The Ramanujan master theorem and its implications for special functions

We study a number of possible extensions of the Ramanujan master theorem, which is formulated here by using methods of Umbral nature. We discuss the implications of the procedure for the theory of special functions, like the derivation of formulae concerning the integrals of products of families of Bessel functions and the successive derivatives of Bessel type functions. We stress also that the procedure we propose allows a unified treatment of many problems appearing in applications, which can formally be reduced to the evaluation of exponential- or Gaussian-like integrals.Comment: 12 page

Two-dimensional vortex behavior in highly underdoped YBa_2Cu_3O_{6+x} observed by scanning Hall probe microscopy

We report scanning Hall probe microscopy of highly underdoped superconducting YBa_2Cu_3O_{6+x} with T_c ranging from 5 to 15 K which showed distinct flux bundles with less than one superconducting flux quantum (Phi_0) through the sample surface. The sub-Phi_0 features occurred more frequently for lower T_c, were more mobile than conventional vortices, and occurred more readily when the sample was cooled with an in-plane field component. We show that these features are consistent with kinked stacks of pancake vortices.Comment: 11 pages, 8 figures, accepted for publication in Physical Review

Preparation and Characterization of Homogeneous YBCO Single Crystals with Doping Level near the SC-AFM Boundary

High-purity and homogeneous YBa2Cu3Oy single crystals with carrier doping level near the AFM-SC boundary have been obtained in the oxygen content range between y = 6.340 and 6.370. The crystals are ortho-II phase at room temperature and undergo the orthorhombic to tetragonal transition at about 140_Degree_C. They show sharp superconducting transitions, with Tc between 4 and 20 K. Tc changes by 0.8 K when the oxygen content y is changed by 0.001, and is also sensitive to annealing conditions near room temperature, due to the dependence of doping on oxygen ordering correlation lengths. Crystals with oxygen content y lower than 6.345 are non-superconducting.Comment: 6 page

Phase transition from a dx2−y2d_{x^2-y^2} to dx2−y2+dxyd_{x^2-y^2}+d_{xy} superconductor

We study the phase transition from a $d_{x^2-y^2}$ to $d_{x^2-y^2}+d_{xy}$ superconductor using the tight-binding model of two-dimensional cuprates. As the temperature is lowered past the critical temperature $T_c$, first a $d_{x^2-y^2}$ superconducting phase is created. With further reduction of temperature, the $d_{x^2-y^2}+d_{xy}$ phase is created at temperature $T=T_{c1}$. We study the temperature dependencies of the order parameter, specific heat and spin susceptibility in these mixed-angular-momentum states on square lattice and on a lattice with orthorhombic distortion. The above-mentioned phase transitions are identified by two jumps in specific heat at $T_c$ and $T_{c1}$.Comment: Latex file, 5 pages, 6 postscript figures, Accepted in Physical Review

What do young athletes implicitly understand about psychological skills?

One reason sport psychologists teach psychological skills is to enhance performance in sport; but the value of psychological skills for young athletes is questionable because of the qualitative and quantitative differences between children and adults in their understanding of abstract concepts such as mental skills. To teach these skills effectively to young athletes, sport psychologists need to appreciate what young athletes implicitly understand about such skills because maturational (e.g., cognitive, social) and environmental (e.g., coaches) factors can influence the progressive development of children and youth. In the present qualitative study, we explored young athletes’ (aged 10–15 years) understanding of four basic psychological skills: goal setting, mental imagery, self-talk, and relaxation. Young athletes (n = 118: 75 males and 43 females) completed an open-ended questionnaire to report their understanding of these four basic psychological skills. Compared with the older youth athletes, the younger youth athletes were less able to explain the meaning of each psychological skill. Goal setting and mental imagery were better understood than self-talk and relaxation. Based on these findings, sport psychologists should consider adapting interventions and psychoeducational programs to match young athletes’ age and developmental level

Tilt Grain-Boundary Effects in S- and D-Wave Superconductors

We calculate the s- and d-wave superconductor order parameter in the vicinity of a tilt grain boundary. We do this self-consistently within the Bogoliubov de Gennes equations, using a realistic microscopic model of the grain boundary. We present the first self-consistent calculations of supercurrent flows in such boundaries, obtaining the current-phase characteristics of grain boundaries in both s-wave and d-wave superconductors

