检索结果-南通市图书馆

Sharp bilinear decomposition for products of both anisotropic Hardy spaces and their dual spaces with its applications to endpoint boundedness of commutators

维普期刊数据库评论

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Science China mathematics 2024年第9期67卷 2091-2152页

作者： Jun Liu Dachun Yang Mingdong Zhang School of mathematics China University of Mining and TechnologyXuzhou 221116China laboratory of mathematics and Complex Systems(Ministry of Education of China) School of Mathematical SciencesBeijing Normal UniversityBeijing 100875China

Let a:=(a_(1),...,a_(n))2[1,∞)^(n),p∈(0,1),andα:=1/*** any x∈R^(n)and t∈[0,∞),letΦ_(p)(x,t):={t/1+(t[x]_(a)^(ν))^(1-p)if να■N,t/1+(t[x]_(a)^(ν))^(1-p)[log(e+|x|a)]^(p)if να∈N,let where [·]a:=1+|·|a,|·|a denotes the anisotropic quasi-homogeneous norm with respect to a,and ν:=a_(1)+…+a_(n).Let H_(a)^(p)(R^(n)),L_(a)^(a)(R^(n)),and H_(a)^(Φ_(p))(R^(n))be,respectively,the anisotropic Hardy space,the anisotropic Campanato space,and the anisotropic Musielak-Orlicz Hardy space associated with Φ_(p) on R^(n).In this article,via first establishing the wavelet characterization of anisotropic Campanato spaces,we prove that for any f∈H_(a)^(p)(R^(n))and g∈L_(a)^(a)(R^(n)),the product of f and g can be decomposed into S(f,g)+T(f,g) in the sense of tempered distributions,where S is a bilinear operator bounded from H_(a)^(p)(R^(n))*L_(a)^(a)(R^(Φ_(p))) to L^(1)(R^(n)) and T is a bilinear operator bounded from H_(a)^(p)(R^(n))*L_(a)^(a)(R^(n)) to H_(a)^(Φ_(p))(R^(n)) .Moreover,this bilinear decomposition is sharp in the dual sense that any y■H_(a)^(Φ_(p))(R^(n)) that fits into the above bilinear decomposition should satisfy(L^(1)(R^(n))+y)*=(L^(1)(R^(n)+H_(a)^(Φ_(p))(R^(n))*.As applications,for any non-constant b∈L_(a)^(a)(R^(n)) and any sublinear operator T satisfying some mild bounded assumptions,we find the largest subspace of H_(a)^(p)(R^(n)),denoted by H_(a,b)^(p)(R^(n)),such that the commutator [b,T] is bounded from H_(a,b)^(p)(R^(n))to L^(1)(R^(n)).In addition,when T is an anisotropic CalderónZygmund operator,the boundedness of [b,T] from H_(a,b)^(p)(R^(n))to L^(1)(R^(n))(or to H_(a)^(1)(R^(n)) is also *** key of their proofs is the wavelet characterization of function spaces under consideration.

关键词： anisotropic Euclidean space bilinear decomposition Hardy space Campanato space Musielak-Orlicz Hardy space commutator wavelet

Fourier Transform of Anisotropic Hardy Spaces Associated with Ball Quasi-Banach Function Spaces and its applications to Hardy-Littlewood Inequalities

在线全文

学校读者我要写书评

暂无评论

Acta Mathematicae Applicatae Sinica 2024年

作者： Chao-an LI Xian-jie YAN Da-chun YANG laboratory of mathematics and Complex Systems (Ministry of Education of China) School of Mathematical Sciences Beijing Normal University Institute of Contemporary mathematics School of Mathematics and Statistics Henan University

Let A be a general expansive matrix and X be a ball quasi-Banach function space on ■~n, whose certain power（namely its convexification） supports a Fefferman-Stein vector-valued maximal inequality and the associate space of whose other power supports the boundedness of the powered Hardy-Littlewood maximal *** HXA（■~n） be the anisotropic Hardy space associated with A and *** authors first prove that the Fourier transform of f ∈ HXA（■~n） coincides with a continuous function F on ■~n in the sense of tempered ***,the authors obtain a pointwise inequality that the function F is less than the product of the anisotropic Hardy space norm of f and a step function with respect to the transpose matrix of the expansive matrix *** this,the authors further induce a higher order convergence for the function F at the origin and give a variant of the Hardy-Littlewood inequality in HXA（■~n）.All these results have a wide range of ***,the authors apply these results,respectively,to classical（variable and mixed-norm）Lebesgue spaces,Lorentz spaces,Orlicz spaces,Orlicz-slice spaces,and local generalized Herz spaces and,even on the last four function spaces,the obtained results are completely new.

