Let α≥ 0 and 0 〈 ρ ≤ n/2, the boundedness of hypersingular parameterized Marcinkiewicz integrals μΩ,α^ρ with variable kernels on Sobolev spaces Lα^ρ and HardySobolev spaces Hα^ρ is established.
In this paper,the parameterized Marcinkiewicz integrals with variable kernels defined by μΩ^ρ（f）（x）=（∫0^∞│∫│1-y│≤t Ω（x,x-y）/│x-y│^n-p f（y）dy│^2dt/t1＋2p）^1/2 are investigated.It is proved that ...In this paper,the parameterized Marcinkiewicz integrals with variable kernels defined by μΩ^ρ（f）（x）=（∫0^∞│∫│1-y│≤t Ω（x,x-y）/│x-y│^n-p f（y）dy│^2dt/t1＋2p）^1/2 are investigated.It is proved that if Ω∈ L∞（R^n） × L^r（S^n-1）（r〉（n-n1p＇/n） is an odd function in the second variable y,then the operator μΩ^ρ is bounded from L^p（R^n） to L^p（R^n） for 1 〈 p ≤ max{（n＋1）/2,2}.It is also proved that,if Ω satisfies the L^1-Dini condition,then μΩ^ρ is of type（p,p） for 1 〈 p ≤ 2,of the weak type（1,1） and bounded from H1 to L1.展开更多
Panicle swarm optimization （PSO） is an optimization algorithm based on the swarm intelligent principle. In this paper the modified PSO is applied to a kernel principal component analysis （ KPCA ） for an optimal ke...Panicle swarm optimization （PSO） is an optimization algorithm based on the swarm intelligent principle. In this paper the modified PSO is applied to a kernel principal component analysis （ KPCA ） for an optimal kernel function parameter. We first comprehensively considered within-class scatter and between-class scatter of the sample features. Then, the fitness function of an optimized kernel function parameter is constructed, and the particle swarm optimization algorithm with adaptive acceleration （CPSO） is applied to optimizing it. It is used for gearbox condi- tion recognition, and the result is compared with the recognized results based on principal component analysis （PCA）. The results show that KPCA optimized by CPSO can effectively recognize fault conditions of the gearbox by reducing bind set-up of the kernel function parameter, and its results of fault recognition outperform those of PCA. We draw the conclusion that KPCA based on CPSO has an advantage in nonlinear feature extraction of mechanical failure, and is helpful for fault condition recognition of complicated machines.展开更多
We assessed chemical composition and variation in oil content and seed weight of 40 wild-growing almonds（Prunus L. spp.） accessions collected from different parts of Iran. There were significant differences in kerne...We assessed chemical composition and variation in oil content and seed weight of 40 wild-growing almonds（Prunus L. spp.） accessions collected from different parts of Iran. There were significant differences in kernel weight and oil parameters. Accessions ranged from0.20 to 1.5 g in kernel weight, 0.2–3.0 mm in shell thickness, and 16–55 % in oil content. The predominant vegetable oil components of kernels were 4.6–9.5 % palmitic acid, 0.4–0.8 % palmitoleic acid, 1.0–3.4 % stearic acid,48.8–88.4 % oleic acid and 11.3–33.2 % linoleic acid.Linolenic acid was detected in 15 accessions. High heritability was recorded for all studied traits and was maximum for shell thickness（98.5 %） and minimum for oil content（97.1 %）. Maximum and minimum ‘Euclidean＇pair wise dissimilarities were 17.9 and 0.5, respectively.All 40 accessions were grouped into two major clusters.展开更多
The support vector machine （SVM） is a novel machine learning tool in data mining. In this paper, the geometric approach based on the compressed convex hull （CCH） with a mathematical framework is introduced to solv...The support vector machine （SVM） is a novel machine learning tool in data mining. In this paper, the geometric approach based on the compressed convex hull （CCH） with a mathematical framework is introduced to solve SVM classification problems. Compared with the reduced convex hull （RCH）, CCH preserves the shape of geometric solids for data sets; meanwhile, it is easy to give the necessary and sufficient condition for determining its extreme points. As practical applications of CCH, spare and probabilistic speed-up geometric algorithms are developed. Results of numerical experiments show that the proposed algorithms can reduce kernel calculations and display nice performances.展开更多
Parameterized computation is a new method dealing with NP-hard problems, which has attracted a lot of attentions in theoretical computer science. As a practical preprocessing method for NP-hard problems, kernelizaiton...Parameterized computation is a new method dealing with NP-hard problems, which has attracted a lot of attentions in theoretical computer science. As a practical preprocessing method for NP-hard problems, kernelizaiton in parameterized computation has recently become an active research area. In this paper, we discuss several kernelizaiton techniques, such as crown decomposition, planar graph vertex partition, randomized methods, and kernel lower bounds, which have been used widely in the kernelization of many hard problems.展开更多
基金Supported by the National Natural Science Foundation of China(1057115610871173)
文摘Let α≥ 0 and 0 〈 ρ ≤ n/2, the boundedness of hypersingular parameterized Marcinkiewicz integrals μΩ,α^ρ with variable kernels on Sobolev spaces Lα^ρ and HardySobolev spaces Hα^ρ is established.
