Expected Supremum of a Random Linear Combination of Shifted Kernels

We address the expected supremum of a linear combination of shifts of the sinc kernel with random coefficients. When the coefficients are Gaussian, the expected supremum is of order \sqrt{\log n}, where n is the number of shifts. When the coefficients are uniformly bounded, the expected supremum is of order \log\log n. This is a noteworthy difference to orthonormal functions on the unit interval, where the expected supremum is of order \sqrt{n\log n} for all reasonable coefficient statistics.Comment: To appear in the Journal of Fourier Analysis and Application

Elliptic CMB Sky

The ellipticity of the anisotropy spots of the Cosmic Microwave Background measured by the Wilkinson Microwave Anisotropy Probe (WMAP) has been studied. We find an average ellipticity of about 2, confirming with a far larger statistics similar results found first for the COBE-DMR CMB maps, and then for the BOOMERanG CMB maps. There are no preferred directions for the obliquity of the anisotropy spots. The average ellipticity is independent of temperature threshold and is present on scales both smaller and larger than the horizon at the last scattering. The measured ellipticity characteristics are consistent with being the effect of geodesics mixing occurring in an hyperbolic Universe, and can mark the emergence of CMB ellipticity as a new observable constant describing the Universe. There is no way of simulating this effect. Therefore we cannot exclude that the observed behavior of the measured ellipticity can result from a trivial topology in the popular flat $\Lambda$-CDM model, or from a non-trivial topology.Comment: 10 pages, 5 figures, the version to appear in Mod.Phys.Lett.

Effect of ultrasonic sufrace treatment on the structure and properties of polycrystalline and nanostructured titanium

The effects of ultrasonic surface treatment on the structural and phase-state of subsurface layers of polycrystalline and ultrafine-grained titanium are investigated. The changes in microhardness, mechanical properties, and regularities of microplastic deformation buildup are studied under static and cyclic loading. It is found that the characteristics of polycrystalline titanium suffer most from the ultrasonic treatment, while its influence on ultrafinegrained titanium is considerably weake

Influence of surface modification of nitinol with silicon using plasma-immersion ion implantation on the alloy corrosion resistance in artificial physiological solutions

Cyclic voltammetry and potentiostatic polarization have been applied to study electrochemical behavior and to determine corrosion resistance of nitinol, which surface was modified with silicon using plasma-immersion ion implantation, in 0.9% NaCl solution and in artificial blood plasma. It was found out that continuous, and also homogeneous in composition, thin Si-containing layers are resistant to corrosion damage at high positive potentials in artificial physiological solutions due to formation of stable passive films. Breakdown potential Eb of Si-modified NiTi depends on the character of silicon and Ni distribution at the alloy surface, Eb values amounted to 0.9–1.5 V (Ag/AgCl/KCl sat.) for the alloy samples with continuous Si-containing surface layers and with decreased Ni surface concentration

Phase diagram as a function of temperature and magnetic field for magnetic semiconductors

Using an extension of the Nagaev model of phase separation (E.L. Nagaev, and A.I. Podel'shchikov, Sov. Phys. JETP, 71 (1990) 1108), we calculate the phase diagram for degenerate antiferromagnetic semiconductors in the T-H plane for different current carrier densities. Both, wide-band semiconductors and 'double-exchange' materials, are investigated.Comment: 5 pages, 6 figures, RevTex, Accepted for publication in PR

Is there a common origin for the WMAP low multipole and for the ellipticity in BOOMERanG CMB maps?

We have measured the ellipticity of several degree scale anisotropies in the BOOMERanG maps of the Cosmic Microwave Background (CMB) at 150 GHz. The average ellipticity is around 2.6-2.7. The biases of the estimator of the ellipticity and for the noise are small in this case. Large spot elongation had been detected also for COBE-DMR maps. If this effect is due to geodesic mixing, it would indicate a non precisely zero curvature of the Universe which is among the discussed reasons of the WMAP low multipole anomaly. Both effects are related to the diameter of the Universe: the geodesics mixing through hyperbolic geometry, low multipoles through boundary conditions.This common reason can also be related with the origin of the the cosmological constant: the modes of vacuum fluctuations conditioned by the boundary conditions lead to a value of the cosmological constant being in remarkable agreement with the supernovae observations.Comment: Added: two co-authors and a comment on the possible relation of the discussed CMB properties with the origin of the observed value of the cosmological constan

WMAP confirming the ellipticity in BOOMERanG and COBE CMB maps

The recent study of BOOMERanG 150 GHz Cosmic Microwave Background (CMB) radiation maps have detected ellipticity of the temperature anisotropy spots independent on the temperature threshold. The effect has been found for spots up to several degrees in size, where the biases of the ellipticity estimator and of the noise are small. To check the effect, now we have studied, with the same algorithm and in the same sky region, the WMAP maps. We find ellipticity of the same average value also in WMAP maps, despite of the different sensitivity of the two experiments to low multipoles. Large spot elongations had been detected also for the COBE-DMR maps. If this effect is due to geodesic mixing and hence due to non precisely zero curvature of the hyperbolic Universe, it can be linked to the origin of WMAP low multipoles anomaly.Comment: More explanations and two references adde

Structural phase states in nickel-titanium surface layers doped with silicon by plasma immersion ion implantation

The paper reports on a study of NiTi-based alloys used for manufacturing self-expanding intravascular stents to elucidate how the technological modes of plasma immersion ion implantation with silicon influence the chemical an