Search results for "Mathematical physics"
showing 10 items of 2687 documents
Fast nonstationary preconditioned iterative methods for ill-posed problems, with application to image deblurring
2013
We introduce a new iterative scheme for solving linear ill-posed problems, similar to nonstationary iterated Tikhonov regularization, but with an approximation of the underlying operator to be used for the Tikhonov equations. For image deblurring problems, such an approximation can be a discrete deconvolution that operates entirely in the Fourier domain. We provide a theoretical analysis of the new scheme, using regularization parameters that are chosen by a certain adaptive strategy. The numerical performance of this method turns out to be superior to state-of-the-art iterative methods, including the conjugate gradient iteration for the normal equation, with and without additional precondi…
Relation between quasirigidity andL-rigidity in space-times of constant curvature and weak fields
1997
The relation between quasirigidity andL-rigidity in space-times of constant nonzero curvature and in space-times with small curvature (weak fields) is studied. The covariant expansion of bitensors about a point is considered. We obtain an increase in the order of magnitude, underL-rigidity conditions, of the rate of change with respect to a comoving orthonormal frame of the linear momentum, angular momentum, and reduced multipole moments of the energy-momentum tensor. Thus,L-rigidity leads to quasirigidity in such space-times.
Vacuum type I spacetimes and aligned Papapetrou fields: symmetries
2003
We analyze type I vacuum solutions admitting an isometry whose Killing 2--form is aligned with a principal bivector of the Weyl tensor, and we show that these solutions belong to a family of type I metrics which admit a group $G_3$ of isometries. We give a classification of this family and we study the Bianchi type for each class. The classes compatible with an aligned Killing 2--form are also determined. The Szekeres-Brans theorem is extended to non vacuum spacetimes with vanishing Cotton tensor.
On the classification of type D space–times
2002
We give a classification of the type D spacetimes based on the invariant differential properties of the Weyl principal structure. Our classification is established using tensorial invariants of the Weyl tensor and, consequently, besides its intrinsic nature, it is valid for the whole set of the type D metrics and it applies on both, vacuum and non-vacuum solutions. We consider the Cotton-zero type D metrics and we study the classes that are compatible with this condition. The subfamily of spacetimes with constant argument of the Weyl eigenvalue is analyzed in more detail by offering a canonical expression for the metric tensor and by giving a generalization of some results about the non-exi…
Weak Levi-Civita Connection for the Damped Metric on the Riemannian Path Space and Vanishing of Ricci Tensor in Adapted Differential Geometry
2001
Abstract We shall establish in the context of adapted differential geometry on the path space P m o ( M ) a Weitzenbock formula which generalizes that in (A. B. Cruzeiro and P. Malliavin, J. Funct. Anal . 177 (2000), 219–253), without hypothesis on the Ricci tensor. The renormalized Ricci tensor will be vanished. The connection introduced in (A. B. Cruzeiro and S. Fang, 1997, J. Funct. Anal. 143 , 400–414) will play a central role.
Relations between multi-resolution analysis and quantum mechanics
2005
We discuss a procedure to construct multiresolution analyses (MRA) of L2 (R) starting from a given seed function h (s) which should satisfy some conditions. Our method, originally related to the quantum mechanical Hamiltonian of the fractional quantum Hall effect, is shown to be model independent. The role of a canonical map between certain canonically conjugate operators is discussed. This clarifies our previous procedure and makes much easier most of the original formulas, producing a convenient framework to produce examples of MRA. © 2005 American Institute of Physics.
Resolution of the ATLAS muon spectrometer monitored drift tubes in LHC Run 2
2019
The momentum measurement capability of the ATLAS muon spectrometer relies fundamentally on the intrinsic single-hit spatial resolution of the monitored drift tube precision tracking chambers. Optimal resolution is achieved with a dedicated calibration program that addresses the specific operating conditions of the 354 000 high-pressure drift tubes in the spectrometer. The calibrations consist of a set of timing offsets and drift time to drift distance transfer relations, and result in chamber resolution functions. This paper describes novel algorithms to obtain precision calibrations from data collected by ATLAS in LHC Run 2 and from a gas monitoring chamber, deployed in a dedicated gas fac…
On the Reception of Grassmann’s Work in Germany during the 1870’s
1996
It has often been remarked that Grassmann’s mathematics was not widely appreciated during his lifetime. Although awareness of the dimensions of his achievements began to spread in the early 1870’s, even in Germany relatively few mathematicians appear to have been well acquainted with either the original 1844 edition of Grassmann’s Ausdehnungslehre or the mathematically more accessible edition of 1862. The main reasons for this weak and rather delayed reception have been described often enough---Grassmann’s isolated working environment and his nearly impenetrable language---but there are a number of related aspects that still deserve closer consideration.1
Variances as order parameter and complexity measure for random Boolean networks
2005
Several order parameters have been considered to predict and characterize the transition between ordered and disordered phases in random Boolean networks, such as the Hamming distance between replicas or the stable core, which have been successfully used. In this work, we propose a natural and clear new order parameter: the temporal variance. We compute its value analytically and compare it with the results of numerical experiments. Finally, we propose a complexity measure based on the compromise between temporal and spatial variances. This new order parameter and its related complexity measure can be easily applied to other complex systems.
Rates of convergence to equilibrium for collisionless kinetic equations in slab geometry
2017
This work deals with free transport equations with partly diffuse stochastic boundary operators in slab geometry. Such equations are governed by stochastic semigroups in $L^{1}$ spaces$.\ $We prove convergence to equilibrium at the rate $O\left( t^{-\frac{k}{2(k+1)+1}}\right) \ (t\rightarrow +\infty )$ for $L^{1}$ initial data $g$ in a suitable subspace of the domain of the generator $T$ where $k\in \mathbb{N}$ depends on the properties of the boundary operators near the tangential velocities to the slab. This result is derived from a quantified version of Ingham's tauberian theorem by showing that $F_{g}(s):=\lim_{\varepsilon \rightarrow 0_{+}}\left( is+\varepsilon -T\right) ^{-1}g$ exists…