Related papers: On a simple proof the Poincare Conjecture
We present a simple short proof of the Fundamental Theorem of Algebra, without complex analysis and with a minimal use of topology. It can be taught in a first year calculus class.
We showed with J. P. Gollin that if a (possibly infinite) homogeneous linear equation system has only the trivial solution, then there exists an injective function from the variables to the equations such that each variable appears with…
Yoshida's Conjecture formulated by H. Yoshida in 1989 states that in $\mathbb{C}^{2N}$ equipped with the canonical symplectic form $\mathrm{d}\mathbf{p} \wedge \mathrm{d} \mathbf{q},$ the Hamiltonian flow corresponding to the Hamiltonian…
In \cite{Luo0}, Feng Luo conjectured that the discrete Yamabe flow will converge to the constant curvature PL-metric after finite number of surgeries on the triangulation. In this paper, we prove that the flow can always be extended…
By finding orthogonal representation for a family of simple connected called $\delta$-graphs it is possible to show that $\delta$-graphs satisfy delta conjecture. An extension of the argument to graphs of the form…
In a recent paper the first two authors proved that the generating series of the Poincare polynomials of the quasihomogeneous Hilbert schemes of points in the plane has a simple decomposition in an infinite product. In this paper we give a…
In this note, using the derangement polynomials and their umbral representation, we give another simple proof of an identity conjectured by Lacasse in the study of the PAC-Bayesian machine learning theory.
We give a simple proof on the Poincar\'e's conjecture which states that every compact smooth $3-$manifold which is homotopically equivalent to $S^3$ is diffeomorphic to $S^3$.
Two BPHZ convergence theorems are proved directly in Euclidean position space, without exponentiating the propagators, making use of the Cluster Convergence Theorem presented previously. The first theorem proves the absolute convergence of…
In this paper, we provide an essentially self-contained and detailed account of the fundamental works of Hamilton and the recent breakthrough of Perelman on the Ricci flow and their application to the geometrization of three-manifolds. In…
We give a simple proof of the following result: There exists a non-convex polyhedron whose surface is isometric to the surface of a cube of smaller volume.
In [GH1] and [GH2] (see also [GH3]) we presented full proof of the equalities NP = coNP = PSPACE. These results have been obtained by the novel proof theoretic tree-to-dag compressing techniques adapted to Prawitz's Natural Deduction (ND)…
In this paper, by use of techniques associated to cobordism theory and Morse theory,we give a simple proof of Poincare conjecture, i.e. Every compact smooth simply connected 3-manifold is homeomorphic to 3-sphere.
The purpose of this note is to give an affirmative answer to a conjecture appearing in [Integral Transforms Spec. Funct. 26 (2015) 90-95].
The PC algorithm is the state-of-the-art algorithm for causal structure discovery on observational data. It can be computationally expensive in the worst case due to the conditional independence tests are performed in an…
We propose a one-way coupled model that tracks individual primary particles in a conceptually simple cellular flow setup to predict flocculation in turbulence. This computationally efficient model accounts for Stokes drag, lubrication,…
In this paper, we construct smooth forward Ricci flow evolutions of singular initial metrics resulting from rotationally symmetric neckpinches on S^(n+1), without performing an intervening surgery. In the restrictive context of rotational…
Recently we have obtained two simple proofs of Sharkovsky's theorem, one with directed graphs [7] and the other without [8]. In this note, we present yet more simple proofs of Sharkovsky's theorem.
In this paper we present a more transparent upgrade of our proofs and comment on Jerabek's paper [8].
This memoire consists of two main results. In the first one we describe Ricci flow theory and we give an educative way for proving Elliptization Conjecture and then we prove Poincare conjecture which is the second proof of Perelman for…