In this paper,the following two results are obtained:(1) If Γ is a Jordan curve of 2,∞∈Γ,then Γ is a quasicircle if and only if there exists a constant k,1≤k<+∞,such that for any four points z 1,z 2,w 1,w...In this paper,the following two results are obtained:(1) If Γ is a Jordan curve of 2,∞∈Γ,then Γ is a quasicircle if and only if there exists a constant k,1≤k<+∞,such that for any four points z 1,z 2,w 1,w 2∈Γ,there exists a k-quasiconformal mapping h of 2 with h(∞)=∞,h(Γ)=Γ and h(z j)=w j(j=1,2).(2)If Γ is a Jordan curve of 2, then Γ is a quasicircle if and only if Γ is a bounded circular distortion curve.展开更多
In this paper,the weak(1,1)boundedness of oscillatory singular integral with variable phase P(x)γ(y)for any x,y∈R,Tf(x):=p.v.∫∞-∞eiP(x)γ(y)f(x?y)dy/y is studied,where P is a real monic polynomial on R.
Let M be a complete Riemannian manifold, A be its Laplacian, ▽ be the gradient operator. The Riesz transform ▽（-△）<sup>-1/2</sup> was introduced first by R. S. Stritrartz, and earlier on, E. M. Stein ...Let M be a complete Riemannian manifold, A be its Laplacian, ▽ be the gradient operator. The Riesz transform ▽（-△）<sup>-1/2</sup> was introduced first by R. S. Stritrartz, and earlier on, E. M. Stein had introduced Riesz transform on Lie groups. Stritrartz proved展开更多
In this article,we prove the existence of quasi-periodic solutions and the boundedness of all solutions of the p-Laplacian equation(φ_(p)(x’))’+aφ_(p)(x+)-bφ_(p)(x-)=g(x,t)+f(t),where g(x,t)and f(t)are quasi-peri...In this article,we prove the existence of quasi-periodic solutions and the boundedness of all solutions of the p-Laplacian equation(φ_(p)(x’))’+aφ_(p)(x+)-bφ_(p)(x-)=g(x,t)+f(t),where g(x,t)and f(t)are quasi-periodic in t with Diophantine frequency.A new method is presented to obtain the generating function to construct canonical transformation by solving a quasi-periodic homological equation.展开更多
The authors study the Lagrangian stability for the sublinear Duffing equationsx+e(t)|x|^(α-1) x=p(t)with 0<α<1,where e and p are real analytic quasi-periodic functions with frequencyω.It is proved that if the...The authors study the Lagrangian stability for the sublinear Duffing equationsx+e(t)|x|^(α-1) x=p(t)with 0<α<1,where e and p are real analytic quasi-periodic functions with frequencyω.It is proved that if the mean value of e is positive and the frequencyωsatisfies Diophantine condition,then every solution of the equation is bounded.展开更多
Squeezed quantum vacua seems to violate the averaged null energy conditions (ANEC’s), because they have a negative energy density. When treated as a perfect fluid, rapidly rotating Casimir plates will create vorticit...Squeezed quantum vacua seems to violate the averaged null energy conditions (ANEC’s), because they have a negative energy density. When treated as a perfect fluid, rapidly rotating Casimir plates will create vorticity in the vacuum bounded by them. The geometry resulting from an arbitrarily extended Casimir plates along their axis of rotation is similar to van Stockum spacetime. We observe closed timelike curves (CTC’s) forming in the exterior of the system resulting from frame dragging. The exterior geometry of this system is similar to Kerr geometry, but because of violation of ANEC, the Cauchy horizon lies outside the system unlike Kerr blackholes, giving more emphasis on whether spacetime is multiply connected at the microscopic level.展开更多
