Necessary condition for the existence of the S matrix outside the scope of perturbation theory

Using the Maslov—Shvedov complex-germ method due to Maslov—Shvedov, we obtain a necessary condition for the existence of the quantum-field S matrix outside the scope of perturbation theory in the leading order of semiclassical approximation. This condition consists in that the tangent symplectic transformation to the evolution operator of the nonlinear classical field equation is realized by a unitary transformation of Fock space. It follows from the results of the book of Maslov and Shvedov that this condition always holds.     

The quasi-orthogonality of the derivatives of semi-classical polynomials

The distributional equation of a semi-classical functional allows an efficient study of other characterizations and properties of the semi-classical OPS/functionals. In [6] an extensive survey of this approach has been presented. A particular case of semi-classical OPS/functionals are the classical ones. For the distributional equation of a classical functional a regularity condition holds. We have give a family counterexamples to show that the regularity condition does not hold in general for semi-classical functionals [9]. Here we investigate the consequences of the failure of the regularity condition in the quasi-orthogonality of the derivatives of the semi-classical OPS and, in general, the behaviour of the derivatives of order k. This study leads us to another condition that holds for the distributional equation of classical functional, the coprimality condition.     

Regularity of a class of subLaplacians on the 3-dimensional torus

In this paper we present a necessary and sufficient condition for a family of sums of squares operators to be globally hypoelliptic on a torus. This condition says that either a Diophantine condition is satisfied or there exists a point of finite type. Also, we describe the analytic and Gevrey versions of this result. The proof is based on L²-estimates and microlocal analysis.     

Splice diagram singularities and the universal abelian cover of graph orbifolds

Given a rational homology 3-sphere M whose splice diagram \(\varGamma (M)\) satisfies the semigroup condition, Neumann and Wahl define a complete intersection surface singularity called a splice diagram singularity. Under an additional hypothesis on M called the congruence condition they show that the link of this singularity is the universal abelian cover of M. They ask if this still holds if the congruence condition fails. In this article we generalize the congruence condition to orientable graph orbifolds. We show that under a small additional hypothesis this orbifold congruence condition implies that the link of the splice diagram singularity is the universal abelian cover. By showing that any two-node splice diagram satisfying the semigroup condition is the splice diagram of an orbifold satisfying the orbifold congruence condition, we answer the question of Neumann and Wahl affirmatively for two-node diagrams. However, examples show this approach to their question no longer works for three nodes.     

Existence and consistency of the maximum likelihood estimator for the extreme value index

The paper is about the asymptotic properties of the maximum likelihood estimator for the extreme value index. Under the second order condition, Drees et al. [H. Drees, A. Ferreira, L. de Haan, On maximum likelihood estimation of the extreme value index, Ann. Appl. Probab. 14 (2004) 1179-1201] proved asymptotic normality for any solution of the likelihood equations (with shape parameter γ>−1/2) that is not too far off the real value. But they did not prove that there is a solution of the equations satisfying the restrictions.In this paper, the existence is proved, even for γ>−1. The proof just uses the domain of attraction condition (first order condition), not the second order condition. It is also proved that the estimator is consistent. When the second order condition is valid, following the current proof, the existence of a solution satisfying the restrictions in the above-cited reference is a direct consequence.     

On the global wellposedness of the 3-D Navier-Stokes equations with large initial data

We give a condition for the periodic, three-dimensional, incompressible Navier-Stokes equations to be globally wellposed. This condition is not a smallness condition on the initial data, as the data is allowed to be arbitrarily large in the scale invariant space , which contains all the known spaces in which there is a global solution for small data. The smallness condition is rather a nonlinear type condition on the initial data; an explicit example of such initial data is constructed, which is arbitrarily large and yet gives rise to a global, smooth solution.     

On the existence of Lp solutions of the magnetohydrodynamic equations in a bounded domain

In this paper, we show the existence of L^p solutions of the magnetohydrodynamic equations with the non-slip boundary condition and the perfect conducting wall boundary condition. The magnetohydrodynamic equations are a phenomenological model for magnetic fluid.     

A new condition for the uniform convergence of certain trigonometric series

Summary The present paper proposes a new condition to replace both the (O-regularly varying) quasimonotone condition and a certain type of bounded variation condition, and shows the same conclusion for the uniform convergence of certain trigonometric series still holds.     

On the Cayley factorization of calotte conditions

The calotte condition is the projective condition that a cycle of lines radiating from the vertices of a planen-gon be the correct projection of a ring of faces surrounding ann-gonal piece of plane in space, the spatial figure being not entirely coplanar. This condition can be expressed as a homogeneous bracket polynomial. In general, this polynomial is not Cayley factorable. Henry Crapo conjectured that it becomes so when multiplied by a product ofn−4 brackets. It is the purpose of this article to prove this conjecture.