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ZmZFP2 encoding a C4HC3-type RING zinc finger protein regulates kernel size and weight in maize
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作者 Long Zhang Qilei Wang +12 位作者 Wenyu Li Qi Zheng Miaomiao Fu Han Wang Xinyu Li Yan Wang Lingwei Hu Weigang Yao Lifeng Wang Huiyong Li Yongbin Dong Yongrui Wu Yuling Li 《The Crop Journal》 2025年第2期418-431,共14页
The development of maize(Zea mays)kernels is a complex physiological process regulated by numerous genes in a spatially and temporally coordinated manner.However,many regulatory genes involved in this process remain u... The development of maize(Zea mays)kernels is a complex physiological process regulated by numerous genes in a spatially and temporally coordinated manner.However,many regulatory genes involved in this process remain unidentified.In this study,we identified ZmZFP2,a gene encoding a C4HC3-type RING zinc finger protein,which regulates kernel size and weight.This discovery was based on suppression subtractive hybridization from maize endosperm in our previous research.We further investigated the role of ZmZFP2 in regulating kernel development.The zmzfp2-ems mutant exhibited significantly reduced kernel size and weight,accompanied by fewer endosperm cells and altered starch and protein accumulation.CRISPR/Cas9-mediated knockouts and overexpression lines confirmed that ZmZFP2 positively regulates kernel size and weight,with overexpression leading to increased kernel size and weight.Transcriptome analysis revealed that ZmZFP2 regulates genes involved in zeatin biosynthesis,starch metabolism,and protein processing,further supporting its role in kernel development.Additionally,ZmZFP2 was shown to interact with the transcription factor ZmEREB98,implicating it in the gene regulatory network during grain filling.Together,these findings demonstrate that ZmZFP2 is a key regulator of maize kernel size and weight,functioning through its E3 ubiquitin ligase activity and interactions with various metabolic pathways.This study provides novel insights into the genetic regulation of kernel development and presents potential strategies for improving maize yield and quality. 展开更多
关键词 MAIZE kernel weight and size Starch and protein accumulation E3 ubiquitin ligase Transcriptome analysis
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Relative-Density-Viewpoint-Based Weighted Kernel Fuzzy Clustering
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作者 Yuhan Xia Xu Li +2 位作者 Ye Liu Wenbo Zhou Yiming Tang 《Computers, Materials & Continua》 2025年第7期625-651,共27页
Applying domain knowledge in fuzzy clustering algorithms continuously promotes the development of clustering technology.The combination of domain knowledge and fuzzy clustering algorithms has some problems,such as ini... Applying domain knowledge in fuzzy clustering algorithms continuously promotes the development of clustering technology.The combination of domain knowledge and fuzzy clustering algorithms has some problems,such as initialization sensitivity and information granule weight optimization.Therefore,we propose a weighted kernel fuzzy clustering algorithm based on a relative density view(RDVWKFC).Compared with the traditional density-based methods,RDVWKFC can capture the intrinsic structure of the data more accurately,thus improving the initial quality of the clustering.By introducing a Relative Density based Knowledge Extraction Method(RDKM)and adaptive weight optimization mechanism,we effectively solve the limitations of view initialization and information granule weight optimization.RDKM can accurately identify high-density regions and optimize the initialization process.The adaptive weight mechanism can reduce noise and outliers’interference in the initial cluster centre selection by dynamically allocating weights.Experimental results on 14 benchmark datasets show that the proposed algorithm is superior to the existing algorithms in terms of clustering accuracy,stability,and convergence speed.It shows adaptability and robustness,especially when dealing with different data distributions and noise interference.Moreover,RDVWKFC can also show significant advantages when dealing with data with complex structures and high-dimensional features.These advancements provide versatile tools for real-world applications such as bioinformatics,image segmentation,and anomaly detection. 展开更多
