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	1. Normal Families and Shared Values concerning　Differential Polynomial
	Shi Zhongchun
	Mathematics 28 December 2007
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	Abstract:Let F be a family of meromorphic functions on the plane domain D ,all of　whose zeros have multiplicity at least k＞＝1 ,and if f(z)L(w(z)) = a <==>f(k)(z) = b for all f 2 F andz 2 D (where a 6= 0 and b are fixed complex numbers,L(w(z)) be a differential polynomial,m>=2 be a positive integer),then F is normal on D .
	TO cite this article:Shi Zhongchun. Normal Families and Shared Values concerning　Differential Polynomial[OL].[28 December 2007] http://en.paper.edu.cn/en_releasepaper/content/17513


	2. Generalization performance of graph-based semi-supervised classification
	Chen Hong,Li Luoqing
	Mathematics 28 December 2007
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	Abstract:Semi-supervised learning has been of growing interest over the past few years and many methods have been proposed. Although there are various algorithms to implement semi-supervised learning, the crucial issue of dependence of generalization error on the number of labeled and unlabeled examples is still poorly understood. In this paper, we consider a regularization graph-based semi-supervised classification algorithm. By introducing a definition of graph cut, we illustrate some relations of graph cut and regularization error. Then, based on the structural invariants of the data graph, generalization error bounds of the graph-based algorithm are established
	TO cite this article:Chen Hong,Li Luoqing. Generalization performance of graph-based semi-supervised classification[OL].[28 December 2007] http://en.paper.edu.cn/en_releasepaper/content/17492

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	3. Strongly Singular Calder＇{o}n-Zygmund Operators
	Yan Lin,Shanzhen Lu
	Mathematics 28 November 2007
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	Abstract:In this paper, the authors obtain two kinds of endpoint estimates for strongly singular Calder＇{o}n-Zygmund operators. Moreover, the pointwise estimate for sharp maximal function of commutators generated by strongly singular Calder＇{o}n-Zygmund operators and BMO functions is also established. As its applications, the boundedness of the commutators on Morrey type spaces will be obtained.
	TO cite this article:Yan Lin,Shanzhen Lu. Strongly Singular Calder＇{o}n-Zygmund Operators[OL].[28 November 2007] http://en.paper.edu.cn/en_releasepaper/content/16631


	4. The Generalization Performance of ERM Algorithm with Strongly Mixing Observations
	Zou Bin,Li Luoqing
	Mathematics 27 November 2007
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	Abstract:The generalization performance is the main purpose of machine learning theoretical research. The previous main bounds describing the generalization ability of ERM algorithm are based on independent and identically distributed (i.i.d.) samples. When the complexity of the given function set is high, the problem of solving the ERM algorithm is usually ill-posed and overfitting may happen. In order to study the generalization performance of ERM algorithm with dependent observations, in this paper we decompose firstly the given function set into different compact subsets, and then we establish the exponential bound on the rate of relative uniform convergence on these compact subsets for ERM algorithm with strongly mixing observations. In the end, we obtain the bounds on the generalization ability of ERM algorithm with strongly mixing observations over the given function set, which extend the previous results of i.i.d. observations to the case of strongly mixing observations.
	TO cite this article:Zou Bin,Li Luoqing. The Generalization Performance of ERM Algorithm with Strongly Mixing Observations[OL].[27 November 2007] http://en.paper.edu.cn/en_releasepaper/content/16592


	5. On Marcinkiewicz integral with rough kernels
	Lu Shanzhen
	Mathematics 23 November 2007
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	Abstract:In this summary paper, the author would like to introduce some recent progress in the theory of Marcinkiewicz integral and will pay more attention to the case of rough kernels. It consists of six sections. 1. Introduction 2. $L^p$-boundedness of Marcinkiewicz integral 3. Weighted $L^p$-boundedness of Marcinkiewicz integral 4. Boundedness of Marcinkiewicz integral on the other spaces 5. Commutators generated by Marcinkiewicz integral 6. Marcinkiewicz integral on product spaces.
	TO cite this article:Lu Shanzhen . On Marcinkiewicz integral with rough kernels[OL].[23 November 2007] http://en.paper.edu.cn/en_releasepaper/content/16548


