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	1. Nonuniform Sampling for Random Signals Bandlimited in the Linear Canonical Transform Domain
	HUO Haiye,SUN Wenchang
	Mathematics 21 May 2016
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	Abstract:The nonuniform sampling for random signals which are bandlimited in the linear canonical transform (LCT) domain is studied in this paper.It was shown that the nonuniform sampling for a random signal bandlimited in the LCT domainis equal to the uniform sampling in the sense of second order statistic characters after a pre-filter in the LCTdomain. Moreover, an approximate recovery approach for nonuniform sampling of random signals bandlimited in the LCT domain is proposed.Finally, the mean square error of the nonuniform sampling is studied.
	TO cite this article:HUO Haiye,SUN Wenchang. Nonuniform Sampling for Random Signals Bandlimited in the Linear Canonical Transform Domain[OL].[21 May 2016] http://en.paper.edu.cn/en_releasepaper/content/4690388


	2. Stable Recovery of Block Sparse Signals via Mixed $l_{p}/l_{q}$ Optimization Algorithm
	HUO Haiye,SUN Wenchang
	Mathematics 18 May 2016
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	Abstract:In this paper, the stable recovery of block sparse signals is investigated.A general mixed $l_{p}/l_{q}$ optimization algorithm is proposed, under which the block restricted isometry property (block RIP) and the block null space property (block NSP) are both shown to be sufficient conditions on a measurement matrix for stable recovery of block-sparse signals. Moreover, a new concept of the block sparse approximationproperty (block SAP) is defined in this paper. It is shown that the block SAP is also a sufficient condition on a measurement matrix for stably recovering block-sparse signals based on the mixed $l_{p}/l_{q}$ optimization algorithm. Finally, the relationship between the block SAP, the block RIP, and the block NSP are studied.
	TO cite this article:HUO Haiye,SUN Wenchang. Stable Recovery of Block Sparse Signals via Mixed $l_{p}/l_{q}$ Optimization Algorithm[OL].[18 May 2016] http://en.paper.edu.cn/en_releasepaper/content/4690394

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	3. Strong summation of Cesaro means of Fourier-Laplace series
	Zhang Wei,Zhang Xi-Rong
	Mathematics 10 October 2013
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	Abstract:The strong summation of Fourier-Laplace series in logarithmic subclasses of $L^{2}(sum_{d})$ defined in terms of moduli of continuity is of interest.In this note,the almost everywhere convergence rates of the Cesaro means for Fourier-Laplace series of the convex subclasses areobtained.The strong approximation order of the Cesaro means and the partial summation operators are also presented.
	TO cite this article:Zhang Wei,Zhang Xi-Rong. Strong summation of Cesaro means of Fourier-Laplace series[OL].[10 October 2013] http://en.paper.edu.cn/en_releasepaper/content/4563503


	4. Optimal recovery of functions on the sphere on a Sobolev spaces with a Gaussian measure in the average case setting
	HUANG Zexia,WANG He-Ping
	Mathematics 11 January 2013
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	Abstract:Optimal recovery means that using finitely manyarbitrary function values f(x) for some x∈D to reconstruct(recovery) functions f from a given classes with the least possible errors. Optimal recovery constitutes a important ingredient innumerical analysis and has many important practical applications.There are two most important case setting: worst case setting andaverage case setting as far as error measure is concerned. In thispaper, optimal recovery (reconstruction) of functions on the spherein the average case setting is studied. The asymptotic orders ofaverage sampling numbers of a Sobolev space on the sphere with aGaussian measure in the Lq(sd-1) metric for 1≤q≤∞ are obtained, and it is shown that some worst-caseasymptotically optimal algorithms are also asymptotically optimal in the average case setting inthe Lq(sd-1) metric for 1≤q≤∞.
	TO cite this article:HUANG Zexia,WANG He-Ping. Optimal recovery of functions on the sphere on a Sobolev spaces with a Gaussian measure in the average case setting[OL].[11 January 2013] http://en.paper.edu.cn/en_releasepaper/content/4514337