基金Supported by the National Natural Science Foundation of China (1057115610871173)
文摘In this paper,the parameterized Marcinkiewicz integrals with variable kernels defined by μΩ^ρ（f）（x）=（∫0^∞│∫│1-y│≤t Ω（x,x-y）/│x-y│^n-p f（y）dy│^2dt/t1＋2p）^1/2 are investigated.It is proved that if Ω∈ L∞（R^n） × L^r（S^n-1）（r〉（n-n1p＇/n） is an odd function in the second variable y,then the operator μΩ^ρ is bounded from L^p（R^n） to L^p（R^n） for 1 〈 p ≤ max{（n＋1）/2,2}.It is also proved that,if Ω satisfies the L^1-Dini condition,then μΩ^ρ is of type（p,p） for 1 〈 p ≤ 2,of the weak type（1,1） and bounded from H1 to L1.
基金supported by National Natural Science Foundation under Grant No.50875247Shanxi Province Natural Science Foundation under Grant No.2009011026-1
文摘Panicle swarm optimization （PSO） is an optimization algorithm based on the swarm intelligent principle. In this paper the modified PSO is applied to a kernel principal component analysis （ KPCA ） for an optimal kernel function parameter. We first comprehensively considered within-class scatter and between-class scatter of the sample features. Then, the fitness function of an optimized kernel function parameter is constructed, and the particle swarm optimization algorithm with adaptive acceleration （CPSO） is applied to optimizing it. It is used for gearbox condi- tion recognition, and the result is compared with the recognized results based on principal component analysis （PCA）. The results show that KPCA optimized by CPSO can effectively recognize fault conditions of the gearbox by reducing bind set-up of the kernel function parameter, and its results of fault recognition outperform those of PCA. We draw the conclusion that KPCA based on CPSO has an advantage in nonlinear feature extraction of mechanical failure, and is helpful for fault condition recognition of complicated machines.
基金financially supported by Payam-e-Noor University
文摘We assessed chemical composition and variation in oil content and seed weight of 40 wild-growing almonds（Prunus L. spp.） accessions collected from different parts of Iran. There were significant differences in kernel weight and oil parameters. Accessions ranged from0.20 to 1.5 g in kernel weight, 0.2–3.0 mm in shell thickness, and 16–55 % in oil content. The predominant vegetable oil components of kernels were 4.6–9.5 % palmitic acid, 0.4–0.8 % palmitoleic acid, 1.0–3.4 % stearic acid,48.8–88.4 % oleic acid and 11.3–33.2 % linoleic acid.Linolenic acid was detected in 15 accessions. High heritability was recorded for all studied traits and was maximum for shell thickness（98.5 %） and minimum for oil content（97.1 %）. Maximum and minimum ‘Euclidean＇pair wise dissimilarities were 17.9 and 0.5, respectively.All 40 accessions were grouped into two major clusters.
基金Supported by the National Natural Science Foundation of China under Grant Nos.6043302060773111(国家自然科学基金)+1 种基金the Program for New Century Excellent Talents in University of China under Grant No.NCET-05-0683(新世纪优秀人才支持计划)the Program for Changjiang Scholars and Innovative Research Team in University of China under Grant No.IRT0661(长江学者和创新团队发展计划)
基金Supported by the National Natural Science Foundation of China (No. 30571059)the National High-Tech Research and Development Program of China (No. 2006AA02Z190)Shanghai Leading Academic Discipline Project (No. 530405)
文摘The support vector machine （SVM） is a novel machine learning tool in data mining. In this paper, the geometric approach based on the compressed convex hull （CCH） with a mathematical framework is introduced to solve SVM classification problems. Compared with the reduced convex hull （RCH）, CCH preserves the shape of geometric solids for data sets; meanwhile, it is easy to give the necessary and sufficient condition for determining its extreme points. As practical applications of CCH, spare and probabilistic speed-up geometric algorithms are developed. Results of numerical experiments show that the proposed algorithms can reduce kernel calculations and display nice performances.
基金supported by the National Natural Science Foundation of China (Nos. 61173051, 61103033, and 61232001)
文摘Parameterized computation is a new method dealing with NP-hard problems, which has attracted a lot of attentions in theoretical computer science. As a practical preprocessing method for NP-hard problems, kernelizaiton in parameterized computation has recently become an active research area. In this paper, we discuss several kernelizaiton techniques, such as crown decomposition, planar graph vertex partition, randomized methods, and kernel lower bounds, which have been used widely in the kernelization of many hard problems.
