Results in Nonlinear Analysis

A RELIABLE ALGORITHM FOR SOLVING BLASIUS BOUNDARY VALUE PROBLEM

2024-08-07T21:36:20+03:00

The Blasius equation is a well-known third-order nonlinear
ordinary differential equation that can be found in some fluid dynamics boundary layer problems.

In this paper, we convert the nonlinear differential equation to an integral equation, this integral equation has
a shifted kernel. Our goal is to propose an efficient modification of the
standard Adomian decomposition method, combined with the Laplace
transform, for solving the Blasius equation. The main impediment to
solving the Blasius equation is the absence of the second derivative at
zero. Once this derivative has been correctly evaluated, an analytical
solution to the Blasius problem can be easily found; as a result, we use
our approximate solution to estimate the value of y′′(0), also known asthe

Blasius constant. Understanding the Blasius constant is essential
for calculating shear stress at a plate. Furthermore, once this value
is determined, we have the initial value problem, which can be solved
numerically

SOLUTION TECHNIQUES FOR TIME DEPENDENT AVAILABILITY IN COMPLEX AND REPAIRABLE SYSTEM: A COMPARATIVE STUDY

2023-11-27T12:02:08+03:00

The paper elucidates two distinct techniques for conducting a comparative study aimed at ascertaining the transient availability of a repairable system. The use of Markov modeling forms the basis of this investigation strategy. The set of differential equations in the current study is formulated, and they are then solved using the Laplace transform method and the matrix method, respectively. To help with a clearer understanding of the system, these approaches are subjected to a thorough evaluation and comparative study. Availability guarantees that critical processes, failure analysis and services continue to run smoothly, which is essential for business continuity. In sectors like finance, public health, and telecommunications, this is especially crucial. Productivity and availability are directly related. Systems that are continuously available allow workers and resources to be used to their greatest potential, increasing productivity and efficiency.

ON RECURRENCE IN DENDRITE FLOWS

2024-07-31T11:35:37+03:00

Consider a subgroup generated by a finite subset G that acts on
a dendrite X by transformations. (G, X) is called a flow. In this note, it was
proven that the flowing properties are equivalent:
(1) the flow (G, X) is pointwise recurrent;
(2) the flow (G, X) is almost periodic;
(3) the orbit closure relation of the flow (G, X) is closed;
(4) the flow (G, X) is equicontinuous.
Furthermore, we give a transitive flow having only two recurrent points

Controlling the movement of hexacopter along the intended route

2024-08-11T17:28:49+03:00

The article examines the issue of controlling the movement of a hexacopter-type unmanned aerial vehicle along the intended route. The movement of the hexcopter is assumed as the movement of a solid body, gravity and aerodynamic drag forces are taken into account. It is assumed that the feedback data during control (accelerometer and gyroscope data) ise obtained from MPU6050 type sensors. MPU6050 type sensors do not measure orientation angles, but their rate of change, therefore, quaternions were used as orientation parameters in the mathematical model of hexocopter movement. In this article, the movement route is described as a trajectory consisting of straight sections, and an algorithm for calculating the base values of the control parameters is given, which ensures stable flight in each straight section of the trajectory , when all the engines of the hexocopter are working normally. During the study, the issue of ensuring straight-line movement of hexacopters when any of the hexacopter engines is faulty (out of order) was also considered, in this case, the optimal control parameters ensuring straight-line flight of the hexacopter were determined.

NONLINEAR CONTRACTION MAPPING IN PROBABILISTIC CONTROLLED GENERALIZED METRIC SPACES

2024-07-27T19:54:10+03:00

This paper presents a new framework referred to as "probabilistic
controlled generalized metric spaces," extending the theory of probabilistic metric
spaces. The aim is to examine the correlation between this innovative class and the
traditional axioms of probabilistic metric spaces. Moreover, the paper delves into
proving the existence of fixed points for the }-probabilistic contraction mapping,
even without the presence of the Hausdorff condition. The paper will also feature
illustrative examples to underscore the practicality and efficacy of the theories and
methodologies presented.

