检索结果-南通市图书馆

GLOBAL WEAK SOLUTIONS OF COMPRESSIBLE NAVIER-STOKES-LANDAU-LIFSHITZ-MAXWELL EQUATIONS FOR QUANTUM FLUIDS IN DIMENSION THREE

在线全文

学校读者我要写书评

暂无评论

Acta Mathematica Scientia 2023年第1期43卷 25-42页

作者：酒全森马琳 School of Mathematical Sciences Capital Normal UniversityBeijing100048China

In this paper,we consider the weak solutions of compressible Navier-StokesLandau-Lifshitz-Maxwell(CNSLLM)system for quantum fluids with a linear density dependent viscosity in a 3D *** introducing the cold pressure Pc,we prove the global existence of weak solutions with the pressure P+Pc,where P=Aργwithγ≥*** main result extends the one in[13]on the quantum Navier-Stokes equations to the CNSLLM system.

关键词： compressible Navier-Stokes-Landau-Lifshitz-Maxwell equations global existence weak solutions quantum fluid

Homogeneous Finsler spaces with only one orbit of prime closed geodesics

在线全文

学校读者我要写书评

暂无评论

Science China Mathematics 2020年第11期63卷 2321-2342页

作者： Ming Xu School of Mathematical Sciences Capital Normal UniversityBeijing 100048China

When a closed Finsler manifold admits continuous isometric actions,estimating the number of orbits of prime closed geodesics seems a more reasonable substitution for estimating the number of prime closed *** extend the results of Duan,Long,Rademacher,Wang and others on the existence of two prime closed geodesics to the equivariant situation,we propose the question if a closed Finsler manifold has only one orbit of prime closed geodesics if and only if it is a compact rank-one Riemannian symmetric *** this paper,we study this problem in homogeneous Finsler geometry,and get a positive answer when the dimension is even or the metric is *** guess the rank inequality and the algebraic techniques in this paper may continue to play an important role for discussing our question in the non-homogeneous situation.

关键词： homogeneous Finsler space closed geodesic compact rank-one symmetric space connected isometry group Killing vector field

Difference Cochains and Reidemeister Traces

在线全文

学校读者我要写书评

暂无评论

Chinese Annals of Mathematics,Series B 2017年第6期38卷 1365-1372页

作者： Baoqun ZHANG Xuezhi ZHAO Department of Mathematics Capital Normal UniversityBeijing 100048China.

The authors consider the difference of Reidemeister traces and difference cochain of given two self-maps, and find out a relation involving these two *** an application, an inductive formula of the Reidemeister traces... 详细信息

关键词： Fixed point Reidemeister trace Difference cochain Spherical manifold

Variance Variation Criterion and Consistency in Estimating the Number of Significant Signals of High-dimensional PCA

在线全文

学校读者我要写书评

暂无评论

Acta Mathematicae Applicatae Sinica 2022年第3期38卷 513-531页

作者： Guan-peng WANG Heng-jian CUI School of Mathematical Sciences Capital Normal UniversityBeijing 100048China

In this paper,we propose a criterion based on the variance variation of the sample eigenvalues to correctly estimate the number of significant components in high-dimensional principal component analysis(PCA),and it corresponds to the number of significant eigenvalues of the covariance matrix for p-dimensional *** the random matrix theory,we derive that the consistent properties of the proposed criterion for the situations that the significant eigenvalues tend to infinity,as well as that the bounded significant population *** simulation shows that the probability of estimator is correct by our variance variation criterion converges to 1 is faster than that by criterion of Passemier and Yao[Estimation of the number of spikes,possibly equal,in the high-dimensional *** Anal.,(2014)](PYC),AIC and BIC under the finite fourth moment condition as the dominant population eigenvalues tend to ***,in the case of the maximum eigenvalue bounded,once the gap condition is satisfied,the rate of convergence to 1 is faster than that of PYC and AIC,especially the effect is better than AIC when the sample size is *** is worth noting that the variance variation criterion significantly improves the accuracy of model selection compared with PYC and AIC when the random variable is a heavy-tailed distribution or finite fourth moment not exists.

