Jurnal Diferensial

Solution of Direct and Inverse Dynamic Problem for the Previously Disturbed Dynamical Systems

Roman Voliansky — 2024-06-04

The paper deals with developing backgrounds to study and design the controllers for a wide class of dynamical systems that can be found in various branches of human life. We offer to use the known approach based on the solution of direct and inverse dynamic problems. This approach us to define system motions by external signals that are given to it as well as define these signals by known motion trajectories. Since the used approach operates with the transfer functions apparatus we offer to generalize these functions by taking into account the system's non-zero initial state while performing the Laplace-Carson's transformation. Such an approach gives us the possibility to consider the generalized transfer function as some matrix differential operator that defines free and perturbed system motions. We study this operator in our paper and show the patterns of its determination and implementation. Our study allows us to supplement the definition of direct and inverse dynamic problems and consider the last one as the problem with several solutions that define the control signal, external efforts, and initial conditions. We use them to define the generalized direct and inverse transfer functions.

Coupled Effects of Magnetohydrodynamics and Nanoparticles on Nonlinear Stretching Wedge Flow with Multiple Slips and Non-Uniform Heating

Victor Adetayo akinrimade — 2024-06-04

This study investigates the complex interplay between magnetohydrodynamics (MHD), nanoparticle behavior, and fluid flow characteristics in the context of a nonlinear stretching wedge with multiple slips and non-uniform heating. The flow is driven by a water-based fluid containing nano-sized particles of aluminum oxide and copper $\left( Al_2O_3-Cu/H_2O\right)$ . The governing equations of the problem are derived and then solved using appropriate numerical techniques. The effects of various parameters such as the magnetic field strength, nanoparticle volume fraction, wedge angle, slip parameters, and non-uniform heat source are thoroughly analyzed. Results reveal significant alterations in the flow behavior due to the presence of nanoparticles and the applied magnetic field. The interaction between the fluid flow and magnetic field induces a substantial change in velocity and temperature distributions along the wedge surface. Moreover, the slip effects and non-uniform heat source further modify the flow characteristics. This investigation provides valuable insights into the coupled effects of MHD, nanoparticles, and slip conditions on the flow dynamics and thermal behavior in nonlinear stretching wedge configurations. Such insights are crucial for understanding and optimizing processes involving fluid flow and heat transfer in engineering applications, particularly those utilizing nano-fluids and magnetic fields.

Dynamics of COVID-19 Incorporating Preventive Measures and Treatment

Eirene O Arierhie — 2024-06-04

The surge of Coronavirus disease (COVID-19) was felt all over the world greatly after it was declared a pandemic in the year 2020. After 3 years in 2023, the disease passed the pandemic phase
and entered an endemic phase. But that didn’t reduce the global threat of the disease as the disease continues to still claim lives daily. In this work, we examined the dynamics of the coronavirus
disease from a mathematical view using a deterministic SEIAISQVRIP LP model. This consists of
investigating the disease-free and endemic equilibria, basic reproduction number and stability. The
local stability of the disease-free equilibrium was determined by solving the Jacobian matrix of the
system of the system of differential equations while the basic reproduction number was calculated
using the next generation matrix method. Numerical simulations to determine the active factor(s) in
the transmission, preventive and possible elimination of the disease were carried out using a computational software called Maple. It was revealed that over time when all modalities are out into place the rate of recovery increases and as the rate of the pathogen virus death increases, the pathogen virus gradually fades from the environment.

The Topological Indices of Coprime Graph for Integer Module Group

Abdurahim Abdurahim — 2024-08-04

This study delves into the fascinating realm of coprime graphs within the integer modulo group, revealing a fundamental property where these graphs manifest as star graphs when the order corresponds to a prime power. This pivotal insight, as elucidated by [1], plays a crucial role in the determination of topological indices for these graphs. The research culminates in the formulation of formulas for the First Zagreb index and the Second index of coprime graphs in the context of integer modulo groups, unveiled in the last two theorems. These numerical topological indices are poised to unveil intricate correlations among group elements, contingent upon their order, echoing the foundational principles of chemical graph theory. This exploration not only enriches our understanding of group structu.Coprime Graph

