Related papers: Mahler formula on the projective n-space
A new method involving the effective wave function is used to define the mass of a particle in a standard five-dimensional extension of general relativity. The mass is inversely proportional to the magnitude of the scalar field of the extra…
We introduce the notion of a ``projective hull'' for subsets of complex projective varieties, parallel to the idea of the polynomial hull in affine varieties. With this concept, a generalization of J. Wermer's classical theorem on the hull…
As was recently shown, non-relativistic quantum theory can be derived by means of a projection method from a continuum of classical solutions for (massive) particles. In this paper we show that Maxwell's equations in empty space can be…
A famous pre-Newtonian formula for $\pi$ is obtained directly from the variational approach to the spectrum of the hydrogen atom in spaces of arbitrary dimensions greater than one, including the physical three dimensions.
Projective metrics on vector spaces over finite fields, introduced by Gabidulin and Simonis in 1997, generalize classical metrics in coding theory like the Hamming metric, rank metric, and combinatorial metrics. While these specific metrics…
This short note describes a connection between algorithmic dimensions of individual points and classical pointwise dimensions of measures.
A polarizable endomorphism on a projective variety enables us to consider given morphism as constant multiplication in the height function. In this paper, we will generalize it for arbitrary dominant endomorphism by defining the height…
We propose a new method to define theories of random geometries, using an explicit and simple map between metrics and large hermitian matrices. We outline some of the many possible applications of the formalism. For example, a…
Maximal estimates for Schr\"odinger means and convergence almost everywhere of sequences of Schr\"odinger means are studied.
In this paper we prove using quite elementary methods, with a combinatorial nature, two general results related to Marstrand's projection theorem in a quite general formulation over metric spaces under a suitable transversality condition…
Two Kaehler metrics on one complex manifold are said to be c-projectively equivalent if their J-planar curves, i.e., curves defined by the property that their acceleration is complex proportional to their velocity, coincide. The degree of…
Define the height function h(a) = min{k+(ka\mod p): k=1,2,...,p-1} for a = 0,1,...,p-1. It is proved that the height has peaks at p, (p+1)/2, and (p+c)/3, that these peaks occur at a= [p/3], (p-3)/2, (p-1)/2, [2p/3], p-3,p-2, and p-1, and…
The purpose of this article is to propose a new method to define and calculate path integrals over metrics on a K\"ahler manifold. The main idea is to use finite dimensional spaces of Bergman metrics, as an approximation to the full space…
Projections of finite dimensional sets and their measures are investigated in infinite-dimensional power measure spaces. The starting point is the known algebraic formula, expressing \ the $y$-projection of a finite-dimensional set $a$ as a…
It is well known that quantum mechanics admits a geometric formulation on the complex projective space as a Kahler manifold. In this paper we consider the notion of mutual information among continuous random variables in relation to the…
Here we describe the distribution of rational points on the Hilbert scheme of two points in the projective plane. More specifically, we explicitly describe a two-parameter family of height functions $H_{s, t}$, such that the height function…
The Maxwell equations are formulated on an arbitrary (1+3)-dimensional manifold. Then, imposing a (constrained) linear constitutive relation between electromagnetic field $(E,B)$ and excitation $({\cal D},{\cal H})$, we derive the metric of…
Under very mild assumptions, we give formulas for the correlation and local dimensions of measures on the limit set of a Moran construction by means of the data used to construct the set.
Finite-dimensional Quantum Mechanics can be geometrically formulated as a proper classical-like Hamiltonian theory in a projective Hilbert space. The description of composite quantum systems within the geometric Hamiltonian framework is…
In ZM theory the direction of time has a non-zero projection onto space and this projection corresponds to the local velocity relative to the observer. Classical trajectories can be obtained by following the local direction of time. The…