关键词 Fuzzy clustering fuzzy c-means feature weighting information granule
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Aqueous Ionic Liquid Mediated Hydrolysis of Native Corn Starch to Obtain Different Low Molecular Weight Starch
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作者 YANG Rui WANG Xiaolin +1 位作者 DANG Qian LIU Zhengping 《高等学校化学学报》 北大核心 2026年第1期153-161,共9页
In this work,we proposed a strategy for the hydrolysis of native corn starch after the treatment of corn starch in an ionic liquid aqueous solution,and it is an awfully“green”and simple means to obtain starch with l... In this work,we proposed a strategy for the hydrolysis of native corn starch after the treatment of corn starch in an ionic liquid aqueous solution,and it is an awfully“green”and simple means to obtain starch with low molecular weight and amorphous state.X-ray diffraction results revealed that the natural starch crystalline region was largely disrupted by ionic liquid owing to the broken intermolecular and intramolecular hydrogen bonds.After hydrolysis,the morphology of starch changed from particles of native corn starch into little pieces,and their molecular weight could be effectively regulated during the hydrolysis process,and also the hydrolyzed starch samples exhibited decreased thermal stability with the extension of hydrolysis time.This work would counsel as a powerful tool for the development of native starch in realistic applications. 展开更多
关键词 Native corn starch Ionic liquid HYDROLYSIS Molecular weight
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FedCW: Client Selection with Adaptive Weight in Heterogeneous Federated Learning
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作者 Haotian Wu Jiaming Pei Jinhai Li 《Computers, Materials & Continua》 2026年第1期1551-1570,共20页
With the increasing complexity of vehicular networks and the proliferation of connected vehicles,Federated Learning(FL)has emerged as a critical framework for decentralized model training while preserving data privacy... With the increasing complexity of vehicular networks and the proliferation of connected vehicles,Federated Learning(FL)has emerged as a critical framework for decentralized model training while preserving data privacy.However,efficient client selection and adaptive weight allocation in heterogeneous and non-IID environments remain challenging.To address these issues,we propose Federated Learning with Client Selection and Adaptive Weighting(FedCW),a novel algorithm that leverages adaptive client selection and dynamic weight allocation for optimizing model convergence in real-time vehicular networks.FedCW selects clients based on their Euclidean distance from the global model and dynamically adjusts aggregation weights to optimize both data diversity and model convergence.Experimental results show that FedCW significantly outperforms existing FL algorithms such as FedAvg,FedProx,and SCAFFOLD,particularly in non-IID settings,achieving faster convergence,higher accuracy,and reduced communication overhead.These findings demonstrate that FedCW provides an effective solution for enhancing the performance of FL in heterogeneous,edge-based computing environments. 展开更多
关键词 Federated learning non-IID client selection weight allocation vehicular networks
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Weighted L^p-boundedness of Multilinear Oscillatory Singular Integrals with Calderón-Zygmund Kernel
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作者 田东风 燕敦验 《Chinese Quarterly Journal of Mathematics》 CSCD 2002年第1期33-40,共8页
In this paper, weighted L p-boundedness is obtained for a class of multilinear oscillatory singular integrals with Calderón-Zygmund kernel.
