共查询到20条相似文献,搜索用时 15 毫秒
1.
Let X(t) be an N parameter generalized Lévy sheet taking values in ℝd with a lower index α, ℜ = {(s, t] = ∏
i=1
N
(s
i, t
i], s
i < t
i}, E(x, Q) = {t ∈ Q: X(t) = x}, Q ∈ ℜ be the level set of X at x and X(Q) = {x: ∃t ∈ Q such that X(t) = x} be the image of X on Q. In this paper, the problems of the existence and increment size of the local times for X(t) are studied. In addition, the Hausdorff dimension of E(x, Q) and the upper bound of a uniform dimension for X(Q) are also established. 相似文献
2.
Svatoslav STANEK 《数学学报(英文版)》2006,22(6):1891-1914
The paper presents the conditions which guarantee that for some positive value of μ there are positive solutions of the differential equation (Ф(x'))'+μQ(t, x, x') = 0 satisfying the Dirichlet boundary conditions x(0) = x(T) = 0. Here Q is a continuous function on the set [0, T] × (0, ∞) ~ (R / {0}) of the semipositone type and Q is singular at the value zero of its phase variables. 相似文献
3.
Szymon Gła̧b 《Central European Journal of Mathematics》2009,7(4):732-740
Let $
\mathcal{K}
$
\mathcal{K}
(ℝ) stand for the hyperspace of all nonempty compact sets on the real line and let d
±(x;E) denote the (right- or left-hand) Lebesgue density of a measurable set E ⊂ ℝ at a point x∈ ℝ. In [3] it was proved that
$
\{ K \in \mathcal{K}(\mathbb{R}):\forall _x \in K(d^ + (x,K) = 1ord^ - (x,K) = 1)\}
$
\{ K \in \mathcal{K}(\mathbb{R}):\forall _x \in K(d^ + (x,K) = 1ord^ - (x,K) = 1)\}
相似文献
4.
LeiE(ℝn) be the space of all functions on ℝn which can continue to the entire holomorphic functions on ℂn. We define Riesz transformation Rj of distributions as a linear transformation of the quotient spaceD′(ℝn)/E(ℝn) to itself, j=1,2,..., n. These generalized Riesz transformations share the same properties with the classical ones, such
as
. As applications we generalize further a theorem of F. & M. Riesz generalized by Stein and Weiss, and then define a generalized
Hardy space, of which some properties are studied. 相似文献
5.
The scattering problem is studied, which is described by the equation (-Δ
x
+q(x,x/ɛ)−E)ψ = f(x), where ψ = ψ (x,ɛ) ∈ ℂ, x ℂ ℝ
d
, ɛ > 0, E > 0, the function q(x,y) is periodic with respect to y, and the function f is compactly supported. The solution satisfying radiation conditions at infinity is considered, and its asymptotic behavior
as ɛ → O is described. The asymptotic behavior of the scattering amplitude of a plane wave is also considered. It is shown
that in principal order both the solution and the scattering amplitude are described by the homogenized equation with potential
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