A class of Nevanlinna functions related to singular Sturm-Liouville problems

The class of Nevanlinna functions consists of functions which are holomorphic off the real axis, which are symmetric with respect to the real axis, and whose imaginary part is nonnegative in the upper halfplane. The Kac subclass of Nevanlinna functions is defined by an integrability condition on the imaginary part. In this note a further subclass of these Kac functions is introduced. It involves an integrability condition on the modulus of the Nevanlinna functions (instead of the imaginary part). The characteristic properties of this class are investigated. The definition of the new class is motivated by the fact that the Titchmarsh-Weyl coefficients of various classes of Sturm-Liouville problems (under mild conditions on the coefficients) actually belong to this class.

     

Identification of extracellular nanoparticle subsets by nuclear magnetic resonance

Exosomes are a subset of secreted lipid envelope-encapsulated extracellular vesicles (EVs) of 50–150 nm diameter that can transfer cargo from donor to acceptor cells. In the current purification protocols of exosomes, many smaller and larger nanoparticles such as lipoproteins, exomers and microvesicles are typically co-isolated as well. Particle size distribution is one important characteristics of EV samples, as it reflects the cellular origin of EVs and the purity of the isolation. However, most of the physicochemical analytical methods today cannot illustrate the smallest exosomes and other small particles like the exomers. Here, we demonstrate that diffusion ordered spectroscopy (DOSY) nuclear magnetic resonance (NMR) method enables the determination of a very broad distribution of extracellular nanoparticles, ranging from 1 to 500 nm. The range covers sizes of all particles included in EV samples after isolation. The method is non-invasive, as it does not require any labelling or other chemical modification. We investigated EVs secreted from milk as well as embryonic kidney and renal carcinoma cells. Western blot analysis and immuno-electron microscopy confirmed expression of exosomal markers such as ALIX, TSG101, CD81, CD9, and CD63 in the EV samples. In addition to the larger particles observed by nanoparticle tracking analysis (NTA) in the range of 70–500 nm, the DOSY distributions include a significant number of smaller particles in the range of 10–70 nm, which are visible also in transmission electron microscopy images but invisible in NTA. Furthermore, we demonstrate that hyperpolarized chemical exchange saturation transfer (Hyper-CEST) with ¹²⁹Xe NMR indicates also the existence of smaller and larger nanoparticles in the EV samples, providing also additional support for DOSY results. The method implies also that the Xe exchange is significantly faster in the EV pool than in the lipoprotein/exomer pool.

Diffusion and xenon NMR based methods to determine a very broad range of sizes and sub-sets of extracellular vesicles.     

Effects of various washing procedures on the chromium content of human scalp hair

The effects of four wash procedures on the concentration of chromium in a pooled sample of human scalp hair are compared. The wash solutions examined are Triton X-100, sodium lauryl sulphate, acetone, and a mixture (1 + 1) of hexane and ethanol. The plateaux reached for hair chromium concentration are functions of the number of washings, and are characteristic for each wash solution. The wash procedure recommended involves two 20-min washes with aqueous 1% sodium lauryl sulphate solution after a hexane rinse.     

Liquid chromatography/atmospheric pressure ionization-mass spectrometry in drug metabolism studies

The study of the metabolic fate of drugs is an essential and important part of the drug development process. The analysis of metabolites is a challenging task and several different analytical methods have been used in these studies. However, after the introduction of the atmospheric pressure ionization (API) technique, electrospray and atmospheric pressure chemical ionization, liquid chromatography/mass spectrometry (LC/MS) has become an important and widely used method in the analysis of metabolites owing to its superior specificity, sensitivity and efficiency. In this paper the feasibility of LC/API-MS techniques in the identification, structure characterization and quantitation of drug metabolites is reviewed. Sample preparation, LC techniques, isotope labeling, suitability of different MS techniques, such as tandem mass spectrometry, and high-resolution MS in drug metabolite analysis, are summarized and discussed. Automation of data acquisition and interpretation, special techniques and possible future trends are also the topics of the review.     

On a classical Nicoletti boundary value problem

We shall derive existence, uniqueness and comparison results for the functional differential equationx(t)=f(t, x), a. e.tI, with classical Nicoletti boundary conditionsx _i(t_i)=y _iX, iA, whereI is a real interval,A is a nonempty set andX is a Banach space.     

Commutative and noncommutative representations of matrix-valued herglotz-nevanlinna functions

Operator realizations of matrix-valued Herglotz-Nevanlinna functions play an important and essential role in system theory, in the spectral theory of bounded nonselfadjoint operators, and in interpolation problems. Here, a generalization for realization results of the Brodskiǐ-Livsic type is given for Herglotz-Nevanlinna functions whose spectral measures are compactly supported.     

Z→E Photoisomerization of Homoactivated Carbon Carbon Double Bonds

Z-configured 1,4-diene or β,γ-unsaturated carbonyl systems are readily available by the Wittig reaction. Isomerization required for access into the E-series can easily be accomplished by irradiation using an ordinary tungsten lamp and diphenyl disulphide sensitizer. There is very little formation of conjugated isomers (less than 1%).     

Preparation of 4-Vinyl-2(5H)-Furanoid Structural Unit via Organosilicon and - Selenium Intermediates

Two syntheses of the 2(5H)-furanoid structural unit (especially the 3-methyl derivative 1) have been reported from this laboratory.^1,2 The unit 1 is found in many naturally occurring compounds (especially sesqui terpenes). The 4-substi tuted d erivatives of 1 also occur frequently i n natural products, e.g. furospongolide³ 2.     

Regioselective Mono-<Emphasis Type="Italic">O</Emphasis>-Carboxymethylation of Polyhydroxyisoflavones

Optimized conditions are described for the regioselective mono-O-alkylation of daidzein 1a, genistein 1b, and biochanin A 1c with ethyl bromoacetate.     

Singular Sturm-Liouville problems whose coefficients depend rationally on the eigenvalue parameter

Let −Dω(·,z)D+q be a differential operator in L²(0,∞) whose leading coefficient contains the eigenvalue parameter z. For the case that ω(·,z) has the particular form