关键词：

Polarization engineering in porous organic polymers for charge separation efficiency and its applications in photocatalytic aerobic oxidations

在线全文

同方期刊数据库

学校读者我要写书评

暂无评论

Science China Chemistry 2024年第3期67卷 1000-1007页

作者： Kun Wu Pei-Wen Cheng Xin-Yi Liu Ji Zheng Xiao-Wei Zhu Mo Xie Puxin Weng Weigang Lu Dan Li College of Chemistry and Materials Science Guangdong Provincial Key Laboratory of Functional Supramolecular Coordination Materials and ApplicationsJinan UniversityGuangzhou 510632China Guangdong Rare Earth Photofunctional Materials Engineering Technology Research Center School of Chemistry and EnvironmentJiaying UniversityMeizhou 514015China

Photocatalytic aerobic oxidation reactions are largely governed by the efficiency of charge separation and subsequent reactive oxygen species(ROS) generation. Herein, we report a polarization engineering strategy to promote the charge separation and ROS generation efficiency by substituting the benzene unit with furan/thiophene in porous organic polymers(POPs). Benefiting from the extent of local polarization, the thiophene-containing POP(JNU-218) exhibits the best photocatalytic performance in aerobic oxidation reactions, with a yield much higher than those for the furan-containing POP(JNU-217) and the benzenecontaining POP(JNU-216). Experimental studies and theoretical calculations reveal that the increase of local polarization can indeed reduce the exciton binding energy, and therefore facilitate the separation of electron-hole pairs. This work demonstrates a viable strategy to tune charge separation and ROS generation efficiency by modulating the dipole moments of the building blocks in porous polymeric organic semiconductors.

关键词： porous organic polymer local polarization photocatalytic aerobic oxidation charge separation reactive oxygen species exciton binding energy

CNF Characterization of Sets over Z~n and its applications in Cryptography

在线全文

学校读者我要写书评

暂无评论

Journal of Systems Science & Complexity 2024年

作者： HU Xiaobo XU Shengyuan TU Yinzi FENG Xiutao ZHANG Weihan Beijing Smartchip Microelectronics Technology Company Limited Key laboratory of mathematics Mechanization Academy of Mathematics and Systems Science Chinese Academy of Sciences University of Chinese Academy of Sciences Winchester College

In recent years, automatic search has been widely used to search differential characteristics and linear approximations with high probability/correlation in symmetric-key cryptanalyses. Among these methods, the automatic search with the Boolean satisfiability problem（SAT, in short） gradually becomes a powerful cryptanalysis tool. A key problem in the SAT-based automatic search method is how to fully characterize a set S ? {0, 1}~n with as few Conjunctive normal form（CNF, in short）clauses as possible, which is called a full CNF characterization（FCC, in short） problem. In this work,the authors establish a complete theory to solve a best solution of an FCC problem. Specifically, the authors start from plain sets, which can be characterized by exactly one clause. By exploring mergeable sets, the authors give a sufficient and necessary condition for characterizing a plain set. Based on the properties of plain sets, the authors further provide an algorithm of solving an FCC problem for a given set S, which can generate all the minimal plain closures of S and produce a best FCC theoretically. As application, the authors apply the proposed algorithm to many common S-boxes used in block ciphers to characterize their differential distribution tables and linear approximation tables and get their FCCs,all of which are the best-known results at present.

关键词：

On Multi-Granulation Rough Sets with its applications

在线全文

同方期刊数据库

学校读者我要写书评

暂无评论

Computers, Materials & Continua 2024年第4期79卷 1025-1038页

作者： Radwan Abu-Gdairi R.Mareay M.Badr Department of mathematics Faculty of ScienceZarqa UniversityZarqa13132Jordan Department of mathematics Faculty of ScienceKafrelsheikh UniversityKafrelsheikh33516Egypt Department of mathematics Faculty of ScienceNew Valley UniversityEl Kharga72713Egypt

Recently,much interest has been given tomulti-granulation rough sets (MGRS), and various types ofMGRSmodelshave been developed from different viewpoints. In this paper, we introduce two techniques for the classificationof MGRS. Firstly, we generate multi-topologies from multi-relations defined in the universe. Hence, a novelapproximation space is established by leveraging the underlying topological structure. The characteristics of thenewly proposed approximation space are *** introduce an algorithmfor the reduction ***, a new approach for the classification ofMGRS based on neighborhood concepts is introduced. Finally, areal-life application from medical records is introduced via our approach to the classification of MGRS.

