Related papers: Garrett approximation revisited
We consider the most general action for gravity which is quadratic in curvature. In this case first order and second order formalisms are not equivalent. This framework is a good candidate for a unitary and renormalizable theory of the…
We present cylindrically symmetric solutions for a type of the Gauss-Bonnet gravity, in details. We derive the full system of the field equations and show that there exist seven families of exact solutions for three forms of viable models.…
Gauss-Bonnet gravity provides one of the most promising frameworks to study curvature corrections to the Einstein action in supersymmetric string theories, while avoiding ghosts and keeping second order field equations. Although…
The paper investigates the approximation of the symmetric Total Variation functional on graphs. Such an approximation is given in terms of a discrete and symmetric finite difference model defined on point clouds obtained by randomly…
We use the covariant formulation proposed in Tattersall et al (2017) to analyse the structure of linear perturbations about a spherically symmetric background in different families of gravity theories, and hence study how quasi-normal modes…
In this review we present the theoretical background for treating General Relativity as an effective field theory and focus on the concrete results of such a treatment. As a result we present the calculations of the low-energy leading…
An extension of the Gauss-Newton algorithm is proposed to find local minimizers of penalized nonlinear least squares problems, under generalized Lipschitz assumptions. Convergence results of local type are obtained, as well as an estimate…
We extend the theory of the gauging of classical quadratically nonlinear algebras without a central charge but with a coset structure, to the quantum level. Inserting the minimal anomalies into the classical transformation rules of the…
We discuss various aspects of the post-Newtonian approximation in general relativity. After presenting the foundation based on the Newtonian limit, we use the (3+1) formalism to formulate the post-Newtonian approximation for the perfect…
In this paper, a variable-coefficient Gardner equation is considered. By using the classical symmetry analysis method symmetries for this equation are obtained. Then, the generalized Jacobi elliptic function expansion method is used to…
A new method of approximation scheme with potential application to a general interacting quantum system is presented. The method is non-perturbative, self- consistent, systematically improvable and uniformly applicable for arbitrary…
In the asymptotic safety programme for quantum gravity, it is important to go beyond polynomial truncations. Three such approximations have been derived where the restriction is only to a general function f(R) of the curvature R>0. We…
We show the equivalence between the three approximation schemes for self-interacting (1+1)-D scalar field theories. Based on rigorous results of [1, 2], we are able to prove that the Gaussian approximation is very precise for certain limits…
We construct the most general, to cubic order in curvature, theory of gravity whose (most general) static spherically symmetric vacuum solutions are fully described by a single field equation. The theory possess the following remarkable…
It is shown that quadrature formulas in many different applications can be derived from rational approximation of the Cauchy transform of a weight function. Since rational approximation is now a routine technology, this provides an easy new…
This is a brief tutorial on the least square estimation technique that is straightforward yet effective for parameter estimation. The tutorial is focused on the linear LSEs instead of nonlinear versions, since most nonlinear LSEs can be…
This paper pursues a twofold goal. First, we introduce and study in detail a new notion of variational analysis called generalized metric subregularity, which is a far-going extension of the conventional metric subregularity conditions. Our…
We consider a variant of the art gallery problem where all guards are limited to seeing to the right inside a monotone polygon. We call such guards: half-guards. We provide a polynomial-time approximation for point guarding the entire…
Resource-efficient and high-precision approximate synthesis of quantum circuits expressed in the Clifford+T gate set is vital for Fault-Tolerant quantum computing. Efficient optimal methods are known for single-qubit RZ unitaries, otherwise…
We analyse the accuracy of the approximate WKB quantization for the case of general one-dimensional quartic potential. In particular, we are interested in the validity of semiclassically predicted energy eigenvalues when approaching the…