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Polynomials,Higher Order Sobolev Extension Theorems and Interpolation Inequalities on Weighted Folland-Stein Spaces on Stratified Groups

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Acta Mathematica Sinica,English Series 2000年第3期16卷 405-444页

作者： guozhen lu department of mathematics,wayne state university,detroit,mi 48202,usa department of mathematics Wayne State University Detroit USA

This paper consists of three main *** of them is to develop local and global Sobolev interpolation inequalities of any higher order for the nonisotropic Sobolev spaces on stratified nilpotent Lie *** the extensive research after Jerison’s work[3]on Poincaré-type inequalities for Hrmander’s vector fields over the years,our results given here even in the nonweighted case appear to be *** interpolation inequalities have crucial applications to subelliptic or parabolic PDE’s involving vector *** main tools to prove such inequalities are approximating the Sobolev func- tions by polynomials associated with the left invariant vector fields on *** very useful properties for polynomials associated with the functions are given here and they appear to have independent interests in their own *** the existence of such polynomials is the second main part of this *** results of these two parts have been announced in the author’s paper in Mathematical Research Letters[38]. The third main part of this paper contains extension theorems on anisotropic Sobolev spaces on stratified groups and their applications to proving Sobolev interpolation inequalities on(εδ)domains. Some results of weighted Sobolev spaces are also given *** construct a linear extension operator which is bounded on different Sobolev spaces *** particular,we are able to construct a bounded linear extension operator such that the derivatives of the extended function can be controlled by the same order of derivatives of the given Sobolev *** are stated and proved for weighted anisotropic Sobolev spaces on stratified groups.

关键词： Poincaré inequalities Extension theorems Interpolation inequalities Anisotropic Sobolev spaces A_p weights (ε,δ)domains Vector fields Polynomials on stratified groups

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Harnessing the potential of hydrogels for advanced therapeutic applications: current achievements and future directions

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Signal Transduction and Targeted Therapy 2024年第8期9卷 3176-3241页

作者： Pelin lu Dongxue Ruan Meiqi Huang mi Tian Kangshun Zhu Ziqi Gan Zecong Xiao Nanomedicine Research Center The Third Affiliated Hospital of Sun Yat-sen UniversityGuangzhou 510630PR China department of minimally Invasive Interventional Radiology and Laboratory of Interventional RadiologyThe Second Affiliated Hospital of Guangzhou Medical UniversityGuangzhou 510260PR China state Key Laboratory of Respiratory Disease National Clinical Research Center for Respiratory DiseaseNational Center for Respiratory MedicineDepartment of Respiratory and Critical Care MedicineGuangzhou Institute for Respiratory HealthThe First Affiliated Hospital of Guangzhou Medical UniversityGuangzhou 510120PR China department of Stomatology Chengdu Second People's HospitalChengdu 610021PR China Hospital of Stomatology Guangdong Provincial Key Laboratory of StomatologyGuanghua School of StomatologySun Yat-sen UniversityGuangzhou 510055PR China

The applications of hydrogels have expanded significantly due to their versatile,highly tunable properties and breakthroughs in biomaterial *** this review,we cover the major achievements and the potential of hydrogels in therapeutic applications,focusing primarily on two areas:emerging cell-based therapies and promising non-cell therapeutic *** the context of cell therapy,we discuss the capacity of hydrogels to overcome the existing translational challenges faced by mainstream cell therapy paradigms,provide a detailed discussion on the advantages and principal design considerations of hydrogels for boosting the efficacy of cell therapy,as well as list specific examples of their applications in different disease *** then explore the potential of hydrogels in drug delivery,physical intervention therapies,and other non-cell therapeutic areas(e.g.,bioadhesives,artificial tissues,and biosensors),emphasizing their utility beyond mere delivery ***,we complement our discussion on the latest progress and challenges in the clinical application of hydrogels and outline future research directions,particularly in terms of integration with advanced biomanufacturing *** review aims to present a comprehensive view and critical insights into the design and selection of hydrogels for both cell therapy and noncell therapies,tailored to meet the therapeutic requirements of diverse diseases and situations.

