On the Fourier transform of the characteristic functions of domains with C1C^1 -smooth boundary

We consider domains $D\subseteq\mathbb R^n$ with $C^1$ -smooth boundary and study the following question: when the Fourier transform $\hat{1_D}$ of the characteristic function $1_D$ belongs to $L^p(\mathbb R^n)$?Comment: added two references; added footnotes on pages 6 and 1

Size-independent Young's modulus of inverted conical GaAs nanowire resonators

We explore mechanical properties of top down fabricated, singly clamped inverted conical GaAs nanowires. Combining nanowire lengths of 2-9 $\mu$m with foot diameters of 36-935 nm yields fundamental flexural eigenmodes spanning two orders of magnitude from 200 kHz to 42 MHz. We extract a size-independent value of Young's modulus of (45$\pm$3) GPa. With foot diameters down to a few tens of nanometers, the investigated nanowires are promising candidates for ultra-flexible and ultra-sensitive nanomechanical devices

Estimates in Beurling--Helson type theorems. Multidimensional case

We consider the spaces $A_p(\mathbb T^m)$ of functions $f$ on the $m$ -dimensional torus $\mathbb T^m$ such that the sequence of the Fourier coefficients $\hat{f}=\{\hat{f}(k), ~k \in \mathbb Z^m\}$ belongs to $l^p(\mathbb Z^m), ~1\leq p<2$. The norm on $A_p(\mathbb T^m)$ is defined by $\|f\|_{A_p(\mathbb T^m)}=\|\hat{f}\|_{l^p(\mathbb Z^m)}$. We study the rate of growth of the norms $\|e^{i\lambda\varphi}\|_{A_p(\mathbb T^m)}$ as $|\lambda|\rightarrow \infty, ~\lambda\in\mathbb R,$ for $C^1$ -smooth real functions $\varphi$ on $\mathbb T^m$ (the one-dimensional case was investigated by the author earlier). The lower estimates that we obtain have direct analogues for the spaces $A_p(\mathbb R^m)$

Two-loop Compton and annihilation processes in thermal QCD

We calculate the Compton and annihilation production of a soft static lepton pair in a quark-gluon plasma in the two-loop approximation. We work in the context of the effective perturbative expansion based on the resummation of hard thermal loops. Double counting is avoided by subtracting appropriate counterterms. It is found that the two-loop diagrams give contributions of the same order as the one-loop diagram. Furthermore, these contributions are necessary to obtain agreement with the naive perturbative expansion in the limit of vanishing thermal masses.Comment: Latex, 24 pages, postscript figures included with the package graphic

Comment on ``Damping of energetic gluons and quarks in high-temperature QCD''

Burgess and Marini have recently pointed out that the leading contribution to the damping rate of energetic gluons and quarks in the QCD plasma, given by $\gamma=c g^2\ln(1/g)T$, can be obtained by simple arguments obviating the need of a fully resummed perturbation theory as developed by Braaten and Pisarski. Their calculation confirmed previous results of Braaten and Pisarski, but contradicted those proposed by Lebedev and Smilga. While agreeing with the general considerations made by Burgess and Marini, I correct their actual calculation of the damping rates, which is based on a wrong expression for the static limit of the resummed gluon propagator. The effect of this, however, turns out to be cancelled fortuitously by another mistake, so as to leave all of their conclusions unchanged. I also verify the gauge independence of the results, which in the corrected calculation arises in a less obvious manner.Comment: 5 page

High‐Latitude Geomagnetic Secular Variation at the End of the Cretaceous Normal Superchron Recorded by Volcanic Flows From the Okhotsk‐Chukotka Volcanic Belt

The Cretaceous Normal Superchron (CNS, 84–121 Ma) is a singular period of the geodynamo's history, identified by a prolonged absence of polarity reversals. To better characterize the paleosecular variation (PSV) of the geomagnetic field at the end of this interval, we sampled seven continuous sequences of lava flows from the Okhotsk-Chukotka Volcanic Belt, emplaced 84–89 Ma in the vicinity of the Kupol ore deposit (NE Russia). From a collection of 1,024 paleomagnetic cores out of 82 investigated lava flows, we successfully determined the paleodirections of 78 lava flows, which led to 57 directional groups after removing the serial correlations. The resulting paleomagnetic pole is located at 170.0°E, 76.8°N (A95 = 5.2°, N = 57), in good agreement with previous estimates for north-eastern Eurasia. Aiming at quantifying PSV at a reconstructed paleolatitude (λ) of ∼80°N, we obtained a virtual geomagnetic pole (VGP) scatter , the value of which was corrected for within-site dispersion and is little dependent on the choice of the selection criteria. Compared to previous paleodirectional data sets characterizing PSV at various paleolatitudes during the CNS, our Sb estimate confirms a relative latitudinal increase Sb(λ = 90°)/Sb(λ = 0°) on the order of 2–2.5. Focusing on PSV at high paleolatitude within the 70°–90° range, we show that Sb was ∼15% lower at the end of the CNS than during the past 10 Myr, confirming that the singular polarity regime of the geodynamo observed during the CNS is likely accompanied with reduced PSV

Molecular Density Functional Theory of Water describing Hydrophobicity at Short and Long Length Scales

We present an extension of our recently introduced molecular density functional theory of water [G. Jeanmairet et al., J. Phys. Chem. Lett. 4, 619, 2013] to the solvation of hydrophobic solutes of various sizes, going from angstroms to nanometers. The theory is based on the quadratic expansion of the excess free energy in terms of two classical density fields, the particle density and the multipolar polarization density. Its implementation requires as input a molecular model of water and three measurable bulk properties, namely the structure factor and the k-dependent longitudinal and transverse dielectric susceptibilities. The fine three-dimensional water structure around small hydrophobic molecules is found to be well reproduced. In contrast the computed solvation free-energies appear overestimated and do not exhibit the correct qualitative behavior when the hydrophobic solute is grown in size. These shortcomings are corrected, in the spirit of the Lum-Chandler-Weeks theory, by complementing the functional with a truncated hard-sphere functional acting beyond quadratic order in density. It makes the resulting functional compatible with the Van-der-Waals theory of liquid-vapor coexistence at long range. Compared to available molecular simulations, the approach yields reasonable solvation structure and free energy of hard or soft spheres of increasing size, with a correct qualitative transition from a volume-driven to a surface-driven regime at the nanometer scale.Comment: 24 pages, 8 figure

Computer Microscopy of Biological Fluid Dry Patterns for Medical Diagnostics

We elaborate hardware and software system that implements the principle of diagnosis based on the standard procedure of pattern preparation including digital recognition of image and its computer analysis based on specially developed algorithms by comparing with the expert descriptors and extensive database of dry pattern samples obtained from clinical treatments which include more than 1500 samples to high selective and accuracy recognition of pathologies, for recognition of wide range of pathologies, in particular, the endogenous intoxication. Keywords: biological fluids, image analysis, medical diagnostics, endogenous intoxication