This paper is devoted to studying the commutators of the multilinear singular integral operators with the non-smooth kernels and the weighted Lipschitz functions. Some mapping properties for two types of commutators o...This paper is devoted to studying the commutators of the multilinear singular integral operators with the non-smooth kernels and the weighted Lipschitz functions. Some mapping properties for two types of commutators on the weighted Lebesgue spaces, which extend and generalize some previous results, are obtained.展开更多
In this paper,a new full-Newton step primal-dual interior-point algorithm for solving the special weighted linear complementarity problem is designed and analyzed.The algorithm employs a kernel function with a linear ...In this paper,a new full-Newton step primal-dual interior-point algorithm for solving the special weighted linear complementarity problem is designed and analyzed.The algorithm employs a kernel function with a linear growth term to derive the search direction,and by introducing new technical results and selecting suitable parameters,we prove that the iteration bound of the algorithm is as good as best-known polynomial complexity of interior-point methods.Furthermore,numerical results illustrate the efficiency of the proposed method.展开更多
This paper is concerned with certain multilinear commutators of BMO functions and multilinear singular integral operators with non-smooth kernels. By the sharp maximal functions estimates, the weighted norm inequaliti...This paper is concerned with certain multilinear commutators of BMO functions and multilinear singular integral operators with non-smooth kernels. By the sharp maximal functions estimates, the weighted norm inequalities for this kind of commutators are established.展开更多
Suppose T^k,l and T^k,2 are singular integrals with variable kernels and mixed homogeneity or ±I （the identity operator）. Denote the Toeplitz type operator by T^b=k=1∑^QT^k,1M^bT^k,2 where M^bf= bf. In this pa...Suppose T^k,l and T^k,2 are singular integrals with variable kernels and mixed homogeneity or ±I （the identity operator）. Denote the Toeplitz type operator by T^b=k=1∑^QT^k,1M^bT^k,2 where M^bf= bf. In this paper, the boundedness of Tb on weighted Morrey space are obtained when b belongs to the weighted Lipschitz function space and weighted BMO function space, respectively.展开更多
The aim of the present paper is to study 2-complex symmetric bounded weighted composition operators on the Fock space of C^(N) with the conjugations J and J_(t,A,b) defined by ■ respectively,where k(z_(1),...,z_N)=(...The aim of the present paper is to study 2-complex symmetric bounded weighted composition operators on the Fock space of C^(N) with the conjugations J and J_(t,A,b) defined by ■ respectively,where k(z_(1),...,z_N)=(■,...,■),t∈C,b∈C^(N) and A is a linear operator on C^(N).An example of 2-complex symmetric bounded weighted composition operator with the conjugation J_(t,A,b) is given.展开更多
In this paper, the weighted boundedness of parametric Marcinkiewicz integral and its commutator with rough kernels are considered. In addition, the weak type norm inequalities for parametric Marcinkiewicz integral and...In this paper, the weighted boundedness of parametric Marcinkiewicz integral and its commutator with rough kernels are considered. In addition, the weak type norm inequalities for parametric Marcinkiewicz integral and its commutator with different weight functions and Dini kernel are also discussed.展开更多
α-diversity describes species diversity at local scales.The Simpson’s and Shannon-Wiener indices are widely used to characterizeα-diversity based on species abundances within a fixed study site(e.g.,a quadrat or pl...α-diversity describes species diversity at local scales.The Simpson’s and Shannon-Wiener indices are widely used to characterizeα-diversity based on species abundances within a fixed study site(e.g.,a quadrat or plot).Although such indices provide overall diversity estimates that can be analyzed,their values are not spatially continuous nor applicable in theory to any point within the study region,and thus they cannot be treated as spatial covariates for analyses of other variables.Herein,we extended the Simpson’s and Shannon-Wiener indices to create point estimates ofα-diversity for any location based on spatially explicit species occurrences within different bandwidths(i.e.,radii,with the location of interest as the center).For an arbitrary point in the study region,species occurrences within the circle plotting the bandwidth were weighted according to their distance from the center using a tri-cube kernel function,with occurrences closer to the center having greater weight than more distant ones.These novel kernel-basedα-diversity indices were tested using a tree dataset from a 400 m×400 m study region comprising a 200 m×200 m core region surrounded by a 100-m width buffer zone.Our newly extendedα-diversity indices did not disagree qualitatively with the traditional indices,and the former were slightly lower than the latter by<2%at medium and large band widths.The present work demonstrates the feasibility of using kernel-basedα-diversity indices to estimate diversity at any location in the study region and allows them to be used as quantifiable spatial covariates or predictors for other dependent variables of interest in future ecological studies.Spatially continuousα-diversity indices are useful to compare and monitor species trends in space and time,which is valuable for conservation practitioners.展开更多
