Search results for "dimensional space"
showing 10 items of 20 documents
On i-topological spaces: generalization of the concept of a topological space via ideals
2006
[EN] The aim of this paper is to generalize the structure of a topological space, preserving its certain topological properties. The main idea is to consider the union and intersection of sets modulo “small” sets which are defined via ideals. Developing the concept of an i-topological space and studying structures with compatible ideals, we are concerned to clarify the necessary and sufficient conditions for a new space to be homeomorphic, in some certain sense, to a topological space.
Sufficient conditions for coincidence in ℓ1 multifacility location problems
1997
We consider the problem of finding the optimal way of locating a finite number of facilities in a finite dimensional space, in order to minimize a weighted sum of the distances between these and other pre-existent facilities which are already positioned. We study the specific case where distance is measured in the @?"1, giving a new sufficient condition for identifying groups of facilities whose position will coincide at optimality.
Smoothness spaces of higher order on lower dimensional subsets of the Euclidean space
2015
We study Sobolev type spaces defined in terms of sharp maximal functions on Ahlfors regular subsets of R n and the relation between these spaces and traces of classical Sobolev spaces. This extends in a certain way the results of Shvartsman (20) to the case of lower dimensional subsets of the Euclidean space.
Positioning in a flat two-dimensional space-time: the delay master equation
2010
The basic theory on relativistic positioning systems in a two-dimensional space-time has been presented in two previous papers [Phys. Rev. D {\bf 73}, 084017 (2006); {\bf 74}, 104003 (2006)], where the possibility of making relativistic gravimetry with these systems has been analyzed by considering specific examples. Here we study generic relativistic positioning systems in the Minkowski plane. We analyze the information that can be obtained from the data received by a user of the positioning system. We show that the accelerations of the emitters and of the user along their trajectories are determined by the sole knowledge of the emitter positioning data and of the acceleration of only one …
Numerical Study of the semiclassical limit of the Davey-Stewartson II equations
2014
We present the first detailed numerical study of the semiclassical limit of the Davey–Stewartson II equations both for the focusing and the defocusing variant. We concentrate on rapidly decreasing initial data with a single hump. The formal limit of these equations for vanishing semiclassical parameter , the semiclassical equations, is numerically integrated up to the formation of a shock. The use of parallelized algorithms allows one to determine the critical time tc and the critical solution for these 2 + 1-dimensional shocks. It is shown that the solutions generically break in isolated points similarly to the case of the 1 + 1-dimensional cubic nonlinear Schrodinger equation, i.e., cubic…
Positioning in a flat two-dimensional space-time
2008
The basic theory on relativistic positioning systems in a two-dimensional space-time and the analysis of the possibility of making relativistic gravimetry with these systems have been presented elsewhere [Phys. Rev. D 73 , 084017 (2006); Phys. Rev. D 74 , 104003 (2006)]. Here we summarize these results and we outline new issues on the relativistic positioning systems in Minkowski plane. We point out that the accelerations of the emitters and of the user along their trajectories are determined by the sole knowledge of the emitter positioning data and of the acceleration of only one of the emitters and only during a light echo interval.
Parallel Computing for the study of the focusing Davey-Stewartson II equation in semiclassical limit
2012
The asymptotic description of the semiclassical limit of nonlinear Schrödinger equations is a major challenge with so far only scattered results in 1 + 1 dimensions. In this limit, solutions to the NLS equations can have zones of rapid modulated oscillations or blow up. We numerically study in this work the Davey-Stewartson system, a 2 + 1 dimensional nonlinear Schrödinger equation with a nonlocal term, by using parallel computing. This leads to the first results on the semiclassical limit for the Davey-Stewartson equations.
Subjective Refraction Techniques in the Frame of the Three-Dimensional Dioptric Space
2001
A novel heuristic approach to the well-known representation of the dioptric power in a three-dimensional space is presented. It is shown how this theoretical framework is ideal for discussing the principles of several subjective refraction methods. In particular, this formalism is used to justify the stenopaic slit refraction, the Barnes subjective refraction technique, and the Jackson cross-cylinder procedure. In view of this analysis, some modifications to the traditional procedures are proposed.
Positioning with stationary emitters in a two-dimensional space-time
2006
The basic elements of the relativistic positioning systems in a two-dimensional space-time have been introduced in a previous work [Phys. Rev. D {\bf 73}, 084017 (2006)] where geodesic positioning systems, constituted by two geodesic emitters, have been considered in a flat space-time. Here, we want to show in what precise senses positioning systems allow to make {\em relativistic gravimetry}. For this purpose, we consider stationary positioning systems, constituted by two uniformly accelerated emitters separated by a constant distance, in two different situations: absence of gravitational field (Minkowski plane) and presence of a gravitational mass (Schwarzschild plane). The physical coord…
A simple microsuperspace model in 2 + 1 spacetime dimensions
1992
Abstract We quantize the closed Friedmann model in 2 + 1 spacetime dimensions using euclidean path-integral approach and a simple microsuperspace model. A relationship between integration measure and operator ordering in the Wheeler-DeWitt equation is found within our model. Solutions to the Wheeler-DeWitt equation are exactly reproduced from the path integral using suitable integration contours in the complex plane.