Search results for "topology."

Basic Definitions and Facts

2001

Symbol is treated here as a primitive entity as point or line in geometry. Let Con = {f α : α < β} be a well-ordered set of symbols called a language type. β is an ordinal number. The elements of the above set are called connectives. To each connective f α a natural number α(α) ∈ w called the rank of f α or the arity of f α is assigned. The arity α(α) defines the number of arguments of f α . Thus we speak of nullary, unary, or binary connectives, etc. In the sequel Con is assumed to be fixed but arbitrary.

Counting degree sequences of spanning trees in bipartite graphs: A graph‐theoretic proof

2019

Normed vector spaces consisting of classes of convex sets

1965

Compactness of a conformal boundary of the Euclidean unit ball

2011

We study conformal metrics d‰ on the Euclidean unit ball B n : We assume that either the density ‰ associated with the metric d‰ satisfies a logarithmic volume growth condition for small balls or that ‰ satisfies a Harnack inequality and a suitable sub-Euclidean volume growth condition. We prove that the ‰-boundary @‰ B n is homeomorphic to S ni1 if and only if @‰ B n is compact. In the planar case, the compactness of @‰ B 2 is further equivalent to local connectivity of the ‰-boundary together with the boundedness of (B 2 ;d‰):

Thin Points of Brownian Motion Intersection Local Times

2005

Let \(\ell \) be the projected intersection local time of two independent Brownian paths in \(\mathbb{R}^d \) for d = 2, 3. We determine the lower tail of the random variable \(\ell \)(B(0, 1)), where B(0, 1) is the unit ball. The answer is given in terms of intersection exponents, which are explicitly known in the case of planar Brownian motion. We use this result to obtain the multifractal spectrum, or spectrum of thin points, for the intersection local times.

The index of stable critical points

2002

Abstract In this paper we show that in dimension greater or equal than 3 the index of a stable critical point can be any integer. More concretely, given any k∈ Z and n⩾3 we construct a C ∞ vector field on R n with a unique critical point which is stable (in positive and negative time) and has index equal to k. This result extends previous ones on the index of stable critical points.

Compensation of the impact of low-cost manufacturing techniques in the design of E-plane multiport waveguide junctions

2016

In this work, a full-wave tool for the accurate analysis and design of compensated E-plane multiport junctions is proposed. The implemented tool is capable of evaluating the undesired effects related to the use of low-cost manufacturing techniques, which are mostly due to the introduction of rounded corners in the cross section of the rectangular waveguides of the device. The obtained results show that, although stringent mechanical effects are imposed, it is possible to compensate for the impact of the cited low-cost manufacturing techniques by redesigning the matching elements considered in the original device. Several new designs concerning a great variety of E-plane components (such as …

Rigorous Multimode Equivalent Network Representation of Multilayer Planar Circuits

2018

The objective of this paper is to extend the use of the Multimode Equivalent Network formulation, originally developed to analyze waveguide junctions, to the analysis of planar circuits that include arbitrary rectangular printed, zero thickness metallizations together with internal and external ports in the transverse plane. The theoretical derivations lead to an accurate and computationally efficient tool for the analysis of boxed, multilayer microwave printed circuits. In addition to theory, the tool developed is used here to analyze two practical examples: a dual-bandpass and a 4-pole bandpass boxed microstrip filters. Good agreement with respect to commercial software tools and measurem…

Boundary communication: how smartphone use after hours is associated with work-life conflict and organizational identification

2020

This study investigates how boundary communication mediates the effects of smartphone use for work after hours on work-life conflict and organizational identification. It draws upon boundary theory, work-family border theory, and a structurational view of organizational identification. The research site was a large Scandinavian company operating in the telecommunications industry, with 367 employees responding to a survey at two time periods. In contrast to many studies, the use of information and communication technologies (here, smartphones) for after-hours work was not associated with work-life conflict, but was positively associated with organizational identification. However, communica…

A comparison theorem for the mean exit time from a domain in a K�hler manifold

1992

Let M be a Kahler manifold with Ricci and antiholomorphic Ricci curvature bounded from below. Let ω be a domain in M with some bounds on the mean and JN-mean curvatures of its boundary ∂ω. The main result of this paper is a comparison theorem between the Mean Exit Time function defined on ω and the Mean Exit Time from a geodesic ball of the complex projective space ℂℙ n (λ) which involves a characterization of the geodesic balls among the domain ω. In order to achieve this, we prove a comparison theorem for the mean curvatures of hypersurfaces parallel to the boundary of ω, using the Index Lemma for Submanifolds.