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Continuity in weak topology:higher order linear systems of ODE

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Science china mathematics 2008年第6期51卷 1036-1058页

作者： ZHANG MeiRong Department of Mathematical Sciences,zhou pei-{2. center for applied mathematics,tsinghua University,beijing 100084,china Department of Mathematical Sciences Zhou Pei-Yuan Center for Applied Mathematics Tsinghua University Beijing 100084 China

We will introduce a type of Fredholm operators which are shown to have a certain con- tinuity in weak *** this,we will prove that the fundamental matrix solutions of k-th, k≥2.order linear systems of ordinary differential equations are continuous in coefficient matrixes with weak ***,Floquet multipliers and Lyapunov exponents for periodic systems are continuous in weak ***,for the scalar Hill’s equations,Sturm-Liouville eigenvalues, periodic and anti-periodic eigenvalues,and rotation numbers are all continuous in potentials with weak *** results will lead to many interesting variational problems.

关键词： continuity weak topology Fredholm operator linear system Hill’s equation eigenvalue rotation number Lyapunov exponent 34A30 34L40 37E45 34D08 58C07 46B50

An attempt to differential Galois theory of second order polynomial system and solvable subgroup of Mbius transformations

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Science china mathematics 2007年第5期50卷 748-760页

作者： Ke-ying GUAN & Jin-zhi LEI School of Science, beijing Jiaotong University, beijing 100044, {2. zhou pei-yuan center for applied mathematics, tsinghua University, beijing 100084, {2. School of Science Beijing Jiaotong University Beijing 100044 China zhou pei-{2. center for applied mathematics Tsinghua University Beijing 100084 China

By introducing the conception "relativistic differential Galois group" for the second order polynomial systems, we establish the relation between the conformal relativistic differential Galois group and the subgroup of Mobius transformations, and prove that the system is integrable in the sense of Liouville if its conformal relativistic differential Galois group is solvable with a derived length at most 2. Some omissions on the structures of solvable subgroups of Mobius transformations at the first author’s article published in this journal in 1996 are refreshed in this paper.

关键词： conformed differential Galois group Mobius transformations integrability in the sense of Liouville

A New Method for Deriving High-Vertical-Resolution Wind Vector Data from the L-Band Radar Sounding System in china

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Advances in Atmospheric Sciences 2024年第11期41卷 2192-2202页

作者： Fang yuan Zijiang zhou Jie LIAO National Meteorological Information center China Meteorological AdministrationBeijing 100081China

High-vertical-resolution radiosonde wind data are highly valuable for describing the dynamics of the meso-and microscale atmosphere. However, the current algorithm used in china's L-band radar sounding system for calculating highvertical-resolution wind vectors excessively smooths the data, resulting in significant underestimation of the calculated kinetic energy of gravity waves compared to similar products from other countries, which greatly limits the effective utilization of the data. To address this issue, this study proposes a novel method to calculate high-vertical-resolution wind vectors that utilizes the elevation angle, azimuth angle, and slant range from L-band radar. In order to obtain wind data with a stable quality, a two-step automatic quality control procedure, including the RMSE-F(root-mean-square error F) test and elemental consistency test are first applied to the slant range data, to eliminate continuous erroneous data caused by unstable signals or radar malfunctions. Then, a wind calculation scheme based on a sliding second-order polynomial fitting is utilized to derive the high-vertical-resolution radiosonde wind vectors. The evaluation results demonstrate that the wind data obtained through the proposed method show a high level of consistency with the high-resolution wind data observed using the Vaisala Global Positioning System and the data observed by the new Beidou Navigation Sounding System. The calculation of the kinetic energy of gravity waves in the recalculated wind data also reaches a level comparable to the Vaisala observations.

