Pub Date : 2024-02-01DOI: 10.1051/wujns/2024291001
Jizhen Zhou, Hejie Sun
In this paper, [see formula in PDF] acts as an interpolating sequence for [see formula in PDF]. An analytic function f is constructed, and [see formula in PDF] for any [see formula in PDF], where f and [see formula in PDF] belong to [see formula in PDF]. As a result, the study achieves a comparable outcome for [see formula in PDF].
在本文中，[见 PDF 中的公式] 充当[见 PDF 中的公式]的插值序列。本文构造了一个解析函数 f，并对任意 [见 PDF 中的公式] 提出了 [见 PDF 中的公式]，其中 f 和 [见 PDF 中的公式] 都属于 [见 PDF 中的公式]。因此，该研究对[见 PDF 中的公式]取得了类似的结果。
{"title":"A Note of the Interpolating Sequence in Qp∩H∞","authors":"Jizhen Zhou, Hejie Sun","doi":"10.1051/wujns/2024291001","DOIUrl":"https://doi.org/10.1051/wujns/2024291001","url":null,"abstract":"In this paper, [see formula in PDF] acts as an interpolating sequence for [see formula in PDF]. An analytic function f is constructed, and [see formula in PDF] for any [see formula in PDF], where f and [see formula in PDF] belong to [see formula in PDF]. As a result, the study achieves a comparable outcome for [see formula in PDF].","PeriodicalId":23976,"journal":{"name":"Wuhan University Journal of Natural Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140465046","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-02-01DOI: 10.1051/wujns/2024291051
Yongwei Zhang
Label correlations are an essential technique for data mining that solves the possible correlation problem between different labels in multi-label classification. Although this technique is widely used in multi-label classification problems, batch learning deals with most issues, which consumes a lot of time and space resources. Unlike traditional batch learning methods, online learning represents a promising family of efficient and scalable machine learning algorithms for large-scale datasets. However, existing online learning research has done little to consider correlations between labels. On the basis of existing research, this paper proposes a multi-label online learning algorithm based on label correlations by maximizing the interval between related labels and unrelated labels in multi-label samples. We evaluate the performance of the proposed algorithm on several public datasets. Experiments show the effectiveness of our algorithm.
{"title":"Learning Label Correlations for Multi-Label Online Passive Aggressive Classification Algorithm","authors":"Yongwei Zhang","doi":"10.1051/wujns/2024291051","DOIUrl":"https://doi.org/10.1051/wujns/2024291051","url":null,"abstract":"Label correlations are an essential technique for data mining that solves the possible correlation problem between different labels in multi-label classification. Although this technique is widely used in multi-label classification problems, batch learning deals with most issues, which consumes a lot of time and space resources. Unlike traditional batch learning methods, online learning represents a promising family of efficient and scalable machine learning algorithms for large-scale datasets. However, existing online learning research has done little to consider correlations between labels. On the basis of existing research, this paper proposes a multi-label online learning algorithm based on label correlations by maximizing the interval between related labels and unrelated labels in multi-label samples. We evaluate the performance of the proposed algorithm on several public datasets. Experiments show the effectiveness of our algorithm.","PeriodicalId":23976,"journal":{"name":"Wuhan University Journal of Natural Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140465866","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-01DOI: 10.1051/wujns/2023285373
Yingzhen XUE
In this paper, a class of slow reaction-diffusion equations with nonlocal source and inner absorption terms are studied. By using the technique of improved differential inequality, the lower bounds of blow up time for the system under either homogeneous Dirichlet or nonhomogeneous Neumann boundary conditions are obtained.
