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Nonlinear Maps Satisfying Derivability on the Parabolic Subalgebras of the Full Matrix Algebras

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Journal of Mathematical Research and Exposition 2011年第5期31卷 791-800页

作者： zheng xin chen Yu E ZHAO School of Mathematics and Computer Science Fujian Normal University Fujian 350007 P. R. China School of Mathematics Science Qingdao University Shandong 266071 P. R. China

Let F be a field of characteristic 0, Mn（F） the full matrix algebra over F, t the subalgebra of Mn（F） consisting of all upper triangular matrices. Any subalgebra of Mn（F） containing t is called a parabolic subalgebra of Mn（F）. Let P be a parabolic subalgebra of Mn（F）. A map φ on P is said to satisfy derivability if φ（x·y） = φ（x）·y＋x·φ（y） for all x,y ∈ P, where φ is not necessarily linear. Note that a map satisfying derivability on P is not necessarily a derivation on P. In this paper, we prove that a map φ on P satisfies derivability if and only if φ is a sum of an inner derivation and an additive quasi-derivation on P. In particular, any derivation of parabolic subalgebras of Mn（F） is an inner derivation.

关键词： maps satisfying derivability parabolic subalgebras inner derivations quasi-derivations.

Pulmonary contusion mimicking COVID-19:A case report

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World Journal of Clinical Cases 2020年第8期8卷 1554-1560页

作者： Li-Ru chen zheng-xin chen Yang-Chun Liu Lei Peng Ye Zhang Quan Xu Qing Lin Yun-Ming Tao Hao Wu Sui Yin Ye-Ji Hu Department of Thoracic Surgery Jiangxi Provincial People’s Hospital Affiliated to Nanchang UniversityNanchang 330006Jiangxi ProvinceChina Department of Surgery Yongxin County People's HospitalJi’an 343400Jiangxi ProvinceChina

BACKGROUND Coronavirus disease 2019(COVID-19)is a major public health emergency with obvious characteristics of human-to-human transmission,and there are infective asymptomatic *** identification and proper management of patients with COVID-19 are *** in chest computed tomography(CT)can facilitate identifying newly infected ***,CT findings of some lung contusions are similar to those of COVID-19,as shown in the present *** SUMMARY A 46-year-old woman was admitted to hospital for backache and foot pain caused by a fall injury 1 d before *** was suspected of having COVID-19,since there was a confirmed COVID-19 case near her *** she had no fever,cough,chest tightness,difficult breathing,nausea,vomiting,or diarrhea,*** physical examination,the lower posterior chest of both sides showed dullness on percussion and moist rales at the end of inspiration on *** white blood cell count and lymphocyte count were 10.88×109/L and 1.04×109/L,*** performed on February 7,2020 revealed that both lungs were scattered with patchy ground-glass *** patient was diagnosed with pulmonary contusion with thoracic spinal fracture(T12),calcaneal fracture,and pelvic *** day 9 after conservative treatment,her condition was *** review of the chest CT,the previous shadows were significantly *** Differential diagnosis of lung contusion and COVID-19 must be *** conditions require effective prompt actions,especially COVID-19.

关键词： COVID-19 Pulmonary contusion Computed tomography Differential diagnosis Case report Ground-glass opacity

Optimized cardiac resynchronization therapy in patients with congestive heart failure

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Chinese Medical Journal 2007年第7期120卷 605-607页

作者： NIU Hong-xia HUA Wei ZHANG Shu SUN xin chen Ke-ping WANG Fang-zheng chen xin Center of Arrhythmia Diagnosis and Treatment Fuwai Hospital and Cardiovascular Institute Chinese Academy and Medical Sciences ＆ Peking Union Medical College Beijing 100037 China

Heart failure was a major and increasing public health problem, with an almost ＂epidemic＂ increase in the number of patients. Despite recent advances in pharmacotherapy, the prognosis remains poor. Cardiac resynchronization therapy （CRT）, by pacing right and left ventricles, has been proved to improve symptoms and reduce mortality for heart failure patients with cardiac dyssynchrony, However, 20% to 30% of patients did not respond to CRT. The good cardiac synchronicity before CRT and the remaining atrioventficular, inter- and intra-ventricular dyssynchrony after CRT may explain the non-response. New echocardiographic techniques, and in particular tissue Doppler imaging （TDI） analysis, has been proved to be a helpful tool in evaluating cardiac dyssynchrony, as well as in assessing the degree of cardiac resynchronization after biventricular device implantation. So, in this study, we optimized the pacing parameters to determine whether echo-guided optimizing of AV/VV delays would enhance the effect of CRT on cardiac function and synchronicity.