关键词： directions overcome breakthrough

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计及需求响应和季节性氢储的多微网合作运行策略

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三峡大学学报（自然科学版） 2024年第4期46卷 96-104页

作者：徐艳春宋文宇汪平王霖 mi lu 梯级水电站运行与控制湖北省重点实验室(三峡大学) 湖北宜昌443002 国家电网湖北省电力有限公司武汉供电公司洪山供电中心武汉430000 德克萨斯农工大学电气与计算机工程学院美国德克萨斯州卡城77840

为促进可再生能源的消纳,解决综合能源系统中源荷季节性不平衡的问题,提出一种计及需求响应和季节性氢储的多微网合作运行策略.首先对综合能源系统中的季节性氢储系统和用户的需求响应行为进行建模,随后通过电力通道将多个微网连接成多... 详细信息

为促进可再生能源的消纳,解决综合能源系统中源荷季节性不平衡的问题,提出一种计及需求响应和季节性氢储的多微网合作运行策略.首先对综合能源系统中的季节性氢储系统和用户的需求响应行为进行建模,随后通过电力通道将多个微网连接成多微网系统.由于各个微网属于不同的利益主体,微网与用户之间也存在利益交互,因此引入合作-主从博弈框架对本文多利益主体博弈进行描述,其中主从博弈中多微网系统为领导者,能源用户为跟随者.在对主从博弈求解完成后,最后提出一种议价能力对各微网联盟的贡献进行描述,利用纳什议价对各微网的合作利益进行合理分配.算例表明,本文策略可有效促进可再生能源的消纳,降低用户购能成本和促进各微网能源传输.

关键词：季节性氢存储需求响应主从合作博弈纳什谈判多微网系统

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EMBEDDING THEOREMS ON CAMPANATO-MORREY SPACES FOR VECTOR FIELDS OF HoRMANDER TYPE

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Analysis in Theory and Applications 1998年第1期14卷 69-80页

作者： guozhen lu (Wright state university, usa) department of mathematics and Statistics Wright State University Dayton USA

This paper deals with embedding theorems on Campanato-Marrey spaces formed by degenerate vector fields, which include Honnander and Grushin type of vector fields. These embedding theorems are somewhat different from the known Poincare estimates. The main ingredients of the proofs rely on the fractional maximal functions. These results evidently have applications to the regularity of subelliptic PDE.

关键词： EMBEDDING THEOREMS ON CAMPANATO-MORREY SPACES FOR VECTOR FIELDS OF HoRMANDER TYPE Math

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A critical Trudinger-Moser inequality involving a degenerate potential and nonlinear Schrodinger equations

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Science China mathematics 2021年第7期64卷 1391-1410页

作者： lu Chen guozhen lu Maochun Zhu School of mathematics and Statistics Beijing Institute of TechnologyBeijing 100081China department of mathematics University of ConnecticutStorrsCT 06269USA School of Mathematical Sciences Institute of Applied System AnalysisJiangsu UniversityZhenjiang 212013China

The classical critical Trudinger-Moser inequality in R^(2)under the constraint∫_(R_(2))(|▽u|^(2)+|u|^(2))dx≤1 was established through the technique of blow-up analysis or the rearrangement-free argument:for anyτ>0,it holds that sup u∈H^(1)(r^(2)fR^(2)(τ|U|^(2)+|▽u|^(2)dx≤1∫_(R^(2)(E^4π|u|^(2)-1)dx≤C(τ)state solutions to the following Sciridinger equations with critical exponeitial growth:-Δu+V(x)u=f u)in R^(2),(0.1)where V(x)≥0 and vanishes on an open set of R^(2)and f has critical exponential *** a positive constant lower bound for the potential V(x)(e.g.,the Rabinowitz type potential)has been the standard assumption when one deals with the existence of solutions to the above Schrodinger equations when the nonlinear term has the exponential *** existence result seems to be the first one without this standard assumption.

