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THE BSE PROPERTY FOR SOME VECTOR-VALUED BANACH FUNCTION ALGEBRAS
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作者 Fatemeh ABTAHI Ali REJALI Farshad SAYAF 《Acta Mathematica Scientia》 SCIE CSCD 2024年第5期1945-1954,共10页
In this paper,X is a locally compact Hausdorff space and A is a Banach algebra.First,we study some basic features of C0(X,A)related to BSE concept,which are gotten from A.In particular,we prove that if C0(X,A)has the ... In this paper,X is a locally compact Hausdorff space and A is a Banach algebra.First,we study some basic features of C0(X,A)related to BSE concept,which are gotten from A.In particular,we prove that if C0(X,A)has the BSE property then A has so.We also establish the converse of this result,whenever X is discrete and A has the BSE-norm property.Furthermore,we prove the same result for the BSE property of type I.Finally,we prove that C0(X,A)has the BSE-norm property if and only if A has so. 展开更多
关键词 BSE algebras BSE-function BSE norm multiplier algebra SEMISIMPLE without order
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REFINEMENTS OF THE NORM OF TWO ORTHOGONAL PROJECTIONS
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作者 Xiaohui LI Meiqi LIU Chunyuan DENG 《Acta Mathematica Scientia》 SCIE CSCD 2024年第4期1229-1243,共15页
In this paper,some refinements of norm equalities and inequalities of combination of two orthogonal projections are established.We use certain norm inequalities for positive contraction operator to establish norm ineq... In this paper,some refinements of norm equalities and inequalities of combination of two orthogonal projections are established.We use certain norm inequalities for positive contraction operator to establish norm inequalities for combination of orthogonal projections on a Hilbert space.Furthermore,we give necessary and sufficient conditions under which the norm of the above combination of o`rthogonal projections attains its optimal value. 展开更多
关键词 NORM orthogonal projection positive operator SPECTRAL block operator valued matrix
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Weighted multilinear p-adic Hardy operators and commutators on p-adic Herz-type spaces
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作者 MA Teng ZHOU Jiang 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2024年第3期554-570,共17页
In this paper,we introduce the weighted multilinear p-adic Hardy operator and weighted multilinear p-adic Ces`aro operator,we also obtain the boundedness of these two operators on the product of p-adic Herz spaces and... In this paper,we introduce the weighted multilinear p-adic Hardy operator and weighted multilinear p-adic Ces`aro operator,we also obtain the boundedness of these two operators on the product of p-adic Herz spaces and p-adic Morrey-Herz spaces,the corresponding operator norms are also established in each case.Moreover,the boundedness of commutators of these two operators with symbols in central bounded mean oscillation spaces and Lipschitz spaces on p-adic Morrey-Herz spaces are also given. 展开更多
关键词 Morrey-Herz spaces weighted multilinear p-adic Hardy operator COMMUTATORS operator norms
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Channel Estimation for Reconfigurable Intelligent Surface Aided Multiuser Millimeter-Wave/THz Systems
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作者 Chu Hongyun Pan Xue Li Baijiang 《China Communications》 SCIE CSCD 2024年第3期91-103,共13页
It is assumed that reconfigurable intelligent surface(RIS)is a key technology to enable the potential of mmWave communications.The passivity of the RIS makes channel estimation difficult because the channel can only b... It is assumed that reconfigurable intelligent surface(RIS)is a key technology to enable the potential of mmWave communications.The passivity of the RIS makes channel estimation difficult because the channel can only be measured at the transceiver and not at the RIS.In this paper,we propose a novel separate channel estimator via exploiting the cascaded sparsity in the continuously valued angular domain of the cascaded channel for the RIS-enabled millimeter-wave/Tera-Hz systems,i.e.,the two-stage estimation method where the cascaded channel is separated into the base station(BS)-RIS and the RIS-user(UE)ones.Specifically,we first reveal the cascaded sparsity,i.e.,the sparsity exists in the hybrid angular domains of BS-RIS and the RIS-UEs separated channels,to construct the specific sparsity structure for RIS enabled multi-user systems.Then,we formulate the channel estimation problem using atomic norm minimization(ANM)to enhance the proposed sparsity structure in the continuous angular domains,where a low-complexity channel estimator via Alternating Direction Method of Multipliers(ADMM)is proposed.Simulation findings demonstrate that the proposed channel estimator outperforms the current state-of-the-arts in terms of performance. 展开更多
关键词 atomic norm minimization cascaded channel estimation convex optimization mmWave/THz reconfigurable intelligent surface(RIS) sparsity