关键词： heart failure dysynchrony cardiac resynchronization therapy atrioventricular delay interventricular delay tissue Doppler imaging

Tubular algebras and affine Kac-Moody algebras

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Science China Mathematics 2007年第4期50卷 521-532页

作者： zheng-xin chen & Ya-nan LIN School of Mathematics and Computer Science, Pujian Normal University, Fuzhou 350007, China School of Mathematical Sciences, Xiamen University, Xiamen 361005, China 1. School of Mathematics and Computer Science Fujian Normal University Fuzhou 350007 China 2. School of Mathematical Sciences Xiamen University Xiamen 361005 China

The purpose of this paper is to construct quotient algebras L(A) 1 ? /I(A) of complex degenerate composition Lie algebras L(A) 1 ? by some ideals, where L(A 1 ? is defined via Hall algebras of tubular algebras A, and to prove that the quotient algebras L(A) 1 ? /I(A) are isomorphic to the corresponding affine Kac-Moody algebras. Moreover, it is shown that the Lie algebra L re(A) 1 ? generated by A-modules with a real root coincides with the degenerate composition Lie algebra L(A) 1 ? generated by simple A-modules.

关键词： tubular algebras affine Kac-Moody algebras Hall algebras degenerate composition Lie algebras modules with real root 16G70 17B67

Prognostic factors affecting the all-cause death and sudden cardiac death rates of post myocardial infarction patients with low left ventricular ejection fraction

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Chinese Medical Journal 2009年第7期122卷 802-806页

作者： DAI Shi-mo ZHANG Shu chen Ke-ping HUA Wei WANG Fang-zheng chen xin Center for Arrhythmia Diagnosis and Treatment Fu Wai Hospitaland Cardiovascular Institute Chinese Academy of MedicalSciences & Peking Union Medical College Beijing 100037 China

Background Post myocardial infarction （post-MI） patients with low left ventricular ejection fraction （LVEF） have been candidates for an implantable cardioverter-defibrillator （ICD） since the Multicenter Automatic Defibrillator Implantation Trail Ⅱ （MADIT Ⅱ）. However, due to the high costs of ICDs, widespread usage has not been accepted. Therefore, further risk stratification for post-MI patients with low LVEF may aid in the selection of patients that will benefit most from ICD treatment. Methods Four hundred and seventeen post-MI patients with low LVEF （≤35%） were enrolled in the study. All the patients received standard examination and proper treatment and were followed up to observe the all-cause death rate and sudden cardiac death （SCD） rate. Then COX proportional-hazards regression model was used to investigate the clinical factors which affect the all-cause death rate and SCD rate. Results Of 55 patients who died during （32±24） months of follow-up, 37 （67%） died suddenly. After adjusting for baseline clinical characteristics, multivariate COX proportional-hazards regression model identified the following variables associated with death from all causes： New York Heart Association （NYHA） heart failure class ≥Ⅲ （Hazard ratio： 2.361）, LVEF ≤20% （Hazard ratio： 2.514）, sustained ventricular tachycardia （Hazard ratio： 6.453）, and age 〉70 years （Hazard ratio： 3.116）. The presence of sustained ventricular tachycardia （Hazard ratio： 6.491） and age ≥70 years （Hazard ratio： 2.694） were specifically associated with SCD. Conclusions In the post-MI patients with low LVEF, factors as LVEF ≤20%, age ≥70 years, presence of ventricular tachycardia, and NYHA heart failure class ≥111 predict an adverse outcome. The presence of sustained ventricular tachycardia and age ≥70 years was associated with occurrence of SCD in these patients.

