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Epsilon: Jurnal Matematika Murni dan Terapan

epsilon
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Published by Universitas Lambung Mangkurat

ISSN : 19784422 EISSN : 26567660 DOI : http://dx.doi.org/10.20527

Core Subject : Science, Engineering,

Decision Sciences, Operations Research & Management Transportation

Jurnal Matematika Murni dan Terapan Epsilon is a mathematics journal which is devoted to research articles from all fields of pure and applied mathematics including 1. Mathematical Analysis 2. Applied Mathematics 3. Algebra 4. Statistics 5. Computational Mathematics

Arjuna Subject : Matematika - Matematika Terapan

Articles 220 Documents

14 15 16 17 18

BILANGAN RAINBOW CONNECTION PADA GRAF-H Ayu Nanie Maretha; Muhammad Mahfuzh Shiddiq; Na'imah Hijriati
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol. 15(1), 2021
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Pada teori graf terdapat konsep pewarnaan yaitu pewarnaan sisi dan pewarnaan titik. Apabila ada dua titik yang terhubung oleh lintasan rainbow maka pewarnaan sisi graf disebut rainbow connected. Bilangan rainbow connection yang dinotasikan dengan rc(G) adalah bilangan terkecil dari warna yang dibutuhkan agar terbentuk graf bersifat rainbow connected. Pewarnaan titik pada graf disebut rainbow connected jika sebarang dua titik pada graf berwarna titik dihubungkan oleh lintasan rainbow vertex. Bilangan rainbow vertex connection yang dinotasikan dengan rvc(G) adalah bilangan terkecil dari warna yang dibutuhkan agar terbentuk graf bersifat rainbow vertex connected. Graf- merupakan graf yang berbentuk seperti huruf . Operasi korona merupakan cara untuk menghasilkan dua buah graf menjadi suatu graf baru. Tujuan dari penelitian ini adalah menentukan bilangan rainbow connection dan bilangan rainbow vertex connection pada graf-H. Hasil penelitian yang diperoleh yaitu bilangan rainbow connection pada graf-H yaitu 2n-1 , bilangan rainbow vertex connection pada graf-H yaitu 2n-4 dan bilangan rainbow vertex connection pada graf H korona mK_1 adalah 2n.

GENERALISASI ATURAN CRAMER Ferry Syahriandi; Thresye Thresye; Akhmad Yusuf
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol 11, No 2 (2017): JURNAL EPSILON VOLUME 11 NOMOR 2
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Sistem persamaan linier ????????=????,????∈????????,????∈???????? dan ????≥???? di mana ????=????????????????????????×???? adalah matriks riil yang dapat mempunyai solusi tunggal, tak hingga banyaknya solusi, atau tidak mempunyai solusi. Ketika ????≥????, sistem mempunyai solusi tunggal dengan norm minimum yang diberikan oleh invers Moore-Penrose, dinotasikan dengan ????+ dan berbentuk ????+????=????????(????????????)−1???? dengan det(????????????)≠0. Tujuan dari penelitian ini adalah membuktikan aturan Cramer yang telah digeneralisasi sehingga dapat digunakan untuk menentukan solusi sistem persamaan linier yang demikian. Penelitian ini bersifat studi literatur. Hasil penelitian yang diperoleh dengan menggunakan invers Moore-Penrose dan aturan Cramer adalah aturan Cramer yang digeneralisasi. Rumus tersebut dapat digunakan untuk menentukan solusi sistem persamaan linier ????????=???? di mana ????=????????????????????????×???? dan ????≥????.Kata kunci: Sistem persamaan linier, aturan Cramer, invers Moore-PenroseSistem persamaan linier ????????=????,????∈????????,????∈???????? dan ????≥???? di mana ????=????????????????????????×???? adalah matriks riil yang dapat mempunyai solusi tunggal, tak hingga banyaknya solusi, atau tidak mempunyai solusi. Ketika ????≥????, sistem mempunyai solusi tunggal dengan norm minimum yang diberikan oleh invers Moore-Penrose, dinotasikan dengan ????+ dan berbentuk ????+????=????????(????????????)−1???? dengan det(????????????)≠0. Tujuan dari penelitian ini adalah membuktikan aturan Cramer yang telah digeneralisasi sehingga dapat digunakan untuk menentukan solusi sistem persamaan linier yang demikian. Penelitian ini bersifat studi literatur. Hasil penelitian yang diperoleh dengan menggunakan invers Moore-Penrose dan aturan Cramer adalah aturan Cramer yang digeneralisasi. Rumus tersebut dapat digunakan untuk menentukan solusi sistem persamaan linier ????????=???? di mana ????=????????????????????????×???? dan ????≥????.Kata kunci: Sistem persamaan linier, aturan Cramer, invers Moore-PenroseSistem persamaan linier ????????=????,????∈????????,????∈???????? dan ????≥???? di mana ????=????????????????????????×???? adalah matriks riil yang dapat mempunyai solusi tunggal, tak hingga banyaknya solusi, atau tidak mempunyai solusi. Ketika ????≥????, sistem mempunyai solusi tunggal dengan norm minimum yang diberikan oleh invers Moore-Penrose, dinotasikan dengan ????+ dan berbentuk ????+????=????????(????????????)−1???? dengan det(????????????)≠0. Tujuan dari penelitian ini adalah membuktikan aturan Cramer yang telah digeneralisasi sehingga dapat digunakan untuk menentukan solusi sistem persamaan linier yang demikian. Penelitian ini bersifat studi literatur. Hasil penelitian yang diperoleh dengan menggunakan invers Moore-Penrose dan aturan Cramer adalah aturan Cramer yang digeneralisasi. Rumus tersebut dapat digunakan untuk menentukan solusi sistem persamaan linier ????????=???? di mana ????=????????????????????????×???? dan ????≥????.Kata kunci: Sistem persamaan linier, aturan Cramer, invers Moore-PenroseSistem persamaan linier ????????=????,????∈????????,????∈???????? dan ????≥???? di mana ????=????????????????????????×???? adalah matriks riil yang dapat mempunyai solusi tunggal, tak hingga banyaknya solusi, atau tidak mempunyai solusi. Ketika ????≥????, sistem mempunyai solusi tunggal dengan norm minimum yang diberikan oleh invers Moore-Penrose, dinotasikan dengan ????+ dan berbentuk ????+????=????????(????????????)−1???? dengan det(????????????)≠0. Tujuan dari penelitian ini adalah membuktikan aturan Cramer yang telah digeneralisasi sehingga dapat digunakan untuk menentukan solusi sistem persamaan linier yang demikian. Penelitian ini bersifat studi literatur. Hasil penelitian yang diperoleh dengan menggunakan invers Moore-Penrose dan aturan Cramer adalah aturan Cramer yang digeneralisasi. Rumus tersebut dapat digunakan untuk menentukan solusi sistem persamaan linier ????????=???? di mana ????=????????????????????????×???? dan ????≥????.Kata kunci: Sistem persamaan linier, aturan Cramer, invers Moore-Penrose

