connected semisimple algebraic group over an algebraically closed field k of characteristic 0 and let V be a rational simple G-module. If G/H ⊂ P(V) is a spherical orbit and if X = [`(G/H)] X = \overline {G/H} is its closure, then we describe the orbits of X and those of its normalization [(X)\tilde] \tilde{X} . If, moreover, the wonderful completion of G/H is strict, then we give necessary and sufficient combinatorial conditions so that the normalization morphism [(X)\tilde] ? X \tilde{X} \to X is a homeomorphism. Such conditions are trivially fulfilled if G is simply laced or if H is a symmetric subgroup. 相似文献
12.
Markus Haase 《Integral Equations and Operator Theory》2006,56(2):197-228
We generalize a Hilbert space result by Auscher, McIntosh and Nahmod to arbitrary Banach spaces X and to not densely defined injective sectorial operators A. A convenient tool proves to be a certain universal extrapolation space associated with A. We characterize the real interpolation space
( X,D( Aa ) ?R( Aa ) )q,p{\left( {X,\mathcal{D}{\left( {A^{\alpha } } \right)} \cap \mathcal{R}{\left( {A^{\alpha } } \right)}} \right)}_{{\theta ,p}}
as
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