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Parameters Optimization and Performance Evaluation of the Tuned Inerter Damper for the Seismic Protection of Adjacent Building Structures
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作者 Xiaofang Kang Jian Wu +1 位作者 Xinqi Wang Shancheng Lei 《Computer Modeling in Engineering & Sciences》 SCIE EI 2024年第1期551-593,共43页
In order to improve the seismic performance of adjacent buildings,two types of tuned inerter damper(TID)damping systems for adjacent buildings are proposed,which are composed of springs,inerter devices and dampers in ... In order to improve the seismic performance of adjacent buildings,two types of tuned inerter damper(TID)damping systems for adjacent buildings are proposed,which are composed of springs,inerter devices and dampers in serial or in parallel.The dynamic equations of TID adjacent building damping systems were derived,and the H2 norm criterion was used to optimize and adjust them,so that the system had the optimum damping performance under white noise random excitation.Taking TID frequency ratio and damping ratio as optimization parameters,the optimum analytical solutions of the displacement frequency response of the undamped structure under white noise excitation were obtained.The results showed that compared with the classic TMD,TID could obtain a better damping effect in the adjacent buildings.Comparing the TIDs composed of serial or parallel,it was found that the parallel TIDs had more significant advantages in controlling the peak displacement frequency response,while the H2 norm of the displacement frequency response of the damping system under the coupling of serial TID was smaller.Taking the adjacent building composed of two ten-story frame structures as an example,the displacement and energy collection time history analysis of the adjacent building coupled with the optimum design parameter TIDs were carried out.It was found that TID had a better damping effect in the full-time range compared with the classic TMD.This paper also studied the potential power of TID in adjacent buildings,which can be converted into available power resources during earthquakes. 展开更多
关键词 Adjacent buildings tuned inerter damper(TID) H2 norm optimization vibration control energy harvesting
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Promoting sustainable consumption and circular economy:the intention of Vietnamese youth consumers to purchase products made from recycled plastics
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作者 Hong Thi Thu Nguyen 《Chinese Journal of Population,Resources and Environment》 2024年第2期194-203,共10页
Recycling is viewed as a key component in a circular economy and serves as an ideal solution for promoting sustainability.During the global plastic crisis,plastic recycling practices have been adopted worldwide,leadin... Recycling is viewed as a key component in a circular economy and serves as an ideal solution for promoting sustainability.During the global plastic crisis,plastic recycling practices have been adopted worldwide,leading to the production of various products made from recycled plastics(PRP).Nevertheless,a gap persists between consumption and demand for such products,which is primarily attributed to a lack of comprehension from the consumer perspective.Given the pivotal role consumers play in the adoption of these products,this study explores consumers’intentions to purchase PRP.This is particularly significant in Vietnam,which is an emerging economy aspiring to achieve the objectives of a circular economy and sustainable development.Utilizing an integrated cognitive-emotional framework comprising the Valence Theory and the Norm Activation Model,data from 564 Vietnamese students were gathered and analyzed using structural equation modeling.The results show that awareness of consequences is a major driver of consumer purchase intentions,followed by perceived ease of application and monetary incentives.The results also indicate that health concerns have the strongest effect on purchase intention and in the negative side,meaning that the health-related risk is the primary concern for consumers during the decision-making process.This research holds substantial value for academics and managers,as it aids in the theoretical exploration and the formulation of strategies to improve consumer acceptance of PRP. 展开更多
关键词 Recycled plastics Purchase intention Sustainable consumption Circular economy Valence theory Norm activation model
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Coarse-fine joint target parameter estimation method based on AN-RSC in OFDM passive radar
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作者 WANG Chujun WAN Xianrong +1 位作者 YI Jianxin CHENG Feng 《Journal of Systems Engineering and Electronics》 SCIE CSCD 2024年第2期339-349,共11页
