Zero-Mean Cosine Polynomials which are Non-Negative for as Long as Possible

For a given integer n, all zero-mean cosine polynomials of orderat most n which are non-negative on [0,(n/(n+1))] are found,and it is shown that this is the longest interval [0,] on whichsuch cosine polynomials exist. Also, the longest interval [0,]on which there is a non-negative zero-mean cosine polynomialwith non-negative coefficients is found. As an immediate consequence of these results, the correspondingproblems of the longest intervals [,] on which there are non-positivecosine polynomials of degree n are solved. For both of these problems, all extremal polynomials are found.Applications of these polynomials to Diophantine approximationare suggested.     

Bioavailability studies of oral dosage forms containing levodopa and carbidopa using column-switching chromatography followed by electrochemical detection

A reliable multi-dimensional column chromatographic method employing amperometric detection using a carbon fibre microelectrode procedure was used for monitoring the plasma profiles and to evaluate the pharmacokinetics and bioavailability of levodopa (L-dopa) and carbidopa (C-dopa), after ingestion of oral formulations containing these drugs. The peak currents obtained for the different analytes were directly proportional to the analyte over the concentration range 0.02-4 micrograms ml-1. Using this method, the minimum detectable concentration was estimated to be 5 and 8 ng ml-1 for L-dopa and C-dopa, respectively. Recovery studies ranged from 93.83 to 89.76%, with a relative standard deviation of less than 7%. The study was carried out in two separate weeks on five healthy non-patient fasted male/female volunteers in the age range 20-37 years and weighing between 60 kg and 78 kg. The pharmacokinetic profile of two controlled-release products containing both L-dopa and C-dopa (Sinemet CR3 and CR4) was compared on the one hand and Sinemet conventional tablets on the other. The pharmacokinetic parameters, peak concentration (Cmax), the time taken to obtain this level (Tmax), elimination half-time T1/2, elimination rate constant (Kel), plasma level ratio, fluctuation index (FI) and the area under the time-concentration curve (AUC0-8), were investigated for each individual formulation. A comparison of the uptake of L-dopa from the conventional formulation showed that L-dopa entered the plasma and achieved peak levels higher than that of the controlled release formulations. However, it showed a much higher fluctuation index and the plasma concentrations were more stable with the controlled release formulations. The data also indicated a very low accumulation of both levodopa and carbidopa following repeated administration of the drugs, which was consistent with their relatively short half-lives (less than 2 h). In contrast, the half-life for the metabolite 3-orthomethyl dopa (3-OMD) is in the order of 13 h. As a result, there was an extensive accumulation of 3-OMD and its levels were significantly higher than those of levodopa or carbidopa upon repeated administration. Urine recoveries of the three analytes over one 8 h dosing interval showed that the majority of the excreted levodopa and carbidopa was recovered during the first 4 h, and there is proportionally greater excretion of the carbidopa dose than the levodopa dose.     

Single-Proton Pickup Reaction of the Halo Nucleus ^6He on a ^9Be Target at 25 MeV/nucleon

The inclusive differential cross sections of the ^7 Li nucleus in a reaction induced by ^6He on a ^9Be target are measured at an incident energy of 25 MeV/nucleon. Finite-range distorted-wave Born approximation calculations suggest that these ^7 Li particles are formed in a direct single-proton pickup reaction ^9Be（^6He,^7 Li）^8Li. The experimental data can be well reproduced by taking into account of the contributions of both the ground states and the first excited states of ^7Li and ^8Li.     

关于拓扑对策中的I~2(K)I(K)问题

证明了如果空间类κ为D-空间类或闭遗传不可约空间类,则I(κ)(∈)κ.这一结果对于κ为D空间类和闭遗传不可约空间类,肯定地回答了I(κ)是否包含I2(κ)问题.     

Asymptotic description of solitary wave trains in fully nonlinear shallow-water theory

We derive an asymptotic formula for the amplitude distribution in a fully nonlinear shallow-water solitary wave train which is formed as the long-time outcome of the initial-value problem for the Su–Gardner (or one-dimensional Green–Naghdi) system. Our analysis is based on the properties of the characteristics of the associated Whitham modulation system which describes an intermediate “undular bore” stage of the evolution. The resulting formula represents a “non-integrable” analogue of the well-known semi-classical distribution for the Korteweg–de Vries equation, which is usually obtained through the inverse scattering transform. Our analytical results are shown to agree with the results of direct numerical simulations of the Su–Gardner system. Our analysis can be generalised to other weakly dispersive, fully nonlinear systems which are not necessarily completely integrable.     

S-烷基异硫脲盐作为硫醇替代物经环氧开环反应合成β-羟基硫化物

S-烷基异硫脲盐作为一种无毒、无味、易于制备的硫醇替代物，在碱性水介质中、室温下与多种环氧化合物发生环氧开环反应，区域选择性、高收率地合成了一系列β-羟基硫化物。     

Application of electrospray mass spectrometry in the detection and determination of Remazol textile dyes.

The electrospray (ES) behaviour of selected Remazol textile dyes, their hydrolysis products and the latters' reaction, following elution from a strong anion-exchange cartridge, with 30% concentrated HCl in MeOH, is studied and applied to the direct analysis of dye containing effluent. For unambiguous identification and determination of these textile dyes in effluents, it is necessary to resort to ES utilising MS-MS and MS3. Further, a tabular review of recent applications of HPLC-ES-MS and, to a lesser extent, CE-ES-MS with reference to drug and pesticide analysis is presented.