Related papers: A Note on the Reduction Formulas for Some Systems …
This paper deals with reduction of non-homogeneous linear systems of first order operator equations with constant coefficients. An equivalent reduced system, consisting of higher order linear operator equations having only one variable and…
We consider the model reduction problem for linear time-invariant dynamical systems having nonzero (but otherwise indeterminate) initial conditions. Building upon the observation that the full system response is decomposable as a…
Nonholonomic mechanical systems have been attracting more interest in recent years because of their rich geometric properties and their applications in Engineering. In all generality, we discuss the reduction of a Hamilton-Jacobi theory for…
A method is presented that reduces the number of terms of systems of linear equations (algebraic, ordinary and partial differential equations). As a byproduct these systems have a tendency to become partially decoupled and are more likely…
We consider the semiconjugate factorization and reduction of order for non-autonomous, nonlinear, higher order difference equations containing linear arguments. These equations have appeared in several mathematical models in biology and…
In this paper we consider a reduction of a non-homogeneous linear system of first order operator equations to a totally reduced system. Obtained results are applied to Cauchy problem for linear differential systems with constant…
The reduction operators, i.e., the operators of nonclassical (conditional) symmetry, of (1+1)-dimensional second order linear parabolic partial differential equations and all the possible reductions of these equations to ordinary…
In a recent paper [J.Math.Phys. vol42, 2236-2265 (2001)], we discussed differential operators within a quaternionic formulation of quantum mechanics. In particular, we proposed a practical method to solve quaternionic and complex linear…
This article generalizes a recently introduced procedure to solve nonlinear systems of equations, radically departing from the conventional Newton-Raphson scheme. The original nonlinear system is first unfolded into three simpler…
We provide an analytical framework for balanced realization model order reduction of linear control systems which depend on an unknown parameter. Besides recovering known results for the first order corrections, we obtain explicit novel…
It is sometimes desirable to produce for a nonlinear system of ODEs a new representation of simpler structural form, but it is well known that this goal may imply an increase in the dimension of the system. This is what happens if in this…
Reduction operators (called also nonclassical or $Q$-conditional symmetries) of variable coefficient semilinear reaction-diffusion equations with exponential source $f(x)u_t=(g(x)u_x)_x+h(x)e^{mu}$ are investigated using the algorithm…
Certain linear matrix operators arise naturally in systems analysis and design problems involving cascade interconnections of linear time-invariant systems, including problems of stabilization, estimation, and model order reduction. We…
In this paper we consider disjoint decomposition of algebraic and non-linear partial differential systems of equations and inequations into so-called simple subsystems. We exploit Thomas decomposition ideas and develop them into a new…
Fundamental matrix operations and solving linear systems of equations are ubiquitous in scientific investigations. Using the "Sender-Receiver" model, we propose quantum algorithms for matrix operations such as matrix-vector product,…
The nonlinear dynamics of a system with periodic structure can be analyzed using a square matrix. We show that because the special property of the square matrix constructed for nonlinear dynamics, we can reduce the dimension of the matrix…
We analyze two reduction methods for nonholonomic systems that are invariant under the action of a Lie group on the configuration space. Our approach for obtaining the reduced equations is entirely based on the observation that the dynamics…
Symmetry reductions of systems of two nonlinear partial differential equations are studied. We find ansatzes reducing system of partial differential equations to system of ordinary differential equations. The method is applied to system…
We introduce some basic notions and results for quaternionic linear operators analogous to those for complex linear operators. Our main result is to prove the additive and multiplicative Jordan-Chevalley decompositions for quaternionic…
In this note we mainly study the fine Jordan-Chevalley decomposition: a refinement of the classical Jordan-Chevalley decomposition of a matrix and we pay a particular attention to the field of the coefficients of the matrix. Moreover we…