Journal of Fundamental Mathematics and Applications (JFMA)
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HIERARCHICAL BAYESIAN SMALL AREA ESTIMATION ON OVERDISPERSED DATA: WORKERS WITH DISABILITIES IN INDONESIA
Get PDFPersons with disabilities encounterdifficulties in accessing essentialservices, including employment, healthcare, information, and political participation. In line with the target 8.5 of the SDGs, efforts have been made to promotefull, productive, and decent employment for all, including for persons with disabilities. However, the majority ofworkers with disabilities in Indonesia remain concentrated in the informal sector during the period of 2022–2023. Unfortunately, data on workers with disabilities is currently only available at the national level. This limitation arises because the sample size of workers with disabilities is insufficient to meet the minimum requirements for direct estimation at the provincial level. Therefore, a Small Area Estimation approach is necessary to assess the participationof persons with disabilities in the workforce at more granular level, such as provinces. In this study, auxiliary variables such as the sex ratio, the number of residents who are shackled, and the availability of computer skills infrastructure were incorporated to the Small Area Estimation (SAE) framework. The Hierarchical Bayesian Poisson-Gamma was employed to improve the precision of direct estimation. The research results show that the HB Poisson-gamma estimator has better precision compared to the direct estimator
A note on outer-connected hop Roman dominating function in graphs
Get PDFLet be a simple, connected, and finite graph with vertex set and edge set . Let be an HRDF on , and for each , let . A function is an outer-connected hop Roman dominating function (OcHRDF) on if, for every , there exists such that and either or the sub-graph is connected. The weigth of OcHRDF denoted by and defined by =|V_1|+2|V_2|G\widetilde{\gamma}_{chR}(G)\widetilde{\gamma}_{chR}(G)=min\{. Moreover, any OcHRDF on with \widetilde{\omega}_G^{chR}(\phi)\overline{\gamma}_{chR}G$. In this paper, a new restricted parameter of a hop Roman domination in graphs is introduced, and some combinatorial properties are discussed
SOME PROPERTIES OF MODULAR TOPOLOGY IN THE ORLICZ SEQUENCE SPACE
Get PDFIn this article, we examined some properties of modular topology on the Orlicz sequence space. Discussions were conducted by constructing the topology on the sequence space using a modular neighborhood of zero. The neighborhood forms a local base that is balanced, absorbing, and symmetrical. Furthermore, if the Orlicz function that grows not soo rapidly, the modular neighborhood induces a topological vector space. We also characterize the modular boundedness, modular convergence, and modular closed set on the sequence space
Sharper Upper Bounds for Roots of Polynomials Generated by Positive Sequences
Get PDFFinding sharp and easily computable upper bounds for the moduli of the roots of polynomials with real coefficients is a long-standing problem with applications in numerical analysis, control theory, and the study of linear recurrence relations. The classical bounds of Cauchy and Lagrange, despite their age, remain the most frequently used estimates because of their extreme simplicity. This paper introduces a new family of upper bounds specifically designed for polynomials whose coefficients are the initial terms of a positive real sequence a_n that does not grow too rapidly. For each such polynomial we construct an explicit number by taking the two largest values appearing among the (i+1)-th roots of the successive absolute differences of the sequence together with the simple quantity a_1+1, and adding them. We prove that the resulting value rigorously bounds the modulus of every root. A companion bound based on second differences is obtained as an immediate corollary. Extensive numerical tests on constant, arithmetic, harmonic, and exponential sequences show that the new estimates are often several times tighter than Cauchy’s bound and, in many cases, also outperform recently published refinements. The contribution is twofold: (i) a new, fully explicit bound using first differences, and (ii) an even sharper variant using second differences presented as a corollary
PMC-Labeling of Certain Classes of Graphs
Get PDFIn this paper, we investigate the PMC-labeling behavior of some new graphs such as the double fan graph, triple fan graph, --enriched fan graph, C_{n}--snake, stripe blade graph, G_{n}, Sf_{n} + K_{1}, armed helm graph, alternate armed helm graph and spectrum graph
