On a result of R. R. Hall

An upper bound for the mean value of a non-negative submultiplicative function by R. R. Hall [3] is sharpened and generalised. Hall's inequality implies a certain rather accurate upper sieve estimate, and this aspect of Hall's result is exploited in deriving good lower bounds for π(x) via the sieve.     

华罗庚

华罗庚教授曾在 194 8— 195 0年间任伊利诺伊大学的教授 ,回国之后与哈贝斯坦的友谊保持终生。哈贝斯坦教授的这篇有关著名数学家华罗庚的传记文章 ,发表在美国科学院出版的《科学家传记》第 81卷 (Biographical Memoirs,Vol.81,The National Academy Press,Washington,D.C.2 0 0 2 )中。该传记丛书每卷大约 5 0 0页 ,包括 2 0名科学家。据查 ,在70— 81卷中 ,只收录了一位大陆科学家——华罗庚。本传记中的观点均属于作者本人 ,并不一定反映美国国家科学院的观点。本刊特别约请著名数学家王元教授将此文翻译成中文 ,以飨广大读者。     

PRESSURE-VELOCITY EQUILIBRIUM HYDRODYNAMIC MODELS

This article describes mathematical models for phase separated mixtures of materials that are in pressure and velocity equilibrium but not necessarily temperature equilibrium. General conditions for constitutive models for such mixtures that exhibit a single mixture sound speed are discussed and specific examples are described.     

The Learned Symmetry Concept in Revealing Quantitative Structure-Activity Relationships With Artificial Neural Networks

Abstract

A method to build QSAR models based on substituent constants for congeneric sets of compounds having several topologically equivalent substituent positions was proposed. The approach is based on the application of artificial neural networks (learning to construct nonlinear structure-activity relationships taking into account necessary symmetry properties of training set structures) to a training set expanded by adding the copies of compounds with the same activity values but with permuted assignment of equivalent substituent positions. The better predictive power of these constructed models, as compared with the performances of neural network models for non-expanded sets was demonstrated for the calcium channel blockers of 1,4-dihydropyridine type and for hallucinogenic phenylalkylamines.     

An approach to the interpretation of backpropagation neural network models in QSAR studies

An approach to the interpretation of backpropagation neural network models for quantitative structure-activity and structure-property relationships (QSAR/QSPR) studies is proposed. The method is based on analyzing the first and second moments of distribution of the values of the first and the second partial derivatives of neural network outputs with respect to inputs calculated at data points. The use of such statistics makes it possible not only to obtain actually the same characteristics as for the case of traditional "interpretable" statistical methods, such as the linear regression analysis, but also to reveal important additional information regarding the non-linear character of QSAR/QSPR relationships. The approach is illustrated by an example of interpreting a backpropagation neural network model for predicting position of the long-wave absorption band of cyane dyes.     

Correlation between biological activity and energies of electronic transitions in benzodiazepines. Negative ion mass spectrometry and ultraviolet absorption spectroscopy study of some derivatives

A correlation between the energies of electronic singlet transitions in benzodiazepines and their biological activity, which was revealed earlier by means of negative ion mass spectrometry with resonance electron capture, has been verified with a UV absorption spectroscopy investigation. Also, it has been noted that the energies of electronic singlet transitions in benzodiazepines are close in value to the ionization energies of atoms Cs, Rb, K, Na, Li and Tl, the cations of which are known to play an important role in nerve cell excitation processes. Copyright 1999 John Wiley & Sons, Ltd.     

Gas-phase deprotonation of arylalkylamines. A collision-induced dissociation study

The collision-induced dissociation (CID) of deprotonated arylalkylamines of general formula R(1)C(6)H(4)CHR(2)CH(2)NR(3)(2) (where R(1) = H, OH, F or NO(2); R(2) = H or OH; R(3) = H or CH(3)) generated by negative chemical ionization with H(2)O and D(2)O as ionizing reagents, is discussed. The negative chemical ionization mass spectra show that, in the absence of a hydroxy group in the aromatic ring, deprotonation takes place at the benzylic position whereas the proton is lost from the OH group when present. The nitro compound forms only M(-.) ions. The CID spectra of the deprotonated molecules show that fragmentations are strongly dependent on the structural features of the molecules, namely the presence or absence of substituents in the aromatic ring or aliphatic chain. Copyright 1999 John Wiley & Sons, Ltd.     

Purification and Characterization of Agarase from Marine Bacteria <Emphasis Type="Italic">Acinetobacter</Emphasis> sp. PS12B and Its Use for Preparing Bioactive Hydrolysate from Agarophyte Red Seaweed <Emphasis Type="Italic">Gracilaria verrucosa</Emphasis>

Acinetobacter strain PS12B was isolated from marine sediment and was found to be a good candidate to degrade agar and produce agarase enzyme. The extracellular agarase enzyme from strain PS12B was purified by ammonium sulfate precipitation followed by DEAE-cellulose ion-exchange chromatography. The specific activity of the crude enzyme which was 1.52 U increased to 45.76 U, after two-stage purification, with an enzyme yield of 9.76%. Purified enzyme had a molecular mass of 24 kDa. The optimum pH and temperature for activity of purified agarase were found to be 8.0 and 40 °C, respectively. The K_m and V_max values for agarase were 4.69 mg/ml and 0.5 μmol/min, respectively. Treatment with EDTA reduced the agarase activity by 58% at 5 mM concentration. The enzyme activity was stimulated by the presence of Fe²⁺, Mn²⁺, and Ca2⁺ ions while reducing reagents (β-mercaptoethanol and dithiothreitol, DTT) enhanced its activity by 30–40%. The purified agarase exhibited tolerance to both detergents and organic solvents. Major hydrolysis products of agar were DP4 and also a mixture of longer oligosaccharides DP6 and DP7. The enzyme hydrolysed seaweed (Gracilaria verrucosa) exhibited strong antioxidant activity in vitro. Successful hydrolysis of seaweed indicates the potential use of the enzyme to produce seaweed hydrolysate having health benefits as well as the industrial application like the production of biofuels.