On uniform convergence of Fourier series

We consider the space $U(\mathbb T)$ of all continuous functions on the circle $\mathbb T$ with uniformly convergent Fourier series. We show that if $\varphi: \mathbb T\rightarrow\mathbb T$ is a continuous piecewise linear but not linear map, then $\|e^{in\varphi}\|_{U(\mathbb T)}\simeq\log n$

The census of complex organic molecules in the solar type protostar IRAS16293-2422

Complex Organic Molecules (COMs) are considered crucial molecules, since they are connected with organic chemistry, at the basis of the terrestrial life. More pragmatically, they are molecules in principle difficult to synthetize in the harsh interstellar environments and, therefore, a crucial test for astrochemical models. Current models assume that several COMs are synthesised on the lukewarm grain surfaces ($\gtrsim$30-40 K), and released in the gas phase at dust temperatures $\gtrsim$100 K. However, recent detections of COMs in $\lesssim$20 K gas demonstrate that we still need important pieces to complete the puzzle of the COMs formation. We present here a complete census of the oxygen and nitrogen bearing COMs, previously detected in different ISM regions, towards the solar type protostar IRAS16293-2422. The census was obtained from the millimeter-submillimeter unbiased spectral survey TIMASSS. Six COMs, out of the 29 searched for, were detected: methyl cyanide, ketene, acetaldehyde, formamide, dimethyl ether, and methyl formate. The multifrequency analysis of the last five COMs provides clear evidence that they are present in the cold ($\lesssim$30 K) envelope of IRAS16293-2422, with abundances 0.03-2 $\times 10^{-10}$. Our data do not allow to support the hypothesis that the COMs abundance increases with increasing dust temperature in the cold envelope, as expected if COMs were predominately formed on the lukewarm grain surfaces. Finally, when considering also other ISM sources, we find a strong correlation over five orders of magnitude, between the methyl formate and dimethyl ether and methyl formate and formamide abundances, which may point to a link between these two couples of species, in cold and warm gas

Investigation of Axial-flow Fan and Compressor Rotors Designed for Three-dimensional Flow

An investigation has been conducted to determine whether three-dimensional flows may be utilized in axial-flow fan and compressor rotors so that the spanwise load distribution may be varied to obtain high pressure rise. Two rotors, one with approximately uniform and one with solid-body downstream tangential-velocity distributions, were designed and tested at the design blade angle. Radial surveys of total pressure, static pressure, and flow angle were made upstream and downstream of the test rotors through a quantity-coefficient range. Tests of the solid-body rotor were also conducted at a large value of tip clearance. The results indicated that the three-dimensional flows may be utilized with high efficiency and that the three-dimensional theory used in conjunction with two-dimensional cascade data is sufficiently accurate for design purposes. The tests also showed that the tip-clearance losses of rotors highly loaded at the tips are not excessive. The existing three-dimensional theory in simplified for and an illustrative rotor design are presented in appendixes

Approximated maximum likelihood estimation in multifractal random walks

We present an approximated maximum likelihood method for the multifractal random walk processes of [E. Bacry et al., Phys. Rev. E 64, 026103 (2001)]. The likelihood is computed using a Laplace approximation and a truncation in the dependency structure for the latent volatility. The procedure is implemented as a package in the R computer language. Its performance is tested on synthetic data and compared to an inference approach based on the generalized method of moments. The method is applied to estimate parameters for various financial stock indices.Comment: 8 pages, 3 figures, 2 table

Weak radiative corrections to the Drell-Yan process for large invariant mass of a dilepton pair

The weak radiative corrections to the Drell-Yan process above the Z-peak have been studied. The compact asymptotic expression for the two heavy boson exchange - one of the significant contributions to the investigated process - has been obtained, the results expand in the powers of the Sudakov electroweak logarithms. At the quark level we compare the weak radiative corrections to the total cross section and forward-backward asymmetry with the existing results and achieve a rather good coincidence at \sqrt{s}>= 0.5 TeV. The numerical analysis has been performed in the high energy region corresponding to the future experiments at the CERN Large Hadron Collider (LHC). To simulate the detector acceptance we used the standard CMS detector cuts. It was shown that double Sudakov logarithms of the WW boxes are the dominant contributions in hadronic cross section. The considered radiative corrections are significant at high dilepton mass M and change the dilepton mass distribution up to ~+3(-12)% at the LHC energies and M=1(5) TeV.Comment: Changed content; 13 pp, 4 fig, 1 tabl

The Value of Sex in Procreative Reasons

Copyright Taylor and Francis Group, LLC. This is an open access article distributed under the Supplemental Terms and Conditions for iOpenAccess articles published in Taylor & Francis journals, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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 $A_p(\mathbb R^m)$

Elastic and Raman scattering of 9.0 and 11.4 MeV photons from Au, Dy and In

Monoenergetic photons between 8.8 and 11.4 MeV were scattered elastically and in elastically (Raman) from natural targets of Au, Dy and In.15 new cross sections were measured. Evidence is presented for a slight deformation in the 197Au nucleus, generally believed to be spherical. It is predicted, on the basis of these measurements, that the Giant Dipole Resonance of Dy is very similar to that of 160Gd. A narrow isolated resonance at 9.0 MeV is observed in In.Comment: 31 pages, 11 figure