Related papers: Classification of stacked central configurations i…

The topological classification of gerbes, as principal bundles with the structure group the projective unitary group of a complex Hilbert space, over a topological space $H$ is given by the third cohomology $\text{H}^3(H, \Bbb Z)$. When $H$…

Let k be a separably closed field. Let K_i=[A_i \to B_i] (for i=1,2,3) be three 1-motives defined over k. We define the geometrical notions of extension of K_1 by K_3 and of biextension of (K_1,K_2) by K_3. We then compute the homological…

On objects of a triangulated category with a stability condition, we construct a topology.

Central configurations have been of great interest over many years, with the earliest examples due to Euler and Lagrange. There are numerous results in the literature demonstrating the existence of central configurations with specific…

The results from the article [Strachan I.A.B., Szablikowski B.M., Stud. Appl. Math. 133 (2014), 84-117] are extended over consideration of central extensions allowing the introducing of additional independent variables. Algebraic conditions…

We give a self-contained introduction to the theory of secondary polytopes and geometric bistellar flips in triangulations of polytopes and point sets, as well as a review of some of the known results and connections to algebraic geometry,…

The aim of this short note is to develop a (co)homology theory for topological spaces together with the specialisation preorder. A known way to construct such a (co)homology is to define a partial order on the topological space starting…

We study the dynamics of the collinear points in the planar, restricted three-body problem, assuming that the primaries move on an elliptic orbit around a common barycenter. The equations of motion can be conveniently written in a rotating…

In this note we present the classification of non-symplectic automorphisms of prime order on K3 surfaces, i.e.we describe the topological structure of their fixed locus and determine the invariant lattice in cohomology. We provide new…

In this paper, we study the following coupled nonlinear Schr\"{o}dinger system in $\R^3$ $$ \left\{% \begin{array}{ll} -\epsilon^2\Delta u +P(x)u=\mu_1 u^3+\beta v^2u,~~&x\in \R^3,\vspace{0.15cm}\\ -\epsilon^2\Delta v +Q(x)v=\mu_2 v^3+\beta…

We develop a theory of cosupport and costratification in tensor triangular geometry. We study the geometric relationship between support and cosupport, provide a conceptual foundation for cosupport as categorically dual to support, and…

We construct a simply connected $2-$complex $C$ embeddable in $3-$space such that for any embedding of $C$ in $\mathbb S^3$, any edge contraction forms a minor of the $2-$complex not embeddable in $3-$space. We achieve this by proving that…

Central configurations are solutions of the equations $\lambda m_j\boldsymbol{q}_j = \frac{\partial U}{\partial \boldsymbol{q}_j}$, where $U$ denotes the potential function and each $\boldsymbol{q}_j$ is a point in the $d$-dimensional…

In the first part of the paper we characterize certain systems of first order nonlinear differential equations whose space of solutions is an $\mathfrak{sl}_2(\mathbb{C})$-module. We prove that such systems, called Ramanujan systems of…

We give a proof of existence of centre manifolds within large domains for systems with an integral of motion. The proof is based on a combination of topological tools, normal forms and rigorous-computer-assisted computations. We apply our…

We explain how the notion of homotopy colimits gives rise to that of mapping spaces, even in categories which are not simplicial. We apply the technique of model approximations and use elementary properties of the category of spaces to be…

Group classification of systems of two coupled nonlinear reaction-diffusion equation with a diagonal diffusion matrix is carried out. Symmetries of diffusion systems with singular diffusion matrix and additional first order derivative terms…

In an earlier paper \cite{yu2021Finiteness}, we showed that there are finitely many stationary configurations (consisting of equilibria, rigidly translating configurations, relative equilibria and collapse configurations) in the planar…

In this paper we study embeddings of oriented connected closed surfaces in $\mathbb S^3$. We define a complete invariant, the fundamental span, for such embeddings, generalizing the notion of the peripheral system of a knot group. From the…

We give a classification of ordered five points in $\mathbb P^3$ under the diagonal action of $GL_4$ over an algebraically closed field of characteristic $0$, by an explicit description of the diagonal action of $GL_4$ on the quintuple of…