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On spectral theory of the Riemann zeta function

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Science China Mathematics 2019年第11期62卷 2317-2330页

作者： Xian-jin li Department of Mathematics Brigham Young University

Every nontrivial zero of the Riemann zeta function is associated as eigenvalue with an eigenfunction of the fundamental differential operator on a Hilbert-P′olya space. It has geometric multiplicity one. A relation between nontrivial zeros of the zeta function and eigenvalues of the convolution operator is given. It is an analogue of the Selberg transform in Selberg’s trace formula. Elements of the Hilbert-P′olya space are characterized by the Poisson summation formula.

关键词： Hilbert-Pólya space spectrum of operators zeros of zeta function

Kinematics of the high-excitation HH 890 jet in the Rosette Nebula

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Chinese Journal of Astronomy and Astrophysics 2009年第5期9卷 577-584页

作者： jin-Zeng li National Astronomical Observatory Chinese Academy of Sciences Beijing 100012 China

Photoionized jets immersed in HII regions display special properties, which made them a distinctive category of Herbig-Haro （HH） flows. Detailed studies of such jet systems became one of the key issues in our understanding of jet production and evolution. HH 890, initially called the Rosette HH2 jet, is the second photoionized jet discovered in the spectacular HII region of the Rosette Nebula. Contrary to conventional impressions of a jet, its discrete components are found to be unexpectedly broad and spatially detached from the proposed energy source. The jet displays additional unusual features which point to the disputable nature of the system. Here, we investigate the kinematics of the jet through high-quality echelle spectrograms. It is distinctively resolved into a fast component with a mean approaching velocity of-39 km s^-1 with respect to the systemic rest frame and a slow component with radial velocity centered at -9 km s^-1. The slow component indicates an apparently larger dispersion in radial velocity in various emission lines and is likely dissolving at roughly the speed of sound, which favors a photoevaporated origin. The [SII] doublet ratios indicate an electron density of -1.1×10^3 cm^-3 in the collimated jet and ,-9×10^2 cm^-3 in the HII region. This, along with the diffuse appearance of the extensive part of the jet, leads to a dissipation of the jet in the fully ionized medium of Rosette. In addition, time series of photometric observations provide evidence for remarkable light variations of the energy source. Its amplitudes of variation amount to 〉 1 mag in both R and I, which is commensurate with the young evolutionary status of the source as indicated by a red, late type optical spectrum.

关键词： accretion disks -- ISM jets and outflows -- stars formation -- stars premain-sequence

On Weil's explicit formula

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Science China Mathematics 2015年第5期58卷 915-982页

作者： li Xian-jin Department of Mathematics Brigham Young University

A program of proving the Riemann hypothesis by using the Fourier analysis on global fields is given by Connes(1999). The difficulty for realizing the program lies in proving the validity of Connes' global trace formula on an L2-space. In this paper, a new global trace formula is obtained on a Fr′echet space which gives the Weil distribution △(h).

关键词： global trace formula nuclear locally convex space Riemann hypothesis

A Second-order Fluid Queue with Subordinator Input and Markov-modulated linear Output

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Acta Mathematicae Applicatae Sinica 2009年第2期25卷 345-352页

作者： jin-zhi li College of Sciences Minzu University of China Beijing 100081 China

We consider an infinite capacity second-order fluid queue with subordinator input and Markovmodulated linear release rate. The fluid queue level is described by a generalized Langevin stochastic differential equation （SDE）. Applying infinitesimal generator, we obtain the stationary distribution that satisfies an integro-differential equation. We derive the solution of the SDE and study the transient level＇s convergence in distribution. When the coefficients of the SDE are constants, we deduce the system transient property.

关键词： Second-order fluid queue subordinator Markov chain linear release rate

语言模型辅助的英语科技论文摘要语步语料库构建研究

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外语学刊 2025年第1期 29-38页

作者：李洪政王若锦刘芳冯冲北京理工大学外国语学院北京102488 语言工程与认知计算工信部重点实验室北京102488 北京理工大学计算机学院北京100081

语步结构是学术论文中的文本语篇单位,在学术用途英语等方面具有重要价值。尽管关于学术论文的语步研究非常丰富,但语步标注数据资源仍然相对较少。本研究借助自然语言处理领域的语言模型构建了涵盖多个学科领域的英语科技论文摘要语步... 详细信息

语步结构是学术论文中的文本语篇单位,在学术用途英语等方面具有重要价值。尽管关于学术论文的语步研究非常丰富,但语步标注数据资源仍然相对较少。本研究借助自然语言处理领域的语言模型构建了涵盖多个学科领域的英语科技论文摘要语步标注语料库,包括近3.4万个语步结构。语料库构建的第一阶段依靠专家标注形成高质量语料,在第二阶段也是主要阶段,采用基于BERT架构的自动标注模型,在保证标注质量的同时能够快速提升标注速度、扩大标注规模。本研究随后开展了摘要语步自动标注识别实验,对比自动标注模型与大语言模型ChatGPT和Claude3识别不同学科领域的语步结构的效果,验证了模型和语料库的价值。该研究能为科技论文写作智能批改等自然语言处理任务以及学术用途英语等外语教学与研究等提供必要的数据资源,也验证了大语言模型辅助构建语言资源的可能性,体现了语言智能驱动的智慧外语教育的重要性,能有效推动外语教育数字化转型。

