Journal of Fundamental Mathematics and Applications (JFMA)
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ANALYSIS OF TUBERCULOSIS DYNAMICAL MODEL WITH DIFFERENT EFFECTS OF TREATMENT
Get PDFA tuberculosis model that integrates pre-infection and active infection stages along with two treatment parameters was studied. The model also considered the death rate due to pre-tuberculosis infection. The basic reproduction ratio was used to investigate the local and global stability of the equilibrium point. The local stability of uninfected equilibrium was analysed using Routh Hurwitz criteria. The existence of endemic equilibrium was given. After we achieved the endemic equilibrium, the global stability of the endemic equilibrium was analyzed using the Lyapunov function. A numerical simulation was studied to illustrate the effect of the treatment on the spread of the tuberculosis disease.
BEBERAPA SIFAT (R,S)-SUBMODUL PRIMA-α GABUNGAN
No full textDiberikan dan merupakan ring komutatif. Keprimaan pada suatu ring telah mengalami perkembangan ke dalam struktur modul. Namun, definisi keprimaan yang ada selama ini hanya berfokus pada operasi pergandaan skalar di dalam modul. Submodul prima-α merupakan salah satu perumuman dari submodul prima yang melibatkan operasi aditif dan pergandaan skalar di dalam modul. Pada artikel ini disajikan generalisasi dari submodul prima-α ke dalam struktur (R,S)-modul, yang selanjutnya disebut (R,S)-submodul prima-α gabungan. Selanjutnya, disajikan beberapa sifat dari (R,S)-submodul prima-α gabungan. Beberapa sifat tersebut diantaranya adalah syarat perlu dan syarat cukup suatu (R,S)-submodul membentuk (R,S)-submodul prima-α gabungan; sifat (R,S)-submodul prima-α gabungan yang berkaitan dengan homomorfisma (R,S)-modul; serta syarat perlu dan syarat cukup suatu (R,S)-submodul faktor membentuk (R,S)-submodul prima-α gabungan. Beberapa sifat (R,S)-submodul prima-α gabungan tersebut diperoleh dari pengembangan sifat keprimaan dalam struktur modul
ON EVEN-TO-ODD MEAN LABELING OF SOME TREES
Get PDFLet G=(V(G), E(G)) be a connected graph with order |V(G)|=p and size |E(G)|=q. A graph G is said to be even-to-odd mean graph if there exists a bijection function phi:V(G) to {2, 4, ..., 2p} such that the induced mapping phi^*:E(G) to {3, 5, ..., 2p-1} defined by phi^*(uv)=[phi(u)+phi(v)]/2 for all uv element of E(G) is also bijective. The function is called an even-to-odd mean labeling of graph . This paper aimed to introduce a new technique in graph labeling. Hence, the concepts of even-to-odd mean labeling has been evaluated for some trees. In addition, we examined some properties of tree graphs that admits even-to-odd mean labeling and discussed some important results
REDUCING THE CLOCKWISE-ALGORITHM TO k LENGTH CLASSES
Get PDFIn the present paper, we consider an optimization problem related to the extension in k-dimensions of the well known 3x3 points problem by Sam Loyd. In particular, thanks to a variation of the so called “clockwise-algorithm”, we show how it is possible to visit all the 3^k points of the k-dimensional grid given by the Cartesian product of (0, 1, 2) using covering trails formed by h(k)=(3^k-1)/2 links who belong to k (Euclidean) length classes. We can do this under the additional constraint of allowing only turning points which belong to the set B(k):={(0, 3) x (0, 3) x ... x (0, 3)}
LOGISTIC MODEL DEVELOPMENT OF COVID-19 SPREAD WITH PHYSICAL DISTANCING INTERVENTION
Get PDFIn early 2020, covid-19 spread fast in the worldwide and cause the high death. The disease started from the Asian region which resulted in a viral pandemic in 2020. In order to anticipate the increasing of the cases, a strategy is needed to inhibit its transmission. The mathematical model approach is important tool for predicting of covid-19 spread in populations. In this paper we propose and analyze the dynamical behaviour of a developed logistic model by considering the effect of the contact patterns in reducing the covid-19 spread process. To verify the developed logistic model, numerical simulation was given with case study of covid-19 spread for patients under supervision in Central Java Province, Indonesia. Based on simulation results, it was found that physical distancing can reduce the growth of the covid-19 spread for patient under supervision. It can be seen from the number of covid-19 spread for patients under supervision with physical distancing intervention smaller compared to without physical distancing intervention
