Journal of Mathematics Computations and Statistics最新文献

{"title":"Suatu Kajian Tentang B-Aljabar","authors":"Wahi Sanusi, Muhammad Abdy, Sahlan Sidjara, Asriani Arsita Asni","doi":"10.35580/JMATHCOS.V3I2.19191","DOIUrl":"https://doi.org/10.35580/JMATHCOS.V3I2.19191","url":null,"abstract":"Abstrak. Penelitian ini merupakan penelitian kajian kepustakaan yang bertujuan untuk mengkaji konsep dan sifat-sifat terkait B-Aljabar. Konsep B-Aljabar dalam penelitian ini berdasarkan penelitian yang telah dilakukan oleh Neggers dan Kim serta Allen. Seluruh pembahasan dalam penelitian ini menggunakan himpunan tegas, baik himpunan berhingga maupun himpunan tidak berhingga. Hasilnya, dapat diberikan bukti yang lebih lengkap dari sifat-sifat B-Aljabar serta hubungannya dengan grup. Suatu grup dengan definisi operasi khusus dan elemen identitas  merupakan B-Aljabar. Lebih lanjut dapat diturunkan beberapa teorema grup kedalam B-Aljabar seperti pemetaan natural dan Teorema Isomorfisma 1 yang dalam pembuktiannya memiliki kemiripan dengan pembuktian pada grup dengan tetap menggunakan sifat-sifat B-Aljabar itu sendiri.Kata Kunci: B-Aljabar, B-Subaljabar, B-Homomorfisma, B-IsomorfismaAbstract. This research is a literature studies that aims at reviewing the concepts and properties of B-Algebras. The concept of B-Algebras in this article is based on research that has been done by Neggers and Kim and Allen. All discussions in this article use the firm sets, both finite sets and infinite sets. As a result, more complete evidence of the properties of B-Algebras can be given and its relationship with the group. A group with a specific operation and has  as an identity element is a B-Algebras. Moreover, a number of group theorems can be derived into B-Algebra such as natural mapping and the First Isomorphism Theorems which in their proof have similarities to the proofs of groups while still using the properties of B-Algebra itself.Keywords: B-Algebras, B-Subalgebras, B-Homomorphism, B-Isomorphism","PeriodicalId":363413,"journal":{"name":"Journal of Mathematics Computations and Statistics","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129888121","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Model Generalized Poisson Regression (GPR) dan Penerapannya pada Angka Pengangguran bagi Penduduk Usia Kerja di Provinsi Sulawesi Selatan","authors":"Hisyam Ihsan, Wahidah Sanusi, Risna Ulfadwiyanti","doi":"10.35580/JMATHCOS.V3I2.19190","DOIUrl":"https://doi.org/10.35580/JMATHCOS.V3I2.19190","url":null,"abstract":"Abstrak. Penelitian ini membahas tentang pembentukan model Generalized Poisson Regression (GPR) dan penerapannya pada angka pengangguran bagi penduduk usia kerja di Provinsi Sulawesi Selatan. Jenis penelitian ini adalah penelitian terapan yang menggunakan model regresi nonlinear, yaitu model regresi Poisson dan model GPR. Variabel respon yang digunakan adalah jumlah angka pengangguran pada usia kerja yang termasuk angkatan kerja di Provinsi Sulawesi Selatan pada tahun 2017. Adapun variabel-variabel prediktor yang digunakan yaitu persentase angkatan kerja terhadap penduduk usia kerja, Indeks Pembangunan Manusia, persentase bekerja terhadap angkatan kerja, kepadatan penduduk, dan pertumbuhan ekonomi. Penelitian menggunakan metode Maximum Likelihood Estimation (MLE) untuk mengestimasikan parameter dan menghasilkan sebuah model GPR. Variabel prediktor yang memberikan pengaruh secara signifikan adalah Indeks Pembangunan Manusia dan  persentase bekerja terhadap angkatan kerja.Kata kunci: Angka Pengangguran, Regresi Poisson, Overdispersi, Generalized Poisson Regression, Maximum Likelihood Estimation  Abstract. This study discusses the formation of the Generalized Poisson Regression (GPR) model and its application to the unemployment rate for the working age population in South Sulawesi Province. This type of research is applied research that uses the Poisson regression model, namely Poisson regression and GPR models. The response variabel used is the total unemployment rate at working age which includes the workforce in South Sulawesi Province in 2017. The predictor variables used are the percentage of the workforce on the working age population, the Human Development Index, the percentage of work on the labor force, population density, and economic growth. This research uses the Maximum Likelihood Estimation (MLE) method to estimate parameters and produce a GPR model. The predictor variables which have a significant influence are the Human Development Index and the percentage of work on the labor force.Keywords: Unemployment Rate, Poisson Regression, Overdispersion, Generalized Poisson Regression, Maximum Likelihood Estimation","PeriodicalId":363413,"journal":{"name":"Journal of Mathematics Computations and Statistics","volume":"91 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127911142","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Model SEIRS Penyebaran Penyakit Tuberkulosis di Kota Makassar","authors":"Rahmat Syam, Syafruddin Side, Citra Suci Said","doi":"10.35580/JMATHCOS.V3I1.19180","DOIUrl":"https://doi.org/10.35580/JMATHCOS.V3I1.19180","url":null,"abstract":"Abstrak. Penelitian ini  bertujuan untuk membangun model penyebaran penyakit tuberkulosis tipe SEIRS (Susceptible- Exposed- Infected- Recovered- Susceptible) dengan menambahkan asumsi bahwa manusia yang pulih dapat rentan kembali terkena tuberkulosis. Model ini dibagi menjadi empat kelas yaitu, rentan, terinfeksi tapi belum aktif, terinfeksi, dan sembuh. Data yang digunakan adalah data jumlah penderita penyakit tuberkulosis dari Dinas Kesehatan Kota Makassar tahun 2017. Model matematika tipe SEIRS digunakan untuk menentukan titik equilibrium. Berdasarkan hasil simulasi model SEIRS diperoleh bilangan reproduksi dasar ( ) sebesar 0,312 berarti bahwa seseorang yang terinfeksi penyakit tuberkulosis tidak menyebabkan orang lain terkena penyakit tuberkulosis di wilayah Kota Makassar.Kata Kunci: Titik Equilibrium, Bilangan Reproduksi Dasar, Tuberkulosis, Model SEIRS, Pemodelan.Abstract. This research aims to model of tuberculosis type SEIRS (Susceptible-Exposed-Infected-Recovery-Susceptible) by adding assumption that human that has been recovered can be suspected again by Tuberculosis. This model can be divided to  four classes, those are suspected, exposed, infected, and recovered. The data that used is data on the number of tuberculosis sufferer from Health Department in  Makassar City 2017.  Mathematicsl model of SEIRS type is used to determine the equilibrium point. According to the simulation results of SEIRS model, obtained the base reproduction number ( )  is  0.312 means that people who infected by tuberculosis does not causes other people get tuberculosis in Makassat city.Keywords: Equilibrium Point, Basic Reproduction Numbers, Tuberculosis, SEIRS Model, modeling.","PeriodicalId":363413,"journal":{"name":"Journal of Mathematics Computations and Statistics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129011006","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Fuzzy Linear Programming Dalam Optimalisasi Pelayanan Air Bersih Perusahaan Daerah Air Minum (PDAM) Kab. Jeneponto Menggunakan Metode Sabiha","authors":"Wahidah Sanusi, S. Sukarna, Irham Aryandi Basir","doi":"10.35580/JMATHCOS.V3I1.19183","DOIUrl":"https://doi.org/10.35580/JMATHCOS.V3I1.19183","url":null,"abstract":"Abstrak. Fuzzy linear programing  merupakan pengembangan model program linear dalam menentukan nilai optimal yang mengandung bilangan fuzzy. Metode yang dapat digunakan dalam menyelesaikan fuzzy linear programing yaitu metode Sabiha. Penggunaan metode Sabiha didasarkan pada bilangan linear fuzzy real yang berbentuk bilangan triplet. Pada penelitian ini digunakan model Fuzzy linear programing dalam menentukan nilai optimal pelayanan PDAM Kab. Jeneponto dengan metode sabiha. Menyusun setiap indikator fungsi tujuan (Z) dan fungsi kendala untuk dioptimalkan.. Hasil penyelesaian model diperoleh nilai optimal  total pelanggan 9075,999999999990. Untuk setiap variabel tujuan dengan nilai optimal 8896, 999999999990 untuk jenis pelanggan rumah tangga, 96,0000000000112 untuk jenis pelanggan sosial khusus, dan 82,9999999999982 untuk jenis pelanggan sosial umum. Dengan total pendapatan optimal Rp. 4.753.125.000 dan total permintaan air 1.082.303 m3.Kata Kunci : Program Linear, Fuzzy Linear Programing, Linear Fuzzy Number. Metode Sabiha, Optimalisasi.Abstract. Linear fuzzy programing is advance model for linear programing to determin the optimal result  that contains fuzzy numbers. Linear Fuzzy programing can be solved using Sabiha’s method. Which is based on real linear fuzzy numbers in triplet numbers form. This paper used linear fuzzy programming