The Cauchy problem for the nonlinear wave equation with a critical potential type of damping coefficient（1＋│x│）-1 and a nonlinearity │u│p-1u is studied.The total energy decay estimates of the global solutions a...The Cauchy problem for the nonlinear wave equation with a critical potential type of damping coefficient（1＋│x│）-1 and a nonlinearity │u│p-1u is studied.The total energy decay estimates of the global solutions are obtained by using multiplier techniques to establish identity ddtE（t）＋F（t）=0 and skillfully selecting f（t）,g（t）,h（t）when the initial data have a compact support.Using the similar method,the Cauchy problem for the nonlinear wave equation with a critical potential type of damping coefficient（1＋│x│＋t）-1 and a nonlinearity │u│p-1u is studied,similar solutions are obtained when the initial data have a compact support.展开更多
Based on the test data in dynamic water and static water, the main factors, which influence the fine sediment flocculation, are analyzed with a gray model method of correlation theory. It is shown that the main influe...Based on the test data in dynamic water and static water, the main factors, which influence the fine sediment flocculation, are analyzed with a gray model method of correlation theory. It is shown that the main influencing factors are water temperature, settling time, salinity, grain size, sediment concentration and current velocity according to the correlation coefficients. Among them, the salinity and the sediment grain size are critical type influencing factors (CrTIF); the settling time, the sediment concentration and the velocity are continuous type influencing factors (CoTIF); and the water temperature has the characteristics of both. When the critical values of CrTIF are reached or exceeded, the fine sediments will be flocculated, but values of CrTIF will not influence the settlement strength of floes. The influence of CoTIF is continuous. The values of the CoTIF will not only influence the occurrence of flocculation but also the settlement strength of the floes.展开更多
In this paper,a class of Kirchhoff type equations in R^(N)(N≥3)with zero mass and a critical term is studied.Under some appropriate conditions,the existence of multiple solutions is obtained by using variational meth...In this paper,a class of Kirchhoff type equations in R^(N)(N≥3)with zero mass and a critical term is studied.Under some appropriate conditions,the existence of multiple solutions is obtained by using variational methods and a variant of Symmetric Mountain Pass theorem.The Second Concentration Compactness lemma is used to overcome the lack of compactness in critical problem.Compared to the usual Kirchhoff-type problems,we only require the nonlinearity to satisfy the classical superquadratic condition(Ambrosetti-Rabinowitz condition).展开更多
The paper proposes the conception of Beads type fold system. The mechanical analyses of the typical tectonic system are made by means of elastic stability theory, mathematical and mechanical method and rheology. The...The paper proposes the conception of Beads type fold system. The mechanical analyses of the typical tectonic system are made by means of elastic stability theory, mathematical and mechanical method and rheology. The relation among the deflections of folds and time, external forces, and distribution of stresses, strain energy density are analyzed to explain the causing mechanism of folding earthquake.展开更多
Positive entire solutions of the equation where 1 〈 p ≤ N, q 〉 0, are classified via their Morse indices. It is seen that there is a critical power q = qc such that this equation has no positive radial entire solut...Positive entire solutions of the equation where 1 〈 p ≤ N, q 〉 0, are classified via their Morse indices. It is seen that there is a critical power q = qc such that this equation has no positive radial entire solution that has finite Morse index when q 〉 qc but it admits a family of stable positive radial entire solutions when 0 〈 q ≤ qc- Proof of the stability of positive radial entire solutions of the equation when 1 〈 p 〈 2 and 0 〈 q ≤ qc relies on Caffarelli-Kohn Nirenberg＇s inequality. Similar Liouville type result still holds for general positive entire solutions when 2 〈 p ≤ N and q 〉 qc. The case of 1 〈 p 〈 2 is still open. Our main results imply that the structure of positive entire solutions of the equation is similar to that of the equation with p = 2 obtained previously. Some new ideas are introduced to overcome the technical difficulties arising from the p-Laplace operator.展开更多