关键词： Trudinger-Moser inequalities degenerate potential ground state solutions Schrodinger equations Nehari manifold

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On second order minimal Lagrangian submanifolds in complex space forms

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Science China mathematics 2005年第11期48卷 1505-1516页

作者： DONG Yuxin lu guozhen Institute of mathematics Fudan University Shanghai 200433 China Department of Mathematics Wayne State University Detroit MI48202 USA

In this paper, we determine all second order minimal Lagrangian submanifolds in complex space forms whose cubic forms have the largest non-trivial continuous symmetries. We describe these minimal Lagrangian submanifol... 详细信息

关键词： exterior differential systems,minimal Lagrangian submanifold

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Mast cell activation syndrome:An up-to-date review of literature

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World Journal of Clinical Pediatrics 2024年第2期13卷 104-113页

作者： ÖnerÖzdemir Gökçe Kasımoğlu Ayşegül Bak Hüseyin Sütlüoğlu Süreyya Savaşan department of Pediatric Allergy and Immunology Sakarya UniversitySakaryaAdapazarı54100Türkiye department of Pediatrics Sakarya UniversitySakaryaAdapazarı54100Türkiye department of Pediatrics Kocaeli City HospitalKocaeli 50123Türkiye department of Pediatrics Children’s Hospital of MichiganHematology/OncologyCentral Michigan University College of MedicineMount PleasantMI 48859United States Barbara Ann Karmanos Cancer Institute Wayne State UniversityDetroitMI 12345United States

Mast cells are a subtype of white blood cells and are involved in the immune *** cells contain many chemical substances called mediators,which are involved in the allergic *** fact that mast cells play a role in many events that require urgent intervention,especially anaphylaxis,has led to a more detailed study of these *** diseases also caused by dysfunctions of mast cells have been examined in many *** instance,mast cell activation syndrome is known as an augmented number of cells due to decreased cell death,resulting in clinical symptoms affecting many *** main common symptoms include flushing,hypotension,urticaria,angioedema,headache,vomiting and *** the underlying mechanism is not yet clearly known,we aim to review the literature in a broad perspective and bring together the existing knowledge in the light of the literature due to the diversity of its involvement in the body and the fact that it is a little known syndrome.

关键词： Mast cell Mast cell activation syndrome Tryptase Histamine

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Low dose and short-term therapy of tibolone reduces the cardiovascular disease risk in postmenopausal women

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生殖医学杂志 2004年第Z1期13卷 8-13页

作者： Ye Bi-lu Cheng Jing Ye Lian department of Reproductive Medicine the 1st Hospital of Wenzhou Medical College Wenzhou Zhejiang 325000 China Department of Reproductive Medicine the 1st Hospital of Wenzhou Medical College Wenzhou Zhejiang 325000 China Department of Reproductive Medicine the 1st Hospital of Wenzhou Medical College Wenzhou Zhejiang 325000 China department of Obstetrics & Gynecology Wayne State UniversityDetroit MI 48201USA

Objective:To investigate the effects of low dose tibolone short-term therapy on clinic, endocrine and markers of cardiovascular disease in healthy postmenopausal ***: A prospective study involved a total of 42 eligible postmenopausal women. 22 cases as group A and 20 cases as group B. Complete baseline work-up including Kupperman score,body mass index (Bmi), gonadotropin (FSH, LH), estrogen (E2), testosterone (T), sex hormone binding globulin (SHBG), plasminogen activator inhibitor type 1 (PAI-1), tissue plasminogen activator (tPA), high-sensitivity C-response protein (hs-CRP), nitrogen oxide (NO)and fasting lipid, glucose(FPG), insulin(FINS) were performed in all subjects. Postmenopausal women in group A were treated with 1.25 mg tibolone daily. Women in group B were treated with 0. 625 mg tibolone daily. Women both in group A and group B were given calcium 600 mg with vitamin D 125IU per day. At the end of the 12-weeks therapy, subjects were re-evaluated and above parameters were ***:No significant differences between group A and group B were found at ***-eight cases (fourteen cases in each group) completed the study. Kupperman score decreased from (22.1±8.0) and (25.4±7.5) to (7.7±4.5) and (5.2±4.5) and plasminogen activator inhibitor type 1 decreased from (95.8±32.4)μg/L and (102.9±42.6)μg/L to (72.2±39.6)μg/L and (79.9±30. 1) μg/L significantly in group A and group B respectively after treatment. In group A, Blood pressure decreased significantly from (120 ± 10)/(83 ± 6) mmHg to (110±14)/(77± 9) mmHg (P＜0.05), testosterone increased significantly from (0. 6 ±0. 4)nmol/L to (1.3 ± 1.1) nmol/L (P＜0. 05), free testosterone increased from (0. 001 ±0. 002)nmol/L to (0. 003±0. 003) nmol/L significantly (P＜0.01), SHBG decreased from (7.6±4. 9)nmol/L to (4. 3±2.9) nmol/L significantly (P＜0.05), total cholesterol decreased from (5.4±0. 8) mmol/L to (5.0±0.8) mmol/L significantly (P＜0.01), ApoA decreased from (1.8±0.3)mg/dl to (1.7±0. 3