The kernel of interval grey number is most likely the real number,which can be used to represent whitenization value of interval grey number.A novel method for calculating kernel of interval grey number is constructed...The kernel of interval grey number is most likely the real number,which can be used to represent whitenization value of interval grey number.A novel method for calculating kernel of interval grey number is constructed based on the geometric barycenter of whitenization weight function in the two-dimensional coordinate plane,and the calculation of kernel is converted to the calculation of barycenter in geometric figures.The method fully considers the effect of all information contained in whitenization weight function on the calculation result of kernel,and is the extension and perfection of the existing methods in the scope of application.展开更多
Through using weight function, we give a new Hilbert-type integral inequality with two independent parameters and two pair of conjugate exponents, which is a best extension of a Hilbert-type integral inequality with t...Through using weight function, we give a new Hilbert-type integral inequality with two independent parameters and two pair of conjugate exponents, which is a best extension of a Hilbert-type integral inequality with the homogeneous kernel of 0-degree. The equivalent form, the reverses and some particular results are considered.展开更多
In this paper, the normal approximation rate and the random weighting approximation rate of error distribution of the kernel estimator of conditional density function f(y|x) are studied. The results may be used to...In this paper, the normal approximation rate and the random weighting approximation rate of error distribution of the kernel estimator of conditional density function f(y|x) are studied. The results may be used to construct the confidence interval of f(y|x) .展开更多
In some sample based regression tasks,the observed samples are quite few or not informative enough.As a result,the conflict between the number of samples and the model complexity emerges,and the regression method will...In some sample based regression tasks,the observed samples are quite few or not informative enough.As a result,the conflict between the number of samples and the model complexity emerges,and the regression method will confront the dilemma whether to choose a complex model or not.Incorporating the prior knowledge is a potential solution for this dilemma.In this paper,a sort of the prior knowledge is investigated and a novel method to incorporate it into the kernel based regression scheme is proposed.The proposed prior knowledge based kernel regression(PKBKR)method includes two subproblems:representing the prior knowledge in the function space,and combining this representation and the training samples to obtain the regression function.A greedy algorithm for the representing step and a weighted loss function for the incorporation step axe proposed.Finally,experiments are performed to validate the proposed PKBKR method,wherein the results show that the proposed method can achieve relatively high regression performance with appropriate model complexity,especially when the number of samples is small or the observation noise is large.展开更多
针对最小二乘孪生支持向量机受误差值影响大,对噪声样本敏感及核函数、核参数选择困难等问题,提出一种Critic特征加权的多核最小二乘孪生支持向量机(Multi-Kernel Least-Squares Twin Support Vector Machine based on Critic weighted,...针对最小二乘孪生支持向量机受误差值影响大,对噪声样本敏感及核函数、核参数选择困难等问题,提出一种Critic特征加权的多核最小二乘孪生支持向量机(Multi-Kernel Least-Squares Twin Support Vector Machine based on Critic weighted,CMKLSTSVM)分类方法。首先,CMKLSTSVM使用Critic法赋予特征权重,反映不同特征间重要性差异,降低冗余特征及噪声样本影响。其次,根据混合多核学习策略构造了一种新的多核权重系数确定方法。该方法通过基核与理想核间的混合核对齐值判断核函数相似程度,确定权重系数,可以合理地组合多个核函数,最大程度地发挥不同核函数的映射能力。最后,采用加权求和的方式将特征权重与核权重进行统一并构造多核结构,使数据表达更全面,提高模型灵活性。在UCI数据集上的对比实验表明,CMKLSTSVM的分类准确率优于单核结构的SVM(support vector machine)算法,同时在高光谱图像上的对比实验反映了CMKLSTSVM对于包含噪声的真实分类问题的有效性。展开更多
Under weaker conditions on the kernel functions,we discuss the boundedness of bilinear square functions associated with non-smooth kernels on the product of weighted Lebesgue spaces.Moreover,we investigate the weighte...Under weaker conditions on the kernel functions,we discuss the boundedness of bilinear square functions associated with non-smooth kernels on the product of weighted Lebesgue spaces.Moreover,we investigate the weighted boundedness of the commutators of bilinear square functions(with symbols which are BMO functions and their weighted version,respectively)on the product of Lebesgue spaces.As an application,we deduce the corresponding boundedness of bilinear Marcinkiewicz integrals and bilinear Littlewood-Paley^-functions.展开更多
基金Supported by the National Natural Science Foundation of China (10771054,11071200)the NFS of Fujian Province of China (No. 2010J01013)
文摘This paper is devoted to studying the commutators of the multilinear singular integral operators with the non-smooth kernels and the weighted Lipschitz functions. Some mapping properties for two types of commutators on the weighted Lebesgue spaces, which extend and generalize some previous results, are obtained.
