398 Results Found

We introduce the Hamiltonian pseudorandom function (HPRF), a new symmetric cryptographic primitive in which the function family $\left\{F_k\right\}$ is defined by $F_k\left(q\right)=\nabla S_k\left(q\right)$, the gradient of the generating function of a secret Lagrangian submanifold $L_k$ on th...

DC microgrid applications include electric vehicle systems, shipboard power systems, and More Electric Aircraft (MEA), which produce power at a low voltage level. Rapid developments in hydrogen fuel cell (FC) energy have extended the applications of...

The discussion revolves around the most recent outcomes in the realm of approximating functional integrals through calculations. Review of works devoted to the application of functional integrals in quantum mechanics and quantum field theory, nuclear...

In this paper, we argue in favor of first-order homogeneous Lagrangians in the velocities. The relevant form of such Lagrangians is discussed and justified physically and geometrically. Such Lagrangian systems possess Reparametrization Invariance (RI...

The idea of the normalisation of the Hamiltonian system is to simplify the system by transforming Hamiltonian canonically to an easy system. It is under symplectic conditions that the Hamiltonian is preserved under a specific transformation—the so-ca...

This review is devoted to the universal algebraic and geometric properties of the non-relativistic quantum current algebra symmetry and to their representations subject to applications in describing geometrical and analytical properties of quantum an...

In the theory of open quantum systems, the Markovian approximation is very widespread. Usually, it assumes the Gorini–Kossakowski–Sudarshan–Lindblad (GKSL) equation for density matrix dynamics and quantum regression formulae for mul...

The aim of this paper is to develop an algebraically feasible approach to solutions of the oriented associativity equations. Our approach was based on a modification of the Adler–Kostant–Symes integrability scheme and applied to the co-adjoint orbits...

This article presents alternative Hamiltonian and Lagrangian formalisms for relativistic mechanics using proper time and proper Lagrangian coordinates in 1 + 1 dimensions as parameters of evolution. The Lagrangian and Hamiltonian formalisms for a hyp...

Establishing precise and reliable quadrotor dynamics model is crucial for safe and stable tracking control in obstacle environments. However, obtaining such models is challenging, as it requires precise inertia identification and accounting for compl...

With large-scale development of offshore wind power and the increasing scale of power grid interconnection, more and more attention has been drawn to the stable operation of wind power units. When the wide area measurement system (WAMS) is applied to...

This express brief deals with the problem of the state variables regulation in the ball and beam system by applying the discrete-inverse optimal control approach. The ball and beam system model is defined by a set of four-order nonlinear differential...

This paper presents a new method of describing the electronic spectrum and electrical conductivity of disordered crystals based on the Hamiltonian of electrons and phonons. Electronic states of a system are described by the tight-binding model. Expre...

Nonlinear transverse free vibrations of porous functionally-graded (FG) Bernoulli–Euler nanobeams in hygrothermal environments through the local/nonlocal stress gradient theory of elasticity were studied. By using the Galerkin method, the gover...

The classical Lotka–Volterra predator–prey system is often used in modeling species competition. The two-species nonlinear system is expressed in terms of a single positive coupling parameter $\lambda$. Based on a standard functional trans...

Following the celebrated postulates of quantum mechanics, we write the quantum mechanical wavefunction as a convergent series of suitably selected complete square-integrable basis functions in configuration space. The expansion coefficients of the se...

We present a series of pyrazolato-bridged copper complexes with interesting structures that can be considered prototypic patterns for tri-, hexa- and hepta- nuclear systems. The trinuclear shows an almost regular triangle with a μ₃-OH central group....

Bigravity is one of the most natural modifications of General Relativity (GR), as it is based on the equivalence principle. However, its canonical structure appears rather complicated because of the unusual form of the interaction between two metrics...

In this study, a new optimal control law associated with the sliding mode control is developed for the linear time-varying system based on the Bolza-Meyer criterion. The salient characteristic of the controller proposed in this work is to have adjust...

The divergence function in information geometry, and the discrete Lagrangian in discrete geometric mechanics each induce a differential geometric structure on the product manifold $Q\times Q$ . We aim to investigate the relationship between these tw...

In this paper, exact solutions of the new Hamiltonian amplitude equation and Fokas-Lenells equation are successfully obtained. The extended trial equation method (ETEM) and generalized Kudryashov method (GKM) are applied to find several exact soluti...

The functional Schrödinger representation of a nonlinear scalar quantum field theory in curved space-time is shown to emerge as a singular limit from the formulation based on precanonical quantization. The previously established relationship bet...

Time reversal invariance (TRI) of particles systems has many consequences, among which the celebrated Onsager reciprocal relations, a milestone in Statistical Mechanics dating back to 1931. Because for a long time it was believed that (TRI) dos not h...

The effective spin Hamiltonian method has drawn considerable attention for its power to explain and predict magnetic properties in various intriguing materials. In this review, we summarize different types of interactions between spins (hereafter, sp...

In recent times, ab initio density functional theory has emerged as a powerful tool for making the connection between models and materials. Insulating transition metal oxides with a small spin forms a fascinating class of strongly correlated systems...

