Pub Date : 2022-01-01DOI: 10.23952/jnva.6.2022.1.08
Xiangling Zhu
. In this paper, we characterize the q -Carleson measure for Dirichlet type spaces D p α on the unit ball when 0 < p < q < ∞ and α > − 1 by using Carleson blocks and Carleson tubes.
． 本文利用Carleson块和Carleson管刻画了单位球上Dirichlet型空间D p α当0 < p < q <∞和α > - 1时的q -Carleson测度。
{"title":"A note on the Carleson measure for Dirichlet type spaces on the unit ball of $C^n$","authors":"Xiangling Zhu","doi":"10.23952/jnva.6.2022.1.08","DOIUrl":"https://doi.org/10.23952/jnva.6.2022.1.08","url":null,"abstract":". In this paper, we characterize the q -Carleson measure for Dirichlet type spaces D p α on the unit ball when 0 < p < q < ∞ and α > − 1 by using Carleson blocks and Carleson tubes.","PeriodicalId":48488,"journal":{"name":"Journal of Nonlinear and Variational Analysis","volume":"80 4 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77404395","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 10.23952/jnva.6.2022.1.02
Xiang Zhu, Zhiling Cai, Y. Ziniu, Junliang Wu, William Zhu
. As one of the mainstream clustering methods, the spectral clustering has aroused more and more attention recently because of its good performance, especially in nonlinear data sets. However, traditional spectral clustering models have high computational complexity. Meanwhile, most of these models fail in distinguishing the noisy and useful features in practice, which leads to the limitation of clustering performance. In this paper, we propose a new fast spectral clustering with self-weighted features (FSCSWF) to achieve good clustering performance through learning and assigning optimal weights for features in a low computational complexity. Specifically, the FSCSWF selects anchors from original samples, then learns the weights of features and the similarity between anchors and samples interactively in a local structure learning framework. This interactive learning makes the learnt similarity can better measure the relationship between anchors, and samples due to the optimal weights make the data points become more discriminative. Moreover, the connectivity constraint are embedded to make sure that the connected components of bipartite graph constructed by the learnt similarity can indicate clusters di-rectly. In this way, the FSCSWF can achieve good clustering performance and has a low computational complexity, which is linear to the number of samples. Extensive experiments on synthetic and practical data sets illustrate the effectiveness and efficiency of the FSCSWF with respect to state-of-the-art methods.
{"title":"Fast spectral clustering with self-weighted features","authors":"Xiang Zhu, Zhiling Cai, Y. Ziniu, Junliang Wu, William Zhu","doi":"10.23952/jnva.6.2022.1.02","DOIUrl":"https://doi.org/10.23952/jnva.6.2022.1.02","url":null,"abstract":". As one of the mainstream clustering methods, the spectral clustering has aroused more and more attention recently because of its good performance, especially in nonlinear data sets. However, traditional spectral clustering models have high computational complexity. Meanwhile, most of these models fail in distinguishing the noisy and useful features in practice, which leads to the limitation of clustering performance. In this paper, we propose a new fast spectral clustering with self-weighted features (FSCSWF) to achieve good clustering performance through learning and assigning optimal weights for features in a low computational complexity. Specifically, the FSCSWF selects anchors from original samples, then learns the weights of features and the similarity between anchors and samples interactively in a local structure learning framework. This interactive learning makes the learnt similarity can better measure the relationship between anchors, and samples due to the optimal weights make the data points become more discriminative. Moreover, the connectivity constraint are embedded to make sure that the connected components of bipartite graph constructed by the learnt similarity can indicate clusters di-rectly. In this way, the FSCSWF can achieve good clustering performance and has a low computational complexity, which is linear to the number of samples. Extensive experiments on synthetic and practical data sets illustrate the effectiveness and efficiency of the FSCSWF with respect to state-of-the-art methods.","PeriodicalId":48488,"journal":{"name":"Journal of Nonlinear and Variational Analysis","volume":"48 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82616710","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 10.23952/jnva.6.2022.3.06
{"title":"On metrizable vector spaces with the Lebesgue property","authors":"","doi":"10.23952/jnva.6.2022.3.06","DOIUrl":"https://doi.org/10.23952/jnva.6.2022.3.06","url":null,"abstract":"","PeriodicalId":48488,"journal":{"name":"Journal of Nonlinear and Variational Analysis","volume":"12 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75637726","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 10.23952/jnva.6.2022.6.01
{"title":"A special issue on the theory and numerical methods for vector optimization problems with respect to variable domination structures","authors":"","doi":"10.23952/jnva.6.2022.6.01","DOIUrl":"https://doi.org/10.23952/jnva.6.2022.6.01","url":null,"abstract":"","PeriodicalId":48488,"journal":{"name":"Journal of Nonlinear and Variational Analysis","volume":"16 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73010829","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 10.23952/jnva.6.2022.4.01
H. Srivastava, R. Chandel, H. Kumar
. In this paper, we introduce and investigate various properties and relations involving some general families of double and multiple Hurwitz-Lerch type zeta functions which are associated with the Srivastava-Daoust class of hypergeometric functions in two and more variables. Relevant connections with other (known or new) results for functions of the analytic number theory are also considered.
