Related papers: Hilbert's 16th Problem for Quadratic Systems. New …
We construct all (2+1)-dimensional PDEs depending only on 2nd-order derivatives of unknown which have the Euler-Lagrange form and determine the corresponding Lagrangians. We convert these equations and their Lagrangians to two-component…
A symplectic theory approach is devised for solving the problem of algebraic-analytical construction of integral submanifold imbeddings for integrable (via the nonabelian Liouville-Arnold theorem) Hamiltonian systems on canonically…
We study a family of Li\'enard--type equations. Such equations are used for the description of various processes in physics, mechanics and biology and also appear as traveling--wave reductions of some nonlinear partial differential…
Classes of kinetic differential equations are delineated which do have a quadratic first integral, and classes which can not have one. Example reactions corresponding to the obtained kinetic differential equations are shown, and a few…
Recently, the covariant formulation of the geometric bifurcation theory, developed in a previous paper, has been applied to two elementary problems: the study of limit cycles of dynamical systems and the second part of Hilbert's sixteenth…
In this paper, we study the bifurcation of limit cycles in Lienard systems of the form dot(x)=y-F(x), dot(y)=-x, where F(x) is an odd polynomial that contains, in general, several free parameters. By using a method introduced in a previous…
This paper studies the nature of fractional linear transformations in a general relativity context as well as in a quantum theoretical framework. Two features are found to deserve special attention: the first is the possibility of…
Any Hilbert space with composite dimension can be factorized into a tensor product of smaller Hilbert spaces. This allows to decompose a quantum system into subsystems. We propose a simple tractable model for a constructive study of…
A necessary and sufficient condition for a parameter transformation that leaves invariant the energy of a one dimensional autonomous system is obtained. Using a parameter transformation the Hamilton-Jacobi equation is solved by a…
We analyze, mainly using bifurcation methods, an elliptic superlinear problem in one-dimension with periodic boundary conditions. One of the main novelties is that we follow for the first time a bifurcation approach, relying on a…
Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…
In this paper, we consider operator realizations of quadratic algebras generated by second-order superintegrable systems in 2D. At least one such realization is given for each set of St\"ackel equivalent systems for both degenerate and…
We introduce a version of the Hamiltonian formalism based on the Clairaut equation theory, which allows us a self-consistent description of systems with degenerate (or singular) Lagrangian. A generalization of the Legendre transform to the…
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…
Symmetries impose structure on the Hilbert space of a quantum mechanical model. The mathematical units of this structure are the irreducible representations of symmetry groups and I consider how they function as conceptual units of…
An introductory theory of frames on finite dimensional quaternion Hilbert spaces is demonstrated along the lines of their complex counterpart.
A three-dimensional Riccati differential equation of complex quaternion-valued functions is studied. Many properties similar to those of the ordinary differential Riccati equation such that linearization and Picard theorem are obtained. Lie…
The fractional quantization of singular systems with second order Lagrangian is examined. The fractional singular Lagrangian is presented. The equations of motion are written as total differential equations within fractional calculus. Also,…
The second part of the Hilbert's sixteenth problem consists in determining the upper bound $\mathcal{H}(n)$ for the number of limit cycles that planar polynomial vector fields of degree $n$ can have. For $n\geq2$, it is still unknown…
We consider transport processes that are modeled by first order hyperbolic partial differential equations. Our goal is to find a full state feedback that makes a given reference profile locally asymptotically stable. To accomplish this we…