基金Supported by University Science Research Project of Anhui Province(2023AH052921)Outstanding Youth Talent Project of Anhui Province(gxyq2021254)。
文摘In this paper,a new full-Newton step primal-dual interior-point algorithm for solving the special weighted linear complementarity problem is designed and analyzed.The algorithm employs a kernel function with a linear growth term to derive the search direction,and by introducing new technical results and selecting suitable parameters,we prove that the iteration bound of the algorithm is as good as best-known polynomial complexity of interior-point methods.Furthermore,numerical results illustrate the efficiency of the proposed method.
基金Supported by the National Natural Science Foundation of China (10771054, 10771221, 11071200)the Youth Foundation of Wuyi University (No. xq0930)
文摘This paper is concerned with certain multilinear commutators of BMO functions and multilinear singular integral operators with non-smooth kernels. By the sharp maximal functions estimates, the weighted norm inequalities for this kind of commutators are established.
文摘Suppose T^k,l and T^k,2 are singular integrals with variable kernels and mixed homogeneity or ±I （the identity operator）. Denote the Toeplitz type operator by T^b=k=1∑^QT^k,1M^bT^k,2 where M^bf= bf. In this paper, the boundedness of Tb on weighted Morrey space are obtained when b belongs to the weighted Lipschitz function space and weighted BMO function space, respectively.
基金Supported by Sichuan Science and Technology Program (No.2022ZYD0010)。
文摘The aim of the present paper is to study 2-complex symmetric bounded weighted composition operators on the Fock space of C^(N) with the conjugations J and J_(t,A,b) defined by ■ respectively,where k(z_(1),...,z_N)=(■,...,■),t∈C,b∈C^(N) and A is a linear operator on C^(N).An example of 2-complex symmetric bounded weighted composition operator with the conjugation J_(t,A,b) is given.
文摘In this paper, the weighted boundedness of parametric Marcinkiewicz integral and its commutator with rough kernels are considered. In addition, the weak type norm inequalities for parametric Marcinkiewicz integral and its commutator with different weight functions and Dini kernel are also discussed.
基金supported by Natural Science Foundation of Xinjiang Uygur Autonomous Region(2022D01A213)。
文摘α-diversity describes species diversity at local scales.The Simpson’s and Shannon-Wiener indices are widely used to characterizeα-diversity based on species abundances within a fixed study site(e.g.,a quadrat or plot).Although such indices provide overall diversity estimates that can be analyzed,their values are not spatially continuous nor applicable in theory to any point within the study region,and thus they cannot be treated as spatial covariates for analyses of other variables.Herein,we extended the Simpson’s and Shannon-Wiener indices to create point estimates ofα-diversity for any location based on spatially explicit species occurrences within different bandwidths(i.e.,radii,with the location of interest as the center).For an arbitrary point in the study region,species occurrences within the circle plotting the bandwidth were weighted according to their distance from the center using a tri-cube kernel function,with occurrences closer to the center having greater weight than more distant ones.These novel kernel-basedα-diversity indices were tested using a tree dataset from a 400 m×400 m study region comprising a 200 m×200 m core region surrounded by a 100-m width buffer zone.Our newly extendedα-diversity indices did not disagree qualitatively with the traditional indices,and the former were slightly lower than the latter by<2%at medium and large band widths.The present work demonstrates the feasibility of using kernel-basedα-diversity indices to estimate diversity at any location in the study region and allows them to be used as quantifiable spatial covariates or predictors for other dependent variables of interest in future ecological studies.Spatially continuousα-diversity indices are useful to compare and monitor species trends in space and time,which is valuable for conservation practitioners.