关键词 multilinear oscillatory integrals Calderón-Zygmund kernel A p-weight
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Maize kernel weight responses to sowing dateassociated variation in weather conditions 被引量:23
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作者 Baoyuan Zhou Yang Yue +3 位作者 Xuefang Sun Zaisong Ding Wei Ma Ming Zhao 《The Crop Journal》 SCIE CAS CSCD 2017年第1期43-51,共9页
Variation in weather conditions during grain filling has substantial effects on maize kernel weight(KW). The objective of this work was to characterize variation in KW with sowing date-associated weather conditions an... Variation in weather conditions during grain filling has substantial effects on maize kernel weight(KW). The objective of this work was to characterize variation in KW with sowing date-associated weather conditions and examine the relationship between KW, grain filling parameters, and weather factors. Maize was sown on eight sowing dates(SD) at 15–20-day intervals from mid-March to mid-July during 2012 and 2013 in the North China Plain. With sowing date delay, KW increased initially and later declined, and the greatest KW was obtained at SD6 in both years. The increased KW at SD6 was attributed mainly to kernel growth rate(Gmean), and effective grain-filling period(P). Variations in temperature and radiation were the primary factors that influenced KW and grain-filling parameters. When the effective cumulative temperature(AT) and radiation(Ra)during grain filling were 950 °C and 1005.4 MJ m-2, respectively, P and KW were greatest. High temperatures(daily maximum temperature [Tmax] > 30.2 °C) during grain filling under early sowing conditions, or low temperatures(daily minimum temperature [Tmin] < 20.7 °C) under late sowing conditions combined with high diurnal temperature range(Tmax-min> 7.1 °C) decreased kernel growth rate and ultimately final KW. When sowing was performed from May 25 through June 27, higher KW and yield of maize were obtained. We conclude that variations in environmental conditions(temperature and radiation) during grain filling markedly affect growth rate and duration of grain filling and eventually affect kernel weight and yield of maize. 展开更多
关键词 MAIZE Sowing date Weather conditions kernel weight Grain filling
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A Multi-model Approach for Soft Sensor Development Based on Feature Extraction Using Weighted Kernel Fisher Criterion 被引量:7
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作者 吕业 杨慧中 《Chinese Journal of Chemical Engineering》 SCIE EI CAS CSCD 2014年第2期146-152,共7页
Multi-model approach can significantly improve the prediction performance of soft sensors in the process with multiple operational conditions.However,traditional clustering algorithms may result in overlapping phenome... Multi-model approach can significantly improve the prediction performance of soft sensors in the process with multiple operational conditions.However,traditional clustering algorithms may result in overlapping phenomenon in subclasses,so that edge classes and outliers cannot be effectively dealt with and the modeling result is not satisfactory.In order to solve these problems,a new feature extraction method based on weighted kernel Fisher criterion is presented to improve the clustering accuracy,in which feature mapping is adopted to bring the edge classes and outliers closer to other normal subclasses.Furthermore,the classified data are used to develop a multiple model based on support vector machine.The proposed method is applied to a bisphenol A production process for prediction of the quality index.The simulation results demonstrate its ability in improving the data classification and the prediction performance of the soft sensor. 展开更多
关键词 feature extraction weighted kernel Fisher criterion CLASSIFICATION soft sensor
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The Boundedness of Littlewood-Paley Operators with Rough Kernels on Weighted (L^q , L^p )~α (R^n) Spaces 被引量:5
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作者 Ximei Wei Shuangping Tao 《Analysis in Theory and Applications》 2013年第2期135-148,共14页
In this paper, we shall deal with the boundedness of the Littlewood-Paley operators with rough kernel. We prove the boundedness of the Lusin-area integral μΩs and Littlewood-Paley functions μΩ and μλ^* on the w... In this paper, we shall deal with the boundedness of the Littlewood-Paley operators with rough kernel. We prove the boundedness of the Lusin-area integral μΩs and Littlewood-Paley functions μΩ and μλ^* on the weighted amalgam spaces (Lω^q,L^p)^α(R^n)as 1〈q≤α〈p≤∞. 展开更多
关键词 Littlewood-Paley operator weighted amalgam space rough kernel Ap weight.
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Commutators of Weighted Lipschitz Functions and Multilinear Singular Integrals with Non-Smooth Kernels 被引量:3
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作者 LIAN Jia-li MA Bo-lin WU Huo-xiong 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2011年第3期353-367,共15页
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
关键词 COMMUTATOR multilinear singular integral non-smooth kernel weighted Lipschitz function weights.
