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On Reproducing Kernel Banach Spaces:Generic Definitions and Unified Framework of Constructions

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Acta Mathematica Sinica,English Series 2022年第8期38卷 1459-1483页

作者： rong rong LIN Hai Zhang ZHANG Jun ZHANG School of Mathematics and Statistics Guangdong University of TechnologyGuangzhou 510520P.R.China School of Mathematics(Zhuhai) and Guangdong Province Key Laboratory of Computational ScienceSun Yat-sen UniversityZhuhai 519082P.R.China Department of Psychology and Department of Statistics University of MichiganAnn ArborMI48109USA

Recently,there has been emerging interest in constructing reproducing kernel Banach spaces(RKBS)for applied and theoretical purposes such as machine learning,sampling reconstruction,sparse approximation and functional *** constructions include the reflexive RKBS via a bilinear form,the semi-inner-product RKBS,the RKBS with?~1 norm,the p-norm RKBS via generalized Mercer kernels,*** definitions of RKBS and the associated reproducing kernel in those references are dependent on the ***,relations among those constructions are *** explore a generic definition of RKBS and the reproducing kernel for RKBS that is independent of ***,we propose a framework of constructing RKBSs that leads to new RKBSs based on Orlicz spaces and unifies existing constructions mentioned above via a continuous bilinear form and a pair of feature ***,we develop representer theorems for machine learning in RKBSs constructed in our framework,which also unifies representer theorems in existing RKBSs.

关键词： Reproducing kernel Banach spaces feature maps reproducing kernels machine learning the representer theorem

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Zero-Hopf bifurcation for an infection-age structured epidemic model with a nonlinear incidence rate

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Science China Mathematics 2017年第8期60卷 1371-1398页

作者： LIU ZhiHua YUAN rong School of Mathematical Sciences Beijing Normal University

An infection-age structured epidemic model with a nonlinear incidence rate is *** formulate the model as an abstract non-densely defined Cauchy problem and derive the condition which guarantees the existence and uniqueness for positive age-dependent equilibrium of the *** analyzing the associated characteristic transcendental equation and applying the normal form theory presented recently for non-densely defined semilinear equations,we show that the SIR(susceptible-infected-recovered)epidemic model undergoes Zero-Hopf bifurcation at the positive equilibrium which is the main result of this paper.

关键词： infection-age structured epidemic non-densely defined stability normal form zero-Hopf bifurcation

The role of initial signals in the tropical Pacific Ocean in predictions of negative Indian Ocean Dipole events

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Science China Earth Sciences 2018年第12期61卷 1832-1843页

作者： rong FENG Wansuo DUAN LASG Institute of Atmospheric PhysicsChinese Academy of SciencesBeijing 100029China University of Chinese Academy of Sciences Beijing 100049China

Using reanalysis data, the role of initial signals in the tropical Pacific Ocean in predictions of negative Indian Ocean Dipole(IOD) events were analyzed. It was found that the summer predictability barrier(SPB) phenomenon exists in predictions,which is closely related to initial sea temperature errors in the tropical Pacific Ocean, with type-1 initial errors presenting a significant west-east dipole pattern in the tropical Pacific Ocean, and type-2 initial errors showing the opposite spatial pattern. In contrast, SPB-related initial sea temperature errors in the tropical Indian Ocean are relatively small. The initial errors in the tropical Pacific Ocean induce anomalous winds in the tropical Indian Ocean by modulating the Walker circulation in the tropical oceans. In the first half of the prediction year, the anomalous winds, combined with the climatological winds in the tropical Indian Ocean, induce a basin-wide mode of sea surface temperature(SST) errors in the tropical Indian Ocean. With the reversal of the climatological wind in the second half of the prediction year, a west-east dipole pattern of SSTerrors appears in the tropical Indian Ocean, which is further strengthened under the Bjerknes feedback, yielding a significant SPB. Moreover, two types of precursors were also identified: a significant west-east dipole pattern in the tropical Pacific Ocean and relatively small temperature anomalies in the tropical Indian Ocean. Under the combined effects of temperature anomalies in the tropical Indian and Pacific oceans, northwest wind anomalies appear in the tropical Indian Ocean, which induce a significant west-east dipole pattern of SST anomalies, and yield a negative IOD event.

