GENERALIZED FORELLI-RUDIN TYPE OPERATORS BETWEEN SEVERAL FUNCTION SPACES ON THE UNIT BALL OF C^(N)

In this paper,we investigate sufficient and necessary conditions such that generalized Forelli-Rudin type operators T_(λ,τ,k),S_(λ,τ,k),Q_(λ,τ,k)and R_(λ,τ,k)are bounded between Lebesgue type spaces.In order to prove the main results,we first give some bidirectional estimates for several typical integrals.

SCHWARZ-PICK ESTIMATES FOR PARTIAL DERIVATIVES OF ARBITARY ORDER OF BOUNDED HOLOMORPHIC FUNCTIONS IN THE UNIT BALL OF C^n

This paper gives a Schwarz-Pick estimate for bounded holomorphic functions in the unit ball of C n .

AVERAGE σ-WIDTHS OF THE UNIT BALL OF I_1~∞(R)IN I_2~∞(R)

In this paper we study the average σ-K width and the average σ-linear width of the unit ball of l;（R） inl;（R）. The exact values of these widths are calculated and an optimal subspace with the optimal linear opera-tor （for the σ- linear width） are identified.

Solving Neumann Boundary Problem with Kernel-Regularized Learning Approach

We provide a kernel-regularized method to give theory solutions for Neumann boundary value problem on the unit ball. We define the reproducing kernel Hilbert space with the spherical harmonics associated with an inner product defined on both the unit ball and the unit sphere, construct the kernel-regularized learning algorithm from the view of semi-supervised learning and bound the upper bounds for the learning rates. The theory analysis shows that the learning algorithm has better uniform convergence according to the number of samples. The research can be regarded as an application of kernel-regularized semi-supervised learning.

AN INTEGRAL ESTIMATE AND THE EQUIVALENT NORMS ON F(p, q, s, k) SPACES IN THE UNIT BALL

In this article, the authors give a typical integral＇s bidirectional estimates for allcases. At the same time, several equivalent characterizations on the F（p, q, s, k） space in theunit ball of Cn are given.

UNIFORMLY STARLIKE MAPPINGS AND UNIFORMLY CONVEX MAPPINGS ON THE UNIT BALL B^n

In this article, we extend the definition of uniformly starlike functions and uni- formly convex functions on the unit disk to the unit ball in C^n, give the discriminant criterions for them, and get some inequalities for them.

Modeling and Experiment on Contact Stiffness and Accuracy Analysis of Ball Linear Guide Feed Unit

The contact stiffness and the error analysis have an important effect on the manufacture and the optimization of Ball Linear Guide Feed Unit( BLGFU). In order to analyze the contact stiffness and linear errors or angle errors of BLGFU,in this paper,the contact stress and deformation mechanics between the ball and rail is analyzed. Based on Hertz theory of contact and theory of the multi-body system,a model of the contact stiffness considering the changes in contact angle is established. With the increasing of the external load,the varying trend of the contact deformation can be obtained. Therefore, the motion accuracy degradation of the BLGFU can be analyzed. By using a special experimental device and test system of the rolling linear guide worktable,the horizontal contact stiffness and the vertical linear stiffness are obtained,respectively. By comparing the contact stiffness of the experiment dates and the simulation results,the variation tendency of two curves is consisted and the difference between the measured values and the theoretical values is less than 18%. It is obvious that the model of the contact stiffness considering changes of contact angle has accuracy and feasibility. Thus,while external force point locating at different positions; the contact stiffness and the accuracy analysis of the BLGFU are proved validity by simulations.

Weighted composition operators from F(p,q,s) spaces to Bers-type spaces in the unit ball

This paper deals with the boundedness and compactness of the weighted composition operators from the F（p, q, s） spaces, including Hardy space, Bergman space, Qp space, BMOA space, Besov space and α-Bloch space, to Bers-type spaces Hv^∞（ or little Bers-type spaces Hv,o∞ ）, where v is normal.

A SCHWARZ LEMMA FOR HARMONIC FUNCTIONS IN THE REAL UNIT BALL

We establish a precise Schwarz lemma for real-valued and bounded harmonic functions in the real unit ball of dimension n. This extends Chen's Schwarz-Pick lemma for real-valued and bounded planar harmonic mapping.

A BOUNDARY SCHWARZ LEMMA FOR PLURIHARMONIC MAPPINGS FROM THE UNIT POLYDISK TO THE UNIT BALL

In this article, we present a Schwarz lemma at the boundary for pluriharmonic mappings from the unit polydisk to the unit ball, which generalizes classical Schwarz lemma for bounded harmonic functions to higher dimensions. It is proved that if the pluriharmonic mapping f ∈ P（Dn, BN） is C1＋α at z0 ∈ ErDn with f（0） = 0 and f（z0） = ω0∈BN for any n,N ≥ 1, then there exist a nonnegative vector λf =（λ1,0,…,λr,0,…,0）T∈R2 nsatisfying λi≥1/（22 n-1） for 1 ≤ i ≤ r such that where z’0 and w’0 are real versions of z0 and w0, respectively.

