A note on Makeev's conjectures

A counterexample is given for the Knaster-like conjecture of Makeev for functions on $S^2$. Some particular cases of another conjecture of Makeev, on inscribing a quadrangle into a smooth simple closed curve, are solved positively

Almost-Euclidean subspaces of ℓ1N\ell_1^N via tensor products: a simple approach to randomness reduction

It has been known since 1970's that the N-dimensional $\ell_1$-space contains nearly Euclidean subspaces whose dimension is $\Omega(N)$. However, proofs of existence of such subspaces were probabilistic, hence non-constructive, which made the results not-quite-suitable for subsequently discovered applications to high-dimensional nearest neighbor search, error-correcting codes over the reals, compressive sensing and other computational problems. In this paper we present a "low-tech" scheme which, for any $a > 0$, allows to exhibit nearly Euclidean $\Omega(N)$-dimensional subspaces of $\ell_1^N$ while using only $N^a$ random bits. Our results extend and complement (particularly) recent work by Guruswami-Lee-Wigderson. Characteristic features of our approach include (1) simplicity (we use only tensor products) and (2) yielding "almost Euclidean" subspaces with arbitrarily small distortions.Comment: 11 pages; title change, abstract and references added, other minor change

Kolmogorov analysis detecting radio and Fermi gamma-ray sources in cosmic microwave background maps

The Kolmogorov stochasticity parameter is shown to act as a tool to detect point sources in the cosmic microwave background (CMB) radiation temperature maps. Kolmogorov CMB map constructed for the WMAP's 7-year datasets reveals tiny structures which in part coincide with point radio and Fermi/LAT gamma-ray sources. In the first application of this method, we identified several sources not present in the then available 0FGL Fermi catalog. Subsequently they were confirmed in the more recent and more complete 1FGL catalog, thus strengthening the evidence for the power of this methodology.Comment: 4 pages, 3 figs, 1 Table; to match the published versio

Detection of X-ray galaxy clusters based on the Kolmogorov method

The detection of clusters of galaxies in large surveys plays an important part in extragalactic astronomy, and particularly in cosmology, since cluster counts can give strong constraints on cosmological parameters. X-ray imaging is in particular a reliable means to discover new clusters, and large X-ray surveys are now available. Considering XMM-Newton data for a sample of 40 Abell clusters, we show that their analysis with a Kolmogorov distribution can provide a distinctive signature for galaxy clusters. The Kolmogorov method is sensitive to the correlations in the cluster X-ray properties and can therefore be used for their identification, thus allowing to search reliably for clusters in a simple way

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

Plasma immersion ion implantation for surface treatment of complex branched structures

The paper presents experimental results demonstrating the capabilities of plasma immersion ion implantation of silicon (Si) for surface treatment of complex branched structures such are self-expanding intravascular nickel-titanium (NiTi) stents. Using NiTi stents of diameter 4 and 8 mm, it is shown that plasma immersion ion implantation can provide rather homogeneous doping of their outer and inner surfaces with Si atoms. Also presented are research data on the processes that determine the thickness, composition, and structure of surface layers subjected to this type of treatment

Correlation effects in insulating surface nanostructures

We study the role of static and dynamical Coulomb correlation effects on the electronic and magnetic properties of individual Mn, Fe and Co adatoms deposited on the CuN surface. For these purposes, we construct a realistic Anderson model, solve it by using finite-temperature exact diagonalization method and compare the calculated one-particle spectral functions with the LDA+$U$ densities of states. In contrast to Mn/CuN and Fe/CuN, the cobalt system tends to form the electronic excitations at the Fermi level. Based on the calculated magnetic response functions, the relative relaxation times for the magnetic moments of impurity orbitals are estimated. To study the effect of the dynamical correlations on the exchange interaction in nanoclusters, we solve the two-impurity Anderson model for the Mn dimer on the CuN surface. It is found that the experimental exchange interaction can be well reproduced by employing $U$=3 eV, which is two times smaller than the value used in static mean-field LDA+$U$ calculations. This suggests on important role of dynamical correlations in the interaction between adatoms on a surface.Comment: 8 pages, 8 figure

Microstructure and properties of a silicon coating deposited on a titanium nickelide substrate using molecular-beam epitaxy equipment

The microstructure and properties of a silicon coating on a titanium nickelide substrate were studied to assess the possibility of using such a coating to improve the biocompatibility of medical implants. The silicon coating with thickness of 4.0±0.5 microns was applied to the TiNi substrate on a molecular beam epitaxy unit. The coating had a submicrocrystalline structure with a crystallite size of 0.1...0.2 microns, a developed surface, and high crack resistance

Orbitally-resolved ferromagnetism of monolayer CrI3

Few-layer CrI3 is the most known example among two-dimensional (2D) ferromagnets, which have attracted growing interest in recent years. Despite considerable efforts and progress in understanding the properties of 2D magnets both from theory and experiment, the mechanism behind the formation of in-plane magnetic ordering in chromium halides is still under debate. Here, we propose a microscopic orbitally-resolved description of ferromagnetism in monolayer CrI3. Starting from first-principles calculations, we construct a low-energy model for the isotropic Heisenberg exchange interactions. We find that there are two competing contributions to the long-range magnetic ordering in CrI3: (i) Antiferromagnetic Anderson's superexchange between half-filled t 2g orbitals of Cr atoms; and (ii) Ferromagnetic exchange governed by the Kugel-Khomskii mechanism, involving the transitions between half-filled t 2g and empty e g orbitals. Using numerical calculations, we estimate the exchange interactions in momentum-space, which allows us to restore the spin-wave spectrum, as well as estimate the Curie temperature. Contrary to the nearest-neighbor effective models, our calculations suggest the presence of sharp resonances in the spin-wave spectrum at 5-7 meV, depending on the vertical bias voltage. Our estimation of the Curie temperature in monolayer CrI3 yields 55-65 K, which is in good agreement with experimental data. © 2020 IOP Publishing Ltd