{"title":"Lower Bounds of Blow Up Time for a Class of Slow Reaction Diffusion Equations with Inner Absorption Terms","authors":"Yingzhen XUE","doi":"10.1051/wujns/2023285373","DOIUrl":"https://doi.org/10.1051/wujns/2023285373","url":null,"abstract":"In this paper, a class of slow reaction-diffusion equations with nonlocal source and inner absorption terms are studied. By using the technique of improved differential inequality, the lower bounds of blow up time for the system under either homogeneous Dirichlet or nonhomogeneous Neumann boundary conditions are obtained.","PeriodicalId":23976,"journal":{"name":"Wuhan University Journal of Natural Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136206444","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-01DOI: 10.1051/wujns/2023285369
Shuangnian HU, Shihan WANG, Yanyan LI, Yujun NIU
Let [see formula in PDF] be the finite field, [see formula in PDF], with [see formula in PDF] being a prime and [see formula in PDF] being a positive integer. Let [see formula in PDF] be the multiplicative group of [see formula in PDF], that is [see formula in PDF]. In this paper, by using the Jacobi sums and an analog of Hasse-Davenport theorem, an explicit formula for the number of solutions of cubic diagonal equation [see formula in PDF] over [see formula in PDF] is given, where [see formula in PDF] and [see formula in PDF]. This extends earlier results.
{"title":"Note on the Number of Solutions of Cubic Diagonal Equations over Finite Fields","authors":"Shuangnian HU, Shihan WANG, Yanyan LI, Yujun NIU","doi":"10.1051/wujns/2023285369","DOIUrl":"https://doi.org/10.1051/wujns/2023285369","url":null,"abstract":"Let [see formula in PDF] be the finite field, [see formula in PDF], with [see formula in PDF] being a prime and [see formula in PDF] being a positive integer. Let [see formula in PDF] be the multiplicative group of [see formula in PDF], that is [see formula in PDF]. In this paper, by using the Jacobi sums and an analog of Hasse-Davenport theorem, an explicit formula for the number of solutions of cubic diagonal equation [see formula in PDF] over [see formula in PDF] is given, where [see formula in PDF] and [see formula in PDF]. This extends earlier results.","PeriodicalId":23976,"journal":{"name":"Wuhan University Journal of Natural Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136206457","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-01DOI: 10.1051/wujns/2023285411
Jiamin SHI, Zhongshu LU, Luyi ZHANG, Sunjia LU, Yao CHENG
This paper concerns a discontinuous Galerkin (DG) method for a one-dimensional singularly perturbed problem which possesses essential characteristic of second order convection-diffusion problem after some simple transformations. We derive an optimal convergence of the DG method for eight layer-adapted meshes in a general framework. The convergence rate is valid independent of the small parameter. Furthermore, we establish a sharper L 2 -error estimate if the true solution has a special regular component. Numerical experiments are also given.
{"title":"Uniform Convergence Analysis of the Discontinuous Galerkin Method on Layer-Adapted Meshes for Singularly Perturbed Problem","authors":"Jiamin SHI, Zhongshu LU, Luyi ZHANG, Sunjia LU, Yao CHENG","doi":"10.1051/wujns/2023285411","DOIUrl":"https://doi.org/10.1051/wujns/2023285411","url":null,"abstract":"This paper concerns a discontinuous Galerkin (DG) method for a one-dimensional singularly perturbed problem which possesses essential characteristic of second order convection-diffusion problem after some simple transformations. We derive an optimal convergence of the DG method for eight layer-adapted meshes in a general framework. The convergence rate is valid independent of the small parameter. Furthermore, we establish a sharper L 2 -error estimate if the true solution has a special regular component. Numerical experiments are also given.","PeriodicalId":23976,"journal":{"name":"Wuhan University Journal of Natural Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136206461","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-01DOI: 10.1051/wujns/2023285379
Fangjuan ZHANG, Xinhong ZHU
Let [see formula in PDF] be a unital *-algebra with the unit [see formula in PDF] and a nontrivial projection [see formula in PDF]. Suppose that [see formula in PDF] satisfies [see formula in PDF] implies [see formula in PDF] and [see formula in PDF] implies [see formula in PDF] In this paper, we prove that [see formula in PDF] is a nonlinear [see formula in PDF] type derivation on [see formula in PDF] if and only if [see formula in PDF] is an additive *-derivation. This is then applied to prime *-algebra, von Neumann algebras with no central summands of type [see formula in PDF] factor von Neumann algebras and standard operator algebras.
