正则局部Lipschitz函数可微性的几何条件

Ｂａｎａｃｈ空间的范数可微性可用它的单位球面来刻画．本文把这些范数可微性的几何条件推广到正则局部Ｌｉｐｓｃｈｉｔｚ函数情形．     

Critical exponents for Fréedericskz transition in nematics between concentric cylinders

The equilibrium tilt angle profile in a cell limited by two concentric cylinders filled with nematic liquid crystals is determined for strong homeotropic anchoring at the surfaces. The anchoring condition is such that the nematic director is perpendicular to the cylinder axes and a radial nonuniform electric field is applied to investigate a Fréedericksz transition. The distortions induced by the field remain in the plane perpendicular to the cylinder axes, and a threshold field is analytically determined indicating a transition from a pure splay to a splay-bend conformation of the director. It is shown that this transition can be induced by the thickness of the region between the two cylinders, and can be detected even in the absence of an external field. If the maximum value of the tilt angle is assumed as an order parameter, its behavior near to the transition can be used to obtain the critical exponent, which is the same as the one obtained in the mean field approximation. These results are indications that nontrivial consequences may occur when complex fluids are subject to non-planar geometries.     

Ellagitannin Digestion in Moth Larvae and a New Dimeric Ellagitannin from the Leaves of Platycarya strobilacea

Ellagitannins (ETs) are plant polyphenols with various health benefits. Recent studies have indicated that the biological activities of ETs are attributable to their degradation products, including ellagic acid and its gut microflora metabolites, such as urolithins. Insect tea produced in the Guangxi region, China, is made from the frass of moth larvae that feed on the ET-rich leaves of Platycarya strobilacea. Chromatographic separation of the Guangxi insect tea showed that the major phenolic constituents are ellagic acid, brevifolin carboxylic acid, gallic acid, brevifolin, and polymeric polyphenols. Chemical investigation of the feed of the larvae, the fresh leaves of P. strobilacea, showed that the major polyphenols are ETs including pedunculagin, casuarictin, strictinin, and a new ET named platycaryanin E. The new ET was confirmed as a dimer of strictinin having a tergalloyl group. The insect tea and the leaves of P. strobilacea contained polymeric polyphenols, both of which were shown to be composed of ETs and proanthocyanidins by acid hydrolysis and thiol degradation. This study clarified that Guangxi insect tea contains ET metabolites produced in the digestive tract of moth larvae, and the metabolites probably have higher bioavailabilities than the original large-molecular ETs of the leaves of P. strobilacea.     

Reduction of surface coverage of finite systems due to geometrical steps

The coverage of vicinal, stepped surfaces with molecules is simulated with the help of a two-dimensional Ising model including local distortions and an Ehrlich-Schwoebel barrier term at the steps. An effective two-spin model is capable to describe the main properties of this distorted Ising model. It is employed to analyze the behavior of the system close to the critical points. Within a well-defined regime of bonding strengths and Ehrlich-Schwoebel barriers we find a reduction of coverage (magnetization) at low temperatures due to the presence of the surface step. This results in a second, low-temperature transition besides the standard Ising order-disorder transition. The additional transition is characterized by a divergence of the susceptibility as a finite-size effect. Due to the surface step the mean-field specific heat diverges with a power law.     

Determination of positron beam parameters by various diagnostic techniques

Various diagnostic techniques have been applied at the neutron-induced positron source Munich NEPOMUC in order to determine the positron beam parameters such as intensity, beam shape and energy distribution. The positron beam intensity is determined by the detection of the annihilation radiation of positrons, which annihilate in a movable target. The use of a micro-channel plate (MCP) detector with a CCD-camera allows a direct measurement of the positron beam shape and the lateral resolved intensity distribution. At NEPOMUC a movable MCP-assembly inside the evacuated beam line enables a quick examination of the beam shape during operation. A retarding grid was mounted inside the homogeneous magnetic guiding field in order to determine the distribution of the longitudinal positron momentum, and hence estimate the energy distribution of the positrons.     

Progress of the intense positron beam project EPOS

EPOS (the ELBE POsitron Source) is a running project to build an intense, bunched positron beam for materials research. It makes use of the bunched electron beam of the ELBE radiation source (Electron Linac with high Brilliance and low Emittance) at the Research Centre Dresden-Rossendorf (40 MeV, 1 mA). ELBE has unique timing properties, the bunch length is <5 ps and the repetition time is 77 ns. In contrast to other Linacs made for Free Electron Lasers (e.g., TTF at DESY, Hamburg), ELBE can be operated in full cw-mode, i.e., with an uninterrupted sequence of bunches. The article continues an earlier publication. It concentrates on details of the timing system and describes issues of radiation protection.     

