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PENYELESAIAN MODIFIKASI MODEL PREDATOR PREY LESLIE-GOWER DENGAN SEBAGIAN PREY TERINFEKSI MENGGUNAKAN ADAMS BASHFORTH MOULTON ORDE EMPAT Arianti, Liatri; Hidayat, Rusli; Purnomo, Kosala Dwija
Majalah Ilmiah Matematika dan Statistika Vol 19 No 2 (2019): Majalah Ilmiah Matematika dan Statistika
Publisher : Jurusan Matematika FMIPA Universitas Jember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/mims.v19i2.17268

Eco-epidemiology is a science that studies the spread of infectious diseases in a population in an ecosystem where two or more species interact like a predator prey. In this paper discusses about how to solve modification Leslie Gower of predator prey models (with Holling II response function) with some prey infected using fourth order Adams Bashforth Moulton method. This paper used a simple disease-spreading model that is Susceptible-Infected (SI). The model is divided into three populations: the sound prey (which is susceptible), the infected prey and predator population. Keywords: Adams Basforth Moulton, Eco-epidemiology Holling Tipe II, Local stability, Leslie-Gower, Predator-Prey model

PERBANDINGAN ALGORITMA PARTICLE SWARM OPTIMIZATION (PSO) DAN ALGORITMA GLOWWORM SWARM OPTIMIZATION (GSO) DALAM PENYELESAIAN SISTEM PERSAMAAN NON LINIER Azmi, Ana Ulul; Hidayat, Rusli; Arif, M Ziaul
Majalah Ilmiah Matematika dan Statistika Vol 19 No 1 (2019): Majalah Ilmiah Matematika dan Statistika
Publisher : Jurusan Matematika FMIPA Universitas Jember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/mims.v19i1.17263

Non-linear equation system is one of the mathematics problems which difficult to solve. Several methods have been introduced to solve the problems. Newton-Raphson method is the most common and widely used as the basis for evolving the latest numerical methods. However, this method requires the derivative of each equation with respect to every variable when calculating the Jacobian. Naturally, obtaining the derivative is challenging in certain cases. In addition, it needs a proper initial value to obtain the converged solution. Therefore, the new technique with a simple random initial value is urgently needed. In this study, it is shown the implementation of the two metaheuristic optimization methods, including Particle Swarm Optimization (PSO) and the Glowworm Swarm Optimization (GSO) to estimate the solution of a non-linear equation system. Several examples of nonlinear equation system were used for evaluating and testing the performance and the accuracy of both algorithms. In this simulation, the results show that PSO converged to the exact solution (global optimum) better than Glowworm Swarm Optimization (GSO). Keywords: Non-Linear Equation Systems, Particle Swarm Optimization (PSO), Glowworm Swarm Optimization (GSO)

PENERAPAN COCKROACH SWARM OPTIMIZATION ALGORITHM (CSOA) PADA PENYELESAIAN PERSAMAAN POLINOMIAL YANG MEMILIKI AKAR KOMPLEKS Farikha, Ema Fahma; Hidayat, Rusli; Arif, Muhammad Ziaul
Majalah Ilmiah Matematika dan Statistika Vol 18 No 2 (2018): Majalah Ilmiah Matematika dan Statistika
Publisher : Jurusan Matematika FMIPA Universitas Jember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/mims.v18i2.17251

In this paper, we use a metaheuristic algorithm for solving non-linear equations (polynomial equations) which have a set of complex roots (complex numbers). The metaheuristic algorithm is the Cockroach Swarm Optimization Algorithm (CSOA) which imitate various types of natural cockroach behaviors such as chase-swarming, dispersing and ruthlessness when hunting for food sources. In this study, several examples of non-linear polynomial equations were used for evaluating the accuracy of CSOA. In this simulation, the accuracy comparison has been accomplished. It is shown that CSOA results are more accurate compared to the Newton-Raphson results. Keywords: Cockroach Swarm Optimization Algorithm, Complex roots of polynomial, Newton-Raphson, Non-Linear equation.

Projectile Motion Modeling with Linear Resistance Hidayat, Rusli
Majalah Ilmiah Matematika dan Statistika Vol 16 No 2 (2016): Majalah Ilmiah Matematika dan Statistika
Publisher : Jurusan Matematika FMIPA Universitas Jember

Show Abstract | Download Original | Original Source | Check in Google Scholar

When the projectile is shot into the air, the main force affecting the motion of projectile, other than gravity, is air resistance. This slowing down force is drag force, and it acts in a direction opposite to the velocity of the projectile. For the projectiles moving through the air at relatively low speeds, however, the drag force is proportional to the speed and so is called linear. The aim of this paper is to discuss the projectile motion by considering air friction as linear resistance. The results obtained show that the projectile motion model with linear resistance is more complex in formulating maximum height and range than the model without air friction force.

Profile of Wave Equation Using Boundary Condition Akhsan, Mokhamad; Hidayat, Rusli; Pradjaningsih, Agustina
Majalah Ilmiah Matematika dan Statistika Vol 16 No 1 (2016): Majalah Ilmiah Matematika dan Statistika
Publisher : Jurusan Matematika FMIPA Universitas Jember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/mims.v16i1.23731

The wave equation is one of hyperbolic equation forms which its solution can be solved by various methods, such as Alembert and series approximation methods. Basically, the Alembert method is a coordinate transfer technique and the series approximation method is the classical separation of variable. Performance of the wave equation can be known by both of the methods with the variation of boundary conditions. The results show that both of the methods gave some equalities or differences of the profile. The different values of the velocity c ’s will have the same performance of the wave equation in the case of Dirichlet and Von Neumann boundary conditions. Calculating the profiles with a discrete version of the solution and showing some profiles at various times have been done resulting oscillation wave and moving wave.

