共查询到20条相似文献,搜索用时 31 毫秒
1.
Let E be a compact subset of with connected, regular complement and let G(z) denote Green’s function of Ω with pole at ∞. For a sequence (pn)nΛ of polynomials with degpn=n, we investigate the value-distribution of pn in a neighbourhood U of a boundary point z0 of E if G(z) is an exact harmonic majorant of the subharmonic functions in . The result holds for partial sums of power series, best polynomial approximations, maximally convergent polynomials and can be extended to rational functions with a bounded number of poles. 相似文献
2.
Dehong Ji Yu Tian Weigao Ge 《Nonlinear Analysis: Theory, Methods & Applications》2009,71(11):5406-5416
This paper deals with the existence of positive solutions for the one-dimensional p-Laplacian subject to the boundary value conditions: where p(s)=|s|p−2s,p>1. We show that it has at least one or two positive solutions under some assumptions by applying the fixed point theorem. The interesting points are that the nonlinear term f is involved with the first-order derivative explicitly and f may change sign. 相似文献
3.
This paper gives upper and lower bounds of the Christoffel-type functions , for the m-orthogonal polynomials for a Freud weight W=e-Q, which are given as follows. Let an=an(Q) be the nth Mhaskar–Rahmanov–Saff number, φn(x)=max{n-2/3,1-|x|/an}, and d>0. Assume that QC(R) is even, , and for some A,B>1Then for xRand for |x|an(1+dn-2/3) 相似文献
4.
We relate asymptotics of Jacobi parameters to asymptotics of the spectral weights near the edges. Typical of our results is that for an≡1, bn=−Cn−β (), one has on (−2,2), and near x=2, where 相似文献
5.
Let X be a metric space andμa finite Borel measure on X. Let pμq,t and pμq,t be the packing premeasure and the packing measure on X, respectively, defined by the gauge (μB(x,r))q(2r)t, where q, t∈R. For any compact set E of finite packing premeasure the authors prove: (1) if q≤0 then pμq,t(E)=pμq,t(E);(2)if q>0 andμis doubling on E then pμq,t(E) and pμq,t(E) are both zero or neither. 相似文献
6.
There is a strong connection between Sobolev orthogonality and Simultaneous Best Approximation and Interpolation. In particular, we consider very general interpolatory constraints , defined by where f belongs to a certain Sobolev space, aij() are piecewise continuous functions over [a,b], bijk are real numbers, and the points tk belong to [a,b] (the nonnegative integer m depends on each concrete interpolation scheme). For each f in this Sobolev space and for each integer l greater than or equal to the number of constraints considered, we compute the unique best approximation of f in , denoted by pf, which fulfills the interpolatory data , and also the condition that best approximates f(n) in (with respect to the norm induced by the continuous part of the original discrete–continuous bilinear form considered). 相似文献
7.
Blow-up analysis for a system of heat equations with nonlinear flux which obey different laws 总被引:1,自引:0,他引:1
We consider a system of heat equations ut=Δu and vt=Δv in Ω×(0,T) completely coupled by nonlinear boundary conditions We prove that the solutions always blow up in finite time for non-zero and non-negative initial values. Also, the blow-up only occurs on ∂Ω with for p,q>0, 0≤α<1 and 0≤β<p. 相似文献
8.
Let F be any field. Let p(F) be the characteristic of F if F is not of characteristic zero, and let p(F)=+∞ otherwise. Let A1,…,An be finite nonempty subsets of F, and let with k{1,2,3,…}, a1,…,anF{0} and degg<k. We show that When kn and |Ai|i for i=1,…,n, we also have consequently, if nk then for any finite subset A of F we have In the case n>k, we propose a further conjecture which extends the Erdős–Heilbronn conjecture in a new direction. 相似文献
9.
Let K be an arbitrary field of characteristic zero, Pn:=K[x1,…,xn] be a polynomial algebra, and , for n2. Let σ′AutK(Pn) be given by It is proved that the algebra of invariants, , is a polynomial algebra in n−1 variables which is generated by quadratic and cubic (free) generators that are given explicitly.Let σAutK(Pn) be given by It is well known that the algebra of invariants, , is finitely generated (theorem of Weitzenböck [R. Weitzenböck, Über die invarianten Gruppen, Acta Math. 58 (1932) 453–494]), has transcendence degree n−1, and that one can give an explicit transcendence basis in which the elements have degrees 1,2,3,…,n−1. However, it is an old open problem to find explicit generators for Fn. We find an explicit vector space basis for the quadratic invariants, and prove that the algebra of invariants is a polynomial algebra over in n−2 variables which is generated by quadratic and cubic (free) generators that are given explicitly.The coefficients of these quadratic and cubic invariants throw light on the ‘unpredictable combinatorics’ of invariants of affine automorphisms and of SL2-invariants. 相似文献
10.
Galerkin methods are used to approximate the singular integral equation with solution φ having weak singularity at the endpoint −1, where a, b≠0 are constants. In this case φ is decomposed as φ(x)=(1−x)α(1+x)βu(x), where β=−α, 0<α<1. Jacobi polynomials are used in the discussions. Under the conditions fHμ[−1,1] and k(t,x)Hμ,μ[−1,1]×[−1,1], 0<μ<1, the error estimate under a weighted L2 norm is O(n−μ). Under the strengthened conditions f″Hμ[−1,1] and , 2α−<μ<1, the error estimate under maximum norm is proved to be O(n2α−−μ+), where , >0 is a small enough constant. 相似文献
11.
Composite implicit iteration process for common fixed points of a finite family of strictly pseudocontractive maps 总被引:2,自引:0,他引:2
Let E be a real Banach space and let K be a nonempty closed convex subset of E. Let be N strictly pseudocontractive self-maps of K such that , where F(Ti)={xK:Tix=x} and let be two real sequence satisfying the conditions: where L1 is common Lipschitz constant of . For x0K, let be new implicit process defined by
xn=αnxn−1+(1−αn)Tnyn,