Optimisation of the ultrasound-assisted extraction of betalains and polyphenols from Amaranthus hypochondriacus var. Nutrisol

The present study optimised the ultrasound-assisted extraction (UAE) of bioactive compounds from Amaranthus hypochondriacus var. Nutrisol. Influence of temperature (25.86–54.14 °C) and ultrasonic power densities (UPD) (76.01–273.99 mW/mL) on total betalains (BT), betacyanins (BC), betaxanthins (BX), total polyphenols (TP), antioxidant activity (AA), colour parameters (L*, a*, and b*), amaranthine (A), and isoamaranthine (IA) were evaluated using response surface methodology. Moreover, betalain extraction kinetics and mass transfer coefficients (K_La) were determined for each experimental condition. BT, BC, BX, TP, AA, b*, K_La, and A were significantly affected (p < 0.05) by temperature extraction and UPD, whereas L*, a*, and IA were only affected (p < 0.05) by temperature. All response models were significantly validated with regression coefficients (R²) ranging from 87.46 to 99.29%. BT, A, IA, and K_La in UAE were 1.38, 1.65, 1.50, and 29.93 times higher than determined using conventional extraction, respectively. Optimal UAE conditions were obtained at 41.80 °C and 188.84 mW/mL using the desired function methodology. Under these conditions, the experimental values for BC, BX, BT, TP, AA, L*, a*, b*, K_La, A, and IA were closely related to the predicted values, indicating the suitability of the developed quadratic models. This study proposes a simple and efficient UAE method to obtain betalains and polyphenols with high antioxidant activity, which can be used in several applications within the food industry.     

Can electrospray ionization help the characterization of iron gall inks? Investigation on the interactions of gallic acid with iron ions in aqueous solutions

In the present work, an investigation has been conducted by electrospray ionization (ESI) experiments to characterize the structures of iron gall ink complexes in solution. Simple mono and polyphenolic acid molecules added to iron sulfate salts were chosen to model the recipes of ink composition. Theoretical calculations have been used (1) to determine the stability of the ionic complexes generated in the gas phase, (2) to explain which structures are more likely generated in the electrospray ion source, and (3) to determine which mechanisms are likely involved in their formation. Fragmentation pathways of the derived structures have also been investigated and rationalized to facilitate the interpretation of the data obtained under collisionally induced dissociation (CID) conditions.The present study confirms the assumption that ESI experiments with ions that are preformed in solution must be considered carefully. As a matter of fact, the study of ion formation mechanisms in the ion source is necessary to establish relationships between the ion structures in the condensed phase and the gas phase.     

Validated high-performance thin-layer chromatographic method for quantification of gallic acid and ellagic acid in fruits of Terminalia chebula,Phyllanthus emblica,and Quercus infectoria

A simple and rapid high-performance thin-layer chromatographic method for quantification of gallic acid and ellagic acid in dried fruits of Terminalia chebula, Phyllanthus emblica, and Quercus infectoria has been developed. The chromatographic development was carried out on precoated silica gel 60 F₂₅₄ plates in a mixture of toluene:ethyl acetate:chloroform:formic acid (4:8:1:3 v/v/v/v). The plate was scanned densitometrically at a wavelength of 280 nm. The retention factor value of gallic acid and ellagic acid was found to be 0.63 ± 0.2 and 0.53 ± 0.1, respectively. The developed method was validated in terms of linearity, precision, accuracy, sensitivity, robustness, specificity and stability as per the international conference of harmonization guidelines. The method showed good linear relationship over a range of 100–600 ng/band (gallic acid) and 100–500 ng/band (ellagic acid) with a regression coefficient (r²) of 0.997 (gallic acid) and 0.996 (ellagic acid). The method showed high accuracy (99.65%–100.85%). The percentage relative standard deviation of intra-day and inter-day precision studies was not more than 2%. The method is highly robust and has displayed high specificity. The developed method is new, simple, and accurate and can be successfully employed in routine analysis of raw materials and formulations containing gallic acid and ellagic acid.     

The correlation length of commodity markets 1. Empirical evidence

It is a common belief nowadays that the world economy is fairly well “integrated”. Yet, this belief often turns out to be in contradiction with empirical evidence. As a matter of fact the way distant markets interact is a question that has largely been ignored by economists. In this series of two papers we examine the role that space, that is to say geographical distance, plays in the economics of commodity markets. The first of these papers presents the empirical evidence while the second develops a theoretical framework. The empirical enquiry discloses several noteworthy features, e.g. (i) with respect to spatial interaction there is a sharp contrast between stock markets and commodity markets. While there is almost perfect spatial arbitrage in the first case, this is not true for commodity markets. (ii) In spite of their chaotic behavior in the course of time commodity prices display well defined spatial patterns, (iii) as in statistical physics and fluid dynamics interactions can be described in terms of correlation length. The correlation length of a set of markets is seen to increase along with the number of transactions; it also increases when transport costs decline as was the case during the “transportation revolution” of the mid-nineteenth century. Using the notion of correlation length one is able to give a quantitative meaning to the otherwise ill-defined concept of market integration. Received 17 May 1999 and Received in final form 31 May 1999