We determine the consistency strength of some model theoretic extension properties for cardinals.
We shall study properties of box spline operators: cardinal interpolation, convolution, and the Bernstein-Schnabl operator. We prove the saturation theorem.
We provide several necessary and sufficient conditions for a Markov chain on a general state space to be positive Harris recurrent. The conditions only concern asymptotic properties of the expected occupation measures.
The Gauss linear system on the theta divisor of the Jacobian of a nonhyperelliptic curve has two striking properties:
1) the branch divisor of the Gauss map on the theta divisor is dual to the canonical model of the curve;
2) those divisors in the Gauss system parametrized by the canonical curve are reducible.
In contrast, Beauville and Debarre prove on a general Prym theta divisor of dimension all Gauss divisors are irreducible and normal. One is led to ask whether properties 1) and 2) may characterize the Gauss system of the theta divisor of a Jacobian. Since for a Prym theta divisor, the most distinguished curve in the Gauss system is the Prym canonical curve, the natural analog of the canonical curve for a Jacobian, in the present paper we analyze whether the analogs of properties 1) or 2) can ever hold for the Prym canonical curve. We note that both those properties would imply that the general Prym canonical Gauss divisor would be nonnormal. Then we find an explicit geometric model for the Prym canonical Gauss divisors and prove the following results using Beauville's singularities criterion for special subvarieties of Prym varieties:
Theorem. For all smooth doubly covered nonhyperelliptic curves of genus , the general Prym canonical Gauss divisor is normal and irreducible.
Corollary. For all smooth doubly covered nonhyperelliptic curves of genus , the Prym canonical curve is not dual to the branch divisor of the Gauss map.
In this paper, we extend a type of Strassen's theorem for the existence of probability measures with given marginals to positive vector measures with values in the dual of a barreled locally convex space which has certain order conditions. In this process of the extension we also give some useful properties for vector measures with values in dual spaces.
This paper studies the topological and connectivity properties of the level sets of additive Brownian motion. More precisely, for each excursion set of this process from a fixed level, we give an explicit construction of a closed Jordan curve contained in the boundary of this excursion set, and in particular, in the level set of this process.
The incidence relations between a Pfaffian system and the characteristic system of its first derived system lead to obtain a characterization of Pfaffian systems with derived length one. Also, for flag systems, several properties are studied. In particular, an intrinsic proof of a result which determines the class of a system and of all the derived systems is given.
In this paper we consider the problem of global Gevrey and analytic regularity for a class of partial differential operators on a torus in the form of a sum of squares of vector fields, which may not satisfy the bracket condition. We show that these operators are globally Gevrey or analytic hypoelliptic on the torus if and only if the coefficients satisfy certain Diophantine approximation properties.
In this paper we consider the regularity of solutions of semilinear differential equations principal parts of which consist of linear polynomial operators constructed from real vector fields. Based on the study of fine properties of the principal linear parts we then obtain the regularity of solutions of the nonlinear equations. Some results obtained in this article are also new in the frame of linear theory.
We prove that fully residually free groups have the Howson property, that is the intersection of any two finitely generated subgroups in such a group is again finitely generated. We also establish some commensurability properties for finitely generated fully residually free groups which are similar to those of free groups. Finally we prove that for a finitely generated fully residually free group the membership problem is solvable with respect to any finitely generated subgroup.
This paper is concerned with the time discretization of nonlinear evolution equations. We work in an abstract Banach space setting of analytic semigroups that covers fully nonlinear parabolic initial-boundary value problems with smooth coefficients. We prove convergence of variable stepsize backward Euler discretizations under various smoothness assumptions on the exact solution. We further show that the geometric properties near a hyperbolic equilibrium are well captured by the discretization. A numerical example is given.
In this short note we suggest a refinement for the definition of viscosity solutions for parabolic equations. The new version of the definition is equivalent to the usual one and it better adapts to the properties of parabolic equations. The basic idea is to determine the admissibility of a test function based on its behavior prior to the given moment of time and ignore what happens at times after that.