相关论文: Perturbation analysis of tensor $(\mathcal{B},\mat…

Tensor operations play an essential role in various fields of science and engineering, including multiway data analysis. In this study, we establish a few basic properties of the range and null space of a tensor using block circulant…

We investigate the tensor perturbation in the inflation model driven by a massive-scalar field in Eddington-inspired Born-Infeld gravity. For short wave-length modes, the perturbation feature is very similar to that of the usual chaotic…

The study of long wavelength scalar perturbations, in particular the existence of conserved quantities when the perturbations are adiabatic, plays an important role in e.g. inflationary cosmology. In this paper we present some new conserved…

We prove the Einstein relation, relating the velocity under a small perturbation to the diffusivity in equilibrium, for certain biased random walks on Galton--Watson trees. This provides the first example where the Einstein relation is…

We provide a systematic formula, in terms of integer partitions, that generates perturbation theory explicitly at an arbitrary order. Our approach naturally includes an infinite number of perturbations and uses a single matrix equation that…

Higher order tensor inversion is possible for even order. We have shown that a tensor group endowed with the Einstein (contracted) product is isomorphic to the general linear group of degree $n$. With the isomorphic group structures, we…

We study the Jordan frame formulation of generalizations of scalar-tensor theories conceived by replacing the scalar with other fields such as vectors. The generic theory in this family contains higher order time derivative terms in the…

The probabilistic model of parton distributions, previously developed by one of the authors, is generalized to include the transversity distribution. When interference effects are attributed to quark level only, the intrinsic quark motion…

The back reaction of gravitational perturbations in a homogeneous background is determined by an effective energy-momentum tensor quadratic in the perturbations. We show that this nonlinear feedback effect is important in the case of long…

Based on the gauge invariant variables proposed in our previous paper [K. Nakamura, Prog. Theor. Phys. vol.110 (2003), 723.], some formulae of the perturbative curvatures of each order are derived. We follow the general framework of the…

Understanding the invasive nature of quantum measurement and its implications in quantum foundations and information science demands a mathematically rigorous and physically well-grounded characterization of intrinsic back-action in general…

A tensor description of perturbative Einsteinian gravity about an arbitrary background spacetime is developed. By analogy with the covariant laws of electromagnetism in spacetime, gravito-electromagnetic potentials and fields are defined to…

The linear and quadratic perturbations for a scalar-tensor model with non-minimal coupling to curvature, coupling to the Gauss-Bonnet invariant and non-minimal kinetic coupling to the Einstein tensor are developed. The quadratic action for…

In this paper, we establish a model-independent framework based on the Isaacson picture to analyze the gravitational-wave effects in the most general vector-tensor theory that yields second-order field equations. Within this framework, we…

We investigate the Moore-Penrose pseudoinverse and generalized inverse of a matrix product $A=CR$ to establish a unifying framework for generalized and randomized matrix inverses. This analysis is rooted in first principles, focusing on the…

We consider the Einstein equation, where the common electromagnetic energy momentum tensor is replaced by its generalized equivalent as suggested in our earlier paper (A.L. Kholmetskii et al. Phys. Scr. 83, 055406 (2011)). Now we show that…

In current paper we refer to the geometrical classification of the Einstein equations which has been developed by one of the authors of this paper. This classification was based on the classical theory for decomposition of the tensor…

We consider the evolution of relativistic perturbations in the Einstein-de Sitter cosmological model, including second-order effects. The perturbations are considered in two different settings: the widely used synchronous gauge and the…

We show that the splitting feature of the Einstein tensor, as the first term of the Lovelock tensor, into two parts, namely the Ricci tensor and the term proportional to the curvature scalar, with the trace relation between them is a common…

Invariant tensors are states in the (local) SU(2) tensor product representation but invariant under global SU(2) action. They are of importance in the study of loop quantum gravity. A random tensor is an ensemble of tensor states. An…