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本文研究2+1维的扩展经典Boussinesq系统.首先,研究了系统的Lax对,找出了一个形式十分新颖的带有一个任意函数的Backlund变换.然后,又导出了Lax对的特征函数的生成公式.最后,利用Backlund变换和Lax对特征函数生成公式相结合得出了Lax对的递推求解公式.利用此递推公式,求出了一些Lax对的解. 相似文献
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李建林 《数学年刊A辑(中文版)》2013,34(1):1-12
研究了与压缩迭代函数系和扩张迭代函数系相关的自仿测度的谱性质.在和谐对的条件下,分别确定了谱对形成的一些充分条件和必要条件.首先,给出了Strichartz谱对准则的几个等价形式.其次,得到了这个谱对成立的两个必要条件.最后,提供了Strichartz谱对准则的一个严格而详细的证明. 相似文献
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《数学的实践与认识》2015,(9)
随着单独二胎政策的放开,计划生育政策再次引起了人们的关注.为评估生育胎次对中国人口数量的影响,本文建立了关于人口增长的动力学模型.首先,分别对辽宁省和新疆自治区的人口数据进行了拟合,评估了"二胎"政策对两地区人口的影响.其次,对全国人口数据和抚养比进行了拟合和预测.最后,通过参数敏感性分析,评估各因素对总人口增长的影响. 相似文献
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Browder[1]已得到了Schauder不动点定理的加强形式.许多作者从不同方向推广了Browder的结果.最近H.M.Ko;K.K.Tan[2]在放松紧性条件下得到了Browder定理的改进,K.K.Tan[3]将Browder定理推广到了集值映象对的重合定理,在本文中我们得到了集值映象对的某些重合定理,它们分别改进和推广了[1,2,3]中主要结果. 相似文献
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本文研究了用以描述单物种人口模型的延迟Logistic方程的数值振动性.对方程应用隐式Euler方法进行求解,针对离散格式定义了指数隐式Euler方法,证明了该方法的收敛阶为1.根据线性振动性理论获得了数值解振动的充分条件.进而还对非振动数值解的性质作了讨论.最后用数值算例对理论结果进行了验证. 相似文献
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It is known that a strictly piecewise monotone function with nonmonotonicity height ≥ 2 on a compact interval has no iterative roots of order greater than the number of forts. An open question is: Does it have iterative roots of order less than or equal to the number of forts? An answer was given recently in the case of "equal to". Since many theories of resultant and algebraic varieties can be applied to computation of polynomials, a special class of strictly piecewise monotone functions, in this paper we investigate the question in the case of "less than" for polynomials. For this purpose we extend the question from a compact interval to the whole real line and give a procedure of computation for real polynomial iterative roots. Applying the procedure together with the theory of discriminants, we find all real quartic polynomials of non-monotonicity height 2 which have quadratic polynomial iterative roots of order 2 and answer the question. 相似文献
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Hemant Kumar Pathak 《Numerical Functional Analysis & Optimization》2018,39(4):449-466
A new 𝒮-generated Ishikawa iteration with errors is proposed for a pair of quasi-nonexpansive mapping and uniformly L-Lipschitzian asymptotically pseudo-contractive mapping in real Banach spaces. We show that the proposed iterative scheme converges strongly to a common solution of quasi-nonexpansive mapping and uniformly L-Lipschitzian asymptotically pseudo-contractive mapping in real Banach spaces. A comparison table is prepared using a numeric example which shows that the proposed iterative algorithm is faster than some known iterative algorithms. 相似文献
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基于一个广义迭代算法,考虑了逼近一类拟变分包含问题解集与一族无限多个非扩张映象公共不动点集的某一公共元问题.在实Hilbert空间的框架下,证明了由次广义迭代算法产生的迭代序列强收敛到某一公共元. 相似文献
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实对称矩阵的特征值问题,无论是低阶稠密矩阵的全部特征值问题,或高阶稀疏矩阵的部分特征值问题,都已有许多有效的计算方法,迄今最重要的一些成果已总结在[5]中。本文利用规范矩阵的一些重要性质将对于Hermite矩阵(特别是对弥矩阵)特征值问题的一些有效算法推广到规范矩阵的特征值问题,由于对复规范阵的推广是简单的,而且实际上常遇到的是实矩阵(这时常要求只用实运算),因此我们着重讨论实规范矩阵的特征值问题。 相似文献
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This paper is concerned with iterative solutions to a class of complex matrix equations. By applying the hierarchical identification principle, an iterative algorithm is constructed to solve this class of complex matrix equations. The range of the convergence factor is given to guarantee that the proposed algorithm is convergent for arbitrary initial matrix by applying a real representation of a complex matrix as a tool. By using some properties of the real representation, a sufficient convergence condition that is easier to compute is also given by original coefficient matrices. Two numerical examples are given to illustrate the effectiveness of the proposed methods. 相似文献
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This paper is concerned with iterative solutions to a class of complex matrix equations, which include some previously investigated matrix equations as special cases. By applying the hierarchical identification principle, an iterative algorithm is constructed to solve this class of matrix equations. A sufficient condition is presented to guarantee that the proposed algorithm is convergent for an arbitrary initial matrix with a real representation of a complex matrix as tools. By using some properties of the real representation, a convergence condition that is easier to compute is also given in terms of original coefficient matrices. A numerical example is employed to illustrate the effectiveness of the proposed methods. 相似文献
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Yekini Shehu 《Numerical Functional Analysis & Optimization》2016,37(8):1021-1036
The purpose of this article is to study the iterative approximation of solution to multiple sets split feasibility problems in p-uniformly convex real Banach spaces that are also uniformly smooth. We propose an iterative algorithm for solving multiple sets split feasibility problems and prove a strong convergence theorem of the sequence generated by our algorithm under some appropriate conditions in p-uniformly convex real Banach spaces that are also uniformly smooth. 相似文献
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《Optimization》2012,61(12):2587-2597
AbstractOur purpose in this paper is to obtain strong convergence result for approximation of solution to constrained convex minimization problem using a new iterative scheme in a real Hilbert space. Furthermore, we give numerical analysis of our iterative scheme. 相似文献
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In this article, we first introduce an iterative method based on the hybrid viscosity approximation method and the hybrid steepest-descent method for finding a fixed point of a Lipschitz pseudocontractive mapping (assuming existence) and prove that our proposed scheme has strong convergence under some mild conditions imposed on algorithm parameters in real Hilbert spaces. Next, we introduce a new iterative method for a solution of a nonlinear integral equation of Hammerstein type and obtain strong convergence in real Hilbert spaces. Our results presented in this article generalize and extend the corresponding results on Lipschitz pseudocontractive mapping and nonlinear integral equation of Hammerstein type reported by some authors recently. We compare our iterative scheme numerically with other iterative scheme for solving non-linear integral equation of Hammerstein type to verify the efficiency and implementation of our new method. 相似文献