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Identification of loci and candidate genes controlling kernel weight in barley based on a population for which whole genome assemblies are available for both parents 被引量:2
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作者 Hong Zhou Wei Luo +6 位作者 Shang Gao Jian Ma Meixue Zhou Yuming Wei Youliang Zheng Yaxi Liu Chunji Liu 《The Crop Journal》 SCIE CSCD 2021年第4期854-861,共8页
Kernel weight(KW), together with kernel number per unit area, determines yield of cereal crops. Here,two barley recombinant inbred lines(RILs) populations with a shared parent were used to identify loci controlling KW... Kernel weight(KW), together with kernel number per unit area, determines yield of cereal crops. Here,two barley recombinant inbred lines(RILs) populations with a shared parent were used to identify loci controlling KW. One is Baudin/AWCS276(BA) for which a linkage map was available. Several largeeffect QTL controlling KW were detected in this population. Another is Morex/AWCS276(MA). A linkage map with 5273 makers formed 1454 clusters, was constructed by the genotyping by sequence(GBS) data of 201 RILs from this population. A single marker was selected to represent each of the clusters and the linkage map constructed with these markers covers a total length of 1022.4 c M with an average interval of approximately 0.7 cM between loci. Three of the large-effect loci controlling KW(located on 2 HL, 6 HL,and 7 HL, respectively) identified from the BA population were also detected in the MA population under different environments. The locus on 6 HL was detected in each of the experiments conducted for both populations thus was selected for developing near isogenic lines(NILs). Apart from KW, the two isolines for each pair of the putative NILs obtained showed no significant difference for any of the morphological characteristics assessed. The average difference in KW between the isolines for all the NILs obtained was about 15% based on assessments under both glasshouse and field conditions. Taken advantage that high quality genome assemblies for both Morex and AWCS276 are available, we identified candidate genes underlying two of the three loci based on an orthologous analysis. The NILs developed and the candidate genes identified in this study should facilitate the cloning and functional analysis of genes regulating KW in barley. 展开更多
关键词 BARLEY kernel weight Near isogenic lines AWCS276
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Toeplitz Type Operator Associated to Singular Integral Operator with Variable Kernel on Weighted Morrey Spaces 被引量:1
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作者 Yuexiang He Yueshan Wang 《Analysis in Theory and Applications》 CSCD 2016年第1期90-102,共13页
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
关键词 Toeplitz type operator singular integral operator variable Calderon-Zygmund kernel weighted BMO function weighted Lipschitz function weighted Morrey space.
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Boundedness for the Singular Integral with Variable Kernel and Fractional Differentiation on Weighted Morrey Spaces 被引量:1
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作者 Chao Xue Kai Zhu Yanping Chen 《Analysis in Theory and Applications》 CSCD 2016年第3期205-214,共10页
Let T be the singular integral operator with variable kernel, T* be the adjoint of T and T# be the pseudo-adjoint of T. Let TIT2 be the product of T1 and T2, T1 o T2 be the pseudo product of T1 and T2. In this paper,... Let T be the singular integral operator with variable kernel, T* be the adjoint of T and T# be the pseudo-adjoint of T. Let TIT2 be the product of T1 and T2, T1 o T2 be the pseudo product of T1 and T2. In this paper, we establish the boundedness for commutators of these operators and the fractional differentiation operator D^γ on the weighted Morrey spaces. 展开更多
关键词 Singular integral variable kernel fractional differentiation BMO Sobolev space weighted Morrey spaces
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The Boundedness of the Singular Integral Operator with Variable Calder′on-Zygmund Kernel on Weighted Morrey Spaces 被引量:1
