Related papers: Realisation and Splitting for Poincar\'e Duality P…
In this paper, we introduce and develop the notion of a Manin triple for a Lie superalgebra $\mathfrak g$ defined over a field of characteristic $p=2$. We find cohomological necessary conditions for the pair $(\mathfrak g, \mathfrak g^*)$…
Let $(A, I)$ be a bounded prism, and $X$ be a smooth $p$-adic formal scheme over $\Spf(A/I)$. We consider the notion of crystals on Bhatt--Scholze's prismatic site $(X/A)_{\prism}$ of $X$ relative to $A$. We prove that if $X$ is proper over…
The $P_1$--nonconforming quadrilateral finite element space with periodic boundary condition is investigated. The dimension and basis for the space are characterized with the concept of minimally essential discrete boundary conditions. We…
It is well known that a three dimensional (closed, connected and compact) manifold is obtained by identifying boundary faces from a polyhedron P. The study of (\partial P)/~, the boundary \partial P with the polygonal faces identified in…
In this paper, we seek analytically checkable necessary and sufficient condition for copositivity of a three-dimensional symmetric tensor. We first show that for a general third order three-dimensional symmetric tensor, this means to solve…
Let $\Lambda$ be a finite-dimensional associative algebra over a field. A semibrick pair is a finite set of $\Lambda$-modules for which certain Hom- and Ext-sets vanish. A semibrick pair is completable if it can be enlarged so that a…
The aim of the work is to prove the following main theorem. Theorem. Let M3 be a three-dimensional, connected, simple-connected, closed, compact, smooth manifold. Tnen the manifold M3 is diffeomorphic to the three-dimensional sphere.
I introduce an extended configuration space for classical mechanical systems, called pair-space, which is spanned by the relative positions of all the pairs of bodies. To overcome the non-independence of this basis, one adds to the…
In this paper we find a realization for the D'B'-boundary conditions, which imposes vanishing normal derivatives of the normal components of the D and B fields. The implementation of the DB boundary, requiring vanishing normal components of…
We give necessary conditions satisfied by the set of odd prime divisors of binary perfect polynomials. This allows us to get a new characterization of all the known perfect binary polynomials.
v1: In this paper, we will give an elementary proof by the Heegaard splittings of the 3-dimentional Poincare conjecture in point of view of PL topology. This paper is of the same theory in [4](1983) excluding the last three lines of the…
Poincar\'e's Polyhedron Theorem is a widely known valuable tool in constructing manifolds endowed with a prescribed geometric structure. It is one of the few criteria providing discreteness of groups of isometries. This work contains a…
The problem of nonintegrability of the circular restricted three-body problem is very classical and important in dynamical systems. In the first volume of his masterpieces, Henri Poincar\'e showed the nonexistence of a real-analytic first…
This is a first in a series of papers, devoted to the relation betwwen three-manifolds and number fields. The present paper studies first homology of finite coverings of a three-manifold with primary interest in the Thurston $b_1$…
The state of an entangled q-bit pair is specified by 15 numerical parameters that are naturally regarded as the components of two 3-vectors and a $3\times3$-dyadic. There are easy-to-use criteria to check whether a given pair of 3-vectors…
We find a necessary and sufficient condition for a doubling metric space to carry a (1,p)-Poincare inequality. The condition involves discretizations of the metric space and Poincare inequalities on graphs.
It is shown how in 3+3 dimensions, it is possible to have a superparticle Lagrangian that has manifest supersymmetry both on the world line and in the target space.
We establish necessary and sufficient condition for existence of solutions for a class of semilinear Dirichlet problems with the linear part at resonance at eigenvalues of multiplicity two. The result is applied to give a condition for…
We study local, global and local-to-global properties of threefolds with certain singularities. We prove criteria for these threefolds to be rational homology manifolds and conditions for threefolds to satisfy rational Poincar\'e duality.…
In this article, we mainly give the strictly copositive conditions of a special class of third order three dimensional symmetric tensors. More specifically, by means of the polynomial decomposition method, the analytic sufficient and…