Let E/Q be an elliptic curve and p a prime of supersingular reduction for E. Denote by K∞ the anticyclotomic Zp-extension of an imaginary quadratic field K which satisfies the Heegner hypothesis. Assuming that p splits in K/Q, we prove that X(K∞, E)p∞ has trivial Λ-corank and, in the process, also show that HSel(K∞, Ep∞) and E(K∞)⊗Qp/Zp both have Λ-corank two.

— We classify all quadratic imaginary number fields that have a Euclidean ideal class. There are seven of them, they are of class number at most two, and in each case the unique class that generates the class-group is moreover norm-Euclidean.

TABLE DES MATI`ERES Introduction 1. Structure galoisienne de courbes modulaires 2. Le cas p = 23 3. Méthode et Résultats Remerciements Bibliographie Nous construisons 53 corps quadratiques imaginaires ayant un 11-rangégaì a 3, et sept corps quadratiques réels de 11-rangégaì a 2. Ce sont, ` a notre connaissance, les premiers exemples de tels corps. We construct 53 imaginary quadratic fields of 1...

We show that if the derivative of the Riemann zeta function has sufficiently many zeros close to the critical line, then the zeta function has many closely spaced zeros. This gives a condition on the zeros of the derivative of the zeta function which implies a lower bound of the class numbers of imaginary quadratic fields.

For an odd prime number p, let Fanti be the Zp-anticyclotomic extension of an imaginary quadratic field F . We focus on the non-normal subextension K∞ of Fanti fixed by a subgroup of order 2 in Gal(Fanti/Q). After providing a general result for dihedral extensions, we study the growth of the p-part of the class group of the subfields ofK∞/Q, providing a formula of Iwasawa type. Furthermore, we ...

The optical and magnetic properties of dust grains are reviewed , as they relate to the problem of interstellar grain alignment. Grain geometry plays an important role in determining the optical properties , and scattering and absorption of starlight will produce radiative torques which may drive grains to suprathermal rates of rotation in in-terstellar clouds; these radiative torques appear li...

The corrosion inhibition effect of N,N′-bis(n-Hydroxybenzaldehyde)-1,3-Propandiimine on mild steel has been investigated in 1 M HCl using electrochemical impedance spectroscopy. A predictive model was presented for Nyquist plots using an artificial neural network. The proposed model predicted the imaginary impedance based on the real part of the impedance as a function of time. The model to...

We discuss whether or not local information on the potential energy surface embodied by the distribution of unstable instantaneous normal modes can be used to predict the hopping rates and barrier heights for Zwanzig’s model of self-diffusion @R. Zwanzig, J. Chem. Phys. 79, 4507 ~1983!# in simple liquids. Results from a set of simulations of Lennard-Jones particles done at multiple temperatures...

In a recent publication [1] it was shown how the geometric algebra G4,1 , the algebra of 5-dimensional space-time, can generate relativistic dynamics from the simple principle that only null geodesics should be allowed. The same paper showed also that Dirac equation could be derived from the condition that a function should be monogenic in that algebra; this construction of the Dirac equation a...