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Acta Mathematica Sinica,English Series 2024年第9期40卷 2091-2152页

作者： Qi An GUAN Zhi Tong MI Zheng YUAN School of mathematical sciences Peking UniversityBeijing 100871P.R.China School of Mathematics and Statistics Beijing Jiaotong UniversityBeijing 100044P.R.China institute of Mathematics Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190P.R.China

In this article,we consider a modified version of minimal L^(2) integrals on sublevel sets of plurisubharmonic functions related to modules at boundary points,and obtain a concavity property of the modified *** applications,we give characterizations for the concavity degenerating to linearity on open Riemann surfaces and on fibrations over open Riemann surfaces.

关键词： Minimal L^(2)integrals plurisubharmonic functions boundary points weakly pseudoconvex Kähler manifold

Miyaoka-type inequalities for terminal threefolds with nef anti-canonical divisors

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Science china Mathematics 2024年

作者： Masataka Iwai chen Jiang Haidong Liu department of Mathematics Graduate School of Science Osaka University Shanghai center for mathematical sciences & School of mathematical sciences Fudan University department of mathematics Sun Yat-sen University

In this paper,we study Miyaoka-type inequalities on chern classes of terminal projective 3-folds with nef anti-canonical *** X be a terminal projective 3-fold such that-KXis *** show that if c1（X）·c2（X）≠0,then c1（X）·c2（X）≥1/252;if further X is not rationally connected,then c1（X）·c2（X）≥4/5 and this inequality is *** order to prove this,we give a partial classification of such varieties along with many *** also study the nonvanishing of c1（X）dimX-2·c2（X） for terminal weak Fano varieties and prove a Miyaoka-Kawamata-type inequality.

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BIG HANKEL OPERATORS ON HARdY SPAcES OF STRONGLY PSEUdOcONVEX dOMAINS

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Acta Mathematica Scientia 2024年第3期44卷 789-809页

作者：陈伯勇江良英 School of mathematical sciences Fudan UniversityShanghai200433China department of Statistics and Mathematics Shanghai Lixin University of Accounting and FinanceShanghai201209China

In this article,we investigate the(big) Hankel operator H_(f) on the Hardy spaces of bounded strongly pseudoconvex domains Ω in c^(n).We observe that H_(f ) is bounded on H~p(Ω)(1

d we ... 详细信息

In this article,we investigate the(big) Hankel operator H_(f) on the Hardy spaces of bounded strongly pseudoconvex domains Ω in c^(n).We observe that H_(f ) is bounded on H~p(Ω)(1 d we obtain some characterizations for Hf on H^(2)(Ω) of other pseudoconvex *** these arguments,Amar's L^(p)-estimations and Berndtsson's L^(2)-estimations for solutions of the ■_(b)-equation play a crucial *** addition,we solve Gleason's problem for Hardy spaces H^(p)(Ω)(1 ≤p≤∞) of bounded strongly pseudoconvex domains.

关键词： Hankel operator Hardy space Bergman space pseudoconvex domain

Prediction of solar activities:Sunspot numbers and solar magnetic synoptic maps

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Science china Earth sciences 2024年第8期67卷 2460-2477页

作者： Rui ZHUO Jiansen HE die dUAN Rong LIN Ziqi WU Limei YAN Yong WEI School of Earth and Space sciences Peking UniversityBeijing 100091China college of Advanced Interdisciplinary Studies National University of Defense TechnologyChangsha 410073China centre for mathematical Plasma Astrophysics Department of MathematicsKU LeuvenLeuven 3001Belgium Key Laboratory of Earth and Planetary Physics Institute of Geology and GeophysicsChinese Academy of SciencesBeijing 100029China college of Earth and Planetary sciences University of Chinese Academy of SciencesBeijing 100049China

The evolution of solar magnetic fields is significant for understanding and predicting solar *** our knowledge of solar magnetic fields largely depends on the photospheric magnetic *** this paper,based on the spherical harmonic expansion of the photospheric magnetic field observed by Wilcox Solar Observatory,we analyze the time series of spherical harmonic coefficients and predict Sunspot Number as well as synoptic maps for Solar cycle *** find that solar maximum years have complex short-period disturbances,and the time series of coefficient g_(7)~0 is nearly in-phase with Sunspot Number,which may be related to solar meridional *** Long Short-Term Memory networks(LSTM),our prediction suggests that the maximum of Solar cycle 25 is likely to occur in June 2024 with an error of 8 months,the peak sunspot number may be 166.9±22.6,and the next solar minimum may occur around January *** incorporating Empirical Mode decomposition,we enhance our forecast of synoptic maps truncated to Order 5,validating their relative *** prediction not only addresses a gap in forecasting the global distribution of the solar magnetic field but also holds potential reference value for forthcoming solar observation plans.