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作者 潘亚丽 李昌文 温宗良 《Chinese Quarterly Journal of Mathematics》 2015年第1期39-46,共8页
In this paper, we will study the boundedness of the singular integral operator with variable Calder′on-Zygmund kernel on the weighted Morrey spaces Lp,κ(ω) for q′≤ p < ∞and 0 < κ < 1. Furthermore, the ... In this paper, we will study the boundedness of the singular integral operator with variable Calder′on-Zygmund kernel on the weighted Morrey spaces Lp,κ(ω) for q′≤ p < ∞and 0 < κ < 1. Furthermore, the boundedness for the commutator with BMO functions is also obtained. 展开更多
关键词 variable Calder′on-Zygmund kernels weighted Morrey spaces BMO
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A Full-Newton Step Feasible Interior-Point Algorithm for the Special Weighted Linear Complementarity Problems Based on a Kernel Function 被引量:2
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作者 GENG Jie ZHANG Mingwang ZHU Dechun 《Wuhan University Journal of Natural Sciences》 CAS CSCD 2024年第1期29-37,共9页
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
关键词 interior-point algorithm weighted linear complementarity problem full-Newton step kernel function iteration complexity
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Effects of Powdery Mildew on 1 000-Kernel Weight, Crude Protein Content and Yield of Winter Wheat in Three Consecutive Growing Seasons 被引量:3
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作者 CAO Xue-ren YAO Dong-ming +4 位作者 DUAN Xia-yu LIU Wei FAN Jie-ru DING Ke-jian ZHOU Yi-lin 《Journal of Integrative Agriculture》 SCIE CAS CSCD 2014年第7期1530-1537,共8页
In order to clarify the impact posed by wheat powdery mildew (Blumeria graminis f. sp. tritici) on the yield and yield components in different epidemic seasons, field trials were conducted in three growing seasons, ... In order to clarify the impact posed by wheat powdery mildew (Blumeria graminis f. sp. tritici) on the yield and yield components in different epidemic seasons, field trials were conducted in three growing seasons, 2009-2010, 2010-2011 and 2011-2012, in Langfang City, Hebei Province, China. The relationships between 1000-kernel weight, crude protein content of grain and yield and disease index (DI), as well as area under disease progress curve (AUDPC) were studied. The models of the percentage of loss of 1000-kernel weight, crude protein content and yield were constructed using DI at critical point (CP) of growth stages (GS) and AUDPC in the three growing seasons, respectively. The CPs for estimating 1 000-kernel weight, crude protein content of grain and yield of wheat caused by powdery mildew were GS 11.1, GS 10.5.3 and GS l 0.5.3, respectively. Models based on DI at CP to estimate the percentage of loss of 1000-kernel weight, crude protein content of grain and yield were better than models based on AUDPC. And models of the percentage of loss of 1000-kernel weight, crude protein content and yield for 2011-2012 season were significant different from these for 2009-2010 and 2010-2011 seasons. These results indicated that besides powdery mildew, weather conditions also had influence on 1 000-kernel weight, crude protein content of grain and yield loss of wheat when powdery mildew occurred. 展开更多
关键词 wheat powdery mildew YIELD 1000-kemel weight crude protein content LOSS
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Some Estimates for Commutators of Fractional Integrals Associated to Operators with Gaussian Kernel Bounds on Weighted Morrey Spaces 被引量:3
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作者 Hua Wang 《Analysis in Theory and Applications》 2013年第1期72-85,共14页
Let L be the infinitesimal generator of an analytic semigroup on L^2 (R^n) with Gaussian kernel bound, and let L^-α/2 be the fractional integrals of L for 0 〈 α 〈 n. In this paper, we will obtain some boundedn... Let L be the infinitesimal generator of an analytic semigroup on L^2 (R^n) with Gaussian kernel bound, and let L^-α/2 be the fractional integrals of L for 0 〈 α 〈 n. In this paper, we will obtain some boundedness properties of commutators [b, L^-α/2] on weighted Morrey spaces L^p,k(w) when the symbol b belongs to BMO(Rn) or the homogeneous Lipschitz space. 展开更多
关键词 Gaussian upper bound fractional integral weighted Morrey space commutator.
