Search results for "Compact"
showing 10 items of 531 documents
Pressure solution compaction of sodium chlorate and implications for pressure solution in NaCl
1999
Sodium chloride (NaCl) has been extensively used as a material to develop, test and improve pressure solution (PS) rock deformation models. However, unlike silicate and carbonate rocks, NaCl can deform plastically at very low stresses (0.5 MPa). This could mean that NaCl is less suitable for use as an analogue for rocks that do not deform plastically at conditions where PS is important. In order to test the reliability of NaCl as a rock analogue, we carried out a series of uniaxial compaction experiments on sodium chlorate (NaClO3) at room pressure and temperature (P‐T) conditions and applied effective stresses of 2.4 and 5.0 Mpa. NaClO3 is a very soluble, elastic‐brittle salt, that cannot …
Quasihyperbolic boundary condition: Compactness of the inner boundary
2011
We prove that if a metric space satisfies a suitable growth condition in the quasihyperbolic metric and the Gehring–Hayman theorem in the original metric, then the inner boundary of the space is homeomorphic to the Gromov boundary. Thus, the inner boundary is compact. peerReviewed
Metric Lie groups admitting dilations
2019
We consider left-invariant distances $d$ on a Lie group $G$ with the property that there exists a multiplicative one-parameter group of Lie automorphisms $(0, \infty)\rightarrow\mathtt{Aut}(G)$, $\lambda\mapsto\delta_\lambda$, so that $ d(\delta_\lambda x,\delta_\lambda y) = \lambda d(x,y)$, for all $x,y\in G$ and all $\lambda>0$. First, we show that all such distances are admissible, that is, they induce the manifold topology. Second, we characterize multiplicative one-parameter groups of Lie automorphisms that are dilations for some left-invariant distance in terms of algebraic properties of their infinitesimal generator. Third, we show that an admissible left-invariant distance on a Lie …
The probability that $x$ and $y$ commute in a compact group
2010
We show that a compact group $G$ has finite conjugacy classes, i.e., is an FC-group if and only if its center $Z(G)$ is open if and only if its commutator subgroup $G'$ is finite. Let $d(G)$ denote the Haar measure of the set of all pairs $(x,y)$ in $G \times G$ for which $[x,y] = 1$; this, formally, is the probability that two randomly picked elements commute. We prove that $d(G)$ is always rational and that it is positive if and only if $G$ is an extension of an FC-group by a finite group. This entails that $G$ is abelian by finite. The proofs involve measure theory, transformation groups, Lie theory of arbitrary compact groups, and representation theory of compact groups. Examples and re…
The probability that $x^m$ and $y^n$ commute in a compact group
2013
In a recent article [K.H. Hofmann and F.G. Russo, The probability that $x$ and $y$ commute in a compact group, Math. Proc. Cambridge Phil. Soc., to appear] we calculated for a compact group $G$ the probability $d(G)$ that two randomly picked elements $x, y\in G$ satisfy $xy=yx$, and we discussed the remarkable consequences on the structure of $G$ which follow from the assumption that $d(G)$ is positive. In this note we consider two natural numbers $m$ and $n$ and the probabilty $d_{m,n}(G)$ that for two randomly selected elements $x, y\in G$ the relation $x^my^n=y^nx^m$ holds. The situation is more complicated whenever $n,m>1$. If $G$ is a compact Lie group and if its identity component $G_…
Finding Invariants of Group Actions on Function Spaces, a General Methodology from Non-Abelian Harmonic Analysis
2008
In this paper, we describe a general method using the abstract non-Abelian Fourier transform to construct “rich” invariants of group actions on functional spaces.
The Obstacle Problem in a Non-Linear Potential Theory
1988
M. Brelot gave rise to the concept harmonic space when he extended classical potential theory on ℝn to an axiomatic system on a locally compact space. I have recently constructed1 a non-linear harmonic space by dropping the assumption that the sum of two harmonic functions is harmonic and considering some other axioms instead. This approach has its origin in the work of O. Martio, P. Lindqvist and S. Granlund2,3,4, who have developed a non-linear potential theory on ℝn connected with variational integrals of the type ∫ F(x,∇u(x)) dm(x), where F(x, h) ≈ |h|p.
THE NONCOMPACTION OF THE LEFT VENTRICULAR MYOCARDIUM: OUR PEDIATRIC EXPERIENCE
2007
OBJECTIVES: The noncompaction of the left ventricular myocardium is a rare congenital heart disease, characterized by an excessive prominence of trabecular meshwork, spaced out by deep intertrabecular recesses, consequent to the arrest of the normal myocardium embryogenesis. Although there are numerous descriptions, the physiopathological effects of the structural alterations, just like the clinical spectrum and the evolution of the disease, are not totally clarified. In the present study, we have evaluated the natural history of the disease, the familial incidence and the alterations of the systolic and diastolic function. METHODS: We collected a series of 21 young patients who were affect…
INSUFFICIENZA CARDIACA ACUTA E CARDIOMIOPATIE: UN CASO CLINICO
2007
Isolated noncompaction of left ventricular myocardium is a rare congenital heart disease, characterized by an excessive prominence of trabecular meshwork, spaced out by deep intertrabecular recesses, consequent to the arrest of the normal myocardial embryogenesis. Although there are numerous descriptions, the pathophysiological effects of the structural alterations, like the clinical spectrum and the evolution of the disease, are not fully clarified. In this paper we evaluated the natural history of the disease, the family incidence and the alterations of the systolic and diastolic function. An interesting case report is described concerning a patient affected by noncompaction and atrial fi…
Ville et fortifications : de l'héritage à la production du territoire urbain
2015
A large number of french cities host military historical edifices (citadels, barracks, bastions, defensive walls, etc.). Although their initial defensive functions have been lost over time, these edifices remain deeply rooted in the urban fabric of their host cities. They continue exerting an impact on these cities’ urban morphology and modern-time functions as well as the way in which the concept of city is understood. Cities nowadays face some new challenges,the increasing awareness of urban sprawl and its consequences, coupled with an urge to promote a renewed and sustainable urbanism, invites us to adopt new approaches to study urban fortifications. In addition to their symbolic aspect,…