Journal of Fundamental Mathematics and Applications (JFMA)
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CLUSTERING LARGE APPLICATION USING METAHEURISTICS (CLAM) FOR GROUPING DISTRICTS BASED ON PRIMARY SCHOOL DATA ON THE ISLAND OF SUMATRA
Get PDFK-medoids is one of the partitioning methods with the medoid as its center cluster, where medoid is the most centrally located object in a cluster, which is robust to outliers. The k-medoids algorithm used in this study is Clustering Large Application Using Metaheuristics (CLAM), where CLAM is a development of the Clustering Large Application based on Randomized Search (CLARANS) algorithm in improving the quality of cluster analysis by using hybrid metaheuristics between Tabu Search (TS) and Variable Neighborhood Search (VNS). In the case study, the best cluster analysis method for classifying sub-districts on the island of Sumatra based on elementary school availability and elementary school process standards is the CLAM method with k=6, num local = 2, max neighbor = 154, tls = 50 and set radius = 100-10:5. It can be seen that based on the overall average silhouette width value, the CLAM method is better than the CLARANS method
OPTIMIZATION ALGORITHMS FOR PROJECTILE MOTION: MAXIMIZING RANGE AND DETERMINING OPTIMAL LAUNCH ANGLE
Get PDFIn this paper, we undertake an in-depth exploration of the optimization of parameters governing the trajectory of a projectile. Our primary objective is the determination of the optimal launch angle and initial velocity that yield the maximum achievable range for the projectile. To accomplish this, we leverage five distinct optimization methodologies, specifically the Nelder-Mead, Powell, L-BFGS-B, TNC, and SLSQP algorithms, in pursuit of our research goals. This paper offers a comprehensive analysis of the optimization procedures, shedding light on the impact of these diverse algorithms on the resultant outcomes. For each set of optimized parameters, the manuscript conducts extensive simulations of the projectileโs trajectory, presenting visual depictions of the paths traversed by the projectile. Additionally, our study incorporates comparative charts to emphasize the performance distinctions among various algorithms with respect to both maximum range and launch angle
EXPLORING PHYSICS-INFORMED NEURAL NETWORKS FOR SOLVING BOUNDARY LAYER PROBLEMS
Get PDFIn this paper, we explore a cutting-edge technique called as Physics- Informed Neural Networks (PINN) to tackle boundary layer problems. We here examine four different cases of boundary layers of second-order ODE: a linear ODEwith constant coefficients, a nonlinear ODE with homogeneous boundary conditions, an ODE with non-constant coefficients, and an ODE featuring multiple boundary layers. We adapt the line of PINN technique for handling those problems, and our results show that the accuracy of the resulted solutions depends on how we choose the most reliable and robust activation functions when designing the architecture of the PINN. Beside that, through our explorations, we aim to improve our understanding on how the PINN technique works better for boundary layer problems. Especially, the use of the SiLU (Sigmoid-Weighted Linear Unit) activation function in PINN has proven to be particularly remarkable in handling our boundary layer problems
A CLOSER LOOK AT A PATH DOMINATION NUMBER IN GRID GRAPHS
Get PDFThis article exposes the combinatorial formula that determines the pathdomination number in a grid graph and discusses some of its properties. Seven propertiesare derived regarding the path domination number of grid graphs. Furthermore, some additional properties as direct consequences of the derived main properties are alsodiscussed
MODIFIED HOUSEHOLDER METHOD OF FIFTH ORDER OF CONVERGENCE AND ITS DYNAMICS ON COMPLEX PLANE
Get PDFIn this paper, a modified Householder method of fifth order is proposed for solving nonlinear equations. The modification is done by adapting a cubic interpolation polynomial to approximate the second derivative in the Householder method. Weprovide a theorem to prove the order of convergence of the proposed method. The simulations reveal that the proposed method needs fewer iterations, even with challenging initial guesses, and excels in sending a large portion of initial points to convergence and exhibits rapid convergence
MATHEMATICAL MODEL OF MEASLES DISEASE SPREAD WITH TWO-DOSE VACCINATION AND TREATMENT
Get PDFThis study developed a model for the spread of measles based on the SEIR model by adding the factors of using the first dose of vaccination, the second dose of vaccination, and treatment. Making this model begins with making a compartment diagram of the spread of the disease, which consists of seven subpopulations, namely susceptible subpopulations, subpopulations that have received the first dose of vaccination, subpopulations that have received the second dose vaccination, exposed subpopulations, infected subpopulations, subpopulations that have received treatment, and subpopulations healed. After the model is formed, the disease-free equilibrium point, endemic equilibrium point, and basic reproduction number (R_0) are obtained. Analysis of the stability of the disease-for equilibrium point was locally asymptotically stable when (R_0)<1. The backward bifurcation analysis occurs when (R_C) is present and R_C<R_0. Numerical simulations of disease-free and endemic equilibrium points are carried out to provide an overview of the results analyzed with parameter values from several sources. The results of the numerical simulation are in line with the analysis carried out. From the model analysis, the disease will disappear more quickly when the level of vaccine used and individuals who carry out treatment are enlarged