RELASI FUZZY PADA GRUP FAKTOR FUZZY Ahmad Madani; Saman Abdurrahman; Na'imah Hijriati
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol 14, No 1 (2020): JURNAL EPSILON VOLUME 14 NOMOR 1
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Fuzzy subsets on the non-empty set is a mapping of this set to the interval . The concept of fuzzy subgroups introduced from advanced concept of fuzzy set in group theory. In concept of fuzzy set there is the concept of relations is fuzzy relations. In this study examined that fuzzy relations related to the equivalence and congruence on a fuzzy group and fuzzy factor group. The results of this study was to show that a fuzzy relation if and if is a fuzzy congruence relations on fuzzy group and a fuzzy relation defined of is a fuzzy congruence relations on fuzzy factor group.

MENENTUKAN SOLUSI OPTIMAL PADA PEMROGRAMAN LINIER DENGAN n FUNGSI OBJEKTIF MENGGUNAKAN SOLVER METODE SIMPLEKS Dewi Anggraini; Faisal Faisal
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol 4, No 1 (2010): JURNAL EPSILON VOLUME 4 NOMOR 1
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Linear programming is a Mathematical model that uses programming language technique tomodel and solve optimization problems with linear objective functions and constraints.A Mathematical model for optimization problems such as, linear programming with one objectivefunction can be written as:Objective Function: Minimum or Maximum f X1,X2 ,...,Xn Constraints:     m n mk n knf X ,X ,...,X bf X ,X ,...,X bf X ,X ,...,X b1 21 21 1 2 1X1,X2 ,...,Xn  0However, in fact there are sometimes more than one objective functions that should be reached,either be maximized, minimized or both. This research aims to determine procedures in obtainingthe optimal solution of linear programming with n objective functions using Solver simplexmethod in a sample case.The method of this research is a literature study by collecting and studying references that arerelevant about linear programming models with n objective functions, Solver Parameters, andsimplex method. Then, determining procedures to obtain the optimal solution to the model ina sample case.The result shows that the procedures of obtaining optimal solution in a linear programmingmodel with n objective functions using Solver simplex method are: identifying and understandingthe problem; determining decision variables Xi, objective functions fi Xi, and constraintsgi Xi; formulating components in linear programming model into a spreadsheet MS Excel;solving the optimal value for each objective function with Solver Parameters; determining theoptimal value for i th objective function as the i th goal value; determining deviation function foreach objective function; giving weights wi for the deviation function of each objective function;determining the maximum value of feasible deviation function from its objective functions(variable Q); minimizing variable Q to obtain the optimal solution; and making decision.