Pairing symmetry and long range pair potential in a weak coupling theory of superconductivity

We study the superconducting phase with two component order parameter scenario, such as, $d_{x^2-y^2} + e^{i\theta}s_{\alpha}$, where $\alpha = xy, x^2+y^2$. We show, that in absence of orthorhombocity, the usual $d_{x^2-y^2}$ does not mix with usual $s_{x^2+y^2}$ symmetry gap in an anisotropic band structure. But the $s_{xy}$ symmetry does mix with the usual d-wave for $\theta =0$. The d-wave symmetry with higher harmonics present in it also mixes with higher order extended $s$ wave symmetry. The required pair potential to obtain higher anisotropic $d_{x^2-y^2}$ and extended s-wave symmetries, is derived by considering longer ranged two-body attractive potential in the spirit of tight binding lattice. We demonstrate that the dominant pairing symmetry changes drastically from $d$ to $s$ like as the attractive pair potential is obtained from longer ranged interaction. More specifically, a typical length scale of interaction $\xi$, which could be even/odd multiples of lattice spacing leads to predominant $s/d$ wave symmetry. The role of long range interaction on pairing symmetry has further been emphasized by studying the typical interplay in the temperature dependencies of these higher order $d$ and $s$ wave pairing symmetries.Comment: Revtex 8 pages, 7 figures embeded in the text, To appear in PR

Identification of the bulk pairing symmetry in high-temperature superconductors: Evidence for an extended s-wave with eight line nodes

we identify the intrinsic bulk pairing symmetry for both electron and hole-doped cuprates from the existing bulk- and nearly bulk-sensitive experimental results such as magnetic penetration depth, Raman scattering, single-particle tunneling, Andreev reflection, nonlinear Meissner effect, neutron scattering, thermal conductivity, specific heat, and angle-resolved photoemission spectroscopy. These experiments consistently show that the dominant bulk pairing symmetry in hole-doped cuprates is of extended s-wave with eight line nodes, and of anisotropic s-wave in electron-doped cuprates. The proposed pairing symmetries do not contradict some surface- and phase-sensitive experiments which show a predominant d-wave pairing symmetry at the degraded surfaces. We also quantitatively explain the phase-sensitive experiments along the c-axis for both Bi_{2}Sr_{2}CaCu_{2}O_{8+y} and YBa_{2}Cu_{3}O_{7-y}.Comment: 11 pages, 9 figure

Design, Commissioning and Performance of the PIBETA Detector at PSI

We describe the design, construction and performance of the PIBETA detector built for the precise measurement of the branching ratio of pion beta decay, pi+ -> pi0 e+ nu, at the Paul Scherrer Institute. The central part of the detector is a 240-module spherical pure CsI calorimeter covering 3*pi sr solid angle. The calorimeter is supplemented with an active collimator/beam degrader system, an active segmented plastic target, a pair of low-mass cylindrical wire chambers and a 20-element cylindrical plastic scintillator hodoscope. The whole detector system is housed inside a temperature-controlled lead brick enclosure which in turn is lined with cosmic muon plastic veto counters. Commissioning and calibration data were taken during two three-month beam periods in 1999/2000 with pi+ stopping rates between 1.3*E3 pi+/s and 1.3*E6 pi+/s. We examine the timing, energy and angular detector resolution for photons, positrons and protons in the energy range of 5-150 MeV, as well as the response of the detector to cosmic muons. We illustrate the detector signatures for the assorted rare pion and muon decays and their associated backgrounds.Comment: 117 pages, 48 Postscript figures, 5 tables, Elsevier LaTeX, submitted to Nucl. Instrum. Meth.

'Universal' FitzGerald Contractions

The model of a universe with a preferred frame, which nevertheless shares the main properties with traditional special and general relativity theories, is considered. We adopt Mach's interpretation of inertia and show that the energy balance equation, which includes the Machian energy of gravitational interactions with the universe, can imitate standard relativistic formulas.Comment: The version accepted by Eur. Phys. J.