关键词： consistency variance variation criterion significant eigenvalues high dimension spiked model

The Minkowski norm and Hessian isometry induced by an isoparametric foliation on the unit sphere

在线全文

学校读者我要写书评

暂无评论

Science China Mathematics 2022年第7期65卷 1485-1516页

作者： Ming Xu School of Mathematical Sciences Capital Normal UniversityBeijing 100048China

Let M_(t) be an isoparametric foliation on the unit sphere(S^(n−1)(1),g^(st))with d principal *** the spherical coordinatesinduced by M_(t),we construct a Minkowski norm with the representation F=r√2f(t),which generalizes the notions of(α,β)-norm and(α1,α2)-*** the technique of the spherical local frame,we givean exact and explicit answer to the question when F=r√2 f(t)really defines a Minkowski *** the similar technique,we study the Hessian isometry Φ between two Minkowski norms induced by M_(t),which preservesthe orientation and fixes the spherical ξ-*** aretwo ways to describe this Φ,either by a system of ODEs,or by its restriction toany normal plane for M_(t),which is then reduced to a Hessian isometry between Minkowski norms on R^(2) satisfying certain symmetry and(d)-*** d>2,we prove that this Φ can be obtained by gluing positive scalar multiplications and compositions of the Legendre transformation and positive scalar multiplications,so it must satisfy the(d)-property for any orthogonal decomposition R^(n)=V'+V'',i.e.,for any nonzero x=x'+x'' and Φ(x)=x=x'+x''with x',x'∈V'and x'',x''∈V'',we have g_(x)^(F1)(x'',x)=g_(x)^(F2)x(x'',x).As byproducts,we prove the following *** the indicatrix(S_(F,g)),where F is a Minkowski norm induced by M_(t) and g is the Hessian metric,the foliation N_(t)=S_(F)∩R>_(0)M_(0) is *** Conjecture is valid for a Minkowski norm F induced by M_(t),i.e.,if its Hessian metric g is flat on R^(n)\normalwith n>2,then F is Euclidean.

关键词： Minkowski norm Hessian isometry Hessian metric isoparametric foliation Laugwitz Conjecture Legendre transformation

Spatiotemporal differentiation and development process of tidal creek network morphological characteristics in the Yellow River Delta

在线全文

学校读者我要写书评

暂无评论

Journal of Geographical Sciences 2021年第11期31卷 1633-1654页

作者： MOU Kuinan GONG Zhaoning QIU Huachang College of Resource Environment and Tourism Capital Normal UniversityBeijing 100048China MCA Key Laboratory of Disaster Assessment and Risk Prevention Capital Normal UniversityBeijing 100048China

Tidal creeks are the main channels of land-sea ecosystem interactions,and their high dynamics are an important factor affecting the hydrological connectivity of tidal *** the Yellow River Delta as the research area,we selected remote sensing images obtained during five periods from 1998 to 2018 as the data *** on the spatial analysis function in GIS,the typical morphological characteristics of tidal creeks,such as the level,length,density,curvature,bifurcation ratio,and overmarsh path length(OPL),were extracted to characterize the degree of development of the tidal creeks in the Yellow River Delta *** spatio-temporal evolution of the tidal creeks was studied,and the development process and the characteristics of the tidal creeks during the different stages of development were *** results revealed that(1)The number,density,and bifurcation ratio of tidal creeks exhibit an increasing trend,but the growth of the trend is *** number of tidal creeks increased by 44.9%from the initial stage of the Yellow River diversion to the late stage of the wetland restoration,but it only increased by 26.2%from the late stage of the wetland restoration to the slow expansion of the Spartina alterniflora.(2)The curvature of the tidal creeks on the landward side is greater than that on the seaward side.(3)The development degree of tidal creek has spatial heterogenetiy,which is AreaⅢ>AreaⅡ>AreaⅠ.(4)The drainage efficiency is significantly correlated with the tidal creak density and bifurcation *** on the analysis of the various morphological parameters and the drainage efficiency,it was found that after the rapid change in the tidal creek system in the early stage,the tidal creeks entered a state of slow change,and the development state of the tidal creeks tends to be in dynamic *** results of this study are expected to provide scientific support for the sustainable development and utilization of coastal tidal flats.

