Related papers: Realization of Einsteins Machian Program
This study is an extented analogue to conformal geometry of the paper given by [14]. Also, the geometric and physical results related to bi-para-conformal-dynamical systems are also presented.
Reconstruction theorem for the Moufang loops is proved.
We present an astonishingly simple and elegant proof of the celebrated Basel problem.
Given a closed Riemannian manifold $(M, g_M)$ of dimension $n \geq 3$, we prove the existence of a conformally compact Einstein metric $g_{+}$ defined on a collar neighborhood $M \times (0,1]$ whose conformal infinity is $[g_M]$.
In this paper, we study an important class of Finsler metrics--square metrics. We give two expressions of such metrics in terms of a Riemannian metric and a 1-form. We show that Einstein square metrics can be classified up to the…
This is an introductory article to the theory of multiple gaps.
We provide a polynomial time cutting plane algorithm based on split cuts to solve integer programs in the plane. We also prove that the split closure of a polyhedron in the plane has polynomial size.
We derive a unique continuation theorem for the vacuum Einstein equations. Our method of proof utilizes Carleman estimates (most importantly one obtained recently by Ionescu and Klainerman), but also relies strongly on certain geometric…
This paper considers the existence of conformally compact Einstein metrics on 4-manifolds. A reasonably complete understanding is obtained for the existence of such metrics with prescribed conformal infinity, when the conformal infinity is…
We study self-consistent cosmological solutions for an Einstein universe in a graph-based induced gravity model. Especially, we demonstrate specific results for cycle graphs.
The Minimal Euclidean Function on the Gaussian Integers
New estimates on the maximal function associated to the linear Schrodinger equation are established
In this paper an algebraic proof of Christoph's theorem is provided. This theorem from algebraic-geometry is about the existence of a finite automaton for computing coefficient of a series for an algebraic function.
This paper describes an algorithm of interest. This is a preliminary version and we intend on writing a better descripition of it and getting bounds for its complexity.
The classification of the Einstein spaces with the Stackel metric of the (3.0) has been done. These spaces are invariant under the action of the three-parameter abelian group of motions and belong to the first type Bianchi spaces. Thus the…
Riemann numerically approximated at least three zeta zeros. According to Edwards, Riemann even took steps to verify that the lowest zero he computed was indeed the first zeta zero. This approach to verification is developed, improved, and…
In this paper the Gaussian integral is proven using contour integration on $\frac{1}{e^{x^2}+1}$ and linking it using a limit to said Gaussian integral. The limit is alsorelated to the Riemann Zeta function using a few manipulations. This…
We prove that every complete Einstein (Riemannian or pseudo-Riemannian) metric $g$ is geodesically rigid: if any other complete metric $\bar g$ has the same (unparametrized) geodesics with $g$, then the Levi-Civita connections of $g$ and…
Universal quantum filter (UQF) is introduced and proved to exist. Optical realization of UQF is proposed in experiment.
We prove existence of a non-round Einstein metric $g$ on $S^{12}$ that is invariant under the usual cohomogeneity one action of $\mathsf{O}(3)\times\mathsf{O}(10)$ on $S^{12}\subset \mathbb{R}^{13}= \mathbb{R}^3\oplus \mathbb{R}^{10}$. The…