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Dec 29, 2023Open    Access

Dynamical Localization of the Quasi-Periodic Schrödinger Operators

Walid Refai
In this paper, we study the spectral properties of a family of discrete one-dimensional quasi-periodic Schrödinger operators (depending on a phase theta). In the perturbative regime and in large disorder, under some conditions on v and a diophantine rotation number, we prove by using KAM theory that this operator satisfies both Anderson and dynamical localization for all θ∈[0,2π).
Open Access Library J.   Vol.10, 2023
Doi:10.4236/oalib.1110966


Jun 28, 2023Open    Access

On Some Chaos Notions of Supra Topological Space

Malouh Baloush, Syahida Che Dzul-Kifli
In this paper, we investigate the dynamics of supra topological space. We introduce some concepts of supra chaos notions, i.e., supra transitive, supra minimal, supra totally transitive, supra mixing, supra locally everywhere onto (briefly, supra l.e.o), and supra weakly blending. First, we investigate some properties of supra transitive map, after that we figure out the relations of the supra chaos notions with the classical chaos notions and showed that supra l.e.o, supra mixing, supra totally...
Open Access Library J.   Vol.10, 2023
Doi:10.4236/oalib.1108609


Nov 28, 2022Open    Access

Application and Popularization of Formal Calculation

Ji Peng
Formal Calculation, formerly known as the Shape of Numbers, is suitable for calculating some nested sums. The formula has been obtained, and the calculation problem of various combinations of arithmetic sequences has been solved. This paper analysis the coefficients of the formulas and obtain some simplified identities. Furthermore, the Formal Calculation is extended from binomial coefficient to Gaussian coefficient, and the application is extended from two parameters forms to multiparameter for...
Open Access Library J.   Vol.9, 2022
Doi:10.4236/oalib.1109483


Oct 25, 2022Open    Access

Mathematical Modelling of Diabetes under a Constrained Hospitalisation Resources

Robert N. Andima, Winifred N. Mutuku, Nyabadza Farai, Kennedy Awuor, Abayomi Samuel Oke
Diabetes is a chronic disease in which the body is unable to convert the excess sugar into a useable form. It is chronic disease that is fast becoming a menace in the Kenyan communities. In this study, the response of the complicated diabetic cases is examined under a constrained hospitalisation setting. The mathematical model is formulated by incorporating the carrying capacity and the per capita hospitalization rate. The models are numerically solved in MATLAB using the explicit Runge-Kutta (4...
Open Access Library J.   Vol.9, 2022
Doi:10.4236/oalib.1109371


Aug 26, 2022Open    Access

Evidence of a Dark Matter that Is Not an Exotic Matter: WLM’s Case

Stéphane Le Corre
A recent article reports new observations of the gaseous content of Wolf-Lundmark-Melotte (WLM), an archetype of isolated, gas-rich field dwarf galaxies in the Local Universe, which presents an unexpected situation, four trailing, extended gas clouds lying in the direction opposite to WLM’s spatial motion, as well as a spatial offset between the WLM gas and stars, which rules out the near-completion merger hypothesis and suggests a process called ram-pressure stripping. For these authors, this f...
Open Access Library J.   Vol.9, 2022
Doi:10.4236/oalib.1109086


Jun 29, 2022Open    Access

The Redshift Effect as an Electrodynamic Concept

Isaak Man’kin
We discuss the nature of the redshift effect by assuming that the frequency and the speed of light decrease in time while it propagates from a stationary source of light relative to a stationary observer. This concept differs in a principal way from the modern model of the redshift effect, which states that the observed increase in the wavelength of emitted light from far-away objects is due to cosmological expansion of the universe. Precisely, an increase in the distance between a light source ...
Open Access Library J.   Vol.9, 2022
Doi:10.4236/oalib.1108917


Aug 06, 2021Open    Access

Numerical and Chaotic Analysis of Proposed SIR Model

Maysoon M. Aziz, Arqam S. Mahmood
In this paper, we use the classic mathematical model SIR with the three differential equations as a non-linear system and combine it with the Runge-Kutta numerical method of the fourth order and the sixth and seventh order of the same method to generate simulated data in each of the mentioned ranks (for susceptible people, Infected and recovered from the disease) for the epidemic disease COVID-19 by giving the initial values (initial conditions) for the population in a certain country of the wor...
Open Access Library J.   Vol.8, 2021
Doi:10.4236/oalib.1107618


Jul 29, 2021Open    Access

The Second Wave of Covid-19 and the Present and Continuing Challenges of the Health and Care System from the Side of a Numerical Analysis

Mariam Almahdi Mohammed Mu’lla, Munirah Oudah Alanazi
The second wave of Covid-19 presents new and ongoing challenges to the health and care system. The main objective of this study is to take into account the quality of health work and health guidelines in anticipation of the health care systems not collapsing, thus saving more time in the fight against this epidemic and appropriate preparation for each emergency situation arising from this epidemic. In this study we will deal with Covid19 in terms of mathematics, to look at this epidemic from mul...
Open Access Library J.   Vol.8, 2021
Doi:10.4236/oalib.1107665


Jun 23, 2021Open    Access

Stability and Chaos Tests of 2D Discrete Time Dynamical System with Hidden Attractors

Maysoon M. Aziz, Omar M. Jihad
In this research two-dimensional dynamical system was taken. The system was analyzed through its fixed points, stability analysis, chaos diagnoses and adaptive control technique. It was found that the system had a hidden attractor and unstable fixed points. The largest value of Lyapunov exponent equals 1.853981 and from binary test we get: k = 0.9305, which indicates that the system is chaotic. Adaptive control technique was performed, and it was found that the system is stable and regular after...
Open Access Library J.   Vol.8, 2021
Doi:10.4236/oalib.1107501


May 31, 2021Open    Access

Homoclinic Bifurcation of a Quadratic Family of Real Functions with Two Parameters

Salma M. Farris, Karam N. Abdul-Kareem
In this work the homoclinic bifurcation of the family H={h(a,b)(x)=ax2 b:a∈R/{0},b∈R} is studied. We proved that this family has a homoclinic tangency associated to x=0 of P1 for b=-2/a. Also we proved that Wu(P1) does not intersect the backward orbit of P1 for b>-2/a, but has intersection for b<-2/a with a>0. So H has this type of the bifurcation.
Open Access Library J.   Vol.8, 2021
Doi:10.4236/oalib.1107300


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