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1.
In this short note we prove that if 1 < c < 81/40, c ≠ 2, N is a large real number, then the Diophantine inequality
is solvable, where p
1,···,p
5 are primes. 相似文献
2.
Yingchun Cai 《数学学报(英文版)》1999,15(3):387-394
Let 1<c<11/10. In the present paper it is proved that there exists a numberN(c)>0 such that for each real numberN>N(c) the inequality
is solvable in prime numbersp
1,p
2,p
3, wherec
1 is some absolute positive constant.
Project supported by the National Natural Science Foundation of China (grant: 19801021) and by MCSEC 相似文献
3.
Nam Q. Le 《Geometriae Dedicata》2011,151(1):361-371
Consider a family of smooth immersions
F(·,t) : Mn? \mathbbRn+1{F(\cdot,t)\,:\,{M^n\to \mathbb{R}^{n+1}}} of closed hypersurfaces in
\mathbbRn+1{\mathbb{R}^{n+1}} moving by the mean curvature flow
\frac?F(p,t)?t = -H(p,t)·n(p,t){\frac{\partial F(p,t)}{\partial t} = -H(p,t)\cdot \nu(p,t)}, for t ? [0,T){t\in [0,T)}. We show that at the first singular time of the mean curvature flow, certain subcritical quantities concerning the second
fundamental form, for example
ò0tòMs\frac|A|n + 2 log (2 + |A|) dmds,{\int_{0}^{t}\int_{M_{s}}\frac{{\vert{\it A}\vert}^{n + 2}}{ log (2 + {\vert{\it A}\vert})}} d\mu ds, blow up. Our result is a log improvement of recent results of Le-Sesum, Xu-Ye-Zhao where the scaling invariant quantities
were considered. 相似文献
4.
LetR
n be n-dimensional Euclidean space with n>-3. Demote by Ω
n
the unit sphere inR
n. ForfɛL(Ω
n
) we denote by σ
N
δ
its Cesàro means of order σ for spherical harmonic expansions. The special value
l = \tfracn - 22\lambda = \tfrac{{n - 2}}{2}
of σ is known as the critical one. For 0<σ≤λ, we set
p0 = \tfrac2ld+ lp_0 = \tfrac{{2\lambda }}{{\delta + \lambda }}
.
This paper proves that
limN ? ¥ || sNd (f) - f ||p0 = 0\mathop {\lim }\limits_{N \to \infty } \left\| {\sigma _N^\delta (f) - f} \right\|p_0 = 0 相似文献
5.
O. N. Nesterenko T. D. Tymoshkevych A. V. Chaikovs’kyi 《Ukrainian Mathematical Journal》2009,61(2):277-291
We prove that the inequality ||g (·/ n ) ||L1[-1,1] ||Pn+k||L1[-1,1] £ 2 ||gPn+k||L1[-1,1]\vert\vert g (\cdot / n ) \vert\vert_{L_{1}[-1,1]} \vert\vert P_{n+k}\vert\vert_{L_{1}[-1,1]} \leq 2 \vert\vert gP_{n+k}\vert\vert_{L_{1}[-1,1]}, where g : [-1, 1]→ℝ is a monotone odd function and P
n+k
is an algebraic polynomial of degree not higher than n + k, is true for all natural n for k = 0 and all natural n ≥ 2 for k = 1. We also propose some other new pairs (n, k) for which this inequality holds. Some conditions on the polynomial P
n+k
under which this inequality turns into the equality are established. Some generalizations of this inequality are proposed. 相似文献
6.
Petros Galanopoulos Daniel Girela Rodrigo Hernández 《Journal of Geometric Analysis》2011,21(3):665-682
This paper is concerned mainly with the logarithmic Bloch space ℬlog which consists of those functions f which are analytic in the unit disc
\mathbbD{\mathbb{D}} and satisfy
sup|z| < 1(1-|z|)log\frac11-|z||f¢(z)| < ¥\sup_{\vert z\vert <1}(1-\vert z\vert )\log\frac{1}{1-\vert z\vert}\vert f^{\prime}(z)\vert <\infty , and the analytic Besov spaces B
p
, 1≤p<∞. They are all subspaces of the space VMOA. We study the relation between these spaces, paying special attention to the membership of univalent functions in them. We
give explicit examples of:
|