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showing 10 items of 257 documents
Applications to Algebraic Cycles: Nori's Theorem
2017
Deligne cohomology is a tool that makes it possible to unify the study of cycles through an object that classifies extensions of ( p , p )-cycles by points in the p -th intermediate Jacobian (which is the target of the Abel–Jacobi map on cycles of codimension p ). This is treated in Section 10.1 with applications to normal functions. Before giving the proof of Nori's theorem in Section 10.6, we need some results from mixed Hodge theory. These are proven in Section 10.2 where we also state different variants of the theorem. Sections 10.3 and 10.4 treat a localto- global principle and an extension of the method of Jacobian representations of cohomology which are both essential for the proof. …
Optional Sampling Theorems
2020
In Chapter 9 we saw that martingales are transformed into martingales if we apply certain admissible gambling strategies. In this chapter, we establish a similar stability property for martingales that are stopped at a random time (optional sampling and optional stopping). In order also to obtain these results for submartingales and supermartingales, in the first section, we start with a decomposition theorem for adapted processes. We show the optional sampling and optional stopping theorems in the second section. The chapter finishes with the investigation of random stopping times with an infinite time horizon.
Well-behaved *-Representations
2002
This chapter is devoted to the study of the so-called well-behaved *-representations of (partial) *-algebras. Actually one may define are two notions of well-behavedness and we will discuss the relation between them. These notions are introduced in order to avoid pathologies which may arise for general *-representations and to select “nice” representations, which may have a richer theory. In Section 8.1, we construct a class {π p } of *-representations, starting from an unbounded C*-seminorm p and we define nice *-representations in {π p }, called well-behaved. We also characterize their existence. In Section 8.2, we introduce the well-behaved *-representations associated with a compatible …
Review of Classical Non-self-adjoint Spectral Theory
2019
The first section of this chapter deals with Fredholm theory in the spirit of Appendix A in Helffer and Sjostrand (Mm Soc Math Fr (NS) 24–25:1–228, 1986), see also an appendix in Melin and Sjostrand (Asterique 284:181–244, 2003) and Sjostrand and Zworski (Ann Inst Fourier 57:2095–2141, 2007). The remaining sections give a brief account of the very beautiful classical theory of non-self-adjoint operators, taken from a section in Sjostrand (Lectures on Resonances) which is a brief account of parts of the classical book by Gohberg and Krein (Introduction to the Theory of Linear Non-Selfadjoint Operators. Translations of Mathematical Monographs, vol 18. AMS, Providence, 1969).
Die Schmieghyperebenen an die Veronese-Mannigfaltigkeit bei Beliebiger Charakteristik
1982
By means of linear algebra a base-free definition of a Veronese variety V(n,r) is given and also an illuminating description of its osculating primes from which can be deduced in a general form and without difficulty the phenomena of degeneracy in case of small characteristics. (Instance best known: For characteristic 2 all tangents of a conic are confluent.) The last section investigates special problems for the V(1,r) in characteristic p: So the osculating primes of a V(1,p) intersect its node in a V(1,p-2). Furthermore it becomes clearer why for 2<r<¦K¦−1 no elation can fix a V(1,r) (in case of a perfect field).
General Theory: Algebraic Point of View
2009
It is convenient to divide our study of pip-spaces into two stages. In the first one, we consider only the algebraic aspects. That is, we explore the structure generated by a linear compatibility relation on a vector space V , as introduced in Section I.2, without any other ingredient. This will lead us to another equivalent formulation, in terms of particular coverings of V by families of subspaces. This first approach, purely algebraic, is the subject matter of the present chapter. Then, in a second stage, we introduce topologies on the so-called assaying subspaces \(\{V_r \}\). Indeed, as already mentioned in Section I.2, assuming the partial inner product to be nondegenerate implies tha…
A RAPID METHOD FOR CALCULATING THE TRANSVERSAL STRAIN IN THE MOIRE TECHNIQUE ALONG SECTIONS OF SYMMETRY
1970
An approximate rapid method is described for calculating in the moire technique the transversal strain directly from the longitudinal strain distribution across sections of symmetry. The method is based on evaluation of the load transmitted through the section and is corroborated by two examples.
Triangular irreducibility of congruences in quasivarieties
2014
Certain forms of irreducibility as well as of equational definability of relative congruences in quasivarieties are investigated. For any integer \({m \geqslant 3}\) and a quasivariety Q, the notion of an m-triangularily meet-irreducible Q-congruence in the algebras of Q is defined. In Section 2, some characterizations of finitely generated quasivarieties involving this notion are provided. Section 3 deals with quasivarieties with equationally definable m-triangular meets of relatively principal congruences. References to finitely based quasivarieties and varieties are discussed.
Some Special Foliations
2014
In this chapter we study two classes of ubiquitous foliations: Riccati foliations and turbulent foliations. A section will also be devoted to a very special foliation, which will play an important role in the minimal model theory.
Explanation of Notation
1991
For the presentation of all 288 polarization observables in the next section we have adopted the following scheme. Each observable is a function of the angle and the photon energy. With respect to the latter we have chosen five energies, namely 4.5 MeV, the maximum of the total cross section, 20 MeV, 60 MeV, 100 MeV, and 140 MeV. For each observable and for each of these energies we have studied the following topics: (i) The influence of meson exchange currents (MEC), isobar configurations (IC) and relativistic corrections (RC). Since the various potential models give qualitatively very similar results, we use in this case the r-space version of the Bonn model (OBEPR). (ii) The contribution…