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Weak and Strong Solutions for the Stokes Approximation of Non-homogeneous Incompressible Navier-Stokes Equations

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Acta Mathematicae Applicatae Sinica 2007年第4期23卷 637-650页

作者： xiao-jing cai Quan-sen Jiu Chun-yan Xue School of Mathematical Sciences Capital Normal University Beijing 100037 China Department of Mathematics Beijing Information Science and Technology University Beijing 100101 China

In this paper, the Dirichlet problem of Stokes approximate of non-homogeneous incompressible Navier-Stokes equations is studied. It is shown that there exist global weak solutions as well as global and unique strong solution for this problem, under the assumption that initial density po（x） is bounded away from 0 and other appropriate assumptions （see Theorem 1 and Theorem 2）. The semi-Galerkin method is applied to construct the approximate solutions and a prior estimates are made to elaborate upon the compactness of the approximate solutions.

关键词： Non-homogeneous Navier-Stokes equations Stokes approximate weak solutions strong solution

Global L^2 Stability of the Nonhomogeneous Incompressible Navier–Stokes Equations

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Acta Mathematica Sinica,English Series 2013年第11期29卷 2087-2098页

作者： xiao jing cai Quan Sen JIU Yan Jie ZHOU Department of Mathematics Beijing Technology and Business University Department of Applied Mathematics Beijing University of Technology School of Mathematical Sciences Capital Normal University

In this paper, the problem of the global L^2 stability for large solutions to the nonhomogeneous incompressible Navier-Stokes equations in 3D bounded or unbounded domains is studied. By delicate energy estimates and under the suitable condition of the large solutions, it shows that if the initial data are small perturbation on those of the known strong solutions, the large solutions are stable.

关键词： Nonhomogeneous incompressible Navier-Stokes equations strong solutions stability

Clinical feature and predictive factor analysis for spontaneous regression of retinopathy of prematurity in a Chinese population

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International Journal of Ophthalmology(English edition) 2022年第12期15卷 1978-1984页

作者： Yi-An Li xiao-Hong Zhou xiao-jing cai Chen-Hao Yang Department of Ophthalmology Children’s Hospital of Fudan UniversityShanghai 201102China

AIM:To investigate the ratio of spontaneous regression of retinopathy of prematurity(ROP)and to explore the possible relevant predictive ***:A retrospective review of 405 infants who were diagnosed with ROP and mother during pregnancy were ***,zone,and duration of ROP were *** analysis was performed on 51 possible predictive ***:Totally 356 infants showed spontaneous *** incidence was 100%,95.3%,and 22.7%in stage 1,2,and 3,*** 13.4%of the ROP with plus disease eventually resolved *** affected eyes of aggressive posterior retinopathy of prematurity(APROP)failed to spontaneously *** mean duration of ROP was 7.2wk in patients with spontaneous resolution of *** of mechanical ventilation(OR=0.981,95%CI,0.965-0.997,P=0.021),retinal hemorrhage(OR=0.173,95%CI,0.064-0.470,P=0.001),delivery pattern(OR=2.750,95%CI,1.132-6.681,P=0.025),maternal anemia in pregnancy(OR=0.142,95%CI,0.036-0.563,P=0.005),the stages(at initial diagnosis OR=0.183,95%CI,0.041-0.816,P=0.026;at final diagnosis OR=0.031,95%CI,0.006-0.167,P<0.001),and with plus disease or not(OR=0.005,95%CI,0.001-0.031,P<0.001)were independent predictive factors of the spontaneous regression of ***:Most mild ROP can spontaneously *** treatment is still recommended for stage 3 ROP,zone I ROP,AP-ROP,and ROP with plus *** mechanical ventilation and concurrent retinal hemorrhage reduce the likelihood of spontaneous ROP *** pattern of delivery and the mother's anemia during pregnancy can also affect the prognosis of ROP.

关键词： retinopathy of prematurity predictive factors spontaneous regression anemia during pregnancy mechanical ventilation pattern of delivery retinal hemorrhage

Some Remarks on Planar Boussinesq Equations

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Acta Mathematicae Applicatae Sinica 2012年第3期28卷 525-534页

作者： xiao-jing cai Chun-yan XUE Xian-jin LI Ying LIU Quan-sen JIU Department of Mathematics Beijing Technology and Business UniversityBeijing 100048China College of Applied Sciences Beijing University of TechnologyBeijing 100124China Department of Mathematics Beijing Information Science and Technology UniversityBeijing 100101China Institute of Mechanics Chinese Academy of SciencesBeijing 100190China Fundamental Department of the Academy of Armored Force Engineering Beijing 100072China School of Mathematical Sciences Capital Normal UniversityBeijing 100048China

The main purpose of this paper is to prove the well-posedness of the two-dimensional Boussinesq equations when the initial vorticity wo C L^1 （R^2）（or the finite Radon measure space）. Using the stream function form of the equations and the Schauder fixed-point theorem to get the new proof of these results, we get that when the initial vorticity is smooth, there exists a unique classical solutions for the Cauchy problem of the two dimensional Boussinesq equations.