EPIDEMIC ANALYSIS, MATHEMATICAL MODELLING AND NUMERICAL SIMULATION OF COVID-19 TRANSMISSION
Get PDFThis research develops a model with seven compartments SEIQDHR for the spread of COVID-19, with detected and treated individual behavior changes affecting disease transmission. The Next Generation Matrix is used to analyze local and global stability and to calculate the basic reproduction number. Then, the analysis of disease-free equilibrium and endemic equilibrium. Stability analysis shows that the equilibrium point is locally asymptotically stable when the basic reproduction number is less than one and globally asymptotically stable when it is greater than one. The results of the sensitivity analysis show that the transmission rate, the progression rate from exposure, and the detection rate are parameters that significantly influence the dynamics of disease spread. Numerical simulations were used to validate the analysis results and identify key parameters that contribute most to the spread of the disease among affected, infected, quarantined, diagnosed, and hospitalized individuals
STABILITY ANALYSIS OF THE MODEL SVEI_a I_sR ON COVID-19 SPREAD
No full text The COVID-19 pandemic has presented a major challenge in understanding the dynamics of disease transmission in a region. DKI Jakarta is the province with the highest number of COVID-19 cases in Indonesia. In this article, the SVEIₐIₛR model (Susceptible, Vaccinated, Exposed, Asymptomatic, Symptomatic, and Recovered) is examined to model the spread of COVID-19 in DKI Jakarta Province. The basic reproduction number is obtained through the Next Generation Matrix (NGM) approach, whereas the local stability analysis is carried out using the Routh–Hurwitz criterion. Furthermore, there are two equilibrium points obtained, which are the disease-free equilibrium and the endemic equilibrium. The stability of the equilibrium point is analyzed based on the value of the basic reproduction number. The endemic equilibrium point is considered asymptotically stable if the basic reproduction number is less than one. To demonstrate the behavior of the COVID-19 transmission model, numerical simulations are conducted using data obtained from DKI Jakarta Province. The results of the analysis indicate that, the COVID-19 transmission model is asymptotically stable at the diseas-free equilibrium point with R0=0.001897843854. This indicates that, over time, the COVID-19 disease will eventually disappear from the population.
An Algorithm for Generalized Conversion to Normal Distribution for Independent and Identically Distributed Random Variables
Get PDFThe paper analyzes an efficient alternative to the Box-Cox and Johnson’s transformation to normality methods which operates under fairly general settings. The method hinges on two results in mathematical statistics: the fact that the cumulative distribution function F(x) of a random variable x always has a U(0,1) distribution and the Box-Mueller transformation of uniform random variables to standard normal random variables. Bounds for the Kolmogorov-Smirnov statistic between the distribution of the transformed observations and the normal distribution are provided by numerical simulation and by appealing to the Dvoretzky-Kiefer- Wolfowitz inequality
BOUNDING LINEAR-WIDTH AND DISTANCE-WIDTH USING FEEDBACK VERTEX SET AND MM-WIDTH FOR GRAPH
Get PDFStudying the upper and lower bounds of graph parameters is crucial for understanding the complexity and tractability of computational problems, optimizing algorithms, and revealing structural properties of various graph classes. In this brief paper, we explore the upper and lower bounds of graph parameters, including path-distance-width, MM-Width, Feedback Vertex Set, and linear-width. These bounds are crucial for understanding the complexity and structure of graphs
Corrected Trapezoidal Rule For The Riemann-Stieltjes Integral
Get PDFThis study investigates the derivation of a corrected trapezoidal rule for approximating the Riemann-Stieltjes integral. The corrected trapezoidal rule is derived by approximating certain monomial functions to obtain optimal method coefficients. The proposed method has an accuracy of order three. Furthermore, an error analysis is conducted to assess the accuracy of the obtained approximation. In the final section, numerical computations are presented to compare the performance of the proposed method with existing methods. The results demonstrate that the proposed method produces smaller errors compared to previously developed approaches