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All Journal Zero : Jurnal Sains, Matematika, dan Terapan
Faigle, Ulrich
University of Twente
Agriculture, Biological Sciences & Forestry Chemistry Mathematics Physics

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Analysis of the Stability of The Smoking Distribution Model with Educational Factors and Return to Smoking Factors Hasibuan, Iman Kamarullah; Faigle, Ulrich; Ikhwan, Ali; Hutapea, Tri Andri; Nasution, Hamidah
ZERO: Jurnal Sains, Matematika dan Terapan Vol 8, No 2 (2024): Zero: Jurnal Sains Matematika dan Terapan
Publisher : UIN Sumatera Utara

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30829/zero.v8i2.23477

Abstract

Smoking has become a serious health problem that occurs in various countries including Indonesia. Smoking causes a person to experience various health problems and also has an impact from exposure to cigarette smoke. Mathematical modeling is one of the techniques to present complex systems into mathematical models of problems that occur in the real world in the form of mathematical statements. This study aims to analyze the stability of the smoker distribution model based on the parameters  to obtain simulation results of the smoker distribution system model with education factors and smoking recurrence factors. The method used in this research is literature study. The model built is a modification of the model (Syari'ah & Prawoto 2022), which is formed in the compartment diagram used to construct the model. The model used in this study is the PLSQ model. From the model, the smoker-free equilibrium point and the non-smoker-free equilibrium point can be determined. Furthermore, linearization is carried out on the system of equations so that the Jacobian matrix is obtained which is used to find eigenvalues, by determining the basic reproduction number to analyze the type of stability of the equilibrium point. Then, numerical simulation is done using matlab 23b software with the Runga-Kutta method of Order 4. Based on the results of the discussion, the stability analysis states that the smoker-free equilibrium point will be stable when   and the non-smoker-free equilibrium point will be stable when . So that by adding transmission by heavy smokers and passive smokers, it takes longer to reach the equilibrium point.
Algebras of Interaction and Cooperation Faigle, Ulrich; Schonhuth, Alexander
ZERO: Jurnal Sains, Matematika dan Terapan Vol 8, No 1 (2024): Zero: Jurnal Sains Matematika dan Terapan
Publisher : UIN Sumatera Utara

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30829/zero.v8i1.19947

Abstract

Systems of cooperation and interaction are usually studied in the context of real or complex vector spaces. Additional insight, however, is gained when such systems are represented in vector spaces with ultiplicative structures, i.e., in algebras. Algebras, on the other hand, are conveniently viewed as polynomial algebras. In particular, basic nterpretations of natural numbers yield natural polynomial algebras and offer a new unifying view on cooperation and interaction. For example, the concept of Galois transforms and zero-dividends of cooperative games is introduced as a nonlinear analogue of the classical Harsanyi dividends. Moreover, the polynomial model unifies various versions of Fourier transforms. Tensor products of polynomial spaces establish a unifying model with quantum theory and allow to study classical cooperative games as interaction activities in a quantum-theoretic context.
Co-Authors Hasibuan, Iman Kamarullah Ikhwan, Ali Nasution, Hamidah . Schonhuth, Alexander Tri Andri Hutapea