关键词： Boussinesq equations classical solutions Schauder fixed-point theorem

Impact of Intercultural Learning Program on Language Learners＇ Intercultural Competence

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Sino-US English Teaching 2015年第8期12卷 631-640页

作者： xiao Dan cai jing Southwest University Chongqing China

As institutions of higher education continue to internationalize, the number of exchanged students climbs ever higher in China. It is important to know what they have gained in the intercultural learning experiences in terms of attitudes, awareness, and knowledge, which are the three constructed dimensions of Intercultural Competence in this study. A qualitative research is conducted by using interview and seven English language learners are investigated to explore their learning outcomes in the intercultural learning program. From the thematic analysis of the interviews, it can be found that these English language learners＇ intercultural competence has been improved during their stay in USA. They successfully overcome cultural shock, hold positive attitudes toward target culture and people, become more confident in English study, and acquire more cultural knowledge. The research outcomes contribute to promoting intercultural learning effectiveness and improving learners＇ intercultural competence.

关键词： intercultural program intercultural learning intercultural competence English learners

Highly conductive and stable iodine doped argyrodite electrolyte for all-solid-state lithium batteries

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Journal of Energy Chemistry 2025年第1期100卷 50-58页

作者： Gaozhan Liu jing Zhang jing Yang jinghui Chen Xingyue xiao Xiayin Yao Ningbo Institute of Materials Technology and Engineering Chinese Academy of Sciences Center of Materials Science and Optoelectronics Engineering University of Chinese Academy of Sciences

Lithium argyrodites with high ionic conductivity and low cost are considered as one of the most prospective solid electrolytes for all-solid-state lithium ***,the poor chemical stability and compatibility with lithium metal limit their ***,Li5.4PS4.4Cl1.4I0.2solid electrolyte with high ionic conductivity of 11.49 m S cm-1and improved chemical stability is synthesized by iodine *** ultra-thin Li5.4PS4.4Cl1.4I0.2membrane with thickness of 10μm can be obtained by wet coating process,exhibiting a high ionic conductivity of 2.09 mS cm-1and low areal resistance of 1.17Ω***,iodine doping could in-situ form LiI at the lithium/electrolyte interface and improve the critical current density of Li5.4PS4.4Cl1.6from 0.8 to 1.35 mA *** resultant LiCoO2/Li5.4PS4.4Cl1.4I0.2/Li battery shows excellent cycling stability at 1 C,with a reversible specific capacity of 110.1 mA h g-1and a retention of 80.5% after 1000 *** addition,the assembled LiCoO2/Li5.4PS4.4Cl1.4I0.2membrane/Li pouch cell delivers an initial discharge capacity of 110.4 mA h g-1and 80.5% capacity retention after 100 cycles.

关键词： Argyrodite electrolytes Iodine doping Ionic conductivity Stability All-solid-state lithium battery

miRNA-21-5p is an important contributor to the promotion of injured peripheral nerve regeneration using hypoxia-pretreated bone marrow-derived neural crest cells

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Neural Regeneration Research 2025年第1期20卷 277-290页

作者： Meng Cong jing-jing Hu Yan Yu xiao-Li Li xiao-Ting Sun Li-Ting Wang Xia Wu Ling-Jie Zhu xiao-Jia Yang Qian-Ru He Fei Ding Hai-Yan Shi School of Medicine Nantong UniversityNantongJiangsu ProvinceChina Key Laboratory of Neuroregeneration of Jiangsu and Ministry of Education and Coinnovation Center of Neuroregeneration Nantong UniversityNantongJiangsu ProvinceChina Department of Physiology Jiangsu Health Vocational CollegeNanjingJiangsu ProvinceChina Department of Pathology Affiliated Hospital of Nantong UniversityNantongJiangsu ProvinceChina Jiangsu Clinical Medicine Center of Tissue Engineering and Nerve Injury Repair Affiliated Hospital of Nantong UniversityNantongJiangsu ProvinceChina

Our previous study found that rat bone marrow–derived neural crest cells(acting as Schwann cell progenitors)have the potential to promote long-distance nerve ***-based therapy can enhance peripheral nerve repair and regeneration through paracrine bioactive factors and intercellular ***,the complex contributions of various types of soluble cytokines and extracellular vesicle cargos to the secretome remain *** investigate the role of the secretome and extracellular vesicles in repairing damaged peripheral nerves,we collected conditioned culture medium from hypoxia-pretreated neural crest cells,and found that it significantly promoted the repair of sensory neurons damaged by oxygen-glucose *** mRNA expression of trophic factors was highly expressed in hypoxia-pretreated neural crest *** performed RNA sequencing and bioinformatics analysis and found that miR-21-5p was enriched in hypoxia-pretreated extracellular vesicles of neural crest ***,to further clarify the role of hypoxia-pretreated neural crest cell extracellular vesicles rich in miR-21-5p in axonal growth and regeneration of sensory neurons,we used a microfluidic axonal dissociation model of sensory neurons in vitro,and found that hypoxia-pretreated neural crest cell extracellular vesicles promoted axonal growth and regeneration of sensory neurons,which was greatly dependent on loaded ***,we constructed a miR-21-5p-loaded neural conduit to repair the sciatic nerve defect in rats and found that the motor and sensory functions of injured rat hind limb,as well as muscle tissue morphology of the hind limbs,were obviously *** findings suggest that hypoxia-pretreated neural crest extracellular vesicles are natural nanoparticles rich in ***-21-5p is one of the main contributors to promoting nerve regeneration by the neural crest cell *** helps to explain the mechanism of action of the secretome and e