{"title":"Nonlinear <i>A*B+B*A</i> Type Derivations on *-Algebras","authors":"Fangjuan ZHANG, Xinhong ZHU","doi":"10.1051/wujns/2023285379","DOIUrl":"https://doi.org/10.1051/wujns/2023285379","url":null,"abstract":"Let [see formula in PDF] be a unital *-algebra with the unit [see formula in PDF] and a nontrivial projection [see formula in PDF]. Suppose that [see formula in PDF] satisfies [see formula in PDF] implies [see formula in PDF] and [see formula in PDF] implies [see formula in PDF] In this paper, we prove that [see formula in PDF] is a nonlinear [see formula in PDF] type derivation on [see formula in PDF] if and only if [see formula in PDF] is an additive *-derivation. This is then applied to prime *-algebra, von Neumann algebras with no central summands of type [see formula in PDF] factor von Neumann algebras and standard operator algebras.","PeriodicalId":23976,"journal":{"name":"Wuhan University Journal of Natural Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136206448","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-01DOI: 10.1051/wujns/2023285421
Fang WANG, Jiangang ZHANG
Response and bifurcation of fractional Duffing oscillator under recycling noise and time-delayed feedback control are investigated. Firstly, based on the principle of the minimum mean square error and small time-delayed approximation and linearize the cubic stiffness term, the fractional derivative is equivalent to a linear combination of damping and restoring forces, and the original system is simplified into an equivalent integer order system. Secondly, the Itô differential equations and one-dimensional Markov process are obtained according to stochastic averaging method, and the stochastic stability and stochastic bifurcation of the system are analyzed. Lastly, through joint probability density function diagram and the stationary probability density function diagram, the stochastic bifurcation behavior of system under the different time-delay, fractional order and noise intensity are discussed respectively, the validity of the theory and the occurrence of bifurcation phenomenon are verified.
{"title":"Response and Bifurcation of Fractional Duffing Oscillator under Combined Recycling Noise and Time-Delayed Feedback Control","authors":"Fang WANG, Jiangang ZHANG","doi":"10.1051/wujns/2023285421","DOIUrl":"https://doi.org/10.1051/wujns/2023285421","url":null,"abstract":"Response and bifurcation of fractional Duffing oscillator under recycling noise and time-delayed feedback control are investigated. Firstly, based on the principle of the minimum mean square error and small time-delayed approximation and linearize the cubic stiffness term, the fractional derivative is equivalent to a linear combination of damping and restoring forces, and the original system is simplified into an equivalent integer order system. Secondly, the Itô differential equations and one-dimensional Markov process are obtained according to stochastic averaging method, and the stochastic stability and stochastic bifurcation of the system are analyzed. Lastly, through joint probability density function diagram and the stationary probability density function diagram, the stochastic bifurcation behavior of system under the different time-delay, fractional order and noise intensity are discussed respectively, the validity of the theory and the occurrence of bifurcation phenomenon are verified.","PeriodicalId":23976,"journal":{"name":"Wuhan University Journal of Natural Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136206442","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-01DOI: 10.1051/wujns/2023285433
Jian GUAN, Geng LIN, Huibin FENG, Zhiqiang RUAN
The double row layout problem (DRLP) is to assign facilities on two rows in parallel so that the total cost of material handling among facilities is minimized. Since it is vital to save cost and enhance productivity, the DRLP plays an important role in many application fields. Nevertheless, it is very hard to handle the DRLP because of its complex model. In this paper, we consider a new simplified model for the DRLP (SM-DRLP) and provide a mixed integer programming (MIP) formulation for it. The continuous decision variables of the DRLP are divided into two parts: start points of double rows and adjustable clearances between adjacent facilities. The former one is considered in the new simplified model for the DRLP with the purpose of maintaining solution quality, while the latter one is not taken into account with the purpose of reducing computational time. To evaluate its performance, our SM-DRLP is compared with the model of a general DRLP and the model of another simplified DRLP. The experimental results show the efficiency of our proposed model.