We consider a class of cooperative differential games with continuous updating making use of the Pontryagin maximum principle. It is assumed that at each moment, players have or use information about the game structure defined in a closed time interv...

Diagnostics of power and energy systems is obviously an important matter. In this paper we present a contribution of using new methodology for the purpose of signal type recognition (for example, faulty/healthy or different types of faults). Our appr...

This paper presents an adaptive control to stabilize the output voltage of a DC–DC boost converter that feeds an unknown constant power load (CPL). The proposed controller employs passivity-based control (PBC), which assigns a desired system en...

Projector theory can serve as a powerful tool to perform the symmetric computation of molecular systems. The work of William Harter has long demonstrated the effectiveness of this theory in molecular spectroscopy; however, it seems its usefulness has...

The recent developments in dynamical systems theory and non-equilibrium statistical mechanics have allowed the birth of new challenges and research perspectives. In particular, different frameworks have been proposed for the modeling of complex emerg...

In this survey-cum-expository work, we primarily seek to study many families of the renowned Hurwitz–Lerch Zeta mapping, including the so-called generalized Hurwitz–Lerch Zeta mappings. The purpose of this study is to examine a new subcla...

This paper explores solitary wave solutions arising in the deformations of a hyperelastic compressible plate. Explicit traveling wave solution expressions with various parameters for the hyperelastic compressible plate are obtained and visualized. To...

This paper presents a quantum formulation for classical abstract dynamical systems (ADS), defined by coupled sets of first-order differential equations. They are referred to as “abstract” because their dynamical variables can be of differ...

The performance of embedding methods is directly tied to the quality of the bath orbital construction. In this paper, we develop a versatile framework, enabling the investigation of the optimal construction of the orbitals of the bath. As of today, i...

The reaction of benzene with fluorine atoms may be of interest as a source of phenyl and ipso-fluorocyclohexadienyl radicals or as a method for fluorobenzene gas phase synthesis. The structures and electronic energies of the equilibrium configuration...

Renewable energy and electric vehicles have become involved in power systems, which has attracted researchers to stochastic continuous disturbances (SDEs). This paper addresses stochastic analysis issues for the stability of a power system with losse...

Despite its importance in general relativity, a quantum notion of general covariance has not yet been established in quantum gravity and cosmology, where, given the a priori absence of coordinates, it is necessary to replace classical frames with dyn...

The mechanical and quantum properties of a nanomechanical resonator can be improved by connecting it to a superconducting resonator in a way that the resonator exhibits new phenomena that are possibly available to novel quantum technologies. The quan...

We employ Green’s function method for describing multiband models with magnetic impurities and apply the formalism to the problem of chromium impurities adsorbed onto a carbon nanotube. Density functional theory is used to determine the bandstr...

In this study, we use the dynamic programming method introduced by Mirică (2004) to solve the well-known war game of attrition and attack as formulated by Isaacs (1965). By using this modern approach, we extend the classical framework to explore...

Aiming at the problem of ultra-low-frequency oscillation (ULFO) caused by an irrational setting of governor parameters of high-head hydraulic turbine units, this paper proposes a method to optimize the additional damping control parameters of the gov...

In this paper, the Caputo-based fractional derivative optimal control model is looked at to learn more about how the human respiratory syncytial virus (RSV) spreads. Model solution properties such as boundedness and non-negativity are checked and fou...

This study focuses on the formulation and analysis of problems that are dual to those defined by convex set-valued mappings. Various important classes of optimization problems—such as the classical problems of mathematical and linear programmin...

This paper develops a measurable unified electric–thermal energy indicator for converter-dominated microgrids, containing virtual synchronous generator (VSG) and virtual asynchronous machine (VAM) dynamics. The principal contribution comprises...

The aim of this paper is to develop a Hamilton–Jacobi theory for contact Hamiltonian systems. We find several forms for a suitable Hamilton–Jacobi equation accordingly to the Hamiltonian and the evolution vector fields for a given Hamiltonian functio...

A diesel engine is a typical dynamic system. In this paper, a dynamics method is proposed to establish the Hamiltonian model of the diesel engine, which solves the main difficulty of constructing a Hamiltonian function under the multi-field coupling...

Hamiltonian Neural Networks (HNNs) provide structure-preserving learning of Hamiltonian systems. In this paper, we extend HNNs to structure-preserving inversion of stochastic Hamiltonian systems (SHSs) from observational data. We propose the quadratu...

This paper studies the number of small limit cycles produced around an elementary center for Hamiltonian differential systems with the elliptic Hamiltonian function $H=\frac{1}{2}{y}^2+\frac{1}{2}{x}^2-\frac{2}{3}{x}^3+\frac{a}{4}{x}^4(a\ne 0)$ under two types of polynomial perturbations of de...

In this paper, a three-terminal memristor is constructed and studied through changing dual-port output instead of one-port. A new conservative memristor-based chaotic system is built by embedding this three-terminal memristor into a newly proposed fo...

We study two seminal approaches, developed by B. Simon and J. Kisyński, to the well-posedness of the Schrödinger equation with a time-dependent Hamiltonian. In both cases, the Hamiltonian is assumed to be semibounded from below and to have...