关键词： L-band radar sounding system upper air high-vertical-resolution radiosonde wind vectors quality control polynomial fitting

Photonic neuromorphic architecture for tens-of-task lifelong learning

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Light(Science & Applications) 2024年第3期13卷 519-530页

作者： yuan Cheng Jianing Zhang Tiankuang zhou Yuyan Wang Zhihao Xu Xiaoyun yuan Lu Fang Sigma Laboratory Department of Electronic EngineeringTsinghua UniversityBeijing 100084China beijing National Research center for Information Science and Technology(BNRist) Beijing 100084China Institute for Brain and Cognitive Science Tsinghua University(THUIBCS)Beijing 100084China

Scalable,high-capacity,and low-power computing architecture is the primary assurance for increasingly manifold and large-scale machine learning *** electronic artificial agents by conventional power-hungry processors have faced the issues of energy and scaling walls,hindering them from the sustainable performance improvement and iterative multi-task *** to another modality of light,photonic computing has been progressively applied in high-efficient neuromorphic ***,we innovate a reconfigurable lifelong-learning optical neural network(L2.ONN),for highly-integrated tens-of-task machine intelligence with elaborated algorithm-hardware *** from the inherent sparsity and parallelism in massive photonic connections,L2.ONN learns each single task by adaptively activating sparse photonic neuron connections in the coherent light field,while incrementally acquiring expertise on various tasks by gradually enlarging the *** multi-task optical features are parallelly processed by multi-spectrum representations allocated with different *** evaluations on freespace and on-chip architectures confirm that for the first time,L2.ONN avoided the catastrophic forgetting issue of photonic computing,owning versatile skills on challenging tens-of-tasks(vision classification,voice recognition,medical diagnosis,etc.)with a single ***,L2.ONN achieves more than an order of magnitude higher efficiency than the representative electronic artificial neural networks,and 14×larger capacity than existing optical neural networks while maintaining competitive performance on each individual *** proposed photonic neuromorphic architecture points out a new form of lifelong learning scheme,permitting terminal/edge AI systems with light-speed efficiency and unprecedented scalability.

关键词： life neural versatile

Spin Evolution of the Magnetar SGR J1935+2.54

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Research in Astronomy and Astrophysics 2024年第1期24卷 201-211页

作者： Ming-Yu Ge yuan-pei Yang Fang-Jun Lu Shi-Qi {2. Long Ji Shuang-Nan Zhang Bing Zhang Liang Zhang pei Wang Kejia Lee Weiwei Zhu Jian Li Xian Hou Qiao-Chu Li Key Laboratory of Particle Astrophysics Institute of High Energy PhysicsChinese Academy of SciencesBeijing 100049China South-Western Institute For Astronomy Research Yunnan UniversityKunming 650504China Purple Mountain Observatory Chinese Academy of SciencesNanjing 210023China Key Laboratory of Stellar and Interstellar Physics and School of Physics and Optoelectronics Xiangtan UniversityXiangtan 411105China School of Physics and Astronomy Sun Yat-Sen UniversityZhuhai 519082China University of Chinese Academy of Sciences Chinese Academy of SciencesBeijing 100049China Nevada center for Astrophysics University of NevadaLas VegasNV 89154USA Department of Physics and Astronomy University of NevadaLas VegasNV 89154USA National Astronomical Observatories Chinese Academy of SciencesBeijing 100101China Department of Astronomy Peking UniversityBeijing 100871China CAS Key Laboratory for Research in Galaxies and Cosmology Department of AstronomyUniversity of Science and Technology of ChinaHefei 230026China School of Astronomy and Space Science University of Science and Technology of ChinaHefei 230026China Yunnan Observatories Chinese Academy of SciencesKunming 650216China School of Astronomy and Space Science Nanjing UniversityNanjing 210023China Key laboratory of Modern Astronomy and Astrophysics Nanjing UniversityNanjing 210023China

Fast radio bursts(FRBs)are short pulses observed in radio frequencies usually originating from cosmological *** discovery of FRB 2.042. and its X-ray counterpart from the Galactic magnetar SGR J1935+2.54suggests that at least some FRBs can be generated by ***,the majority of X-ray bursts from magnetars are not associated with radio *** fact that only in rare cases can an FRB be generated raises the question regarding the special triggering mechanism of *** we report long time spin evolution of SGR J1935+2.54 until the end of *** to v and v,the spin evolution of SGR J1935+2.54 could be divided into two *** first stage evolves relatively steady evolution until 2.2. April *** the burst activity in2.2.,the spin of SGR J1935+2.54 shows strong variations,especially for *** the burst activity in 2.2.October,a new spin-down glitch with△v/v=(-7.2.0.6)×10^(-6)is detected around MJD 59876,which is the second event in SGR J1935+*** the end,spin frequency and pulse profile do not show variations around the time of FRB 2.042. and radio bursts 2.1014 and 2.102.,which supply strong clues to constrain the trigger mechanism of FRBs or radio bursts.