Design Of Evolutive Pipe Shape Kusno, Kusno; Hidayat, Rusli; Juliyanto, Bagus
Majalah Ilmiah Matematika dan Statistika Vol 16 No 1 (2016): Majalah Ilmiah Matematika dan Statistika
Publisher : Jurusan Matematika FMIPA Universitas Jember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/mims.v16i1.23733

We formulate evolution tube defined by Bezier dan natural curve in three steps as the following. Firstly, calculating the parametric surfaces of Bezier and natural evolution tube defined by Serret Frenet frame is done. Secondly, we formulate parametric continuity for joining the tubes. Finally, the application of those formulas for modeling the tubes by using computer are simulated.

Determination of Fractal Area of the Koch Snowflake Kamil, Abdul; Hidayat, Rusli; Purnomo, Kosala Dwidja
Majalah Ilmiah Matematika dan Statistika Vol 17 No 1 (2017): Majalah Ilmiah Matematika dan Statistika
Publisher : Jurusan Matematika FMIPA Universitas Jember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/mims.v17i1.23750

The Koch Snowflake Island (Koch Snowflake) is composed of three Koch curves rotated by suitable angles and fitted together. The Koch curve is constructed using an iterative procedure beginning with the initiator of the set as the unit line segment. The unit line segment is divided into thirds and the middle third removed, then replaced with equilateral triangle without base. In this article to get formulation of the area fractals Koch Snowflake and its variations, generated by generator equilateral triangle, isosceles triangle and square to the sides of the regular polygon which has n sides.

Application of Difference Equations Model in Determining Genotype Probability Offspring with Two Different Characteristic Dwi Agus Wijayanto; Rusli Hidayat; Moh. Hasan
Jurnal ILMU DASAR Vol 14 No 2 (2013)
Publisher : Fakultas Matematika dan Ilmu Pengetahuan Alam Universitas Jember

Population genetics is a branch of biology which studies about the gene composition from population and the change of the gene composition is effect from some factors. One of them is lethal gene factor. The change of gene composition will influence the genotype probabilities in the population. In this paper discussed about determining the genotype for the probability of the n-th offspring genotypes in dihybrid mating by observing linkage between the two loci. The mating occurred randomly and without concern ethics in mating. This research was done by making mathematics model to determine allele pair, using difference equation, then from this model will be determined genotypes probability. The result show that the mating happened normally had the same genotype probability of each generation, meanwhile in abnormal mating, the genotype probability whose had lethal gene would decrease and the genotype probability whose did not have lethal gene would increase in each generation.Keywords : Difference equation, dihybrid mating, lethal gene, population genetics, probability

OPTIMASI PROSES PENGERINGAN KOPI DI PABRIK KOPI PTPN XII GUMITIR DENGAN MENGGUNAKAN MASON DRYER Rusli Hidayat; Firdaus Ubaidillah; Hadi Siswanto
Jurnal Ilmiah Matematika dan Pendidikan Matematika Vol 10 No 2 (2018): Jurnal Ilmiah Matematika dan Pendidikan Matematika
Publisher : Jurusan Matematika FMIPA Universitas Jenderal Soedirman

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20884/1.jmp.2018.10.2.2841

Coffee Processing Plant of the PTPN XII Gumitir is a coffee drying factory that was built in 1910 using a giant barch dryer called Mason Dryer as many as four units, each of which has a capacity of 20 tons, so factory is capable of processing 80 tons for a single simultaneous process. The ambient temperature used is 120oC with a residency time of 18 hours and desirable level of reduction in water content of 9%. To optimize the process, a mathematical model of the process is needed to predict energy use, heat distribution (heat profile in coffe beans) and residency time (heat penetration time required by coffee beans). Existing process models are still limited to models for drying the coffe beans. To optimize the process, a heat transfer temperature from ambient temperature (heating temperature) is neededto enter the Mason Dryer which function as the ambient temperature of the coffee beans at each location/ position of the coffee beans in Mason Dryer. With the discoveryof the model for ambient temperaturewill complement the existing model.

OPTIMASI PROSES PENGERINGAN KOPI DI PABRIK KOPI PTPN XII GUMITIR DENGAN MENGGUNAKAN MASON DRYER Rusli Hidayat; Firdaus Ubaidillah; Hadi Siswanto
Jurnal Ilmiah Matematika dan Pendidikan Matematika (JMP) Vol 10 No 2 (2018): Jurnal Ilmiah Matematika dan Pendidikan Matematika (JMP)
Publisher : Universitas Jenderal Soedirman

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20884/1.jmp.2018.10.2.2841

Coffee Processing Plant of the PTPN XII Gumitir is a coffee drying factory that was built in 1910 using a giant barch dryer called Mason Dryer as many as four units, each of which has a capacity of 20 tons, so factory is capable of processing 80 tons for a single simultaneous process. The ambient temperature used is 120oC with a residency time of 18 hours and desirable level of reduction in water content of 9%. To optimize the process, a mathematical model of the process is needed to predict energy use, heat distribution (heat profile in coffe beans) and residency time (heat penetration time required by coffee beans). Existing process models are still limited to models for drying the coffe beans. To optimize the process, a heat transfer temperature from ambient temperature (heating temperature) is neededto enter the Mason Dryer which function as the ambient temperature of the coffee beans at each location/ position of the coffee beans in Mason Dryer. With the discoveryof the model for ambient temperaturewill complement the existing model.

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