{"title":"Some general Hurwitz-Lerch type Zeta functions associated with the Srivastava-Daoust multiple hypergeometric functions","authors":"H. Srivastava, R. Chandel, H. Kumar","doi":"10.23952/jnva.6.2022.4.01","DOIUrl":"https://doi.org/10.23952/jnva.6.2022.4.01","url":null,"abstract":". In this paper, we introduce and investigate various properties and relations involving some general families of double and multiple Hurwitz-Lerch type zeta functions which are associated with the Srivastava-Daoust class of hypergeometric functions in two and more variables. Relevant connections with other (known or new) results for functions of the analytic number theory are also considered.","PeriodicalId":48488,"journal":{"name":"Journal of Nonlinear and Variational Analysis","volume":"148 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75064082","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 10.23952/jnva.6.2022.5.08
Jun Chen, Zhenhai Liu, F. Lomovtsev, V. Obukhovskii
. The goal of this paper is to study optimal feedback control for a class of non-autonomous second-order evolution inclusions with Clarke’s subdifferential in a separable reflexive Banach space. We only assume that the second order evolution operator involved satisfies the strong continuity condition instead of the compactness, which was used in previous literature. By using the properties of multimaps and Clarke’s subdifferential, we assume some sufficient conditions to ensure the existence of feasible pairs of the feedback control systems. Furthermore, we also prove the existence of optimal control pairs
{"title":"Optimal feedback control for a class of second-order evolution differential inclusions with Clarke’s subdifferential","authors":"Jun Chen, Zhenhai Liu, F. Lomovtsev, V. Obukhovskii","doi":"10.23952/jnva.6.2022.5.08","DOIUrl":"https://doi.org/10.23952/jnva.6.2022.5.08","url":null,"abstract":". The goal of this paper is to study optimal feedback control for a class of non-autonomous second-order evolution inclusions with Clarke’s subdifferential in a separable reflexive Banach space. We only assume that the second order evolution operator involved satisfies the strong continuity condition instead of the compactness, which was used in previous literature. By using the properties of multimaps and Clarke’s subdifferential, we assume some sufficient conditions to ensure the existence of feasible pairs of the feedback control systems. Furthermore, we also prove the existence of optimal control pairs","PeriodicalId":48488,"journal":{"name":"Journal of Nonlinear and Variational Analysis","volume":"31 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73861673","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 10.23952/jnva.6.2022.3.04
{"title":"A new tensor projection method for tensor variational inequalities","authors":"","doi":"10.23952/jnva.6.2022.3.04","DOIUrl":"https://doi.org/10.23952/jnva.6.2022.3.04","url":null,"abstract":"","PeriodicalId":48488,"journal":{"name":"Journal of Nonlinear and Variational Analysis","volume":"34 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87148744","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 10.23952/jnva.6.2022.6.09
{"title":"A first bibliography on set and vector optimization problems with respect to variable domination structures","authors":"","doi":"10.23952/jnva.6.2022.6.09","DOIUrl":"https://doi.org/10.23952/jnva.6.2022.6.09","url":null,"abstract":"","PeriodicalId":48488,"journal":{"name":"Journal of Nonlinear and Variational Analysis","volume":"41 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74399519","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 10.23952/jnva.6.2022.4.03
{"title":"Approximation of solutions of the split minimization problem with multiple output sets and common fixed point problems in real Banach spaces","authors":"","doi":"10.23952/jnva.6.2022.4.03","DOIUrl":"https://doi.org/10.23952/jnva.6.2022.4.03","url":null,"abstract":"","PeriodicalId":48488,"journal":{"name":"Journal of Nonlinear and Variational Analysis","volume":"78 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90490688","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01DOI: 10.23952/jnva.6.2022.6.04
{"title":"Optimal payoffs for directionally closed acceptance sets","authors":"","doi":"10.23952/jnva.6.2022.6.04","DOIUrl":"https://doi.org/10.23952/jnva.6.2022.6.04","url":null,"abstract":"","PeriodicalId":48488,"journal":{"name":"Journal of Nonlinear and Variational Analysis","volume":"123 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86236444","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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