Ion acceleration by circularly polarized laser pulses interacting with foil targets is studied using two dimensional particle-in-cell simulations. It is shown that laser pulses with transverse super-Gaussian profile help in avoiding target deformation as compared with the usual Gaussian pulse. This improves monochromaticity of the accelerated ion spectrum. Two kinds of surface instabilities have been found during the interaction. These instabilities can potentially break the target and destroy the quasimonoenergetic character of the final ion spectrum. Combined laser pulses with super-Hermite and Gaussian modes are used to improve the ion acceleration and transverse collimation.
We study a class of orientifold compactifications of type IIB supergravity with fluxes down to 4D in connection with truncations of half-maximal gauged supergravities yielding isotropic STU-models with minimal supersymmetry. In this context, we make use of a group-theoretical approach in order to derive flux-induced superpotentials for different IIB backgrounds. We first review the toroidal case yielding CEP-like superpotentials characterised by their no-scale behaviour. We then turn to S-3 x S-3 and S-3 x T-3, which, surprisingly, give rise to effective descriptions of non-geometric Q- and P-fluxes through globally geometric non-toroidal compactifications. As a consequence, such constructions break the no-scale symmetry without invoking any non-perturbative effects.
In the context of two-loop Finite Supersymmetric Theories with gauge group SU(5), we present parametric solutions to the finiteness conditions using Q(6) as a family symmetry group. Assuming an MSSM scenario with just one pair of light Higgs doublets, we obtain mass matrices at the GUT scale for this class of theories.
Let q be an odd prime. Let c > 1 and t be positive integers such that q(t) + 1 =3D 2c(2). Using elementary method and a result due to Ljunggren concerning the Diophantine equation x(n)-1/x-1 =3D y(2), we show that the Diophantine equation x(2) + q(m) =3D c(2n) has the only positive integer solution (x, m, n) =3D (c(2) - 1, t, 2). As applications of this result some new results on the Diophantine equation x(2) + q(m) =3D c(n) and the Diophantine equation x(2) + (2c - 1)(m) =3D c(n) are obtained. In particular, we prove that Terai's conjecture is true for c =3D 12,24. Combining this result with Terai's results we conclude that Terai's conjecture is true for 2 <=3D c <=3D 30.
Let S be a non-empty finite set of prime numbers and Q(S) the abelian number field whose Galois group is topologically isomorphic to the direct product of the p-adic integer rings for all p in S. We denote by Omega(S) the composite of p(n)-th cyclotomic fields for all p in S and all positive integers n. Let l be a prime number which is not in S and we define an explicit constant (G) over tilde (S, F) which depends only on S and the decomposition field F of l for Omega(S) over Q. Then l does not divide the class numbers of all intermediate fields of Q(S) with finite degree over Q if l is greater than (G) over tilde (S, F). Our proof refines Horie's method. (C) 2012 Elsevier Inc. All rights reserved.
By means of principal isotopes H(a, b) of the algebra H [25], we give an exhaustive and not repetitive description of all 4-dimensional absolute-valued algebras satisfying (x(p), x(q), x(r)) = 0 for fixed integers p, q, r is an element of {1, 2}. For such algebras, the number N(p, q, r) of isomorphism classes is either 2 or 3, or is infinite. Concretely: 1. N(1, 1, 1) = N(1, 1, 2) = N(1, 2, 1) = N(2, 1, 1) = 2; 2. N(1, 2, 2) = N(2, 2, 1) = 3; 3. N(2, 1, 2) = N(2, 2, 2) = infinity. Besides, each one of the above algebras contains 2-dimensional subalgebras. However, the problem in dimension 8 is far from being completely solved. In fact, there are 8-dimensional absolute-valued algebras, containing no 4-dimensional subalgebras, satisfying (x(2), x, x(2)) = (x(2), x(2), x(2)) = 0.
Capuzzo Dolcetta, Italo; Leoni, Fabiana; Vitolo, Antonio
We consider fully nonlinear degenerate elliptic equations with zero and first order terms. We provide a priori upper bounds and characterize the existence of entire subsolutions under growth conditions on the lower order coefficients which extend the classical Keller-Osserman condition for semilinear equations.
Let f be a fixed (holomorphic or Maass) modular cusp form. Let chi(q) be a Dirichlet character mod q. We describe a fast algorithm that computes the value L(1/2, f x chi(q)) up to any specified precision. In the case when q is smooth or highly composite integer, the time complexity of the algorithm is given by O(1 + vertical bar q vertical bar(5/6+o(1))). (C) 2012 Elsevier Inc. All rights reserved.