The primary goal of the demonstration project endorsed by the Scientific and Technical Committee for IDNDR in 1992 is to ensure that national agencies are able to assess seismic hazard in a regionally coordinated fash...The primary goal of the demonstration project endorsed by the Scientific and Technical Committee for IDNDR in 1992 is to ensure that national agencies are able to assess seismic hazard in a regionally coordinated fashion by using advanced methods.China,as a Regional Center of Central Southern Asia,has contacted with countries of the region to realistically practice seismic hazard assessments of Continental Asia.A test area located in the collision boundary between the Indian and Eurasian plates was chosen to examine the seismic hazard assessment approach in the regional coordinates.The seismotectonics and three versions of seismic sources of the test area are described in this paper and under the Global Seismic Hazard Assessment Program(GSHAP),guidelines an earthquake catalogue of the test area was assembled.Because of the incompleteness of earthquake data in different countries,we adopt different time windows for different magnitude intervals in order to obtain the seismicity parameters of sources.By展开更多
Basing on a lot of examinations, according to the fundamental inage processing theories and methods, getting touch with the property of wood anatomical structure image,we put forward the optimum method and theory whic...Basing on a lot of examinations, according to the fundamental inage processing theories and methods, getting touch with the property of wood anatomical structure image,we put forward the optimum method and theory which are suitable for the binary processing of the wood anatomical structure image. After the wood image has been processed binary, with the help of computer vision technology, the boundary of wood anatomical structure molecular binary image was sought This kind of theory and method lay a solid foundaion on the collection of feature and the pottern recognition and other high level processing of wood anatomical structure molecular image.展开更多
The influence of a nontotal reflection on the interaction of a reflected shock wave with the boundary layer in a reflected shock tunnel has been investigated. The calculating method of the velocity, the temperature an...The influence of a nontotal reflection on the interaction of a reflected shock wave with the boundary layer in a reflected shock tunnel has been investigated. The calculating method of the velocity, the temperature and the Mach number profiles in the boundary layer in reflected shock fixed coordinates has been obtained. To account for equilibrium real gas effects of nitrogen, the numerical results show that the minimum Mach number in the boundary layer has been moved from the wall into the boundary layer with the increasing of the incident shock Mach number. The minimum Mach number, the shock angle in the bifurcated foot and the jet velocity along the wall to the end plate are reduced owing to the Increasing of the area of nozzle throat. The numerical results are in good agreement with measurements.展开更多
The boundary element method (KEM) which a used to solve the elastic problems has more advantages than other numerical methods. Especially, it can resolve rapidly varying internal stress and strain fields more accurate...The boundary element method (KEM) which a used to solve the elastic problems has more advantages than other numerical methods. Especially, it can resolve rapidly varying internal stress and strain fields more accurately. However, it is of en fails in the region near the boundary because of the singularity of the solutions. Though we can increase the boundary meshes more and more, the solutions of stress on the boundary can't be given directly; which has obstructed the applications of the HEM to some extent.In this paper we proposed the boudary expanding-contracting principle and the boundary expanding-contracting method (BECM) based on the principle. With this method, not only the solutions in the region near or on the boundary can be obtained directly, but the iterative processes can also he used conveniently to improve the accuracy of the solutions.展开更多