In this paper,we study the accuracy of delay-Doppler parameter estimation of targets in a passive radar using orthogonal frequency division multiplexing(OFDM)signal.A coarse-fine joint estimation method is proposed to... In this paper,we study the accuracy of delay-Doppler parameter estimation of targets in a passive radar using orthogonal frequency division multiplexing(OFDM)signal.A coarse-fine joint estimation method is proposed to achieve better estimation accuracy of target parameters without excessive computational burden.Firstly,the modulation symbol domain(MSD)method is used to roughly estimate the delay and Doppler of targets.Then,to obtain high-precision Doppler estimation,the atomic norm(AN)based on the multiple measurement vectors(MMV)model(MMV-AN)is used to manifest the signal sparsity in the continuous Doppler domain.At the same time,a reference signal compensation(RSC)method is presented to obtain highprecision delay estimation.Simulation results based on the OFDM signal show that the coarse-fine joint estimation method based on AN-RSC can obtain a more accurate estimation of target parameters compared with other algorithms.In addition,the proposed method also possesses computational advantages compared with the joint parameter estimation. 展开更多
关键词 passive radar orthogonal frequency division multiplexing(OFDM)signal atomic norm(AN) parameter estimation
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两类加权空间间的积分算子与离散算子的有界性及算子范数估计
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作者 洪勇 赵茜 《Chinese Quarterly Journal of Mathematics》 2024年第1期59-67,共9页
Using the weight coefficient method, we first discuss semi-discrete Hilbert-type inequalities, and then discuss boundedness of integral and discrete operators and operator norm estimates based on Hilbert-type inequali... Using the weight coefficient method, we first discuss semi-discrete Hilbert-type inequalities, and then discuss boundedness of integral and discrete operators and operator norm estimates based on Hilbert-type inequalities in weighted Lebesgue space and weighted normed sequence space. 展开更多
关键词 Weighted Lebesgue space Weighted normed sequence space Semi-discrete Hilbert-type inequalities Integral operator Discrete operator Bounded operator Operator norm
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日本的全球安全发展问题探析
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作者 刘云 田正 《Contemporary International Relations》 2024年第2期56-78,共23页
Against the backdrop of the current international situation,which remains complex and fast-changing, Japan dances to America's tune, attempting to rebuild its industrial power featuring “strategic indispensabili... Against the backdrop of the current international situation,which remains complex and fast-changing, Japan dances to America's tune, attempting to rebuild its industrial power featuring “strategic indispensability,” establish resource power based on the independent and stable supply of strategic materials, and construct normative power to influence or even dominate the international economic order. Such an approach closely echoes the current three strategic preferences of Japan:re-emergence as a global power has been Japan's long-held political aspiration, conservatism defines the country's way of thinking, and liberalization and openness reflect realistic needs. Japan relies excessively on conservative thinking, overemphasizes “small security,” and stresses “strategic autonomy.” However, the greater importance it places on security, the less secure it will become. Similarly, decoupling and supply chain disruption will only retard the development of Japan, pushing the country into the trap of Braess' s Paradox. The rise of the East, the decline of the West, and the advent of the Asian century are historical trends.Japan cannot achieve secure development in isolation from Asia and the East, much less from China. 展开更多
关键词 industrial power JAPAN normative power resource power secure development
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Assessment of Radiological Hazards of Sedimentary, Igneous and Sediments Natural Rocks
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作者 Wafaa Arafa Hala Mahmoud +3 位作者 Eman Yousf Ashry Ashry Ibrahim Elaassy Ahmed Elsersy 《World Journal of Nuclear Science and Technology》 CAS 2024年第2期131-145,共15页
Gamma-ray spectroscopy based on a 100% efficiency hyper-pure germanium detector was used to evaluate the activity concentrations of <sup>226</sup>Ra, <sup>232</sup>Th, and <sup>40</sup... Gamma-ray spectroscopy based on a 100% efficiency hyper-pure germanium detector was used to evaluate the activity concentrations of <sup>226</sup>Ra, <sup>232</sup>Th, and <sup>40</sup>K natural radionuclides in sedimentary, conglomerate, igneous and sedi-ments rock samples collected from four different locations in Eastern desert in Egypt. The obtained activity concentrations are used to evaluate the radi-ological hazards indices, absorbed dose rate, annual effective dose equivalent in air, radium equivalent, external and internal hazard index, radiation level index, annual gonadal dose equivalent, excess lifetime cancer risk and expo-sure rate. The results show that 1) the absorbed dose rate depends on the rock type, 2) the annual effective dose equivalent in air in 71% of sample below 20 mSvy<sup>-1</sup> (permissible limit for workers), 3) the conglomerate rocks show low radioactivity level, 4) sedimentary rocks are rich in radium while igneous rocks are rich in thorium and the sediments rocks are rich in both radium and thorium. 展开更多
