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661.
In this paper, we establish distortion theorems for both normalized p-Bloch functions with branch points and normalized locally univalent p-Bloch functions defined on the unit disk, respectively. These distortion theorems give lower bounds on |f′(z)| and ■f′(z). As applications of these distortion theorems, the lower bounds of the radius of the largest schlicht disk on these Bloch functions are given, respectively. Notice that when p = 1, our results reduce to that of Liu and Minda. 相似文献
662.
We obtain a global estimate for the weak solution to an elliptic partial differential equation of -Laplacian type with BMO coefficients in a Lipschitz domain with small Lipschitz constant.
663.
Yoshiharu Kohayakawa Vojtěch Rödl Mathias Schacht Papa Sissokho 《Journal of Combinatorial Theory, Series A》2007,114(4):631-657
The generalized Turán number ex(G,H) of two graphs G and H is the maximum number of edges in a subgraph of G not containing H. When G is the complete graph Km on m vertices, the value of ex(Km,H) is , where o(1)→0 as m→∞, by the Erd?s-Stone-Simonovits theorem.In this paper we give an analogous result for triangle-free graphs H and pseudo-random graphs G. Our concept of pseudo-randomness is inspired by the jumbled graphs introduced by Thomason [A. Thomason, Pseudorandom graphs, in: Random Graphs '85, Poznań, 1985, North-Holland, Amsterdam, 1987, pp. 307-331. MR 89d:05158]. A graph G is (q,β)-bi-jumbled if
664.
In this paper, we study the existence of periodic solutions of the second order differential equations x″+f(x)x′+g(x)=e(t). Using continuation lemma, we obtain the existence of periodic solutions provided that F(x) () is sublinear when x tends to positive infinity and g(x) satisfies a new condition where M, d are two positive constants. 相似文献
665.
Daniela Kühn Richard Mycroft Deryk Osthus 《Journal of Combinatorial Theory, Series B》2011,101(6):415-447
Sumner?s universal tournament conjecture states that any tournament on 2n−2 vertices contains a copy of any directed tree on n vertices. We prove an asymptotic version of this conjecture, namely that any tournament on (2+o(1))n vertices contains a copy of any directed tree on n vertices. In addition, we prove an asymptotically best possible result for trees of bounded degree, namely that for any fixed Δ, any tournament on (1+o(1))n vertices contains a copy of any directed tree on n vertices with maximum degree at most Δ. 相似文献
666.
J. Djoko Kamdem 《Mathematical Methods in the Applied Sciences》2011,34(12):1487-1498
In this work, we study the structural stability of the fully implicit Euler scheme for the Brinkman‐Forchheimer equations. More precisely, we consider the time discretization scheme of the unsteady Brinkman–Forchheimer equations, and we prove the existence of solutions. Moreover, we derive somebia priori estimates of the discrete in time solutions. Next, with the aid of the discrete Gronwall lemma, we show that the numerical solutions depend continuously on the Brinkman and the Forchheimer coefficient. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
667.
Ibrahima N’Doye Michel Zasadzinski Mohamed Darouach Nour-Eddine Radhy Abdelhaq Bouaziz 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(18):7333-7341
In this paper, stabilizing control design for a class of nonlinear affine systems is presented by using a new generalized Gronwall–Bellman lemma approach. The nonlinear systems under consideration can be non Lipschitz. Two cases are treated for the exponential stabilization: the static state feedback and the static output feedback. The robustness of the proposed control laws with regards to parameter uncertainties is also studied. A numerical example is given to show the effectiveness of the proposed method. 相似文献
668.
Douglas R. Woodall 《Journal of Graph Theory》2011,66(2):98-103
A graph G with maximum degree Δ and edge chromatic number χ′(G)>Δ is edge‐Δ‐critical if χ′(G?e)=Δ for every edge e of G. It is proved here that the vertex independence number of an edge‐Δ‐critical graph of order n is less than . For large Δ, this improves on the best bound previously known, which was roughly ; the bound conjectured by Vizing, which would be best possible, is . © 2010 Wiley Periodicals, Inc. J Graph Theory 66:98‐103, 2011 相似文献
669.
670.