关键词：语步结构语料库摘要文本大语言模型

The key parameter of shale oil resource evaluation: Oil content

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Petroleum Science 2022年第4期19卷 1443-1459页

作者： Min Wang Ming li jin-Bu li liang Xu jin-Xu Zhang State Key Laboratory of Shale Oil and Gas Enrichment Mechanisms and Effective Development Beijing102206China SINOPEC Key Laboratory of Petroleum Accumulation Mechanisms WuxiJiangsu 214126China Shandong Provincial Key Laboratory of Deep Oil and Gas QingdaoShandong 266580China School of Geoscience China University of Petroleum(East China)QingdaoShandong 266580China

The United States has become the world's largest oil producer of shale oil. China has abundant shale oil resources, but its resource potential has not yet been exploited. The core of the evaluation is the selection of parameters and their reliability. By combining the parameters of the shale oil resource evaluation, we investigated the key parameters in the evaluation model and reviewed the research results. The adsorption and retention of heavy hydrocarbons, loss of light hydrocarbons, and original oil saturation are key in the evaluation of shale oil resources. The adsorption and retention of heavy hydrocarbons can be determined by the pyrolysis, FID curve, and hydrocarbon generation kinetics of shale before and after extraction. The loss of light hydrocarbons mainly occurs in coring(change in temperature and pressure),sample treatment, which can be evaluated using the GC spectrum, rock pyrolysis, crude oil volume coefficient, mass balance, component hydrocarbon generation kinetics, and other methods. The original oil saturation evaluation includes indirect, direct, logging, and simulation methods. The most reliable parameters can be obtained by using the sealed or pressure-maintained coring immediately after thawing(without crushing), and the recovery of light hydrocarbon loss is critical for the resource evaluation of medium to high mature shale. Therefore, the experimental determination of shale oil content and the study of the influencing factors of the parameters should be strengthened.

关键词： Shale oil Oil content Oil saturation light hydrocarbon recovery Resource evaluation

Optimal and suboptimal structured algorithms of binary linear block codes

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Journal of Systems Engineering and Electronics 2011年第6期22卷 1010-1014页

作者： Yijun Luo jin li School of Electronic Information Wuhan University Wuhan 430079 R R. China

The optimal and suboptimal structured algorithms of linear block codes from the geometrical perspective are *** minimum distance and weight property lemmas and the theorem are proved for the generator *** upon the property of generator matrix,the structured algorithms of linear block codes are *** the complexity of optimal structured algorithm is very high,the binary linear block codes is searched by using the suboptimal structured *** comparison with Bose-Chaudhuri-Hocquenqhem（BCH） codes shows that the searched linear block codes are equivalent on minimum distance and can be designed for more block *** the linear block codes are used widely in communication systems and digital applications,the optimal and suboptimal structured algorithms must have great future being widely used in many applications and perspectives.

关键词： channel coding linear block codes generator matrix minimum distance.

Vertex-transitive Diameter Two Graphs

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Acta Mathematicae Applicatae Sinica 2022年第1期38卷 209-222页

作者： Wei jin li TAN School of Statistics Jiangxi University of Finance and EconomicsNanchang 330013China School of Mathematics and Statistics HNP-LAMACentral South UniversityChangsha 410075China Research Center of Applied Statistics Jiangxi University of Finance and EconomicsNanchang 330013China

We investigate the family of vertex-transitive graphs with diameter ***Γbe such a *** that its automorphism group is transitive on the set of ordered non-adjacent vertex *** eitherΓis distance-transitive orΓhas girth at most ***,ifΓhas valency 2,thenΓ≌C4 or C5;and for any integer n≥3,there exist such graphsΓof valency n such that its automorphism group is not transitive on the set of ***,we determine this family of graphs of valency less than ***,the family of diameter 2 circulants is characterized.

关键词： vertex-transitive graph diameter automorphism group

On the mean field limit of the Random Batch Method for interacting particle systems

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Science China Mathematics 2022年第1期65卷 169-202页

作者： Shi jin Lei li School of Mathematical Sciences Institute of Natural SciencesMOE-LSCShanghai Jiao Tong UniversityShanghai 200240China

The Random Batch Method proposed in our previous work(jin et al.J Comput Phys,2020)is not only a numerical method for interacting particle systems and its mean-field limit,but also can be viewed as a model of the particle system in which particles interact,at discrete time,with randomly selected mini-batch of *** this paper,we investigate the mean-field limit of this model as the number of particles N→∞.Unlike the classical mean field limit for interacting particle systems where the law of large numbers plays the role and the chaos is propagated to later times,the mean field limit now does not rely on the law of large numbers and the chaos is imposed at every discrete *** this,we will not only justify this mean-field limit(discrete in time)but will also show that the limit,as the discrete time intervalτ→0,approaches to the solution of a nonlinear Fokker-Planck equation arising as the mean-field limit of the original interacting particle system in the Wasserstein distance.

关键词： Random Batch Method mean field limit chaos Wasserstein distance nonlinear Fokker-Planck equation