Beurling type theorem on the Bergman space via the Hardy space of the bidisk

In this paper,by lifting the Bergman shift as the compression of an isometry on a subspace of the Hardy space of the bidisk,we give a proof of the Beurling type theorem on the Bergman space of Aleman,Richter and Sundberg(1996) via the Hardy space of the bidisk.     

Analytical elastostatic stiffness modeling of parallel manipulators considering the compliance of the link and joint

This paper discusses the analytical elastostatic stiffness modeling of parallel manipulators (PMs) considering the compliance of the link and joint. The proposed modeling is implemented in three steps: (1) the limb constraint wrenches are formulated based on screw theory; (2) the strain energy of the link and the joint is formulated using material mechanics and a mapping matrix, respectively, and the concentrated limb stiffness matrix corresponding to the constraint wrenches is obtained by summing the strain energy of the links and joints in the limb; and (3) the overall stiffness matrix is assembled based on the deformation compatibility equations. The strain energy factor index (SEFI) is adopted to describe the influence of the elastic components on the stiffness performance of the mechanism. Matrix structural analysis (MSA) using Timoshenko beam elements is applied to obtain analytical expressions for the compliance matrices of different joints through a three-step process: (1) formulate the element stiffness equation for each element; (2) extend the element stiffness equation to obtain the element contribution matrix, allowing the extended overall stiffness matrix to be obtained by summing the element contribution matrices; and (3) determine the stiffness matrices of joints by extracting the node stiffness matrix from the extended overall stiffness matrix and then releasing the degrees of freedom of twist. A comparison with MSA using Euler–Bernoulli beam elements demonstrates the superiority of using Timoshenko beam elements. The 2PRU-UPR PM is presented to illustrate the effectiveness of the proposed approach. Finally, the global SEFI and scatter matrix are used to identify the elastic component with the weakest stiffness performance, providing a new approach for effectively improving the stiffness performance of the mechanism.     

侧向加热腔体中的多圈型对流斑图

基于流体力学方程组的数值模拟,研究了倾角θ=90°时侧向加热的大高宽比腔体中的对流斑图.对于Prandtl数Pr=6.99的流体,在相对Rayleigh数2≤Ra r≤25的范围内,腔体中发生的是单圈型对流斑图.对于Pr=0.0272的流体,取Ra r=13.9,随着计算时间的发展,腔体中由最初的单圈型对流斑图过渡到多圈型对流斑图,这是出现在侧向加热大高宽比腔体中的新型对流斑图.对不同Ra r情况的计算结果表明,Ra r对对流斑图的形成存在明显的影响.当Ra r≤4.4时是单圈型对流滚动;当Ra r=8.9~11.1时是过渡状态;当Ra r≥13.9时是多圈型对流滚动.对流最大振幅和Nusselt数Nu随着相对Rayleigh数的增加而增加.该对流斑图与Pr=6.99时对流斑图的比较说明,对流斑图的形成依赖于Prandtl数.     

Approximation of maximum of Gaussian random fields

This contribution is concerned with Gumbel limiting results for supremum ${\mathbb{M}}_{\mathit{n}}={\sup }_{\mathit{t}\in [\mathbf{0},{\mathit{T}}_{\mathit{n}}]}?|X_{\mathit{n}}(\mathit{t})|$ with $X_{\mathit{n}},\mathit{n}\in {\mathbb{N}}^2$ centered Gaussian random fields with continuous trajectories. We show first the convergence of a related point process to a Poisson point process thereby extending previous results obtained in [8] for Gaussian processes. Furthermore, we derive Gumbel limit results for ${\mathbb{M}}_{\mathit{n}}$ as $\mathit{n}\to \infty$ and show a second-order approximation for $\mathbb{E}{\{{\mathbb{M}}_{\mathit{n}}^p\}}^{1/p}$ for any $p\ge 1$.     

常数磁场中薛定谔算子的黎斯平均的L2有界性估计

为了研究常数磁场下的薛定谔算子的黎斯平均L2有界性问题,本文在Stein研究的Fowrier变换的工作基础上,通过研究Mpf（x）,得到所要的估计.     

Solid phase extractors derived by functionalising sub-micro silica gel with chelating agents and their pH-tunable adsorbing capability towards Pb(II) and Ag(I)

Three novel solid phase extraction agents were developed by functionalising sub-micron sized silica gel with organic functional moieties possessing {SN}-ligating atoms. The extractors were characterised by FTIR and TGA. Their capability of adsorbing the ions Fe(III), Cu(II), Zn(II), Cd(II), Cr(VI), Hg(II), Pb(II), Co(II), Ni(II), and Ag(I) is described. The extractors show pH-tunable selectivity for Ag(I) and/or Pb(II). By adjusting the pH to 5 or 6, high affinity is found for both Ag(I) and Pb(II), with little or no interference by the other metal ions. At pH values of <2, the extractors become highly selective for Ag(I), with an adsorption capacity of 35 mg g^?1. Little mechanical stirring is required due to the size of the particles. The recovery rates for both Ag(I) and Pb(II) were better 90% even after five repetitive adsorption-desorption cycles.     

Study on the Interaction between a Novel Ionic Liquid Probe and Anionic Surfactants Using Resonance Light Scattering Spectra and Its Analytical Application

The interaction between anionic surfactants (AS) and 1‐hexadecyl‐3‐methylimidazolium bromide [C₁₆mim]Br was studied by using resonance light scattering (RLS) technique, UV‐Vis spectrophotometry and fluorometric methods. In Britton Robinson (BR) buffer (pH 6.0), [C₁₆mim]Br reacted with AS to form supermolecular complex which resulted in enhancement in RLS intensity. Their maximum RLS wavelengths were all at 390 nm. Some important interacting experimental variables, such as the solution acidity, [C₁₆mim]Br concentration, salt effect and addition order of the reagents, were investigated and optimized. Under the optimum conditions, quantitative determination ranges were 0.001–7 μg·mL^?1 for dodecyl sodium sulfate (SDS), 0.001–6 μg·mL^?1 for sodium dodecylbenzene sulfonate (SDBS) and 0.005–7 μg·mL^?1 for sodium lauryl sulfonate (SLS), respectively, while the detection limits were 1.3 ng·mL^?1 for SDS, 1.0 ng·mL^?1 for SDBS and 5.1 ng·mL^?1 for SLS, respectively. Based on the ion‐association reaction, a highly sensitive, simple and rapid method has been established for the determination of AS.     

Anti-periodic solutions for a class of nonlinear th-order differential equations with delays

In this paper, we use the Leray–Schauder degree theory to establish new results on the existence and uniqueness of anti-periodic solutions for a class of nonlinear nth-order differential equations with delays of the form

x⁽ⁿ⁾(t)+f(t,x⁽ⁿ⁻¹⁾(t))+g(t,x(t−τ(t)))=e(t).