Objective:To investigate in the CT manifestations of severe and critical coronavirus disease 2019(COVID-19)patients.Methods:Medical data was collected for 2 severe patients and 4 critical COVID-19 patients from onset ...Objective:To investigate in the CT manifestations of severe and critical coronavirus disease 2019(COVID-19)patients.Methods:Medical data was collected for 2 severe patients and 4 critical COVID-19 patients from onset to their recovery.Three or four CT scans for each patient were taken.The semi-quantitative analysis method was introduced for lesion and its distribution area.Results:The ground-glass opacities(GGO)and mixed GGO with consolidation were found as the most frequent features.Consolidation followed,and the appearance of stripes which showed an increasing trend before the patient was discharged.Consolidation was associated with clinical severity and disease progression,and the rapid change of the lesion in a short period of time was also a notable feature within 2e3 weeks.After being discharged,the efficacy of treatment could be demonstrated by a follow up CT scan.The distribution of lesion also showed dynamic progress in the follow up CT scan.Conclusion:CT scans in the whole course provided the entire inflammation information to assess clinical severity,disease progression and the treatment efficacy for COVID-19.展开更多
Coronavirus disease 2019(COVID-19)is a highly contagious disease and a serious threat to human health.COVID-19 can cause multiple organ dysfunction,such as respiratory and circulatory failure,liver and kidney injury,d...Coronavirus disease 2019(COVID-19)is a highly contagious disease and a serious threat to human health.COVID-19 can cause multiple organ dysfunction,such as respiratory and circulatory failure,liver and kidney injury,disseminated intravascular coagulation,and thromboembolism,and even death.The World Health Organization reports that the mortality rate of severe-type COVID-19 is over 50%.Currently,the number of severe cases worldwide has increased rapidly,but the experience in the treatment of infected patients is still limited.Given the lack of specific antiviral drugs,multi-organ function support treatment is important for patients with COVID-19.To improve the cure rate and reduce the mortality of patients with severe-and critical-type COVID-19,this paper summarizes the experience of organ function support in patients with severe-and criticaltype COVID-19 in Optical Valley Branch of Tongji Hospital,Wuhan,China.This paper systematically summarizes the procedures of functional support therapies for multiple organs and systems,including respiratory,circulatory,renal,hepatic,and hematological systems,among patients with severe-and critical-type COVID-19.This paper provides a clinical reference and a new strategy for the optimal treatment of COVID-19 worldwide.展开更多
基金The National Natural Science Foundation of China(No.10771032)
文摘The Cauchy problem for the nonlinear wave equation with a critical potential type of damping coefficient（1＋│x│）-1 and a nonlinearity │u│p-1u is studied.The total energy decay estimates of the global solutions are obtained by using multiplier techniques to establish identity ddtE（t）＋F（t）=0 and skillfully selecting f（t）,g（t）,h（t）when the initial data have a compact support.Using the similar method,the Cauchy problem for the nonlinear wave equation with a critical potential type of damping coefficient（1＋│x│＋t）-1 and a nonlinearity │u│p-1u is studied,similar solutions are obtained when the initial data have a compact support.
基金The study was supported by the National Natural Science Foundation of China under contract No. 49976023 the Natural Science Foundation of Zhejiang Province under contract No. N29985.
文摘Based on the test data in dynamic water and static water, the main factors, which influence the fine sediment flocculation, are analyzed with a gray model method of correlation theory. It is shown that the main influencing factors are water temperature, settling time, salinity, grain size, sediment concentration and current velocity according to the correlation coefficients. Among them, the salinity and the sediment grain size are critical type influencing factors (CrTIF); the settling time, the sediment concentration and the velocity are continuous type influencing factors (CoTIF); and the water temperature has the characteristics of both. When the critical values of CrTIF are reached or exceeded, the fine sediments will be flocculated, but values of CrTIF will not influence the settlement strength of floes. The influence of CoTIF is continuous. The values of the CoTIF will not only influence the occurrence of flocculation but also the settlement strength of the floes.
基金This work was supported by the National Natural Science Foundation of China(Grant Nos.11701346,11671239,11801338)the Natural Science Foundation of Shanxi Province(Grant No.201801D211001)+1 种基金the Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi(Grant No.2019L0024)the Research Project Supported by Shanxi Scholarship Council of China(Grant No.2020-005).