基金Supported by the National Natural Science Foundation of China(71271226,70971064,71101159)the Humanities and Social Science Foundation of Ministry of Education(11YJC630273,12YJC630140)+4 种基金the Program for Chongqing Innovation Team in University(KJTD201313)the Science and Technology Research Projects of Chongqing Education Commission(KJ120706)the Open Foundation of Chongqing Key Laboratory of Electronic Commerce and Supply Chain System(2012ECSC0101)the Special Fund of Chongqing Key Laboratory of Electronic Commerce and Supply Chain System(2012ECSC0217)the Chongqing City Board of Education Science and Technology Research Projects(1202010)
文摘The kernel of interval grey number is most likely the real number,which can be used to represent whitenization value of interval grey number.A novel method for calculating kernel of interval grey number is constructed based on the geometric barycenter of whitenization weight function in the two-dimensional coordinate plane,and the calculation of kernel is converted to the calculation of barycenter in geometric figures.The method fully considers the effect of all information contained in whitenization weight function on the calculation result of kernel,and is the extension and perfection of the existing methods in the scope of application.
基金Project supported by the Natural Science Foundation of the Institutions of Higher Learning of Guangdong Province (GrantNo.05Z026)the Natural Science Foundation of Guangdong Province (Grant No.7004344)
文摘Through using weight function, we give a new Hilbert-type integral inequality with two independent parameters and two pair of conjugate exponents, which is a best extension of a Hilbert-type integral inequality with the homogeneous kernel of 0-degree. The equivalent form, the reverses and some particular results are considered.
基金Supported by Natural Science Foundation of Beijing City and National Natural Science Foundation ofChina(2 2 30 4 1 0 0 1 30 1
文摘In this paper, the normal approximation rate and the random weighting approximation rate of error distribution of the kernel estimator of conditional density function f(y|x) are studied. The results may be used to construct the confidence interval of f(y|x) .
基金Supported_by National Key Technologies Research and De-velopment Program of China during the 11th Five-year Plan(2006AA060206)Basic Research Foundation of Tsinghua Uni-versity(JC2007024)
文摘In some sample based regression tasks,the observed samples are quite few or not informative enough.As a result,the conflict between the number of samples and the model complexity emerges,and the regression method will confront the dilemma whether to choose a complex model or not.Incorporating the prior knowledge is a potential solution for this dilemma.In this paper,a sort of the prior knowledge is investigated and a novel method to incorporate it into the kernel based regression scheme is proposed.The proposed prior knowledge based kernel regression(PKBKR)method includes two subproblems:representing the prior knowledge in the function space,and combining this representation and the training samples to obtain the regression function.A greedy algorithm for the representing step and a weighted loss function for the incorporation step axe proposed.Finally,experiments are performed to validate the proposed PKBKR method,wherein the results show that the proposed method can achieve relatively high regression performance with appropriate model complexity,especially when the number of samples is small or the observation noise is large.
文摘针对最小二乘孪生支持向量机受误差值影响大,对噪声样本敏感及核函数、核参数选择困难等问题,提出一种Critic特征加权的多核最小二乘孪生支持向量机(Multi-Kernel Least-Squares Twin Support Vector Machine based on Critic weighted,CMKLSTSVM)分类方法。首先,CMKLSTSVM使用Critic法赋予特征权重,反映不同特征间重要性差异,降低冗余特征及噪声样本影响。其次,根据混合多核学习策略构造了一种新的多核权重系数确定方法。该方法通过基核与理想核间的混合核对齐值判断核函数相似程度,确定权重系数,可以合理地组合多个核函数,最大程度地发挥不同核函数的映射能力。最后,采用加权求和的方式将特征权重与核权重进行统一并构造多核结构,使数据表达更全面,提高模型灵活性。在UCI数据集上的对比实验表明,CMKLSTSVM的分类准确率优于单核结构的SVM(support vector machine)算法,同时在高光谱图像上的对比实验反映了CMKLSTSVM对于包含噪声的真实分类问题的有效性。
基金This work was supported by the National Natural Science Foundation of China(Grant Nos.11671185,11571306,11671363,11771195)the Natural Science Foundation of Shandong Province(Grant Nos.ZR2018PA004,ZR2016AB07,ZR2018LA002,ZR2019YQ04).
文摘Under weaker conditions on the kernel functions,we discuss the boundedness of bilinear square functions associated with non-smooth kernels on the product of weighted Lebesgue spaces.Moreover,we investigate the weighted boundedness of the commutators of bilinear square functions(with symbols which are BMO functions and their weighted version,respectively)on the product of Lebesgue spaces.As an application,we deduce the corresponding boundedness of bilinear Marcinkiewicz integrals and bilinear Littlewood-Paley^-functions.
