Padua and Pisa are exponentially far apart

We answer the question posed by Ian Stewart which Padovan numbers are at the same time Fibonacci numbers. We give a result on the difference between Padovan and Fibonacci numbers, and on the growth of Padovan numbers with negative indices

s and d-wave symmetries of the solutions of the Eliashberg equations

We examine the different possible symmetries of the superconducting gap obtained by solving the Eliashberg equations. We consider an electron-phonon interaction in a strong coupling scenario. The Coulomb pseudopotential plays the crucial role of providing the repulsion needed to favour the d-wave symmetry. But the key parameter that allows very anisotropic solutions even with very strong coupling is the small angular range of the interaction due to predominantly electron-phonon forward scattering that is found in the high-Tc superconductors. We find both s and d-wave solutions whose stability depends mainly on the angular range of the interaction.Comment: Uuencoded LaTeX file anf 6 Postscript figures (14 pages). Accepted for publication in Physica

Itinerant-electron Ferromagnetism in W(Nb)O3-d

The crystal structure and the magnetic properties of the W1-xNbxO3-d, (x<0.03) system have been investigated. In contrast to the orthorhombic diamagnetic WO3, the material with x=0.01 is paramagnetic down to 5 K. Introducing of 2.5 at. % of Nb into WO3 leads to a tetragonal structure and to a weak itinerant ferromagnetic ordering below TC= 225 K. The saturation magnetic moment at 5 K is 1.07*10-3 mB, whereas the paramagnetic effective moment is 0.06 mB per mole. This high ratio indicates itinerant ferromagnetism in W0.975Nb0.025O3-d.Comment: accepted to Physica

Specific heat studies of pure Nb3Sn single crystals at low temperature

Specific heat measurements performed on high purity vapor-grown Nb$_3$Sn crystals show clear features related to both the martensitic and superconducting transitions. Our measurements indicate that the martensitic anomaly does not display hysteresis, meaning that the martensitic transition could be a weak first or a second order thermodynamic transition. Careful measurements of the two transition temperatures display an inverse correlation between both temperatures. At low temperature specific heat measurements show the existence of a single superconducting energy gap feature.Comment: Accepted in Journal of Physics: Condensed Matte

Arithmetic properties of blocks of consecutive integers

This paper provides a survey of results on the greatest prime factor, the number of distinct prime factors, the greatest squarefree factor and the greatest m-th powerfree part of a block of consecutive integers, both without any assumption and under assumption of the abc-conjecture. Finally we prove that the explicit abc-conjecture implies the Erd\H{o}s-Woods conjecture for each k>2.Comment: A slightly corrected and extended version of a paper which will appear in January 2017 in the book From Arithmetic to Zeta-functions published by Springe

Stripes, Non-Fermi-Liquid Behavior, and High-Tc Superconductivity

The electronic structure of the high-Tc cuprates is studied in terms of "large-U" and "small-U" orbitals. A striped structure and three types of quasiparticles are obtained, polaron-like "stripons" carrying charge, "svivons" carrying spin, and "quasielectrons" carrying both. The anomalous properties are explained, and specifically the behavior of the resistivity, Hall constant, and thermoelectric power. High-temperature superconductivity results from transitions between pair states of quasielectrons and stripons.Comment: 4 page

Anharmonic effects in the A15 compounds induced by sublattice distortions

We demonstrate that elastic anomalies and lattice instabilities in the the A15 compounds are describable in terms of first-principles LDA electronic structure calculations. We show that at T=0 V_3Si, V_3Ge, and Nb_3Sn are intrinsically unstable against shears with elastic moduli C_11-C_12 and C_44, and that the zone center phonons, Gamma_2 and Gamma_12, are either unstable or extremely soft. We demonstrate that sublattice relaxation (internal strain) effects are key to understanding the behavior of the A15 materials.Comment: 5 pages, RevTex, 3 postscript figures, Submitted to Phys. Rev. Lett. Apr. 23, 1997 July 7, 1997: minor corrections, final accepted versio

«Белая дача» А.П. Чехова – как часть культурного ландшафта Крыма

Данная работа написана в рамках научного проекта кафедры культурологии «Культурные ландшафты Крыма» и посвящена рассмотрению «Белой дачи» А.П. Чехова (ныне Дом-музей А.П. Чехова в Ялте) как культурному ландшафту – результату сотворчества человека и природы

Quantum Mechanics of Multi-Prong Potentials

We describe the bound state and scattering properties of a quantum mechanical particle in a scalar $N$-prong potential. Such a study is of special interest since these situations are intermediate between one and two dimensions. The energy levels for the special case of $N$ identical prongs exhibit an alternating pattern of non-degeneracy and $(N-1)$ fold degeneracy. It is shown that the techniques of supersymmetric quantum mechanics can be used to generate new solutions. Solutions for prongs of arbitrary lengths are developed. Discussions of tunneling in $N$-well potentials and of scattering for piecewise constant potentials are given. Since our treatment is for general values of $N$, the results can be studied in the large $N$ limit. A somewhat surprising result is that a free particle incident on an $N$-prong vertex undergoes continuously increased backscattering as the number of prongs is increased.Comment: 17 pages. LATEX. On request, TOP_DRAW files or hard copies available for 7 figure