SOME RESULTS ON GEOMETRIC PROPERTIES OF FRAMES IN BANACH SPACES

2024-09-01T19:46:33+03:00

In this paper, we have defined A- cone and related concepts in Banach spaces and prove a result concerning convergence of a sequence in an A- cone. Also, atomic system for a subset of a Banach space is defined and proved that if a Banach space has an atomic system, then every subset of it also has an atomic system.

On uniform ideals and finite Goldie dimension in $R$-groups

2024-09-04T16:05:20+03:00

We consider an $R$-group $G$, where $R$ is a (right) nearring. We introduce the notions relative uniform and strictly relative uniform ideals (or $R$-subgroup) which are not uniform, in general. We prove important properties and obtain a characterization for an $R$-subgroup to have finite Goldie dimension, in terms of strictly relative uniform $R$-subgroups. We provide the necessary examples.

Graded 2r-Ideals

2024-06-11T20:51:17+03:00

Let G be a group and R be a commutative G-graded ring with nonzero unity. In this article, we establish the concept of graded 2r-ideals, which lies somewhere between graded r-ideals and graded uniformly pr-ideals. A proper graded ideal P of R is said to be a graded 2r-ideal of R if whenever x, y ∈ h(R) such that xy ∈ P , then either x² ∈ P or y ∈ zd(R), where zd(R) is the set of all zero divisors of R. Several properties of graded 2r-ideals have been achieved, and various results have been investigated.

Remarks on the fixed point theory for quasi-metric spaces

2024-07-04T14:38:26+03:00

Motivated by a recent and interesting article by S. Park [Results in Nonlinear Analysis 6 (2023) No. 4, 116–127], we recall several different notions of quasi-metric completeness that appear in the literature and revise how they influence on the fixed point theory in quasi-metric spaces. In particular, we point out that there are several classical fixed point theorems that cannot be directly transferred to the quasi-metric setting without extra conditions, when Park's approach is considered. We also recall some emblematic examples that can help to clarify some aspects of the fixed point theory for these spaces.

SUBCLASSES OF YAMAKAWA-TYPE BI-STARLIKE FUNCTIONS SUBORDINATE TO GEGENBAUR POLYNOMIALS ASSOCIATED WITH QUANTUM CALCULUS

2024-07-25T13:30:21+03:00

In this paper, we present a novel class of Yamakawa-type bi-starlike functions. These functions are defined using Gegenbauer polynomials associated with q-calculus. We have derived estimates for the Maclaurin coefficients |a₂| and |a₃| for functions in the Yamakawa-type bi-starlike function class. Additionally, we have solved the Fekete-Szegö problems for functions in this new subclass. By specializing the parameters in our main results, we have obtained several new findings.

MATHEMATICAL MODELLING FOR JOINING CARBON NANOSTRUCTURES: FULLERENE AND TORUS

2024-10-09T15:06:49+03:00

Dierent congurations of carbon nanostructures, includ-
ing carbon nanotori and carbon fullerenes, have been identied using
experimental techniques. These structures are used at the nanoscale in
many dierent elds, and their inclusion may lead to novel combina-
tions with improved features and applications. In this study, a carbon
fullerene and nanotorus combination was identied. Two dierent ap-
proaches that depend on energy minimization were used to predict the
conjoining curves. The primary model targets the reduction of elastic
energy focusing on axial curvature alone, but the alternative model in-
corporates the Willmore energy, that accounts both the rotational and
the axial curvatures. Due to the catenoid status as an optimal min-
imiser of this energy, a segment of it employed to facilitate the fusion
of two nanostructures. Our ndings reveal that both proposed models
successfully identify the junction area among nanostructures, allowing
for the creation of integrated nanostructures through either method.

Study stabilizability and solvability for chemical kinetics of the delayed oregonator model

2024-11-18T08:48:48+03:00

Delays naturally appear in chemical reactions and they are often responsible for presence of complex behaviours, we will be take delay effects in Beulosuv-Zhabotonksiy reaction this mechanism is represented by a simple model, called the Oregonator model. Chemical kinetics of the considered Oregonator model will be taken by use of delay mass-action law and study the stabilizability and solvability by backstepping method after formally introduce the chain approximation for kinetic scheme of delayed Oregonator model. We will compar stabilizability results output between backstepping with method of steps and backstepping with chain method