Search results for " Classical"
showing 10 items of 301 documents
A function whose graph has positive doubling measure
2014
We show that a doubling measure on the plane can give positive measure to the graph of a continuous function. This answers a question by Wang, Wen and Wen. Moreover we show that the doubling constant of the measure can be chosen to be arbitrarily close to the doubling constant of the Lebesgue measure.
Planar maps whose second iterate has a unique fixed point
2007
Let a>0, F: R^2 -> R^2 be a differentiable (not necessarily C^1) map and Spec(F) be the set of (complex) eigenvalues of the derivative F'(p) when p varies in R^2. (a) If Spec(F) is disjoint of the interval [1,1+a[, then Fix(F) has at most one element, where Fix(F) denotes the set of fixed points of F. (b) If Spec(F) is disjoint of the real line R, then Fix(F^2) has at most one element. (c) If F is a C^1 map and, for all p belonging to R^2, the derivative F'(p) is neither a homothety nor has simple real eigenvalues, then Fix(F^2) has at most one element, provided that Spec(F) is disjoint of either (c1) the union of the number 0 with the intervals ]-\infty, -1] and [1,\infty[, or (c2) t…
Resonance between Cantor sets
2007
Let $C_a$ be the central Cantor set obtained by removing a central interval of length $1-2a$ from the unit interval, and continuing this process inductively on each of the remaining two intervals. We prove that if $\log b/\log a$ is irrational, then \[ \dim(C_a+C_b) = \min(\dim(C_a) + \dim(C_b),1), \] where $\dim$ is Hausdorff dimension. More generally, given two self-similar sets $K,K'$ in $\RR$ and a scaling parameter $s>0$, if the dimension of the arithmetic sum $K+sK'$ is strictly smaller than $\dim(K)+\dim(K') \le 1$ (``geometric resonance''), then there exists $r<1$ such that all contraction ratios of the similitudes defining $K$ and $K'$ are powers of $r$ (``algebraic resonance…
Unitary Groups Acting on Grassmannians Associated with a Quadratic Extension of Fields
2006
Let (V, H) be an anisotropic Hermitian space of finite dimension over the algebraic closure of a real closed field K. We determine the orbits of the group of isometries of (V, H) in the set of K-subspaces of V . Throughout the paper K denotes a real closed field and K its algebraic closure. Then it is well known (see, for example, [4, Chapter 2], [23]; see also [8]) that K = K(i) with i = √−1. Also we let (V,H) be an anisotropic Hermitian space (with respect to the involution underlying the quadratic field extension K/K) of finite dimension n over K. In this context we consider the natural action of the unitary group U = U(V,H) of isometries of (V,H) on the set Xd of all ddimensional K-subs…
Dimensions of random affine code tree fractals
2014
We calculate the almost sure Hausdorff dimension for a general class of random affine planar code tree fractals. The set of probability measures describing the randomness includes natural measures in random $V$-variable and homogeneous Markov constructions.
The Action of the Symplectic Group Associated with a Quadratic Extension of Fields
1999
Abstract Given a quadratic extension L/K of fields and a regular alternating space (V, f) of finite dimension over L, we classify K-subspaces of V which do not split into the orthogonal sum of two proper K-subspaces. This allows one to determine the orbits of the group SpL(V, f) in the set of K-subspaces of V.
Cross-reinstatement between 3,4-methylenedioxypyrovalerone (MDPV) and cocaine using conditioned place preference.
2019
Abstract 3,4-Methylenedioxypyrovalerone (MDPV) is a new psychoactive substance (NPS) considered to be a cocaine-like psychostimulant. The substitution of an established illicit drug as cocaine with an NPS is a pattern of use reported among drug users. The aim of this study was to investigate the relationship between cocaine and MDPV in the reinstatement of the conditioned place preference (CPP) paradigm, in order to establish whether there is cross-reinstatement between the two psychostimulants. Four experimental groups of male OF1 mice were subjected to the CPP paradigm: MDPV-MDPV, Cocaine-Cocaine, Cocaine-MDPV, and MDPV-Cocaine. The first drug refers to the substance with which the animal…
Structure of distributions generated by the scenery flow
2015
We expand the ergodic theory developed by Furstenberg and Hochman on dynamical systems that are obtained from magnifications of measures. We prove that any fractal distribution in the sense of Hochman is generated by a uniformly scaling measure, which provides a converse to a regularity theorem on the structure of distributions generated by the scenery flow. We further show that the collection of fractal distributions is closed under the weak topology and, moreover, is a Poulsen simplex, that is, extremal points are dense. We apply these to show that a Baire generic measure is as far as possible from being uniformly scaling: at almost all points, it has all fractal distributions as tangent …
Adam Smith on Monopoly Theory. Making good a lacuna
2014
This article analyses Adam Smith's views on monopoly by focusing on Book IV and V of The Wealth of Nations. It argues that the majority of scholars have assessed Smith's analysis of monopoly starting from premises different from those, actually though implicitly, used by Smith. We show that Smith makes use of the word 'monopoly' to refer to a heterogeneous collection of market outcomes, besides that of a single seller market, and that Smith's account of monopolists' behaviour is richer than that provided by later theorists. We also show that Smith was aware of the growth-retarding effect of monopoly and urged State regulation. © 2014 Scottish Economic Society.
Allusioni plautine ne «Gli ultimi giorni di Pompei» di Edward Bulwer-Lytton
2021
This note presents the summary and the analysis of citations, allusions and references to Plautus’s comedies in «The Last Days of Pompeii» by Edward Bulwer-Lytton. From the analysis here conducted it emerges that the English writer used Plautus for precise purposes, for ironic and satirical resolutions, appropriately contextualizing the allusions to Plautus within the plot of the novel.