在文献[1],[2]中,路见可从力学中的实际问题出发,提出了带复平移的奇异积分方程问题,在文献[3],[4]中,路见可、杜金元分别解决了在常系数情形带复平移的奇异积分方程和积分方程组的问题。本文推广文献[4]的结果,讨论如下的变系数带复平...在文献[1],[2]中,路见可从力学中的实际问题出发,提出了带复平移的奇异积分方程问题,在文献[3],[4]中,路见可、杜金元分别解决了在常系数情形带复平移的奇异积分方程和积分方程组的问题。本文推广文献[4]的结果,讨论如下的变系数带复平移奇异积分方程组 A(x)φ(x)+B(x)/(πi) integral from x φ(τ)dτ/(τ-x)+C(x)/(2πi) integral from x φ(τ)dτ/(τ-x-α)+D(x)/(2πi) integral from x φ(τ)dτ/(τ-x-β)=f(x) x∈X (1)上式中,X表示实数轴,1mα>0,1mβ<0,A(x),B(x),C(x),D(x)为n阶函数矩阵f(x)是n维向量函数,f(x)∈(?)_0,A(x)±B(x)∈(?)方程为正则型的,det(A(x)±B(x))=0(x∈X)对C(x),D(x)的要求下面根据需要确定,我们目的是,求n维向量φ(τ),τ∈X,φ(τ)∈(?)。展开更多
As the most import fault of the Late Pleistocene in the Lhasa area,the Nalinlaka fault is a left-lateral thrust fault,striking NWW,dipping SSW with a high dip angle,and extending over 33km.According to studies on the ...As the most import fault of the Late Pleistocene in the Lhasa area,the Nalinlaka fault is a left-lateral thrust fault,striking NWW,dipping SSW with a high dip angle,and extending over 33km.According to studies on the latest strata on the Nalinlaka fault zone,this fault zone has been obviously active since the Late Pleistocene and the movement left behind some geomorphologic phenomena on the earth's surface,especially at the sites of the gully west of Cijiaolin and around Xiecun village.For example,some rivers,ridges and terraces are displaced,forming beheaded gullies and fault escarps.The horizontal displacements since the Late Pleistocene at the above two places are 54m ～ 87m,20m ～ 67m,respectively.Based on studies on the 4 trenches along the fault using the progressive constraining method,we conclude that there might have been 5 paleoearthquake events along the Nalinlaka fault since 70ka B.P.,the ages of each paleoearthquake are 68.53,54.40,< 41.23,21.96,9.86ka B.P.,and the average recurrence interval is 14.67ka.Because of the limits of trenches and earthquake events exposed by each trench,no single trench completely revealed all 5 events.There may therefore be some errors in determining the upper and lower limits of some events in this article.展开更多
Objective：Debate continues regarding the management of calcaneal fractures,between open reduction and internal fixation and closed treatment.Hence we aim at evaluating the radiological and functional outcomes of open...Objective：Debate continues regarding the management of calcaneal fractures,between open reduction and internal fixation and closed treatment.Hence we aim at evaluating the radiological and functional outcomes of open reduction and internal fixation in displaced joint depression type of calcaneal fractures fixed with locking calcaneal plate.Methods：In this series,28 patients （26 unilateral and 2 bilateral） with joint depression type of calcaneal fractures as per Essex-Lopresti classification system were operated on with locking calcaneal plate within 3 weeks of injury.Patients were evaluated in terms of associated injuries and X-rays of anteroposterior,lateral and axial views of the calcaneum.CT scan was done to assess the amount ofcomminution and articular depression.Patients were followed up clinically and radiologically at least for 1 year.Radiological assessment was done by Bohler＇s angle and Gissane＇s angle along with measurement ofcalcaneal height and width.Functional outcome was assessed using the American Orthopaedics Foot and Ankle Society （AOFAS） scale.Results：At average follow-up of 14.5 months,average AOFAS score was 86.3 （range 66 to 97）,with 86% having excellent to good results and 2 （7.7%） and 1 （3.7%） having fair and poor results respectively.All patients had stable ankle joint with all having dorsiflexion and plantar flexion more than 30°.Average subtalar range of motion was 17°.The mean Bohler＇s angle,mean Gissane＇s angle,calcaneal height and width were 25.47°,121.3°,4.32 cm and 3.81cm respectively at final follow-up.Three patients had flap necrosis at incision site and one had superficial and deep infection.Subtalar arthritis was seen in 5 patients,whereas sural nerve hypoaesthesia in 1 patient.None of the patients had compartment syndrome,heel pad problems,peroneal tendinitis,reflex sympathetic dystropy or implant failure.Conclusion：Open reduction and internal fixation with locking calcaneal plate gives sound functional outcome,i.e.restoring anatomically reconstruction of height,width,Bohler＇s and Gissiane＇s angles of the calcaneum,and allowing early mobilization.展开更多
Superconvergence and recovery type a posteriori error estimators are analyzed for Pian and Sumihara's 4-node hybrid stress quadrilateral finite element method for linear elasticity problems. Superconvergence of or...Superconvergence and recovery type a posteriori error estimators are analyzed for Pian and Sumihara's 4-node hybrid stress quadrilateral finite element method for linear elasticity problems. Superconvergence of order O(h^(1+min){α,1}) is established for both the displacement approximation in H^1-norm and the stress approximation in L^2-norm under a mesh assumption, where α > 0 is a parameter characterizing the distortion of meshes from parallelograms to quadrilaterals. Recovery type approximations for the displacement gradients and the stress tensor are constructed, and a posteriori error estimators based on the recovered quantities are shown to be asymptotically exact. Numerical experiments confirm the theoretical results.展开更多
