共查询到20条相似文献,搜索用时 46 毫秒
1.
Katarzyna Jesse-Józefczyk 《Central European Journal of Mathematics》2012,10(3):1113-1124
Let G = (V, E) be a graph. A global secure set SD ⊆ V is a dominating set which satisfies the condition: for all X ⊆ SD, |N[X] ∩ SD| ≥ | N[X] − SD|. A global defensive alliance is a set of vertices A that is dominating and satisfies a weakened condition: for all x ∈ A, |N[x] ∩ A| ≥ |N[x] − A|. We give an upper bound on the cardinality of minimum global secure sets in cactus trees. We also present some results for
trees, and we relate them to the known bounds on the minimum cardinality of global defensive alliances. 相似文献
2.
In approximate halfspace range counting, one is given a set P of n points in ℝ
d
, and an ε>0, and the goal is to preprocess P into a data structure which can answer efficiently queries of the form: Given a halfspace h, compute an estimate N such that (1−ε)|P∩h|≤N≤(1+ε)|P∩h|. 相似文献
3.
We generalize a result by H. Brezis, Y. Y. Li and I. Shafrir [6] and obtain an Harnack type inequality for solutions of −Δu = |x|2α Ve u in Ω for Ω ⊂ ℝ2 open, α ∈ (−1, 0) and V any Lipschitz continuous function satisfying 0 < a ≤ V ≤ b < ∞ and ‖∇V‖∞ ≤ A. 相似文献
4.
We study the boundary value problem wt=ℵ0Δw+ℵ1w-ℵ2w|w|2,w|∂Ω0=0 in the domain Ω0={(x,y):0 ≤ x ≤ l1,0 ≤ y ≤ l2}. Here, w is a complex-valued function, Δ is the laplace operator, and ℵj, j=0,1,2, are complex constants withRe ℵj > 0. We show that under a rather general choice of the parameters l1 and l2, the number of stable invariant tori in the problem, as well as their dimensions, grows infinitely asRe ℵ0 → 0 andRe ℵ0 → 0.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 125, No. 2, pp. 205–220, November, 2000. 相似文献
5.
Let Δ3 be the set of functions three times continuously differentiable on [−1, 1] and such that f″′(x) ≥ 0, x ∈ [−1, 1]. We prove that, for any n ∈ ℕ and r ≥ 5, there exists a function f ∈ C
r
[−1, 1] ⋂ Δ3 [−1, 1] such that ∥f
(r)∥
C[−1, 1] ≤ 1 and, for an arbitrary algebraic polynomial P ∈ Δ3 [−1, 1], there exists x such that
| f(x) - P(x) | 3 C?n \uprhonr(x), \left| {f(x) - P(x)} \right| \geq C\sqrt n {{\uprho}}_n^r(x), 相似文献
6.
Summary In this note we present new properties of cliques induced constraints straintsX(C
r
+
)-X(C
r
-
) ≤ 1 - |C
r
-
| for λ εS, whereS is the set of cliques that are implied by 0–1 mixed integer programs. These properties allow to further fixing of 0–1 variables,
to detect instance's infeasibility and to imply new cliques. 相似文献
7.
Domain constants are numbers attached to regions in the complex plane ℂ. For a region Ω in ℂ, letd(Ω) denote a generic domain constant. If there is an absolute constantM such thatM
−1≤d(Ω)/d(Δ)≤M whenever Ω and Δ are conformally equivalent, then the domain constant is called quasiinvariant under conformal mappings.
IfM=1, the domain constant is conformally invariant. There are several standard problems to consider for domain constants. One
is to obtain relationships among different domain constants. Another is to determine whether a given domain constant is conformally
invariant or quasi-invariant. In the latter case one would like to determine the best bound for quasi-invariance. We also
consider a third type of result. For certain domain constants we show there is an absolute constantN such that |d(Ω)−d(Δ)|≤N whenever Ω and Δ and conformally equivalent, sometimes determing the best possible constantN. This distortion inequality is often stronger than quasi-invariance. We establish results of this type for six domain constants.
Research partially supported by a National Science Foundation Grant. 相似文献
8.
A set N ⊂ ℝ
d
is called a weak
ɛ-net (with respect to convex sets) for a finite X ⊂ ℝ
d
if N intersects every convex set C with |X ∩ C| ≥ ɛ|X|. For every fixed d ≥ 2 and every r ≥ 1 we construct sets X ⊂ ℝ
d
for which every weak 1/r -net has at least Ω(r log
d−1
r) points; this is the first superlinear lower bound for weak ɛ-nets in a fixed dimension. 相似文献
9.
Alejandro Illanes 《Rendiconti del Circolo Matematico di Palermo》2001,50(3):483-498
Adendroid is an arcwise connected hereditarily unicoherent continuum. Ashore set in a dendroidX is a subsetA ofX such that, for each ε>0, there exists a subdendroidB ofX such that the Hausdorff distance fromB toX is less then ε andB∩A=θ.
Answering a question by I. Puga, in this paper we prove that the finite union of pairwise disjoint shore subdendroids of a
dendroidX is a shore set. We also show that the hypothesis that the shore subdendroids are disjoint is necessary. It is still unknown
if the union of two closed disjoint shore subsets of a dendroidX is also shore set. 相似文献
10.
Paweł Strzelecki Heiko von der Mosel 《Calculus of Variations and Partial Differential Equations》2006,25(4):431-467
Motivated by previous work on elastic rods with self-contact, involving the concept of the global radius of curvature for
curves (as defined by Gonzalez and Maddocks), we define the global radius of curvature Δ[X] for a wide class of continuous parametric surfaces X for which the tangent plane exists on a dense set of parameters. It turns out that in this class of surfaces a positive lower
bound Δ[X] ≥ θ > 0 provides, naively speaking, the surface with a thickness of magnitude θ; it serves as an excluded volume constraint
for X, prevents self-intersections, and implies that the image of X is an embedded C1-manifold with a Lipschitz continuous normal. We also obtain a convergence and a compactness result for such thick surfaces,
and show one possible application to variational problems for embedded objects: the existence of ideal surfaces of fixed genus
in each isotopy class.
The proofs are based on a mixture of elementary topological, geometric and analytic arguments, combined with a notion of the
reach of a set, introduced by Federer in 1959.
Mathematics Subject Classification (2000) 49Q10, 53A05, 53C45, 57R52, 74K15 相似文献
11.
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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