共查询到20条相似文献,搜索用时 31 毫秒
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Sizhong Zhou 《Comptes Rendus Mathematique》2009,347(21-22):1223-1226
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Let denote the maximal number of limit cycles of polynomial systems of degree m. It is called the Hilbert number. The main part of Hilbert?s 16th problem posed in 1900 is to find its value. The problem is still open even for . However, there have been many interesting results on the lower bound of it for . In this paper, we give some new lower bounds of this number. The results obtained in this paper improve all existing results for all based on some known results for . In particular, we obtain that grows at least as rapidly as for all large m. 相似文献
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Let X be a complex nonsingular projective 3-fold of general type. We show that there are positive constants c, and such that and for all . 相似文献
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Annamria Kovcs 《Journal of Discrete Algorithms》2009,7(3):327-340
denotes the problem of scheduling n jobs on m machines of different speeds such that the makespan is minimized. In the paper two special cases of are considered: case I, when machine speeds are equal, and there is only one faster machine; and case II, when machine speeds are all powers of 2 (2-divisible machines). Case I has been widely studied in the literature, while case II is significant in an approach to design so called monotone algorithms for the scheduling problem.We deal with the worst case approximation ratio of the classic list scheduling algorithm ‘Largest Processing Time (LPT)’. We provide an analysis of this ratio for both special cases: For ‘one fast machine’, a tight bound of is given. For 2-divisible machines, we show that in the worst case . Besides, we prove another lower bound of when LPT breaks ties arbitrarily.To our knowledge, the best previous lower and upper bounds were in case I [T. Gonzalez, O.H. Ibarra, S. Sahni, Bounds for LPT schedules on uniform processors, SIAM Journal on Computing 6 (1) (1977) 155–166], respectively in case II [R.L. Graham, Bounds on multiprocessing timing anomalies, SIAM Journal on Applied Mathematics 17 (1969) 416–429; A. Kovács, Fast monotone 3-approximation algorithm for scheduling related machines, in: Proc. 13th Europ. Symp. on Algs. (ESA), in: LNCS, vol. 3669, Springer, 2005, pp. 616–627]. Moreover, Gonzalez et al. conjectured the lower bound 4/3 to be tight in the ‘one fast machine’ case [T. Gonzalez, O.H. Ibarra, S. Sahni, Bounds for LPT schedules on uniform processors, SIAM Journal on Computing 6 (1) (1977) 155–166]. 相似文献
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Gábor Korchmáros Maria Montanucci Pietro Speziali 《Journal of Pure and Applied Algebra》2018,222(7):1810-1826
Let be the algebraic closure of a finite field of odd characteristic p. For a positive integer m prime to p, let be the transcendence degree 1 function field defined by . Let and . The extension is a non-Galois extension. Let K be the Galois closure of F with respect to H. By Stichtenoth [20], K has genus , p-rank (Hasse–Witt invariant) and a -automorphism group of order at least . In this paper we prove that this subgroup is the full -automorphism group of K; more precisely where Δ is an elementary abelian p-group of order and D has an index 2 cyclic subgroup of order . In particular, , and if K is ordinary (i.e. ) then . On the other hand, if G is a solvable subgroup of the -automorphism group of an ordinary, transcendence degree 1 function field L of genus defined over , then ; see [15]. This shows that K hits this bound up to the constant .Since has several subgroups, the fixed subfield of such a subgroup N may happen to have many automorphisms provided that the normalizer of N in is large enough. This possibility is worked out for subgroups of Δ. 相似文献
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A vertex-deleted subgraph of a graph G is a card. A dacard specifies the degree of the deleted vertex along with the card. The adversary degree-associated reconstruction number is the least k such that every set of k dacards determines G. We determine , where the double-broom with is the tree with vertices obtained from a path with p vertices by appending m leaves at one end and n leaves at the other end. We determine for all . For , usually , except and . There are exceptions when or . For the usual value is 4, with exceptions when or . 相似文献
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Duo-Yuan Chen Min-Jei Huang 《Journal of Mathematical Analysis and Applications》2012,389(2):1251-1258
We consider two types of Schrödinger operators and defined on , where q is an even potential that is bounded from below, A is a constant, and is a parameter. We assume that has at least two eigenvalues below its essential spectrum; and we denote by and the lowest eigenvalue and the second one, respectively. The purpose of this paper is to study the asymptotics of the gap in the limit as . 相似文献
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Dong Dong 《Comptes Rendus Mathematique》2017,355(5):538-542
We prove that for a large class of functions P and Q, the discrete bilinear operator is bounded from into for any . 相似文献
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We consider the nonlinear Schrödinger equation associated to a singular potential of the form , for some , on a possible unbounded domain. We use some suitable energy methods to prove that if and if the initial and right hand side data have compact support then any possible solution must also have a compact support for any . This property contrasts with the behavior of solutions associated to regular potentials . Related results are proved also for the associated stationary problem and for self-similar solution on the whole space and potential . The existence of solutions is obtained by some compactness methods under additional conditions. To cite this article: P. Bégout, J.I. Díaz, C. R. Acad. Sci. Paris, Ser. I 342 (2006). 相似文献
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A.J.W. Hilton 《Discrete Mathematics》2008,308(5-6):645-669
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Jean-Pierre Marco 《Comptes Rendus Mathematique》2005,340(11):839-842
Let m be an integer ?3, set for , and consider a badly approximable vector . Fix , and . We construct a sequence of Hamiltonian functions of , which converges to ? when , such that for each N the system generated by possesses a -dimensional hyperbolic invariant torus with fixed frequency vector , which admits a homoclinic point with splitting matrix of the form , with , where and . To cite this article: J.-P. Marco, C. R. Acad. Sci. Paris, Ser. I 340 (2005). 相似文献