关于非方常数问题的一个反例

通过一个反例,证明了非方常数为2~(1/2)的相关猜想.     

The Domínguez–Lorenzo condition and multivalued nonexpansive mappings

Let E be a nonempty bounded closed convex separable subset of a reflexive Banach space X   which satisfies the Domínguez–Lorenzo condition, i.e., an inequality concerning the asymptotic radius of a sequence and the Chebyshev radius of its asymptotic center. We prove that a multivalued nonexpansive mapping T:E→2^X$T:E\to 2^X$ which is compact convex valued and such that T(E)$T(E)$ is bounded and satisfies an inwardness condition has a fixed point. As a consequence, we obtain a fixed-point theorem for multivalued nonexpansive mappings in uniformly nonsquare Banach spaces which satisfy the property WORTH, extending a known result for the case of nonexpansive single-valued mappings. We also prove a common fixed point theorem for two nonexpansive commuting mappings t:E→E$t:E\to E$ and T:E→KC(E)$T:E\to \mathit{KC}(E)$ (where KC(E)$\mathit{KC}(E)$ denotes the class of all compact convex subsets of E) when X is a uniformly convex Banach space.     

二阶常系数线性微分方程的积分形式通解及首次积分

利用一阶线性微分方程的通解 ,导出了二阶常系数线性微分方程的积分形式通解 .研究了通解的结构 ,并给出了首次积分 .     

On the Constant Type of Almost Hermitian Manifolds

We suggest a most natural generalization of the notion of constant type for nearly Kählerian manifolds introduced by A. Gray to arbitrary almost Hermitian manifolds. We prove that the class of almost Hermitian manifolds of zero constant type coincides with the class of Hermitian manifolds. We show that the class of G ₁-manifolds of zero constant type coincides with the class of 6-dimensional G ₁-manifolds with a non-integrable structure. Finally, we prove that the class of normal G ₂-manifolds of nonzero constant type coincides with the class of 4-dimensional G ₂-manifolds with a nonintegrable structure.     

一类分段常数变量线性中立型泛函微分方程解的振动性质

本研究分段常数变量线性中立型泛函微分方程的振动性。用不同的方法研究所考虑的方程,获得存在振动解的两个判定定理。     

Approximation Constants in Equidistant Lagrange Interpolation

In this paper we present a new limit relation for the equidistant Lagrange interpolation polynomials to |x|, (0, 1] on the internal [–1, 1]. The result extends a well-known result of D. L. Berman and S. M. Losinskii. Furthermore, we briefly discuss on a possible connection of the limit relation to another prominent constant in best uniform polynomial approximation for |x| - the so-called Bernstein constant.     

Some new results on planar harmonic mappings

This survey paper contains some new results on the Landau theorem, Bloch theorem and Schwarz-Pick lemma for planar harmonic mappings.     

Approximation by an iterative method of a low‐Mach model with temperature dependent viscosity

In this work, we prove the existence and the uniqueness of the strong solution of a low‐Mach model, for which the dynamic viscosity of the fluid is a given function of its temperature. The method is based on the convergence study of a sequence towards the solution, for which the rates are also given. The originality of the approach is to consider the system in terms of the temperature and the velocity, leading to a nonlinear temperature equation and the development of some specific tools and results.