Related papers: Potentials for transverse trace-free tensors
Most currently used tensor regression models for high-dimensional data are based on Tucker decomposition, which has good properties but loses its efficiency in compressing tensors very quickly as the order of tensors increases, say greater…
A four-index tensor is constructed with terms both quadratic in the Riemann tensor and linear in its second derivatives, which has zero divergence for space-times with vanishing scalar curvature. This tensor reduces in vacuum to the…
This paper investigates the teleparallel Robertson--Walker (TRW) $F(T)$ gravity solutions for a scalar field source. We use the TRW $F(T)$ gravity field equations (FEs) for each $k$-parameter value case added by a scalar field to find new…
Intrinsic and extrinsic geometric properties of string world sheets in curved space-time background are explored. In our formulation, the only dynamical degrees of freedom of the string are its immersion coordinates. Classical equation of…
A key bottleneck in quantum machine learning is the computational cost of repeated quantum circuit evaluations during the inference phase. To address this, we present a framework for constructing fast, cheap, provably accurate classical…
We consider (2+1)-QFT at finite temperature on a product of time with a static spatial geometry. The suitably defined difference of thermal vacuum free energy for the QFT on a deformation of flat space from its value on flat space is a UV…
The trace formula for the density of single-particle levels in the two-dimensional radial power-law potentials, which nicely approximate the radial dependence of the Woods-Saxon potential and quantum spectra in a bound region, was derived…
We consider metric f(R) theories of gravity without mapping them to their scalar-tensor counterpart, but using the Ricci scalar itself as an "extra" degree of freedom. This approach avoids then the introduction of a scalar-field potential…
Compressed sensing extends from the recovery of sparse vectors from undersampled measurements via efficient algorithms to the recovery of matrices of low rank from incomplete information. Here we consider a further extension to the…
We consider Friedmann-Lema\^{\i}tre-Robertson-Walker flat cosmological models in the framework of general Jordan frame scalar-tensor theories of gravity with arbitrary coupling function and potential. For the era when the cosmological…
Theories of physics can be considered viable if the initial value problem and the energy conditions are formulated self-consistently. The former allow a uniquely determined dynamical evolution of the system, and the latter guarantee that…
This article introduces a trace-based metric on the space of positive semi-definite (PSD) tensors, offering a geometric perspective that connects their algebraic structure to their intrinsic geometric properties. It defines the…
The aim of the current paper is to clarify some aspects of the formalism used for describing the scalar-tensor gravity characterized by four arbitrary local functionals of the scalar field. We recall the objects that are invariant with…
In the case of a constant uniform magnetic field it can be assumed, without the loss of generality, that the vector potential (the gauge) is a linear function of position, i.e. it could be considered as a three-dimensional real matrix or,…
This is the fourth article in a series where we succeed in enlarging the class of exactly solvable quantum systems. We do that by working in a complete set of square integrable basis that carries a tridiagonal matrix representation for the…
Tensors are often compressed by expressing them in low rank tensor formats. In this paper, we develop three methodologies that bound the compressibility of a tensor: (1) Algebraic structure, (2) Smoothness, and (3) Displacement structure.…
We give the curvatures of the free differential algebra (FDA) of M--theory compactified to D=4 on a twisted seven--torus with the 4--form flux switched on. Two formulations are given, depending on whether the 1--form field strengths of the…
Global properties of vacuum static, spherically symmetric configurations are studied in a general class of scalar-tensor theories (STT) of gravity in various dimensions. The conformal mapping between the Jordan and Einstein frames is used…
In the framework of teleparallel gravity, the Friedman-Robertson-Walker cosmological model with scalar tensor theory where scalar field is non-minimally coupled to both the torsion scalar and boundary term is studied. Utilizing the Noether…
The Hamiltonian formulation of scalar-tensor theories of gravity is derived from their Lagrangian formulation by Hamiltonian analysis. The Hamiltonian formalism marks off two sectors of the theories by the coupling parameter $\omega(\phi)$.…