On smoothers for multigrid of the second kind

We study smoothers for the multigrid method of the second kind arising from Fredholm integral equations. Our model problems use nonlocal governing operators that enforce local boundary conditions. For discretization, we utilize the Nyström method with the trapezoidal rule. We find the eigenvalues of matrices associated to periodic, antiperiodic, and Dirichlet problems in terms of the nonlocality parameter and mesh size. Knowing explicitly the spectrum of the matrices enables us to analyze the behavior of smoothers. Although spectral analyses exist for finding effective smoothers for 1D elliptic model problems, to the best of our knowledge, a guiding spectral analysis is not available for smoothers of a multigrid of the second kind. We fill this gap in the literature. The Picard iteration has been the default smoother for a multigrid of the second kind. Jacobi‐like methods have not been considered as viable options. We propose two strategies. The first one focuses on the most oscillatory mode and aims to damp it effectively. For this choice, we show that weighted‐Jacobi relaxation is equivalent to the Picard iteration. The second strategy focuses on the set of oscillatory modes and aims to damp them as quickly as possible, simultaneously. Although the Picard iteration is an effective smoother for model nonlocal problems under consideration, we show that it is possible to find better than ones using the second strategy. We also shed some light on internal mechanism of the Picard iteration and provide an example where the Picard iteration cannot be used as a smoother.     

Content of selected secondary metabolites in wild hop

We focused on the determination of biologically active secondary metabolites in wild hops over the course of the vegetation period in four selected sites in Pie??any. Hop was collected in four collection periods in 2010. The objects of research were the leaves of male and female plants, and female cones. Analysis of the extracts from wild hop confirmed differences in total content of polyphenols, flavonoids between the localities and in the growing seasons over the vegetation period. The extracts from leaves from the first harvest in localities “gSládkovi?ova” and the river Vah showed higher levels of polyphenols (4.91–6.93 mg g^?1 of dry mass), flavonoids (2.28–2.99 mg g^?1 of dry mass) than the extracts from cones collected at the end of the vegetation period (polyphenols 3.63–5.33 mg g^?1 of dry mass, flavonoids 1.86–2.16 mg g^?1 of dry mass). The extracts from leaves from the first harvest from the “tennis court” site showed lower values of polyphenols and flavonoids. Our findings were that the leaves from the first harvest at the beginning of the growing season contained higher amounts of the secondary metabolites investigated than the cones at the end of the growing season. The content of α-bitter acids in wild hop cones ranged from 1.64 % to 2.91 %, in leaves from 0.11 % to 0.99%. Concentration of β-bitter acids in cones varied from 1.63 % to 1.93 % and in leaves from 0.02 % to 0.61 %.     

New Heterocyclic Phosphorus Ylides: Synthesis,Crystal Structure,and Theoretical Calculation of Alkyl Substituted 3-(4-Benzoyl-1,5-diphenyl-2,3-dihydro-1H-pyrazol-3-yl)-3-oxo-2-(triphenylphosphoranylidene) Propanoates

Novel alkyl substituted 3-(4-benzoyl-1,5-diphenyl-2,3-dihydro-1H-pyrazol-3-yl)-3-oxo-2-(triphenylphosphoranylidene) propanoates (3) were synthesized from 4-benzoyl-1,5-diphenyl-1H-pyrazole-3-carbonylchloride (1) and alkyl (triphenylphosphoranylidene) acetates (2a–b). The synthesized compounds were characterized by elemental analysis, spectroscopic studies (3a–b), and single crystal X-ray diffraction (3a). The mechanism of the reaction between (1) and (2a) was studied by AM1, and the geometrical parameters of the studied molecules were also carried out in B3LYP methods with the standard 6–31G (d,p) basis set. NBO analysis were studied for 1 and 2a B3LYP methods with the standard 6–31G (d,p) basis set.     