Two terranes formed since the Late Palaeozoic can be distinguished in southwestern China. One is charac-terized by the Permo-Carboniferous ice-rafted marine gravel-bearing clastic formation and the cold-water faunaof ...Two terranes formed since the Late Palaeozoic can be distinguished in southwestern China. One is charac-terized by the Permo-Carboniferous ice-rafted marine gravel-bearing clastic formation and the cold-water faunaof the Gondwana facies, including the Gangmar Co, Lhasa, Sa' gya, Tengchong and Baoshan terranes and theother is marked by the Upper Palaeozoic of the Yangtze type with the Cathaysian flora and the Pacific-typefusulinids, comprising the Changning-Menglian, Shuangjiang-Lancang, Qamdo and Bayan Har terranes. TheLongmu Co-Shuanghu-Dengqen-North Lancang River-Kejie-Mengding suture zone between the two groups ofterranes is the boundary between Gondwana and Pacifica in southwestern China. On the grounds of thesedimentary formation and successive southwestward migration of the Asian nonmarine Jurassic-Cretaceousendemic bivalves, the ages of the suture and some terranes to the southwest of the suture zone are discussed.The Baoshan terrane and the Nyainrong-Sog terrane in the Lhasa composite terrane were firstly pieced togeth-er with the Asian continent in the early Early Jurassic. The northern Tibet-western Yunnan microplate, in-cluding the Gangmar Co, Lhasa and Tengchong terranes, collided with the Asian continent at the end of theEarly Cretaceous Neocomian.展开更多
Two aspects of a new method,which can be used for seismic zoning,are introduced in this paper.On the one hand,the approach to estimate b value and annual activity rate proposed by Kijko and Sellevoll needs to use the ...Two aspects of a new method,which can be used for seismic zoning,are introduced in this paper.On the one hand,the approach to estimate b value and annual activity rate proposed by Kijko and Sellevoll needs to use the earthquake catalogue.The existing earthquake catalogue contains both historical and recent instrumental data sets and it is inadequate to use only one part.Combining the large number of historical events with recent complete records and taking the magnitude uncertainty into account,Kijko’s method gives the maximum likelihood estimation of b value and annual activity rate,which might be more realistic.On the other hand,this method considers the source zone boundary uncertainty in seismic hazard analysis,which means the earthquake activity rate across a boundary of a source zone changes smoothly instead of abruptly and avoids too large a gradient in the calculated results.展开更多
Let R_Ⅲ(n) be the classical domain of type Ⅲ with n≥2. This article is devoted to a deep study of the Schwarz lemma on R_Ⅲ(n) via not only exploring the smooth boundary points of R_Ⅲ(n) but also proving the Schwa...Let R_Ⅲ(n) be the classical domain of type Ⅲ with n≥2. This article is devoted to a deep study of the Schwarz lemma on R_Ⅲ(n) via not only exploring the smooth boundary points of R_Ⅲ(n) but also proving the Schwarz lemma at the smooth boundary point for holomorphic self-mappings of R_Ⅲ(n).展开更多
The mechanism of acoustic radiation from the boundary layer of an axisymmetric body is analyzed, and its sound pressure spectrum is predicted. It is shown that the acoustic radiation results from the transition region...The mechanism of acoustic radiation from the boundary layer of an axisymmetric body is analyzed, and its sound pressure spectrum is predicted. It is shown that the acoustic radiation results from the transition region and the turbulent boundary layer; and that the acoustic radiation from transition region is predominant at low frequencies; while the turbulent boundary layer has the decisive effect on acoustic radiation at high frequencies. The calculated values are in good agreement with the experimental data.展开更多
The vertical transport of mass at the top of the boundary layer is considered as a link between the boundary layer and free atmosphere.The adjustment of the wind and pressure fields in the boundary layer is studied un...The vertical transport of mass at the top of the boundary layer is considered as a link between the boundary layer and free atmosphere.The adjustment of the wind and pressure fields in the boundary layer is studied under the consideration of the interaction between the boundary layer and free atmosphere.The vertical motion at the top of the boundary layer is evaluated.The results show that the distinguished differ- ences of the present results from classical Ekman layer do exist and they are discussed in the paper.展开更多
By use of geostrophic momentum approximation,the analytical expressions of the wind distribution within the planetary boundary layer and the vertical velocity at the top of the boundary layer are obtained when the dis...By use of geostrophic momentum approximation,the analytical expressions of the wind distribution within the planetary boundary layer and the vertical velocity at the top of the boundary layer are obtained when the distribution of eddy transfer coefficient k is divided into three sections:k_1z(z_0≤z<h_1),k_2(h_1≤z<h_2), and k_3(h_2≤z).The results are in agreement with the observations.In particular,the wind profile in the surface layer(z_0≤z<h_1)coincides with the logarithmic distribution.The maximum angle between winds near the surface and at the bottom of the free atmosphere is only about 30°.This work improves the work of Wu and Blumen(1982)who introduced the geostrophic momentum approximation to the boundary layer.The solutions in barotropic and neutral conditions have been also extended to the baroclinic and stratified atmosphere.展开更多
