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This paper is concerned with the linear quadratic optimal control of discrete-time time-varying system with terminal state constraint. The main contribution is to propose a Q-learning algorithm for the optimal controller when the…
The Painlev\'{e} and weak Painlev\'{e} conjectures have been used widely to identify new integrable nonlinear dynamical systems. For a system which passes the Painlev\'{e} test, the calculation of the integrals relies on a variety of…
Quadratic systems with lossless quadratic terms arise in many applications, including models of atmosphere and incompressible fluid flows. Such systems have a trapping region if all trajectories eventually converge to and stay within a…
We study limit laws for return time processes defined on infinite conservative ergodic measure preserving dynamical systems. Especially for the critical cases with purely atomic limiting distribution we derive distorted processes posessing…
Optimization of convex functions subject to eigenvalue constraints is intriguing because of peculiar analytical properties of eigenvalues, and is of practical interest because of wide range of applications in fields such as structural…
It is commonly known that Killing vectors and tensors are in one-to-one correspondence with polynomial first integrals of the geodesic equation. In this work, metrics admitting nonpolynomial first integrals of the geodesic equation are…
We consider a superintegrable Hamiltonian system in a two-dimensional space with a scalar potential that allows one quadratic and one cubic integral of motion. We construct the most general cubic algebra and we present specific…
This article shows in detail the computations made for the poster presented at the Symposium "Frontiers of Fundamental Physics" in July 2014. As was shown in a previous publication, a quantum gravity formulation exists on the basis of…
Since the expense of the numerical integration of large scale dynamical systems is often computationally prohibitive, model reduction methods, which approximate such systems by simpler and much lower order ones, are often employed to reduce…
We consider the following first order systems of mathematical physics. 1.The Dirac equation with scalar potential. 2.The Dirac equation with electric potential. 3.The Dirac equation with pseudoscalar potential. 4.The system describing…
The Qth-power algorithm produces a useful canonical P-module presentation for the integral closures of certain integral extensions of $P:=\mathbf{F}[x_n,...,x_1]$, a polyonomial ring over the finite field $\mathbf{F}:=\mathbf{Z}_q$ of $q$…
We consider a superintegrable Hamiltonian system in a two-dimensional space with a scalar potential that allows one quadratic and one cubic integral of motion. We construct the most general associative cubic algebra and we present specific…
We address nonautonomous initial boundary value problems for decoupled linear first-order one-dimensional hyperbolic systems, investigating the phenomenon of finite time stabilization. We establish sufficient and necessary conditions…
We discuss the prospects of performing high-order perturbative calculations in systems characterized by a vanishing temperature but finite density. In particular, we show that the determination of generic Feynman integrals containing…
Two non-commutative dynamical entropies are studied in connection with the classical limit. For systems with a strongly chaotic classical limit, the Kolmogorov-Sinai invariant is recovered on time scales that are logarithmic in the…
We propose a quantum metrology protocol based on a two-step joint evolution of the probe system and an ancillary qubit and quantum measurement. With a proper initial state of the ancillary qubit and an optimized evolution time, the quantum…
In this note we find a 6-dimensional h-spaces of the $[(21...1)(21...1)...(1...1)]$ type and then determine quadratic first integrals of the geodesic equations of these h-spaces.
We review Kitaev's celebrated "periodic table" for topological phases of condensed matter, which identifies ground states (Fermi projections) of gapped periodic quantum systems up to continuous deformations. We study families of projections…
An unsteady problem is considered for a space-fractional equation in a bounded domain. A first-order evolutionary equation involves a fractional power of an elliptic operator of second order. Finite element approximation in space is…
Quantum control protocols are typically devised in the time domain, leaving their spectral behavior to emerge only a posteriori. Here, we invert this paradigm. Starting from a target frequency-domain filter, we employ the…