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1.
Abstract. It is proved that the semilinear elliptic problem with zero boundary value  相似文献   

2.
In this paper, we prove that if G is 3-connected noncomplete graph of order n satisfying min{max{d(u),d(v)}:d(u,v)=2}=μ, then for each edge e, G has a cycle containing e of length at least min{n,2μ}, unless G is a spanning subgraph of Kμ + Kcn−μ or K3+(lKμ−2Ks), where n=l(μ−2)+s+3,1≤sμ−2. Partially supported by NNSFC(No. 60172005); Partially supported by NNSFC(No. 10431020);  相似文献   

3.
Let τ D . denote the lifetime of a diffusion process on domainDR d. This paper presents a sufficient condition for the exponential moment of τ D to be finite. Here, both of the domain and the diffusion operator are general. As an application, the main result of Gao (1995) for conditioned diffusions is improved on. Research supported in part by NNSFC (19631060) and Beijing Normal University  相似文献   

4.
In this paper we investigate some algebra properties of dual Toeplitz operators on the orthogonal complement of the Dirichlet space in the Sobolev space. We completely characterize commuting dual Toeplitz operators with harmonic symbols, and show that a dual Toeplitz operator commutes with a nonconstant analytic dual Toeplitz operator if and only if its symbol is analytic. We also obtain the sufficient and necessary conditions on the harmonic symbols for SφSφψ= Sφψ.  相似文献   

5.
Paracontact and para Sasakian manifoldsM carryingr(1<r≤dimM) Reed vector filds ξ r have been especially studied by A. Bucki [2], [3], [4]. In the present paper, we consider a (2m+2)-dimensional para Sasakian manifoldM(ϕ, ξ r , η r g), whose Reed convectors η r r b are exact 1-forms and the covariant derivatives of ξ r are given by ∇ξ r =f r dp , wheredp means the horizontal component of the soldering formdp andf r∈CM satisfydf r =cη r ,c=constant. It is proved that such a manifold may be viewed as the local Riemannian productM=M ×M, where
i)  M is a flat surface tangent to ξ r ;
ii)  M is a pseudo-umbilical 2m-dimensional submanifold, having ξ=f r ξ r as mean curvature vector field.
It is pointed-out thatM can not be compact. Some distinguished vector fields onM are constructed and infinitesimal transformations induced by them on the Lie algebra are discussed.  相似文献   

6.
We prove that, under certain conditions on a positive functionl continuous on [0, +∞], there exists an entire transcendental functionf of boundedl-index such that lnlnM f(r)lnL(r),r→∞, whereM f (r)=max {|f(z)|: |z|=r} andL(r)=∫ 0 r l(t)dt. Ifl(r)=r p-1 forr≥1, 0<ρ<∞, then there exists an entire functionf of boundedl-index such thatM f (r)≈r p . Lvov University, Lvov. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 48, No. 9, pp. 1166–1182, September, 1996.  相似文献   

7.
In this paper we study the approximation on set of full measure for functions in Sobolev spaces L m 1 (R n) (m∈ℕ) by Bochner-Riesz means of conjugate Fourier integrals below the critical index. A theorem concerning the precise approximation orders with relation to the number m of space L m 1 (R n) and the index of Bochner-Riesz means is obtained. Supported by NNSFC.  相似文献   

8.
Approximation order provided by refinable function vectors   总被引:1,自引:0,他引:1  
In this paper we considerL p-approximation by integer translates of a finite set of functionsϕ v (v=0, ...,r − 1) which are not necessarily compactly supported, but have a suitable decay rate. Assuming that the function vectorϕ=(ϕ =0/ r−1 is refinable, necessary and sufficient conditions for the refinement mask are derived. In particular, if algebraic polynomials can be exactly reproduced by integer translates ofϕ v, then a factorization of the refinement mask ofϕ can be given. This result is a natural generalization of the result for a single functionϕ, where the refinement mask ofϕ contains the factor ((1 +e iu )/2) m if approximation orderm is achieved. Dedicated to Professor L. Berg on the occasion of his 65th birthday  相似文献   

9.
The cluster-galaxy cross-correlation and the average infall velocity around cluster for the tilted CDM models, the hot-cold mixed dark matter models (MDM) and theA CDM models are calculated. And it is found that the prediction of the cluster-galaxy cross-correlation of theA CDM models with ΩA=0.9, ΩC=0.1,h=1,b = 1 or 2 is much higher than that of observation for the radius larger than 10 h−1 Mpc (H0 = 100 h.kms−1Mpc−1), and the other models are compatible with the observation on the scale of (3–20) h Mpc. The results can be used to compare with new observations to restrict the nature of the dark matter and the biasing factor. Project supported by the National Natural Science Foundation of China (Grant No. 19733001).  相似文献   

10.
Given a basic hypergeometric series with numerator parametersa 1,a 2, ...,a r and denominator parametersb 2, ...,b r, we say it isalmost poised ifb i, =a 1 q δ,i a ii = 0, 1 or 2, for 2 ≤ir. Identities are given for almost poised series withr = 3 andr = 5 when a1, =q −2n. Partially supported by N.S.F. Grant No. DMS-8521580.  相似文献   

11.
Corresponding to the irreducible 0–1 matrix (a ij ) n×n , take similitude contraction mappingsϕ ij for eacha ij =1, ina ij =1, in R d with ratio 0<r ij <1. There are unique nonempty compact setsF 1,…,F n satisfying for each1≤i≤n, F i. We prove that open set condition holds if and only ifF i is ans-set for some1≤i≤n, wheres is such that the spectral radius of matrix (r ij 3 ) n x n is 1. Partly supported by Natural Science Foundation of China, and partly by Natural Science Foundation of Hubei Province  相似文献   