In this article, the sharp growth theorem for almost starlike mappings of complex order λ is given firstly. Secondly, distortion theorem along a unit direction is also established as the application of the growth the...In this article, the sharp growth theorem for almost starlike mappings of complex order λ is given firstly. Secondly, distortion theorem along a unit direction is also established as the application of the growth theorem. In particular, using our results can reduce to some well-known results.展开更多
plane with the strike of 127°, the dip of 79° and the rake of 171°. The rupture process inversion result of MS=7.9 earthquake shows that the total rupture duration is about 37 s, the scalar moment tenso...plane with the strike of 127°, the dip of 79° and the rake of 171°. The rupture process inversion result of MS=7.9 earthquake shows that the total rupture duration is about 37 s, the scalar moment tensor is M0=0.97 × 1020 N·m. Rupture mainly occurred on the shallow area with 110 km long and 30 km wide, the location in which the rupture initiated is not where the main rupture took place, and the area with slip greater than 0.5 m basically lies within 35 km deep middle-crust under the earth surface. The maximum static slip is 3.6 m. There are two distinct areas with slip larger than 2.0 m. We noticed that when the rupture propagated towards northwest and closed to the area around the MS=7.3 hypocenter, the slip decreased rapidly, which may indicate that the rupture process was stopped by barriers. The consistence of spatial distribution of slip on the fault plane with the distribution of aftershocks also supports that the rupture is a heterogeneous process owing to the presence of barriers.展开更多
For a class of nonlinear filtration equation with nonlinear second-third boundary value condition, it is shown that a priori boundary of the solution can be estimated and controlled by initial data and integral on the...For a class of nonlinear filtration equation with nonlinear second-third boundary value condition, it is shown that a priori boundary of the solution can be estimated and controlled by initial data and integral on the boundary of the region. The priori estimate of the solutions was established by iterative method. By using this estimate the solutions may blow-up on the boundary of the region and thus it may have asymptotic non-stability.展开更多
In this paper, problems of the flow over a fat plate in the large Reynolds numbercase are studied by using the method of multiple scales ̄[1,2].We have obtained N-orderuniformly valid asymptotic solutions of the Naver...In this paper, problems of the flow over a fat plate in the large Reynolds numbercase are studied by using the method of multiple scales ̄[1,2].We have obtained N-orderuniformly valid asymptotic solutions of the Naver-Stodes equations.展开更多
A dynamic study on Ekman characteristics by using 1998 SCSMEX and TIPEX boundary layer data is made. The results are as follows: (1) Similar dynamical Ekman characteristics are observed in the Tibetan Plateau and in t...A dynamic study on Ekman characteristics by using 1998 SCSMEX and TIPEX boundary layer data is made. The results are as follows: (1) Similar dynamical Ekman characteristics are observed in the Tibetan Plateau and in the South China Sea and its surrounding area. (2) The thickness of the boundary layer is about 2250 m over the Tibetan Plateau, and considering its variation, the thickness could be up to 2250–2750 m. In the tropical southwest Pacific, the thickness of the boundary layer is about 2000 m, and the variation is smaller; a smaller thickness of the boundary layer is in the plain area of the Bohai Sea. (3) Because of the difference in elevation between the Tibetan Plateau and the tropical ocean area, the influence of the boundary layer on the atmosphere is quite different although the two areas have almost the same thickness for the boundary layer, the height where the friction forcing occurs is quite different. (4) The vertical structure of turbulence friction is quite different in the Plateau and in the tropical ocean area. Calculations by 1998 SCSMEX and TIPEX boundary layer data indicate that even in the lowest levels, eddy viscosity in the Tibetan Plateauan can be 2.3 times than in the tropical ocean area.展开更多
