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1.
In 1943, Erdos stated a famous result concerning interpolatory polynomials,but no proof given. Since this theorem is a fundamental and frequently quoted resultof the theory of interpolation, Erdos et al. published a proof in[2] (1989) recently.Three deep lemmas have been established in [2] in order to give this proof. However,we found that the proof of lemma 2 of [2] is not correct. The main purpose of this 相似文献
2.
In this paper, we consider the existence of homoclinic solutions in periodic nonlinear difference equations with superlinear nonlinearity. The classical Ambrosetti–Rabinowitz superlinear condition is improved by a general superlinear one. The proof is based on the critical point theory in combination with periodic approximations of solutions. 相似文献
3.
HUANG Zhiyong~ JIANG Yunping~ 《中国科学A辑(英文版)》2005,48(10):1411-1420
We study a conformal measure for an infinitely renormalizable quadratic poly- nomial.We prove that the conformal measure is ergodic if the polynomial is unbranched and has complex bounds.The main technique we use in the proof is the three-dimensional puzzle for an infinitely renormalizable quadratic polynomial. 相似文献
4.
《数学物理学报(B辑英文版)》2015,(4)
The initial–boundary value problem for a general balance law in a bounded domain is proved to be well posed. Indeed, we show the existence of an entropy solution, its uniqueness and its Lipschitz continuity as a function of time, of the initial datum and of the boundary datum. The proof follows the general lines in [4], striving to provide a rigorous treatment and detailed references. 相似文献
5.
《数学学报(英文版)》2021,(7)
We review the recent proof of the N. Takahashi's conjecture on genus 0 Gromov–Witten invariants of(P~2, E), where E is a smooth cubic curve in the complex projective plane P~2. The main idea is the use of the algebraic notion of scattering diagram as a bridge between the world of Gromov–Witten invariants of(P~2, E) and the world of moduli spaces of coherent sheaves on P~2. Using this bridge, the N. Takahashi's conjecture can be translated into a manageable question about moduli spaces of coherent sheaves on P~2. This survey is based on a three hours lecture series given as part of the Beijing–Zurich moduli workshop in Beijing, 9–12 September 2019. 相似文献
6.
ZHAO Shizhong~ & FU Hongguang~.Chengdu Institute of Computer Applications Chinese Academy of Sciences Chengdu China.Software Engineering Institute East China Normal University Shanghai China 《中国科学A辑(英文版)》2005,48(1):131-143
In recent years,the Dixon resultant matrix has been used widely in the re-sultant elimination to solve nonlinear polynomial equations and many researchers havestudied its efficient algorithms.The recursive algorithm is a very efficient algorithm,butwhich deals with the case of three polynomial equations with two variables at most.Inthis paper,we extend the algorithm to the general case of n 1 polynomial equations in nvariables.The algorithm has been implemented in Maple 9.By testing the random polyno-mial equations,the results demonstrate that the efficiency of our program is much betterthan the previous methods,and it is exciting that the necessary condition for the existenceof common intersection points on four general surfaces in which the degree with respectto every variable is not greater than 2 is given out in 48×48 Dixon matrix firstly by ourprogram. 相似文献
7.
The Hilbert's sixteenth problem, that is the problem on the rlurnber anddistribution of limit cycles of planar polynomial system, has not solved fOr acentury. Since the original problem is so difficuIt, in 1977, V.I.Arnold posed"weakened Hilbert's sixteenth problem"-- the possibility of the number anddistribution of limit cycles fOr polynomial HamiItonian system of degrees n -- lunder perturbation of the polynomial of degrees m 1. From l983, Prof.Li Jibin etc. began to study cubic vecto… 相似文献
8.
一类可积非哈密顿系统的极限环个数的上界 总被引:3,自引:0,他引:3
In this paper, we consider the perturbations of two non-Hamiltonian integrable systems(1.3)μ, (4.1)μ. For the former,it is proved that the system under the polynomial perturbations hasat most f-n/2] limit cycles in the finite plane and the upper bound is sharp. The proof relies on acareful analysis of a related Abelian integral. For the latter, we obtain an estimate number of isolatedzeros of the corresponding Abelian integral. 相似文献
9.
Convergence conclusions of Pade approximants in the univariate case can be found in various papers.However,resuhs in the multivariate case are few.A.Cuyt seems to be the only one who discusses convergencefor multivariate Pade approximants,she gives in[2]a de Montessus de Bollore type theorem.In this paper,wewill discuss the zero set of a real multivariate polynomial,and present a convergence theorem in measure ofmultivariate Pade approximant.The proof technique used in this paper is quite different from that used in theunivariate case. 相似文献
10.
The rigorous proof of the relation det is given. This relation has been used to obtain the exact critical surface and the correlation length exponents of the one-dimensional directed bond percolation problem with bonds connecting 1~Lth nearest neighbours. A~((L)) is related to the transfer-matrix by (7). q_i is related to the occupation probability of the i-th nearest neighbour bond p_i by q_i=1-p_i (i=1, 2, ..., L). f_L is a multi-varlable polynomial in q_4's. 相似文献
11.
