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Theory of parameter estimation

Ryszard Zieliński (1997)

Banach Center Publications

0. Introduction and summary. The analysis of data from the gravitational-wave detectors that are currently under construction in several countries will be a challenging problem. The reason is that gravitational-vawe signals are expected to be extremely weak and often very rare. Therefore it will be of great importance to implement optimal statistical methods to extract all possible information about the signals from the noisy data sets. Careful statistical analysis based on correct application of...

Theory of spacecraft Doppler tracking

Massimo Tinto (1997)

Banach Center Publications

We present a review of the spacecraft Doppler tracking technique used in broad band searches for gravitational waves in the millihertz frequency band. After deriving the transfer functions of a gravitational wave pulse and of the noise sources entering into the Doppler observable, we summarize the upper limits for the amplitudes of gravitational wave bursts, continuous, and of a stochastic background estimated by Doppler tracking experiments.

Three dimensional near-horizon metrics that are Einstein-Weyl

Matthew Randall (2017)

Archivum Mathematicum

We investigate which three dimensional near-horizon metrics g N H admit a compatible 1-form X such that ( X , [ g N H ] ) defines an Einstein-Weyl structure. We find explicit examples and see that some of the solutions give rise to Einstein-Weyl structures of dispersionless KP type and dispersionless Hirota (aka hyperCR) type.

TT-tensors and conformally flat structures on 3-manifolds

R. Beig (1997)

Banach Center Publications

We study TT-tensors on conformally flat 3-manifolds (M,g). The Cotton-York tensor linearized at g maps every symmetric tracefree tensor into one which is TT. The question as to whether this is the general solution to the TT-condition is viewed as a cohomological problem within an elliptic complex first found by Gasqui and Goldschmidt and reviewed in the present paper. The question is answered affirmatively when M is simply connected and has vanishing 2nd de Rham cohomology.

Two new estimates for eigenvalues of Dirac operators

Wenmin Gong, Guangcun Lu (2016)

Annales Polonici Mathematici

We establish lower and upper eigenvalue estimates for Dirac operators in different settings, a new Kirchberg type estimate for the first eigenvalue of the Dirac operator on a compact Kähler spin manifold in terms of the energy momentum tensor, and an upper bound for the smallest eigenvalues of the twisted Dirac operator on Legendrian submanifolds of Sasakian manifolds. The sharpness of those estimates is also discussed.

Two-spinor tetrad and Lie derivatives of Einstein-Cartan-Dirac fields

Daniel Canarutto (2018)

Archivum Mathematicum

An integrated approach to Lie derivatives of spinors, spinor connections and the gravitational field is presented, in the context of a previously proposed, partly original formulation of a theory of Einstein-Cartan-Maxwell-Dirac fields based on “minimal geometric data”: the needed underlying structure is determined, via geometric constructions, from the unique assumption of a complex vector bundle S M with 2-dimensional fibers, called a 2 -spinor bundle. Any further considered object is assumed to...

Una classe di soluzioni con zeri dell'equazione funzionale di Aleksandrov.

Constanza Borelli Forti (1992)

Stochastica

In this paper we consider the Aleksandrov equation f(L + x) = f(L) + f(x) where L is contained in Rn and f: L --> R and we describe the class of solutions bounded from below, with zeros and assuming on the boundary of the set of zeros only values multiple of a fixed a > 0. This class is the natural generalization of that described by Aleksandrov itself in the one-dimensional case.

Variational theory of non-perfect relativistic fluids.

A. Fernández, P. L. García (1999)

Extracta Mathematicae

A basic question in General Relativity from the point of view of the general field theory is to obtain the Einstein equations coupled with the stress-energy-momentum tensor of a dissipative fluid from a variational principle. We believe that this problem, whose solution for perfect fluids is well known, has not been faced in a systematic way, maybe by the thought of a possible nonsense, for the concept of dissipation is believed to be incompatible with the essentially conservative character of the...

Wavelet transform and binary coalescence detection

Jean-Michel Innocent, Bruno Torrésani (1997)

Banach Center Publications

We give a short account of some time-frequency methods which are relevant in the context of gravity waves detection. We focus on the case of wavelet analysis which we believe is particularly appropriate. We show how wavelet transforms can lead to efficient algorithms for detection and parameter estimation of binary coalescence signals. In addition, we give in an appendix some of the ingredients needed for the construction of discrete wavelet decompositions and corresponding fast algorithms.

Weakly regular T 2 -symmetric spacetimes. The global geometry of future Cauchy developments

Philippe LeFloch, Jacques Smulevici (2015)

Journal of the European Mathematical Society

We provide a geometric well-posedness theory for the Einstein equations within the class of weakly regular vacuum spacetimes with T 2 -symmetry, as defined in the present paper, and we investigate their global causal structure. Our assumptions allow us to give a meaning to the Einstein equations under weak regularity as well as to solve the initial value problem under the assumed symmetry. First, introducing a frame adapted to the symmetry and identifying certain cancellation properties taking place...

Well posed reduced systems for the Einstein equations

Yvonne Choquet-Bruhat, James York (1997)

Banach Center Publications

We review some well posed formulations of the evolution part of the Cauchy problem of General Relativity that we have recently obtained. We include also a new first order symmetric hyperbolic system based directly on the Riemann tensor and the full Bianchi identities. It has only physical characteristics and matter sources can be included. It is completely equivalent to our other system with these properties.

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