关键词 Gamma Spectrometry Radiological Hazard Indices NORM SEDIMENTARY CONGLOMERATE IGNEOUS SEDIMENTS
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Rational Presupposition, Normativity and Pluralist Expression: A Cross-Cultural Perspective on the Universality of Philosophy
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作者 Cheng Lesong 黄德远 《Social Sciences in China》 2022年第1期88-103,共16页
The question of the universality of philosophy is highlighted when seen from a cross-cultural perspective,for it reveals the tension between particularity and universality,as well as the connotations of the universali... The question of the universality of philosophy is highlighted when seen from a cross-cultural perspective,for it reveals the tension between particularity and universality,as well as the connotations of the universality of philosophy.In terms of philosophical activities concerned with the content of Chinese life experience,the universality of philosophy,the particularity of Chinese thought,and the uniqueness of Chinese expression together constitute a persistent theoretical tension.We distinguish the universality of philosophy from universal philosophy;the former stems from the universal presupposition of rational capacity and points to the richness and pluralism of the empirical world while maintaining a dynamic balance between universality and pluralism in normative attitudes of discourse practice and conceptual activity.From the perspective of cultural subjectivity,it is necessary to avoid misleading views that equate the universality of philosophy with Western philosophy;moreover,normativity cannot be understood as specific censorship rules.The universality of philosophy requires a sense of boundaries and a normative attitude that will ensure that people from different contexts can enter into dialogue on the basis of rational ability and construct a space for dialogue and understanding.The concern for diverse objects based on the richness of experience gives philosophical concepts and arguments pluralist differences that encompass cultural differences and autonomy at the level of expression.All in all,it is only on the basis of the universality of philosophy that we can understand the normative requirements of philosophical activities and the pluralism of cross-cultural philosophical reflection. 展开更多
关键词 universality of philosophy universal philosophy presupposition of rational capacity normativity
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Judging the Normativity of PAF Based on TFN and NAN
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作者 LI Zhiqiang BAO Jinsong +1 位作者 LIU Tianyuan WANG Jiacheng 《Journal of Shanghai Jiaotong university(Science)》 EI 2020年第5期569-577,共9页
The normativity of workers'actions during producing has a great impact on the quality of the products and the safety of the operation process.Previous studies mainly focused on the normativity of each single produ... The normativity of workers'actions during producing has a great impact on the quality of the products and the safety of the operation process.Previous studies mainly focused on the normativity of each single producing action instead of considering the normativity of continuous producing actions,which is defined as producing action flow(PAF)in this paper,during operation process.For this issue,a normativity judging method based on two-LSTM fusion network(TFN)and normativity-aware attention network(NAN)is proposed.First,TFN is designed to detect and recognize the producing actions based on skeleton sequences of a worker during complete operation process,and PAF data in sequential form are obtained.Then.NAN is built to allocate difTerent levels of attention to each producing action within the sequence of PAF.and by this means,an efficient normativity judging is conducted.The combustor surface cleaning(CSC)process of rocket engine is taken as the experimental case,and the CSC-Action2D dataset is established for evaluation.Experiment results show the high performance of TFN and NAN.demonstrating the effectiveness of the proposed method for PAF normativity judging. 展开更多
关键词 producing action normativity sequential model attention mechanism deep learning
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Generalized Hopf Bifurcation in a Delay Model of Neutrophil Cells Model
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作者 Suqi Ma S. J. Hogan 《International Journal of Modern Nonlinear Theory and Application》 2024年第2期11-28,共18页
The DDE-Biftool software is applied to solve the dynamical stability and bifurcation problem of the neutrophil cells model. Based on Hopf point finding with the stability property of the equilibrium solution loss, the... The DDE-Biftool software is applied to solve the dynamical stability and bifurcation problem of the neutrophil cells model. Based on Hopf point finding with the stability property of the equilibrium solution loss, the continuation of the bifurcating periodical solution starting from Hopf point is exploited. The generalized Hopf point is tracked by seeking for the critical value of free parameter of the switching phenomena of the open loop, which describes the lineup of bifurcating periodical solutions from Hopf point. The normal form near the generalized Hopf point is computed by Lyapunov-Schimdt reduction scheme combined with the center manifold analytical technique. The near dynamics is classified by geometrically different topological phase portraits. 展开更多