关键词： axotomy cell-free therapy conditioned medium extracellular vesicles hypoxic preconditioning microRNA oxygen-glucose deprivation peripheral nerve injury Schwann cell precursors

Progress of research in the application of ultrasound technology for the treatment of Alzheimer’s disease

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Neural Regeneration Research 2025年第10期20卷 2823-2837页

作者： Qiuquan cai Lianghui Meng Meina Quan Ling Wang jing Ren Chenguang Zheng Jiajia Yang Dong Ming Academy of Medical Engineering and Translational Medicine Tianjin UniversityTianjinChina Innovation Center for Neurological Disorders Xuanwu HospitalCapital Medical UniversityBeijingChina Brain-Computer Interaction and Human-Machine Fusion Haihe Laboratory Tianjin UniversityTianjinChina Tianjin Key Laboratory of Brain Science and Neural Engineering Tianjin UniversityTianjinChina

Alzheimer’s disease is a common neurodegenerative disorder defined by decreased reasoning abilities,memory loss,and cognitive *** presence of the blood-brain barrier presents a major obstacle to the development of effective drug therapies for Alzheimer’s *** use of ultrasound as a novel physical modulation approach has garnered widespread attention in recent *** a safe and feasible therapeutic and drug-delivery method,ultrasound has shown promise in improving cognitive *** article provides a summary of the application of ultrasound technology for treating Alzheimer’s disease over the past 5 years,including standalone ultrasound treatment,ultrasound combined with microbubbles or drug therapy,and magnetic resonance imaging-guided focused ultrasound *** is placed on the benefits of introducing these treatment methods and their potential *** found that several ultrasound methods can open the blood-brain barrier and effectively alleviate amyloid-βplaque *** believe that ultrasound is an effective therapy for Alzheimer’s disease,and this review provides a theoretical basis for future ultrasound treatment methods.

关键词： Alzheimer’s disease blood-brain barrier drugs magnetic resonance imaging-guided focused ultrasound microbubbles scanning ultrasound ultrasound ultrasound stimulation

Effects of the extrusion parameters on microstructure,texture and room temperature mechanical properties of extruded Mg-2.49Nd-1.82Gd-0.2Zn-0.2Zr alloy

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International Journal of Minerals,Metallurgy and Materials 2025年第1期32卷 136-146页

作者： Chenjin Zhang Guangyu Yang Lei xiao Zhiyong Kan jing Guo Qiang Li Wanqi Jie State Key Laboratory of Solidification Processing Northwestern Polytechnical UniversityXi’an 710072China College of Materials Science and Engineering Fuzhou UniversityFuzhou 350108China College of Chemistry and Environmental Science Qujing Normal UniversityQujing 655011China

Microstructure,texture,and mechanical properties of the extruded Mg-2.49Nd-1.82Gd-0.2Zn-0.2Zr alloy were investigated at different extrusion temperatures(260 and 320℃),extrusion ratios(10:1,15:1,and 30:1),and extrusion speeds(3 and 6 mm/s).The experimental results exhibited that the grain sizes after extrusion were much finer than that of the homogenized alloy,and the second phase showed streamline distribution along the extrusion direction(ED).With extrusion temperature increased from 260 to 320℃,the microstructure,texture,and mechanical properties of alloys changed *** dynamic recrystallization(DRX)degree and grain sizes enhanced as the extrusion ratio increased from 10:1 to 30:1,and the strength gradually decreased but elongation(EL)*** the extrusion speed increased from 3 to 6 mm/s,the grain sizes and DRX degree increased significantly,and the samples presented the typical-rare-earth(RE)*** alloy extruded at 260℃ with extrusion ratio of 10:1 and extrusion speed of 3 mm/s showed the tensile yield strength(TYS)of 213 MPa and EL of 30.6%.After quantitatively analyzing the contribution of strengthening mechanisms,it was found that the grain boundary strengthening and dislocation strengthening played major roles among strengthening *** results provide some guidelines for enlarging the industrial application of extruded Mg-RE alloy.

关键词： Mg-rare earth alloys extrusion temperature extrusion ratio extrusion speed strengthening mechanisms