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1.
The purpose of this paper is to evaluate the limit γ(a) of the sequence , where a ∈ (0, + ∞ ).   相似文献   

2.
In the present paper, necessary and sufficient conditions are given for the equality of the power rezidue symbols ( \fracaa )n {\left( {\frac{\alpha }{a}} \right)_n} and ( \fracaa )n {\left( {\frac{\alpha }{a}} \right)_n} in the cyclotomic field ℚ(ζ n ), 2 ∤ n, for a ∈ ℤ, (a, n) = 1. This result is a generalization of the classical Eisenstein reciprocity law and its continuation in a Hasse’s paper. Bibliography: 3 titles.  相似文献   

3.
We consider asymptotically flat Riemannian manifolds with non-negative scalar curvature that are conformal to \mathbbRn\ W, n 3 3{\mathbb{R}^{n}{\setminus} \Omega, n\ge 3}, and so that their boundary is a minimal hypersurface. (Here, W ì \mathbbRn{\Omega\subset \mathbb{R}^{n}} is open bounded with smooth mean-convex boundary.) We prove that the ADM mass of any such manifold is bounded below by \frac12(V/bn)(n-2)/n{\frac{1}{2}\left(V/\beta_{n}\right)^{(n-2)/n}}, where V is the Euclidean volume of Ω and β n is the volume of the Euclidean unit n-ball. This gives a partial proof to a conjecture of Bray and Iga (Commun. Anal. Geom. 10:999–1016, 2002). Surprisingly, we do not require the boundary to be outermost.  相似文献   

4.
Let X, X1, X2,... be i.i.d, random variables with mean zero and positive, finite variance σ^2, and set Sn = X1 +... + Xn, n≥1. The author proves that, if EX^2I{|X|≥t} = 0((log log t)^-1) as t→∞, then for any a〉-1 and b〉 -1,lim ε↑1/√1+a(1/√1+a-ε)b+1 ∑n=1^∞(logn)^a(loglogn)^b/nP{max κ≤n|Sκ|≤√σ^2π^2n/8loglogn(ε+an)}=4/π(1/2(1+a)^3/2)^b+1 Г(b+1),whenever an = o(1/log log n). The author obtains the sufficient and necessary conditions for this kind of results to hold.  相似文献   

5.
Let E \subset(-1,1) be a compact set, let μ be a positive Borel measure with support \supp μ =E , and let H p (G), 1≤ p ≤∈fty, be the Hardy space of analytic functions on the open unit disk G with circumference Γ={z \colon |z|=1} . Let Δ n,p be the error in best approximation of the Markov function \frac{1}{2π i} ∈t_E \frac{d μ(x)}{z-x} in the space L p (Γ) by meromorphic functions that can be represented in the form h=P/Q , where P ∈ H p (G), Q is a polynomial of degree at most n , Q\not \equiv 0 . We investigate the rate of decrease of Δ n,p , 1≤ p ≤∈fty , and its connection with n -widths. The convergence of the best meromorphic approximants and the limiting distribution of poles of the best approximants are described in the case when 1<p≤∈fty and the measure μ with support E=[a,b] satisfies the Szegő condition ∈t_a^b \frac{\log(d μ/ d x)}{\sqrt{(x-a)(b-x)}} dx >- ∈fty. July 27, 2000. Final version received: May 19, 2001.  相似文献   

6.
We consider the problem of existence of solutions of the equation in natural numbers for differentmN. We prove that this equation possesses solutions in natural numbers form=a 2+5,aZ, and does not have solutions ifm=4p 2,pN, andp is not divisible by 3. We also prove that, forn≥12, the equation
possesses solutions in natural numbers if and only ifmn,mN. Kiev University, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 52, No. 6, pp. 831–836, June, 2000.  相似文献   

7.
In this paper, we introduce the concept of (1, 1)-q-coherent pair of linear functionals (U,V)(\mathcal{U},\mathcal{V}) as the q-analogue to the generalized coherent pair studied by Delgado and Marcellán in (Methods Appl Anal 11(2):273–266, 2004). This means that their corresponding sequences of monic orthogonal polynomials {P n (x)} n ≥ 0 and {R n (x)} n ≥ 0 satisfy
\frac(DqPn+1)(x)[n+1]q + an\frac(DqPn)(x)[n]q = Rn(x) + bnRn-1(x)  ,     an 1 0,  n 3 1, \frac{\left(D_qP_{n+1}\right)(x)}{[n+1]_q} + a_{n}\frac{\left(D_qP_{n}\right)(x)}{[n]_q} = R_{n}(x) + b_{\!n}R_{n-1}(x) \,, \quad\, a_{n}\neq0,\,\, n\geq1,  相似文献   

8.
Let 2≤n≤4. We show that for an arbitrary measure μ with even continuous density in ℝ n and any origin-symmetric convex body K in ℝ n ,
m(K) £ \fracnn-1\frac|B2n|\fracn-1n|B2n-1|maxx ? Sn-1 m(K?x^)\operatornameVoln(K)1/n,\mu(K) \le\frac{n}{n-1}\frac{|B_2^n|^{\frac{n-1}{n}}}{|B_2^{n-1}|}\max_{\xi\in S^{n-1}} \mu\bigl(K\cap\xi^\bot\bigr)\operatorname{Vol}_n(K)^{1/n},  相似文献   

9.
The equations under consideration have the following structure:
where 0 < x n < ∞, (x 1, …, x n−1) ∈ Ω, Ω is a bounded Lipschitz domain, is a function that is continuous and monotonic with respect to u, and all coefficients are bounded measurable functions. Asymptotic formulas are established for solutions of such equations as x n → + ∞; the solutions are assumed to satisfy zero Dirichlet or Neumann boundary conditions on ∂Ω. Previously, such formulas were obtained in the case of a ij, ai depending only on (x 1, …, x n−1). __________ Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 25, pp. 98–111, 2005.  相似文献   

10.
Let s : S 2G(2, n) be a linearly full totally unramified non-degenerate holomorphic curve in a complex Grassmann manifold G(2, n), and let K(s) be its Gaussian curvature. It is proved that K(s) = \frac4n-2{K(s) = \frac{4}{n-2}} if K(s) satisfies K(s) 3 \frac4n-2{K(s) \geq \frac{4}{n-2}} or K(s) £ \frac4n-2 {K(s) \leq \frac{4}{n-2} } everywhere on S 2. In particular, K(s) = \frac4n-2{K(s) = \frac{4}{n-2}} if K(s) is constant.  相似文献   

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