关键词： (stars:)pulsars:general (stars:)pulsars:individual(SGR J1935+2.54) X-rays:bursts

Quantifying the natural growth rate of hepatocellular carcinoma:A real-world retrospective study in southwestern china

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World Journal of Hepatology 2024年第5期16卷 800-808页

作者： Li Tu Hong Xie Qi Li Ping-Gui Lei pei-Ling Zhao Fan Yang Chi Gong yuan-Lin Yao Shi {2. Department of General Practice The Affiliated Hospital of Guizhou Medical UniversityGuiyang 550004Guizhou ProvinceChina Clinical Medicine Soochow UniversitySuzhou 215123Jiangsu ProvinceChina Department of Radiology The Affiliated Hospital of Guizhou Medical UniversityGuiyang 550004Guizhou ProvinceChina Department of Clinical Laboratory center The Affiliated Hospital of Guizhou Medical UniversityGuiyang 550004Guizhou ProvinceChina Key Laboratory of Biology and Medical Engineering Guizhou Medical UniversityGuiyang 550025Guizhou ProvinceChina Department of Radiology Yanhe Tujia Autonomous County People's HospitalTongren 565300Guizhou ProvinceChina Department of Radiology The Qiandongnan Miao and Dong Autonomous Prefecture People's HospitalKaili 556000Guizhou ProvinceChina Department of Interventional Radiology The Affiliated Hospital of Guizhou Medical UniversityGuiyang 550004Guizhou ProvinceChina

BACKGROUND In recent years,approximately half of the newly diagnosed cases and mortalities attributed to hepatocellular carcinoma(HCC)have been reported in *** the high incidence of HCC,there remains a paucity of data regarding the natural growth pattern and the determination of optimal surveillance intervals specific to the Chinese *** To quantify the natural tumor growth pattern of HCC in regional *** A retrospective analysis was performed on patients from a single institution in Southwest china who had undergone two or more serial dynamic computed tomography or magnetic resonance imaging scans between 2.14 and 2.2.,without having received any anti-cancer *** growth was assessed using tumor volume doubling time(TVDT)and tumor growth rate(TGR),with volumes measured manually by experienced *** univariate linear regression and descriptive analysis were applied to explore associations between growth rates and clinical *** This study identifies the median TVDT for HCC as 163.4 d,interquartile range(IQR)72.1 to 302.3 d,with a daily TGR of 0.42.(IQR 0.2.6%-0.97%).HCC growth patterns reveal that about one-third of tumors grow indolently with TVDT exceeding 2.0 d,another one-third of tumors exhibit rapid growth with TVDT under 90 d,and the remaining tumors show intermediate growth rates,with TVDT ranging between 3 to 9 *** The identified TGRs support biannual surveillance and follow-up for HCC patients in certain regions of *** the observed heterogeneity in HCC growth,further investigation is warranted.

关键词： Hepatocellular carcinoma Natural tumor growth pattern Tumor volume doubling time Tumor growth rate Realworld retrospective study

The unconditional stable and convergent difference methods with intrinsic parallelism for quasilinear parabolic systems

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Science china mathematics 2004年第3期47卷 453-472页

作者： zhou Yulin yuan Guangwei SHEN Longjun Laboratory of Computational Physics, {2. of Nonlinear Studies, Institute of applied Physics and Computational mathematics, beijing 100088, china 1. Laboratory of Computational Physics Center of Nonlinear Studies Institute of Applied Physics and Computational Mathematics 100088 Beijing China