关键词 Generalized Hopf Bifurcation DDE-Biftool Software Norm Form
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Image Dehazing with Hybrid λ2-λ0 Penalty Mode
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作者 Yuxuan Zhou Dongjiang Ji Chunyu Xu 《Journal of Computer and Communications》 2024年第10期132-152,共21页
Due to the presence of turbid media, such as microdust and water vapor in the environment, outdoor pictures taken under hazy weather circumstances are typically degraded. To enhance the quality of such images, this wo... Due to the presence of turbid media, such as microdust and water vapor in the environment, outdoor pictures taken under hazy weather circumstances are typically degraded. To enhance the quality of such images, this work proposes a new hybrid λ2-λ0 penalty model for image dehazing. This model performs a weighted fusion of two distinct transmission maps, generated by imposing λ2 and λ0 norm penalties on the approximate regression coefficients of the transmission map. This approach effectively balances the sparsity and smoothness associated with the λ0 and λ2 norms, thereby optimizing the transmittance map. Specifically, when the λ2 norm is penalized in the model, an updated guided image is obtained after implementing λ0 penalty. The resulting optimization problem is effectively solved using the least square method and the alternating direction algorithm. The dehazing framework combines the advantages of λ2 and λ0 norms, enhancing sparse and smoothness, resulting in higher quality images with clearer details and preserved edges. 展开更多
关键词 Atmospheric Scattering Model Guided Filter with 2 Norm 0 Gradient Minimization Single Image Dehazing Transmission Map Ridge Regression
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The Barrier of the Child and Parent Expected Models for Entering the School System-A Secondary Publication
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作者 Xavier Conus 《Journal of Contemporary Educational Research》 2024年第2期243-255,共13页
The recognition of the positive value of student diversity and their right to full participation are key aspects of inclusion as a means of managing heterogeneity of the school population from an equality perspective.... The recognition of the positive value of student diversity and their right to full participation are key aspects of inclusion as a means of managing heterogeneity of the school population from an equality perspective.As the school cannot welcome the diversity of children without including their families,the same logic needs to apply to the relationship between the school and parents,particularly in the current environment where the school-family partnership appears as a privileged institutional leverage in the fight against inequalities at school.Based on an ethnographical study exploring how the relationship between the school and the families builds up in a Swiss school located in a context of strong cultural diversity,this paper interrogates how the school norm can be the main limitation to the inclusion of students and parents who are unfamiliar with the school.Derived from field observations and interviews,our results show how the teachers tend to approach their relationship with new students and their parents from the standpoint of narrowly defined expected models,leading them to engage in a vain attempt to conform the students and parents when they deviate from these models.The possibility of entering the school system for students and parents unfamiliar with school is hindered by the exclusive and excluding normativity on which the models of the child and the parent expected by the teachers are grounded.Based on these observations,we discuss how an inclusive approach seems to us to require in the first place a necessary process of decentering from the school and teachers,as a condition for recognition of the actual child and parent. 展开更多
关键词 Educational inclusion and exclusion Family and education Norms and regulations Primary and elementary education Switzerland
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Hierarchical Media Ethics in the Digital Age: An Analysis of the “Primary School Student Lost Homework in Paris” Incident
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作者 ZHAO Yifei 《Journalism and Mass Communication》 2024年第3期205-208,共4页