Transient rate decline curve analysis for constant pressure production is presented in this pa- per for a naturally fractured reservoir. This approach is based on exponential and constant bottom-hole pressure solution...Transient rate decline curve analysis for constant pressure production is presented in this pa- per for a naturally fractured reservoir. This approach is based on exponential and constant bottom-hole pressure solution. Based on this method, when In （flow rate） is plotted versus time, two straight lines are ob- tained which can be used for estimating different parameters of a naturally fractured reservoir. Parameters such as storage capacity ratio （co）, reservoir drainage area （A）, reservoir shape factor （CA）, fracture per- meability （ky）, interporosity flow parameter （,~） and the other parameters can be determined by this ap- proach. The equations are based on a model originally presented by Warren and Root and extended by Da Prat et al. and Mavor and Cinco-Ley. The proposed method has been developed to be used for naturally fractured reservoirs with different geometries. This method does not involve the use of any chart and by us- ing the pseudo steady state flow regime, the influence of wellbore storage on the value of the parameters ob- tained from this technique is negligible. In this technique, all the parameters can be obtained directly while in conventional approaches like type curve matching method, parameters such as co and g should be ob- tained by other methods like build-up test analysis and this is one of the most important advantages of this method that could save time during reservoir analyses. Different simulated and field examples were used for testing the proposed technique. Comparison between the obtained results by this approach and the results of type curve matching method shows a high performance of decline curves in well testing.展开更多
In 1993, Tsai proved that a proper holomorphic mapping f: Ω → Ω′ from an irreducible bounded symmetric domain Ω of rank ? 2 into a bounded symmetric domain Ω′ is necessarily totally geodesic provided that r′:=...In 1993, Tsai proved that a proper holomorphic mapping f: Ω → Ω′ from an irreducible bounded symmetric domain Ω of rank ? 2 into a bounded symmetric domain Ω′ is necessarily totally geodesic provided that r′:= rank(Ωg’) ? rank(Ω):= r, proving a conjecture of the author’s motivated by Hermitian metric rigidity. As a first step in the proof, Tsai showed that df preserves almost everywhere the set of tangent vectors of rank 1. Identifying bounded symmetric domains as open subsets of their compact duals by means of the Borel embedding, this means that the germ of f at a general point preserves the varieties of minimal rational tangents (VMRTs).In another completely different direction Hwang-Mok established with very few exceptions the Cartan-Fubini extension priniciple for germs of local biholomorphisms between Fano manifolds of Picard number 1, showing that the germ of map extends to a global biholomorphism provided that it preserves VMRTs. We propose to isolate the problem of characterization of special holomorphic embeddings between Fano manifolds of Picard number 1, especially in the case of classical manifolds such as rational homogeneous spaces of Picard number 1, by a non-equidimensional analogue of the Cartan-Fubini extension principle. As an illustration we show along this line that standard embeddings between complex Grassmann manifolds of rank ? 2 can be characterized by the VMRT-preserving property and a non-degeneracy condition, giving a new proof of a result of Neretin’s which on the one hand paves the way for far-reaching generalizations to the context of rational homogeneous spaces and more generally Fano manifolds of Picard number 1, on the other hand should be applicable to the study of proper holomorphic mappings between bounded domains carrying some form of geometric structures.展开更多
In this paper,we prove the existence of quasi-periodic solutions and the boundedness of all the solutions of the general semilinear quasi-periodic differential equation x′′+ax^(+)-bx^(-)=G_x(x,t)+f (t),where x^(+)=m...In this paper,we prove the existence of quasi-periodic solutions and the boundedness of all the solutions of the general semilinear quasi-periodic differential equation x′′+ax^(+)-bx^(-)=G_x(x,t)+f (t),where x^(+)=max{x,0},x^(-)=max{-x,0},a and b are two different positive constants,f(t) is C^(39) smooth in t,G(x,t)is C^(35) smooth in x and t,f (t) and G(x,t) are quasi-periodic in t with the Diophantine frequency ω=(ω_(1),ω_(2)),and D_(x)^(i)D_(t)^(j)G(x,t) is bounded for 0≤i+j≤35.展开更多
