Bounds on supremum norms for Hecke eigenfunctions of quantized cat maps

We study extreme values of desymmetrized eigenfunctions (so called Hecke eigenfunctions) for the quantized cat map, a quantization of a hyperbolic linear map of the torus. In a previous paper it was shown that for prime values of the inverse Planck constant N=1/h, such that the map is diagonalizable (but not upper triangular) modulo N, the Hecke eigenfunctions are uniformly bounded. The purpose of this paper is to show that the same holds for any prime N provided that the map is not upper triangular modulo N. We also find that the supremum norms of Hecke eigenfunctions are << N^epsilon for all epsilon>0 in the case of N square free.Comment: 16 pages. Introduction expanded; comparison with supremum norms of eigenfunctions of the Laplacian added. Bound for square free N adde

Superconformal symmetry in the interacting theory of (2,0) tensor multiplets and self-dual strings

We investigate the concept of superconformal symmetry in six dimensions, applied to the interacting theory of (2,0) tensor multiplets and self-dual strings. The action of a superconformal transformation on the superspace coordinates is found, both from a six-dimensional perspective and by using a superspace with eight bosonic and four fermionic dimensions. The transformation laws for all fields in the theory are derived, as well as general expressions for the transformation of on-shell superfields. Superconformal invariance is shown for the interaction of a self-dual string with a background consisting of on-shell tensor multiplet fields, and we also find an interesting relationship between the requirements of superconformal invariance and those of a local fermionic kappa-symmetry. Finally, we try to construct a superspace analogue of the Poincare dual to the string world-sheet and consider its properties under superconformal transformations.Comment: 31 pages, LaTeX. v2: clarifications and minor correction

A novel route to phase formation of cobalt oxyhydrates using KMnO4 as an oxidizing agent

We have first succeefully synthesized the sodium cobalt oxyhydrate superconductors using KMnO4 as a de-intercalating and oxidizing agent. It is a novel route to form the superconductive phase of NaxCoO2.yH2O without resorting to the commonly used Br2/CH3CN solution. The role of the KMnO4 is to de-intercalate the Na+ from the parent compound Na0.7CoO2 and oxidize the Co ion as a result. The higher molar ratio of KMnO4 relative to the sodium content tends to remove more Na+ from the parent compound and results in a slight expansion of the c-axis in the unit cell. The superconducting transition temperature is 4.6-3.8 K for samples treated by the aqueous KMnO4 solution with the molar ratio of KMnO4 relative to the sodium content in the range of 0.3 and 2.29.Comment: 10 pages, 3 figure

Quantum Ergodicity for Point Scatterers on Arithmetic Tori

We prove an analogue of Shnirelman, Zelditch and Colin de Verdiere's Quantum Ergodicity Theorems in a case where there is no underlying classical ergodicity. The system we consider is the Laplacian with a delta potential on the square torus. There are two types of wave functions: old eigenfunctions of the Laplacian, which are not affected by the scatterer, and new eigenfunctions which have a logarithmic singularity at the position of the scatterer. We prove that a full density subsequence of the new eigenfunctions equidistribute in phase space. Our estimates are uniform with respect to the coupling parameter, in particular the equidistribution holds for both the weak and strong coupling quantizations of the point scatterer.Comment: 22 pages, 1 figure, Geom. Funct. Anal. (GAFA) to appea

Primitive divisors of Lucas and Lehmer sequences

Stewart reduced the problem of determining all Lucas and Lehmer sequences whose $n$-th element does not have a primitive divisor to solving certain Thue equations. Using the method of Tzanakis and de Weger for solving Thue equations, we determine such sequences for $n \leq 30$. Further computations lead us to conjecture that, for $n > 30$, the $n$-th element of such sequences always has a primitive divisor

Value distribution for eigenfunctions of desymmetrized quantum maps

We study the value distribution and extreme values of eigenfunctions for the ``quantized cat map''. This is the quantization of a hyperbolic linear map of the torus. In a previous paper it was observed that there are quantum symmetries of the quantum map - a commutative group of unitary operators which commute with the map, which we called ``Hecke operators''. The eigenspaces of the quantum map thus admit an orthonormal basis consisting of eigenfunctions of all the Hecke operators, which we call ``Hecke eigenfunctions''. In this note we investigate suprema and value distribution of the Hecke eigenfunctions. For prime values of the inverse Planck constant N for which the map is diagonalizable modulo N (the ``split primes'' for the map), we show that the Hecke eigenfunctions are uniformly bounded and their absolute values (amplitudes) are either constant or have a semi-circle value distribution as N tends to infinity. Moreover in the latter case different eigenfunctions become statistically independent. We obtain these results via the Riemann hypothesis for curves over a finite field (Weil's theorem) and recent results of N. Katz on exponential sums. For general N we obtain a nontrivial bound on the supremum norm of these Hecke eigenfunctions

Evaluation of Lactation Promotion as Part of Baby Friendly Hospital

Decrease of maternal and infant mortality as well as increasing of the exclusive breastfeeding are major public health priorities in Indonesia. In decreasing the maternal and infant mortality, the government developed a program for the community as Baby Friendly Hospital (BFH) to prevent the effects, to support, and to promote breastfeeding. PKU Muhammadiyah hospital in Yogyakarta was one of the BFH program managers. The purpose of this study was to determine the breastfeeding promotion activities as part of BFH at PKU Muhammadiyah Hospital in Yogyakarta.This was a qualitative descriptive study. The findings of this study were inputs consisting of 1) the knowledge and skills to better convey information indicates the quality of human resources. 2) promotion of the policies for all workers to reach the goal. 3) financial promotion is supported by the operating system in the hospital. 4) supporting facility to promote lactation leaflets, posters, ANC class, a breastfeeding counselor and nursing areas. Implementation of lactation promotion was conducted in accordance with program planning of BFH