12.
 Let 𝒞⊆ℙ r K be a non-degenerate projective curve of degree d>r+1 of maximal regularity so that 𝒞 has an extremal secant line . We show that 𝒞∪ is arithmetically Cohen Macaulay if d<2r−1 and we study the Betti numbers and the Hartshorne-Rao module of the curve 𝒞. Received: 27 March 2002; in final form: 24 May 2002 / Published online: 1 April 2003 Mathematics Subject Classification (1991): 14H45, 13D02. The second author was partially supported by Swiss National Science Foundation (Projects No. 20-52762.97 and 20-59237.99).  相似文献   

13.
In this paper, we solve the problem proposed by Lan Wen for the case of dimM = 3. Roughly speaking, we prove that for fixed i, f has C1 persistently no small angles of index i if and only if f has a dominated splitting of index i on the C1 i-preperiodic set P*i(f).  相似文献   

14.
In this paper, we study composition operators on a Banach space of analytic functions, denoted byX, which includes the Bloch space. This space arises naturally as the dual space of analytic functions in the Bergman spaceL α 1 (D) which admit an atomic decomposition. We characterize the functions which induce compact composition operators and those which induce Fredholm operatorson this space. We also investigate when a composition operator has a closed range. Supported by NNSFC No.19671036  相似文献   

15.
HOMOCLINICORBITSFORSECONDORDERHAMILTONIANSYSTEMWITHQUADRATICGROWTHWUSHAOPINGANDLIUJIAQUANAbstract:Someexistenceandmultiplicit...  相似文献   

16.
The multicolor Ramsey number Rr(H) is defined to be the smallest integer n=n(r) with the property that any r-coloring of the edges of the complete graph Kn must result in a monochromatic subgraph of Kn isomorphic to H. It is well known that 2rm<Rr(C2m+1)<2(r+2)!m and Rr(C2m)≥(r−1)(m−1)+1. In this paper, we prove that Rr(C2m)≥2(r−1)(m−1)+2. This research is supported by NSFC(60373096, 60573022) and SRFDP(20030141003)  相似文献   

17.
Given a positive function F on S^n which satisfies a convexity condition, we introduce the r-th anisotropic mean curvature Mr for hypersurfaces in R^n+1 which is a generalization of the usual r-th mean curvature Hr. We get integral formulas of Minkowski type for compact hypersurfaces in R^n+1. We give some new characterizations of the Wulff shape by the use of our integral formulas of Minkowski type, in case F=1 which reduces to some well-known results.  相似文献   

18.
Assume thatf is an integer transcendental solution of the differential equationP n (z, f, f′)=P n−1(z, f, f′, ... f (p)), whereP n andP n−1 are polynomials in all variables, the degree ofP n with respect tof andf′ is equal ton, and the degree ofP n−1 with respect tof, f′, ... f (p) is at mostn−1. We prove that the order ρ of growth off satisfies the relation 1/2≤ρ<∞. We also prove that if ρ=1/2, then, for a certain real ν, in the domain {z: ν<argz<ν+2π}/E *, whereE * is a certain set of disks with finite sum of radii, the estimate lnf(z)=z 1/2 (β+o(1)), β∈C, holds forz=re iϕ,rr(ϕ)≥0. Furthermore, on the ray {z: argz=ν}, the following relation is true: ln‖f(re iν)‖=o(r 1/2),r→+∞,r>0, , where Δ is a certain set on the semiaxisr>0 with mes Δ<∞. “L'vivs'ka Politekhnika” University, Lvov. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 1, pp. 69–77, January, 1999.  相似文献   

19.
Summary Let Γ=〈g 1〉*〈g 2〉*...*〈g n 〉*... be a free product of cyclic groups with generators {g i }, andC r * (Γ, Λ) be the C*-algebra generated by the reduced group C*-algebraC r * Γ and a set of projectionsP gL associated with a subset Λ of {g i }. We prove the following: (1)C r * (Γ, Λ) is *-isomorphic to the reduced cross product for certain Hausdorff compact spaceX Λ constructed from Γ and its boundary ∂Γ. (2)C r * (Γ, Λ) is either a purely infinite, simple C*-algebra or an extension of a purely infinite, simple C*-altebra, depending on the pair (Γ, Λ). (3)C r * (Г, Λ) is nuclear if and only if the subgroup ΓΛ generated by {g i }/Λ is amenable. Partially supported by RMC grant 45/290/603 from the University of Newcastle Partially supported by NSF grant DMS-9225076 and a Taft travel grant from the University of Cincinnati  相似文献   

20.
In this paper the Cauchy problem for a class of nonhomogeneous Navier-Stokes equations in the infinite cylinderS T =ℝn x [0,T) is considered. We construct a unique local solution inL q([0,T);L p (ℝ n )) for a class of nonhomogeneous Navier-Stokes equations provided that initial data are inL r (ℝ n ), wherer>1 is an exponent determined by the structure of nonlinear terms andp,q are such that 2/q=n(1/r−1/p). Meanwhile under suitable conditions we also obtain thatu(t)L q([0,∞];L p (ℝ n )) provided that initial data are sufficiently small. This work is supported by the National Natural Sciences Foundation of China and the Foundation of LNM Laboratory of Institute of Mechanics of the Chinese Academy of Sciences.  相似文献   

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