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We prove there are finitely many isometry classes of planar central configurations (also called relative equilibria) in the Newtonian 5-body problem, except perhaps if the 5-tuple of positive masses b...
Unlabeled shape analysis is a rapidly emerging and challenging area of statistics. This has been driven by various novel applications in bioinformatics. We consider here the situation where two config...
Let $F$ be a homogeneous polynomial in $S = \mathbb{C}[x_0,...,x_n]$. Our goal is to understand a particular polynomial decomposition of $F$; geometrically, we wish to determine when the hypersurface ...
Abstract: It is shown that on compact hyperbolic manifolds, certain stable configurations of points which mutually repel along all interconnecting geodesics become equidistributed as the number of poi...
Abstract: We construct new monomial quasi-particle bases of Feigin-Stoyanovsky's type subspaces for affine Lie algebra $\mathfrak{sl}(3,\mathbb{C})^{\widetilde{}}$ from which the known fermionic-type ...
Abstract: We consider the Schr\"odinger system with Newton-type interactions that was derived by R. Klein, A. Majda and K. Damodaran [18] to modelize the dynamics of N nearly parallel vortex filaments...
Abstract: For any two configurations of ordered points $p=(p_{1},...,\p_{N})$ and $q=(q_{1},...,q_{N})$ in Euclidean space $E^d$ such that $q$ is an expansion of $p$, there exists a continuous expansi...
We study maximal Hom-free sets in the [2]-orbit category C(Q) of the bounded derived category for the path algebra associated to a Dynkin quiver Q, where  denotes the Auslander-Reiten translation an...
A central hyperplane arrangement in C2 with multiplicity is called a ‘locus configuration if it satisfies a series of ‘locus equations on each hyperplane.Following [CFV99].
We analyze sumsets A+B = {a+b : a in A, b in B} where A,B are sets of integers, A is infinite, and B has positive upper Banach density. For each k, we show that A+B contains at least the expected dens...
We show that if E Fdq , the d-dimensional vector space over the finite field with q elements,and |E| ≥ qd, where q−1 2 ≪  ≤ 1, then E contains an isometric copy of at least cd&#...
We show that the discretized configuration space of k points in the n-simplex is homotopy equivalent to a wedge of spheres of dimen-sion n−k +1. This space is homeomorphic to the order complex o...
In a recent paper the author has published the result, ofsome,investigations on the periodic sequences of Laplace of periodfour with a stratifiable couple of diagonal congruences.Thedeterinination of ...
A basic idea of geometric constraint solving (GCS) is to decompose the constraint problem into smaller ones according to some basic configurations. In this paper, we find all spatial basic configurati...

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