BOUNDEDNESS FROM BELOW OF MULTIPLICATION OPERATORS BETWEEN α-BLOCH SPACES ON THE UNIT BALL

In this article, we characterize the boundedness from below of multiplication operators between α-Bloch spaces on the unit ball.

Little Hankel Operators on the Weighted Bergman Space of the Unit Ball

In this paper we mainly consider little Hankel operators with squareintegrable symbols on the weighted Bergman spaces of the unit ball.We obtain that Schatten class of little Hankel operators is equivalent to Schatten class of positive Toeplitz operators under the conditions that SMO（f） ∈ L p/2 （B n,dλ） and 2 ≤ p ∞,which is very important to research the relation between Toeplitz operators and little Hankel operators.

滚动球变换支持下的TIN-DDM地形特征线自动提取方法

针对传统规则格网数字高程模型地形特征线提取方法中存在阈值难以定量调控、连接方式无法自适应调整以及地形特征线类型不完整的问题,将滚动球变换模型应用于不规则三角网数字水深模型(triangulated irregular network digital depth model,TIN-DDM)地形特征线的自动提取,在构建临界滚动球半径关联的地形特征点定量识别判定准则基础上,引入地形形态边界点概念,采用逆向工程的建模思路,建立了以剖分单元为基础的地形特征线自动提取模型,结合地形类型判定准则的多尺度表达特性及顾及水深数值的地形特征优化模型,提出了可多尺度表达且类型完整的地形特征线自动提取方法。试验结果表明:相比于经典地表流水模拟方法,该方法可实现完整、连续且细分的TIN-DDM地形特征线自动提取及多尺度表达,且提取的地形特征线具有更高的地形重构精度。

Model of Rotation Accuracy of High-Speed Spindles on Ball Bearings

For the purpose to improve a design quality of high-speed spindle units, we have developed mathematical models and software to simulate a rotation accuracy of spindles running on ball bearings. In order to better understand the mechanics of ball bearings, the dynamic interaction of ball bearings and spindle unit, and the influence of the bearing imperfections on the spindle rotation accuracy, we have carried out computer aided analysis and experimental studies. When doing this, we have found that the spindle rotation accuracy can vary drastically with rotational speed. The influence of bearing preload has a secondary importance. Comparison of the results of these studies has demonstrated adequacy of the models developed to the real spindle units.

<i>Q_K</i>Type Spaces and Bloch Type Spaces on the Unit Ball

Different function spaces have certain inclusion or equivalence relations. In this paper, the author introduces a class of M&#246;bius-invariant Banach spaces QK,0 (p,q) of analytic function on the unit ball of Cn, where K:(0,∞)→[0,∞) are non-decreasing functions and 0P∞, p/2-n-1q∞, studies the inclusion relations between QK,0 (p,q) and a class of B0α spaces which was known before, and concludes that QK,0 (p,q) is a subspace of B0(q+n+1)/p, and the sufficient and necessary condition on kernel function K(r) such that QK,0 (p,q)= B0(q+n+1)/p.

ATOMIC DECOMPOSITION OF μ-BERGMAN SPACE IN C^n

Let μ be a normal function on [0, 1）. The atomic decomposition of the μ-Bergman space in the unit ball B is given for all p 〉 0.

A Theorem of Nehari Type on the Bergman Space

In this paper we concern with the characterization of bounded linear operators S acting on the weighted Bergman spaces on the unit ball. It is shown that, if S satisfies the commutation relation STzi = Tzi（i =1,..,n）, where Tzi = zif and Tzi= P（zif） where P is the weighted Bergman projection, then S must be a Hankel operator.

GLEASON'S PROBLEM ON THE SPACE F^(p,q,s)(B) IN C^(n)

Let Ω be a domain in C^(n) and let Y be a function space on Ω.If a∈Ω and g∈Y with g(a)=0,do there exist functions f_(1),f_(2),…,f_(n)∈Y such that g(z)=∑_(l=1)^(n)(z_(l)−a_(l))f_(l)(z)for all z=(z_(1),z_(2),…,z_(n))∈Ω?This is Gleason’s problem.In this paper,we prove that Gleason’s problem is solvable on the boundary general function space F^(p,q,s)(B)in the unit ball B of C^(n).

Commuting Dual Toeplitz Operators on Weighted Bergman Spaces of the Unit Ball

In this paper, we study the commutativity of dual Toeplitz operators on weighted Bergman spaces of the unit ball. We obtain the necessary and sufficient conditions for the commutativity, essential commutativity and essential semi-commutativity of dual Toeplitz operator on the weighted Bergman spaces of the unit ball.