A horadam-based pseudo-random number generator

Uniformly distributed pseudo-random number generators are commonly used in certain numerical algorithms and simulations. In this article a random number generation algorithm based on the geometric properties of complex Horadam sequences was investigated. For certain parameters, the sequence exhibited uniformity in the distribution of arguments. This feature was exploited to design a pseudo-random number generator which was evaluated using Monte Carlo π estimations, and found to perform comparatively with commonly used generators like Multiplicative Lagged Fibonacci and the 'twister' Mersenne

On the masked periodicity of horadam sequences: A generator-based approach

The Horadam sequence is a general second order linear recurrence sequence, dependent on a family of four (possibly complex) parameters|two recurrence coe cients and two initial conditions. In this article we examine a phenomenon identi ed previously and referred to as `masked' periodicity, which links the period of a self-repeating Horadam sequence to its initial conditions. This is presented in the context of cyclicity theory, and then extended to periodic sequences arising from recursion equations of degree three or more.The Horadam sequence is a general second order linear recurrence sequence, dependent on a family of four (possibly complex) parameters|two recurrence coe cients and two initial conditions. In this article we examine a phenomenon identi ed previously and referred to as `masked' periodicity, which links the period of a self-repeating Horadam sequence to its initial conditions. This is presented in the context of cyclicity theory, and then extended to periodic sequences arising from recursion equations of degree three or more

Local maximizers of generalized convex vector-valued functions

Any local maximizer of an explicitly quasiconvex real-valued function is actually a global minimizer, if it belongs to the intrinsic core of the function's domain. In this paper we show that similar properties hold for componentwise explicitly quasiconvex vector-valued functions, with respect to the concepts of ideal, strong and weak optimality. We illustrate these results in the particular framework of linear fractional multicriteria optimization problems.Any local maximizer of an explicitly quasiconvex real-valued function is actually a global minimizer, if it belongs to the intrinsic core of the function's domain. In this paper we show that similar properties hold for componentwise explicitly quasiconvex vector-valued functions, with respect to the concepts of ideal, strong and weak optimality. We illustrate these results in the particular framework of linear fractional multicriteria optimization problems

On the Dynamic Geometry of Kasner Quadrilaterals with Complex Parameter

We explore the dynamics of the sequence of Kasner quadrilaterals (AnBnCnDn)n≥0 defined via a complex parameter α. We extend the results concerning Kasner triangles with a fixed complex parameter obtained in earlier works and determine the values of α for which the generated dynamics are convergent, divergent, periodic, or dense

On the structure of periodic complex horadam orbits

Numerous geometric patterns identified in nature, art or science can be generated from recurrent sequences, such as for example certain fractals or Fermat’s spiral. Fibonacci numbers in particular have been used to design search techniques, pseudo random-number generators and data structures. Complex Horadam sequences are a natural extension of Fibonacci sequence to complex numbers, involving four parameters (two initial values and two in the defining recursion), therefore successive sequence terms can be visualized in the complex plane. Here, a classification of the periodic orbits is proposed, based on divisibility relations between orders of generators (roots of the characteristic polynomial). Regular star polygons, bipartite graphs and multisymmetric patterns can be recovered for selected parameter values. Some applications are also suggested.Numerous geometric patterns identified in nature, art or science can be generated from recurrent sequences, such as for example certain fractals or Fermat’s spiral. Fibonacci numbers in particular have been used to design search techniques, pseudo random-number generators and data structures. Complex Horadam sequences are a natural extension of Fibonacci sequence to complex numbers, involving four parameters (two initial values and two in the defining recursion), therefore successive sequence terms can be visualized in the complex plane. Here, a classification of the periodic orbits is proposed, based on divisibility relations between orders of generators (roots of the characteristic polynomial). Regular star polygons, bipartite graphs and multisymmetric patterns can be recovered for selected parameter values. Some applications are also suggested

Improved results synchronization on secure communication in complex dynamical networks with time-varying delay using delay-dependent feedback control

This article addresses the problem of synchronization on secure communications in complex dynamical networks (CDNs) with the time-varying coupling delay using delay-dependent feedback control. To enhance the security of communication between the master system and each node of CDNs, the ℵ-shift cipher, a cryptographic technique designed to encrypt plain signals, and a public key are used to encrypt the original information signal transmitted from the master system. After fully accounting for the nonlinear function, a unique Lyapunov-Krasovskii functional (LKF) is developed. Subsequently, new criteria are derived using novel integral inequalities and the reciprocally convex combination method to handle the derivative of the LKF, which is finally formulated in terms of linear matrix inequality (LMI). These criteria recover the original information signal on each CDNs node and ensure stable synchronization, thus facilitating secure communication among all nodes of the master system and CDNs. The efficacy and merits of the synchronization criteria are demonstrated using Chua’s circuit in four distinct scenarios

An integral formula for the coefficients of the inverse cyclotomic polynomial

Some recent advances related to an integral formula for the coefficients of inverse cyclotomic polynomials, including applications and numerical simulations are given

An equivalent property of a Hilbert-type integral inequality and its applications

Making use of complex analytic techniques as well as methods involving weight functions, we study a few equivalent conditions of a Hilbert-type integral inequality with nonhomogeneous kernel and parameters. In the form of applications we deduce a few equivalent conditions of a Hilbert-type integral inequality with homogeneous kernel, and we additionally consider operator expressions

Memory-based sampled-data control scheme for vehicle seat suspension system with actuator faults via a looped Lyapunov approach

This paper addresses the problem of controlling the Vehicle Seat Suspension System (VSSS) under actuator faults using a memory-based sampled-data control (MSDC) strategy, incorporating looped Lyapunov functions. While previous works have focused on suspension control or actuator fault tolerance individually, few have combined memory-based control with fault-tolerant strategies specifically for Vehicle Seat Suspension Systems (VSSS). This study fills this gap by constructing a 3-Degrees of Freedom (DOF) seat suspension model and designing a novel memory-dependent sampled-data controller. The proposed method improves stability and vibration control by incorporating memory parameters and handling disturbance attenuation and output constraints through H-infinity control theory. Simulation results, validated under various road conditions, show significant improvements in ride comfort, road holding, and vehicle handling, outperforming traditional control strategies and also the Root Mean Square (RMS) values indicate significant reduction in vibration

Numerical analyses of acoustic vibrational resonance in a Helmholtz resonator

In this study, the numerical analyses of a system, which describes the motion of air particles in the cavity of a Helmholtz resonator (HR), excited by a sound wave, was conducted. The low-frequency (LF) signal in the acoustic field is amplitude-modulated by an additive high-frequency (HF) perturbation, which can enhance the detection of the low-frequency, through Vibrational Resonance (VR) phenomena. The focus was on the combined effect, of amplitude and frequency of the acoustic excitation, on the motion of particles and induction of resonance. It was demonstrated that the system exhibits several nonlinear behaviours, VR ceasing to exist for a particular motion of the particles, which is dictated by the excitation frequency in relation to the resonator’s geometry. Furthermore, the regimes in which the performance of the system can be optimized, was identified, which facilitated the design of broadband acoustic resonators, suitable for most applications