关键词： Multi-granulation rough sets data classifications information systems interior operators closure operators approximation structures

Self-Triggered Set Stabilization of Boolean Control Networks and its applications

维普期刊数据库评论

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

IEEE/CAA Journal of Automatica Sinica 2024年第7期11卷 1631-1642页

作者： Rong Zhao Jun-e Feng Dawei Zhang the School of mathematics Shandong UniversityShandong UniversityJinan 250100China

Set stabilization is one of the essential problems in engineering systems, and self-triggered control(STC) can save the storage space for interactive information, and can be successfully applied in networked control systems with limited communication resources. In this study, the set stabilization problem and STC design of Boolean control networks are investigated via the semi-tensor product technique. On the one hand, the largest control invariant subset is calculated in terms of the strongly connected components of the state transition graph, by which a graph-theoretical condition for set stabilization is derived. On the other hand, a characteristic function is exploited to determine the triggering mechanism and feasible controls. Based on this, the minimum-time and minimum-triggering open-loop, state-feedback and output-feedback STCs for set stabilization are designed,respectively. As classic applications of self-triggered set stabilization, self-triggered synchronization, self-triggered output tracking and self-triggered output regulation are discussed as well. Additionally, several practical examples are given to illustrate the effectiveness of theoretical results.

关键词： Boolean control networks(BCNs) output regulation self-triggered control semi-tensor product of matrices set stabilization synchronization

Mechanical behavior of nanorubber reinforced epoxy over a wide strain rate loading

在线全文

学校读者我要写书评

暂无评论

Nano Materials Science 2024年第1期6卷 106-114页

作者： Yinggang Miao Jianping Yin Wenxuan Du Lianyang Chen Joint International Research laboratory of Impact Dynamics and its Engineering applications School of AeronauticsNorthwestern Polytechnical UniversityXi'anShaanxi710072China State Key laboratory for Strength and Vibration of Mechanical Structures Xi'an Jiaotong UniversityXi'anShaanxi710049China Shaanxi Key laboratory of Impact Dynamics and its Engineering Application School of AeronauticsNorthwestern Polytechnical UniversityXi'anShaanxi710072China

Nanorubber/epoxy composites containing 0,2,6 and 10 wt%nanorubber are subjected to uniaxial compression over a wide range of strain rate from 8×10^(-4) s^(-1) to~2×10^(4) s^(-1).Unexpectedly,their strain rate sensitivity and strain hardening index increase with increasing nanorubber *** mechanisms are proposed based on numerical simulations using a unit cell *** increase in the strain rate sensitivity with increasing nanorubber content results from the fact that the nanorubber becomes less incompressible at high strain,generating a higher hydro-static *** shear localization starts to occur in the epoxy under a strain rate of 22,000 s^(-1) when the strain exceeds *** presence of nanorubber in the epoxy reduces adiabatic shear localization by preventing it from propagating.

关键词： Strain rate Strain hardening Nano rubber Epoxy Adiabatic shearing localization

Noise Effect on the 2D Stochastic Burgers Equation

在线全文

学校读者我要写书评

暂无评论

Acta Mathematica Sinica,English Series 2024年第9期40卷 2065-2090页

作者： Zhao DONG Jiang Lun WU Guo Li ZHOU RCSDS Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190P.R.China Beijing Normal University-Hong Kong Baptist University United International College Zhuhai 519087P.R.China Guangdong Provincial Key laboratory of Interdisciplinary Research and Application for Data Science(IRADS) UICZhuhai 519087P.R.China School of Statistics and mathematics Chongqing University Key laboratory of Nonlinear Analysis and its applications(Chongqing University) Ministry of EducationChongqing 400044P.R.China

By comprehensive utilizing of the geometry structure of 2D Burgers equation and the stochastic noise,we find the decay properties of the solution to the stochastic 2D Burgers equation with Dirichlet boundary ***,the e... 详细信息

关键词： 2D stochastic Burgers equation regularity

A generalization of Banach's lemma and its applications to perturbations of bounded linear operators

在线全文

学校读者我要写书评

暂无评论

Applied mathematics(A Journal of Chinese Universities) 2024年第2期39卷 363-369页

作者： WANG Zi DING Jiu WANG Yu-wen School of mathematics Sciences Harbin Normal UniversityHarbin 150025China School of mathematics and Natural Sciences The University of Southern MississippiHattiesburg MS 39406-5043USA Academic Committee Harbin Institute of PetroleumHarbin 150027China

Let X be a Banach space and let P:X→X be a bounded linear *** an algebraic inequality on the spectrum of P,we give a new sufficient condition that guarantees the existence of(I-P)^(-1) as a bounded linear operator on X,and a bound on its spectral radius is also *** generalizes the classic Banach *** apply the result to the perturbation analysis of general bounded linear operators on X with commutative perturbations.

关键词： Banach lemma spectral radius generalized inverse perturbation analysis