Let R_I(m,n) be the classical domain of type I in C^(m×n)with 1≤m≤n.We obtain the optimal estimates of the eigenvalues of the Fréchet derivative Df(Z) at a smooth boundary fixed point Z of R_I(m,n)for a ho...Let R_I(m,n) be the classical domain of type I in C^(m×n)with 1≤m≤n.We obtain the optimal estimates of the eigenvalues of the Fréchet derivative Df(Z) at a smooth boundary fixed point Z of R_I(m,n)for a holomorphic self-mapping f of R_L(m,n).We provide a necessary and sufficient condition such that the boundary points of R_I(m,n) are smooth,and give some properties of the smooth boundary points of R_L(m,n).Our results extend the classical Schwarz lemma at the boundary of the unit disk △ to R_I(m,n),which may be applied to get some optimal estimates in several complex variables.展开更多
In this paper, we will use the Schwarz lemma at the boundary to character the distortion theorems of determinant at the extreme points and distortion theorems of matrix on the complex tangent space at the extreme poin...In this paper, we will use the Schwarz lemma at the boundary to character the distortion theorems of determinant at the extreme points and distortion theorems of matrix on the complex tangent space at the extreme points for normalized locally biholomorphic quasi-convex mappings in the unit ball Bn respectively.展开更多
In this paper, we investigate the periodic boundary value problems for nonlinear first order functional differential equations. By establishing a new comparison result, criteria on the existence of maximal and minimal...In this paper, we investigate the periodic boundary value problems for nonlinear first order functional differential equations. By establishing a new comparison result, criteria on the existence of maximal and minimal solutions are obtained.展开更多
In this survey paper we report on recent developments of the hp-version of the boundary element method (BEM). As model problems we consider weakly singular and hypersingular integral equations of the first kind on a...In this survey paper we report on recent developments of the hp-version of the boundary element method (BEM). As model problems we consider weakly singular and hypersingular integral equations of the first kind on a planar, open surface. We show that the Galerkin solutions (computed with the hp-version on geometric meshes) converge exponentially fast towards the exact solutions of the integral equations. An hp-adaptive algorithm is given and the implementation of the hp-version BEM is discussed together with the choice of efficient preconditioners for the ill-conditioned boundary element stiffness matrices. We also comment on the use of the hp-version BEM for solving Signorini contact problems in linear elasticity where the contact conditions are enforced only on the discrete set of Gauss-Lobatto points. Numerical results are presented which underline the theoretical results.展开更多
In this paper, we gave boundary layer estimation of a singular equation of order 4 with limit equation of order 2. The results show that the thickness of boundary layer is intrinsically relative to the reciprocal of t...In this paper, we gave boundary layer estimation of a singular equation of order 4 with limit equation of order 2. The results show that the thickness of boundary layer is intrinsically relative to the reciprocal of the order of equation of and independent of the order of equation of u.展开更多
文摘The primary goal of the demonstration project endorsed by the Scientific and Technical Committee for IDNDR in 1992 is to ensure that national agencies are able to assess seismic hazard in a regionally coordinated fashion by using advanced methods.China,as a Regional Center of Central Southern Asia,has contacted with countries of the region to realistically practice seismic hazard assessments of Continental Asia.A test area located in the collision boundary between the Indian and Eurasian plates was chosen to examine the seismic hazard assessment approach in the regional coordinates.The seismotectonics and three versions of seismic sources of the test area are described in this paper and under the Global Seismic Hazard Assessment Program(GSHAP),guidelines an earthquake catalogue of the test area was assembled.Because of the incompleteness of earthquake data in different countries,we adopt different time windows for different magnitude intervals in order to obtain the seismicity parameters of sources.By
文摘Basing on a lot of examinations, according to the fundamental inage processing theories and methods, getting touch with the property of wood anatomical structure image,we put forward the optimum method and theory which are suitable for the binary processing of the wood anatomical structure image. After the wood image has been processed binary, with the help of computer vision technology, the boundary of wood anatomical structure molecular binary image was sought This kind of theory and method lay a solid foundaion on the collection of feature and the pottern recognition and other high level processing of wood anatomical structure molecular image.
