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1.
Let F={H1,...,Hk}(k> 1) be a family of graphs.The Turán number of the family F is the maximum number of edges in an n-vertex {H1,...,Hk)-free graph,denoted by ex(n,F) or ex(n,{H1,H2,...,Hk}).The blow-up of a graph H is the graph obtained from H by replacing each edge in H by a clique of the same size where the new vertices of the cliques are all different.In this paper we determine the Turán number of the family cons... 相似文献
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《数学研究与评论》1989,(1)
1. Introduction A theorem of Carleson,as generalized by Duren characterizes those positive measure μ on the unit disc U={z∈C:|z|<1} for which the H~p norm domiates the L~q(μ) norm of elements of H~p. Later on, Hasting proved an analogous results with H~p replaced by A~p, the Bergman space of fuctions f 相似文献
3.
A. V. Menovshchikov 《Siberian Mathematical Journal》2017,58(4):649-662
Given a homeomorphism ? ∈ W M 1 , we determine the conditions that guarantee the belonging of the inverse of ? in some Sobolev–Orlicz space W F 1 . We also obtain necessary and sufficient conditions under which a homeomorphism of domains in a Euclidean space induces the bounded composition operator of Sobolev–Orlicz spaces defined by a special class of N-functions. Using these results, we establish requirements on a mapping under which the inverse homeomorphism also induces the bounded composition operator of another pair of Sobolev–Orlicz spaces which is defined by the first pair. 相似文献
4.
In this paper we are concerned with the exceptional set of the sum of two squares of primesand a cube of a prime P;+p;+p;.Noting that竹三1 or 3(mod 6)is a necessary conditionfor the solvability of the equation n=P}+P;+P;(see【1]),we define E(N)=Card{n:n≤N,礼∈三and n≠P;+Pi+P;for any Pi,1≤i s 3), (1)where三={n:n三1 or 3(mod 6)). This and similar problems have been studied by a number of authors.In 1937,Davenportand Heilbronn[2J proved that if后2 3 is an odd integer then almost all posi… 相似文献
5.
In 1923, Hardy and Littlewood[1] conjectured that each integer n can be written asp+m12+ m22 = n,and Linnik[2,3] proved that this conjecture is true. But if these mi with i = 1,2 are restricted to primes Pi, the corresponding result is out of reach at present. We consider the following Diophantine equation 相似文献
6.
InequalityfortheMomentofaFunctionofaRandomVariable¥LiBainianHuShuhe(李柏年,胡舒合)(AnhuiInstituteofFinanceandTrade)(AnhuiUniversity... 相似文献
7.
Xiong Ping DAI Zuo Ling ZHOU 《数学学报(英文版)》2006,22(1):207-210
Let X be a metrizable space and let φ:R× X → X be a continuous flow on X. For any given {φt}-invariant Borel probability measure, this paper presents a {φt}-invariant Borel subset of X satisfying the requirements of the classical ergodic theorem for the contiImous flow (X, {φt}). The set is more restrictive than the ones in the literature, but it might be more useful and convenient, particularly for non-uniformly hyperbolic systems and skew-product flows. 相似文献
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Let be a positive integer, and let denote the cyclic group of residues modulo m. Furthermore, let denote the minimum integer N such that for every function there exist m integers satisfying and (and ). It is shown that for every odd prime m.
Daniel Schaal: Partially supported by a South Dakota Governor’s 2010 Individual Research Seed Grant. 相似文献
10.
Zhi-qiang XU Institute of Computational Math Sci/Eng Computing Academy of Mathematics Systems Science Chinese Academy of Sciences Beijing China 《中国科学A辑(英文版)》2007,50(2):285-291
In this paper, an explicit formulation for multivariate truncated power functions of degree one is given firstly. Based on multivariate truncated power functions of degree one, a formulation is presented which counts the number of non-negative integer solutions of s×(s 1) linear Diophantine equations and it can be considered as a multi-dimensional versions of the formula counting the number of non-negative integer solutions of ax by = n which is given by Popoviciu in 1953. 相似文献
11.
SHEN Liang LMAM School of Mathematical Sciences Peking University Beijing China 《中国科学A辑(英文版)》2006,49(9):1284-1296
Let f(z) = e2πiθz(1 z/d)d,θ∈R\Q be a polynomial. Ifθis an irrational number of bounded type, it is easy to see that f(z) has a Siegel disk centered at 0. In this paper, we will show that the Hausdorff dimension of the Julia set of f(z) satisfies Dim(J(f))<2. 相似文献
12.
