Lebesgue constants of Gaussian cardinal interpolation operators from l (ℤ) into L (ℝ)

Summary In recent years, with the attention to the radial-basis function by mathematicians, more and more research is concentrated on the Gaussian cardinal interpolation. The main purpose of this paper is to discuss the asymptotic behavior of Lebesgue constants of the Gaussian cardinal interpolation operator ℒ_λ from l (ℤ) into L (ℝ), that is, ∥ℒ_λ∥₁. We obtain the strong asymptotic estimate of the Lebesgue constants which improves the results of Riemenschneider and Sivakumar in [11].     

Average σ-K width of convolution function class ofL pq R inL q R

In this paper, we study the average n−K width of the convolution classB (G) (orB which the kernel G(x) is a PF density, in the metricR (orR and obtain some exact results. The author was supported by the National Natural Science Found of China.     

Solvability for a nonlinear second-order three-point boundary value problem

This paper investigates the existence of nontrivial solution for the three-point boundary value problem

     

On the optimal quadrature least L∞-norm of monosplines with free knots on the real axis

In this paper, the exact solutions of the L_∝ norm on some classes of monosplines with free knots on the real axis are obtained, and the optimal quadrature formula and optimal error on the convolution class taking a PF density as its kernal are given.     

Theoretical analysis of multimode fiber amplifiers and lasers containing spatial filters

By the use of the coupling theory of the modes and the multimode rate equations, the performances of the multimode fiber amplifiers or lasers containing a spatial filter have been discussed. After the rate equations applicable to amplifiers are solved, the beam quality factors of the output from a multimode fiber amplifier with and without a single mode filter have been evaluated and compared. By the use of the analytical expression of the threshold pump power applicable to the multimode fiber lasers with the spatial filter and doped with quasi two-energy-level ions, and two example fibers had been selected which may guide 4 and 9 transversal modes, respectively, the threshold pump power for each transversal fiber mode has been evaluated. The results indicate that the single mode filter, does introduce a very strong discrimination for the modes between the high order modes and the fundamental mode. This should considerably favor the operation of the fundamental mode in the lasers with a homogeneously broadened active medium.     

Second cohomology group of extended W-algebras

Let \mathbbF\mathbb{F} be a field of characteristic 0, and let G be an additive subgroup of \mathbbF\mathbb{F}. We define a class of infinite-dimensional Lie algebras \mathbbF\mathbb{F}-basis {L _μ, V _μ, W _μ | μ ∈ G}, which are very closely related to W-algebras. In this paper, the second cohomology group of is determined.     

"One-pot" multicomponent approach to indolizines and pyrido[1,2-a]indoles

A new synthetic protocol for efficient and regiospecifc assembly of indolizines and pyrido[1,2-a]indoles by coupling of substituted methyl bromides and alkynes with corresponding pyrrole-2-carboxaldehyde and 1H-indole-2-carboxaldehyde has been developed. Additionally, a possible mechanism for the reaction is proposed.     

Palladium-catalyzed direct olefination of urea derivatives with n-butyl acrylate by C-H bond activation under mild reaction conditions

Pd(II)-catalyzed aromatic C-H bond activation using urea as a directing group was achieved in a p-TsOH/AcOH medium under mild reaction conditions. The direct olefination products of various urea derivatives were produced from aryl urea derivatives and butyl acrylate in moderate to good yields.     

激光惯性约束聚变靶靶丸制备与表征

激光惯性约束聚变的核心思想是利用球形内爆技术对聚变燃料进行增压,使热核燃料达到高温、高密度的等离子体状态,进而实现聚变点火。基于对称压缩、流体界面不稳定性和实验诊断的考虑,ICF实验对作为热核燃料容器的空心微球的品质在球形度、壁厚均匀性、表面粗糙度以及掺杂水平等方面提出了严格的要求。为满足这些要求,陆续发展了乳液微封装技术、降解芯轴技术、低压等离子体聚合/掺杂技术、干凝胶玻璃微球制备技术等用于多层塑料微球和空心玻璃微球的研制。另一方面,针对ICF靶丸量小、质轻以及表面要求高的特点,发展了相应的非破坏性靶丸参数表征技术,如X光照相技术、4π形貌表征技术、微球掺杂水平测量技术以及微球内燃料负载水平快速测试技术。基于这些制备与表征技术,初步实现了多层塑料微球、玻璃微球、聚-!-甲基苯乙烯芯轴微球、梯度掺杂CH微球的研制,满足了"神光Ⅱ"、"神光Ⅲ原型"及"神光Ⅲ主机"上开展的一系列内爆物理实验的要求,同时为未来点火物理实验用靶丸的研制提供了技术支撑。     

Metal-free carbon-nitrogen bond-forming coupling reaction between arylboronic acids and organic azides

A novel and efficient metal-free carbon-nitrogen bond-forming coupling reaction between arylboronic acids and organic azides is reported. The reaction is fairly general for the preparation of secondary aromatic amines. Furthermore, the reaction is very functional-group tolerant. A possible mechanism is also proposed.