	5. Entropy numbers of Besov classes of generalized smoothness onthe sphere
	WANG Heping,WANG Kai,WANG Jing
	Mathematics 11 January 2013
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	Abstract:Entropy numbers measure the compactness of operators(or the set) in a qualitative way. The asymptotic decay at infinityof the sequence of entropy numbers of a compact operator T describes the degree of compactness of T. They have manyapplication in the theory of function spaces and spectral theory, signal and image processing, probabilitytheory, learning theory,etc.. In this paper, the asymptoticbehavior of the entropy numbers of Besov classes$BB_{p, heta}^{Omega}(mathbb{S}^{d-1})$ of generalized smoothnesson the sphere in $L_q(ss)$ for $1leq p, q, hetaleqinfty$ isinvestigated, and their asymptotic orders are gotten. The exactorders of entropy numbers of Sobolev classes$BW_p^r(mathbb{S}^{d-1})$ in $L_q(mathbb{S}^{d-1})$ when $p$and/or $q$ is equal to $1$ or $infty$ are also obtained. Thisprovides the last piece as far as exact orders of entropy numbers of$BW_p^r(mathbb{S}^{d-1})$ in $L_q(mathbb{S}^{d-1})$ are concerned.
	TO cite this article:WANG Heping,WANG Kai,WANG Jing. Entropy numbers of Besov classes of generalized smoothness onthe sphere[OL].[11 January 2013] http://en.paper.edu.cn/en_releasepaper/content/4514334


	6. Birkhoff Interpolation of Cardinal Splines
	Ling Bo,Liu Yongping
	Mathematics 03 December 2012
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	Abstract:Cardinal SplineInterpolation Problem(CIP) is to consider finding a cardinal splinefunction s(x) of degree n such that s(v)= yv ,∀v∈Z, with given information (yv)v∈Z. Schoenberg solved this problem and the corresponding Cardinal Hermite Spline Interpolation Problem(CHIP) and obtained manygraceful results in about 1970. In this paper, the authors will considerCardinal (ρ0,ρ1,ρr-1) Birkhoff SplineInterpolation Problem(CBIP) using the similar method fromSchoenberg. For this purpose, the cardinal splines spaces S2m-1,∧1 with Birkhoff knots is introduced,where ∧1:={θ0,θ1,...,θr-1}∈ {0,...,2m-1} is an ordered set. The lacunary interpolation problemconsidered is to find the interpolation functions on Z with derivativesinformation of order ∧2:={ρ0,ρ1,...,ρr-1} in the spline space S2m-1,∧1. Here ∧2:={ρ0,ρ1,...,ρr-1}∈ {0,...,2m-1} is an ordered set.The necessary condition and several sufficient conditions on ∧1, ∧2 of the regularity(i.e. existing a uniquesolution) of CBIP are gained, and some results in CHIP areproved to be also true in CBIP.
	TO cite this article:Ling Bo,Liu Yongping. Birkhoff Interpolation of Cardinal Splines[OL].[ 3 December 2012] http://en.paper.edu.cn/en_releasepaper/content/4499694


	7. A Way of Constructing Approximate Interpolating Neural Networks
	ding lei,sheng baohuai
	Mathematics 05 December 2008
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	Abstract:In this paper, we present a type of single-hidden layer feedforward neural networks with thin-plate spline activation function. We find they can approximately interpolate, with arbitrary precision, any set of distinct data in one dimensions or multidimensional. They can uniformly approximate the continuous function of one variable as well as several variables.
	TO cite this article:ding lei,sheng baohuai. A Way of Constructing Approximate Interpolating Neural Networks[OL].[ 5 December 2008] http://en.paper.edu.cn/en_releasepaper/content/26338


	8. Recurrence Formulae for Box Integrals
	Zhi Cao
	Mathematics 11 March 2008
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	Abstract:Applying a formula of the multivariate $f$-Box splines, some recurrence formulae for the so-called box integrals are obtained. They are used to deduce some \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\
	TO cite this article:Zhi Cao. Recurrence Formulae for Box Integrals[OL].[11 March 2008] http://en.paper.edu.cn/en_releasepaper/content/19214


	9. Phase retrieval of time-limited signals
	Fu Yingxiong,Li Luoqing
	Mathematics 25 February 2008
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	Abstract: This paper concerns the problem of determining a time-limited signal for which its phase is known.
	TO cite this article:Fu Yingxiong,Li Luoqing. Phase retrieval of time-limited signals[OL].[25 February 2008] http://en.paper.edu.cn/en_releasepaper/content/18825


	10. 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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