共查询到20条相似文献,搜索用时 62 毫秒
1.
Anthony Flatters 《Journal of Number Theory》2009,129(1):209-219
We study primitive prime divisors of the terms of Δ(u)=(Δn(u))n?1, where Δn(u)=NK/Q(un−1) for K a real quadratic field, and u a unit element of its ring of integers. The methods used allow us to find the terms of the sequence that do not have a primitive prime divisor. 相似文献
2.
Kazuhiro Takimoto 《Journal of Mathematical Analysis and Applications》2005,309(1):227-237
We consider the removability of singular sets for the curvature equations of the form Hk[u]=ψ, which is determined by the kth elementary symmetric function, in an n-dimensional domain Ω. We prove that, for 1?k?n−1 and a compact set K whose (n−k)-dimensional Hausdorff measure is zero, any generalized solution to the curvature equation on Ω?K is always extendable to a generalized solution on the whole domain Ω. 相似文献
3.
Simone Cecchini Rolando Magnanini 《Calculus of Variations and Partial Differential Equations》2010,39(1-2):121-138
We study the minimizer u of a convex functional in the plane which is not Gâteaux-differentiable. Namely, we show that the set of critical points of any C 1-smooth minimizer can not have isolated points. Also, by means of some appropriate approximating scheme and viscosity solutions, we determine an Euler–Lagrange equation that u must satisfy. By applying the same approximating scheme, we can pair u with a function v which may be regarded as the stream function of u in a suitable generalized sense. 相似文献
4.
Van Vu 《Advances in Mathematics》2006,207(1):221-243
Let K be a smooth convex set with volume one in Rd. Choose n random points in K independently according to the uniform distribution. The convex hull of these points, denoted by Kn, is called a random polytope. We prove that several key functionals of Kn satisfy the central limit theorem as n tends to infinity. 相似文献
5.
Theodore Laetsch 《Journal of Mathematical Analysis and Applications》1975,51(3):653-669
We consider the equation u = λAu (λ > 0), where A is a forced isotone positively convex operator in a partially ordered normed space with a complete positive cone K. Let Λ be the set of positive λ for which the equation has a solution u?K, and let Λ0 be the set of positive λ for which a positive solution—necessarily the minimum one—can be obtained by an iteration un = λAun?1, u0 = 0. We show that if K is normal, and if Λ is nonempty, then Λ0 is nonempty, and each set Λ0, Λ is an interval with ; but we may have λ1 ? Λ0 and λ1 ? Λ. Furthermore, if A is bounded on the intersection of K with a neighborhood of 0, then Λ0 is nonempty. Let u0(λ) = limn→∞(λA)n(0) be the minimum positive fixed point corresponding to λ ? Λ0. Then u0(λ) is a continuous isotone convex function of λ on Λ0. 相似文献
6.
Leonid Plachta 《Topology and its Applications》2007,154(15):2880-2887
Recently Stoimenow showed that for every knot K and any n∈N and u0?u(K) there is a prime knot Kn,uo which is n-equivalent to the knot K and has unknotting number u(Kn,uo) equal to u0. The similar result has been obtained for the 4-ball genus gs of a knot. Stoimenow also proved that any admissible value of the Tristram-Levine signature σξ can be realized by a knot with the given Vassiliev invariants of bounded order. In this paper, we show that for every knot K with genus g(K) and any n∈N and m?g(K) there exists a prime knot L which is n-equivalent to K and has genus g(L) equal to m. 相似文献
7.
《Journal de Mathématiques Pures et Appliquées》2003,82(1):43-66
On a Riemannian manifolds (M,g) of dimension n, we prove on compact set K⊂M, that the positive solutions of the equation of prescribed scalar curvature (and the equation of subcritical case) are uniformely bounded.In positive case, when the manifold is compact, we prove that supMu×infMu⩾c>0 if n⩾3 (respectively supMu+infMu⩾c is n=2). 相似文献
8.
Vincent Thilliez 《Journal of Mathematical Analysis and Applications》2007,328(2):1141-1151
Let f be a real-analytic function germ at the origin in Rn, whose critical locus contains a given real-analytic set X, and let Y be a germ of a closed subset at the origin. We study the stability of f under perturbations u that are flat on Y and that belong to a given Denjoy-Carleman non-quasianalytic class. We obtain a condition ensuring that f+u=f○Φ where Φ is a germ of diffeomorphism whose components belong to a (generally larger) Denjoy-Carleman class. Roughly speaking, this condition involves a ?ojasiewicz-type separation property between Y and the complex zeros of a certain ideal associated with f and X. The relationship between the Denjoy-Carleman classes of u and Φ is controlled precisely by the inequality. This result extends, and simplifies, former work of the author on germs with isolated critical points. 相似文献
9.
Jan-Hendrik Evertse 《Indagationes Mathematicae》2004,15(3):347-355
Let K be a field of characteristic 0 and let (K*)n denote the n-fold Cartesian product of K*, endowed with coordinatewise multiplication. Let Γ be a subgroup of (K*)n of finite rank. We consider equations (*) a1x1 + … + anxn = 1 in x = (x1xn)Γ, where a = (a1,an)(K*)n. Two tuples a, b(K*)n are called Γ-equivalent if there is a uΓ such that b = u · a. Gy?ry and the author [Compositio Math. 66 (1988) 329-354] showed that for all but finitely many Γ-equivalence classes of tuples a(K*)n, the set of solutions of (*) is contained in the union of not more than 2(n+1! proper linear subspaces of Kn. Later, this was improved by the author [J. reine angew. Math. 432 (1992) 177-217] to (n!)2n+2. In the present paper we will show that for all but finitely many Γ-equivalence classes of tuples of coefficients, the set of non-degenerate solutions of (*) (i.e., with non-vanishing subsums) is contained in the union of not more than 2n proper linear subspaces of Kn. Further we give an example showing that 2n cannot be replaced by a quantity smaller than n. 相似文献
10.