The purpose of this paper is to discuss representations of high order C0finite element spaces on simplicial meshes in any dimension.When computing with high order piecewise polynomials the conditioning of the basis is likely to be important.The main result of this paper is a construction of representations by frames such that the associated L2condition number is bounded independently of the polynomial degree.To our knowledge,such a representation has not been presented earlier.The main tools we will use for the construction is the bubble transform,introduced previously in[1],and properties of Jacobi polynomials on simplexes in higher dimensions.We also include a brief discussion of preconditioned iterative methods for the finite element systems in the setting of representations by frames. 相似文献
12.
《应用数学年刊》2021,(3)
The Camassa–Holm–Kadomtsev–Petviashvili-I equation(CH-KP-I)is a two dimensional generalization of the Camassa–Holm equation(CH). In this paper, we prove transverse instability of the line solitary waves under periodic transverse perturbations. The proof is based on the framework of [18]. Due to the high nonlinearity, our proof requires necessary modification. Specifically, we first establish the linear instability of the line solitary waves. Then through an approximation procedure, we prove that the linear effect actually dominates the nonlinear behavior. 相似文献
13.
By catching the so-called strictly critical points,this paper presents an effective algorithm for computing the global infimum of a polynomial function.For a multivariate real polynomial f ,the algorithm in this paper is able to decide whether or not the global infimum of f is finite.In the case of f having a finite infimum,the global infimum of f can be accurately coded in the Interval Representation.Another usage of our algorithm to decide whether or not the infimum of f is attained when the global infimum of f is finite.In the design of our algorithm,Wu’s well-known method plays an important role. 相似文献
14.
SBV REGULARITY OF GENUINELY NONLINEAR HYPERBOLIC SYSTEMS OF CONSERVATION LAWS IN ONE SPACE DIMENSION
Stefano Bianchini 《数学物理学报(B辑英文版)》2012,32(1)
The problem of the presence of Cantor part in the derivative of a solution to a hyperbolic system of conservation laws is considered.An overview of the techniques involved in the proof is given,and a c... 相似文献
15.
郑士明 《高等学校计算数学学报(英文版)》1996,(2)
In this note a simple iterative method for simultaneously finding all zeros of a polynomial is established.The method does not require repeated evaluation of the polynomial or its deriva-tives,and is globally convergent for quadratic polynomials. 相似文献
16.
Stefano Bianchini 《数学物理学报(B辑英文版)》2012,(1):380-388
The problem of the presence of Cantor part in the derivative of a solution to a hyperbolic system of conservation laws is considered.An overview of the techniques involved in the proof is given,and a collection of related problems concludes the paper. 相似文献
17.
王益 《数学物理学报(B辑英文版)》2008,28(4):727-748
The zero dissipation limit of the compressible heat-conducting Navier–Stokes equations in the presence of the shock is investigated. It is shown that when the heat conduction coefficient κ and the viscosity coefficient ε satisfy κ = O(ε), κ/ε≥ c 〉 0, as ε→ 0 (see (1.3)), if the solution of the corresponding Euler equations is piecewise smooth with shock wave satisfying the Lax entropy condition, then there exists a smooth solution to the Navier–Stokes equations, which converges to the piecewise smooth shock solution of the Euler equations away from the shock discontinuity at a rate of ε. The proof is given by a combination of the energy estimates and the matched asymptotic analysis introduced in [3]. 相似文献
18.
The existing results of curve degree elevation mainly focus on the degree of algebraic polynomials. The paper considers the elevation of degree of the trigonometric polynomial, from a Bzier curve on the algebraic polynomial space, to a C-B′ezier curve on the algebraic and trigonometric polynomial space. The matrix of degree elevation is obtained by an operator presentation and a derivation pyramid. It possesses not a recursive presentation but a direct expression. The degree elevation process can also be represented as a corner cutting form. 相似文献
19.
Yi ZHOU 《数学年刊B辑(英文版)》2011,32(5):771-780
The author considers the Cauchy problem for quasilinear inhomogeneous hyperbolic
systems. Under the assumption that the system is weakly dissipative, Hanouzet
and Natalini established the global existence of smooth solutions for small initial data (in
Arch. Rational Mech. Anal., Vol. 169, 2003, pp. 89–117). The aim of this paper is to give
a completely different proof of this result with slightly different assumptions. 相似文献
20.
正[1, Theorem 4.4] states that every infinite dimensional Banach space admits a homogenous measure of noncompactness not equivalent to the Hausdorff measure. Howevere, there is a gap in the proof. In fact,we found that [1, Lemma 4.3] is not true. In this erratum, we give a corrected proof of [1, Theorem 4.4]. 相似文献