We prove global weighted Strichartz estimates for radial solutions of linear Schrödinger equation on a class of rotationally symmetric noncompact manifolds, generalizing the known results on hyperbolic and Damek-Ricci spaces. This yields classical Strichartz estimates with a larger class of exponents than in the Euclidian case and improvements for the scattering theory. The manifolds, whose vol...

In spite of many efforts over the past 50 years, the irreducible representations of the Lie algebra of a simple algebraic group over a field of prime characteristic are poorly understood. Recent work on quantum groups at a root of unity has provided new impetus for the subject. This article surveys what has been done and what remains to be done.

Soft constraints have proved to be a versatile tool for the specification and implementation of decision making in adaptive systems. A plethora of formalisms have been devised to capture different notions of preference. Wirsing et al. have proposed partial valuation structures as a unifying algebraic structure for several soft constraint formalisms, including quantitative and qualitative ones, ...

This article concerns the over-determined system of partial differential equations “ k f ”

Consider the normalized partial sums of a real-valued function F of a Markov chain,

We have studied factor VII activation by measuring the ratio of factor VII clotting to coupled amidolytic activity (VIIc/VIIam) and cleavage of 125I-factor VII. In purified systems, a low concentration of Xa or a higher concentration of IXa rapidly activated 125I-factor VII, yielding a VIIc/VIIam ratio of 25 and similar gel profiles of heavy and light chain peaks of VIIa. On further incubation,...

A method of “algebraic estimates” is developed, and used to study the stability properties of integrals of the form ∫ B |f(z)| −δdV , under small deformations of the function f . The estimates are described in terms of a stratification of the space of functions {R(z) = |P (z)|ε/|Q(z)|δ} by algebraic varieties, on each of which the size of the integral of R(z) is given by an explicit algebraic e...

Let f be a computable function from finite sequences of 0’s and 1’s to real numbers. We prove that strong f -randomness implies strong f randomness relative to a PA-degree. We also prove: if X is strongly f -random and Turing reducible to Y where Y is Martin-Löf random relative to Z, then X is strongly f -random relative to Z. In addition, we prove analogous propagation results for other notion...

Notation. The main objects of this paper are n-tuples y = (y1, . . . , yn) of real numbers viewed as linear forms, i.e. as row vectors. In what follows, y will always mean a row vector, and we will be interested in values of a linear form given by y at integer points q = (q1, . . . , qn) T , the latter being a column vector. Thus yq will stand for y1q1 + · · ·+ ynqn. Hopefully it will cause no ...

In this paper we construct examples of uniformly quasiregular (uqr) mappings. These provide counterexamples for a rigidity conjecture in quasiregular dynamics. It states that a closed manifold of dimension at least three, which admits a branched uqr mapping, is quasiconformally equivalent to an ordinary sphere Sn. 1. Statements and results In this paper we construct examples of a certain type o...