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Existence of Optical Vortex Solitons in Pair Plasmas

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Acta Mathematicae Applicatae Sinica 2023年第3期39卷 571-582页

作者： Rui-feng ZHANG school of mathematics and Statistics Henan UniversityKaifeng 475004China

Optical vortices arise as phase dislocations of light fields and they are of importance in modern optical *** this study,we employ the calculus of variations method to develop an existence theory for the steady state vortex solutions of a nonlinear Schr?dinger type equation to model light waves that propagate in a medium with a new focusing-defocusing ***,we demonstrate the existence of positive radially symmetric solutions by constrained minimization,where we give some interesting explicit estimates related to vortex winding numbers and the wave propagation ***,we establish the existence of saddle-point solutions through a mountain-pass argument.

关键词： Calculus of variations mountain-pass theorem pair plasmas nonlinear Schr?dinger type equation optical vortices

Semiparametric Analysis of Longitudinal Data with Informative Observation Times

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Acta Mathematicae Applicatae Sinica 2011年第1期27卷 29-42页

作者： Liu-quan Sun Xiao-yun Mu Zhi-hua Sun Xing-wei Tong Academy of mathematics and Systems science Chinese Academy of Sciences Beijing 100190 China school of mathematical sciences Beijing Normal University Beijing 100875 China

In many longitudinal studies, observation times as well as censoring times may be correlated with longitudinal responses. This paper considers a multiplicative random effects model for the longitudinal response where these correlations may exist and a joint modeling approach is proposed via a shared latent variable. For inference about regression parameters, estimating equation approaches are developed and asymptotic properties of the proposed estimators are established. The finite sample behavior of the methods is examined through simulation studies and an application to a data set from a bladder cancer study is provided for illustration.

关键词： Estimating equations Informative observation times Joint modeling Latent variables,Longitudinal data

Chung’s functional law of the iterated logarithm for the Brownian sheet

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Frontiers of mathematics in China 2022年第6期17卷 1015-1024页

作者： Yonghong LIU Ting ZHANG Yiheng TANG Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation School of Mathematics and Computing ScienceGuilin University of Electronic TechnologyGuilin541004China

In this paper,we investigate functional limit problem for path of a Brownian sheet,Chung’s functional law of the iterated logarithm for a Brownian sheet is *** main tool in the proof is large deviation and small devi... 详细信息

关键词： Brownian sheet Chung’s functional law of the iterated logarithm

Forecasting Container Throughput of Qingdao Port with a Hybrid Model

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Journal of Systems science & Complexity 2015年第1期28卷 105-121页

作者： HUANG Anqiang LAI Kinkeung LI Yinhua WANG Shouyang school of Economy and Management Beihang University Department of Management sciences City University of Hong Kong Research Center on Fictitious Economy and Data science Chinese Academy of Sciences Academy of mathematics and Systems science Chinese Academy of Sciences

This paper proposes a hybrid forecasting method to forecast container throughput of Qingdao *** eliminate the influence of outliers,local outlier factor(lof) is extended to detect outliers in time series,and then different dummy variables are constructed to capture the effect of outliers based on domain ***,a hybrid forecasting model combining projection pursuit regression(PPR) and genetic programming(GP) algorithm is ***,the hybrid model is applied to forecasting container throughput of Qingdao Port and the results show that the proposed method significantly outperforms ANN,SARIMA,and PPR models.

关键词： Container throughput forecast genetic programming algorithm outlier processing projection pursuit regression.

Neural dynamics for improving optimiser in deep learning with noise considered

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CAAI Transactions on Intelligence Technology 2024年第3期9卷 722-737页

作者： Dan Su Predrag S.Stanimirović Ling Bo Han Long Jin school of Information science and Engineering Lanzhou UniversityLanzhouChina Faculty of sciences and mathematics University of NišNišSerbia school of Electronics and Information Engineering Guangdong Ocean UniversityZhanjiangChina

As deep learning evolves,neural network structures become increasingly sophisticated,bringing a series of new optimisation *** example,deep neural networks(DNNs)are vulnerable to a variety of *** neural networks under privacy constraints is a method to alleviate privacy leakage,and one way to do this is to add noise to the ***,the existing optimisers suffer from weak convergence in the presence of increased noise during training,which leads to a low robustness of the *** stabilise and improve the convergence of DNNs,the authors propose a neural dynamics(ND)optimiser,which is inspired by the zeroing neural dynamics originated from zeroing neural *** authors first analyse the relationship be-tween DNNs and control ***,the authors construct the ND optimiser to update network ***,the proposed ND optimiser alleviates the non-convergence problem that may be suffered by adding noise to the gradient from different ***,experiments are conducted on different neural network structures,including ResNet18,ResNet34,Inception-v3,MobileNet,and long and short-term memory *** results using CIFAR,YouTube Faces,and R8 datasets demonstrate that the ND optimiser improves the accuracy and stability of DNNs under noise-free and noise-polluted *** source code is publicly available at https://***/LongJin-lab/ND.

