p-Laplacian Inclusions via Fixed Points for Multifunctions in Posets

We consider the Dirichlet problem for elliptic differential inclusions involving the p-Laplacian and governed by multivalued nonlinearities bounded above and below by single-valued monotone functions not necessarily continuous. The aim of this note is to provide existence and comparison results for the problem under consideration without imposing further regularity assumptions. The main tools used in the proof of our results are existence and comparison results for extremal solutions of (single-valued) nonlinear elliptic equations, and an abstract comparison principle for fixed points of multivalued operators in partially ordered sets (posets).     

Subordinate solutions and spectral measures of canonical systems

The theory of 2×2 trace-normed canonical systems of differential equations on ?⁺ can be put in the framework of abstract extension theory, cf. [9]. This includes the theory of strings as developed by I.S. Kac and M.G. Kre?n. In the present paper the spectral properties of such canonical systems are characterized by means of subordinate solutions. The theory of subordinacy for Schrödinger operators on the halfline ?⁺, was originally developed D.J. Gilbert and D.B. Pearson. Its extension to the framework of canonical systems makes it possible to describe the spectral measure of any Nevanlinna function in terms of subordinate solutions of the corresponding trace-normed canonical system, which is uniquely determined by a result of L. de Branges.     

Midazolam sedation increases fluctuation and synchrony of the resting brain BOLD signal

The blood oxygen level-dependent (BOLD) magnetic resonance signal of functional brain cortices is dominated by very low frequency (VLF) fluctuations in anesthetized child patients. The temporal synchrony of the BOLD signal is also higher in anesthetized children compared with awake adults. The origin of the synchronous fluctuations can be related to maturation, pathological status or the anesthesia used in the imaging. Two of the three confounding variables (maturation and pathology) were controlled in this study. The effect of midazolam (4+/-0.8 mg) sedation on the BOLD signal was assessed in 12 healthy adults (aged 24+/-1.5 years) at 1.5 T. The VLF fluctuation power and temporal synchrony of the BOLD signal increased significantly after the sedation in the auditory and visual cortices. The fast Fourier transformation power spectral baseline fit parameters of the BOLD signal were also found to change significantly after sedation. It is concluded that the VLF fluctuation and temporal synchrony of the BOLD signal become increased after sedation in functional brain regions.     

Electrophysiological evidence of nonlinear distortion products to two-tone stimuli

Spectral analysis of auditory-evoked potential recordings from ten normal-hearing subjects to two-tone signals revealed energy at difference tone (DT = f2-f1) and cubic difference (CDT = 2f1-f2) frequencies that was not present in the acoustic signal. Control experiments and calibrations provided substantial evidence supportive of the biological nature of these auditory nonlinearities, suggesting that they are not the result of electromagnetic, acoustic, or analytic artifact. Amplitudes of DT- and CDT-evoked responses were evaluated for rarefaction and condensation signals with f1 = 510 and 800 Hz across frequency ratios (f2/f1) of 1.16, 1.26, 1.36, and 1.46. Additionally, time-domain summation and subtraction of separately collected evoked responses to rarefaction and condensation signals were performed to demonstrate that these electrophysiological DT and CDT responses reflect their expected quadratic and cubic nature. Suggestions for development of clinical applications of assessing auditory nonlinearities using this methodology are provided.     

High resolutionMNN auger spectra of Ag,Cd, In,Sb, Te,and I

The strongest lines (M ₅ N _4,5 N _4,5 andM ₄ N _4,5 N _4,5) in theMNN Auger spectra of Ag, Cd, In, Sb, Te, and I have been investigated with high resolution by means of an electrostatic cylindrical spectrometer. The measured spectra have been found to have a fine structure corresponding to the splitting of the final states of the Auger transitionsM ₅ N _4,5 N _4,5 andM ₄ N _4,5 N _4,5. This has not been observed for these elements in spectra measured by the retarding field method. The line profiles are discussed.     

A new,facile synthesis of the 3-methyl-2(5H)-furanoid structural unit from ketones

The 3-methyl-2(5H)-furanoid structural unit is prepared from ketones via 1,4-rearrangement of siloxyalkenes on peroxidation and via oxetene rearrangement of 1-diethylaminopropyne in 53–58% overall yield.     

Diffusion Imaging with HyperpolarizedHe Gas

We used MRI of hyperpolarized³He to demonstrate some novel aspects of gas diffusion. Two different techniques were used. First, a slice was burned into a one-dimensional image by inverting the spins in the slice and diffusion was studied by measuring the magnetization as it filled the depleted slice. A diffusion coefficient was determined by the fit of these data. Second, one-dimensional diffusion images were made using a Stejskal–Tanner PGSE method. This was done with and without a temperature gradient present, showing that the effect of temperature can be dynamically monitored by such diffusion images.     

The effect of washing procedures on trace element content of human hair

The effects of four washing procedures on the concentrations of manganese, iron, copper, zinc and cadmium and were investigated for three pooled samples of human head hair. The solutions evaluated were a non-ionic detergent (Triton X-100), an ionic detergent (sodium lauryl sulfate), acetone and a complexing agent (EDTA). The results indicate that for every element determined there is a level below which the concentration cannot be reduced by further washings. The numbers of washings required to reach these levels vary considerably. This effect must be considered in the trace element analysis of hair.     

Studies on the furan series. Part VII. A preparation of 2,3-Di(2-furyl and thienyl)furans

Furoin reacts smoothly with dimethyl acetylenedicarboxylate via a Michael addition, which is followed by a dihydrofuran ring formation. After elimination of water the previously unknown 2,3-di(2-furyl)furan structure is produced. Thenoin gives a side reaction to yield a fumaric acid derivative in addition to the expected 2,3-di(2-thienyl)furan. A mechanism for the side reaction is suggested. The reactivities of the prepared new furan structures towards some oxidation, hydrogenation and electrophilic reagents were determined.