Elementary variational approach to zero-free solutions of a nonlinear eigenvalue problem

A variational approach is employed for obtaining zero-free solutions of a nonlinear eigenvalue problem that appears in several recent studies. Our proofs are elementary but our results are sharp and yield corrections to several existing assertions in the literature.     

On the character of operational solutions of the time-fractional diffusion equation

The nonhomogeneous time-fractional diffusion equation is analyzed in the frames of the Mikusiński calculus. The exact and the approximate solution of the considered problem are constructed and their character is analyzed.     

Compact embeddings and proper mappings

Sufficient conditions are given to assert that a C¹-proper mapping defined on a compact embedding between Banach spaces over K has a fixed point. The proof of the result is based upon continuation methods.     

Thermal Analysis as Part of the Quality System within Industrial Laboratories

The use of thermal analysis as part of a quality system in industry can be effective only if the techniques are made to conform to high standards of quality assurance. Achieving these high standards is not problem free and there remain many issues which require the attention of thermal analysts in industry and academe. Fundamental aspects which have been considered include limitations due to instrument design, problems in computerised control and analysis. A key aim is towards validation of data at international level. This revised version was published online in August 2006 with corrections to the Cover Date.     

Simultaneous determination of β2‐agonists in human urine by fast‐gas chromatography/mass spectrometry: method validation and clinical application

A fast screening protocol was developed and validated for the simultaneous determination of 15 β₂‐agonists in human urine (bambuterol, cimbuterol, clenbuterol, fenoterol, formoterol, isoproterenol, mapenterol, metaproterenol, procaterol, ractopamine, ritodrine, salbutamol, salmeterol, terbutaline, tulobuterol). The overall sample processing includes deconjugation with enzyme hydrolysis, liquid–liquid extraction, followed by derivatization of the extract and detection of β₂‐agonists trimethylsilyl‐derivatives by fast‐gas chromatography/electron impact–mass spectrometry (fast‐GC/EI‐MS). Sample extraction and derivatization were optimized with the purpose of improving recoveries and reaction yields for a variety of analytes with different structures simultaneously, while keeping the procedure simple and reliable. Validation parameters were determined for each analyte under investigation, including selectivity, linearity, intra‐ and inter‐assay precision, extraction recoveries and signal to noise ratio (S/N) at the lowest calibration level. Fast‐GC/MS sequences, based on the use of short columns, high carrier‐gas velocity and fast temperature ramping, allow considerable reduction of the analysis time (7 min), while maintaining adequate chromatographic resolution. The overall GC cycle time was less than 9 min, allowing a processing rate of 6 samples/h. High MS‐sampling rate, using a benchtop quadrupole mass analyzer, resulted in accurate peak shape definition under both scan and selected ion monitoring modes, and high sensitivity in the latter mode. The method was successfully tested on real samples arising from clinical treatments. Copyright © 2009 John Wiley & Sons, Ltd.     

Analysis of Mercury in Skin Lightening Cream by Microwave Plasma Atomic Emission Spectroscopy (MP-AES)

This research aimed at developing an analysis method, which was optimized and validated to determine the content of mercury in skin lightening cream discovered in the market in Bandar Lampung, Indonesia, through the use of microwave plasma atomic emission spectroscopy (MP-AES). The optimization on the analysis method was conducted on pump rate, viewing position, and reductant concentration in order to obtain the highest mercury emission intensity, while the solution stability was optimized to know the stability of mercury in the solution. The result showed that the method developed had precision with a relative standard deviation of 2.67%, recovery value of 92.78%, and linearity with an r value of 0.993, respectively. The sensitivity of the instrument detection had a limit of analysis method detection and quantification of 0.59 and 1.98 µg/L, respectively. The results of the test of the lightening cream (8 of 16 samples) positively contained mercury in the range of 422.61–44,960.79 ng/g. Therefore the method of analysis developed may be used for routine analysis of chemicals in any cosmetics products.     

Modular Total Synthesis of (–)‐Palmyrolide A and (+)‐(5S,7S)‐Palmyrolide A via Ring‐Closing Metathesis and Alkene Isomerization†

A pentamodule assembly approach has been established for total synthesis of the naturally occurring (–)‐palmyrolide A and (+)‐5,7‐epi‐palmyrolide A. By using the racemic tert‐butyl carbinol‐containing alkyl iodide, the two diastereoisomeric macrolides could be obtained from the same sequence of reactions, demonstrating the flexibility of the multimodule assembly strategy for diverted total synthesis.     

Reducing belief simpliciter to degrees of belief

Is it possible to give an explicit definition of belief (simpliciter) in terms of subjective probability, such that believed propositions are guaranteed to have a sufficiently high probability, and yet it is neither the case that belief is stripped of any of its usual logical properties, nor is it the case that believed propositions are bound to have probability 1? We prove the answer is ‘yes’, and that given some plausible logical postulates on belief that involve a contextual “cautiousness” threshold, there is but one way of determining the extension of the concept of belief that does the job. The qualitative concept of belief is not to be eliminated from scientific or philosophical discourse, rather, by reducing qualitative belief to assignments of resiliently high degrees of belief and a “cautiousness” threshold, qualitative and quantitative belief turn out to be governed by one unified theory that offers the prospects of a huge range of applications. Within that theory, logic and probability theory are not opposed to each other but go hand in hand.