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A general mirror equivalence theorem for coset vertex operator algebras

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science China Mathematics 2024年第10期67卷 2237-2282页

作者： Robert McRae Yau mathematical sciences center Tsinghua University

We prove a general mirror duality theorem for a subalgebra U of a simple conformal vertex algebra A and its commutant V=ComA（U）.Specifically,we assume that ■ as a U■V-module,where the U-modules Uiare simple and distinct and are objects of a semisimple braided ribbon category of Umodules,and the V-modules Viare semisimple and contained in a（not necessarily rigid） braided tensor category of *** also assume U=ComA（V）.Under these conditions,we construct a braid-reversed tensor equivalence τ:uA→vA,where uAis the semisimple category of U-modules with simple objects Ui,i∈I,and vAis the category of V-modules whose objects are finite direct sums of *** particular,the V-modules Viare simple and distinct,and vAis a rigid tensor *** an application,we find a rigid semisimple tensor subcategory of modules for the Virasoro algebra at central charge 13+6p+6p-1,p∈Z≥2, which is braided tensor equivalent to an abelian 3-cocycle twist of the category of finite-dimensional ***,the Virasoro vertex operator algebra at central charge 13+6p+6p-1is the PSL2（C）-fixed-point subalgebra of a simple conformal vertex algebra w（-p）,analogous to the realization of the Virasoro vertex operator algebra at central charge 13-6p-6p-1as the PSL2（C）-fixed-point subalgebra of the triplet algebra W（p）.

关键词： vertex operator algebras coset conformal field theory braid-reversed tensor equivalence Virasoro algebra

Hybrid rogue waves and breather solutions on the double-periodic background for the Kundu-DNLS equation

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Communications in Theoretical Physics 2024年第5期76卷 33-48页

作者： DongZhu Jiang Zhaqilao College of Mathematics science Inner Mongolia Normal UniversityHohhot 01022China center for Applied mathematical science Inner MongoliaHohhot 010022China

In this paper,by using the Darboux transformation(DT)method and the Taylor expansion method,a new nth-order determinant of the hybrid rogue waves and breathers solution on the double-periodic background of the Kundu-DNLS equation is constructed when n is *** and rogue waves can be obtained from this determinant,*** to this,the hybrid rogue waves and breathers solutions on the different periodic backgrounds are given explicitly,including the single-periodic background,the double-periodic background and the plane wave background by selecting different *** addition,the form of the obtained solutions is summarized.

关键词： double-periodic background hybrid rogue waves and breather darboux transformation Kundu-DNLS equation

Compressed Data Separation via ℓ_(q)-Split Analysis with ℓ_(∞)-Constraint

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Acta Mathematica Sinica,English Series 2024年第7期40卷 1655-1673页

作者： Ming Yang Gu Song Li Jun Hong Lin School of mathematical science Zhejiang UniversityHangzhou310027P.R.China center for Data science Zhejiang UniversityHangzhou310027P.R.China

In this paper,we study compressed data separation(CDS)problem,i.e.,sparse data separation from a few linear random *** propose the nonconvex ℓ_(q)-split analysis with ℓ_(∞)-constraint and 0 详细信息

In this paper,we study compressed data separation(CDS)problem,i.e.,sparse data separation from a few linear random *** propose the nonconvex ℓ_(q)-split analysis with ℓ_(∞)-constraint and 0

关键词： Data separation ℓ_(q)-split analysis Dantzig selector frames restricted isometry property compressed sensing

The pseudospectrum and spectrum (in)stability of quantum corrected Schwarzschild black hole

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science China(Physics,Mechanics & Astronomy) 2024年第10期Mechanics & Astronomy) .卷 59-79页

作者： Li-Ming Cao Jia-Ning Chen Liang-Bi Wu Libo Xie Yu-Sen Zhou Peng Huanwu center for Fundamental Theory Interdisciplinary center for Theoretical Study and Department of Modern Physics University of Science and Technology of China School of Fundamental Physics and mathematical sciences Hangzhou Institute for Advanced StudyUCAS

In this study, we investigate the pseudospectrum and spectrum(in)stability of quantum corrected Schwarzschild black ***, we use the hyperboloidal framework to cast the quasinormal mode(QNM) problem into an eigenvalue problem associated with a non-selfadjoint operator, and then the spectrum and pseudospectrum are depicted. Besides, the invariant subspace method is exploited to improve the computational efficiency for pseudospectrum. The investigation into the spectrum(in)stability entails two main aspects. On the one hand, we calculate the spectra of the quantum corrected black hole, then by the means of the migration ratio, the impact of the quantum correction effect on the Schwarzschild black hole has been *** results indicate that the so-called “migration ratio instability” will occur for small black holes with small angular momentum number l. In the eikonal limit, the migration ratios remain the same for each overtone. On the other hand, we study the spectrum(in)stability of the quantum corrected black hole by directly adding some particular perturbations into the effective potential,where perturbations are located at the event horizon and null infinity, respectively. There are two interesting observations under the same perturbation energy norm. First, perturbations at infinity are more capable of generating spectrum instability than those at the event horizon. Second, we find that the peak distribution can lead to the instability of QNM spectrum more efficiently than the average distribution.