关键词： myocardial infarction death, sudden, cardiac heart failure

T(2,2,2,2)型tubular代数的合成代数

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数学学报（中文版） 2006年第4期49卷 883-892页

作者：陈正新福建师范大学数学与计算机科学学院

设A为有限域上的T(2,2,2,2)型tubular代数,它是tame遗传代数A0的单点扩张,也是tame遗传代数A∞的单点余扩张．记P0为预投射A0-模集合,L∞是预内射A∞-模集合,则P0,L∞(?)mod A记T=mod A＼(P0∪L∞)．本文证明A的合成代数C(A)具有形为P0... 详细信息

设A为有限域上的T(2,2,2,2)型tubular代数,它是tame遗传代数A0的单点扩张,也是tame遗传代数A∞的单点余扩张．记P0为预投射A0-模集合,L∞是预内射A∞-模集合,则P0,L∞(?)mod A记T=mod A＼(P0∪L∞)．本文证明A的合成代数C(A)具有形为P0·J·L∞的三角分解．

关键词： T(2,2,2,2)型tubular代数合成代数三角分解

n-th Schrödinger代数的Hom-李代数结构

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数学学报（中文版） 2024年第1期67卷 97-104页

作者：王玉陈正新福建师范大学数学与统计学院福州350117

李代数(L,[·])上的一个Hom-结构是满足下面条件的线性映射φ:L→L,[[x,y],φ(z)]+[[z,x],φ(y)]+[[y,z],φ(x)]=0,对任意的x,y,z∈L.进一步,如果φ是L的自同构(或导子),称φ为正则Hom-李结构(或导子双李代数Hom-结构).n-th Schrodinger代数是指单李代数s[2和n-th Heisenberg李代数hn的半直积.本文证明n-th Schrodinger代数的任意的Hom-结构一定是数乘映射与中心Hom-结构的和.进一步推出正则Hom-李代数结构一定是恒等映射,导子双李代数Hom-结构是零映射.

关键词： Hom-李代数结构正则Hom-李代数结构导子双李代数Hom-结构

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有限维单李代数的2-局部导子

数学学报（中文版） 2015年第5期58卷 847-852页

作者：赖璇陈正新福建师范大学数学与计算机科学学院福州350117

设F是特征为零的代数封闭域,g为F上有限维单李代数.g上的一个映射φ称为2-局部导子,如果对任意的x,y∈g,存在导子D_(x,y):g→g,使φ(x)=D_(x,y)(x),φ(y)=D_(x,y)(y).本文证明g上的所有2-局部导子一定是内导子.

关键词： 2-局部导子内导子有限维单李代数

AI-Enhanced Secure Data Aggregation for Smart Grids with Privacy Preservation

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Computers, Materials & Continua 2025年第1期82卷 799-816页

作者： Congcong Wang chen Wang Wenying zheng Wei Gu School of Software Nanjing University of Information Science and TechnologyNanjing210044China School of Information Science and Engineering Zhejiang Sci-Tech UniversityHangzhou310018China State Key Laboratory of Public Big Data Guizhou UniversityGuiyang550025China School of Computer Science and Technology(School of Artificial Intelligence) Zhejiang Sci-Tech UniversityHangzhou310018China School of Computer Science(School of Cyber Science and Engineering) Nanjing University of Information Science and TechnologyNanjing210044China

As smart grid technology rapidly advances,the vast amount of user data collected by smart meter presents significant challenges in data security and privacy *** research emphasizes data security and user privacy concerns within smart ***,existing methods struggle with efficiency and security when processing large-scale *** efficient data processing with stringent privacy protection during data aggregation in smart grids remains an urgent *** paper proposes an AI-based multi-type data aggregation method designed to enhance aggregation efficiency and security by standardizing and normalizing various data *** approach optimizes data preprocessing,integrates Long Short-Term Memory(LSTM)networks for handling time-series data,and employs homomorphic encryption to safeguard user *** also explores the application of Boneh Lynn Shacham(BLS)signatures for user *** proposed scheme’s efficiency,security,and privacy protection capabilities are validated through rigorous security proofs and experimental analysis.

关键词： Smart grid data security privacy protection artificial intelligence data aggregation