Related papers: Notes on the Riccati operator equation in open qua…

The transformation of the Nth- order linear difference equation into a system of the first order difference equations is presented. The proposed transformation gives possibility to get new forms of the N-dimensional system of the first…

An algorithm for solving first order ODEs, by systematically determining symmetries of the form [ xi = F(x), eta = P(x) y + Q(x) ], where xi d/dx + eta d/dy is the symmetry generator - is presented. To these {\it linear} symmetries one can…

An overview of quantum computing and in particular the Hidden Subgroup Problem are presented from a mathematical viewpoint. Detailed proofs are supplied for many important results from the literature, and notation is unified, making it…

We show that Pinney's equation [2] with a constant coefficient can be reduced to its linear part by a simple change of variables. Also, Pinney's original solution is simplified slightly.

We answer affirmatively the open problem proposed by Cabr\'e and Tan in their paper "Positive solutions of nonlinear problems involving the square root of the Laplacian" (see Adv. Math. {\bf 224} (2010), no. 5, 2052-2093).

We first study the linear eigenvalue problem for a planar Dirac system in the open half-line and describe the nodal properties of its solution by means of the rotation number. We then give a global bifurcation result for a planar nonlinear…

This paper proposes a reduction technique for the generalised Riccati difference equation arising in optimal control and optimal filtering. This technique relies on a study on the generalised discrete algebraic Riccati equation. In…

We use a new approach with a matrix transformation to obtain a new global solvability criterion for matrix Riccati equations. The proven theorem completes an well known result in directions of extension of classes of coefficient of…

In this paper, the existence and uniqueness of solution of the Cauchy problem for abstract Boussinesq equation is obtained. By applying this result, the Cauchy problem for systems of Boussinesq equations of finite or infinite orders are…

Contraction properties of the Riccati operator are studied within the context of non-stationary linear-quadratic optimal control. A lifting approach is used to obtain a bound on the rate of strict contraction, with respect to the Riemannian…

Within the frame of a novel treatment we make a complete mathematical analysis of exactly solvable one-dimensional quantum systems with non-constant mass, involving their ordering ambiguities. This work extends the results recently reported…

The nonlinear generalization of the von Neumann equation preserving convexity of the state space is studied in the nontrivial case of the qutrit. This equation can be cast into the integrable classical Riccati system of nonlinear ordinary…

Starting from some results regarding the form of the Ricci scalar at a point $P$ in a spacetime endowed with a minimum distance, we investigate how they might be accommodated, specifically for the case of null separations, in a…

We explore the uncertainty relation for unitary operators in a new way and find two uncertainty equalities for unitary operators, which are minimized by any pure states. Additionally, we derive two sets of uncertainty inequalities that…

This article presents an equivalent formulation of the implicit complementarity problem. We demonstrate that solution of the equivalent formulation is equivalent to the solution of the implicit complementarity problem. Moreover, we provide…

The Riccati equation method is used to establish a new comparison theorem for systems of two linear first order ordinary differential equation. This result is based on a, so called, concept of "null-classes", and is a generalization of…

Analytic interpolation problems with rationality and derivative constraints occur in many applications in systems and control. In this paper we present a new method for the multivariable case, which generalizes our previous results on the…

Analytic interpolation problems with rationality and derivative constraints are ubiquitous in systems and control. This paper provides a new method for such problems, both in the scalar and matrix case, based on a non-standard Riccati-type…

First, we consider generalized wave and scattering operators and derive modifications of commutation relations (between scattering operators and unperturbed operators) when the corresponding deviation factors behave as $\exp\{i t {\mathcal…

In this paper, we bring a complete solution to the Ovals problem, as formulated in [3] and [24].