BONUS MALUS SYSTEM FOR MOTORIZED VEHICLE INSURANCE USING GEOMETRIC DISTRIBUTIONS AND WEIBULL DISTRIBUTIONS
Get PDFThe bonus malus system is one of the systems used to determine the premium amount for the next period based on the claim history of the policyholder. If the policyholder has no claims history or did not file a claim in the previous year, then the policyholder will get a bonus or in other words will get a reduction in the premium rate in the following period. Meanwhile, if the policyholder has a history of claims in the previous year, then the policyholder will be subject to a malus or must pay an increase in the premium rate in the following period. The purpose of this study is to calculate motor vehicle insurance premiums using the classic and optimal bonus malus method which takes into account the frequency of claims with a geometric distribution and the size of claims with a Weibull distribution. The results of this study indicate that the optimal bonus malus system is fairer for policyholders who renew their policies because the premium paid by the policyholder depends on the number of claims and the size of the claim, so that each policyholder will pay a different premium to the number of claims
FROZEN INITIAL LIABILITY METHOD TO DETERMINE NORMAL COST OF PENSION FUND WITH VASICEK INTEREST RATE MODEL
Get PDFCivil servants have an important role in national development, so increasing their productivity is needed. The pension fund program is given as a form of effort by government agencies to ensure employee welfare when entering retirement. This research discusses the normal cost of the defined benefit pension program using one of the actuarial valuation methods, namely Frozen Initial Liability (FIL), by taking into account the stochastic interest rate following the Vasicek model. The data used in this study are lecturers majoring in MIPA, Faculty of Science and Technology, Universitas Jambi, consisting of 8 people of female gender with the status of being a participant since 2022. Based on the calculation results obtained that in the period 0-30 years, the normal cost for each group member is constant, namely ย per year or ย per month. When the working period entered 31 years, one by one the participants began to enter their retirement period, which resulted in a change in the normal cost value. At 38 years of service, there was only one participant with a normal cost of ย per year or by ย per month. Changes in normal cost tend to decrease when retirement program participants also decrease. In the period of more than 38 years, all participants have retired so that normal cost payments are stopped
MATHEMATICAL ANALYSIS OF A TUBERCULOSIS MODEL WITH TWO DIFFERENT STAGES OF INFECTION
Get PDFTuberculosis is an infectious disease. This disease causes death and the world notes that Tuberculosis has a high mortality rate. A mathematical model of Tuberculosis withย two infection stages of individuals, pre infected and actively infected, is studied in this paper. The rate of treatment considered in this model. The stability analysis of the equilibrium is determined by the basic reproduction ratio. Routh Hurwitz linearization is used for investigate the local stability of uninfected equilibrium. While the global stability of endemic equilibrium is investigated by construct Lyapunov function. The effect of treatment in pre infected and actively infected stages can reduce the spread rate of Tuberculosis as shown in numerical simulation
IDEMPOTENT ELEMENTS IN MATRIX RING OF ORDER 2 OVER POLYNOMIAL RING
No full textAn idempotent element in the algebraic structure of a ring is an element that, when multiplied by itself, yields an outcome that remains unchanged and identical to the original element. Any ring with a unity element generally has two idempotent elements, 0 and 1, these particular idempotent elements are commonly referred to as the trivial idempotent elements However, in the case of rings and it is possible to have non-trivial idempotent elements. In this paper, we will investigate the idempotent elements in the polynomial ring with different primes. Furthermore, the form and characteristics of non-trivial idempotent elements in will be investigated. The results showed that there are 4 idempotent elements in and 7 idempotent elements in .An idempotent element in the algebraic structure of a ring is an element that, when multiplied by itself, yields an outcome that remains unchanged and identical to the original element. Any ring with a unity element generally has two idempotent elements, 0 and 1, these particular idempotent elements are commonly referred to as the trivial idempotent elements However, in the case of rings and it is possible to have non-trivial idempotent elements. In this paper, we will investigate the idempotent elements in the polynomial ring with different primes. Furthermore, the form and characteristics of non-trivial idempotent elements in will be investigated. The results showed that there are 4 idempotent elements in and 7 idempotent elements in