In this paper, the authors are concerned with the forced isochronous oscillators with a repulsive singularity and a bounded nonlinearity x'' + V'(x) + g(x) = e(t, x, x'),where the assumptions on V, g a...In this paper, the authors are concerned with the forced isochronous oscillators with a repulsive singularity and a bounded nonlinearity x'' + V'(x) + g(x) = e(t, x, x'),where the assumptions on V, g and e are regular, described precisely in the introduction.Using a variant of Moser's twist theorem of invariant curves, the authors show the existence of quasi-periodic solutions and boundedness of all solutions. This extends the result of Liu to the case of the above system where e depends on the velocity.展开更多
基金Supported by the National Natural Science Foundation of China( 1 0 2 71 0 4 3) and the Natural ScienceFoundation of Zhejiang province ( M1 0 30 87)
文摘In this paper,the following two results are obtained:(1) If Γ is a Jordan curve of 2,∞∈Γ,then Γ is a quasicircle if and only if there exists a constant k,1≤k<+∞,such that for any four points z 1,z 2,w 1,w 2∈Γ,there exists a k-quasiconformal mapping h of 2 with h(∞)=∞,h(Γ)=Γ and h(z j)=w j(j=1,2).(2)If Γ is a Jordan curve of 2, then Γ is a quasicircle if and only if Γ is a bounded circular distortion curve.
文摘In this paper,the weak(1,1)boundedness of oscillatory singular integral with variable phase P(x)γ(y)for any x,y∈R,Tf(x):=p.v.∫∞-∞eiP(x)γ(y)f(x?y)dy/y is studied,where P is a real monic polynomial on R.
文摘Let M be a complete Riemannian manifold, A be its Laplacian, ▽ be the gradient operator. The Riesz transform ▽（-△）<sup>-1/2</sup> was introduced first by R. S. Stritrartz, and earlier on, E. M. Stein had introduced Riesz transform on Lie groups. Stritrartz proved
基金Supported by National Natural Science Foundation of China(Grant Nos.11801295,11971059,12101623)China Postdoctoral Science Foundation(Grant No.2020M680132)Guangdong Basic and Applied Basic Research Foundation(Grant No.2020A1515110382)。
文摘In this article,we prove the existence of quasi-periodic solutions and the boundedness of all solutions of the p-Laplacian equation(φ_(p)(x’))’+aφ_(p)(x+)-bφ_(p)(x-)=g(x,t)+f(t),where g(x,t)and f(t)are quasi-periodic in t with Diophantine frequency.A new method is presented to obtain the generating function to construct canonical transformation by solving a quasi-periodic homological equation.
基金supported by the National Natural Science Foundation of China(Nos.11571327,11971059)。
文摘The authors study the Lagrangian stability for the sublinear Duffing equationsx+e(t)|x|^(α-1) x=p(t)with 0<α<1,where e and p are real analytic quasi-periodic functions with frequencyω.It is proved that if the mean value of e is positive and the frequencyωsatisfies Diophantine condition,then every solution of the equation is bounded.
文摘Squeezed quantum vacua seems to violate the averaged null energy conditions (ANEC’s), because they have a negative energy density. When treated as a perfect fluid, rapidly rotating Casimir plates will create vorticity in the vacuum bounded by them. The geometry resulting from an arbitrarily extended Casimir plates along their axis of rotation is similar to van Stockum spacetime. We observe closed timelike curves (CTC’s) forming in the exterior of the system resulting from frame dragging. The exterior geometry of this system is similar to Kerr geometry, but because of violation of ANEC, the Cauchy horizon lies outside the system unlike Kerr blackholes, giving more emphasis on whether spacetime is multiply connected at the microscopic level.
