The one phase free boundary problem for the -Laplacian with non-constant Bernoulli boundary condition

Our objective, here, is to generalize our earlier results on the existence of classical convex solution to a free boundary problem with a Bernoulli-type boundary gradient condition and with the -Laplacian as the governing operator. The main theorems of this paper assert that the exterior and the interior free boundary problem with a Bernoulli law, i.e. with a prescribed pressure on the ``free' streamline of the flow, have convex solutions provided the initial domains are convex. The continuous function is subject to certain convexity properties. In our earlier results we have considered the case of constant . In the lines of the proof of the main results we also prove the semi-continuity (up to the boundary) of the gradient of the -capacitary potentials in convex rings, with boundaries.

     

Dynamical Determinants via Dynamical Conjugacies for Postcritically Finite Polynomials

We give an analogue of Levin–Sodin–Yuditskii's study of the dynamical Ruelle determinants of hyperbolic rational maps in the case of subhyperbolic quadratic polynomials. Our main tool is to reduce to an expanding situation. We do so by applying a dynamical change of coordinates on the domains of a Markov partition constructed from the landing ray at the postcritical repelling orbit. We express the dynamical determinants as the product of an (entire) determinant with an explicit expression involving the postcritical repelling orbit, thus explaining the poles in d (z).     

Equatorial contra axial polar substituents. The relation of a chemical reaction to stereochemical substituent constants

The established rates of glycoside hydrolysis reactions were analyzed using free energy relationship plots based on substituent constants that depend on whether the substituent is axial or equatorial. In all cases good correlations were found when assuming either that the transition state had a charged ring-oxygen atom or that it had a charged anomeric carbon atom. The spontaneous hydrolysis of 2,4-dinitrophenyl beta-glycopyranosides and the acidic hydrolysis of methyl beta-D-glycopyranosides were found to give a good correlation, when 100% charge at the ring-oxygen in the transition state of these reactions is assumed. The acidic hydrolysis of methyl alpha-glycopyranosides was found to give good correlations regardless of whether 100% charge at the ring-oxygen or 100% charge at the anomeric carbon was assumed. The findings clearly demonstrate how crucial the stereochemistry of even remote polar substituents is for their electronic effect on chemical reaction.     

Integration of a membrane-based desalting step in a microfabricated disposable polymer injector for mass spectrometric protein analysis

A simple desalting procedure for the coupling of a polymer microchip injector to mass spectrometry is proposed. The overall process is based on the adsorption of proteins on a poly(vinylidene difluoride) (PVDF) membrane, which are then directly eluted in the spraying solution. This microchip-based approach has been successfully applied to small drugs, peptides and proteins originally diluted in phosphate-buffered saline (PBS). Moreover, when eluting the retained proteins in small volumes, a preconcentration is obtained. The combination of single-use, mass-produceable, low-sample-consumption, easy-to-automate, miniaturized polymer injectors with easy-to-handle solution-exchange membranes makes this system particularly amenable to screening applications.     

Changes in orcine muscle water characteristics during growth--an in vitro low-field NMR relaxation study

This study investigates the effects of developmental stage and muscle type on the mobility and distribution of water within skeletal muscles, using low-field (1)H-NMR transverse relaxation measurements in vitro on four different porcine muscles (M. longissimus dorsi, M. semitendinosus, M. biceps femoris, M. vastus intermedius) from a total of 48 pigs slaughtered at various weight classes between 25 kg and 150 kg. Principal component analysis (PCA) revealed effects of both slaughter weight and muscle type on the transverse relaxation decay. Independent of developmental stage and muscle type, distributed exponential analysis of the NMR T(2) relaxation data imparted the existence of three distinct water populations, T(2b), T(21), and T(22), with relaxation times of approximately 1-10, 45-120, and 200-500 ms, respectively. The most profound change during muscle growth was a shift toward faster relaxation in the intermediate time constant, T(21). It decreased by approx. 24% in all four muscle types during the period from 25 to 150 kg live weight. Determination of dry matter, fat, and protein content in the muscles showed that the changes in relaxation time of the intermediate time constant, T(21), during growth should be ascribed mainly to a change in protein content, as the protein content explained 77% of the variation in the T(21) time constant. Partial least squares (PLS) regression revealed validated correlations in the region of 0.58 to 0.77 between NMR transverse relaxation data and muscle development for all the four muscle types, which indicates that NMR relaxation measurements may be used in the prediction of muscle developmental stage.     

The effect of heat and IR radiation on the fluorescence of cellulose

The emission spectra of pure cellulose samples of various origins were monitored during several heating/cooling cycles. During heating the emission intensity decreased due to the greater probability for internal conversion at higher temperatures. Cooling resulted in an emission recovery that was nearly reversible over several heating/cooling cycles, provided that the final 0temperature was sufficiently low. The change in the relative emission yield with temperature showed two regimes, both with linear decreases but different slopes, suggesting different mechanisms for the internal conversion in these regions. Heating to temperatures higher than 160°C for filter papers and higher than 145°C for microcrystalline cellulose initiated reactions that caused changes in the emission spectra typical of thermal degradation. If the samples were heated beyond these threshold temperatures the emission recovery on cooling after the first heat treatment occurred to a much higher intensity level than that observed initially, indicating the formation of a multitude of new chromophores due to thermal reactions. Exposure of the samples to IR radiation caused a slow increase in the emission intensity for almost 600h.     

Propagation of Smallness for Harmonic and Analytic Functions in Arbitrary Domains

In this paper the authors develop a new approach to the problemof ‘propagation of smallness’ for harmonic functionsin arbitrary domains, in Rⁿ (n 2). The main result of thispaper is a certain logarithmic-convexity relation for the L²-normsof harmonic functions. As a consequence, new kinds of uniquenessresults for harmonic functions are obtained. The method worksalso for analytic functions in C, with L^p-norms (p > 0).1991 Mathematics Subject Classification 31B05.     

On the reduction number of some graded algebras

The main result of the paper confirms, for generic coordinates, a conjecture which states that . Here is a homogeneous polynomial ideal in and and are the reduction numbers.

     

Continuous separation of lipid particles from erythrocytes by means of laminar flow and acoustic standing wave forces

Improved continuous acoustic particle separation (separation efficiency close to 100%) and separation of erythrocytes (red blood cells) from lipid microemboli in whole blood is reported.     

Measurement of ultraweak transitions in the visible region of molecular oxygen

A highly sensitive cavity-enhanced frequency modulation spectroscopy technique has been used to measure ultraweak transitions in molecular oxygen that had not previously been characterized. The self-broadened half-width and line intensity of the measured transitions are reported. We include 12 high J transitions in the band of ¹⁶O₂ (the so-called A band), 59 transitions in the hot band of ¹⁶O₂, and 17 high J transitions in the band of ¹⁶O¹⁸O. Our measurements of line positions of the ¹⁶O¹⁸O transitions are used to determine improved molecular constants for the excited state of ¹⁶O¹⁸O.