ALGORITMA GENETIKA PADA PENYELESAIAN AKAR PERSAMAAN SEBUAH FUNGSI Akhmad Yusuf; Oni Soesanto
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol 6, No 2 (2012): JURNAL EPSILON VOLUME 6 NOMOR 2
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20527/epsilon.v6i2.87

The Genetic Algorithm is one approach to determining global optimum that is based on the theory of evolution. Outline the steps in this procedure starting with establishing a set of potential solutions and making changes with some iterations with genetic algorithms to get the best solution. Calculation the root of a function is actually a classic problem in mathematics. For that, various methods have been numerically developed. From the results of the implementation of genetic algorithm to find the root of the equation of a function h (x1, x2) = 1000 (x1-2x2) 2+ (1-x1) 2 in can be that FitMax (genome 9) = 10, FitMin (genome 107) = 0, FitAvr = 0.153, FitTot = 30.6, Best Genome: 10011001001000110010, x1 = 1 and x2 = 0.5 and this is the same as the exact value or value actually from the root of the equation

ANALISIS KRIGING UNTUK MENDETEKSI POLA SPASIAL KASUS DBD DI KABUPATEN TANAH LAUT Sri Mulyanie Hardiyanthy; Dewi Sri Susanti; Thresye Thresye
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol 13, No 2 (2019): JURNAL EPSILON VOLUME 13 NOMOR 2
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Geostatistics is a data processing in geological field that contains spatial information in it. Spatial information is information that identifies geographical location, characteristics of natural conditions and boundaries of the earth. Geostatistics is used to handle regionalized variables. One of the method that used to handle regionalized variables is the kriging method. The kriging method has a lot of expansion in its development, including the Simple Kriging method and the Cokriging method. Both of these methods will be applied in case studies of spatial patterns of dengue in Tanah Laut District. The purpose of this study was to estimate the distribution pattern of DHF in Tanah Laut District and compare the results of the RMSE method of Simple Kriging and Cokriging. The smallest RMSE value was compared and selected, followed by estimation using the Cokriging and Simple Kriging methods. From the two methods used the smallest RMSE value is in the Simple Kriging method. But when you looked from the thematic map of the distribution of dengue patients with the Cokriging and Simple Kriging method, it can be seen that the Cokriging method has a more diverse pattern. Keywords: geostatisticts , Cokriging , Simple Kriging , DHF

KARAKTERISTIK UKURAN RISIKO DISTORSI Rusidawati Rusidawati; Aprida Siska Lestia; Saman Abdurrahman
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol. 16(1), 2022
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Insurance is a risk transfer from the insured to the insurer. In general insurance companies are grouped into two types that life insurance and general insurance. For measure risk in general insurance the method used is using a measure of risk. In the study of risk management, there is one method forming risk measure known a distortion function. The purpose of this study is prove theorems of properties a measure of coherent and consistent risk of distortion. In this study explain the formation of a measure of risk distortion using a distortion function, indicates that if the distortion function is a concave function and shows the consistency of risk distortion measures preserve second order stochastic dominance and show coherence and consistency several of distortion risk measures. The results of this study concave distortion function is a necessary condition and sufficient condition for coherence and a strictly concave distortion function is a necessary condition and sufficient condition for strict ordering consistent with preserve second order stochastic dominance.

INVERS TERGENERALISASI MOORE PENROSE Mardiyana Mardiyana; Na'imah Hijriati; Thresye Thresye
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol. 15(2), 2021
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

The generalized inverse is a concept for determining the inverse of a singular matrix and and matrix which has the characteristic of the inverse matrix. There are several types of generalized inverse, one of which is the Moore-Penrose inverse. The matrix is called Moore Penrose inverse of a matrix if it satisfies the four penrose equations and is denoted by . Furthermore, if the matrix satisfies only the first two equations of the Moore-Penrose inverse and , then is called the group inverse of and is denoted by . The purpose of this research was to determine the group inverse of a non-diagonalizable square matrix using Jordan’s canonical form and Moore Penrose’s inverse of a singular matrix, also a non-square matrix using the Singular Value Decomposition (SVD) method. The results of this study are the sufficient condition for a matrix to have a group inverse, i.e., a matrix has an index of 1 if and only if the product of two matrices forming is a full rank factorization and is invertible. Whereas for a singular matrix and a non-square , the Moore-Penrose inverse can be determined using Singular Value Decomposition (SVD). Keywords: generalized matrix inverse, Moore Penrose inverse, group inverse, Jordan canonical form, Singular Value Decomposition.

