14-Membered cyclodepsipeptides with alternating β-hydroxy and α-amino acids by cyclodimerization

The cyclodimerization (twinning) of β-hydroxy acid amides of type 1 under ‘direct amide cyclization’ (DAC) conditions is described. Although other coupling methods also gave moderate results, best yields were obtained via DAC, reaching 88% for the cyclodimer 10. In all cases, when starting with racemic material, only the trans-substituted cyclodepsipeptides were isolated. Simple molecular modeling revealed that the formation of the cyclodimer is thermodynamically slightly more favorable than that of the cyclomonomer. The proposal that cyclodimer formation is preferred because of the presence of intramolecular H-bonds could not be confirmed by X-ray crystallography. The influence of substituents, both in the amino acid and in the hydroxy acid moieties, was also studied. It is shown, that cyclodimerization was successful only when the hydroxy acid moiety is α,α-disubstituted.     

Asymptotic analysis of flow in wavy tubes and simulation of the extrusion process

The paper is devoted to the mathematical modelling of an extrusion process. Usually, an extruder has a very complicated geometry. This generates a lot of difficulties for computations of three‐dimensional flows. In the present paper, we develop and justify the asymptotic domain decomposition strategy in order to parallelize the computational process and reduce the memory. The error estimates are proved for the Stokes steady‐state equation in the two‐dimensional and three‐dimensional cases. Then, the asymptotic domain decomposition procedure is applied for numerical testing and computations of the non‐Newtonian fluid simulating a real process of the polymer extrusion. Copyright © 2007 John Wiley & Sons, Ltd.     

Proportionality of Components,Liouville Theorems and a Priori Estimates for Noncooperative Elliptic Systems

We study qualitative properties of positive solutions of noncooperative, possibly nonvariational, elliptic systems. We obtain new classification and Liouville type theorems in the whole Euclidean space, as well as in half-spaces, and deduce a priori estimates and the existence of positive solutions for related Dirichlet problems. We significantly improve the known results for a large class of systems involving a balance between repulsive and attractive terms. This class contains systems arising in biological models of Lotka–Volterra type, in physical models of Bose–Einstein condensates and in models of chemical reactions.     

人工蚕蛹虫草和冬虫夏草水溶性成分的相对归属分析

为对相近中药的化学指纹图谱进行比较研究,充分利用联用色谱所得的光谱、色谱信息与光谱相关色谱方法,分析了蚕蛹虫草和冬虫夏草的水溶性成分的异同,实现了蚕蛹虫草和冬虫夏草水溶性成分化学指纹图谱中相应化学组分的归属分析。其中,蚕蛹虫草和冬虫夏草有5个共有组分,分别有4个和6个相异组分。实验表明：该方法可对复杂中药成分及其指纹图谱进行快速比较分析。     

Ultrasound‐assisted aqueous two‐phase extraction of phenylethanoid glycosides from Cistanche deserticola Y. C. Ma stems

An efficient ultrasound‐assisted aqueous two‐phase extraction and enrichment process for phenylethanoid glycosides from Cistanche deserticola Y. C. Ma stems was developed in this work. An ethanol/ammonium sulfate system was chosen for the aqueous two‐phase system due to its fine partitioning and recycling behaviors. Single‐factor experiments and response surface methodology were used to optimize the process parameters of the ultrasound‐assisted aqueous two‐phase extraction. The optimal conditions were as follows: a salt concentration of 23.5%, an ethanol concentration of 20%, an extraction time of 37 min, an extraction temperature of 30°C, a liquid/solid ratio of 30:1 w/w, and an ultrasound power of 300 W. Under the above conditions, the extraction yields of echinacoside and acteoside (the main components of phenylethanoid glycosides) reached 5.35 and 6.22 mg/g dry material weight, respectively. The contents of echinacoside and acteoside in the extracts reached 27.56 and 30.23 mg/g, respectively, which were 2.46‐ and 2.58‐fold higher than the amounts obtained in ultrasound‐assisted extraction. In conclusion, ultrasound‐assisted aqueous two‐phase extraction was an efficient, ecofriendly, and economical method, and it may be a promising technique for extracting and enriching bioactive components from plants.     

Finite p-Groups with Few Non-major k-Maximal Subgroups

A subgroup of index p ^k of a finite p-group G is called a k-maximal subgroup of G. Denote by d(G) the number of elements in a minimal generator-system of G and by δ _k (G) the number of k-maximal subgroups which do not contain the Frattini subgroup of G. In this paper, the authors classify the finite p-groups with δ_d(G)(G) ≤ p² and δ_d(G)?1(G) = 0, respectively.     

Existence and regularity results for fully nonlinear equations with singularities

We consider the Dirichlet boundary value problem for a singular elliptic PDE like F[u] = p(x)u ^??? , where p, ?? ?? 0, in a bounded smooth domain of ${\mathbb{R}^n}$ . The nondivergence form operator F is assumed to be of Hamilton?CJacobi?CBellman or Isaacs type. We establish existence and regularity results for such equations.     

Noise perturbation in functional principal component analysis filtering for two-dimensional correlation spectroscopy: its theory and application to infrared spectra of a poly(3-hydroxybutyrate) thin film

A method based on noise perturbation in functional principal component analysis (NPFPCA) is for the first time introduced to overcome the noise interference problem in two-dimensional correlation spectroscopy (2D-COS). By the systematic addition of synthetic noise to the dynamic multivariate spectral data, the functional principal component analysis (FPCA) described in this report is able to accurately determine which eigenvectors are representing significant signals instead of noise in the original data. This feature is especially useful for the data reconstruction and noise filtering. Reconstructed data resulted from the smooth eigenvectors can produce much more reliable 2D correlation spectra by removing the correlation artifacts from noise, which in turn enable more accurate interpretation of the spectral variations. The usefulness of this method is demonstrated with a theoretical framework and applications to the 2D correlation analyses of both simulated data and temperature-dependent reflection-absorption infrared spectra of a poly(3-hydroxybutyrate) (PHB) thin film.