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

In a class of generalized Einstein's gravity theories we derive the equations and general asymptotic solutions describing the evolution of the perturbed universe in unified forms. Our gravity theory considers general couplings between the…

Recently, we presented a unified way of analysing classical cosmological perturbation in generalized gravity theories. In this paper, we derive the perturbation spectrums generated from quantum fluctuations again in unified forms. We…

We study an ensemble of random matrices (the Rosenzweig-Porter model) which, in contrast to the standard Gaussian ensemble, is not invariant under changes of basis. We show that a rather complete understanding of its level correlations can…

In the context of semiclassical gravity, the semiclassical Einstein equation is often invoked when backreaction of quantum matter/fields on the spacetime is at stake. It is expected to hold when quantum fluctuations are small. Yet, it is…

A recent general model of entanglement, [5], that goes much beyond the usual one based on tensor products of vector spaces is further developed here. It is shown that the usual Cartesian product can be seen as two extreme particular…

Although with great successes in explaining phenomena and natural behaviour involving the Universe or a part thereof, the General Theory of Relativity is far from a complete theory. Focusing on its extension within the framework of scalar…

We consider generalized inverses of linear operators on arbitrary vector spaces and study the question when their product in reverse order is again a generalized inverse. This problem is equivalent to the question when the product of two…

In a recent paper we presented a general perturbation result for generators of $C_0$-semigroups. The aim of the present paper is to replace, in case the unperturbed semigroup is analytic, the various conditions appearing in this result by…

In this paper we use abstract vector spaces and their duals without any canonical basis. Some of our results can be extended to infinite dimensional vector spaces too, but here we consider only finite dimensional spaces. We focus on a…

We investigate the inversion of perturbation series and its resummation, and prove that it is related to a recently developed parametric perturbation theory. Results for some illustrative examples show that in some cases series reversion…

The motion of binary star systems is re-examined in the presence of perturbations from the theory of general relativity. The Kepler problem is regularized and linearized with quaternions. In this way first order perturbation results are…

We consider a class of tempered subordinators, namely a class of subordinators with one-dimensional marginal tempered distributions which belong to a family studied in [3]. The main contribution in this paper is a non-central moderate…

In this paper we provide a comprehensive study of statistical inference in linear and allied models which exhibit some analytic perturbations in their design and covariance matrices. We also indicate a few potential applications. In the…

One of the fundamental research problems in the theory of generalized inverses of matrices is to establish reverse order laws for generalized inverses of matrix products. Under the assumption that $A$, $B$, and $C$ are three nonsingular…

Reverse order law for the Moore-Penrose inverses of tensors are useful in the field of multilinear algebra. In this paper, we first prove some more identities involving the Moore-Penrose inverse of tensors. We then obtain a few necessary…

Compensational gravity, which is regarded as a fundamental theory, is an advanced version of semiclassical gravity. It is a construction which extends the Einstein equation. Along with the energy-momentum tensor, the extended Einstein…

Many of the technical complications associated with the general theory of relativity ultimately stem from the nonlinearity of Einstein's equation. It is shown here that an appropriate choice of dynamical variables may be used to eliminate…

Observables in random tensor theory are polynomials in the entries of a tensor of rank $d$ which are invariant under $U(N)^d$. It is notoriously difficult to evaluate the expectations of such polynomials, even in the Gaussian distribution.…

In this paper we consider an extension to Eddington's proposal for the gravitational action. We study tensor perturbations of a homogeneous and isotropic space-time in the Eddington regime, where modifications to Einstein gravity are…

We consider static massive thin cylindrical shells (tubes) as the sources in Einstein's equations. They correspond to $\dl$- and $\dl'$-function type energy-momentum tensors. The corresponding metric components are found explicitly. They…