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THE FIELD ALGEBRA IN HOPF SPIN MODELS DETERMINED BY A HOPF*-SUBALGEBRA AND ITS SYMMETRIC STRUCTURE

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Acta Mathematica Scientia 2021年第3期41卷 907-924页

作者：魏晓敏蒋立宁辛巧玲 school of mathematics and statistics Beijing Institute of TechnologyBeijing 100081China school of mathematical sciences Tianjin Normal UniversityTianjin 300387China

Denote a finite dimensional Hopf C*-algebra by H, and a Hopf *-subalgebra of H by H1. In this paper, we study the construction of the field algebra in Hopf spin models determined by H1 together with its symmetry. More precisely, we consider the quantum double D(H, H_(1)) as the bicrossed product of the opposite dual Hopˆ of H and H1 with respect to the coadjoint representation, the latter acting on the former and vice versa, and under the non-trivial commutation relations between H1 and Ĥ we define the observable algebra AH1. Then using a comodule action of D(H, H1) on AH1, we obtain the field algebra FH1, which is the crossed product AH1⋊D(H,H_(1)), and show that the observable algebra AH1 is exactly a D(H, H1)-invariant subalgebra of FH1. Furthermore, we prove that there exists a duality between D(H, H1) and AH1, implemented by a*-homomorphism of D(H, H_(1)).

关键词： Comodule algebra field algebra observable algebra commutant duality

Multipliers,covers,and stem extensions for Lie superalgebras

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Frontiers of mathematics in China 2021年第4期16卷 979-995页

作者： Wende LIU Xingxue MIAO school of mathematics and statistics Hainan Normal UniversityHaikou 571158China school of mathematical sciences Harbin Normal UniversityHarbin 150025China

Suppose that the underlying field is of characteristic different from 2 and 3.We first prove that the so-called stem deformations of a free presentation of a finite-dimensional Lie superalgebra L exhaust all the maximal stem extensions of L,up to equivalence of extensions.Then we prove that multipliers and covers always exist for a Lie superalgebra and they are unique up to superalgebra isomorphisms.Finally,we describe the multipliers,covers,and maximal stem extensions of Heisenberg superalgebras and model filiform Lie superalgebras.

关键词： Multiplier cover stem extension Heisenberg superalgebra filiform Lie supleralgebra

Upper Bounds for the Spectral Radii of Nonnegative Tensors

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Journal of the Operations Research Society of China 2017年第1期5卷 83-98页

作者： Jing-Jing Jia Qing-Zhi Yang school of mathematical sciences and LPMC Nankai UniversityTianjin 300071China school of mathematics and statistics Kashi UniversityKashi 844006XinjiangChina

In this paper,we present several sharper upper bounds for the M-spectral radius and Z-spectral radius based on the eigenvalues of some unfolding matrices of nonnegative tensors.Meanwhile,we show that these bounds could be tight for some special tensors.For a general nonnegative tensor which can be transformed into a matrix,we prove the maximal singular value of this matrix is an upper bound of its Z-eigenvalues.Some examples are provided to show these proposed bounds greatly improve some existing ones.

关键词： Nonnegative tensor M-eigenvalue Z-eigenvalue Weakly symmetric Spectral radius

Classification of gradient steady Ricci solitons with linear curvature decay

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Science China mathematics 2020年第1期63卷 135-154页

作者： Yuxing Deng Xiaohua Zhu school of mathematics and statistics Beijing Institute of TechnologyBeijing 100081China school of mathematical sciences and BICMR Peking UniversityBeijing 100871China

In this paper,we study steady Ricci solitons with a linear decay of sectional curvature.In particular,we give a complete classification of 3-dimensional steady Ricci solitons and 4-dimensional K-noncollapsed steady Ri... 详细信息

关键词： Ricci flow steady Ricci solitons rotational symmetry

Modeling the early transmission of COVID-19 in New York and San Francisco using a pairwise network model

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Infectious Disease Modelling 2022年第1期7卷 212-230页

作者： Shanshan Feng Xiao-Feng Luo Xin Pei Zhen Jin Mark Lewis Hao Wang Department of mathematics North University of ChinaTaiyuanShanxi030051China College of mathematics Taiyuan University of TechnologyShanxiTaiyuan030024China Complex System Research Center Shanxi UniversityTaiyuan030006ShanxiChina Shanxi key laboratory of mathematical Techniques and Big Data Analysis on Disease Control and Prevention Shanxi UniversityTaiyuan030006ShanxiChina Department of mathematics and statistics sciences University of AlbertaEdmontonAlbertaT6G 2G1Canada Department of Biological sciences University of AlbertaEdmontonAlbertaT6G 2E9Canada

Classical epidemiological models assume mass action.However,this assumption is violated when interactions are not random.With the recent COVID-19 pandemic,and resulting shelter in place social distancing directives,mass action models must be modified to account for limited social interactions.In this paper we apply a pairwise network model with moment closure to study the early transmission of COVID-19 in New York and San Francisco and to investigate the factors determining the severity and duration of outbreak in these two cities.In particular,we consider the role of population density,transmission rates and social distancing on the disease dynamics and outcomes.Sensitivity analysis shows that there is a strongly negative correlation between the clustering coefficient in the pairwise model and the basic reproduction number and the effective reproduction number.The shelter in place policy makes the clustering coefficient increase thereby reducing the basic reproduction number and the effective reproduction number.By switching population densities in New York and San Francisco we demonstrate how the outbreak would progress if New York had the same density as San Francisco and vice-versa.The results underscore the crucial role that population density has in the epidemic outcomes.We also show that under the assumption of no further changes in policy or transmission dynamics not lifting the shelter in place policy would have little effect on final outbreak size in New York,but would reduce the final size in San Francisco by 97%.

