Dependence relation in pregeometries

The aim of this paper is to set a foundation to separate geometric model theory from model theory. Our goal is to explore the possibility to extend results from geometric model theory to non first order logic (e.g. ). We introduce a dependence relation between subsets of a pregeometry and show that it satisfies all the formal properties that forking satisfies in simple first order theories. This happens when one is trying to lift forking to nonelementary classes, in contexts where there exist pregeometries but not necessarily a well-behaved dependence relation (see for example [HySh]). We use these to reproduce S. Buechler's characterization of local modularity in general. These results are used by Lessmann to prove an abstract group configuration theorem in [Le2]. Received February 2, 1999; accepted in final form April 30, 2000.     

The cluster index of regularly varying sequences with applications to limit theory for functions of multivariate Markov chains

We introduce the cluster index of a multivariate stationary sequence and characterize the index in terms of the spectral tail process. This index plays a major role in limit theory for partial sums of sequences. We illustrate the use of the cluster index by characterizing infinite variance stable limit distributions and precise large deviation results for sums of multivariate functions acting on a stationary Markov chain under a drift condition.     

Delandtsheer–Doyen parameters for block-transitive point-imprimitive 2-designs

Designs, Codes and Cryptography - Delandtsheer and Doyen bounded, in terms of the block size, the number of points of a point-imprimitive, block-transitive 2-design. To do this they introduced two...     

Femto/Picosecond Transient Absorption Study of Ring-Opening Dynamics in Perimidinespirocyclohexadienone Derivatives

The ring-opening dynamics of perimidinespirocyclohexadienone derivatives has been studied by means of time-resolved spectroscopy in cyclohexane and acetonitrile solutions. It has been established that molecular isomerisation leading to the open isomer occurs against the background of the S₁-S₀ internal conversion of the cyclic form. In addition, the features of the observed spectral changes in the cyclohexane made it possible to distinguish formation of the photoproduct in the T₁ state and its relaxation via intersystem crossing to the singlet ground state. The corresponding assignments for transient absorption bands were performed on the basis of TD-DFT calculations.     

Oja centers and centers of gravity

Oja depth (Oja 1983) is a generalization of the median to multivariate data that measures the centrality of a point x with respect to a set S of points in such a way that points with smaller Oja depth are more central with respect to S. Two relationships involving Oja depth and centers of mass are presented. The first is a form of Centerpoint Theorem which shows that the center of mass of the convex hull of a point set has low Oja depth. The second is an approximation result which shows that the center of mass of a point set approximates a point of minimum Oja depth.     

The kernel of the neumann operator for a strictly diffractive analytic problem

We consider p a partial differential operator of order 2 and Rⁿ= ω⁺ ∪ ?ω ∪ ω^? a partition of Rⁿ , such that (p, ω⁺) admits a strictly diffractive point (in the sense of Friedlander and Melrose). We compute the trace and the trace of the normal derivative on ?ω of the solution u of the diffraction problem pu= 0 in ω⁺ u satisfying a mixed boundary condition on ?ω, ?ω analytic. That is done using the construction by Lebeau of a Gevrey 3 parametrix in the neighborhood of the strictly diffractive point.

This result generalizes, for a mixed boundary condition, the Gevrey 3 propogation result of Lebeau. We use this result to compute the leading term in the shadow region of the diffracted wave outside a strictly convex analytical obstacle with a mixed boundary condition and a given incoming wave.     

Ramanujan’s Master Theorem

S. Ramanujan introduced a technique, known as Ramanujan??s Master Theorem, which provides an explicit expression for the Mellin transform of a function in terms of the analytic continuation of its Taylor coefficients. The history and proof of this result are reviewed, and a variety of applications is presented. Finally, a multi-dimensional extension of Ramanujan??s Master Theorem is discussed.