关于Landau常数和Euler-Mascheroni常数的渐近展开式以及Stirling级数的系数

文章给出一个递推关系式来确定Landau常数的渐近展开式的系数.考虑了 Euler-Mascheroni常数和n!的渐近展开式,并给出了递推关系式来确定每个展开式的系数,没有利用Bernoulli数.     

Landau常数的逼近公式

对于所有的整数n≥0,Landau常数定义为Gn=nΣk=01/16k(2kk)2.该文建立了Landau常数新的逼近公式.指出了获得的结果与先前已有结果之间的相关联系     

Some sharp estimates of the constants of Landau and Lebesgue

We establish several sharp two-sided inequalities involving the constants of Landau and Lebesgue, which occur and play important roles in two related extremal problems in complex analysis and in Fourier analysis respectively. The main results improves essentially the Watson asymptotic expansion formulas for these constants.     

Well-posedness of the fractional Ginzburg–Landau equation

In this paper, we investigate the well-posedness of the real fractional Ginzburg–Landau equation in several different function spaces, which have been used to deal with the Burgers’ equation, the semilinear heat equation, the Navier–Stokes equations, etc. The long time asymptotic behavior of the nonnegative global solutions is also studied in details.     

A complete asymptotic expansion for a sequence of certain sums

In the present note we derive a complete asymptotic expansion for a sequence of certain sums. A special case of our results solves a problem recently proposed in the Research Group in Mathematical Inequalities and Applications (RGMIA) mailing list. Moreover, the result is connected with a certain combinatorial problem.     

关于Landau不等式

本文给出Landau不等式的一种改进。     

A complete asymptotic expansion of power means

The complete asymptotic expansion of power means in terms of Bell polynomials is obtained. Some results recently obtained by M. Bjelica are generalized.     

Landau定理中上界的一个改进

通过相关文献给出的穿孔平面C\{0,1}的双曲度量的密度函数的新的下界估计,借助广义Schwarz引理我们对Landau定理中关于上界做了进一步改进并得到了一个带参数的上界表达式.并且当参数取到0时,此结论正好为相关文献得到的结果.     

Inequalities for the Landau constants

Alma-Ata. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 32, No. 5, pp. 194–195, September–October, 1991.     

基于Legendre函数的Landau′s型不等式

首先研究了L2ω(-1,1)上关于L egendre多项式Xn(x)的L andau′s型不等式.利用Xn(x)的正交性,建立了代数多项式pn(x)的L andau′s型不等式,并且指出其不等式的系数在某种意义上是最好可能的.     

A note on Markov type constants

We prove that, if a geodesic metric space has Markov type 2 with constant 1, then it is an Alexandrov space of nonnegative curvature. The same technique provides a lower bound of the Markov type 2 constant of a space containing a tripod or a branching point. Received: 28 November 2007     

A note on strong uniqueness constants

We expand a result of Blatt, concerning the strong uniqueness constants of uniform best approximations on [− 1, 1].     

Sharp bounds for the Landau constants

The Landau constants are defined for all integers n≥0 by $$ G_{n}=\sum_{k=0}^{n} \frac{1}{16^k}\binom{2k}{k}^2. $$ We establish sharp bounds for the Landau constants G _n . Relevant connections of the results presented here with those derived in earlier work are also pointed out.     

Landau and Bloch theorems for harmonic mappings

Chen, Gauthier and Hengartner obtained some versions of Landau's theorem for bounded harmonic mappings and Bloch's theorem for harmonic mappings which are quasiregular and for those which are open. Later, Dorff and Nowak improved their estimates concerning Landau's theorem. In this study, we improve these last results by obtaining sharp coefficient estimates for properly normalized harmonic mappings. Furthermore, our estimates allow us to improve Bloch constant for open harmonic mappings.     

A note on partial differential-difference equation

In this paper, we studied a certain partial differential-difference equation which arose from crystal precipitation modeling. The uniqu existence and asymptotic behaviors of the solution were shown     

Global a priori estimates for the inhomogeneous Landau equation with moderately soft potentials

We establish a priori upper bounds for solutions to the spatially inhomogeneous Landau equation in the case of moderately soft potentials, with arbitrary initial data, under the assumption that mass, energy and entropy densities stay under control. Our pointwise estimates decay polynomially in the velocity variable. We also show that if the initial data satisfies a Gaussian upper bound, this bound is propagated for all positive times.     

A note on a modified two-component Camassa-Holm system

We consider the asymptotic behavior of solutions for a modified two-component Camassa-Holm (MCH2) system which arises in shallow water theory. It is proved that the corresponding solution to initial data with algebraic decay at infinity will retain this property in its lifespan.     

Regularizing effects for the classical solutions to the Landau equation in the whole space

The Landau equation describes the binary collisional effects (through long range coulombian interaction) in a plasma. In this paper, we prove that the known classical solutions to the Landau equation near Maxwellian in the whole space have a regularizing effect in all (time, space and velocity) variables, that is, become immediately smooth with respect to all variables.