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

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

Extensive Regulation of Diurnal Transcription and Metabolism by Glucocorticoids.

Altered daily patterns of hormone action are suspected to contribute to metabolic disease. It is poorly understood how the adrenal glucocorticoid hormones contribute to the coordination of daily global patterns of transcription and metabolism. Here, we examined diurnal metabolite and transcriptome patterns in a zebrafish glucocorticoid deficiency model by RNA-Seq, NMR spectroscopy and liquid chromatography-based methods. We observed dysregulation of metabolic pathways including glutaminolysis, the citrate and urea cycles and glyoxylate detoxification. Constant, non-rhythmic glucocorticoid treatment rescued many of these changes, with some notable exceptions among the amino acid related pathways. Surprisingly, the non-rhythmic glucocorticoid treatment rescued almost half of the entire dysregulated diurnal transcriptome patterns. A combination of E-box and glucocorticoid response elements is enriched in the rescued genes. This simple enhancer element combination is sufficient to drive rhythmic circadian reporter gene expression under non-rhythmic glucocorticoid exposure, revealing a permissive function for the hormones in glucocorticoid-dependent circadian transcription. Our work highlights metabolic pathways potentially contributing to morbidity in patients with glucocorticoid deficiency, even under glucocorticoid replacement therapy. Moreover, we provide mechanistic insight into the interaction between the circadian clock and glucocorticoids in the transcriptional regulation of metabolism

До мінералогії сезонних сульфатів мису Фіолент (Південно-Західний Крим)

Комплексом методів вивчено колекцію зразків вторинних мінералів одного з узбережних відслонень зони окиснення сульфідної мінералізації мису Фіолент (Південно-Західний Крим). Установлено, що всі досліджені зразки є полімінеральними утвореннями, в яких одночасно співіснують у різних пропорціях сульфати Mg, Al, Fe²⁺, Fe³⁺, Ca тощо: пікерингіт (найпоширеніший), пікерингіт залізистий, гексагідрит, старкіїт, епсоміт, алуноген, ботріоген, копіапіт, ярозит, гіпс та ін. Старкіїт і ботріоген у Криму виявлено вперше.The collection of secondary minerals from one of littoral occurrences of sulphide zone of oxidation of the Fiolent Cape (South-Western Crimea) is studied by different methods. It was established that all studied samples were polymineral formations which consisted of sulphates of Mg, Al, Fe²⁺, Fe³⁺, Ca, etc. in different proportions: pickeringite (the most wide-spread), ferropickeringite, hexahydrite, starkeyite, epsomite, alunogen, botryogen, copiapite, jarosite, gypsum etc. Starkeyite and botryogen are detected in the Crimea for the first time

Saturation of electrical resistivity

Resistivity saturation is observed in many metallic systems with a large resistivity, i.e., when the resistivity has reached a critical value, its further increase with temperature is substantially reduced. This typically happens when the apparent mean free path is comparable to the interatomic separations - the Ioffe-Regel condition. Recently, several exceptions to this rule have been found. Here, we review experimental results and early theories of resistivity saturation. We then describe more recent theoretical work, addressing cases both where the Ioffe-Regel condition is satisfied and where it is violated. In particular we show how the (semiclassical) Ioffe-Regel condition can be derived quantum-mechanically under certain assumptions about the system and why these assumptions are violated for high-Tc cuprates and alkali-doped fullerides.Comment: 16 pages, RevTeX, 15 eps figures, additional material available at http://www.mpi-stuttgart.mpg.de/andersen/saturation

Critical disorder effects in Josephson-coupled quasi-one-dimensional superconductors

Effects of non-magnetic randomness on the critical temperature T_c and diamagnetism are studied in a class of quasi-one dimensional superconductors. The energy of Josephson-coupling between wires is considered to be random, which is typical for dirty organic superconductors. We show that this randomness destroys phase coherence between the wires and T_c vanishes discontinuously when the randomness reaches a critical value. The parallel and transverse components of the penetration depth are found to diverge at different critical temperatures T_c^{(1)} and T_c, which correspond to pair-breaking and phase-coherence breaking. The interplay between disorder and quantum phase fluctuations results in quantum critical behavior at T=0, manifesting itself as a superconducting-normal metal phase transition of first-order at a critical disorder strength.Comment: 4 pages, 2 figure

Interplay of Electron-Phonon Interaction and Electron Correlation in High Temperature Superconductivity

We study the electron-phonon interaction in the strongly correlated superconducting cuprates. Two types of the electron-phonon interactions are introduced in the $t-J$ model; the diagonal and off-diagonal interactions which modify the formation energy of the Zhang-Rice singlet and its transfer integral, respectively. The characteristic phonon-momentum $(\vec q)$ and electron-momentum $(\vec k)$ dependence resulted from the off-diagonal coupling can explain a variety of experiments. The vertex correction for the electron-phonon interaction is formulated in the SU(2) slave-boson theory by taking into account the collective modes in the superconducting ground states. It is shown that the vertex correction enhances the attractive potential for the d-wave paring mediated by phonon with $\vec q=(\pi(1-\delta), 0)$ around $\delta \cong 0.3$ which corresponds to the half-breathing mode of the oxygen motion.Comment: 14 pages, 13 figure

Efficient Selfconsistent Calculations of Multiband Superconductivity in UPd2_2Al3_3

An efficient physically motivated computational approach to multiband superconductivity is introduced and applied to the study of the gap symmetry in a heavy-fermion, UPd$_2$Al$_3$. Using realistic pairing potentials and accurate energy bands that are computed within density functional theory, self-consistent calculations demonstrate that the only accessible superconducting gap with nodes exhibits d-wave symmetry in the $A_{1g}$ representation of the $D_{6h}$ point group. Our results suggest that in a superconductor with gap nodes the prevailing gap symmetry is dictated by the constraint that nodes must be as far as possible from high-density areas

Interlayer c-axis transport in the normal state of cuprates

A theoretical model of c-axis transport properties in cuprates is proposed. Inter-plane and in-plane charge fluctuations make hopping between planes incoherent and diffusive (the in-plane momentum is not conserved after tunneling). The non-Drude optical conductivity $\sigma_c(\omega)$ and the power-law temperature dependence of the {\it dc} conductivity are generically explained by the strong fluctuations excited in the process of tunneling. Several microscopic models of the charge fluctuation spectrum are considered.Comment: 8 page

Hall effect and conduction anisotropy in the organic conductor TMTSF2PF6

Long missing basic experiments in the normal phase of the anisotropic electron system of TMTSF2PF6 were performed. Both the Hall effect and the ab'-plane conduction anisotropy are directly addressing the unconventional electrical properties of this Bechgaard salt. We found that the dramatic reduction of the carrier density deduced from recent optical data is not reflected in an enhanced Hall-resistance. The pressure- and temperature dependence of the b'-direction resitivity reveal isotropic relaxation time and do not require explanations beyond the Fermi liquid theory. Our results allow a coherent-diffusive transition in the interchain carrier propagation, however the possible crossover to Luttinger liquid behavior is placed to an energy scale above room temperature.Comment: 5 pages, 5 figures, to be published in Phys. Rev. Let