{"title":"A Mixed-Integer Programming Formulation for a Simplified Model of the Double Row Layout Problem","authors":"Jian GUAN, Geng LIN, Huibin FENG, Zhiqiang RUAN","doi":"10.1051/wujns/2023285433","DOIUrl":"https://doi.org/10.1051/wujns/2023285433","url":null,"abstract":"The double row layout problem (DRLP) is to assign facilities on two rows in parallel so that the total cost of material handling among facilities is minimized. Since it is vital to save cost and enhance productivity, the DRLP plays an important role in many application fields. Nevertheless, it is very hard to handle the DRLP because of its complex model. In this paper, we consider a new simplified model for the DRLP (SM-DRLP) and provide a mixed integer programming (MIP) formulation for it. The continuous decision variables of the DRLP are divided into two parts: start points of double rows and adjustable clearances between adjacent facilities. The former one is considered in the new simplified model for the DRLP with the purpose of maintaining solution quality, while the latter one is not taken into account with the purpose of reducing computational time. To evaluate its performance, our SM-DRLP is compared with the model of a general DRLP and the model of another simplified DRLP. The experimental results show the efficiency of our proposed model.","PeriodicalId":23976,"journal":{"name":"Wuhan University Journal of Natural Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136203902","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-01DOI: 10.1051/wujns/2023285392
Chenhui SUN, Ning WANG, Xiaohong CAO
In this paper, a-Browder's theorem and a-Weyl's theorem for bounded linear operators are studied by means of the property of the topological uniform descent. The sufficient and necessary conditions for a bounded linear operator defined on a Hilbert space holding a-Browder's theorem and a-Weyl's theorem are established. As a consequence of the main result, the new judgements of a-Browder's theorem and a-Weyl's theorem for operator function are discussed.
{"title":"Topological Uniform Descent and Judgement of A-Weyl's Theorem","authors":"Chenhui SUN, Ning WANG, Xiaohong CAO","doi":"10.1051/wujns/2023285392","DOIUrl":"https://doi.org/10.1051/wujns/2023285392","url":null,"abstract":"In this paper, a-Browder's theorem and a-Weyl's theorem for bounded linear operators are studied by means of the property of the topological uniform descent. The sufficient and necessary conditions for a bounded linear operator defined on a Hilbert space holding a-Browder's theorem and a-Weyl's theorem are established. As a consequence of the main result, the new judgements of a-Browder's theorem and a-Weyl's theorem for operator function are discussed.","PeriodicalId":23976,"journal":{"name":"Wuhan University Journal of Natural Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136203903","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-01DOI: 10.1051/wujns/2023285399
Xuejing MENG, Linfeng LYU
In this paper, our main aim is to investigate the strong convergence rate of the truncated Euler-Maruyama approximations for stochastic differential equations with superlinearly growing drift coefficients. When the diffusion coefficient is polynomially growing or linearly growing, the strong convergence rate of arbitrarily close to one half is established at a single time T or over a time interval [0, T ], respectively. In both situations, the common one-sided Lipschitz and polynomial growth conditions for the drift coefficients are not required. Two examples are provided to illustrate the theory.
{"title":"Convergence Rates for the Truncated Euler-Maruyama Method for Nonlinear Stochastic Differential Equations","authors":"Xuejing MENG, Linfeng LYU","doi":"10.1051/wujns/2023285399","DOIUrl":"https://doi.org/10.1051/wujns/2023285399","url":null,"abstract":"In this paper, our main aim is to investigate the strong convergence rate of the truncated Euler-Maruyama approximations for stochastic differential equations with superlinearly growing drift coefficients. When the diffusion coefficient is polynomially growing or linearly growing, the strong convergence rate of arbitrarily close to one half is established at a single time T or over a time interval [0, T ], respectively. In both situations, the common one-sided Lipschitz and polynomial growth conditions for the drift coefficients are not required. Two examples are provided to illustrate the theory.","PeriodicalId":23976,"journal":{"name":"Wuhan University Journal of Natural Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136203905","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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