文摘The influence of a nontotal reflection on the interaction of a reflected shock wave with the boundary layer in a reflected shock tunnel has been investigated. The calculating method of the velocity, the temperature and the Mach number profiles in the boundary layer in reflected shock fixed coordinates has been obtained. To account for equilibrium real gas effects of nitrogen, the numerical results show that the minimum Mach number in the boundary layer has been moved from the wall into the boundary layer with the increasing of the incident shock Mach number. The minimum Mach number, the shock angle in the bifurcated foot and the jet velocity along the wall to the end plate are reduced owing to the Increasing of the area of nozzle throat. The numerical results are in good agreement with measurements.
文摘The boundary element method (KEM) which a used to solve the elastic problems has more advantages than other numerical methods. Especially, it can resolve rapidly varying internal stress and strain fields more accurately. However, it is of en fails in the region near the boundary because of the singularity of the solutions. Though we can increase the boundary meshes more and more, the solutions of stress on the boundary can't be given directly; which has obstructed the applications of the HEM to some extent.In this paper we proposed the boudary expanding-contracting principle and the boundary expanding-contracting method (BECM) based on the principle. With this method, not only the solutions in the region near or on the boundary can be obtained directly, but the iterative processes can also he used conveniently to improve the accuracy of the solutions.
文摘Two terranes formed since the Late Palaeozoic can be distinguished in southwestern China. One is charac-terized by the Permo-Carboniferous ice-rafted marine gravel-bearing clastic formation and the cold-water faunaof the Gondwana facies, including the Gangmar Co, Lhasa, Sa' gya, Tengchong and Baoshan terranes and theother is marked by the Upper Palaeozoic of the Yangtze type with the Cathaysian flora and the Pacific-typefusulinids, comprising the Changning-Menglian, Shuangjiang-Lancang, Qamdo and Bayan Har terranes. TheLongmu Co-Shuanghu-Dengqen-North Lancang River-Kejie-Mengding suture zone between the two groups ofterranes is the boundary between Gondwana and Pacifica in southwestern China. On the grounds of thesedimentary formation and successive southwestward migration of the Asian nonmarine Jurassic-Cretaceousendemic bivalves, the ages of the suture and some terranes to the southwest of the suture zone are discussed.The Baoshan terrane and the Nyainrong-Sog terrane in the Lhasa composite terrane were firstly pieced togeth-er with the Asian continent in the early Early Jurassic. The northern Tibet-western Yunnan microplate, in-cluding the Gangmar Co, Lhasa and Tengchong terranes, collided with the Asian continent at the end of theEarly Cretaceous Neocomian.
基金This project was sponsored by the State Seismological Bureau (85070102), China
文摘Two aspects of a new method,which can be used for seismic zoning,are introduced in this paper.On the one hand,the approach to estimate b value and annual activity rate proposed by Kijko and Sellevoll needs to use the earthquake catalogue.The existing earthquake catalogue contains both historical and recent instrumental data sets and it is inadequate to use only one part.Combining the large number of historical events with recent complete records and taking the magnitude uncertainty into account,Kijko’s method gives the maximum likelihood estimation of b value and annual activity rate,which might be more realistic.On the other hand,this method considers the source zone boundary uncertainty in seismic hazard analysis,which means the earthquake activity rate across a boundary of a source zone changes smoothly instead of abruptly and avoids too large a gradient in the calculated results.
基金supported by the National Natural Science Foundation of China(Nos.11571105,11771139)。
文摘Let R_Ⅲ(n) be the classical domain of type Ⅲ with n≥2. This article is devoted to a deep study of the Schwarz lemma on R_Ⅲ(n) via not only exploring the smooth boundary points of R_Ⅲ(n) but also proving the Schwarz lemma at the smooth boundary point for holomorphic self-mappings of R_Ⅲ(n).
