Form sums of nonnegative selfadjoint operators

Summary The sum of two unbounded nonnegative selfadjoint operators is a nonnegative operator which is not necessarily densely defined. In general its selfadjoint extensions exist in the sense of linear relations (multivalued operators). One of its nonnegative selfadjoint extensions is constructed via the form sum associated with A and B. Its relations to the Friedrichs and Krein--von Neumann extensions of A+Bare investigated. For this purpose, the one-to-one correspondence between densely defined closed semibounded forms and semibounded selfadjoint operators is extended to the case of nondensely defined semibounded forms by replacing semibounded selfadjoint operators by semibounded selfadjoint relations. In particular, the inequality between two closed nonnegative forms is shown to be equivalent to a similar inequality between the corresponding nonnegative selfadjoint relations.</o:p>     

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Atmospheric pressure thermospray ionization using a heated microchip nebulizer

When a standard atmospheric pressure chemical ionization (APCI) or atmospheric pressure photoionization (APPI) ion source is used without applying the corona discharge or photoirradiation, atmospheric pressure thermospray ionization (APTSI) of various compounds can be achieved. Although largely ignored, this phenomenon has recently gained interest as an alternative ionization technique. In this study, this technique is performed for the first time on a miniaturized scale using a microchip nebulizer. Sample ionization with the presented microchip‐APTSI (µAPTSI) is achieved by applying only heat and gas flow to a nebulizer chip, without any other methods to promote gas‐phase ionization. To evaluate the performance of the described µAPTSI setup, ionization efficiency for a set of test compounds was monitored as the microchip positioning, temperature, nebulizer gas flow rate, sample solution composition, and solvent flow rate were varied. The µAPTSI mass spectra of the test compounds were also compared to those obtained with ESI and APCI. The µAPTSI produces ESI‐like spectra with low background noise, favoring the formation of protonated or deprotonated molecules of compounds that are ionizable in solution. Multiple charging of peptides without in‐source fragmentation was also observed. Unlike ESI, however, the µAPTSI source can tolerate the presence of mobile phase additives like trifluoroacetic acid (TFA) without significant ion suppression. The µAPTSI source can be used with standard mass spectrometer ion source hardware, being a unique alternative to the present interfacing techniques. Copyright © 2009 John Wiley & Sons, Ltd.     

Uniqueness and existence results for ordinary differential equations

We establish some uniqueness and existence results for first-order ordinary differential equations with constant-signed discontinuous nonlinear parts. Several examples are given to illustrate the applicability of our work.     

An addendum to the multiplication and factorization theorems of brodskiǐ—livšic—potapov

In this paper the classical Brodskiǐ—Liv?ic— operator colligation is generalized to certain pairs of bounded linear operators and the corresponding characteristic operator—valued (transfer) function is introduced. The fundamental results due to M.S. Brodskiǐ, M.S. Liv?ic, and V.P. Potapov are then extended to such colligations. These new types of colligations can be used to obtain, for instance, realization results for general Herglotz—Nevanlinna functions.     

Extensional viscosity in uniaxial extension and contraction flow—Comparison of experimental methods and application of the molecular stress function model

Extensional viscosity of a low-density polyethylene was measured at three temperatures in uniaxial extension by Sentmanat Extension Rheometer, and in contraction flow using the Cogswell analysis. The molecular stress function model was applied to describe the experimental results. The achieved maximum values from uniaxial transient tests were in accordance with the ones obtained by Cogswell method at similar strain level, and the molecular stress function model was able to describe the experimental transient uniaxial extensional data. The steady-state extensional viscosity was not reached in the experiments.     

Enhanced vertical confinement in angled-wall slot waveguides

Optical confinement in slot waveguides with angled sidewalls is studied. Improved vertical optical confinement is observed. Different mode solvers are compared in the modeling of slot waveguides with varying sidewall angles. The finite element method was found best suitable for this task. The effect of the slot waveguide geometry on the vertical optical confinement is studied. The reduced effective mode area is beneficial in all-optical applications due to enhancement of nonlinear effects in the waveguide.     

T1rho Dispersion profile of rat tissues in vitro at very low locking fields

The purpose of this study was to show the T(1rho) dispersion profile in various rat tissues (liver, brain, spleen, kidney, heart and skeletal muscle) at low (0.1 T) B(0) field at very low locking field B1, starting from 10 microT. The T(1rho) dispersion profile showed a quite similar pattern in all tissues. The highest R(1rho) relaxation rates were seen in the liver and muscle followed by the heart, whereas the values for spleen, kidney and brain were rather similar. The greatest difference between R2 relaxation rate and R(1rho) relaxation rate at B1=10 microT was seen in the liver and muscle. The steepest slope for a dispersion curve was seen in the muscle. The value of T(1rho) approximately approached the value of T2 when the locking field B1 approached 0. Except for the liver, the calculated apparent relaxation rate R2' was slightly larger than the calculated one. The potential value of T(1rho) imaging is to combine high R1 contrast of low-field imaging with the high signal-to-noise ratio (SNR) of high static field imaging. T(1rho) relaxation and dispersion data presented in the current study help to optimize the rotating-frame MR imaging.     

Arachidonic acid allows SNARE complex formation in the presence of Munc18

SNARE complex formation underlies intracellular membrane fusion in eukaryotic organisms; however, the factors regulating the SNARE assembly are not well understood. The neuronal SNARE complex is composed of synaptobrevin2, SNAP-25, and syntaxin1, the latter being under tight control by the cytosolic protein Munc18. We found that the inhibition of syntaxin1 by Munc18 both in nerve terminals and in defined in vitro reactions can be overcome by specific detergents. This serendipitous finding led us to screen biologically relevant fatty acids, revealing that unsaturated arachidonic and linolenic acids can stimulate Munc18-regulated SNARE complex formation in a direct manner. The direct effect of arachidonic acid on the syntaxin1/Munc18 complex suggests a mechanism for the activation of the SNARE assembly pathway and provides a lead for the further investigation of fatty acids that may regulate SNARE-mediated membrane fusion in eukaryotes.     

Liquid chromatographic-electrospray ionization mass spectrometric analysis of neutral and charged polyethylene glycols

Poly(ethylene glycols) (PEGs) are widely used water soluble and biocompatible polymers. PEGs are suitable as paracellular probes in biomembrane permeability studies because they are hydrophilic and various oligomers have defined molecular sizes. In previous studies corneal and conjunctival permeability for neutral PEGs has been measured, and the results were used to calculate the number and size of the cellular pores. In this study we have developed a high-performance liquid chromatographic-electrospray ionization-mass spectrometric method for analysis of neutral PEGs and positively changed amino PEGs simultaneously. The new method is fast, accurate, sensitive and specific for high throughput analysis. The method was used to evaluate the paracellular permeability of PEGs through a corneal epithelial cell culture. Paracellular pores are negatively charged and it was in our interest to characterize the interactions of positive charge and size of the molecules with the paracellular pores.