A kind of the general finite difference schemes with intrinsic parallelism for the boundary value problem of the quasilinear parabolic system is studied without assuming heuristically that the original boundary value problem has the unique smooth vector solution. By the method of a priori estimation of the discrete solutions of the nonlinear difference systems, and the interpolation formulas of the various norms of the discrete functions and the fixed-point technique in finite dimensional Euclidean space, the existence and uniqueness of the discrete vector solutions of the nonlinear difference system with intrinsic parallelism are proved. Moreover the unconditional stability of the general finite difference schemes with intrinsic parallelism is justified in the sense of the continuous dependence of the discrete vector solution of the difference schemes on the discrete data of the original problems in the discrete W 2.(2.1) norms. Finally the convergence of the discrete vector solutions of the certain difference schemes with intrinsic parallelism to the unique generalized solution of the original quasilinear parabolic problem is proved.

关键词： difference scheme, intrinsic parallelism,quasilinear parabolic system, convergence, stability.

GENERAL DIFFERENCE SCHEMES WITH INTRINSICPARALLELISM FOR SEMILINEAR PARABOLIC SYSTEMS OFDIVERGENCE TYPE

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Journal of Computational mathematics 1999年第4期17卷 337-352页

作者： Yu-lin zhou Guang-wei yuan(Laboratory of Computational Physics, {2. of Nonlinear Studies, Institute of applied Physics and Computational mathematics, P.O. Box 8009, beijing 100088, china) Laboratory of Computational Physics Center of Nonlinear Studies Institute of Applied Physics and Computational Mathematics P.O. Box 8009 Beijing 100088 China

In this paper the general finite difference schemes with intrinsic parallelism for the boundary value problem of the semilinear parabolic system of divergence type with bounded coefficients are constructed, and the existence and uniqueness of the difference solution for the general schemes are proved. And the convergence of the solutions of the difference schemes to the generalized solution of the original boundary value problem of the semilinear parabolic system is obtained. The multidimensional problems are also studied.

关键词： difference scheme intrinsic parallelism semilinear parabolic system convergence

Mechanism and control of nonuniform phase transformation of microalloyed dual-phase steel during cooling process after hot rolling

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Journal of Iron and Steel Research International 2024年第2期31卷 428-441页

作者： Wen-quan Sun Sheng-yi Yong Tie-heng yuan Chao Liu San-bao zhou Rui-chun Guo Meng-xia Tang National Engineering Research center for Advanced Rolling and Intelligent Manufacturing University of Science and Technology BeijingBeijing100083China Strip Production Plant Xichang Steel and Vanadium Corporation of Pangang GroupXichang615000SichuanChina

After cooling in the hot rolling process,the metallographic structure of microalloyed dual-phase steel is nonuniform along the rolling direction,while the thickness fluctuation of microalloyed dual-phase steel with a nonuniform metallographic structure will occur during cold *** mechanism of nonuniform phase transformation of microalloyed dual-phase steels was studied during the cooling process after hot rolling,and the nonuniform phase transformation of microalloyed dual-phase steel was regulated during the cooling process after hot rolling through process ***,the empirical equation of phase transformation temperature was measured by a dilatometer considering thermal ***,the phase field and temperature field of laminar cooling process were calculated to provide initial boundary conditions for the finite element *** that,the coupling finite element model of the temperature phase transformation of the strip steel in coiling transportation process was *** simulation results show that the different thermal contact conditions of the microalloyed dual-phase steel during coil transportation lead to uneven cooling of the coil,which leads to nonuniform transformation of the coil along the rolling *** addition,by prolonging the time interval from coiling to unloading,the phenomenon of nonuniform phase transformation of microalloyed dual-phase steel can be effectively *** simulation results are applied to industrial *** application results show that prolonging the time interval from coiling to unloading can effectively improve the nonuniform phase transformation of microalloyed dual-phase steel in the cooling process after hot rolling.

关键词： Microalloyed dual-phase steel Thickness fluctuation Cooling Heat conduction Nonuniform phase transition Finite element method