相关论文: Physical Vacuum Properties and Internal Space Dime…

We relate here the vacuum structure of chiral symmetry breaking to a wide class of low energy hadronic properties to examine consistency with experimental results. Phase transition of chiral symmetry breaking is described through explicit…

The explicit relationship is determined between the interior properties of a static cylindrical matter distribution and the metric of the exterior space-time according to Einstein gravity for space-time dimensionality larger or equal to…

We consider the problem of minimising the $k$-th eigenvalue of the Laplacian with some prescribed boundary condition over collections of convex domains of prescribed perimeter or diameter. It is known that these minimisation problems are…

This paper proposes a generalized framework with joint normalization which learns lower-dimensional subspaces with maximum discriminative power by making use of the Riemannian geometry. In particular, we model the similarity/dissimilarity…

If $X$ is an infinite-dimensional uniform algebra, if $X$ has the Daugavet property or if $X$ is a proper $M$-embedded space, every relatively weakly open subset of the unit ball of the Banach space $X$ is known to have diameter 2, i.e.,…

In this paper, we introduce a general framework for analyzing the numerical conditioning of minimal problems in multiple view geometry, using tools from computational algebra and Riemannian geometry. Special motivation comes from the fact…

Employing alternative spacetime volume-forms (generally-covariant integration measure densities) independent of the pertinent Riemannian spacetime metric have profound impact in general relativity. Although formally appearing as…

Gyroscopic systems in classical and quantum field theory are characterized by the presence of at least two scalar degrees of freedom and by terms that mix fields and their time derivatives in the quadratic Lagrangian. In Minkowski…

The problem of finding the maximal dimension of linear or affine subspaces of matrices whose rank is constant, or bounded below, or bounded above, has attracted many mathematicians from the sixties to the present day. The problem has caught…

The existence of both a minimum mass and a minimum density in nature, in the presence of a positive cosmological constant, is one of the most intriguing results in classical general relativity. These results follow rigorously from the…

The semiclassical regime of 2D static Dirac matter is obtained from the Dirac equation in curved space-time. To simplify the formulation, the Cartesian space-time geometry parametrization is transformed to isothermal coordinates using…

Geometrical arrangements of minimum energy of a system of identical repelling particles in two dimensions are studied for different forms of the interaction potential. Stability conditions for the triangular structure are derived, and some…

In this work, the quantization of the most general Bianchi Type I geometry, with and without a cosmological constant, is considered. In the spirit of identifying and subsequently removing as many gauge degrees of freedom as possible, a…

Dimensionality reduction is a popular approach to tackle high-dimensional data with low-dimensional nature. Subspace Restricted Isometry Property, a newly-proposed concept, has proved to be a useful tool in analyzing the effect of…

This paper studies wormhole solutions to Einstein gravity with an arbitrary number of time dependent compact dimensions and a matter-vacuum boundary. A new gauge is utilized which is particularly suited for studies of the wormhole throat.…

The matrix completion problem consists of finding or approximating a low-rank matrix based on a few samples of this matrix. We propose a new algorithm for matrix completion that minimizes the least-square distance on the sampling set over…

Since the 5D canonical metric embeds all 4D vacuum solutions of Einstein's equations, I review its application to the cosmological 'constant', quantized particles, deBroglie waves, scalar fields and wave-particle duality. There are several…

We introduce a vector-valued version of a uniform algebra, called the vector-valued function space over a uniform algebra. The diameter two properties of the vector-valued function space over a uniform algebra on an infinite compact…

One of the basic problems in discrete geometry is to determine the most efficient packing of congruent replicas of a given convex set $K$ in the plane or in space. The most commonly used measure of efficiency is density. Several types of…

We consider the sigma models where the base metric is proportional to the metric of the configuration space. We show that the corresponding sigma model equation admits a Lax pair. We also show that this type of sigma models in two…