Search results for "infinity"
showing 10 items of 74 documents
On nonimmersibility of compact hypersurfaces into a ball of a simply connected space form
1996
We give a nonimmersibility theorem of a compact manifold with nonnegative scalar curvature bounded from above into a geodesic ball of a simply connected space form.
Some notes on a superlinear second order Hamiltonian system
2016
Variational methods are used in order to establish the existence and the multiplicity of nontrivial periodic solutions of a second order dynamical system. The main results are obtained when the potential satisfies different superquadratic conditions at infinity. The particular case of equations with a concave-convex nonlinear term is covered.
Weighted Sobolev spaces and exterior problems for the Helmholtz equation
1987
Weighted Sobolev spaces are used to settle questions of existence and uniqueness of solutions to exterior problems for the Helmholtz equation. Furthermore, it is shown that this approach can cater for inhomogeneous terms in the problem that are only required to vanish asymptotically at infinity. In contrast to the Rellich–Sommerfeld radiation condition which, in a Hilbert space setting, requires that all radiating solutions of the Helmholtz equation should satisfy a condition of the form ( ∂ / ∂ r − i k ) u ∈ L 2 ( Ω ) , r = | x | ∈ Ω ⊂ R n , it is shown here that radiating solutions satisfy a condition of the form ( 1 + r ) − 1 2 ( ln ( e + r ) ) − 1 2 δ u ∈ L 2 ( Ω ) , 0 < δ < 1 2 …
Zero rest-mass fields and the Newman-Penrose constants on flat space
2020
Zero rest-mass fields of spin 1 (the electromagnetic field) and spin 2 propagating on flat space and their corresponding Newman-Penrose (NP) constants are studied near spatial infinity. The aim of this analysis is to clarify the correspondence between data for these fields on a spacelike hypersurface and the value of their corresponding NP constants at future and past null infinity. To do so, Friedrich's framework of the cylinder at spatial infinity is employed to show that, expanding the initial data in terms spherical harmonics and powers of the geodesic spatial distance $\rho$ to spatial infinity, the NP constants correspond to the data for the second highest possible spherical harmonic …
La parola chiave «infinito» nello studio della natura sviluppato dai presocratici
2018
Il concetto di ‘infinito’ sta alla base della ‘fisiologia’, ovvero dell’indagine sulla Physis-Natura, sviluppata dai presocratici a partire dalla Scuola di Mileto sino alla Scuola di Abdera. Sia i primi pensatori della Ionia, a cominciare da Anassimandro, sia gli atomisti con a capo Democrito, infatti, hanno contribuito a elaborare la prima forma di ‘filosofia’ incentrata sulle parole chiave «infinito» e «finito». Alla luce di questi concetti, andrebbe allora rivisitata la filosofia del periodo ellenico ed ellenistico-romano per ritrovare le fondamenta della ‘scienza della natura’ nella sua duplice connotazione di fisica e di matematica. La diade infinito-finito, inoltre, potrebbe essere po…
Hopf bifurcation at infinity for planar vector fields
2007
We study, from a new point of view, families of planar vector fields without singularities $ \{ X_{\mu}$  :  $-\varepsilon < \mu < \varepsilon\} $ defined on the complement of an open ball centered at the origin such that, at $\mu=0$, infinity changes from repellor to attractor, or vice versa. We also study a sort of local stability of some $C^1$ planar vector fields around infinity.
One-Dimensional Transient Analysis of Rainfall Infiltration in Unsaturated Volcanic Ash
2015
The paper presents a one-dimensional hydro-mechanical analysis of rainfall infiltration in a loose volcanic ash and the utilisation of a factor of safety for the implementation of an early-warning system. Three different rainy seasons with different rainfall patterns were analysed . The analysis aims to understand the influence of the antecedent rainfall on the wetting front, the pore-water pressures and the factor of safety. The analysis was carried out in the context of a Master project of the first author at the Laboratory for Soil Mechanics of EPFL.
Robust H∞ filtering for networked control systems with markovian jumps and packet dropouts
2014
Published version of an article in the journal: Modeling, Identification and Control. Also available from the publisher at: http://dx.doi.org/10.4173/mic.2014.3.3 Open Access This paper deals with the H∞ filtering problem for uncertain networked control systems. In the study, network-induced delays, limited communication capacity due to signal quantization and packet dropout are all taken into consideration. The finite distributed delays with probability of occurrence in a random way is introduced in the network.The packet dropout is described by a Bernoulli process. The system is modeled as Markovian jumps system with partially known transition probabilities. A full-order filter is designe…
Some New Symbolic Algorithms for the Computation of Generalized Asymptotes
2022
We present symbolic algorithms for computing the g-asymptotes, or generalized asymptotes, of a plane algebraic curve, C, implicitly or parametrically defined. The g-asymptotes generalize the classical concept of asymptotes of a plane algebraic curve. Both notions have been previously studied for analyzing the geometry and topology of a curve at infinity points, as well as to detect the symmetries that can occur in coordinates far from the origin. Thus, based on this research, and in order to solve practical problems in the fields of science and engineering, we present the pseudocodes and implementations of algorithms based on the Puiseux series expansion to construct the g-asymptotes of a p…
Finite-Time Hâ Filtering for T-S Fuzzy Discrete-Time Systems with Time-Varying Delay and Norm-Bounded Uncertainties
2015
In this paper, we investigate the filtering problem of discrete-time Takagi–Sugeno (T–S) fuzzy uncertain systems subject to time-varying delays. A reduced-order filter is designed. With the augmentation technique, a filtering error system with delayed states is obtained. In order to deal with time delays in system states, the filtering error system is first transformed into two interconnected subsystems. By using a two-term approximation for the time-varying delay, sufficient delay-dependent conditions of finite-time boundedness and $H_{\infty }$ performance of the filtering error system are derived with the Lyapunov function. Based on these conditions, the filter design methods are propose…