共查询到20条相似文献,搜索用时 28 毫秒
1.
For a resistance form ${(X, \mathcal{D}(\varepsilon),\varepsilon)}For a resistance form (X, D(e),e){(X, \mathcal{D}(\varepsilon),\varepsilon)} and a point x0 ? X{x_0 \in X} as boundary, on the space X0:=X \{x0}{X_0:=X {\setminus}\{x_0\}} we consider the Dirichlet space Dx0:={f ? D(e) | f(x0)=0}{\mathcal{D}_{x_0}:=\{f\in\mathcal{D}(\varepsilon)\, |\, f(x_0)=0\}} and we develop a good potential theory. For any finely open subset D of X
0 we consider a localized resistance form (DX0 \ D,eD{\mathcal{D}_{X_0 {\setminus} D},\varepsilon_{D}}) where DX0 \ D:={f ? Dx0 | f=0{\mathcal{D}_{X_0 {\setminus} D}:=\{f\in\mathcal{D}_{x_0}\, |\, f=0} on X0 \ D}, eD(f,g):=e(f,g){X_0 {\setminus} D\},\, \varepsilon_D(f,g):=\varepsilon(f,g)} for all f,g ? DX0 \ D{f,g\in\mathcal{D}_{X_0 {\setminus} D}}. The main result is the equivalence between the local property of the resistance form and the sheaf property for the excessive
elements on finely open sets. 相似文献
2.
Enrique González-Jiménez 《Archiv der Mathematik》2010,95(3):233-241
We study the problem of the existence of arithmetic progressions of three cubes over quadratic number fields ${{\mathbb{Q}(\sqrt{D})}}We study the problem of the existence of arithmetic progressions of three cubes over quadratic number fields
\mathbbQ(?D){{\mathbb{Q}(\sqrt{D})}}, where D is a squarefree integer. For this purpose, we give a characterization in terms of
\mathbbQ(?D){{\mathbb{Q}(\sqrt{D})}}-rational points on the elliptic curve E : y
2 = x
3 − 27. We compute the torsion subgroup of the Mordell–Weil group of this elliptic curve over
\mathbbQ(?D){{\mathbb{Q}(\sqrt{D})}} and we give an explicit answer, in terms of D, to the finiteness of the free part of
E(\mathbbQ(?D)){E({\mathbb{Q}(\sqrt{D})})} for some cases. We translate this task to computing whether the rank of the quadratic D-twist of the modular curve X
0(36) is zero or not. 相似文献
3.
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
4.
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
{ x ? X|t - q\textRea y1 ( tA )x, t - q\textRea y2 ( tA )x ? L*p ( ( 0,¥ );X ) } {\left\{ {x\, \in \,X|t^{{ - \theta {\text{Re}}\alpha }} \psi _{1} {\left( {tA} \right)}x,\,t^{{ - \theta {\text{Re}}\alpha }} \psi _{2} {\left( {tA} \right)}x \in L_{*}^{p} {\left( {{\left( {0,\infty } \right)};X} \right)}} \right\}} 相似文献
5.
Liming Wu 《Journal of Theoretical Probability》2009,22(4):983-991
A beautiful result of Sarmanov (Dokl. Akad. Nauk SSSR 121(1), 52–55, 1958) says that for a Gaussian vector (X,Y),
\operatorname Var(\mathbb E[f(Y)|X]) £ r2\operatorname Var(f(Y))\operatorname {Var}(\mathbb {E}[f(Y)|X])\le \rho^{2}\operatorname {Var}(f(Y))
for all measurable functions f, where ρ is the (linear) correlation coefficient between X and Y. We generalize this result to a general Φ-entropy (a nonlinear version of his result) by means of a previous result of D. Chafai based on Bakry–Emery’s Γ
2-technique and tensorization. 相似文献
6.