文摘In this paper,a class of Kirchhoff type equations in R^(N)(N≥3)with zero mass and a critical term is studied.Under some appropriate conditions,the existence of multiple solutions is obtained by using variational methods and a variant of Symmetric Mountain Pass theorem.The Second Concentration Compactness lemma is used to overcome the lack of compactness in critical problem.Compared to the usual Kirchhoff-type problems,we only require the nonlinearity to satisfy the classical superquadratic condition(Ambrosetti-Rabinowitz condition).
文摘The paper proposes the conception of Beads type fold system. The mechanical analyses of the typical tectonic system are made by means of elastic stability theory, mathematical and mechanical method and rheology. The relation among the deflections of folds and time, external forces, and distribution of stresses, strain energy density are analyzed to explain the causing mechanism of folding earthquake.
基金supported by NSFC(Grant Nos.11171092 and 11571093)supported by NSFC(Grant No.11371117)
文摘Positive entire solutions of the equation where 1 〈 p ≤ N, q 〉 0, are classified via their Morse indices. It is seen that there is a critical power q = qc such that this equation has no positive radial entire solution that has finite Morse index when q 〉 qc but it admits a family of stable positive radial entire solutions when 0 〈 q ≤ qc- Proof of the stability of positive radial entire solutions of the equation when 1 〈 p 〈 2 and 0 〈 q ≤ qc relies on Caffarelli-Kohn Nirenberg＇s inequality. Similar Liouville type result still holds for general positive entire solutions when 2 〈 p ≤ N and q 〉 qc. The case of 1 〈 p 〈 2 is still open. Our main results imply that the structure of positive entire solutions of the equation is similar to that of the equation with p = 2 obtained previously. Some new ideas are introduced to overcome the technical difficulties arising from the p-Laplace operator.
基金supported by the following grants the Capital Characteristic Clinical Application Research Foundation key funding(RXL:No.Z181100001718184)the Beijing Fire Inheritance 3+3 Project(RXL:No.830104)+1 种基金the National Natural Science Foundation of China(RXL:81873293,JLF:81774433)the National Key R&D Program of China(JLF:2018YFC1705802).
文摘Objective:To investigate in the CT manifestations of severe and critical coronavirus disease 2019(COVID-19)patients.Methods:Medical data was collected for 2 severe patients and 4 critical COVID-19 patients from onset to their recovery.Three or four CT scans for each patient were taken.The semi-quantitative analysis method was introduced for lesion and its distribution area.Results:The ground-glass opacities(GGO)and mixed GGO with consolidation were found as the most frequent features.Consolidation followed,and the appearance of stripes which showed an increasing trend before the patient was discharged.Consolidation was associated with clinical severity and disease progression,and the rapid change of the lesion in a short period of time was also a notable feature within 2e3 weeks.After being discharged,the efficacy of treatment could be demonstrated by a follow up CT scan.The distribution of lesion also showed dynamic progress in the follow up CT scan.Conclusion:CT scans in the whole course provided the entire inflammation information to assess clinical severity,disease progression and the treatment efficacy for COVID-19.
文摘Coronavirus disease 2019(COVID-19)is a highly contagious disease and a serious threat to human health.COVID-19 can cause multiple organ dysfunction,such as respiratory and circulatory failure,liver and kidney injury,disseminated intravascular coagulation,and thromboembolism,and even death.The World Health Organization reports that the mortality rate of severe-type COVID-19 is over 50%.Currently,the number of severe cases worldwide has increased rapidly,but the experience in the treatment of infected patients is still limited.Given the lack of specific antiviral drugs,multi-organ function support treatment is important for patients with COVID-19.To improve the cure rate and reduce the mortality of patients with severe-and critical-type COVID-19,this paper summarizes the experience of organ function support in patients with severe-and criticaltype COVID-19 in Optical Valley Branch of Tongji Hospital,Wuhan,China.This paper systematically summarizes the procedures of functional support therapies for multiple organs and systems,including respiratory,circulatory,renal,hepatic,and hematological systems,among patients with severe-and critical-type COVID-19.This paper provides a clinical reference and a new strategy for the optimal treatment of COVID-19 worldwide.
