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Global existence of real roots and random Newton flow algorithm for nonlinear system of equations To memorize Qin's method for 770 anniversaries

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Science China Mathematics 2017年第7期60卷 1341-1352页

作者： CHEN ChuanMiao HU HongLing key laboratory of hpcsip(Ministry of Education of China) College of Mathematics and Computer ScienceHunan Normal University

To solve nonlinear system of equation,F(x) = 0,a continuous Newton flow x_t(t) = V(x) =-(DF(x))^(-1)F(x),x(0) =x^0 and its mathematical properties,such as the central field,global existence and uniqueness of real roots and the structure of the singular surface,are *** concisely introduce random Newton flow algorithm(NFA) for finding all roots,based on discrete Newton flow x^(j+1)=x^j+hV{x^j) with random initial value x^0 and h∈(0,1],and three computable quantities,g_j,d_j and K_*** numerical experiments with dimension n=300 are provided.

关键词： nonlinear system of equation continuous Newton flow real roots global existence and uniqueness random Newton flow algorithm

Dividend-Reinsurance Strategy in the Sparre Andersen Model

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Acta Mathematica Sinica,English Series 2013年第2期29卷 405-416页

作者： Ji Yang TAN Lin XIAO Shao Yue LIU Xiang Qun YANG Department of Statistics Xiangtan University hpcsip key laboratory Ministry of Education Department of Mathematics Hu'nan Normal University

In this paper, we introduce a reinsurance strategy into the Sparre Andersen risk model with a horizon dividend barrier, which is named dividend-reinsurance strategy. It is shown that the value function of the new strategy far exceeds that of the optimal barrier strategy （even that of the optimal dividend strategy）. Some results on the advantages of the new strategy are obtained, and the methods for computing the value functions are provided. Numerical illustrations for Erlang （2） and compound Poisson risk models are also given.

关键词： Sparre Andersen model reinsurance expected discounted penalty function iteration constant dividend barrier

Convergence of Gaussian Quadrature Formulas for Power Orthogonal Polynomials

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Chinese Annals of Mathematics,Series B 2012年第5期33卷 751-766页

作者： Yingguang SHI College of Mathematics and Computer Science Key Laboratory of High Performance Computing and Stochastic Information Processing (HPCSIP) (Ministry of Education of China)

In classical theorems on the convergence of Gaussian quadrature formulas for power orthogonal polynomials with respect to a weight w on I （a,b）, a function G E S（w）= （f： fxlf（x）lw（x）dx 〈 ∞ satisfying the conditions G（2J）（x）：〉 O, x E （a,b）, j = 0, 1 , and growing as fast as possible as x→ a- and x → b-, plays an important role. But to find such a function G is often difficult and complicated. This implies that to prove convergence of Gaussian quadrature formulas, it is enough to find a function G E S（w） with G ≥ 0 satisfying

关键词： Convergence Gaussian quadrature formula Freud weight

Pointwise convergence of some conjugate convolution operators with applications to wavelets

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Applied Mathematics(A Journal of Chinese Universities) 2016年第3期31卷 320-330页

作者： HU Lan SHI Xian-liang College of Mathematics and Computer Science Key Laboratory of High Performance Computing and Stochastic Information Processing (HPCSIP) (Ministry of Education of China) Hunan Normal University

In this paper, we discuss the pointwise convergence of conjugate convolution op- erators with some applications to wavelets. Some criteria of convergence at （C, 1） continuous points, Lebesgue points and almost every... 详细信息

关键词： Hilbert transform pointwise convergence wavelet

An application of Chen's theorem to convergence of Fourier multiplier transforms

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Applied Mathematics(A Journal of Chinese Universities) 2013年第4期28卷 455-464页

作者： SHI Xian-liang CHEN Yang HU Lan College of Mathematics and Computer Science Key Laboratory of High Performance Computing and Stochastic Information Processing (HPCSIP) (Ministry of Education of China) Hunan Normal University

Let V be a star shaped region. In 2006, Colzani, Meaney and Prestini proved that if function f satisfies some condition, then the multiplier transform with the characteristic function of tV as the multiplier tends to f almost everywhere, when t goes to∞. In this paper we use a Theorem established by *** to show that if we change their multiplier, then the condition on f can be weakened.

关键词： Fourier transform multiplier summability convergence almost everywhere

A characterization of generator for multiresolution analysis with composite dilations

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Applied Mathematics(A Journal of Chinese Universities) 2014年第3期29卷 317-328页

作者： SHI Xian-liang CHEN Jie College of Mathematics and Computer Science Key Laboratory of High Performance Computing and Stochastic Information Processing (HPCSIP) (Ministry of Education of China) Hunan Normal University

In this paper, we will introduce multiresolution analysis with composite dilations and give a characterization of generator for multiresolution analysis with composite dilations.

关键词： MRA generator Riesz basis composite dilation characterization.

Boundedness of parammetric Marcinkiewicz integrals on weighted Hardy spaces

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Applied Mathematics(A Journal of Chinese Universities) 2015年第3期30卷 253-262页

作者： SHI Xian-liang SUN Jie College of Mathematics and Computer Science Key Laboratory of High Performance Computing and Stochastic Information Processing (HPCSIP) (Ministry of Education of China) Hunan Normal University

In this paper, several new results on the boundedness of parammetric Marcinkiewicz integrals on the weighted Hardy spaces and the weak weighted Hardy spaces are established.

关键词： parammetric Marcinkiewicz integral weight function weighted Hardy space weak weighted Hardy space

SOLITARY WAVE AND PERIODIC WAVE SOLUTIONS FOR THE NON-NEWTONIAN FILTRATION EQUATIONS WITH NONLINEAR SOURCES AND A TIME-VARYING DELAY

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Acta Mathematica Scientia 2017年第6期37卷 1803-1816页

作者：孔凡超罗治国 key laboratory of High Performance Computing and Stochastic Information Processing(hpcsip)(Ministry of Education of China) College of Mathematics and Computer ScienceHunan Normal UniversityChangsha 410081China

This paper is concerned with the non-Newtonian filtration equations with non- linear sources and a time-varying delay. By an extension of Mawhin＇s continuation theorem and some analysis methods, several sufficient conditions ensuring the existence of solitary wave and periodic wave solutions are obtained. Some corresponding results in the literature are improved and extended. An example is given to illustrate the effectiveness of our results.

关键词： solitary wave periodic wave Mawhin's continuation theorem time:varyingdelay nonlinear sources

Generalized Christoffel Functions for Power Orthogonal Polynomials

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Acta Mathematicae Applicatae Sinica 2014年第3期30卷 819-832页

作者： Xie TAO Yan LIANG Guangdong Country Garden School College of Mathematics and Computer Science Key Laboratory of High Performance Computing and Stochastic Information Processing(HPCSIP)(Ministry of Education of China)Hunan Normal University

In this paper we extend the Christoffel functions to the case of power orthogonal *** existence and uniqueness as well as some properties are given.

关键词： generalized Christoffel function existence uniqueness gaussian quadrature formula Christoffel number