In this paper, firstly using different method and technique we derive the cor-responding integral representation formulas of （0, q）（q 〉 0） differential forms for the twotypes of the bounded domains in complex sub...In this paper, firstly using different method and technique we derive the cor-responding integral representation formulas of （0, q）（q 〉 0） differential forms for the twotypes of the bounded domains in complex submanifolds with codimension-m. Secondly weobtain the unified integral representation formulas of （0, q）（q 〉 0） differential forms for thegeneral bounded domain in complex submanifold with codimension-m, which include Hatzi-afratis formula, i.e. Koppelman type integral formula for the bounded domain with smoothboundary in analytic varieties. In particular, when m -- 0, we obtain the unified integralrepresentation formulas of （0, q）（q 〉 0） differential forms for general bounded domain in Cn,which are the generalization and the embodiment of Koppelman-Leray formula.展开更多
Ⅰ. INTRODUCTIONThe yield criteria are important foundations in the theory of plasticity and the strength of metallic materials. As the shear stress is the major cause for yielding, the yield criteria based on shear s...Ⅰ. INTRODUCTIONThe yield criteria are important foundations in the theory of plasticity and the strength of metallic materials. As the shear stress is the major cause for yielding, the yield criteria based on shear stress as a physical interpretation are: maximum shear stress (Tresca)criteri-展开更多
A fundamental issue in CFD is the role of coordinates and,in particular,the search for“optimal”coordinates.This paper reviews and generalizes the recently developed unified coordinate system(UC).For one-dimensional ...A fundamental issue in CFD is the role of coordinates and,in particular,the search for“optimal”coordinates.This paper reviews and generalizes the recently developed unified coordinate system(UC).For one-dimensional flow,UC uses a material coordinate and thus coincides with Lagrangian system.For two-dimensional flow it uses a material coordinate,with the other coordinate determined so as to preserve mesh othorgonality(or the Jacobian),whereas for three-dimensional flow it uses two material coordinates,with the third one determined so as to preserve mesh skewness(or the Jacobian).The unified coordinate system combines the advantages of both Eulerian and the Lagrangian system and beyond.Specifically,the followings are shown in this paper.(a)For 1-D flow,Lagrangian system plus shock-adaptive Godunov scheme is superior to Eulerian system.(b)The governing equations in any moving multi-dimensional coordinates can be written as a system of closed conservation partial differential equations(PDE)by appending the time evolution equations–called geometric conservation laws–of the coefficients of the transformation(from Cartesian to the moving coordinates)to the physical conservation laws;consequently,effects of coordinate movement on the flow are fully accounted for.(c)The system of Lagrangian gas dynamics equations is written in conservation PDE form,thus providing a foundation for developing Lagrangian schemes as moving mesh schemes.(d)The Lagrangian system of gas dynamics equations in two-and three-dimension are shown to be only weakly hyperbolic,in direct contrast to the Eulerian system which is fully hyperbolic;hence the two systems are not equivalent to each other.(e)The unified coordinate system possesses the advantages of the Lagrangian system in that contact discontinuities(including material interfaces and free surfaces)are resolved sharply.(f)In using the UC,there is no need to generate a body-fitted mesh prior to computing flow past a body;the mesh is automatically generated by the flow.Numerical examples展开更多
Let {X, X_k : k ≥ 1} be a sequence of independent and identically distributed random variables with a common distribution F. In this paper, the authors establish some results on the local precise large and moderate d...Let {X, X_k : k ≥ 1} be a sequence of independent and identically distributed random variables with a common distribution F. In this paper, the authors establish some results on the local precise large and moderate deviation probabilities for partial sums S_n =sum from i=1 to n(X_i) in a unified form in which X may be a random variable of an arbitrary type,which state that under some suitable conditions, for some constants T > 0, a and τ >1/2and for every fixed γ > 0, the relation P(S_n- na ∈(x, x + T ]) ~nF((x + a, x + a + T ]) holds uniformly for all x ≥γn~τ as n→∞, that is, P(Sn- na ∈(x, x + T ]) lim sup- 1 = 0.n→+∞x≥γnτnF((x + a, x + a + T ])The authors also discuss the case where X has an infinite mean.展开更多
文摘In this paper, firstly using different method and technique we derive the cor-responding integral representation formulas of （0, q）（q 〉 0） differential forms for the twotypes of the bounded domains in complex submanifolds with codimension-m. Secondly weobtain the unified integral representation formulas of （0, q）（q 〉 0） differential forms for thegeneral bounded domain in complex submanifold with codimension-m, which include Hatzi-afratis formula, i.e. Koppelman type integral formula for the bounded domain with smoothboundary in analytic varieties. In particular, when m -- 0, we obtain the unified integralrepresentation formulas of （0, q）（q 〉 0） differential forms for general bounded domain in Cn,which are the generalization and the embodiment of Koppelman-Leray formula.
