We present a frequency-independent three-dimensional (3-D) compressional wave attenuation model (indicated by the reciprocal of quality factor Qp) for Kı̄lauea Volcano in Hawai‘i. We apply the simul2000 tomographic algorithm to the attenuation operator t∗ values for the inversion of Qp perturbations through a recent 3-D seismic velocity model and earthquake location catalog. The t∗ values are me...

Given a prime p, the Fermat quotient qp(u) of u with gcd(u, p)= 1 is defined by the conditions qp(u)≡ u p−1 − 1 p mod p, 0≤ qp(u)≤ p − 1. We derive a new bound on multiplicative character sums with Fermat quotients qp(`) at prime arguments `. 2010 Mathematics subject classification: primary 11A07; secondary 11L40, 11N25.

Given a non-negative integer k, we construct a lattice 3-simplex P with the following property: The affine semigroup QP associated to P is not normal, and every element q ∈ QP \ QP has lattice distance at least k above every facet of QP .

In this note, we prove pointwise decay in time of solutions to the 3D energy-critical nonlinear Schrödinger equations assuming data L1∩H3. The main ingredients are boundness propagators Hardy space due Miyachi [9] and a fractional Leibniz rule space. We also extend chain

Soit p un nombre premier impair, K = Qp et soient Kn = Qp(μpn) le corps des racines p-ièmes de l’unité dans une clôture algébriqueQp de Qp, K∞ la réunion des Kn et G∞ = Gal(K∞/K). Soit une courbe elliptique E définie sur Qp. Si E(Kn) est le groupe des points de E définis sur Kn, la limite projective des E(Kn) pour les applications de trace a d’abord été étudiée lorsque E a bonne réduction ordin...

The paper describes the structure of a linear continuous operator on space functions in topology pointwise convergence. corresponding theorem is generalization A.V.Arkhangel'skii's general form functional such spaces.