关键词： quasinormal modes pseudospectrum hyperboloidal coordinate

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NSNO:Neumann Series Neural Operator for Solving Helmholtz Equations in Inhomogeneous Medium

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Journal of Systems science & Complexity 2024年第2期37卷 413-440页

作者： CHEN Fukai LIU Ziyang LIN Guochang CHEN Junqing SHI Zuoqiang Department of mathematical sciences Tsinghua UniversityBeijing 100084China Yau mathematical sciences center Tsinghua UniversityBeijing 100084China Yanqi Lake Beijing Institute of mathematical sciences and Applications Beijing 101408China

In this paper,the authors propose Neumann series neural operator(NSNO)to learn the solution operator of Helmholtz equation from inhomogeneity coefficients and source terms to *** equation is a crucial partial differential equation(PDE)with applications in various scientific and engineering ***,efficient solver of Helmholtz equation is still a big challenge especially in the case of high ***,deep learning has shown great potential in solving PDEs especially in learning solution *** by Neumann series in Helmholtz equation,the authors design a novel network architecture in which U-Net is embedded inside to capture the multiscale *** experiments show that the proposed NSNO significantly outperforms the state-of-the-art FNO with at least 60%lower relative L^(2)-error,especially in the large wavenumber case,and has 50%lower computational cost and less data ***,NSNO can be used as the surrogate model in inverse scattering *** tests show that NSNO is able to give comparable results with traditional finite difference forward solver while the computational cost is reduced tremendously.

关键词： Helmholtz equation inverse problem neumann series neural network solution operator

Relation Between the Eventual Continuity and the E-property for Markov-Feller Semigroups

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Acta Mathematicae Applicatae Sinica 2024年第1期40卷 1-16页

作者： Yong Liu Zi-yu Liu LMAM School of Mathematical SciencePeking UniversityBeijing100871China

We investigate some relations between two kinds of semigroup regularities, namely the e-property and the eventual continuity, both of which contribute to the ergodicity for Markov processes on Polish *** precisely, we prove that for Markov-Feller semigroup in discrete time and stochastically continuous MarkovFeller semigroup in continuous time, if there exists an ergodic measure whose support has a nonempty interior,then the e-property is satisfied on the interior of the support. In particular, it implies that, restricted on the support of each ergodic measure, the e-property and the eventual continuity are equivalent for the discrete-time and the stochastically continuous continuous-time Markov-Feller semigroups.

关键词： Markov-Feller semigroup ergodicity e-property eventual continuity

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

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science China Mathematics 2024年第11期67卷 2515-2540页

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

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

关键词： radial symmetric point defects singular bulk potential Bingham closure stability

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Q-BioLiP:A Comprehensive Resource for Quaternary Structure-based Protein-ligand Interactions

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Genomics, Proteomics & Bioinformatics 2024年第1期22卷 151-159页

作者： Hong Wei Wenkai Wang Zhenling Peng Jianyi Yang School of mathematical sciences Nankai UniversityTianjin 300071China MOE Frontiers science center for Nonlinear Expectations Research Center for Mathematics and Interdisciplinary SciencesShandong UniversityQingdao 266237China

Since its establishment in 2013,BioLiP has become one of the widely used resources for protein-ligand ***,several known issues occurred with it over the past *** example,the protein-ligand interactions are represented in the form of single chain-based tertiary structures,which may be inappropriate as many interactions involve multiple protein chains(known as quaternary structures).We sought to address these issues,resulting in Q-BioLiP,a comprehensive resource for quaternary structure-based protein-ligand *** major features of Q-BioLiP include:(1)representing protein structures in the form of quaternary structures rather than single chain-based tertiary structures;(2)pairing DNA/RNA chains properly rather than separation;(3)providing both experimental and predicted binding affinities;(4)retaining both biologically relevant and irrelevant interactions to alleviate the wrong justification of ligands’biological relevance;and(5)developing a new quaternary structure-based algorithm for the modelling of protein-ligand complex *** these new features,Q-BioLiP is expected to be a valuable resource for studying biomolecule interactions,including protein-small molecule interaction,protein-metal ion interaction,protein-peptide interaction,protein-protein interaction,protein-DNA/RNA interaction,and RNA-small molecule interaction.Q-BioLiP is freely available at https://***/Q-BioLiP/.

关键词： Protein-ligand interaction Quaternary structure Protein-ligand binding site Protein-protein interaction Binding affinity

Trace inequalities, isocapacitary inequalities, and regularity of the complex Hessian equations

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science China Mathematics 2024年第3期67卷 557-576页

作者： Jiaxiang Wang Bin Zhou Beijing International center for mathematical Research Peking UniversityBeijing 100871China School of mathematical sciences Peking UniversityBeijing 100871China

In this paper, we study the relations between trace inequalities(Sobolev and Moser-Trudinger types), isocapacitary inequalities, and the regularity of the complex Hessian and Monge-Amp`ere equations with respect to a general nonnegative Borel measure. We obtain a quantitative characterization for these relations through the properties of the capacity-minimizing functions.

关键词： complex Monge-Ampère equations plurisubharmonic functions Sobolev inequality Moser-Trudinger inequality