A Generalization of the Ramanujan Polynomials and Plane Trees

Generalizing a sequence of Lambert, Cayley and Ramanujan, Chapoton has recently introduced a polynomial sequence Q_n:=Q_n(x,y,z,t) defined by Q_1=1, Q_{n+1}=[x+nz+(y+t)(n+y\partial_y)]Q_n. In this paper we prove Chapoton's conjecture on the duality formula: Q_n(x,y,z,t)=Q_n(x+nz+nt,y,-t,-z), and answer his question about the combinatorial interpretation of Q_n. Actually we give combinatorial interpretations of these polynomials in terms of plane trees, half-mobile trees, and forests of plane trees. Our approach also leads to a general formula that unifies several known results for enumerating trees and plane trees.Comment: 20 pages, 2 tables, 8 figures, see also http://math.univ-lyon1.fr/~gu

The stimulatory effect of albumin on luteinizing hormone-stimulated Leydig cell steroid production depends on its fatty acid content and correlates with conformational changes

__Abstract__ The effects of purified albumin species and albumin fragments (0.2–1% w/v) on short-term (4 h) steroid secretion by immature rat Leydig cells, in the presence of a maximally stimulating dose of luteinizing hormone (LH), were investigated. Human albumin and the peptic fragment (comprising residues 1–387) enhanced pregnenolone production in isolated rat Leydig cells, whereas chicken albumin and the tryptic fragment (comprising residues 198–585) were not active. This stimulatory effect of human albumin and the peptic fragment correlated with the potential of these proteins to undergo a pH-dependent neutral-to-base transition as measured by circular dichroism. The tryptic fragment and chicken albumin did not have the potential to undergo such a transition. The pH-dependent conformational changes of albumin and fragments thereof occurred in parallel with a change in the binding affinity for testosterone and pregnenolone. The fatty acid oleic acid and the drug suramin, only when present in a molar ligand-to-albumin ratio equal to or higher than 2, inhibited the albumin-mediated stimulation of steroid production. These data show that the stimulatory effects of albumin species on LH-induced Leydig cell pregnenolone production depend on their fatty acid content and correlate with the potential of these molecules to undergo conformational changes. It is unknown via which mechanisms albumin exerts its stimulatory effect, but the LH action through the cyclic AMP pathway seems not to be affected

Reversible Band Gap Engineering in Carbon Nanotubes by Radial Deformation

We present a systematic analysis of the effect of radial deformation on the atomic and electronic structure of zigzag and armchair single wall carbon nanotubes using the first principle plane wave method. The nanotubes were deformed by applying a radial strain, which distorts the circular cross section to an elliptical one. The atomic structure of the nanotubes under this strain are fully optimized, and the electronic structure is calculated self-consistently to determine the response of individual bands to the radial deformation. The band gap of the insulating tube is closed and eventually an insulator-metal transition sets in by the radial strain which is in the elastic range. Using this property a multiple quantum well structure with tunable and reversible electronic structure is formed on an individual nanotube and its band-lineup is determined from first-principles. The elastic energy due to the radial deformation and elastic constants are calculated and compared with classical theories.Comment: To be appear in Phys. Rev. B, Apr 15, 200

Quasiclassical description of transport through superconducting contacts

We present a theoretical study of transport properties through superconducting contacts based on a new formulation of boundary conditions that mimics interfaces for the quasiclassical theory of superconductivity. These boundary conditions are based on a description of an interface in terms of a simple Hamiltonian. We show how this Hamiltonian description is incorporated into quasiclassical theory via a T-matrix equation by integrating out irrelevant energy scales right at the onset. The resulting boundary conditions reproduce results obtained by conventional quasiclassical boundary conditions, or by boundary conditions based on the scattering approach. This formalism is well suited for the analysis of magnetically active interfaces as well as for calculating time-dependent properties such as the current-voltage characteristics or as current fluctuations in junctions with arbitrary transmission and bias voltage. This approach is illustrated with the calculation of Josephson currents through a variety of superconducting junctions ranging from conventional to d-wave superconductors, and to the analysis of supercurrent through a ferromagnetic nanoparticle. The calculation of the current-voltage characteristics and of noise is applied to the case of a contact between two d-wave superconductors. In particular, we discuss the use of shot noise for the measurement of charge transferred in a multiple Andreev reflection in d-wave superconductors

Theory of charge transport in diffusive normal metal / unconventional singlet superconductor contacts

We analyze the transport properties of contacts between unconventional superconductor and normal diffusive metal in the framework of the extended circuit theory. We obtain a general boundary condition for the Keldysh-Nambu Green's functions at the interface that is valid for arbitrary transparencies of the interface. This allows us to investigate the voltage-dependent conductance (conductance spectrum) of a diffusive normal metal (DN)/ unconventional singlet superconductor junction in both ballistic and diffusive cases. For d-wave superconductor, we calculate conductance spectra numerically for different orientations of the junctions, resistances, Thouless energies in DN, and transparencies of the interface. We demonstrate that conductance spectra exhibit a variety of features including a $V$-shaped gap-like structure, zero bias conductance peak (ZBCP) and zero bias conductance dip (ZBCD). We show that two distinct mechanisms: (i) coherent Andreev reflection (CAR) in DN and (ii) formation of midgap Andreev bound state (MABS) at the interface of d-wave superconductors, are responsible for ZBCP, their relative importance being dependent on the angle $\alpha$ between the interface normal and the crystal axis of d-wave superconductors. For $\alpha=0$, the ZBCP is due to CAR in the junctions of low transparency with small Thouless energies, this is similar to the case of diffusive normal metal / insulator /s-wave superconductor junctions. With increase of $\alpha$ from zero to $\pi/4$, the MABS contribution to ZBCP becomes more prominent and the effect of CAR is gradually suppressed. Such complex spectral features shall be observable in conductance spectra of realistic high-$T_c$ junctions at very low temperature