关键词： Negative Indian Ocean Dipole Precursor Initial errors Pacific Ocean

Examining the efficacy of revegetation practices in ecosystem restoration programs:insights from a hotspot of sandstorm in northern China

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Frontiers of Earth Science 2021年第4期15卷 922-935页

作者： Ziqiang DU rong rong Zhitao WU Hong ZHANG Institute of Loess Plateau Shanxi UniversityTaiyuan 030006China 2 Shanxi Key Laboratory for Ecological restoration of Loess Plateau Taiyuan 030006China Field Scientific Observation and Research Station of the Ministry of Education of Shanxi Subalpine Grassland Ecosystem Taiyuan 030006China College of Environmental&Resource Sciences Shanxi UniversityTaiyuan 030006China

Retrospectively evaluating the efficacy of revegetation practices is helpful in planning and imple-menting future ecosystem restoration programs(ERP).Having a good understanding of how human activities can affect vegetation cover,both before and after ERP,is particularly important in sandstorm hotspot *** Beijing-Tianjin Sandstorm Source Region(BTSSR)is one such *** conducted an investigation into vegetation dynamics within the *** was done using remote sensing data in conjunction with climate data sets and land use data spanning the 1982-2014 *** relationships between climatic factors(such as precipitation and temperature),and vegetative change were modeled using a neural network *** a process of residual analysis,the proportions of human-induced vegetative change both before and after the ERP were *** results show that:1)before the ERP(1982-2000),40.96%of the study area exhibited significantly progressive vegetation changes(p<0.05).This proportion decreased to encom-pass only 20.23%of the study area in the period following the ERP(2001-2014).2)89.55%of the study area showed signs of human-induced vegetation degradation before the *** 2001 and 2014 however,following ERP,this figure fell to only 27.78%.3)ERP implementation led to visible improvements in vegetative conditions within the BTSSR,especially in areas where ecological restoration measures were directly and anthropogenically *** results highlight the benefits that positive human action(i.e.,revegetation initiatives implemented under the framework of an ERP)have brought to the BTSSR.

关键词： vegetation dynamics human activities ERP neural network model Beijing-Tianjin sandstorm source region

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Science China Earth Sciences 2017年第1期60卷 156-172页

作者： FENG rong DUAN WanSuo State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics (LASG) Institute of Atmospheric Physics Chinese Academy of Sciences Beijing 100029 China

This study explored the spatial patterns of winter predictability barrier(WPB)-related optimal initial errors and optimal precursors for positive Indian Ocean dipole(IOD)events,and the associated physical mechanisms for their developments were analyzed using the Simple Ocean Data Assimilation *** consideration of the effects of model errors on"predictions,"it was assumed that different"predictions"are caused by different initial *** two types of WPB-related optimal initial errors are almost opposite for the start months of July(-1)and July(0),although they both present a west-east dipole pattern in the tropical Indian Ocean,with the maximum errors located at the thermocline *** feedback and ocean waves play important roles in the growth of prediction *** two physical mechanisms compete during July-December and ocean waves dominate during *** spatial patterns of optimal precursors and the physical mechanisms for their developments are similar to those of WPB-related optimal initial *** is worth noting that large values of WPB-related optimal initial errors and optimal precursors are concentrated within a few locations,which probably represent the sensitive areas of targeted observations for positive IOD *** great similarities between WPB-related optimal initial errors and optimal precursors suggest that were intensive observations performed over these areas,this would not only reduce initial errors and thus,prediction errors,but it would also permit the detection of the signal of IOD events in advance,greatly improving the forecast skill of positive IOD events.

关键词： Optimal precursors Initial errors Winter predictability barrier Indian Ocean dipole

UPPER BOUND FOR FINITE-TIME RUIN PROBABILITY IN A MARKOV-MODULATED MARKET

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Journal of Systems Science & Complexity 2011年第2期24卷 308-316页

作者： Jinzhu LI rong WU School of Mathematical Sciences and LPMC Nankai University Tianjin 300071 China.

