Related papers: Computing Invariant Zeros of a Linear System Using…
Moebius number systems represent points using sequences of Moebius transformations. Thorough the paper, we are mainly interested in representing the unit circle (which is equivalent to representing R\cup\{\infty\}). The main aim of the…
We show a Condition Number Theorem for the condition number of zero counting for real polynomial systems. That is, we show that this condition number equals the inverse of the normalized distance to the set of ill-posed systems (i.e., those…
In this paper we present an elementary theory about the existence of eigenvalues for fully nonlinear radially symmetric 1-homogeneous operators. A general theory for first eigenvalues and eigenfunctions of 1-homogeneous fully nonlinear…
Recent results in control systems and numerical integration literature utilize invariant set theory to lift dynamical systems evolving on nonlinear manifolds to those evolving on vector spaces. We leverage this technique to propose an…
We give results on zeros of a polynomial of $\zeta(s),\zeta'(s),\ldots,\zeta^{(k)}(s)$. First, we give a zero free region and prove that there exist zeros corresponding to the trivial zeros of the Riemann zeta function. Next, we estimate…
We study conformal invariants that arise from functions in the nullspace of conformally covariant differential operators. The invariants include nodal sets and the topology of nodal domains of eigenfunctions in the kernel of GJMS operators.…
A central question in verification is characterizing when a system has invariants of a certain form, and then synthesizing them. We say a system has a $k$ linear invariant, $k$-LI in short, if it has a conjunction of $k$ linear (non-strict)…
We present an exact and complete algorithm to isolate the real solutions of a zero-dimensional bivariate polynomial system. The proposed algorithm constitutes an elimination method which improves upon existing approaches in a number of…
This article examines a family of smooth mappings between Banach spaces and establishes conditions for the existence of their zeros. Applications to fixed-point problems and the Implicit Function Theorem are also discussed.
The non-trivial zeros of the Riemann zeta function and the prime numbers can be plotted by a modified von Mangoldt function. The series of non-trivial zeta zeros and prime numbers can be given explicitly by superposition of harmonic waves.…
We introduce and develop the root locus method in mathematics. And we study the distribution of zeros of meromorphic functions by root locus method.
A system of linear equations is normally understood as a linear mapping between two vector spaces. However, most direct solutions (e.g., QR, LU, ...) rely on the inelegant approach of back-substitution: a significant departure from such a…
The eigenvalue problem for a linear function L centers on solving the eigen-equation Lx = rx. This paper generalizes the eigenvalue problem from a single linear function to an iterated function system F consisting of possibly an infinite…
Several root-ratio multipoint methods for finding multiple zeros of univariate functions were recently presented. The characteristic of these methods is that they deal with $m$-th root of ratio of two functions (hence the name root-ratio…
We present an application of equation-free computation to the coarse-grained feedback linearization problem of nonlinear systems described by microscopic/stochastic simulators. Feedback linearization with pole placement requires the…
Binary quantum information can be fault tolerantly encoded in states defined in infinite dimensional Hilbert spaces. Such states define a computational basis, and permit a perfect equivalence between continuous and discrete universal…
We consider the characterization and computation of H-infinity norms for a class of time-delay systems. It is well known that in the finite dimensional case the H-infinity norm of a transfer function can be computed using the connections…
We propose an algorithm for computing bases and dimensions of spaces of invariants of Weil representations of $\mathrm{SL}_2(\mathbb{Z})$ associated to finite quadratic modules. We prove that these spaces are defined over $\mathbb{Z}$, and…
In this paper we consider the problem of computing control invariant sets for linear controlled high-dimensional systems with constraints on the input and on the states. Set inclusions conditions for control invariance are presented that…
The coincidence between polynomial neural networks and matrix Lie maps is discussed in the article. The matrix form of Lie transform is an approximation of the general solution of the nonlinear system of ordinary differential equations. It…