Sergey Bereg Prosenjit Bose Adrian Dumitrescu Ferran Hurtado Pavel Valtr 《Discrete and Computational Geometry》2009,41(4):513-532
Given a finite set of points S in ℝ
d
, consider visiting the points in S with a polygonal path which makes a minimum number of turns, or equivalently, has the minimum number of segments (links).
We call this minimization problem the minimum link spanning path problem. This natural problem has appeared several times in the literature under different variants. The simplest one is
that in which the allowed paths are axis-aligned. Let L(S) be the minimum number of links of an axis-aligned path for S, and let G
n
d
be an n×…×n grid in ℤ
d
. Kranakis et al. (Ars Comb. 38:177–192, 1994) showed that L(G
n
2)=2n−1 and
and conjectured that, for all d≥3,
We prove the conjecture for d=3 by showing the lower bound for L(G
n
3). For d=4, we prove that
For general d, we give new estimates on L(G
n
d
) that are very close to the conjectured value. The new lower bound of
improves previous result by Collins and Moret (Inf. Process. Lett. 68:317–319, 1998), while the new upper bound of
differs from the conjectured value only in the lower order terms.
For arbitrary point sets, we include an exact bound on the minimum number of links needed in an axis-aligned path traversing
any planar n-point set. We obtain similar tight estimates (within 1) in any number of dimensions d. For the general problem of traversing an arbitrary set of points in ℝ
d
with an axis-aligned spanning path having a minimum number of links, we present a constant ratio (depending on the dimension d) approximation algorithm.
Work by A. Dumitrescu was partially supported by NSF CAREER grant CCF-0444188.
Work by F. Hurtado was partially supported by projects MECMTM2006-01267 and Gen. Cat. 2005SGR00692.
Work by P. Valtr was partially supported by the project 1M0545 of the Ministry of Education of the Czech Republic. 相似文献
13.
We prove a conjecture of Zahariuta which itself solves a problem of Kolmogorov on the -entropy of some classes of analytic functions. For a given holomorphically convex compact subset K in a pseudoconvex domain D in Cn, Zahariutas conjecture consists in approximating the relative extremal function u*K,D, uniformly on any compact subset of DK, by pluricomplex Green functions on D with logarithmic poles in the compact subset K. 相似文献
14.
In this paper, we analyze the dynamical behaviour of a bioeconomic model system using differential algebraic equations. The system describes a prey–predator fishery with prey dispersal in a two-patch environment, one of which is a free fishing zone and other is a protected zone. It is observed that a singularity-induced bifurcation phenomenon appears when a variation of the economic interest of harvesting is taken into account. We have incorporated a state feedback controller to stabilize the model system in the case of positive economic interest. A discrete-type gestational delay of predators is incorporated, and its effect on the dynamical behaviour of the model is analyzed. The occurrence of Hopf bifurcation of the proposed model with positive economic profit is shown in the neighbourhood of the coexisting equilibrium point through considering the delay as a bifurcation parameter. Finally, some numerical simulations are given to verify the analytical results, and the system is analyzed through graphical illustrations. 相似文献
15.
Let S be class of functions f(z)=z a_2 z~2 … analytic and univalent in the unit disk D, and let 1.M.Milin proved that Theorem A. If f∈S and then where d_o(h)=1and In fact,the result is deduced from Milan′s Tauberian Theorem. Here 相似文献
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Daxue CHEN Aiguo XIAO Department of Basic Sciences Xiangtan College of Mechanical Electrical Engineering Xiangtan China Department of Mathematics Xiangtan University Xiangtan China e-mail: xiaoag@xtu. edu. cn xag@lsec. cc. ac 《Communications in Nonlinear Science & Numerical Simulation》2000,5(1)
IntroductionIt is important that the discrete dynamical system given by a numerical method appliedto a continuous dynamical system can have the same dynamical properties as the underlyingcontinuous system. Recently, many authors[1--71 have investigated the conditions under whichspurious solutions are not introduced by time discretization, and many interesting results aboutRunge-Kutta methods, linear multistep methods and general linear methods applied to dynamical systems of ordinary different… 相似文献
19.
《数学研究与评论》1986,(4)
Let R and S be two vectors whose components are m and non-negative integers,respectively. Let P be an m×n (0,1)-matrix with column sums at most one. Let (R,S) be the class consisting of all m×n (0,1)-matrices with row sum vector R and columu sum vector S, which cover P. In this paper we derive a lower bound to the cardinality of class (R,S), which can be computed readily. Let R=(r_1,r_2,…,r_m) and S=(s_1,s_2,…, s_n)be vectors with nonnegative 相似文献
20.
OnaConjectureofShapiro's陈志国OnaConjectureofShapiro's¥ChenZhiguo(InstituteofMathematics,FudanUniversity)Abatract:Thisproblemwas... 相似文献