关键词： Postmenopausal women Hormone replacement therapy Tibolone Cardiovascular effects

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Direct Ischemic Postconditioning Following Stroke Thrombectomy:A Promising Therapy for Reperfusion Injury

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Neuroscience Bulletin 2024年第7期40卷 1017-1020页

作者： Jing Wang lu Yang Longfei Wu Sijie Li Changhong Ren Yuchuan Ding ming Wei Xunming Ji Wenbo Zhao department of Neurology Xuanwu HospitalCapital Medical UniversityBeijing 100053China department of Emergency Xuanwu HospitalCapital Medical UniversityBeijing 100053China Beijing Key Laboratory of Hypoxic Conditioning Translational Medicine Xuanwu HospitalCapital Medical UniversityBeijing 100053China department of Neurosurgery Wayne State University School of MedicineDetroitMI48201USA Beijing Institute for Brain Disorders Capital Medical UniversityBeijing 100069China department of Neurosurgery Tianjin Huanhu HospitalTianjin 300222China department of Neurosurgery Xuanwu HospitalCapital Medical UniversityBeijing 100053China

Recanalization of occluded vessels and timely reperfusion are the primary therapies for acute ischemic stroke(AIS),with endovascular thrombectomy proven as the most effective therapy for large-vessel recanalization and improved outcomes of AIS ***,despite a high recanalization rate of 90% or even higher,the rate of 3-month functional independence is approximately 50%,while mortality remains around 15%[1].

关键词： mortality acute Therapy

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Symmetric-key cryptosystem with DNA technology

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Science in China(Series F) 2007年第3期50卷 324-333页

作者： lu mingXin LAI XueJia XIAO guozhen QIN Lei department of Information Management Nanjing UniversityNanjing 210093China state Key Lab of Information Security Institute of Software of Chinese Academy of ScienceBeijing 100049China department of Computer Science&Engineer Shanghai Jiao Tong UniversityShanghai 200030China state Key Lab of ISN Xidian UniversityXi’an 710071China Cancer Research Institute Queen’s UniversityKingstonOntarioK7L3N6Canada

DNA cryptography is a new field which has emerged with progress in the research of DNA computing. In our study, a symmetric-key cryptosystem was designed by applying a modern DNA biotechnology, microarray, into cryptographic technologies. This is referred to as DNA symmetric-key cryptosystem (DNASC). In DNASC, both encryption and decryption keys are formed by DNA probes, while its ciphertext is embedded in a specially designed DNA chip (microarray). The security of this system is mainly rooted in difficult biology processes and problems, rather than conventional computing technology, thus it is unaffected by changes from the attack of the coming quantum computer. The encryption process is a fabrication of a specially designed DNA chip and the decryption process is the DNA hybridization. In DNASC, billions of DNA probes are hybridized and identified at the same time, thus the decryption process is conducted in a massive, parallel way. The great potential in vast parallelism computation and the extraordinary information density of DNA are displayed in DNASC to some degree.

关键词： symmetric-key encryption DNA cryptography DNA computing

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