关键词： COVID-19 Social network Quarantine Social distance Clustering coefficient

Recent Results on Recurrent Solutions and Limit Distributions of SDEs

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Communications in mathematical Research 2023年第3期39卷 476-500页

作者： Zhenxin Liu school of mathematical sciences and State key laboratory of Structural Analysis for Industrial Equipment Dalian University of TechnologyDalian 116024P.R.China

The limit distribution for homogeneous Markov processes is studied extensively and well understood,but it is not the case for inhomogeneous Markov processes.In this paper,we review some recent results on inhomogeneous Markov processes generated by non-autonomous stochastic(partial)differential equations(SDE in short).Under some suitable conditions,we show that the distribution of recurrent solutions of SDEs constitutes the limit distribution of the corresponding inhomogeneous Markov processes.

关键词： Recurrent solution stochastic differential equation invariant measure Markov process

Joint Analysis of Recurrent Event Data with a Dependent Terminal Event

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Journal of Systems Science & Complexity 2017年第6期30卷 1443-1458页

作者： YE Peng DAI Jiajia ZHU Jun school of statistics University of International Business and Economics school of mathematics and statistics Guizhou University Institute of Applied mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences

Recurrent event data frequently occur in many longitudinal studies, and the observation on recurrent events could be stopped by a terminal event such as death. This paper considers joint modeling and analysis of recurrent event and terminal event data through a common subject-specific frailty, in which the proportional intensity model is used for modeling the recurrent event process and the additive hazards model is used for modeling the terminal event time. Estimating equation approaches are developed for parameter estimation and asymptotic properties of the resulting estimators are established. In addition, some procedures are presented for model checking. The finite sample behavior of the proposed estimators is evaluated through simulation studies, and an application to a heart failure study is provided.

关键词： Additive hazards model estimating equation frailty recurrent events terminal event

HFD-exacerbated Metabolic Side Effects of Olanzapine Are Suppressed by ER Stress Inhibitor

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Current Medical Science 2023年第6期43卷 1116-1132页

作者： Yu-feng ZUO Bao-hua ZHANG Ming-rui GUO Ben-ben LI Bao-cui WANG Deng DUAN Yu-xin WANG Jing XI Meng HE Tao-lei SUN school of Chemistry Chemical Engineering and Life SciencesWuhan University of TechnologyWuhan430070China The National Clinical Research Center for Mental Disorders&Beijing key laboratory of Mental Disorders Beijing Anding Hospital&the Advanced Innovation Center for Human Brain ProtectionCapital Medical UniversityBeijing100069China hubei key laboratory of Nanomedicine for Neurodegenerative Diseases School of ChemistryChemical Engineering and Life ScienceWuhan University of TechnologyWuhan430070China

Objective Numerous schizophrenic patients are suffering from obesity primarily attributed to antipsychotic medication and poor dietary habits.This study investigated the progressive deterioration of olanzapine-induced metabolic disorders in the presence of a high-fat diet(HFD)and explored the involvement of endoplasmic reticulum(ER)stress.Methods Female Sprague-Dawley rats fed on a standard chow diet or HFD were treated with olanzapine(3 mg/kg/day)and the ER stress inhibitor 4-phenylbutyric acid(4-PBA,1 and 0.5 g/kg/day)for 8 days.Changes in body weight,food intake,and plasma lipids were assessed.Hepatic fat accumulation was evaluated using oil red O staining.Western blotting and immunofluorescence assays were employed to examine the expression of ER stress markers,NOD-like receptor pyrin domain-containing protein 3(NLRP3),and proopiomelanocortin(POMC)in the hypothalamus or liver.Results Compared to olanzapine alone,olanzapine+HFD induced greater weight gain,increased hyperlipidemia,and enhanced hepatic fat accumulation(P<0.05).Co-treatment with 4-PBA exhibited a dose-dependent inhibition of these effects(P<0.05).Further mechanistic investigations revealed that olanzapine alone activated ER stress,upregulated NLRP3 expression in the hypothalamus and liver,and downregulated hypothalamic POMC expression.The HFD exacerbated these effects by 50%–100%.Moreover,co-administration of 4-PBA dose-dependently attenuated the olanzapine+HFD-induced alterations in ER stress,NLRP3,and POMC expression in the hypothalamus and liver(P<0.05).Conclusion HFD worsened olanzapine-induced weight gain and lipid metabolic disorders,possibly through ER stress-POMC and ER stress-NLRP3 signaling.ER stress inhibitors could be effective in preventing olanzapine+HFD-induced metabolic disorders.

关键词： olanzapine high-fat diet obesity lipid metabolism endoplasmic reticulum stress proopiomelanocortin NOD-like receptor pyrin domain-containing protein 3

Finite Geometry and Deep Holes of Reed-Solomon Codes over Finite Local Rings

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Communications in mathematical Research 2022年第2期38卷 206-222页

作者： Jun Zhang Haiyan Zhou school of mathematical sciences Capital Normal UniversityBeijing 100048P.R.China Institute of mathematics School of Mathematical SciencesNanjing Normal UniversityNanjing 210023P.R.China

In this paper, we first propose the maximum arc problem, normal rational curve conjecture, and extensions of normal rational curves over finite local rings, analogously to the finite geometry over finite fields. We then study the deep hole problem of generalized Reed-Solomon (RS) codes over finite local rings. Several different classes of deep holes are constructed. The relationship between finite geometry and deep holes of RS codes over finite local rings are also studied.

关键词： Finite geometry finite local ring Reed-Solomon code covering radius deep hole