Search results for "Logarithm"
showing 10 items of 182 documents
The Two Loop Crossed Ladder Vertex Diagram with Two Massive Exchanges
2008
We compute the (three) master integrals for the crossed ladder diagram with two exchanged quanta of equal mass. The differential equations obeyed by the master integrals are used to generate power series expansions centered around all the singular (plus some regular) points, which are then matched numerically with high accuracy. The expansions allow a fast and precise numerical calculation of the three master integrals (better than 15 digits with less than 30 terms in the whole real axis). A conspicuous relation with the equal-mass sunrise in two dimensions is found. Comparison with a previous large momentum expansion is made finding complete agreement.
The Crane Beach Conjecture
2002
A language L over an alphabet A is said to have a neutral letter if there is a letter e/spl isin/A such that inserting or deleting e's from any word in A* does not change its membership (or non-membership) in L. The presence of a neutral letter affects the definability of a language in first-order logic. It was conjectured that it renders all numerical predicates apart from the order predicate useless, i.e., that if a language L with a neutral letter is not definable in first-order logic with linear order then it is not definable in first-order. Logic with any set /spl Nscr/ of numerical predicates. We investigate this conjecture in detail, showing that it fails already for /spl Nscr/={+, *…
Counting Zeros of Holomorphic Functions
2019
In this chapter we will generalize Proposition 3.4.6 of Hager about counting the zeros of holomorphic functions of exponential growth. In Hager and Sjostrand (Math Ann 342(1):177–243, 2008. http://arxiv.org/abs/math/0601381) we obtained such a generalization, by weakening the regularity assumptions on the functions ϕ. However, due to some logarithmic losses, we were not quite able to recover Hager’s original result, and we still had a fixed domain Γ with smooth boundary.
On stability of logarithmic tangent sheaves. Symmetric and generic determinants
2021
We prove stability of logarithmic tangent sheaves of singular hypersurfaces D of the projective space with constraints on the dimension and degree of the singularities of D. As main application, we prove that determinants and symmetric determinants have stable logarithmic tangent sheaves and we describe an open dense piece of the associated moduli space.
Logarithmic bundles of deformed Weyl arrangements of type $A_2$
2016
We consider deformations of the Weyl arrangement of type $A_2$, which include the extended Shi and Catalan arrangements. These last ones are well-known to be free. We study their sheaves of logarithmic vector fields in all other cases, and show that they are Steiner bundles. Also, we determine explicitly their unstable lines. As a corollary, some counter-examples to the shift isomorphism problem are given.
Lipschitz continuity of Cheeger-harmonic functions in metric measure spaces
2003
Abstract We use the heat equation to establish the Lipschitz continuity of Cheeger-harmonic functions in certain metric spaces. The metric spaces under consideration are those that are endowed with a doubling measure supporting a (1,2)-Poincare inequality and in addition supporting a corresponding Sobolev–Poincare-type inequality for the modification of the measure obtained via the heat kernel. Examples are given to illustrate the necessity of our assumptions on these spaces. We also provide an example to show that in the general setting the best possible regularity for the Cheeger-harmonic functions is Lipschitz continuity.
Global 1-Forms and Vector Fields
2014
In this chapter we recall some fundamental facts concerning holomorphic 1-forms on compact surfaces: Albanese morphism, Castelnuovo–de Franchis Lemma, Bogomolov Lemma. We also discuss the logarithmic case, which is extremely useful in the study of foliations with an invariant curve. Finally we recall the classification of holomorphic vector fields on compact surfaces. All of this is very classical and can be found, for instance, in [2, Chapter IV] and 24, 35].
The Fatou coordinate for parabolic Dulac germs
2017
We study the class of parabolic Dulac germs of hyperbolic polycycles. For such germs we give a constructive proof of the existence of a unique Fatou coordinate, admitting an asymptotic expansion in the power-iterated log scale.
Classification of Congeneric and QSAR of Homologous Antileukemic S–Alkylcysteine Ketones
2021
Based on a set of six vector properties, the partial correlation diagram is calculated for a set of 28 S-alkylcysteine diazomethyl- and chloromethyl-ketone derivatives. Those with the greatest antileukemic activity in the same class correspond to high partial correlations. A periodic classification is performed based on information entropy. The first four characteristics denote the group, and the last two indicate the period. Compounds in the same period and, especially, group present similar properties. The most active substances are situated at the bottom right. Nine classes are distinguished. The principal component analysis of the homologous compounds shows five subclasses included in t…
Continuous variable tangle, monogamy inequality, and entanglement sharing in Gaussian states of continuous variable systems
2004
For continuous-variable systems, we introduce a measure of entanglement, the continuous variable tangle ({\em contangle}), with the purpose of quantifying the distributed (shared) entanglement in multimode, multipartite Gaussian states. This is achieved by a proper convex roof extension of the squared logarithmic negativity. We prove that the contangle satisfies the Coffman-Kundu-Wootters monogamy inequality in all three--mode Gaussian states, and in all fully symmetric $N$--mode Gaussian states, for arbitrary $N$. For three--mode pure states we prove that the residual entanglement is a genuine tripartite entanglement monotone under Gaussian local operations and classical communication. We …