文摘Transient rate decline curve analysis for constant pressure production is presented in this pa- per for a naturally fractured reservoir. This approach is based on exponential and constant bottom-hole pressure solution. Based on this method, when In （flow rate） is plotted versus time, two straight lines are ob- tained which can be used for estimating different parameters of a naturally fractured reservoir. Parameters such as storage capacity ratio （co）, reservoir drainage area （A）, reservoir shape factor （CA）, fracture per- meability （ky）, interporosity flow parameter （,~） and the other parameters can be determined by this ap- proach. The equations are based on a model originally presented by Warren and Root and extended by Da Prat et al. and Mavor and Cinco-Ley. The proposed method has been developed to be used for naturally fractured reservoirs with different geometries. This method does not involve the use of any chart and by us- ing the pseudo steady state flow regime, the influence of wellbore storage on the value of the parameters ob- tained from this technique is negligible. In this technique, all the parameters can be obtained directly while in conventional approaches like type curve matching method, parameters such as co and g should be ob- tained by other methods like build-up test analysis and this is one of the most important advantages of this method that could save time during reservoir analyses. Different simulated and field examples were used for testing the proposed technique. Comparison between the obtained results by this approach and the results of type curve matching method shows a high performance of decline curves in well testing.
基金This research is partially supported by a Competitive Earmarked Research Grant of the Research Grants Council of Hong Kong,China
文摘In 1993, Tsai proved that a proper holomorphic mapping f: Ω → Ω′ from an irreducible bounded symmetric domain Ω of rank ? 2 into a bounded symmetric domain Ω′ is necessarily totally geodesic provided that r′:= rank(Ωg’) ? rank(Ω):= r, proving a conjecture of the author’s motivated by Hermitian metric rigidity. As a first step in the proof, Tsai showed that df preserves almost everywhere the set of tangent vectors of rank 1. Identifying bounded symmetric domains as open subsets of their compact duals by means of the Borel embedding, this means that the germ of f at a general point preserves the varieties of minimal rational tangents (VMRTs).In another completely different direction Hwang-Mok established with very few exceptions the Cartan-Fubini extension priniciple for germs of local biholomorphisms between Fano manifolds of Picard number 1, showing that the germ of map extends to a global biholomorphism provided that it preserves VMRTs. We propose to isolate the problem of characterization of special holomorphic embeddings between Fano manifolds of Picard number 1, especially in the case of classical manifolds such as rational homogeneous spaces of Picard number 1, by a non-equidimensional analogue of the Cartan-Fubini extension principle. As an illustration we show along this line that standard embeddings between complex Grassmann manifolds of rank ? 2 can be characterized by the VMRT-preserving property and a non-degeneracy condition, giving a new proof of a result of Neretin’s which on the one hand paves the way for far-reaching generalizations to the context of rational homogeneous spaces and more generally Fano manifolds of Picard number 1, on the other hand should be applicable to the study of proper holomorphic mappings between bounded domains carrying some form of geometric structures.
基金supported by National Natural Science Foundation of China (Grant No.11571327)。
文摘In this paper,we prove the existence of quasi-periodic solutions and the boundedness of all the solutions of the general semilinear quasi-periodic differential equation x′′+ax^(+)-bx^(-)=G_x(x,t)+f (t),where x^(+)=max{x,0},x^(-)=max{-x,0},a and b are two different positive constants,f(t) is C^(39) smooth in t,G(x,t)is C^(35) smooth in x and t,f (t) and G(x,t) are quasi-periodic in t with the Diophantine frequency ω=(ω_(1),ω_(2)),and D_(x)^(i)D_(t)^(j)G(x,t) is bounded for 0≤i+j≤35.
基金supported by the National Natural Science Foundation of China(No.10325103)the Chinese Scholarship Council(No.201206010092)
文摘In this paper, the authors are concerned with the forced isochronous oscillators with a repulsive singularity and a bounded nonlinearity x'' + V'(x) + g(x) = e(t, x, x'),where the assumptions on V, g and e are regular, described precisely in the introduction.Using a variant of Moser's twist theorem of invariant curves, the authors show the existence of quasi-periodic solutions and boundedness of all solutions. This extends the result of Liu to the case of the above system where e depends on the velocity.