	6. On the complex oscillation theory of analytic solutions of linear differential equations in the unit disc
	Cao Tingbin,Yi Hongxun
	Mathematics 04 June 2007
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	Abstract:The complex oscillation theory of linear differential equations of the form $$L(f)=f^{(k)}+A_{k-1}(z)f^{(k-1)}+cdots+A_{0}(z)f=F(z)quad(kin textbf{N}),$$ where the coefficients $A_{j}(z) (j=0,cdots,k-1)$ and $F(z)$ are analytic functions in the unit disc $Delta={z:\|z\|<1},$ is investigated. We obtain several precise theorems about the hyper order, the hyper convergence exponent of zero points and fixed points of solutions of differential equations.
	TO cite this article:Cao Tingbin,Yi Hongxun. On the complex oscillation theory of analytic solutions of linear differential equations in the unit disc[OL].[ 4 June 2007] http://en.paper.edu.cn/en_releasepaper/content/13232


	7. The Complexity of Function Approximation by the Linear Monte Carlo Methods
	Fang Gensun ,Duan Liqin
	Mathematics 30 April 2007
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	Abstract:We study the information-based complexity of the approximation problem on the multivariate Sobolev space with bounded mixed derivative by the linear Monte Carlo methods. Applying the Maiorov\\\
	TO cite this article:Fang Gensun ,Duan Liqin . The Complexity of Function Approximation by the Linear Monte Carlo Methods[OL].[30 April 2007] http://en.paper.edu.cn/en_releasepaper/content/12609


	8. Optimal Recovery on the Class of Functions with Bounded Mixed Derivative
	Fang Gensun ,Duan Liqin
	Mathematics 27 April 2007
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	Abstract:In this paper, we determine the asymptotic orders of the optimal recovery on the class of functions with bounded mixed derivative by standard information in Sobolev space, and give a nearly optimal algorithm.
	TO cite this article:Fang Gensun ,Duan Liqin . Optimal Recovery on the Class of Functions with Bounded Mixed Derivative[OL].[27 April 2007] http://en.paper.edu.cn/en_releasepaper/content/12537


	9. A note on a conjecture of Calder′on on weak type L1 boundedness of CZOs
	Chen Jiecheng,Zhu Xiangrong
	Mathematics 01 December 2006
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	Abstract:For $f\\in \\QTR{cal}{S}(R^2)$ and $\\Omega \\in L^1(S^1)$, $\\int_{S^1}\\Omega (x^{\\prime })dx^{\\prime }=0$, define $$T_\\Omega (f)(x)=\\underset{\\epsilon \\rightarrow 0+}\\to{\\lim }\\int_{\\left\| x-y\\right\| \\geq \\epsilon }\\frac{\\Omega (y/\\left\| y\\right\| )}{\\left\| y\\right\| ^2}f(x-y)dy. $$In this paper, we shall prove that there are a class of functions in $H^1(S^1)-L\\ln {}^{+}L(S^1)$ such that $T_\\Omega $ is weak type $L^1-$bounded.
	TO cite this article:Chen Jiecheng,Zhu Xiangrong. A note on a conjecture of Calder′on on weak type L1 boundedness of CZOs[OL].[ 1 December 2006] http://en.paper.edu.cn/en_releasepaper/content/10111


	10. L2--oundedness of Hilbert transforms along variable curves
	Chen Jiecheng,Zhu Xiangrong
	Mathematics 01 December 2006
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	Abstract:For $\phi \in C^1(R^1)$, $\gamma \in C^2(R^1)$, odd or even, $\gamma (0)=\gamma ^{\prime }(0)=0$, convex on $(0,\infty )$, define a Hilbert transform along variable curves by $$H_{\phi ,\gamma }(f)(x_1,x_2)=p.v.\int_{-\infty }^{+\infty }f(x_1-t,x_2-\phi (x_1)\gamma (t))\frac{dt}t. $$In this paper, we shall first give a counter-example to show that under the condition of Nagel-Vance-Wainger-Weinberg on $\gamma $, the $L^2-$boundedness of $H_{\phi ,\gamma }$ may fail even if $\phi \in C^\infty (R^1)$. Then, we relax Bennett
	TO cite this article:Chen Jiecheng,Zhu Xiangrong. L2--oundedness of Hilbert transforms along variable curves[OL].[ 1 December 2006] http://en.paper.edu.cn/en_releasepaper/content/10103

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