关键词： deep learning deep neural networks

Where is the future of China's biogas? Review, forecast,and policy implications

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Petroleum science 2016年第3期13卷 604-624页

作者： Lei Gu Yi-Xin Zhang Jian-Zhou Wang Gina Chen Hugh Battye College of Earth and Environmental sciences Lanzhou University school of mathematics and Statistics Lanzhou University school of Statistics Dongbei University of Finance and Economics school of Law Northwestern University school of History and Culture Lanzhou University Department of Economics The London School of Economics and Political Science

This paper discusses the history and present status of different categories of biogas production in China,most of which are classified into rural household production,agriculture-based engineering production,and industry-based engineering *** evaluate the future biogas production of China,five models including the Hubbert model,the Weibull model,the generalized Weng model,the H-C-Z model,and the Grey model are applied to analyze and forecast the biogas production of each province and the entire *** is proved that those models which originated from oil research can also be applied to other energy *** simulation results reveal that China＇s total biogas production is unlikely to keep on a fast-growing trend in the next few years,mainly due to a recent decrease in rural household production,and this greatly differs from the previous goal set by the official *** addition,China＇s biogas production will present a more uneven pattern among regions in the *** paper will give preliminary explanation for the regional difference of the three biogas sectors and propose some recommendations for instituting corresponding policies and strategies to promote the development of the biogas industry in China.

关键词： Biogas production China Temporal–spatial Forecast Policy

Bounds of the Estrada index of graphs

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Applied mathematics(A Journal of Chinese Universities) 2010年第3期25卷 325-330页

作者： LIU Jian-ping LIU Bo-lian College of mathematics and Computer science Fuzhou University Fujian 350108 China school of Mathematical sciences South China Normal University Cuangzhou 510631 China

Let G be a graph of order n and let λ1, λ2,...,λn be its eigenvalues. The Estrada index[2] of G is defined as EE = EE（G） =∑i=1^n e^λ*** this paper, new bounds for EE are established, as well as some relations b... 详细信息

关键词： Graph spectrum Estrada index bound energy (of graph).

Unified convergence analysis of a second-order method of multipliers for nonlinear conic programming

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science China mathematics 2022年第11期65卷 2397-2422页

作者： Liang Chen Junyuan Zhu Xinyuan Zhao school of mathematics Hunan UniversityChangsha 410082China Hunan Provincial Key Laboratory of Intelligent Information Processing and Applied mathematics Changsha 410082China school of mathematics Beijing University of TechnologyBeijing 100124China

In this paper,we accomplish the unified convergence analysis of a second-order method of multipliers(i.e.,a second-order augmented Lagrangian method)for solving the conventional nonlinear conic optimization ***,the algorithm that we investigate incorporates a specially designed nonsmooth(generalized)Newton step to furnish a second-order update rule for the *** first show in a unified fashion that under a few abstract assumptions,the proposed method is locally convergent and possesses a(nonasymptotic)superlinear convergence rate,even though the penalty parameter is fixed and/or the strict complementarity ***,we demonstrate that for the three typical scenarios,i.e.,the classic nonlinear programming,the nonlinear second-order cone programming and the nonlinear semidefinite programming,these abstract assumptions are nothing but exactly the implications of the iconic sufficient conditions that are assumed for establishing the Q-linear convergence rates of the method of multipliers without assuming the strict complementarity.

关键词： second-order method of multipliers augmented Lagrangian method convergence rate generalized Newton method second-order cone programming semidefinite programming

The best approximation theorems and variational inequalities for discontinuous mappings in Banach spaces

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science China mathematics 2015年第12期58卷 2581-2592页

作者： LIU LiShan KONG DeZhou WU YongHong school of Mathematical sciences Qufu Normal University Department of mathematics and Statistics Curtin University of Technology College of Information science and Engineering Shandong Agricultural University

We discuss Ky Fan's theorem and the variational inequality problem for discontinuous mappings f in a Banach space X. The main tools of analysis are the variational characterizations of the metric projection operator and the order-theoretic fixed point theory. Moreover, we derive some properties of the metric projection operator in Banach spaces. As applications of our best approximation theorems, three fixed point theorems for non-self maps are established and proved under some conditions. Our results are generalizations and improvements of various recent results obtained by many authors.

关键词： best approximation theorem variational inequality discontinuous map Ky Fan’s theorem fixed point Banach spaces