Journal of Fundamental Mathematics and Applications (JFMA)
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SOME PROPERTIES OF ALMOST JOINTLY PRIME (R,S)-SUBMODULES
Get PDFLet and be rings with identity. The definition of prime submodule has been generalized to the almost prime submodule. In addition, the definition of prime submodule has also been carried over to the (,)-module structure, which is called jointly prime (,)-submodules. However, as a generalization of prime submodules, the concept of almost prime submodules has not been carried over to (,)-module structures. In this paper, we construct the definition of almost jointly prime (,)-submodules as the generalization of jointly prime (,)-submodules. We also present several necessary and sufficient conditions for an (,)-submodule to be an almost jointly prime (,)-submodule
Pythagorean Fuzzy Set and Its Application to Determining Student Concentration Using Max-Min-Max Composition
Get PDFPythagorean fuzzy set is a generalization of intuitionistic fuzzy set. As intuitionistic fuzzy set that can be used to help in solving problems regarding decision making, pythagorean fuzzy set can also be done for the same thing. In the pythagorean fuzzy set, a max-min-max composition relation will be formed and used it to solve decision-making problems. Through this research, decision making in determining the concentration for students of the Mathematics undergraduates program at Sunan Kalijaga State Islamic University Yogyakarta is discussed based on data on student grades in compulsory courses that have been taken by students until the 4th semester. Concentration that is in line with the interests and abilities is expected to facilitate the writing of the student's final project
OPTIMAL CONTROL OF MATHEMATICAL MODELS IN BIOENERGY SYSTEMS AS EMPOWERMENT OF SUSTAINABLE ENERGY SOURCES
Get PDFEnergy has a very important role in everyday life. Dependence on non-renewable energy increases its vulnerability to supply instability, making it important to seek alternative energy sources to overcome this dependence. Bioenergy is an alternative energy produced from organic materials such as biomass. Control of renewable energy is needed to increase production and empowerment. In this research, a mathematical model of biogas production growth in the form of differential equations formed with optimal control modifications is proposed. Completion of the model is carried out by forming an objective function, as well as determining the Hamilton function and Lagrange function. Numerical simulations in the model show that providing control can increase biogas production as a sustainable energy source
MIXTURE PURIFICATION MODEL WITH CASCADING TANK CONFIGURATION
Get PDFConsider mixing problems which are often found in Calculus or Differential Equation courses. Under some assumptions, this problem can be used to model the purification process in a polluted mixture. In this case, the cascading configuration will be investigated for modelling the spread of pollution from one mixture to another. There are two main problems: finding time needed so the amount of pollutant in mixture inside the certain tank does not exceed certain threshold and finding the number of tanks needed so that the amount of mixture in the last tank does not exceed certain threshold. The solution for the second problem will be simplified by using Stirling approximation, which approximates factorial into exponential term. For the first problem, the time needed depends on the number of tanks, initial value of the pollutant, the rate of flow, and the volume of solution inside the tanks. For the second problem, the number of tanks only depends on the initial value of the pollutant
A New Path to Accurate Risk Adjustment: Applying CreVaR for Better Financial Reporting under IFRS 17
Get PDFIFRS 17 is an international financial reporting standard that emphasizes the principles of consistency, transparency, and comparability. It divides reserve recording into Present Value of Future Cash Flows (PVFCF), Risk Adjustment (RA), and Contractual Service Margin (CSM). As IFRS 17 does not prescribe a specific calculation method, companies have the flexibility to define their own risk assessment approaches. Value-at-Risk (VaR) is widely used due to its simplicity and ease of application. However, its limitations in handling large datasets can lead to reduced accuracy. Moreover, variations in methods across companies can compromise the comparability of financial standards. This study proposes an enhanced VaR calculation based on credibility theory—Credible Value-at-Risk (CreVaR)—to improve accuracy and promote greater consistency across corporate entities. The Diebold-Mariano (DM) test demonstrates that CreVaR provides a more accurate estimation of RA without overestimation, making it a suitable alternative for calculating RA under IFRS 1
PRIME LABELING OF SOME WEB GRAPHS WITHOUT CENTER
Get PDFThe prime labeling of a graph of order is a bijection function from the set of vertices in to the set of the first positive integers, such that any two adjacent points in have labels that are coprime to each other. In this paper we discuss the primality of the graph along with its combinations with similar graphs and various types of edges subdivisions in the graph . Moreover, it is also presented the necessary and sufficient conditions for the graph to be prime
CONSTRUCTION OF FUNDAMENTAL THEOREMS OF FRACTIONAL CALCULUS
Get PDFThis paper discusses the theory of derivatives and integrals in the form of fractions with a particular order initiated by Lioville. Specifically, regarding the correlation between fractional derivatives and integrals, by examining definitions, determining the kernel function, and applying them to several examples, so a general formula will be obtained regarding the relationship between the two. This formula is the product of the fractional derivative of an order of a polynomial function of m-degree which is equal to the (n+1) th derivative of the related order fractional integral of a polynomial function of -degree that the truth is proved by using Mathematical Induction
ANALYSIS OF THE EFFECT OF STUART NUMBER AND RADIATION ON VISCOUS FLUID FLOW
Get PDFComputational fluid dynamics (CFD) is a numerical solution of fluid flow problems built from applied mathematical modeling. The problem of the flow of a viscous fluid which is influenced by a magnetic field gives rise to a boundary layer, from this boundary layer a dimensional building equation is formed. The governing equation is obtained from the continuity equation, momentum equation, and energy equation, then transformed into a non-dimensional equation by substituting non-dimensional variables and transformed into a similarity equation. The numerical solution to this problem uses the Keller Box method. The numerical simulation results show that the Stuart Number increases the velocity profile, while the temperature profile decreases. The effect of radiation parameters on the velocity profile did not change significantly, but the temperature profile decreased
SOMBOR INDEX AND ITS GENERALIZATION OF POWER GRAPH OF SOME GROUP WITH PRIME POWER ORDER
Get PDFGraphs are an intriguing topic of discussion due to their numerous applications, particularly in chemistry. Topological indices derived from graph representations of molecules enable us to predict various properties of these compounds, including their physical characteristics, chemical reactivity, biological activity, toxicity, and atom-to-atom interactions. More recently, graphs have also been utilized to depict abstract mathematical objects such as groups. A notable example of graph representation in group theory is seen in power graphs. This research explores new graph topological indices based on vertex degrees, inspired by the Euclidean metric, particularly the Sombor index, and its application to the power graph of the integer modulo group and the dihedral group. The primary outcome of this study is the derivation of a general formula for the Sombor index and its generalization
ANALYSIS OF A NON LINEAR DYNAMICS MODEL FOR TRANSMISSION TUBERCULOSIS IN NIGERIA INCORPORATING TREATMENT AND VACCINATION
Get PDFThis work models and analyzes the transmission of tuberculosis infection with the impact of vaccination and treatment on the bacteria in Nigeria from 2010 to 2022 incorporating treatment and vaccination. The susceptible-vaccinated-Exposed-Infected-Recovered (SVEIR) model is used for the transmission of the bacteria in which the with immigrants are exposed to infection infectious individuals, and it is assumed that there is permanent immunity and homogenous mixing against the bacteria. The constant immigration of the infected individuals into the population makes it impossible for the disease to die out and so there is no disease-free equilibrium. The fraction of chemoprophylaxis Bacillus Calmette-Guerin (BCG) was incorporated into the model equation for successful vaccination. Stability analysis shows that a disease free equilibrum is locally asymptotically stable for R01 which can wipe out the whole population. Hence, treatment and vaccination are the measures that can reduce below 1 in order to control tuberculosis