相关论文: Generalized Tensor Analysis Method Applied to Non-…
Principal Component Analysis can be performed over small domains of an embedded Riemannian manifold in order to relate the covariance analysis of the underlying point set with the local extrinsic and intrinsic curvature. We show that the…
Vector is a physical quantity and it does not depend on any co-ordinate system. It need to be expanded in some basis for practical calculation and its components do depend on the chosen basis. The expansion in orthonormal basis is…
This paper studies the relativistic angular momentum for the generalized electromagnetic field, described by $r$-vectors in $(k,n)$ space-time dimensions, with exterior-algebraic methods. First, the angular-momentum tensor is derived from…
Full tensor gravity (FTG) devices provide up to five independent components of the gravity gradient tensor. However, we do not yet have a quantitative understanding of which tensor components or combinations of components are more important…
We explore, in the general relativistic context, the properties of the recently introduced GPS coordinates, as well as those of the associated frames and coframes. We show that they are covariant, and completely independent of any observer.…
In this study, a novel feature coding method that exploits invariance for transformations represented by a finite group of orthogonal matrices is proposed. We prove that the group-invariant feature vector contains sufficient discriminative…
This paper describes a flexible framework for generalized low-rank tensor estimation problems that includes many important instances arising from applications in computational imaging, genomics, and network analysis. The proposed estimator…
A second-order numerical implementation is given for recently derived nonlinear wave equations for general relativity. The Gowdy T$^3$ cosmology is used as a test bed for studying the accuracy and convergence of simulations of…
Gauge-invariant treatments of general-relativistic higher-order perturbations on generic background spacetime is proposed. We show the fact that the linear-order metric perturbation is decomposed into gauge-invariant and gauge-variant…
We discuss the extension of the Lewis and Riesenfeld method of solving the time-dependent Schr\"odinger equation to cases where the invariant has continuous eigenvalues and apply it to the case of a generalized time-dependent inverted…
We develop a generic spacetime model in General Relativity which can be used to build any gravitational model within General Relativity. The generic model uses two types of assumptions: (a) Geometric assumptions additional to the inherent…
In this thesis, I investigate how to construct a self-consistent model of deformed general relativity using canonical methods and metric variables. The specific deformation of general covariance is predicted by some studies into loop…
We discuss theoretical formalisms concerning with experimental verification of General Relativity (GR). Non-metric generalizations of GR are considered and a system of postulates is formulated for metric-affine and Finsler gravitational…
Tensor-based methods are receiving a growing interest in scientific computing for the numerical solution of problems defined in high dimensional tensor product spaces. A family of methods called Proper Generalized Decompositions methods…
A new generalized matrix inverse is derived which is consistent with respect to arbitrary nonsingular diagonal transformations, e.g., it preserves units associated with variables under state space transformations, thus providing a general…
It is known that some cosmological perturbations are conformal invariant. This facilitates the studies of perturbations within some gravitational theories alternative to general relativity, for example the scalar-tensor theory, because it…
The problem of finding a covariant expression for the distribution and conservation of gravitational energy-momentum dates to the 1910s. A suitably covariant infinite-component localization is displayed, reflecting Bergmann's realization…
The aim of the current paper is to study the multiscalar-tensor theories of gravity without derivative couplings. We construct a few basic objects that are invariant under a Weyl rescaling of the metric and transform covariantly when the…
In the present paper, classical tools of convex analysis are used to study the solution set to a certain class of set-inclusive generalized equations. A condition for the solution existence and global error bounds is established, in the…
We present a general method which can be used for geometrical and physical interpretation of an arbitrary spacetime in four or any higher number of dimensions. It is based on the systematic analysis of relative motion of free test…