In the context of the AdS/CFT correspondence, an explicit relation between the physical degrees of freedom of 2+1d gravity and the stress tensor of 1+1d conformal field theory is exhibited. Gravity encodes thermodynamic state variables of conformal field theory, but does not distinguish among different CFT states with the same expectation value for the stress tensor. Simply put, gravity is ther...

The Wasserstein distance on multivariate non-degenerate Gaussian densities is a Riemannian distance. After reviewing the properties of the distance and the metric geodesic, we derive an explicit form of the Riemannian metrics on positive-definite matrices and compute its tensor form with respect to the trace scalar product. The tensor is a matrix, which is the solution of a Lyapunov equation. W...

We develop a mathematical framework for quantifying and understanding multidimensional frequency modulations in digital images. We begin with the widely accepted definition of the instantaneous frequency vector (IF) as the gradient of the phase and define the instantaneous frequency gradient tensor (IFGT) as the tensor of component derivatives of the IF vector. Frequency modulation bounds are d...

We discuss some mathematical aspects of the problem of inverting gravitational field data to extract the underlying mass distribution. While the forward problem of computing the gravity field from a given mass distribution is mathematically straightforward, the inverse of this forward map has some interesting features that make inversion a difficult problem. In particular, the forward map has a...

The three 3-brane system with both positive or negative tension is studied in a low energy regime by using gradient expansion method. The effective equations of motion on the brane is derived and in particular we examine, in the first order, the radion effective lagrangian for this system. In this case, we show the solution of the modified Friedmann equation with dark radiation on the middle br...

We point out that extended gravity theories, the Lagrangian of which is an arbitrary function of scalar curvature R, are equivalent to a class of the scalar tensor theories of gravity. The corresponding gravity theory is ω = 0 BransDicke gravity with a potential for the Brans-Dicke scalar field, which is not compatible with solar system experiments if the field is very light: the case when such...

We study a general Scalar-Tensor Theory with an arbitrary coupling funtion !( ) but also an arbitrary dependence of the gravitational constant G( ) in the cases in which either one of them, or both, do not admit an analytical inverse, as in the hyperextended in ationary scenario. We present the full set of eld equations and study their cosmological behavior. We show that different scalar-tensor...

In this work, we studied the slow-roll approximation of cosmic inflation within context $f(R,T)$ gravity, where $R$ is scalar curvature, and $T$ trace energy-momentum tensor. By choosing a minimal coupling between matter obtained modified parameters, spectral index ($n_s$), tensor ($n_{\textrm{T}}$), tensor-to-scalar ratio ($r$). We computed these quantities for general power-law potential, Nat...

A 78-year-old womanwas found to have a small bronchioloalveolar carcinoma with ground-glass attenuation in the gravity-dependent gradient in the left lower lobe during a preoperative chest computed tomography (CT) evaluation, which was performed for previously-diagnosed adenocarcinoma of the right upper lobe. To remove the gravitational effect of the CT, the patient underwent a thin section CT ...