文摘Ⅰ. INTRODUCTIONThe yield criteria are important foundations in the theory of plasticity and the strength of metallic materials. As the shear stress is the major cause for yielding, the yield criteria based on shear stress as a physical interpretation are: maximum shear stress (Tresca)criteri-
基金supported by a grant(HKUST6138/01P)from the Research Grants Council of Hong Kong.
文摘A fundamental issue in CFD is the role of coordinates and,in particular,the search for“optimal”coordinates.This paper reviews and generalizes the recently developed unified coordinate system(UC).For one-dimensional flow,UC uses a material coordinate and thus coincides with Lagrangian system.For two-dimensional flow it uses a material coordinate,with the other coordinate determined so as to preserve mesh othorgonality(or the Jacobian),whereas for three-dimensional flow it uses two material coordinates,with the third one determined so as to preserve mesh skewness(or the Jacobian).The unified coordinate system combines the advantages of both Eulerian and the Lagrangian system and beyond.Specifically,the followings are shown in this paper.(a)For 1-D flow,Lagrangian system plus shock-adaptive Godunov scheme is superior to Eulerian system.(b)The governing equations in any moving multi-dimensional coordinates can be written as a system of closed conservation partial differential equations(PDE)by appending the time evolution equations–called geometric conservation laws–of the coefficients of the transformation(from Cartesian to the moving coordinates)to the physical conservation laws;consequently,effects of coordinate movement on the flow are fully accounted for.(c)The system of Lagrangian gas dynamics equations is written in conservation PDE form,thus providing a foundation for developing Lagrangian schemes as moving mesh schemes.(d)The Lagrangian system of gas dynamics equations in two-and three-dimension are shown to be only weakly hyperbolic,in direct contrast to the Eulerian system which is fully hyperbolic;hence the two systems are not equivalent to each other.(e)The unified coordinate system possesses the advantages of the Lagrangian system in that contact discontinuities(including material interfaces and free surfaces)are resolved sharply.(f)In using the UC,there is no need to generate a body-fitted mesh prior to computing flow past a body;the mesh is automatically generated by the flow.Numerical examples
基金supported by the National Natural Science Foundation of China(No.11401415)
文摘Let {X, X_k : k ≥ 1} be a sequence of independent and identically distributed random variables with a common distribution F. In this paper, the authors establish some results on the local precise large and moderate deviation probabilities for partial sums S_n =sum from i=1 to n(X_i) in a unified form in which X may be a random variable of an arbitrary type,which state that under some suitable conditions, for some constants T > 0, a and τ >1/2and for every fixed γ > 0, the relation P(S_n- na ∈(x, x + T ]) ~nF((x + a, x + a + T ]) holds uniformly for all x ≥γn~τ as n→∞, that is, P(Sn- na ∈(x, x + T ]) lim sup- 1 = 0.n→+∞x≥γnτnF((x + a, x + a + T ])The authors also discuss the case where X has an infinite mean.