This paper studies the upper bound for finite-time ruin probability of an insurance company which invests its wealth in a stock and a bond. The authors assume that the interest rate of the bond and the volatility of the stock are modulated by a continuous-time stationary Markov chain with finite state. By a pure probabilistic method, the upper bound for the finite-time ruin probability is obtained.

关键词： Finite-time ruin probability jump-diffusion model Markov-modulated process.

Universal FRFT-based algorithm for parameter estimation of chirp signals

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Journal of Systems Engineering and Electronics 2012年第4期23卷 495-501页

作者： rong Chen Yiming Wang School of Electronics and Information Engineering Soochow UniversitySuzhou 215006P.R.China National Laboratory of Information Control Technology for Communication System Jiaxing 314001P.R.China

The realization of the parameter estimation of chirp signals using the fractional Fourier transform （FRFT） is based on the assumption that the sampling duration of practical observed signals would be equal to the time duration of chirp signals contained in the former. However, in many actual circumstances, this assumption seems unreasonable. On the basis of analyzing the practical signal form, this paper derives the estimation error of the existing parameter estimation method and then proposes a novel and universal parameter estimation algorithm. Furthermore, the proposed algorithm is developed which allows the estimation of the practical observed Gaussian windowed chirp signal. Simulation results show that the new algorithm works well.

关键词： fractional Fourier transform (FRFT) chirp signal,parameter estimation observation window.

Image feature optimization based on nonlinear dimensionality reduction

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Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2009年第12期10卷 1720-1737页

作者： rong ZHU Min YAO School of Computer Science and Technology Zhejiang University Hangzhou 310027 China School of lnformation Engineering Jiaxing University Jiaxing 314001 China State Key Laboratory for Novel Software Technology Nanjing University Nanjing 210093 China

Image feature optimization is an important means to deal with high-dimensional image data in image semantic understanding and its applications. We formulate image feature optimization as the establishment of a mapping between highand low-dimensional space via a five-tuple model. Nonlinear dimensionality reduction based on manifold learning provides a feasible way for solving such a problem. We propose a novel globular neighborhood based locally linear embedding (GNLLE) algorithm using neighborhood update and an incremental neighbor search scheme, which not only can handle sparse datasets but also has strong anti-noise capability and good topological stability. Given that the distance measure adopted in nonlinear dimensionality reduction is usually based on pairwise similarity calculation, we also present a globular neighborhood and path clustering based locally linear embedding (GNPCLLE) algorithm based on path-based clustering. Due to its full consideration of correlations between image data, GNPCLLE can eliminate the distortion of the overall topological structure within the dataset on the manifold. Experimental results on two image sets show the effectiveness and efficiency of the proposed algorithms.

关键词： Image feature optimization Nonlinear dimensionality reduction Manifold learning Locally linear embedding (LLE)

Nonlinear free vibration of reticulated shallow spherical shells taking into account transverse shear deformation

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Applied Mathematics and Mechanics(English Edition) 2018年第12期39卷 1825-1836页

作者： rong WANG Guohua NIE School of Aerospace Engineering and Applied Mechanics Tongji University

This paper deals with nonlinear free vibration of reticulated shallow spherical shells taking into account the effect of transverse shear deformation. The shell is formed by beam members placed in two orthogonal directions. The nondimensional fundamental governing equations in terms of the deflection, rotational angle, and force function are presented, and the solution for the nonlinear free frequency is derived by using the asymptotic iteration method. The asymptotic solution can be used readily to perform the parameter analysis of such space structures with numerous geometrical and material parameters. Numerical examples are given to illustrate the characteristic amplitudefrequency relation and softening and hardening nonlinear behaviors as well as the effect of transverse shear on the linear and nonlinear frequencies of reticulated shells and plates.

关键词： nonlinear free vibration reticulated shallow spherical shell transverse shear effect asymptotical iteration method amplitude-frequency relation