A SHORT NOTE ON FIBONACCI NUMBERS IN A GENERALIZED PYTHAGOREAN TRIPLES
Get PDFThis paper aims to construct a new formula that generates a Fibonacci numbers in a generalized Pythagorean triples. In addition, the paper formulates some Fibonacci identities and discuss some important findings
DETERMINAN MATRIKS CENTROSYMMETRIC BENTUK KHUSUS ORDO 4×4 BERPANGKAT BILANGAN BULAT POSITIF
Get PDFPenelitan ini bertujuan untuk menentukan determinan dari suatu matriks centrosymmetric bentuk khusus ordo berpangkat bilangan bulat positif. Dalam menentukan determinan matriks centrosymmetric bentuk khusus terdapat beberapa langkah yang perlu dikerjakan. Pertama perhatikan bentuk pola matriks centrosymmetric bentuk khusus sampai sehingga didapat bentuk umumnya kemudian dibuktikan dengan induksi matematika. Kedua perhatikan bentuk pola determinan matriks centrosymmetric bentuk khusus sampai sehingga didapat bentuk umumnya lalu dibuktikan dengan pembuktian langsung. Hasil akhir dalam penelitian ini diperoleh bentuk umum matriks, determinan dari matriks centrosymmetric berpangkat bilangan bulat positif dengan ganjil dan genap
EASY ENSEMMBLE WITH RANDOM FOREST TO HANDLE IMBALANCED DATA IN CLASSIFICATION
Get PDFImbalanced data might cause some issues in problem definition level, algorithm level, and data level. Some of the methods have been developed to overcome this issue, one of state-of-the-art method is Easy Ensemble. Easy Ensemble was claimed can improve model performance to classify minority class, and overcome the deficiency of random under- sampling. In this paper we discussed the implementation of Easy Ensemble with Random Forest Classifiers to handle imbalance problem in credit scoring case. This combination method is implemented in two datasets which taken from data science competition website, finhacks.id and kaggle.com with class proportion within majority and minority is 70:30 and 94:6. The results showed that resampling with Easy Ensemble can improve Random Forest classifier performance upon minority class. Recall on minority class increased significantly after the resampling. Before resampling, the recall on minority class for the first dataset (finhacks.id) was 0.49, and increased to 0.82 after the resampling. Similar results were obtained for the second data set (kaggle.com), where the recall for the minority class was increased from just 0.14 to 0.73
IMPLEMENTASI METODE BAYES PADA PENGHITUNGAN PREMI ASURANSI KENDARAAN BERMOTOR
Get PDFOne type of general insurance is motor vehicle insurance. Premium pricing of general insurance can be calculated by some methods. In this study, Bayes method will be used. The distribution of claim frequency is Poisson distribution and the distribution of claim severity is Exponential distribution. The premium is calculated by multiplying the expectation of claim frequency and the expectation of claim severity. Based on the historical data analysis using the Bayes method, the highest pure premium of motor vehicle insurance in Indonesia is Hino brand and the lowest pure premium is Honda brand. The result of this premium pricing can be used as a reference for the insurance companies to manage their motor vehicle insurance reserves
FUNGSI WRIGHT SEBAGAI SOLUSI ANALITIK PERSAMAAN DIFUSI-GELOMBANG FRAKSIONAL PADA MEDIA VISKOELASTIS
Get PDFA fractional diffusion-wave equations in a fractional viscoelastic media can be constructed by using equations of motion and kinematic equations of viscoelasticmaterial in fractional order. This article concerns the fractional diffusion-wave equations in the fractional viscoelastic media for semi-infinite regions that satisfies signalling boundary value problems. Fractional derivative was used in Caputo sense. The analytical solution of the fractional diffusion-wave equation in the fractional viscoelastic media was solved by means of Laplace transform techniques in the term of Wright function for simple form solution. For general parameters, Numerical Inverse Laplace Transforms (NILT) was used to determine the solution