Related papers: Limit linear systems and applications
It is shown that a positive linear system on a time scale with a bounded graininess is uniformly exponentially stable if and only if the characteristic polynomial of the matrix defining the system has all its coefficients positive. Then…
We consider a wide class of linear boundary-value problems for systems of $r$-th order ordinary differential equations whose solutions range over the normed complex space $(C^{(n)})^m$ of $n\geq r$ times continuously differentiable…
Delsarte, Goethals, and Seidel (1977) used the linear programming method in order to find bounds for the size of spherical codes endowed with prescribed inner products between distinct points in the code. In this paper, we develop the…
This paper investigates sub-Riemannian geodesics within the jet space of curves. We establish the existence of two distinct families of metric lines, that is, globally minimizing geodesics, in the $2$-jet space of plane curves. This result…
Parametric linear systems are linear systems of equations in which some symbolic parameters, that is, symbols that are not considered to be candidates for elimination or solution in the course of analyzing the problem, appear in the…
We apply polynomial techniques (linear programming) to obtain lower and upper bounds on the covering radius of spherical designs as function of their dimension, strength, and cardinality. In terms of inner products we improve the lower…
This paper illustrates the richness of the concept of regular sets of time bounds and demonstrates its application to problems of computational complexity. There is a universe of bounds whose regular subsets allow to represent several time…
Linear differential equations and recurrences reveal many properties about their solutions. Therefore, these equations are well-suited for representing solutions and computing with special functions. We identify a large class of existing…
We consider several characterizations of $\mathbb R$-linear mappings. In particular, we give a characterization of linear mappings whose range is $\geq$ 2 dimensional, in terms of preservation of lines (and contraction of lines to a point)…
In this paper we prove that for all pairs $(d,m)$ with $d/m \geq 174/55$, the linear system of plane curves of degree $d$ with ten general base points of multiplicity $m$ has the expected dimension.
In this paper we give bounds on the Castelnuovo-Mumford regularity of products of ideals and ideal sheaves. In particular, we show that the regularity of a product of ideals is bounded by the sum of the regularities of its factors if the…
We present necessary conditions for monotonicity, in one form or another, of fixed point iterations of mappings that violate the usual nonexpansive property. We show that most reasonable notions of linear-type monotonicity of fixed point…
Bilinear systems of equations are defined, motivated and analyzed for solvability. Elementary structure is mentioned and it is shown that all solutions may be obtained as rank one completions of a linear matrix polynomial derived from…
We develop a Morse-Lusternik-Schnirelmann theory for the distance between two points of a smoothly embedded circle in a complete Riemannian manifold. This theory suggests very naturally a definition of width that generalises the classical…
We study extensions of the classic \emph{Line Cover} problem, which asks whether a set of $n$ points in the plane can be covered using $k$ lines. Line Cover is known to be NP-hard, and we focus on two natural generalizations. The first is…
We consider the problem of $2$-coloring geometric hypergraphs. Specifically, we show that there is a constant $m$ such that any finite set of points in the plane $\mathcal{S} \subset {\mathbb R}^2$ can be $2$-colored such that every…
We prove an incidence theorem for points and curves in the complex plane. Given a set of $m$ points in ${\mathbb R}^2$ and a set of $n$ curves with $k$ degrees of freedom, Pach and Sharir proved that the number of point-curve incidences is…
This article concerns the question: which subsets of ${\mathbb R}^m$ can be represented with Linear Matrix Inequalities, LMIs? This gives some perspective on the scope and limitations of one of the most powerful techniques commonly used in…
Multinets are certain configurations of lines and points with multiplicities in the complex projective plane P2. They are used in the studies of resonance and characteristic varieties of complex hyperplane arrangement complements and…
Hamiltonian systems with linearly dependent constraints (irregular systems), are classified according to their behavior in the vicinity of the constraint surface. For these systems, the standard Dirac procedure is not directly applicable.…