关键词： Solar activity prediction Solar magnetic field Spherical harmonic expansion Long-Short Term Memory(LSTM) Empirical Mode decomposition(EMd)

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Model-driven cT reconstruction algorithm for nano-resolution x-ray phase contrast imaging

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chinese Physics B 2024年第7期33卷 646-650页

作者：谭雨航蔡学宝杨杰成苏婷郑海荣梁栋朱佩平葛永帅 Research center for Medical Artificial Intelligence Shenzhen Institute of Advanced TechnologyChinese Academy of SciencesShenzhen 518055China institute of Electronic Paper displays South China Academy of Advanced OptoelectronicsSouth China Normal UniversityGuangzhou 510006China Paul c Lauterbur Research center for Biomedical Imaging Shenzhen Institute of Advanced TechnologyChinese Academy of SciencesShenzhen 518055China institute of High Energy Physics Chinese Academy of SciencesBeijing 100049China

The low-density imaging performance of a zone plate-based nano-resolution hard x-ray computed tomography(cT)system can be significantly improved by incorporating a grating-based Lau interferometer. due to the diffraction, however,the acquired nano-resolution phase signal may suffer splitting problem, which impedes the direct reconstruction of phase contrast cT(nPcT) images. To overcome, a new model-driven nPcT image reconstruction algorithm is developed in this study. In it, the diffraction procedure is mathematically modeled into a matrix B, from which the projections without signal splitting can be generated invertedly. Furthermore, a penalized weighted least-square model with total variation(PWLSTV) is employed to denoise these projections, from which nPcT images with high accuracy are directly *** experiments demonstrate that this new algorithm is able to work with phase projections having any splitting distances. Moreover, results also reveal that nPcT images of higher signal-to-noise-ratio(SNR) could be reconstructed from projections having larger splitting distances. In summary, a novel model-driven nPcT image reconstruction algorithm with high accuracy and robustness is verified for the Lau interferometer-based hard x-ray nano-resolution phase contrast imaging.

关键词： splitting phase image reconstruction algorithm grating interferometer

Uniqueness on difference Operators of Meromorphic Functions of Infinite Order

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Acta Mathematica Sinica,English Series 2024年第2期40卷 511-527页

作者： Hui LI Ming Liang FANG Xiao YAO School of Science China University of Mining and TechnologyBeijing 100083P.R.China institute of Mathematics Academy of Mathematics and System SciencesChinese Academy of SciencesBeijing 100190P.R.China School of sciences Hangzhou Dianzi UniversityHangzhou 310012P.R.China School of mathematical sciences and LPMc Nankai UniversityTianjin 300071P.R.China

We investigate the uniqueness problems of meromorphic functions and their difference operators by using a new *** is proved that if a non-constant meromorphic function f shares a non-zero constant and ∞ counting multiplicities with its difference operators Δcf(z) and Δ_(c)^(2)f(z), thenΔcf(z)≡Δ_(c)^(2)f(z).In particular,we give a difference analogue of a result of *** method has two distinct features:(ⅰ) It converts the relations between functions into the corresponding *** makes it possible to deal with the uniqueness problem by linear algebra and combinatorics.(ⅱ) It circumvents the obstacle of the difference logarithmic derivative lemma for meromorphic functions of infinite order,since this method does not depend on the growth of the ***,the idea in this paper can also be applied to the case for several variables.

