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Gelfand-Kirillov Dimension and Reducibility of Scalar Generalized Verma Modules for Classical Lie Algebras

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Acta Mathematica Sinica,English Series 2024年第3期40卷 658-706页

作者： zhan qiang bai Jing JIANG School of Mathematical Sciences Soochow UniversitySuzhou 215006P.R.China E-mail:zqbai@*** jjsd6514@***

Let g be a classical complex simple Lie algebra and q be a parabolic *** M be a generalized Verma module induced from a one dimensional representation of *** M is called a scalar generalized Verma *** this paper,we will determine the reducibility of scalar generalized Verma modules associated to maximal parabolic subalgebras by computing explicitly the Gelfand-Kirillov dimension of the corresponding highest weight modules.

关键词： Generalized Verma module Gelfand-Kirillov dimension Young tableau

Gelfand–Kirillov Dimension and Reducibility of Scalar Generalized Verma Modules

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Acta Mathematica Sinica,English Series 2019年第11期35卷 1854-1860页

作者： zhan qiang bai Wei XIAO School of Mathematical Sciences Soochow UniversitySuzhou 215006P.R.China College of Mathematics and statistics Shenzhen Key Laboratory of Advanced Machine Learning Applications Shenzhen UniversityShenzhen 518060P.R.China

The Gelfand–Kirillov dimension is an invariant which can measure the size of infinitedimensional algebraic structures. In this article, we show that it can also measure the reducibility of scalar generalized Verma modules. In particular, we use it to determine the reducibility of scalar generalized Verma modules associated with maximal parabolic subalgebras in the Hermitian symmetric case.

关键词： Gelfand–Kirillov dimension generalized Verma module reducibility

Irreducible Representations of GL_(n)(C)of Minimal Gelfand-Kirillov Dimension

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Acta Mathematica Sinica,English Series 2024年第3期40卷 639-657页

作者： zhan qiang bai Yang Yang CHEN Dong Wen LIU Bin Yong SUN School of Mathematical Sciences Soochow UniversitySuzhou 215006P.R.China School of Sciences JiangnanUniversityWui214122P.R.China School of Mathematical Sciences Zhejiang UniversityHangzhou 310058P.R.China Institute for Advanced Study in Mathematics Zhejiang UniversityHangzhou 310058P.R.China

In this article,by studying the Bernstein degrees and Goldie rank polynomials,we es-tablish a comparison between the irreducible representations of G=GL_(n)(C)possessing the minimal Gelfand-Kirillov dimension and those induced from finite-dimensional representations of the maximal parabolic subgroup of G of type(n-1,1).We give the transition matrix between the two bases for the corresponding coherent families.

关键词： Bernstein degree coherent continuation Gelfand-Kirillov dimension

Effect of electric pulse on the crystal structure of solidified copper ingots

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International Journal of Minerals,Metallurgy and Materials 2013年第6期20卷 556-562页

作者： Li-hua Zhao Li zhan Hao bai Da-qiang Cang State Key Laboratory of Advanced Metallurgy University of Science and Technology Beijing School of Metallurgical and Ecological Engineering University of Science and Technology Beijing Beijing Shougang Steel Co. Ltd.Sales Company

To obtain advanced quality pure copper, the microstructure of solidified copper was optimized by imposing electric pulse on liquid copper in this study. Experiments were performed to determine the effect of electric pulse voltage, arrangement mode of electrodes, and energy input on the microstructure of solidified copper. The results show that, when the energy input of electric pulse is bigger than 28.95 kJ per ton copper, the percent of fine grains increases noticeably with the increase of energy input; but when the energy input of electric pulse is smaller than 28.95 kJ per ton copper, the percent of fine grains decreases with the increase of energy input. The influence order of above factors on grain refinement is electric pulse voltage 〉 arrangement mode of electrodes 〉 energy input. According to the above experimental results, the optimum process conditions are chosen as the voltage being 400 V and the energy input greater than 28.95 kJ per ton copper. Meanwhile, the best arrangement mode of electrodes should be that, one electrode is immerged in the middle of liquid copper in the crystallizer, and the other is connected to the inner wall of the crystallizer, which is divided into two electrode poles for the symmetrical electric field distribution.

关键词： copper solidification crystal structure electric pulse

Integrating lipidomics and gut microbiota to study the anti-hyperlipidemia effect of Sargentodoxae Caulis extract

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Traditional Medicine Research 2025年第1期10卷 1-11页

作者： Xiao-Xiao zhang Li Jia Xiu-Jun zhan Charity Ngina Qing-Rui zhang Xiao-Ge Li Qi-Bao Jiang Shi bai Miao-Miao Jiang National Key Laboratory of Chinese Medicine Modernization Tianjin University of Traditional Chinese MedicineTianjin 301617China Haihe Laboratory of Modern Chinese Medicine Tianjin 301617China School of Medicine Taizhou UniversityTaizhou 318000China.