文摘The mechanism of acoustic radiation from the boundary layer of an axisymmetric body is analyzed, and its sound pressure spectrum is predicted. It is shown that the acoustic radiation results from the transition region and the turbulent boundary layer; and that the acoustic radiation from transition region is predominant at low frequencies; while the turbulent boundary layer has the decisive effect on acoustic radiation at high frequencies. The calculated values are in good agreement with the experimental data.
文摘The vertical transport of mass at the top of the boundary layer is considered as a link between the boundary layer and free atmosphere.The adjustment of the wind and pressure fields in the boundary layer is studied under the consideration of the interaction between the boundary layer and free atmosphere.The vertical motion at the top of the boundary layer is evaluated.The results show that the distinguished differ- ences of the present results from classical Ekman layer do exist and they are discussed in the paper.
文摘By use of geostrophic momentum approximation,the analytical expressions of the wind distribution within the planetary boundary layer and the vertical velocity at the top of the boundary layer are obtained when the distribution of eddy transfer coefficient k is divided into three sections:k_1z(z_0≤z<h_1),k_2(h_1≤z<h_2), and k_3(h_2≤z).The results are in agreement with the observations.In particular,the wind profile in the surface layer(z_0≤z<h_1)coincides with the logarithmic distribution.The maximum angle between winds near the surface and at the bottom of the free atmosphere is only about 30°.This work improves the work of Wu and Blumen(1982)who introduced the geostrophic momentum approximation to the boundary layer.The solutions in barotropic and neutral conditions have been also extended to the baroclinic and stratified atmosphere.
基金Supported by the National Natural Science Foundation of China(11501198,11701307)the Key Scientific Research Projects in Universities of Henan Province(16B110010)+2 种基金the Zhejiang Natural Science Foundation of China(LY16A010012)the Doctoral Foundation of Pingdingshan University(PXY-BSQD-2015005)the Foster Foundation of Pingdingshan University(PXYPYJJ2016007)
文摘In this article, the sharp growth theorem for almost starlike mappings of complex order λ is given firstly. Secondly, distortion theorem along a unit direction is also established as the application of the growth theorem. In particular, using our results can reduce to some well-known results.
基金The Specialized Funds for National Key Basic Study (G1998040704), the Dual Project of China Earthquake Admini-stration (9691309020301) and National Natural Science Foundation of China (46764010).
文摘plane with the strike of 127°, the dip of 79° and the rake of 171°. The rupture process inversion result of MS=7.9 earthquake shows that the total rupture duration is about 37 s, the scalar moment tensor is M0=0.97 × 1020 N·m. Rupture mainly occurred on the shallow area with 110 km long and 30 km wide, the location in which the rupture initiated is not where the main rupture took place, and the area with slip greater than 0.5 m basically lies within 35 km deep middle-crust under the earth surface. The maximum static slip is 3.6 m. There are two distinct areas with slip larger than 2.0 m. We noticed that when the rupture propagated towards northwest and closed to the area around the MS=7.3 hypocenter, the slip decreased rapidly, which may indicate that the rupture process was stopped by barriers. The consistence of spatial distribution of slip on the fault plane with the distribution of aftershocks also supports that the rupture is a heterogeneous process owing to the presence of barriers.
基金Project supported by the National Natural Science Foundation of China (Nos. 60274008 and 10171084)
文摘For a class of nonlinear filtration equation with nonlinear second-third boundary value condition, it is shown that a priori boundary of the solution can be estimated and controlled by initial data and integral on the boundary of the region. The priori estimate of the solutions was established by iterative method. By using this estimate the solutions may blow-up on the boundary of the region and thus it may have asymptotic non-stability.
文摘In this paper, problems of the flow over a fat plate in the large Reynolds numbercase are studied by using the method of multiple scales ̄[1,2].We have obtained N-orderuniformly valid asymptotic solutions of the Naver-Stodes equations.
