Related papers: Notes on the Leonard system classification
We define observability and detectability for linear switching systems as the possibility of reconstructing and respectively of asymptotically reconstructing the hybrid state of the system from the knowledge of the output for a suitable…
We associate all small subgraph counting problems with a systematic graph encoding/representation system which makes a coherent use of graphlet structures. The system can serve as a unified foundation for studying and connecting many…
We develop a formal framework for the behavioral comparison of linear systems across different time domains. We accomplish this by introducing the notion of system interpolation, which determines whether the input-state trajectories of a…
The goal of this paper is to show how to produce a piece of rigorous bifurcation diagram of periodic orbits for an ODE. We study the Rossler system, one of the textbook examples of ODEs generating nontrivial dynamics, for the parameter…
The motivation of this work is to define cohomology classes in the space of knots that are both easy to find and to evaluate, by reducing the problem to simple linear algebra. We achieve this goal by defining a combinatorial graded cochain…
The purposes of this paper are to classify lower triangular forms and to determine under what conditions a nonlinear system is equivalent to a specific type of lower triangular forms. According to the least multi-indices and the greatest…
For a given poset, we consider its representations by systems of subspaces of a unitary space ordered by inclusion. We classify such systems for all posets for which an explicit classification is possible.
Given a sequence of real numbers, we consider its subsequences converging to possibly different limits and associate to each of them an index of convergence which depends on the density of the associated subsequences. This index turns out…
We study the convergence of the Laurent polynomials of Lagrange interpolation on the unit circle for continuous functions satisfying a condition about their modulus of continuity. The novelty of the result is that now the nodal systems are…
This paper is a survey of two kinds of "compressed" proof schemes, the \emph{matrix method} and \emph{proof nets}, as applied to a variety of logics ranging along the substructural hierarchy from classical all the way down to the…
We consider rank-one non-symmetric tensor estimation and derive simple formulas for the mutual information. We start by the order 2 problem, namely matrix factorization. We treat it completely in a simpler fashion than previous proofs using…
The classical Lorenz system is considered. For many years, this system has been the subject of study by numerous authors. However, until now the structure of the Lorenz attractor is not clear completely yet, and the most important question…
A linear-interval order is the intersection of a linear order and an interval order. For this class of orders, several structural results have been known. This paper introduces a new subclass of linear-interval orders. We call a partial…
A thorough investigation of the foundations of paraconsistent logics. Relations between logical principles are formally studied, a novel notion of consistency is introduced, the logics of formal inconsistency, and the subclasses of…
We investigate infinitary wellfounded systems for linear logic with fixed points, with transfinite branching rules indexed by some closure ordinal $\alpha$ for fixed points. Our main result is that provability in the system for some…
The shard intersection order is a new lattice structure on a finite Coxeter group W which encodes the geometry of the reflection arrangement and the lattice theory of the weak order. In the case where W is the symmetric group, we…
The purpose of this note is to give a new, short proof of a classification of ACM sets of points in $P^1XP^1$ in terms of separators.
Refinement types sharpen systems of simple and dependent types by offering expressive means to more precisely classify well-typed terms. We present a system of refinement types for LF in the style of recent formulations where only canonical…
Index of notation added. Shortening of some section, simplification of some of the arguments, some small added results and strengthening of thm 3.10. Also a significant re-writing of the last section.
Using an alternate description of support varieties of pairs of modules over a complete intersection, we give several new applications of such varieties, including results for support varieties of intermediate complete intersections.…