Background:Sargentodoxae Caulis(SC)is the vine stem of Sargentodoxa Cuneata(Oliv.)Rehd.&*** in ***,and it in traditional Chinese medicine has been known for promoting blood circulation and removing blood stasis as recorded in the ancient book“Illustrated Classics of Materia Medica”.It has been used effectively to treat blood stasis too in modern clinical ***,the anti-hyperlipidemia effect of SC is not fully *** paper aims at exploring the use of SC stems to improve the balance of blood lipids in the body,and its new role in treating ***:The effects of SC extract on hyperlipidemia were explored by combining lipidomics and gut ***,we explored the potential mechanism of SC in treating hyperlipidemia by pathway ***:The results showed that the stem extract of SC could restore the physiological and biochemical indices of hyperlipidemia in mice,as well as repair the morphological and structural damage to *** to the Model group,the SC extract significantly reduced the liver index,epididymal fat index,and Lee’s *** also significantly decreased serum levels of total cholesterol,triglycerides,low-density lipoprotein cholesterol,peroxisome proliferator-activated receptor gamma(PPAR-γ),D-lactate,and free fatty acids,while significantly increasing the relative content of peroxisome proliferator-activated receptor alpha(PPAR-α).These changes were statistically ***-targeted lipidomics,based on LC-MS,were utilized to investigate the lipid metabolism characteristics in serum,liver,and epididymal fat of the *** was observed that,compared to the blank group,the Model group exhibited significant changes primarily in glycerol lipids and *** treatment group also displayed alterations in these lipids.A total of 38,81,and 27 differential lipids were identified in serum,liver,and epididymal fat samples,*** these,14 common differenti

关键词： hyperlipidemia Sargentodoxae Caulis lipidomics intestinal flora

Anomalous Dissipative Quantum Harmonic Oscillator

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Communications in Theoretical Physics 2008年第1期49卷 137-142页

作者： bai zhan-Wu Department of Mathematics and Physics North China Electric Power University Baoding 071003 China

We investigate the low-temperature statistical properties of a harmonic oscillator coupled to a heat bath, where the low-frequency spectrum vanishes. We obtain the exact result of the zero point energy. Due to the low frequency shortage of environmental oscillators＇ spectral density, the coordinate and momentum correlation functions decay as T^-4 arid T^-6 respectively at zero temperature, where T is the correlation time. The low-temperature behavior of the mean energy does not violate the third law of thermodynamics, but differs largely from the Ohmic spectrum case.

关键词： harmonic oscillator harmonic velocity noise zero point energy correlation function the thirdlaw of thermodynamics

Kinematics-based four-state trajectory tracking control of a spherical mobile robot driven by a 2-DOF pendulum

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Chinese Journal of Aeronautics 2019年第6期32卷 1530-1540页

作者： Wei LI qiang zhan Robotics Institute Beihang UniversityBeijing 100083China Ecole Centrale de Pékin Beihang UniversityBeijing 100083China

Spherical mobile robot has compact structure, remarkable stability, and flexible motion,which make it have many advantages over traditional mobile robots when applied in those unmanned environments, such as outer planets. However, spherical mobile robot is a special highly under-actuated nonholonomic system, which cannot be transformed to the classic chained form. At present, there has not been a kinematics-based trajectory tracking controller which could track both the position states and the attitude states of a spherical mobile robot. In this paper, the four-state(two position states and two attitude states) trajectory tracking control of a type of spherical mobile robot driven by a 2-DOF pendulum was studied. A controller based on the shunting model of neurodynamics and the kinematic model was deduced, and its stability was demonstrated with Lyapunov’s direct method. The control priorities of the four states were allocated according to the magnification of each state tracking error in order to firstly ensure the correct tracking of the position states. The outputs(motor speeds) of the controller were regulated according to the maximum speeds and the maximum accelerations of the actuation motors in order to solve the speed jump problem caused by initial state errors, and continuous and bounded outputs were obtained. The effectiveness including the anti-interference ability of the proposed trajectory tracking controller was verified through MATLAB simulations.

关键词： Kinematics Lyapunov methods Neurodynamics Nonholonomic systems Spherical mobile robot Trajectory tracking

Belching,regurgitation,chest tightness and dyspnea:Not gastroesophageal reflux disease but asthma

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World Journal of Gastroenterology 2015年第5期21卷 1680-1683页

作者： Jing-Xi zhang Xian-Bao zhan Chong bai qiang Li Department of Respiratory diseases Changhai Hospitalthe Second Military Medical University Department of Gastroenterology Changhai Hospitalthe Second Military Medical University

Belching is a common symptom of gastroesophageal reflux *** the symptoms are not relieved after anti-reflux treatment,another etiology should be ***,we report a case of a 43-yearold man who presented with belching,regurgitation,chest tightness and dyspnea for 18 mo,which became gradually more *** examination suggested superficial ***-four-houresophageal pH monitoring showed that the Demeester score was 11.4,in the normal ***-resolution manometry showed that integrated relaxation pressure and intrabolus pressure were higher than normal(20 mm Hg and 22.4 mm Hg,respectively),indicating gastroesophageal junction outflow tract *** function test showed severe obstructive ventilation dysfunction [forced expiratory volume in 1 second(FEV1)/forced vital capacity 32%,FEV1 was 1.21 L,occupying 35% predicted value after salbuterol inhalation],and positive bronchial dilation test(△FEV1 260 m L,△FEV1% 27%).Skin prick test showed Dermatophagoides farinae(++),house dust mite(++++),and shrimp protein(++).Fractional exhaled nitric oxide measurement was 76 *** the symptoms were alleviated completely and pulmonary function increased after combination therapy with corticosteroids and long-acting β*** asthma was eventually diagnosed by laboratory tests and the effect of anti-asthmatic treatment,therefore,physicians,especially the Gastrointestinal physicians,should pay attention to the belching symptoms of asthma.

关键词： Asthma Gastroesophageal reflux disease

Role of the Bath Spectrum in the Specific Heat Anomalies of a Damped Oscillator

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Chinese Physics Letters 2012年第6期29卷 54-57页

作者： bai zhan-Wu Department of Mathematics and Physics North China Electric Power UniversityBaoding 071003

The specific heat anomalies are analytically studied in the system in which a harmonic oscillator couples to a heat bath with harmonic *** physical explanation leads to a general spectral dependence of the specific heat *** condition of a dip appearance and the behaviors of the dip can be given according to the shape of the bath's power spectrum by employing the minimal heat bath model.

关键词： harmonic oscillator explanation