Related papers: Harmonic Center of an n-Simplex: Some Properties
In 1991, Yannakakis (J. Comput. System Sci., 1991) proved that no symmetric extended formulation for the matching polytope of the complete graph K_n with n nodes has a number of variables and constraints that is bounded subexponentially in…
For the space of single-variable monic and centered complex polynomial vector fields of arbitrary degree d, it is proved that any bifurcation which preserves the multiplicity of equilibrium points can be realized as a composition of a…
The isotropic harmonic oscillator in N dimensions is shown to have an underlying symmetry group O(2,1)X O(N)which implies a unique result for the energy spectrum of the system. Raising and lowering operators analogous to those of the…
An elementary general result is proved that allows for simple characterizations of well-known location/consensus functions (median, mean and center) on the n-cube. In addition, alternate new characterizations are given for the median and…
The (non-initialized, non-deterministic) asynchronous systems (in the input-output sense) are multi-valued functions from m-dimensional signals to sets of n-dimensional signals, the concept being inspired by the modeling of the asynchronous…
Transforming an asymmetric system into a symmetric system makes it possible to exploit the simplifying properties of symmetry in control problems. We define and characterize the family of symmetrizable systems, which can be transformed into…
We explore the asymptotic behavior of the centroids of random polygons constructed from regular polygons with vertices on the unit circle by extending the rays so that their lengths form a random permutation of the first (n) integers.…
The definition of $n$-width of a bounded subset $A$ in a normed linear space $X$ is based on the existence of $n$-dimensional subspaces. Although the concept of an $n$-dimensional subspace is not available for metric trees, in this paper,…
We give a closed formula for the dimension of all linear systems in $\mathbb{P}^n$ with assigned multiplicity at arbitrary collections of points lying on a rational normal curve of degree $n$. In particular we give a purely geometric…
We introduce symmetric arithmetic circuits, i.e. arithmetic circuits with a natural symmetry restriction. In the context of circuits computing polynomials defined on a matrix of variables, such as the determinant or the permanent, the…
We consider several classes of symmetries of the Dirac Hamiltonian in 3+1 dimensions, with axially-deformed scalar and vector potentials. The symmetries include the known pseudospin and spin limits and additional symmetries which occur when…
We consider the phenomenon of forced symmetry breaking in a symmetric Hamiltonian system on a symplectic manifold. In particular we study the persistence of an initial relative equilibrium subjected to this forced symmetry breaking. We see…
We construct examples of centrally harmonic spaces by generalizing work of Copson and Ruse. We show that these examples are generically not centrally harmonic at other points. We use this construction to exhibit manifolds which are not…
We show that any point in the convex hull of each of (d+1) sets of (d+1) points in general position in \R^d is contained in at least (d+1)^2/2 simplices with one vertex from each set. This improves the known lower bounds for all d >= 4.
The holomorphicity property of N=1 superpotentials or of N=2 F-terms involving vector multiplets is generalized to the case of N=4 1/2-BPS effective operators defined in harmonic superspace. The resulting harmonicity equations are shown to…
We consider the equilibria of point particles under the action of two body central forces in which there are both repulsive and attractive interactions, often known as central configurations, with diverse applications in physics, in…
Our main result in this paper is the following: Given $H^m, H^n$ hyperbolic spaces of dimensional $m$ and $n$ corresponding, and given a Holder function $f=(s^1,...,f^{n-1}):\partial H^m\to \partial H^n$ between geometric boundaries of…
The paper develops elementary linear algebra methods to compute the determinants of the tensor symmetrizations of quadratic and hermitian forms over fields of good characteristic. Explicit results are given for the partitions $(n)$,…
An algorithm is presented that constructs an acyclic partial matching on the cells of a given simplicial complex from a vector-valued function defined on the vertices and extended to each simplex by taking the least common upper bound of…
We characterize homogeneous hypersurfaces in complex space forms which arise as critical points of a higher order energy functional. As a consequence, we obtain existence and non-existence results for $\mathbb{CP}^n$ and $\mathbb{CH}^n$,…