Tracing pore-space heterogeneities in X-type zeolites by diffusion studies

Pore-space homogeneity of zeolite NaX was probed by pulsed field gradient (PFG) NMR diffusion studies with n-butane as a guest molecule. At a loading of 0.75 molecules per supercage, a wide spectrum of diffusivities was observed. Guest molecules in the (well-shaped) zeolite crystallites were thus found to experience pore spaces of quite different properties. After loading enhancement to 3 molecules per supercage, however, molecular propagation ideally followed the laws of normal diffusion in homogeneous media. At sufficiently high guest concentrations, sample heterogeneity was thus found to be of no perceptible influence on the guest mobilities anymore.     

低频噪声干扰的评价标准和控制技术

本文对16—31.5Hz范围的低频噪声对居民的干扰作了调查,对噪声源进行了测试和分析。在控制前,对措施作了分析;在施工过程中,逐项进行了检验。在峻工后作了全面测试。结果表明,在按影响严重性区分的居民区Ⅰ、Ⅱ和Ⅲ中,25Hz峰值声压级分别从原有的95dB降至74dB,91dB降至66dB,83dB降至65dB,达到满意的效果。
我们结合措施设计,对低频隔声作了理论估算并与实验作了比较,证明在劲度控制区利用有效劲度,理论和实验符合很好。还从对居民的调查中,提出一个低频声干扰的初步建议。     

Synthesis and characterization of novel phosphoramidates containing benzimidazole moiety

Novel heterocyclic phosphoramidates were synthesized by a nucleophilic substitution reaction of 2-substitutedbenzimidazoles and diphenyl chlorophosphate (ClPO₃Ph₂) in the presence of potassium hydroxide (KOH) under an argon atmosphere. The structures of the phosphoramidates were characterized by NMR, IR, melting point, and elemental analysis.     

Hybrid thermotropic liquid-crystalline block copolymers

A new approach to the preparation of two classes of block copolymers containing liquid-crystalline segments is reported. Copolymers 1 and 2 are constituted by polytetrahydrofuran and side-chain liquid-crystalline polymethacrylate blocks, whereas block copolymers 3 consist of polystyrene and main-chain liquid-crystalline polyester blocks. The synthetic procedures leading to copolymers 1-3 are extremely versatile and can be used to prepare a great variety of block copolymer architectures. In both copolymer classes the chemically different blocks are strongly segregated in the solid and melt phases and undergo individual phase transitions. The mesophase transition temperatures of the liquid-crystalline blocks are very similar to those of the corresponding homopolymers, and their enthalpies are directly proportional to the content of the liquid-crystalline block.     

Tauberian conditions for the $$(C, \alpha )$$ integrability of functions

For a real-valued continuous function f(x) on \([0,\infty )\), we define

$$\begin{aligned} s(x)=\int _{0}^{x} f(u)du\quad \text {and}\quad \sigma _{\alpha } (x)= \int _{0}^{x}\left( 1-\frac{u}{x}\right) ^{\alpha }f(u)du \end{aligned}$$

for \(x>0\). We say that \(\int _{0}^{\infty } f(u)du\) is \((C, \alpha )\) integrable to L for some \(\alpha >-1\) if the limit \(\lim _{x \rightarrow \infty } \sigma _{\alpha } (x)=L\) exists. It is known that \(\lim _{x \rightarrow \infty } s(x) =L\) implies \(\lim _{x \rightarrow \infty }\sigma _{\alpha } (x) =L\) for all \(\alpha >-1\). The aim of this paper is twofold. First, we introduce some new Tauberian conditions for the \((C, \alpha )\) integrability method under which the converse implication is satisfied, and improve classical Tauberian theorems for the \((C,\alpha )\) integrability method. Next we give short proofs of some classical Tauberian theorems as special cases of some of our results.

     

生物组织多光谱偏振特性研究

生物组织内部结构复杂且具有较强的散射特性,而光作为生物组织检测的重要信息载体,其自身特性包括颜色、幅值、偏振等都对信息获取有较大的影响.结合偏振成像,对生物组织多光谱偏振特性展开了研究,依据不同微粒尺寸的分布建立了均匀单层生物组织模型,结合瑞利和米氏散射理论模拟了基于单个微粒的两种散射事件.瑞利散射具有较好的前向后向散...