In the digital age,traditional media ethics norms lack sufficient explanatory power and binding force in practice.This paper uses the“Primary School Student Lost Homework in Paris”incident as a case study to explore... In the digital age,traditional media ethics norms lack sufficient explanatory power and binding force in practice.This paper uses the“Primary School Student Lost Homework in Paris”incident as a case study to explore the ethical controversies surrounding the dissemination of this event.By adopting a hierarchical media ethics perspective,the paper dynamically examines the ethical conduct of various communicators,elucidates the ethical responsibilities of each party involved,and reveals the complexity of communication ethics in the digital age. 展开更多
关键词 media ethics information dissemination self-media ethics norms “Primary School Student Lost Homework in Paris”
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BANACH SPACES AND INEQUALITIES ASSOCIATED WITH NEW GENERALIZATION OF CESàRO MATRIX 被引量:1
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作者 Feyzi BASAR Hadi ROOPAEI 《Acta Mathematica Scientia》 SCIE CSCD 2023年第4期1518-1536,共19页
Let the triangle matrix A^(ru)be a generalization of the Cesàro matrix and U∈{c_(0),c,l_(∞)}.In this study,we essentially deal with the space U(A^(ru))defined by the domain of A^(ru)in the space U and give the ... Let the triangle matrix A^(ru)be a generalization of the Cesàro matrix and U∈{c_(0),c,l_(∞)}.In this study,we essentially deal with the space U(A^(ru))defined by the domain of A^(ru)in the space U and give the bases,and determine the Kothe-Toeplitz,generalized K?theToeplitz and bounded-duals of the space U(A^(ru)).We characterize the classes(l_(∞)(A^(ru)):l_(∞)),(l_(∞)(A^(ru)):c),(c(A^(ru)):c),and(U:V(A^(ru)))of infinite matrices,where V denotes any given sequence space.Additionally,we also present a Steinhaus type theorem.As an another result of this study,we investigate the l_(p)-norm of the matrix A^(ru)and as a result obtaining a generalized version of Hardy's inequality,and some inclusion relations.Moreover,we compute the norm of well-known operators on the matrix domain l_(p)(A^(ru)). 展开更多
关键词 matrix domain normed sequence space duals and matrix transformations
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长三角医疗卫生领域行政规范性文件协作备案机制的构建 被引量:1
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作者 李幸祥 《中国卫生资源》 CSCD 北大核心 2023年第2期150-156,共7页
长三角医疗卫生领域行政规范性文件的协作制定,对于推动实现医疗卫生领域的一体化具有重要的现实意义。与之伴随的突出问题是,对此类跨行政区划协作制定的行政规范性文件如何进行备案审查。建议将长三角相关省市政府或卫生健康部门拟制... 长三角医疗卫生领域行政规范性文件的协作制定,对于推动实现医疗卫生领域的一体化具有重要的现实意义。与之伴随的突出问题是,对此类跨行政区划协作制定的行政规范性文件如何进行备案审查。建议将长三角相关省市政府或卫生健康部门拟制为行政联合体,将相关省市的备案机关拟制为备案联合体,由行政联合体向备案联合体报送备案。受委托的备案机关代表备案联合体对文件的制定主体、程序、内容进行审查后,由相关省市的备案机关联合出具备案审查意见。 展开更多
关键词 长三角Yangtze River Delta 医疗卫生health care 行政规范性文件administrative normative document 协作备案cooperative filing
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Application and comparison of kernel functions for linear parameter varying model approximation of nonlinear systems
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作者 Faisal Saleem Ahsan Ali +1 位作者 Inam-ul-hassan Shaikh Muhammad Wasim 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2023年第1期58-77,共20页
In this paper,a comparative study for kernel-PCA based linear parameter varying(LPV)model approximation of sufficiently nonlinear and reasonably practical systems is carried out.Linear matrix inequalities(LMIs)to be s... In this paper,a comparative study for kernel-PCA based linear parameter varying(LPV)model approximation of sufficiently nonlinear and reasonably practical systems is carried out.Linear matrix inequalities(LMIs)to be solved in LPV controller design process increase exponentially with the increase in a number of scheduling variables.Fifteen kernel functions are used to obtain the approximate LPV model of highly coupled nonlinear systems.An error to norm ratio of original and approximate LPV models is introduced as a measure of accuracy of the approximate LPV model.Simulation examples conclude the effectiveness of kernel-PCA for LPV model approximation as with the identification of accurate approximate LPV model,computation complexity involved in LPV controller design is decreased exponentially. 展开更多
关键词 kernel-PCA LMIS LPV error to norm ratio computational complexity and control design
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ISOMETRY AND PHASE-ISOMETRY OF NON-ARCHIMEDEAN NORMED SPACES
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作者 王瑞东 姚文婷 《Acta Mathematica Scientia》 SCIE CSCD 2023年第6期2377-2386,共10页
In this paper,we study isometries and phase-isometries of non-Archimedean normed spaces.We show that every isometry f:Sr(X)→Sr(X),where X is a finite-dimensional non-Archimedean normed space and Sr(X)is a sphere with... In this paper,we study isometries and phase-isometries of non-Archimedean normed spaces.We show that every isometry f:Sr(X)→Sr(X),where X is a finite-dimensional non-Archimedean normed space and Sr(X)is a sphere with radius r∈||X||,is surjective if and only if is spherically complete and k is finite.Moreover,we prove that if X and Y are non-Archimedean normed spaces over non-trivially non-Archimedean valued fields with|2|=1,any phase-isometry f:X→Y is phase equivalent to an isometric operator. 展开更多
关键词 non-Archimedean normed spaces isometry extension Wigner's theorem
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