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WEIGHTED AVERAGE OF DIRICHLET KERNELS FOR VILENKIN-LIKE SYSTEM 被引量:1
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作者 张传洲 刘培德 《Acta Mathematica Scientia》 SCIE CSCD 2009年第1期45-55,共11页
For Vilenkin-like system, the authors define a new operator H*f := supn |Hnf|, where Hnf is the weighted average for partial sums, and prove that H* is of type (Hp* (Gm), Lp(Gm)) for all 1/2 < p ≤ ∞. As a consequ... For Vilenkin-like system, the authors define a new operator H*f := supn |Hnf|, where Hnf is the weighted average for partial sums, and prove that H* is of type (Hp* (Gm), Lp(Gm)) for all 1/2 < p ≤ ∞. As a consequence, the authors prove the operator S*f := supn |Snf| is of type (p, p) for 1 < p < ∞, where Snf is the n-partial sum. 展开更多
关键词 Martingale Hardy space Vilenkin-like systems weighted average
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Toeplitz Operator Related to Singular Integral with Non-Smooth Kernel on Weighted Morrey Space
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作者 Yuexiang He 《Analysis in Theory and Applications》 CSCD 2017年第3期240-252,共13页
Let T1 be a singular integral with non-smooth kernel or ±I, let T2 and T4 be the linear operators and let T3 = ± I. Denote the Toeplitz type operator by Tb = T1M^b Ia T2 + T3IaMbT4,where M^bf = bf, and Ib i... Let T1 be a singular integral with non-smooth kernel or ±I, let T2 and T4 be the linear operators and let T3 = ± I. Denote the Toeplitz type operator by Tb = T1M^b Ia T2 + T3IaMbT4,where M^bf = bf, and Ib is the fractional integral operator. In this paper, we investigate the boundedness of the operator Tb on the weighted Morrey space when b belongs to the weighted BMO space. 展开更多
关键词 Toeplitz operator non-smooth kernel weighted BMO fractional integral weighted Morrey space.
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Fine mapping and validation of a stable QTL for thousand-kernel weight in wheat(Triticum aestivum L.) 被引量:1
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作者 Deyuan Meng Aamana Batool +18 位作者 Yazhou Xuan Ruiqing Pan Na Zhang Wei Zhang Liya Zhi Xiaoli Ren Wenqing Li Jijie Li Yanxiao Niu Shuzhi Zheng Jun Ji Xiaoli Shi Lei Wang Hongqing Ling Chunhua Zhao Fa Cui Xigang Liu Junming Li Liqiang Song 《The Crop Journal》 SCIE CSCD 2023年第5期1491-1500,共10页
Thousand-kernel weight(TKW)is a measure of grain weight,a target of wheat breeding.The object of this study was to fine-map a stable quantitative trait loci(QTL)for TKW and identify its candidate gene in a recombinant... Thousand-kernel weight(TKW)is a measure of grain weight,a target of wheat breeding.The object of this study was to fine-map a stable quantitative trait loci(QTL)for TKW and identify its candidate gene in a recombinant inbred line(RIL)population derived from the cross of Kenong 9204(KN9204)and Jing411(J411).On a high-density genetic linkage map,24,26 and 25 QTL were associated with TKW,kernel length(KL),and kernel width(KW),respectively.A major and stable QTL,QTkw-2D,was mapped to an8.3 cM interval on chromosome arm 2DL.By saturation of polymorphic markers in its target region,QTkw-2D was confined to a 9.13 Mb physical interval using a secondary mapping population derived from a residually heterozygous line(F6:7).This interval was further narrowed to 2.52 Mb using QTkw-2D near-isogenic lines(NILs).NILs~(KN9204)had higher fresh and dry weights than NILsJ411at various grain-filling stages.The TKW and KW of NILs~(KN9204)were much higher than those of NILsJ411in field trials.By comparison of both DNA sequence and expression between KN9204 and J411,TraesCS2D02G460300.1(TraesKN2D01HG49350)was assigned as a candidate gene for QTkw-2D.This was confirmed by RNA sequencing(RNA-seq)of QTkw-2D NILs.These results provide the basis of map-based cloning of QTkw-2D,and DNA markers linked to the candidate gene may be used in marker-assisted selection. 展开更多
关键词 WHEAT Thousand-kernel weight Fine mapping Candidate gene
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Weighted estimates for strongly singular integral operators with rough kernels
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作者 黄文礼 陶祥兴 李胜宏 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2010年第6期761-768,共8页
The Fourier transform and the Littlewood-Paley theory are used to give the weighted boundedness of a strongly singular integral operator defined in this paper. The paper shows that the strongly singular integral opera... The Fourier transform and the Littlewood-Paley theory are used to give the weighted boundedness of a strongly singular integral operator defined in this paper. The paper shows that the strongly singular integral operator is bounded from the Sobolev space to the Lebesgue space. 展开更多
关键词 strongly singular integral operators rough kernels Ap weights
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