MATHEMATICAL (SEIRB) MODEL ANALYSIS FOR EVALUATING CHOLERA CONTROL STRATEGIES IN REMOTE DRY SEASON REGION

Zainab Olabisi DERE — 2024-11-01

Cholera, caused by the Vibrio cholerae bacterium, poses a significant public health threat in remote regions of Nigeria, especially during the dry season when access to treated water is limited. This research aims to develop a comprehensive model to understand the rapid spread of cholera in these areas and evaluate the efficacy of control policies, including educational programs, antibiotics, water treatment rates, and environmental cleanliness through resolving the Existence and Uniqueness of the model formulation, Positivity, and Boundedness, Basic Reproduction Number, i.e. the threshold of the disease dynamics. When the versatility of the disease spreads will die out with time and if, the persistence of the disease prevails over time. Local and Global stability analysis of the model was obtained, also the sensitivity analysis for the targeted parameters was analyzed. Additionally, the study incorporates numerical simulations utilizing the homotopy perturbation method to identify the specific impact of the control parameters are for in mitigating the spread of the Vibrio cholerae disease. The result obtained seeks to provide valuable insights into designing effective intervention strategies aforementioned to combat cholera outbreaks in resource-constrained regions, with a focus on improving water accessibility and implementation.

Implementation of K-Nearest Neighbor Algorithm on Density-Based Spatial Clustering Application with Noise Method on Stunting Clustering

Friansyah Gani — 2024-11-01

This paper studies the implementation of the K-Nearest Neighbor (KNN) algorithm on Density-Based Spatial Clustering Application with Noise (DBSCAN) method on stunting Clustering in the eastern region of Indonesia in 2022. The DBSCAN method is used because it is more efficient to perform the Clustering process for irregular Clustering shapes. The main objective of this study is to apply the KNN algorithm to the DBSCAN Clustering technique in 161 Districts/Cities in 11 provinces in eastern Indonesia. A comparison of the performance evaluation of the DBSCAN Clustering technique is done by considering the value of the Silhouette score, BetaCV score, and Davies-Bouldin score indicating the quality of the Clusters formed with the lowest results scores of 0.67 and 1.84 with epsilon value = 3.4 and minimum point value = 2 resulting in 4 Clusters. The results of Clustering 161 Districts and Cities based on the factors that cause stunting formed 4 Clusters where Cluster 0 consists of 119 Districts and Cities with very high stunting characteristics, Cluster 1 consists of 3 Districts and Cities with high stunting characteristics, the results of Cluster 2 consist of 2 Districts and Cities with low stunting characteristics, then the results of Cluster 2 consist of 2 Districts and Cities with low stunting characteristics and Cluster 3 consists of 2 Cities with very low stunting characteristics.

Dimensi k-Metrik Pada Graf Parasut Diperumum

Deddy Rahmadi — 2024-11-01

Given a simple and connected graph $G=(V(G), E(G))$ and positive integer $k$. Set $S \subseteq V(G)$ is $k$-metric generator if for every pairs of distinct vertices $u,v \in V(G)$, there exists at least $k$ vertices $w_{1}, w_{2}, \ldots, w_{k} \in S$ such that $d(u,w_{i}) \neq d(v,w_{i})$ for every $i \in \{1,2,\ldots, k\}$, with $d(u,v)$ is length of shortest path form $u$ ke $v$. The $k$-metric generator with minimum cardinality is called $k$-metric bases, and the cardinalty is $k$-metric dimension of $G$denoted by $dim_{k}(G)$. This research will discuss the $k$-metric dimension of generalized parachute graphs.

Catatan terhadap Turunan Fungsi Bernilai Real pada Ruang Metrik Diskrit

Syamsuddin Mas’ud — 2024-11-01

In these notes, comments will be provided on the paper by Herdiana et al. (Jurnal Ilmiah
Matematika dan Pendidikan Matematika: 15(2), 2023). In that paper, a definition of the derivative
of a function in a metric space is given, along with properties involving discrete metric spaces. The
purpose of these notes is to comment on the section involving discrete metric spaces, specifically
where a derivative is defined for functions in a discrete metric space, despite that discrete metric
spaces do not have limit points. Additionally, if certain modifications are made to the definition of
the derivative to accommodate discrete metric spaces, it would result in the derivative values not
being unique. This makes the discussion of the derivative of functions in discrete metric spaces
meaningless.

Kaitan Fungsi Gamma terhadap Fungsi Trigonometri

Zaidulkhair Hamzi — 2024-11-01

This paper is a literature study on the relationship between real factorials denoted by gamma functions to trigonometric functions. The main objective of this study is to prove the relationship with a different method from what has been done by George E. Andrews in the book “special functions”. In Goerge’s paper, the connection is proved by using the definition of the gamma function in integral form. As for this paper, the proof is done by using the definition of gamma function in a form other than integral.