11.
《Discrete Mathematics》2004,274(1-3):125-135
The classical Ramsey number r(m,n) can be defined as the smallest integer p such that in every two-coloring (R,B) of the edges of Kp, β(B)⩾m or β(R)⩾n, where β(G) denotes the independence number of a graph G. We define the upper domination Ramsey number u(m,n) as the smallest integer p such that in every two-coloring (R,B) of the edges of Kp, Γ(B)⩾m or Γ(R)⩾n, where Γ(G) is the maximum cardinality of a minimal dominating set of a graph G. The mixed domination Ramsey number v(m,n) is defined to be the smallest integer p such that in every two-coloring (R,B) of the edges of Kp, Γ(B)⩾m or β(R)⩾n. Since β(G)⩽Γ(G) for every graph G, u(m,n)⩽v(m,n)⩽r(m,n). We develop techniques to obtain upper bounds for upper domination Ramsey numbers of the form u(3,n) and mixed domination Ramsey numbers of the form v(3,n). We show that u(3,3)=v(3,3)=6, u(3,4)=8, v(3,4)=9, u(3,5)=v(3,5)=12 and u(3,6)=v(3,6)=15. 相似文献
12.
Given a linear recurrence integer sequence U = {un}, un+2 = un+1 + ur, n ? 1, u1 = 1, u2> u1, we prove that the set of positive integers can be partitioned uniquely into two disjoint subsets such that the sum of any two distinct members from any one set can never be in U. We give a graph theoretic interpretation of this result, study related problems and discuss possible generalizations. 相似文献
13.
A representation of the CD 0(K)-space is given in [1, 2] for a compact Hausdorff space K without isolated points. We generalize this to an arbitrary countably compact space K without any assumption on isolated points. 相似文献
14.
Anargyros Katsabekis 《Journal of Pure and Applied Algebra》2003,181(1):75-83
Let D be an integer matrix. A toric set, namely the points in Kn parametrized by the columns of D, and a toric variety are associated to D. The toric set is a subset of the toric variety. We describe the relation between the toric set and the toric variety, in terms of the orbits of the torus action on the toric variety. The toric set depends on the sign (+,−,0) pattern of the matrix D. Finally, we prove that any toric variety over an algebraically closed field can be expressed as a toric set, for an appropriate matrix. 相似文献
15.
We show that an isolated singularity at the origin 0 of a smooth solution (u,p) of the stationary Navier-Stokes equations is removable if the velocity u satisfies u∈Ln or |u(x)|=o(|x|-1) as x→0. Here n?3 denotes the dimension. As a byproduct of the proof, we also obtain a new interior regularity theorem. 相似文献
16.
In this paper we derive a local estimate of a positive singular solution u near its singular set Z of the conformal equation where K(x) is a positive continuous function, Z is a compact subset of , and g satisfies that is nonincreasing for t > 0. Assuming that the order of flatness at critical points of K on Z is no less than , we prove that, through the application of the method of moving planes, the inequality holds for any solution of (0.1) with Cap(Z) = 0. By the same method, we also derive a Harnack-type inequality for smooth positive solutions. Let u satisfy Assume that the order of flatness at critical points of K is no less than n - 2; then the inequality holds for R ≤ 1. We also show by examples that the assumption about the flatness at critical points is optimal for validity of the inequality (0.4). © 1997 John Wiley & Sons, Inc. 相似文献
17.
Igor Kluvánek 《Journal of Functional Analysis》1976,21(3):316-329
For a set K in a locally convex topological vector space X there exists a set T, a σ-algebra of subsets of T and a σ-additive measure m: → X such that K is the closed convex hull of the range {m(E): E ∈ } of the measure m if and only if there exists a conical measure u on X so that K Ku,Ku, the set of resultants of all conical measures v on X such that v < u. 相似文献
18.
《Chaos, solitons, and fractals》2002,13(2):321-330
The genuinely nonlinear dispersive K(m,n) equation, ut+(um)x+(un)xxx=0, which exhibits compactons: solitons with compact support, is investigated. New solitary-wave solutions with compact support are developed. The specific cases, K(2,2) and K(3,3), are used to illustrate the pertinent features of the proposed scheme. An entirely new general formula for the solution of the K(m,n) equation is established, and the existing general formula is modified as well. 相似文献
19.
David Kalaj 《Journal of Mathematical Analysis and Applications》2011,379(2):783-787
In this note we determine all numbers q∈R such that q|u| is a subharmonic function, provided that u is a K-quasiregular harmonic mappings in an open subset Ω of the Euclidean space Rn. 相似文献
20.
A graph G is said to be K n -residual if for every point u in G, the graph obtained by removing the closed neighborhood of u from G is isomorphic to K n . We inductively define a multiply-K n -residual graph by saying that G is m-K n -residual if the removal of the closed neighborhood of any vertex of G results in an (m – 1)-K n -residual graphs. Erdös, Harary and Klawe [2] determined the minimum order of the m?K n -residual graphs for all m and n, which are not necessarily connected, the minimum order of connected; K n -residual graphs, all K n -residual extremal graphs. They also stated some conjectures regarding the connected case. In this paper, we determine the minimum order of a connected 2-K n -residual graph and specify the extremal graphs, expect for n = 3. In particular, we determining only one connected 2-K 4-residual graph of minimal order, and show that there is a connected 2-K 6-residual graph non isomorphic to K 8 × K 3 with minimum order. Finally we present and a revised version of the conjecture in [2]. 相似文献