关键词： Uniqueness meromorphic functions difference operators infinite order

Point defects in 2-d liquid crystals with a singular potential: Profiles and stability

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Science china Mathematics 2024年

作者： Zhiyuan Geng Wei Wang Basque center for Applied Mathematics School of mathematical sciences Zhejiang University

We study radial symmetric point defects with degreek2in the 2-d disk or R2in the Q-tensor framework with a singular bulk energy, which is defined by Bingham closure. First, we obtain the existence of solutions for the profiles of radial symmetric point defects with degreek2in the 2-d disk or R2. Then, we prove that the solution is stable for |k| = 1 and unstable for |k| > 1. Some identities are derived and utilized throughout the proof of existence and stability/instability.

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dimension by dimension Finite Volume HWENO Method for Hyperbolic conservation Laws

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communications on Applied Mathematics and computation 2024年第1期6卷 605-624页

作者： Feng Zheng Jianxian Qiu college of Mathematics and Statistics Fujian Normal UniversityFuzhou350117FujianChina School of mathematical sciences and Fujian Provincial Key Laboratory of mathematical Modeling&High-Performance Scientific computing Xiamen UniversityXiamen361005FujianChina

In this paper,we propose a finite volume Hermite weighted essentially non-oscillatory(HWENO)method based on the dimension by dimension framework to solve hyperbolic conservation *** can maintain the high accuracy in the smooth region and obtain the high resolution solution when the discontinuity appears,and it is compact which will be good for giving the numerical boundary ***,it avoids complicated least square procedure when we implement the genuine two dimensional(2d)finite volume HWENO reconstruction,and it can be regarded as a generalization of the one dimensional(1d)HWENO *** numerical tests are performed to verify the high resolution and high accuracy of the scheme.

关键词： Finite volume dimension by dimension HWENO Hyperbolic conservation laws

The symmetric space,strong isotropy irreducibility and equigeodesic properties

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Science china Mathematics 2024年第1期67卷 129-148页

作者： Ming Xu Ju Tan School of mathematical sciences Capital Normal UniversityBeijing 100048China School of Microelectronics and data Science Anhui University of TechnologyMa'anshan 243032China

A smooth curve on a homogeneous manifold G/H is called a Riemannian equigeodesic if it is a homogeneous geodesic for any G-invariant Riemannian *** homogeneous manifold G/H is called Riemannian equigeodesic,if for any x∈G/H and any nonzero y∈Tx(G/H),there exists a Riemannian equigeodesic c(t) with c(0)=x and ■(0)=*** two notions can be naturally transferred to the Finsler setting,which provides the definitions for Finsler equigeodesics and Finsler equigeodesic *** prove two classification theorems for Riemannian equigeodesic spaces and Finsler equigeodesic spaces,***,a homogeneous manifold G/H with a connected simply connected quasi compact G and a connected H is Riemannian equigeodesic if and only if it can be decomposed as a product of Euclidean factors and compact strongly isotropy irreducible ***,a homogeneous manifold G/H with a compact semisimple G is Finsler equigeodesic if and only if it can be locally decomposed as a product,in which each factor is Spin(7)/G2,G2/SU (3) or a symmetric space of compact *** results imply that the symmetric space and the strongly isotropy irreducible space of compact type can be interpreted by equigeodesic *** an application,we classify the homogeneous manifold G/H with a compact semisimple G such that all the G-invariant Finsler metrics on G/H are *** suggests a new project in homogeneous Finsler geometry,i.e.,to systematically study the homogeneous manifold G/H on which all the G-invariant Finsler metrics satisfy a certain geometric property.

关键词： equigeodesic equigeodesic space flag manifold orbit type stratification symmetric space strongly isotropy irreducible space

Sequential Propagation of chaos for Mean-Field BSdE Systems

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chinese Annals of Mathematics,Series B 2024年第1期45卷 11-40页

作者： Xiaochen LI Kai dU Shanghai center for mathematical sciences Fudan UniversityShanghai 200433China. Shanghai Artificial Intelligence Laboratory 701 Yunjin RoadShanghai 200433China

A new class of backward particle systems with sequential interaction is proposed to approximate the mean-field backward stochastic differential *** is proven that the weighted empirical measure of this particle system converges to the law of the McKean-Vlasov system as the number of particles *** on the Wasserstein met-ric,quantitative propagation of chaos results are obtained for both linear and quadratic growth ***,numerical experiments are conducted to validate our theoretical results.

关键词： Backward propagation of chaos Particle system Sequential interaction McKean-Vlasov BSdE convergence rate