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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, china {2. pei-yuan center for applied mathematics, tsinghua university, Beijing 100084, china 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

Controllable split polarization singularities for ultra-precise displacement sensing

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Photonics Research 2024年第7期12卷 1478-1484页

作者： JIAKANG zhou HAIXIANG MA SHUOSHUO ZHANG WU yuan CHANGJUN MIN XIAOCONG yuan YUQUAN ZHANG Nanophotonics Research Centre Institute of Microscale Optoelectronics&State Key Laboratory of Radio Frequency Heterogeneous IntegrationShenzhen UniversityShenzhen 518060China Research center for Humanoid Sensing Research Institute of Intelligent SensingZhejiang LabHangzhou 311100China Department of Biomedical Engineering The Chinese University of Hong KongHong KongChina

The topic of optical precise displacement measurement has garnered significant attention and generated widespread interest recently. The use of optical singularity offers a potential solution for this purpose, although effectively manipulating the singularity in an ideal manner remains challenging. In this work, we propose a theoretical approach to achieve controllable position modulation of the C-point in the focal plane, whose spatial position can be easily modulated by adjusting the relative offset factor β and the offset angle α of an azimuthal polarization beam(APB), while the interval and orientation of the C-points can be flexibly regulated. Notably, the chiral polarization state undergoes a distinct reversal along the link-line connecting the two C-points, thereby providing a promising approach for accurate displacement sensing. To evaluate its sensing characteristics, the varying pattern of the scattered field intensity is monitored when sweeping a gold helix and nanoparticle along the link-line. The results of simulation quality index Q verify that the equilibrium factor of the scattering field possesses an obvious linear relationship with the displacement, signifying a precise sub-nanometric *** research introduces new methods for the flexible control of polarization singularities in tightly focused fields,thereby enhancing the utilization of circular polarization properties near C-points for displacement *** findings not only enrich the field of nanometer measurement technology but also pave the way for new avenues of research in this domain.

关键词： polarization displacement precise

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

The Active Compensation Technique for Large Reflector Antennas Based on Quadratic Curve Fitting

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Research in Astronomy and Astrophysics 2024年第7期24卷 226-234页

作者： Tian-Xiang Zheng Bin-Bin Xiang Han-Wei Cui Wei Wang pei-yuan Lian Shang-Ming Lin Yang Zhang Jian-Ping {2. Kai Li School of Mechanical Engineering Xinjiang UniversityUrumqi 830017China School of Mechano-Electronic Engineering Xidian UniversityXi’an 710017China Xi’an Institute of Optics and Precision Mechanics Chinese Academy of SciencesXi’an 710119China

Active reflectors are often used to compensate the surface distortion caused by environmental factors that degrade the electromagnetic performance of large high-frequency reflector *** is crucial for maintaining high gain operation in antennas.A distortion compensation method for the active reflector of a large dual-reflector antenna is proposed.A relationship is established between the surface deformation and the optical path difference for the primary reflector by geometric ***,employing finite element analysis,a polynomial fitting approach is used to describe the impact of adjusting points on the reflector surface based on the coordinates of each *** standardizing the positions of various panels on the reflector,the fitting ns can be applied to the reflector panels of similar ***,based on the distribution characteristics of the primary reflector panels,the adjustment equation for the actuators is derived by the influence matrix *** can be used to determine the adjustment amount of actuators to reduce the rms of the optical path ***,the least squares method is employed to resolve the matrix *** example of a 110 m aperture dual-reflector antenna is carried out by finite element analysis and the proposed *** results show that the optical path difference is reduced significantly at various elevation cases,which indicates that the proposed method is effective.

关键词： Methods analytical-Methods numerical-Telescopes

Inter-chromosomal insertions into wild-type chromosomes induced by SCRaMbLE

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Frontiers of Chemical Science and Engineering 2024年第9期18卷 125-135页

作者： Sijie zhou Junyanrui Li Xichen Cui Ying Wang Ying-Jin yuan Frontiers Science center for Synthetic Biology and Key Laboratory of Systems Bioengineering(Ministry of Education) School of Chemical Engineering and TechnologyTianjin UniversityTianjin 300072China Frontiers Research Institute for Synthetic Biology Tianjin UniversityTianjin 300072China

Genomic rearrangements play a crucial role in shaping biological phenotypic diversity and driving species *** chromosome rearrangement and modification by LoxP-mediated evolution(SCRaMbLE)has been applied to explore large-scale genomic rearrangements,yet it has been observed that these rearrangements occur exclusively in genomic regions containing loxPsym ***,we found that SCRaMbLE of synthetic yeast harboring synthetic chromosome V and X can generate a variety of synthetic segment insertions into wild-type chromosomes,ranging from 1 to 300 ***,it was revealed that the novel insertions impacted the transcriptional level of neighboring regions and affected the production of exemplar pathway of ***,our results improve the understanding of the ability of SCRaMbLE to generate complex structural variations in nonsynthetic regions and provide a potential model to explore genomic transposable events.

关键词： genomic rearrangements synthetic yeast genome SCRaMbLE inter-chromosomal insertions synthetic biology

Acetyl coenzyme A carboxylase modulates lipogenesis and sugar homeostasis in Blattella germanica

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Insect Science 2024年第2期31卷 387-404页

作者： Xiaojin pei Tiantian Bai yuan Luo Zhanfeng Zhang Sheng Li Yongliang Fan Tong-Xian Liu Guangdong Provincial Key Laboratory of Insect Developmental Biology and applied Technology and Institute of Insect Science and Technology School of Life SciencesSouth China Normal UniversityGuangzhouChina State Key Laboratory of Crop Stress Biology for Arid Areas and Key Laboratory of Integrated Pest Management on Crops in Northwestern Loess Plateau Ministry of AgricultureNorthwest A&F UniversityYanglingShaanxiChina Guangmeiyuan R&D center Guangdong Provincial Key Laboratory of Insect Developmental Biology and Applied TechnologySouth China Normal UniversityMeizhouGuangdong ProvinceChina Institute of Entomology Guizhou UniversityGuiyangChina

Lipid and sugar homeostasis is critical for insect development and *** this study,we characterized an acetyl coenzyme A carboxylase gene in Blattella germanica(BgACC)that is involved in both lipogenesis and sugar *** found that BgACC was dominantly expressed in the fat body and integument,and was significantly upregulated after *** of BgACC in 5th-instar nymphs did not affect their normal molting to the next nymphal stage,but it caused a lethal phenotype during adult ***-RNA interference(RNAi)significantly downregulated total free fatty acid(FFA)and triacylglycerol(TAG)levels,and also caused a significant decrease of cuticular hydrocarbons(CHCs).Repression of BgACC in adult females affected the development of oocytes and resulted in sterile females,but BgACC-RNAi did not affect the reproductive ability of ***,knockdown of BgACC also changed the expression of insulin-like peptide genes(BglLPs),which mimicked a physiological state of high sugar *** addition,BgACC was upregulated when *** were fed on a high sucrose diet,and repression of BgACC upregulated the expression of the glycogen synthase gene(BgGlyS).Moreover,BgACC-RNAi increased the circulating sugar levels and glycogen storage,and a longevity assay suggested that BgACC was important for the survival of *** under conditions of high sucrose *** results confirm that BgACC is involved in multiple lipid biogenesis and sugar homeostasis processes,which further modulates insect reproduction and sugar *** study benefits our understanding of the crosstalk between lipid and sugar metabolism.

关键词： acetyl-CoA carboxylase German cockroach lipid biosynthesis sugar tolerance

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