We point out an association between anomalies in the Hawking quasilocal mass (or, spherical symmetry, its better known version, Misner-Sharp-Hernandez mass) and unphysical properties of spacetime geometry. While anomalous behaviors show up certain quantum-corrected black holes, they are not unique to this context signal serious physical pathologies isolated gravitating systems general.

We give a mathematically rigorous exposition of the flatness problem, and show how Guth’s original model of inflation is used to resolve it.

We generalize to an arbitrary variety the von Neumann axiom for a ring. We study its implications on the purity of monomorphisms and the flatness of algebras.

Explicit solutions to the conifold equations with complex dimension n = 3, 4 in terms of complex coordinates (fields) are employed to construct the Ricci-flat Kähler metrics on these manifolds. The Kähler 2-forms are found to be closed. The complex realization of these conifold metrics are used in the construction of 2-dimensional non-linear sigma model with the conifolds as target spaces. The ...

Information geometry studies the dually flat structure of a manifold, highlighted by the generalized Pythagorean theorem. The present paper studies a class of Bregman divergences called the (ρ, τ)-divergence. A (ρ, τ)-divergence generates a dually flat structure in the manifold of positive measures, as well as in the manifold of positive-definite matrices. The class is composed of decomposable ...

In this paper, a single-ended quality measurement algorithm for noise suppressed speech is described. The proposed algorithm computes fast approximations of KullbackLeibler distances between Gaussian mixture (GM) reference models of clean, noise corrupted, and noise suppressed speech and a GM model trained online on the test speech signal. The distances, together with a spectral flatness measur...

We present the results of a numerical investigation of the turbulent kinematic dynamo problem in a high Prandtl number regime. The scales of the magnetic turbulence we consider are far smaller than the Kolmogorov dissipative scale, so that the magnetic wavepackets evolve in a nearly smooth velocity field. Firstly, we consider the Kraichnan-Kazantsev model (KKM) in which the strain matrix is tak...

Using the U(4) hybrid formalism, manifestly N=(2,2) worldsheet supersymmetric sigma models are constructed for the Type IIB superstring in Ramond-Ramond backgrounds. The Kahler potential in these N=2 sigma models depends on four chiral and antichiral bosonic superfields and two chiral and antichiral fermionic superfields. When the Kahler potential is quadratic, the model is a free conformal fie...