Remarks on "Resolving isospectral `drums' by counting nodal domains"

In [3] the authors studied the 4-parameter family of isospectral flat 4-tori T^\pm(a,b,c,d) discovered by Conway and Sloane. With a particular method of counting nodal domains they were able to distinguish these tori (numerically) by computing the corresponding nodal sequences relative to a few explicit tuples (a,b,c,d). In this note we confirm the expectation expressed in [3] by proving analytically that their nodal count distinguishes any 4-tuple of distinct positive real numbers.Comment: 5 page

Novel roles for JNK1 in metabolism

Activation of stress-kinase signaling has recently been recognized as an important pathophysiological mechanism in the development of diet-induced obesity, type 2 diabetes mellitus and other aging-related pathologies. Here, c-Jun N-terminal Kinase (JNK) 1 knockout mice have been shown to exhibit protection from diet-induced obesity, glucose intolerance, and insulin resistance. Nonetheless, the tissue-specific role of JNK1-activation in the development of the metabolic syndrome has been poorly defined so far. Recently, it was demonstrated that JNK1 signaling plays a crucial role in the central nervous system (CNS) and in the pituitary to control systemic glucose and lipid metabolism partially through regulation of hormones involved in growth and energy expenditure

Massenspektrometrische Untersuchungen zum Einfluss der Temperatur auf die Bildung und Zusammensetzung tribologischer Schichten nasslaufender Synchronisationsreibkörper

Eine starke Verminderung von Verschleiß, welcher durch mechanische Reibung hervorgerufene wird, erreicht man durch den Einsatz von additivierten Schmierstoffen. Spezielle polare Additive wie etwa das ZDDP oder das Kalziumsulfonat lagern sich an den Reibflächen an und schützen diese so durch Ausbildung einer Phophatglasschicht bzw. durch Reinigung der Reibflächen von Kleinstpartikeln vor Verschleiß. Im Rahmen dieser Arbeit wurde mit Hilfe der Flugzeit-Sekundärionenmassenspektrometrie (ToF-SIMS) die chemische Zusammensetzung dieser sogenannten tribologischen Schichten bei der Entstehung untersucht. Ein Vergleich der Spektren von rein thermische beanspruchten Substraten und den Oberflächen von 100000 mal belasteten Synchronisationsreibkörpern führt zu der Schlussfolgerung, dass alleine die von den Reibbedingungen abhängige Oberflächentemperatur ausschlaggebend für die Zusammensetzung der gebildeten tribologischen Schichten und somit auch für die Reibeigenschaften ist

Lower bounds for nodal sets of eigenfunctions

We prove lower bounds for the Hausdorff measure of nodal sets of eigenfunctions.Comment: To appear in Communications in Mathematical Physics; revised to include two additional references and update bibliographic informatio

Fano resonances in a three-terminal nanodevice

The electron transport through a quantum sphere with three one-dimensional wires attached to it is investigated. An explicit form for the transmission coefficient as a function of the electron energy is found from the first principles. The asymmetric Fano resonances are detected in transmission of the system. The collapse of the resonances is shown to appear under certain conditions. A two-terminal nanodevice with an additional gate lead is studied using the developed approach. Additional resonances and minima of transmission are indicated in the device.Comment: 11 pages, 5 figures, 2 equations are added, misprints in 5 equations are removed, published in Journal of Physics: Condensed Matte

Spin Gap in the Single Spin-1/2 Chain Cuprate Sr1.9_{1.9}Ca0.1_{0.1}CuO3_3

We report $^{63}$Cu nuclear magnetic resonance and muon spin rotation measurements on the S=1/2 antiferromagnetic Heisenberg spin chain compound Sr$_{1.9}$Ca$_{0.1}$CuO$_3$. An exponentially decreasing spin-lattice relaxation rate 1/T$_1$ indicates the opening of a spin gap. This behavior is very similar to what has been observed for the cognate zigzag spin chain compound Sr$_{0.9}$Ca$_{0.1}$CuO$_2$, and confirms that the occurrence of a spin gap upon Ca doping is independent of the interchain exchange coupling $J'$. Our results therefore generally prove the appearance of a spin gap in an antiferromagnetic Heisenberg spin chain induced by a local bond disorder of the intrachain exchange coupling $J$. A low temperature upturn of 1/T$_1$ evidences growing magnetic correlations. However, zero field muon spin rotation measurements down to 1.5 K confirm the absence of magnetic order in this compound which is most likely suppressed by the opening of the spin gap.Comment: 5 pages, 4 figure

Characterization of the glass transition in vitreous silica by temperature scanning small-angle X-ray scattering

The temperature dependence of the x-ray scattering in the region below the first sharp diffraction peak was measured for silica glasses with low and high OH content (GE-124 and Corning 7980). Data were obtained upon scanning the temperature at 10, 40 and 80 K/min between 400 K and 1820 K. The measurements resolve, for the first time, the hysteresis between heating and cooling through the glass transition for silica glass, and the data have a better signal to noise ratio than previous light scattering and differential thermal analysis data. For the glass with the higher hydroxyl concentration the glass transition is broader and at a lower temperature. Fits of the data to the Adam-Gibbs-Fulcher equation provide updated kinetic parameters for this very strong glass. The temperature derivative of the observed X-ray scattering matches that of light scattering to within 14%.Comment: EurophysicsLetters, in pres