We generalize a result of Kostant and Wallach concerning the algebraic integrability of the Gelfand-Zeitlin vector fields
to the full set of strongly regular elements in
\mathfrakg\mathfrakl \mathfrak{g}\mathfrak{l} (n, ℂ). We use decomposition classes to stratify the strongly regular set by subvarieties XD {X_\mathcal{D}} . We construct an étale cover
[^(\mathfrakg)]D {\hat{\mathfrak{g}}}_\mathcal{D} of XD {X_\mathcal{D}} and show that XD {X_\mathcal{D}} and
[^(\mathfrakg)]D {\hat{\mathfrak{g}}}_\mathcal{D} are smooth and irreducible. We then use Poisson geometry to lift the Gelfand-Zeitlin vector fields on XD {X_\mathcal{D}} to Hamiltonian vector fields on
[^(\mathfrakg)]D {\hat{\mathfrak{g}}}_\mathcal{D} and integrate these vector fields to an action of a connected, commutative algebraic group. 相似文献
7.
We take up in this paper the existence of positive continuous solutions for some nonlinear boundary value problems with fractional
differential equation based on the fractional Laplacian
(-D|D)\fraca2{(-\Delta _{|D})^{\frac{\alpha }{2}}} associated to the subordinate killed Brownian motion process ZaD{Z_{\alpha }^{D}} in a bounded C
1,1 domain D. Our arguments are based on potential theory tools on ZaD{Z_{\alpha }^{D}} and properties of an appropriate Kato class of functions K
α
(D). 相似文献
8.
David G. Ebin 《Geometric And Functional Analysis》2012,22(1):202-212
Let M be a compact manifold with a symplectic form ω and consider the group Dw{\mathcal{D}_\omega} consisting of diffeomorphisms that preserve ω. We introduce a Riemannian metric on M which is compatible with ω and use it to define an L
2-inner product on vector fields on M. Extending by right invariance we get a weak Riemannian metric on Dw{\mathcal{D}_\omega} . We show that this metric has geodesics which come from integral curves of a smooth vector field on the tangent bundle of
Dw{\mathcal{D}_\omega} . Then, estimating the growth of such geodesics, we show that they extend globally. 相似文献
9.
We extend a result of ?estakov to compare the complex interpolation method [X 0, X 1]θ with Calderón-Lozanovskii’s construction ${{{{X^{1-\theta}_{0}X^{\theta}_{1}}}}}
10.
We prove that the Jacobi algorithm applied implicitly on a decomposition A = XDX
T of the symmetric matrix A, where D is diagonal, and X is well conditioned, computes all eigenvalues of A to high relative accuracy. The relative error in every eigenvalue is bounded by O(ek(X)){O(\epsilon \kappa (X))} , where e{\epsilon} is the machine precision and k(X) o ||X||2·||X-1||2{\kappa(X)\equiv\|X\|_2\cdot\|X^{-1}\|_2} is the spectral condition number of X. The eigenvectors are also computed accurately in the appropriate sense. We believe that this is the first algorithm to compute
accurate eigenvalues of symmetric (indefinite) matrices that respects and preserves the symmetry of the problem and uses only
orthogonal transformations. 相似文献
11.
John R. Akeroyd 《Arkiv f?r Matematik》2011,49(1):1-16
It is shown that for any t, 0<t<∞, there is a Jordan arc Γ with endpoints 0 and 1 such that
G\{1} í \mathbbD:={z:|z| < 1}\Gamma\setminus\{1\}\subseteq\mathbb{D}:=\{z:|z|<1\}
and with the property that the analytic polynomials are dense in the Bergman space
\mathbbAt(\mathbbD\G)\mathbb{A}^{t}(\mathbb{D}\setminus\Gamma)
. It is also shown that one can go further in the Hardy space setting and find such a Γ that is in fact the graph of a continuous
real-valued function on [0,1], where the polynomials are dense in
Ht(\mathbbD\G)H^{t}(\mathbb{D}\setminus\Gamma)
; improving upon a result in an earlier paper. 相似文献
12.
Let X, X
1, X
2,… be i.i.d.
\mathbbRd {\mathbb{R}^d} -valued real random vectors. Assume that E
X = 0 and that X has a nondegenerate distribution. Let G be a mean zero Gaussian random vector with the same covariance operator as that of X. We study the distributions of nondegenerate quadratic forms
\mathbbQ[ SN ] \mathbb{Q}\left[ {{S_N}} \right] of the normalized sums S
N
= N
−1/2 (X
1 + ⋯ + X
N
) and show that, without any additional conditions,
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