基金the research item of the Second Tibetan Plateau Experiment.
文摘A dynamic study on Ekman characteristics by using 1998 SCSMEX and TIPEX boundary layer data is made. The results are as follows: (1) Similar dynamical Ekman characteristics are observed in the Tibetan Plateau and in the South China Sea and its surrounding area. (2) The thickness of the boundary layer is about 2250 m over the Tibetan Plateau, and considering its variation, the thickness could be up to 2250–2750 m. In the tropical southwest Pacific, the thickness of the boundary layer is about 2000 m, and the variation is smaller; a smaller thickness of the boundary layer is in the plain area of the Bohai Sea. (3) Because of the difference in elevation between the Tibetan Plateau and the tropical ocean area, the influence of the boundary layer on the atmosphere is quite different although the two areas have almost the same thickness for the boundary layer, the height where the friction forcing occurs is quite different. (4) The vertical structure of turbulence friction is quite different in the Plateau and in the tropical ocean area. Calculations by 1998 SCSMEX and TIPEX boundary layer data indicate that even in the lowest levels, eddy viscosity in the Tibetan Plateauan can be 2.3 times than in the tropical ocean area.
基金National Natural Science Foundation of China(Grant Nos. 11571105 and 11471111)Natural Science Foundation of Zhejiang Province(Grant No.LY14A010017)
文摘Let R_I(m,n) be the classical domain of type I in C^(m×n)with 1≤m≤n.We obtain the optimal estimates of the eigenvalues of the Fréchet derivative Df(Z) at a smooth boundary fixed point Z of R_I(m,n)for a holomorphic self-mapping f of R_L(m,n).We provide a necessary and sufficient condition such that the boundary points of R_I(m,n) are smooth,and give some properties of the smooth boundary points of R_L(m,n).Our results extend the classical Schwarz lemma at the boundary of the unit disk △ to R_I(m,n),which may be applied to get some optimal estimates in several complex variables.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11101139,11031008,11301136,11571089,11401159 and 11501198)the Science Foundation of Hebei Province(Grant No.A2014205069)+3 种基金the Key Scientific Research Pro jects in Universities of He’nan Province(Grant No.16B110010)the Doctoral Foundation of Pingdingshan University(Grant No.PXY-BSQD-2015005)the Doctoral Foundation of Hebei Normal University(Grant No.L2015B04)the Foster Foundation of Pingdingshan University(Grant No.PXYPYJJ2016007)
文摘In this paper, we will use the Schwarz lemma at the boundary to character the distortion theorems of determinant at the extreme points and distortion theorems of matrix on the complex tangent space at the extreme points for normalized locally biholomorphic quasi-convex mappings in the unit ball Bn respectively.
基金Research supported by the NSF of Shandong Province (Y2004A01) the foundation of SDAI(XN040101).
文摘In this paper, we investigate the periodic boundary value problems for nonlinear first order functional differential equations. By establishing a new comparison result, criteria on the existence of maximal and minimal solutions are obtained.
文摘In this survey paper we report on recent developments of the hp-version of the boundary element method (BEM). As model problems we consider weakly singular and hypersingular integral equations of the first kind on a planar, open surface. We show that the Galerkin solutions (computed with the hp-version on geometric meshes) converge exponentially fast towards the exact solutions of the integral equations. An hp-adaptive algorithm is given and the implementation of the hp-version BEM is discussed together with the choice of efficient preconditioners for the ill-conditioned boundary element stiffness matrices. We also comment on the use of the hp-version BEM for solving Signorini contact problems in linear elasticity where the contact conditions are enforced only on the discrete set of Gauss-Lobatto points. Numerical results are presented which underline the theoretical results.
文摘In this paper, we gave boundary layer estimation of a singular equation of order 4 with limit equation of order 2. The results show that the thickness of boundary layer is intrinsically relative to the reciprocal of the order of equation of and independent of the order of equation of u.