PEMBENTUKAN PERSAMAAN VAN DER POL DAN SOLUSI MENGGUNAKAN METODE MULTIPLE SCALE Farohatin Na'imah; Yuni Yulida; Muhammad Ahsar Karim
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol 14, No 2 (2020): JURNAL EPSILON VOLUME 14 NOMOR 2
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Mathematical modeling is one of applied mathematics that explains everyday life in mathematical equations, one example is Van der Pol equation. The Van der Pol equation is an ordinary differential equation derived from the Resistor, Inductor, and Capacitor (RLC) circuit problem. The Van der Pol equation is a nonlinear ordinary differential equations that has a perturbation term. Perturbation is a problem in the system, denoted by ε which has a small value 0<E<1. The presence of perturbation tribe result in difficulty in solving the equation using anlytical methode. One method that can solve the Van der Pol equation is a multiple scale method. The purpose of this study is to explain the constructions process of Van der Pol equation, analyze dynamic equations around equilibrium, and determine the solution of Van der Pol equation uses a multiple scale method. From this study it was found that the Van der Pol equation system has one equilibrium. Through stability analysis, the Van der Pol equation system will be stable if E= 0 and -~<E<=-2. The solution of the Van der Pol equation with the multiple scale method is Keywords: Van der Pol equation, equilibrium, stability, multiple scale.

METODE DEKOMPOSISI LAPLACE UNTUK MENENTUKAN SOLUSI PERSAMAAN DIFERENSIAL PARSIAL NONLINIER Sinar Ismaya; Yuni Yulida; Naimah Hijriati
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol 10, No 1 (2016): JURNAL EPSILON VOLUME 10 NOMOR 1
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Partial differential equations are grouped into two parts: linear and nonlinear differential equations. Many natural phenomena are modeled in the form of nonlinear partial differential equations, such as K-dV and Burger equations. To be able to explain natural phenomena in the form of nonlinear partial differential equations required approach method which can then be applied to determine the solution of partial differential equation. One of the methods used to determine the solution of nonlinear differential equations is Laplace Decomposition Method which combines Laplace Transformation theory and Adomian Decomposition Method. This research is conducted by using literature method with the following procedure: Assessing Non-Linear Partial Differential Equation, Method Adomian Decomposition, Laplace Transformation and Laplace Decomposition Method; then determine the settlement of the non-linear differential equation with the Laplace Decomposition Method. The result of this research is obtained by solution of nonlinear partial differential equation of Order one by using Laplace decomposition method that is 0nnuu∞ == Σ with (????????, ????????) = ℒ-1????1????????ℒ {???????? (????????, ????????)} + 1????????ℎ (????????) ???? and ???????????????? + 1 (????????, ????????) = ℒ-1????-1????????ℒ {???????????? ???????? (????????, ????????) } -1????????ℒ {????????????????} ????; ????????≥0 and on the two-order nonlinear partial differential equation is 0nnuu = = Σ with ????????0 (????????, ????????) = ℒ-1????1????????2ℒ {???????? (????????, ????????)} + 1????????ℎ (????????) + 1????????2???????? (????????) ???? and ???????????????? + 1 (????????, ????????) = ℒ-1????-1????????2ℒ {???????????? ???????? (????????, ????????)} - 1????????2ℒ {????????????????} ????; ????????≥0

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Yuni Yulida

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epsilon@ulm.ac.id

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Mathematics Department, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat University. Jl. A. Yani KM.35.8 Banjarbaru, Kalimantan Selatan

Location
Kota banjarmasin,

Kalimantan selatan

INDONESIA

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Home Page

OAI Link

Editorial Team

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Contact Name Yuni Yulida

Contact Email y_yulida@ulm.ac.id

Phone +6281348054202

Journal Mail Official epsilon@ulm.ac.id

Editorial Address Mathematics Department, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat University. Jl. A. Yani KM.35.8 Banjarbaru, Kalimantan Selatan

Location Kota banjarmasin, Kalimantan selatan INDONESIA

Abstract

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Abstract

Abstract

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Abstract

Contact Name
Yuni Yulida

Contact Email
y_yulida@ulm.ac.id

Phone
+6281348054202

Journal Mail Official
epsilon@ulm.ac.id

Editorial Address
Mathematics Department, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat University. Jl. A. Yani KM.35.8 Banjarbaru, Kalimantan Selatan

Location
Kota banjarmasin,

Kalimantan selatan

INDONESIA