Condensations of projective sets onto compacta

For a coanalytic-complete or -complete subspace of a Polish space we prove that there exists a continuous bijection of onto the Hilbert cube . This extends results of Pytkeev. As an application of our main theorem we give an answer to some questions of Arkhangelskii and Christensen.

Under the assumption of Projective Determinacy we also give some generalizations of these results to higher projective classes.

     

Review of fluorescence anisotropy decay analysis by frequency-domain fluorescence spectroscopy

This didactic paper summarizes the mathematical expressions needed for analysis of fluorescence anisotropy decays from polarized frequency-domain fluorescence data. The observed values are the phase angle difference between the polarized components of the emission and the modulated anisotropy, which is the ratio of the polarized and amplitude-modulated components of the emission. This procedure requires a separate measurement of the intensity decay of the total emission. The expressions are suitable for any number of exponential components in both the intensity decay and the anisotropy decay. The formalism is generalized for global analysis of anisotropy decays measured at different excitation wavelengths and for different intensity decay times as the result of quenching. Additionally, we describe the expressions required for associated anisotropy decays, that is, anisotropy decays where each correlation time is associated with a decay time present in the anisotropy decay. And finally, we present expressions appropriate for distributions of correlation times. This article should serve as a reference for researchers using frequency-domain fluorometry.     

The curse of dimensionality for the class of monotone functions and for the class of convex functions

We study the integration and approximation problems for monotone or convex bounded functions that depend on $d$ variables, where $d$ can be arbitrarily large. We consider the worst case error for algorithms that use finitely many function values. We prove that these problems suffer from the curse of dimensionality. That is, one needs exponentially many (in $d$) function values to achieve an error $\epsilon$.     

A new approach to phosphoserine and phosphothreonine analysis in peptides and proteins: chemical modification,enrichment via solid-phase reversible binding,and analysis by mass spectrometry

beta-Elimination of the phosphate group on phosphoserine and phosphothreonine residues and addition of an alkyldithiol is a useful tool for analysis of the phosphorylation states of proteins and peptides. We have explored the influence of several conditions on the efficiency of this PO(4)(3-) elimination reaction upon addition of propanedithiol. In addition to the described influence of different bases, the solvent composition was also found to have a major effect on the yield of the reaction. In particular, an increase in the percentage of DMSO enhances the conversion rate, whereas a higher amount of protic polar solvents, such as water or isopropanol, induces the opposite effect. We have also developed a protocol for enrichment of the modified peptides, which is based on solid-phase covalent capture/release with a dithiopyridino-resin. The procedure for beta-elimination and isolation of phosphorylated peptides by solid-phase capture/release was developed with commercially available alpha-casein. Enriched peptide fragments were characterized by MALDI-TOF mass spectrometric analysis before and after alkylation with iodoacetamide, which allowed rapid confirmation of the purposely introduced thiol moiety. Sensitivity studies, carried out in order to determine the detection limit, demonstrated that samples could be detected even in the low picomolar range by mass spectrometry. The developed solid-phase enrichment procedure based on reversible covalent binding of the modified peptides is more effective and significantly simpler than methods based on the interaction between biotin and avidin, which require additional steps such as tagging the modified peptides and work-up of the samples prior to the affinity capture step.     

Spontaneous Nef reaction of 3-aryl-2-(diethoxyphosphoryl)-4-nitroalkanoic acids

Spontaneous Nef reaction of primary and secondary 3-aryl-2-(diethoxyphosphoryl)-4-nitroalkanoic acids has been observed for the first time. The reaction provides a general and effective, highly diastereoselective synthesis of 3-(diethoxyphosphoryl)-1-hydroxysuccinimides and 2-(diethoxyphosphoryl)-4-oxoalkanoic acids.     

Magneto-Thin-Layer Chromatography as a Tool for the Analysis of Plant Extracts

JPC – Journal of Planar Chromatography – Modern TLC - As it was presented in our previous works, applying external magnetic field during chromatogram development results in changes of...     

Optimization of Adsorbent Layer Type and Developing Solvent in Coccidiostats Sample Preparation with Procedure of Solvent Front Position Extraction

Coccidiostats are drugs used against coccidiosis, a common disease among breeding animals. Their widespread application leads to the appearance of their residues in food, which is potentially harmful for human health and life. The European Union has established limits of concentrations of these drugs in premixtures and food. Nowadays, there are many methods for monitoring coccidiostats’ presence in market products, but their frequent weakness is sample preparation. Solvent Front Position Extraction is a planar chromatography-based sample preparation method that allows for effective assay of samples with coccidiostats when coupled with LC-MS/MS. The purpose of this research was to find common conditions for the effective isolation of eight coccidiostats from biological sample components with both lower and higher retention than the substances of interest. The acquired results were used for effective isolation of monensin and salinomycin from the premixture samples and allowed for their quantitative determination. The application of a semi-automatic device for the development of chromatograms positively impacted the results, confirming the effectiveness of the method for determining coccidiostats in biological samples.     

RESOLUTION OF TWO EMISSION SPECTRA FOR TRYPTOPHAN USING FREQUENCY-DOMAIN PHASE-MODULATION SPECTRA

We describe a novel application of frequency-domain fluorometry which allows resolution of the decay times and emission spectra of samples which display multi-exponential decay kinetics. This method does not require any previous knowledge about the decay times or any assumptions about the shape of the emission spectra. We record the wavelength-dependent phase angles and modulations (phase angle and modulation spectra) using a number of light modulation frequencies. The data is analyzed by non-linear least-squares to recover the emission spectra and their associated decay times. Phase and modulation spectra (PM Spec) were used to recover the emission spectra associated with the two decay times of tryptophan at pH = 7 (0.54 and 3.44 ns). The emission spectra of these components are centered at 340 and 355 nm, respectively, with the amplitude of the 0.54 ns component contributing 6% to the total emission. These results are in agreement with previous time-resolved studies by Szabo and Rayner [J. Am. Chem. Soc. 102, 554-563 (1980)]. Control experiments were performed on mixtures of N-acetyl-L-tryptophanamide (NATA) and PPD, which demonstrate our ability to recover the spectra and decay times from two component mixtures. NATA itself displayed a single decay time and only one emission spectrum.