文摘在文献[1],[2]中,路见可从力学中的实际问题出发,提出了带复平移的奇异积分方程问题,在文献[3],[4]中,路见可、杜金元分别解决了在常系数情形带复平移的奇异积分方程和积分方程组的问题。本文推广文献[4]的结果,讨论如下的变系数带复平移奇异积分方程组 A(x)φ(x)+B(x)/(πi) integral from x φ(τ)dτ/(τ-x)+C(x)/(2πi) integral from x φ(τ)dτ/(τ-x-α)+D(x)/(2πi) integral from x φ(τ)dτ/(τ-x-β)=f(x) x∈X (1)上式中,X表示实数轴,1mα>0,1mβ<0,A(x),B(x),C(x),D(x)为n阶函数矩阵f(x)是n维向量函数,f(x)∈(?)_0,A(x)±B(x)∈(?)方程为正则型的,det(A(x)±B(x))=0(x∈X)对C(x),D(x)的要求下面根据需要确定,我们目的是,求n维向量φ(τ),τ∈X,φ(τ)∈(?)。
基金sponsored by the Specialized Project of Earthquake Profession(201008007),CEA
文摘As the most import fault of the Late Pleistocene in the Lhasa area,the Nalinlaka fault is a left-lateral thrust fault,striking NWW,dipping SSW with a high dip angle,and extending over 33km.According to studies on the latest strata on the Nalinlaka fault zone,this fault zone has been obviously active since the Late Pleistocene and the movement left behind some geomorphologic phenomena on the earth's surface,especially at the sites of the gully west of Cijiaolin and around Xiecun village.For example,some rivers,ridges and terraces are displaced,forming beheaded gullies and fault escarps.The horizontal displacements since the Late Pleistocene at the above two places are 54m ～ 87m,20m ～ 67m,respectively.Based on studies on the 4 trenches along the fault using the progressive constraining method,we conclude that there might have been 5 paleoearthquake events along the Nalinlaka fault since 70ka B.P.,the ages of each paleoearthquake are 68.53,54.40,< 41.23,21.96,9.86ka B.P.,and the average recurrence interval is 14.67ka.Because of the limits of trenches and earthquake events exposed by each trench,no single trench completely revealed all 5 events.There may therefore be some errors in determining the upper and lower limits of some events in this article.
文摘Objective：Debate continues regarding the management of calcaneal fractures,between open reduction and internal fixation and closed treatment.Hence we aim at evaluating the radiological and functional outcomes of open reduction and internal fixation in displaced joint depression type of calcaneal fractures fixed with locking calcaneal plate.Methods：In this series,28 patients （26 unilateral and 2 bilateral） with joint depression type of calcaneal fractures as per Essex-Lopresti classification system were operated on with locking calcaneal plate within 3 weeks of injury.Patients were evaluated in terms of associated injuries and X-rays of anteroposterior,lateral and axial views of the calcaneum.CT scan was done to assess the amount ofcomminution and articular depression.Patients were followed up clinically and radiologically at least for 1 year.Radiological assessment was done by Bohler＇s angle and Gissane＇s angle along with measurement ofcalcaneal height and width.Functional outcome was assessed using the American Orthopaedics Foot and Ankle Society （AOFAS） scale.Results：At average follow-up of 14.5 months,average AOFAS score was 86.3 （range 66 to 97）,with 86% having excellent to good results and 2 （7.7%） and 1 （3.7%） having fair and poor results respectively.All patients had stable ankle joint with all having dorsiflexion and plantar flexion more than 30°.Average subtalar range of motion was 17°.The mean Bohler＇s angle,mean Gissane＇s angle,calcaneal height and width were 25.47°,121.3°,4.32 cm and 3.81cm respectively at final follow-up.Three patients had flap necrosis at incision site and one had superficial and deep infection.Subtalar arthritis was seen in 5 patients,whereas sural nerve hypoaesthesia in 1 patient.None of the patients had compartment syndrome,heel pad problems,peroneal tendinitis,reflex sympathetic dystropy or implant failure.Conclusion：Open reduction and internal fixation with locking calcaneal plate gives sound functional outcome,i.e.restoring anatomically reconstruction of height,width,Bohler＇s and Gissiane＇s angles of the calcaneum,and allowing early mobilization.
基金supported by National Natural Science Foundation of China (Grant No. 11171239)Major Research Plan of National Natural Science Foundation of China (Grant No. 91430105)
文摘Superconvergence and recovery type a posteriori error estimators are analyzed for Pian and Sumihara's 4-node hybrid stress quadrilateral finite element method for linear elasticity problems. Superconvergence of order O(h^(1+min){α,1}) is established for both the displacement approximation in H^1-norm and the stress approximation in L^2-norm under a mesh assumption, where α > 0 is a parameter characterizing the distortion of meshes from parallelograms to quadrilaterals. Recovery type approximations for the displacement gradients and the stress tensor are constructed, and a posteriori error estimators based on the recovered quantities are shown to be asymptotically exact. Numerical experiments confirm the theoretical results.
