Hankel-type operators on the space of bounded harmonic functions

We study Hankel-type operators on the space of bounded harmonic functions on the open unit disk. These operators are related to tight uniform algebras, the Dunford-Pettis property, and Bourgain algebras.

     

The collision frequency of electron-neutral-particle in weakly ionized plasmas with non-Maxwellian velocity distributions

The collision frequencies of electron-neutral-particle in weakly ionized complex plasmas with the non-Maxwellian velocity distributions are studied. The average collision frequencies of electron-neutral-particle in plasmas are accurately derived. We find that these collision frequencies are significantly dependent on the power-law spectral indices of non-Maxwellian distribution functions and so they are generally different from the collision frequencies in plasmas with a Maxwellian velocity distribution, which will affect the transport properties of the charged particles in plasmas. Numerically analyses are made to show the roles of the spectral indices in the average collision frequencies respectively.     

Sharp Estimates of Bounded Solutions to Some Second-order Forced Dissipative Equations

Résumé A l’aide d’inégalités différentielles, on établit une estimation proche de l’optimalité pour la norme dans de l’unique solution bornée de u′′ + cu′ + Au = f(t) lorsque A = A ^* ≥ λ I est un opérateur borné ou non sur un espace de Hilbert réel H, V = D(A ^1/2) et λ, c sont des constantes positives, tandis que . By using differential inequalities, a close-to-optimal bound of the unique bounded solution of u′′ + cu′ + Au = f(t) is obtained whenever A = A ^* ≥ λ I is a bounded or unbounded linear operator on a real Hilbert space H, V = D(A ^1/2) and λ, c are positive constants, while .

---

     

包含$l^{\beta}(0<\beta<1)$渐近等距翻版的有界线性算子空间

Assume X is a normed space,every x ＊ ∈ S（X＊） can reach its norm at some point in B（X）,and Y is a β-normed space.If there is a quotient space of Y which is asymptotically isometric to l β,then L（X,Y） contains an asymptotically isometric copy of l β.Some sufficient conditions are given under which L（X,Y） fails to have the fixed point property for nonexpansive mappings on closed bounded β-convex subsets of L（X,Y）.     

全函数空间和置换空间的一些性质

In this paper, an equivalent relation among the reflexivity, weak sequential completeness and bounded completeness in full function space is given. Some results on weakly sequential compactness of subset and the property （u） in substitution spaces are obtained.     

具线性退化特征场对角型方程组Goursat问题的奇性形成机制

For an inhomogeneous quasilinear hyperbolic system of diagonal form, under the assumptions that the system is linearly degenerate and the C^1 norm of the boundary data is bounded, we show that the mechanism of the formation of singularities of C^1 classical solution to the Goursat problem with C^1 compatibility conditions at the origin must be an ODE type. The similar result is also obtained for the weakly discontinuous solution with C^0 compatibility conditions at the origin.     

囚禁弱相互作用玻色气体的势场优化准则

根据Thomas-Fermi近似,在基于最小动量态上玻色-爱因斯坦凝聚的前提下,研究了囚禁弱相互作用玻色气体势场的最优化问题.导出了指数吸引势阱中有效势场和粒子数极限判据,粒子数给定时,可由此判据求出所需势场强度;势场强度给定时,可由此判据求出粒子数极限.根据吸引相互作用系统的稳定性以及求出的排斥相互作用的最大粒子数极限,结合有效势场判据,分别给出了囚禁吸引和排斥相互作用玻色气体时,势场强度的最佳取值范围. 关键词： 玻色-爱因斯坦凝聚 弱相互作用 粒子数极限 势场强度     

BOUNDED TRAVELING WAVE SOLUTIONS OF VARIANT BOUSSINESQ EQUATION WITH A DISSIPATION TERM AND DISSIPATION EFFECT

This article studies bounded traveling wave solutions of variant Boussinesq equation with a dissipation term and dissipation effect on them. Firstly, we make qualitative analysis to the bounded traveling wave solutions for the above equation by the theory and method of planar dynamical systems, and obtain their existent conditions, number, and general shape. Secondly, we investigate the dissipation effect on the shape evolution of bounded traveling wave solutions. We find out a critical value r*which can characterize the scale of dissipation effect, and prove that the bounded traveling wave solutions appear as kink profile waves if |r| ≥ r*; while they appear as damped oscillatory waves if |r| r*. We also obtain kink profile solitary wave solutions with and without dissipation effect. On the basis of the above discussion, we sensibly design the structure of the approximate damped oscillatory solutions according to the orbits evolution relation corresponding to the component u(ξ) in the global phase portraits, and then obtain the approximate solutions(u(ξ), H(ξ)). Furthermore,by using homogenization principle, we give their error estimates by establishing the integral equation which reflects the relation between exact and approximate solutions. Finally, we discuss the dissipation effect on the amplitude, frequency, and energy decay of the bounded traveling wave solutions.     

ON A NEW CLASS OF ANALYTIC FUNCTION DERIVED BY A FRACTIONAL DIFFERENTIAL OPERATOR

Making use of the fractional differential operator, we impose and study a new class of analytic functions in the unit disk （type fractional differential equation）. The main object of this paper is to investigate inclusion relations, coefficient bound for this class. Moreover, we discuss some geometric properties of the fractional differential operator.     

Non-conflicting ordering cones and vector optimization in inductive limits

Let (E, ξ)= ind (E_n, ξ_n) be an inductive limit of a sequence (E_n, ξ_n)_{n∈ N} of locally convex spaces and let every step (E_n, ξ_n) be endowed with a partial order by a pointed convex (solid) cone S_n. In the framework of inductive limits of partially ordered locally convex spaces, the notions of lastingly efficient points, lastingly weakly efficient points and lastingly globally properly efficient points are introduced. For several ordering cones, the notion of non-conflict is introduced. Under the requirement that the sequence (S_n)_{n∈ N} of ordering cones is non-conflicting, an existence theorem on lastingly weakly efficient points is presented. From this, an existence theorem on lastingly globally properly efficient points is deduced.