关键词： tidal creek network morphological parameter spatiotemporal differentiation developmental stage Yellow River Delta

A Weak∞-Functor in Morse Theory

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11期40卷 2571-2614页

作者： Shan Zhong SUN Chen Xi WANG Department of Mathematics Capital Normal UniversityBeijing100048P.R.China Academy for Multidisciplinary Studies Capital Normal UniversityBeijing100048P.R.China

In the spirit of Morse homology initiated by Witten and Floer,we construct two∞-categories A and *** weak one A comes out of the Morse-Smale pairs and their higher homotopies,and the strict one B concerns the chain complexes of the Morse *** on the boundary structures of the compactified moduli space of gradient flow lines of Morse functions with parameters,we build up a weak∞-functor F:A→*** algebraic structures behind Morse homology are revealed with the perspective of defects in topological quantum field theory.

关键词： Morse function moduli space of gradient flow lines compactifications weak n/∞-category higher morphism homotopy

Robust Estimation of Parameters in Nonlinear Ordinary Differential Equation Models

在线全文

学校读者我要写书评

暂无评论

Journal of Systems Science & Complexity 2016年第1期29卷 41-60页

作者： QIU Yanping HU Tao LIANG Baosheng CUI Hengjian School of Mathematical Sciences Beijing Normal UniversityBeijing 100875China School of Mathematical Sciences and BCMIIS Capital Normal UniversityBeijing 100048China

Ordinary differential equation(ODE) models are widely used to model dynamic processes in many scientific *** estimation is usually a challenging problem,especially in nonlinear ODE *** most popular method,nonlinear least square estimation,is shown to be strongly sensitive to *** this paper,robust estimation of parameters using M-estimators is proposed,and their asymptotic properties are obtained under some regular *** authors also provide a method to adjust Huber parameter automatically according to the ***,a method is presented to estimate the initial values of parameters and state *** efficiency and robustness are well balanced in Huber estimators,which is demonstrated via numerical simulations and chlorides data analysis.

关键词： Asymptotic properties Huber parameter ordinary differential equation robust estimation

Decision making module based on stochastic magnetic tunnel junctions

在线全文

学校读者我要写书评

暂无评论

Science China(Physics,Mechanics & Astronomy) 2025年第1期Mechanics & Astronomy) .卷 202-209页

作者： Yifan Miao Li Zhao Yajun Zhang Zhe Yuan Center for Advanced Quantum Studies and Department of Physics Beijing Normal University Institute for Nanoelectric Devices and Quantum Computing Fudan University Interdisciplinary Center for Theoretical Physics and Information Sciences Fudan University

In biological neural systems, noise is ubiquitous but does not affect the correct decisions made in the complex cognitive ***-making in biological neural system is typically achieved by accumulating input information over a period of *** by recent developments in neurosciences, we design a decision-making module based on spintronic devices, utilizing superparamagnetic tunnel junctions as artificial neurons. The feasibility of this decision-making module is verified through circuit simulations. Taking a multi-layer perceptron as an example, the module significantly improves the accuracy of the perceptron in the handwritten digit recognition task. Furthermore, the spintronic decision-making module offers advantages over the conventional pooling methods, such as adaptive decision time, high performance and the absence of analog-to-digital conversion. The decision-making module is flexible to be integrated into artificial neural networks and provides a general yet effective solution to enhance performance against device noise.

关键词： neuromorphic computing spintronics magnetic tunnel junction neural networks