On Heegner points of large conductors

Given a parametrisation of an elliptic curve over Q by a Shimura curve, we show that the images of almost all Heegner points are of infinite order. For parametrisations of elliptic curves by modular curves this was proven earlier by Nekovar and Schappacher by a different method

The density of ramified primes in semisimple p-adic Galois representations

We prove that the density of ramified primes in semisimple p-adic representations of Galois groups of number fields is 0. Ravi Ramakrishna has produced examples of such representations that are infinitely ramified

Long wavelength ultraviolet photoproduction of amino acids on the primitive earth

Amino acids produced by long UV irradiation of gas mixtures using hydrogen sulfide as initial photon acceptor, simulating prebiological earth condition

Exobiology and the origin of life

Abstracts on planetary studies and the search for extraterrestrial life are presented. Studies of the Jovian atmosphere were conducted. An assessment of the prospects for life on Mars is presented. And, the the means of contacting extraterrestrial civilizations is discussed

On the temperature dependence of possible S8 infrared bands in planetary atmospheres

Measurements of the temperature dependence between 77 and 333 K of the infrared spectrum of cyclic octatomic sulfur are reported. It is suggested that the 23 micrometer Jovian feature is not due to 3 sub 8 and that the temperature dependence of the frequency of the 835/cm band of S sub 8 may be a useful temperature marker in planetary studies

On Some One-Parameter Families of Three-Body Problems in One Dimension: Exchange Operator Formalism in Polar Coordinates and Scattering Properties

We apply the exchange operator formalism in polar coordinates to a one-parameter family of three-body problems in one dimension and prove the integrability of the model both with and without the oscillator potential. We also present exact scattering solution of a new family of three-body problems in one dimension.Comment: 10 pages, LaTeX, no figur

New Shape Invariant Potentials in Supersymmetric Quantum Mechanics

Quantum mechanical potentials satisfying the property of shape invariance are well known to be algebraically solvable. Using a scaling ansatz for the change of parameters, we obtain a large class of new shape invariant potentials which are reflectionless and possess an infinite number of bound states. They can be viewed as q-deformations of the single soliton solution corresponding to the Rosen-Morse potential. Explicit expressions for energy eigenvalues, eigenfunctions and transmission coefficients are given. Included in our potentials as a special case is the self-similar potential recently discussed by Shabat and Spiridonov.Comment: 8pages, Te

Linear Superposition in Nonlinear Equations

Even though the KdV and modified KdV equations are nonlinear, we show that suitable linear combinations of known periodic solutions involving Jacobi elliptic functions yield a large class of additional solutions. This procedure works by virtue of some remarkable new identities satisfied by the elliptic functions.Comment: 7 pages, 1 figur

New supersymmetric partners for the associated Lame potentials

We obtain exact solutions of the one-dimensional Schrodinger equation for some families of associated Lame potentials with arbitrary energy through a suitable ansatz, which may be appropriately extended for other such a families. The formalism of supersymmetric quantum mechanics is used to generate new exactly solvable potentials.Comment: 8 pages, 2 figures, submitted on 24 November 2004 to Phys. Lett.