model and Sabiha’s method, to determin the optimal solution on PDAM Kab. Jeneponto’s operation plan. Each indicator constructed to optimized objective function and constraint function. Results of this research have optimal solution for each objective variable was obtained with an optimal value for total costumer are 9075,999999999990 from 8896,999999999990 the  type of household customer, 96,0000000000112 the type of special social customer, and 82,9999999999982  the type of public social costumer. With an optimal total revenue  Rp. 4,753,125,000 and total water demand 1,082,303 m3.Keywords: Linear Programing, Linear Fuzzy Programing, Linear Fuzzy Number, Sabiha’s Method, Optimalization.","PeriodicalId":363413,"journal":{"name":"Journal of Mathematics Computations and Statistics","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131266809","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Analisis Matematika Pada Pembuatan Rumah Panggung Toraja","authors":"Syafruddin Side, S. Sukarna, J. Jusriadi","doi":"10.35580/JMATHCOS.V3I1.19179","DOIUrl":"https://doi.org/10.35580/JMATHCOS.V3I1.19179","url":null,"abstract":"Geometri merupakan cabang ilmu yang mempelajari tentang hubungan antara titik-titik, garis-garis, dan bidang-bidang serta bangun datar dan bangun ruang. Dalam penerapan matematika geometri sangat membantu dalam kehidupan sehari-hari. Sebagai contoh penentuan tinggi menara dengan menggunakan bantuan cahaya matahari dimana dalam penentuannya bisa menggunakan sistem perbandingan. Kemudian menentukan jarak atau lebar sungai tanpa mengukur secara manual yaitu dengan menggunakan titik bantuan dan garis yang sebangun. Penelitian ini bertujuan mengetahui bagaimana hasil penerapan matematika dalam pembuatan rumah panggung Toraja. Dalam proses analisis dilakukan observasi dan wawancara serta dokumentasi untuk melihat proses pembuatan rumah panggung Toraja. Berdasarkan hasil analisis data yang diperoleh, ditemukan pola barisan pada tiang atau balok di setiap tipe rumah. Kemudian metode penggunaan garis sejajar, perpanjangan garis dan kesebangunan pada atap rumah. aplikasi matematika dapat diterapkan pada rumah panggung Toraja menggunakan persamaan dan fungsi parabola pada penentuan lengkungan atap rumah.Kata kunci: Geometri, Rumah panggung Toraja, Analisis, Persamaan Abstract. Geometry is  branch of science that learning about the relationship between points, lines,  sides , plane figure and solid figure. The application of geometry mathematics is very helpful in daily life. For example, the determination of tower height by using sunlight where in its determination can use the comparison system. Then, determine the distance or width of the river without measuring it manually, that is by using the help points and lines that are congruent. The aim of this research is finding out how the results of the application of mathematics in building Toraja Traditional house. The analysis process is done by observation, interview and documentation to see the process of building Toraja Traditional house. Based on the results of data analysis that is obtained, it was find the sequences pattern on the poles or beams in each type of house. Then the method of using parallel lines, lines extension and similarity on the roof of the house. Mathematics application can be applied in Toraja Traditional house by using parabolic equations and parabolic functions in determining the curvature of house roof.Keyword: Geometry,Toraja Traditional House, Analysis, Equation     ","PeriodicalId":363413,"journal":{"name":"Journal of Mathematics Computations and Statistics","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133408921","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Model Regresi Semiparametrik Spline untuk D ata Longitudinal pada Kasus Demam Berdarah Dengue di Kota Makassar","authors":"Syafruddin Side, Wahidah Sanusi, Mustati'atul Waidah Maksum","doi":"10.35580/JMATHCOS.V3I1.19181","DOIUrl":"https://doi.org/10.35580/JMATHCOS.V3I1.19181","url":null,"abstract":"Abstrak. Regresi semiparametrik merupakan model regresi yang memuat komponen parametrik dan komponen nonparametrik dalam suatu model. Pada penelitian ini digunakan model regresi semiparametrik spline untuk data longitudinal dengan studi kasus penderita Demam Berdarah Dengue (DBD) di Rumah Sakit Universitas Hasanuddin Makassar periode bulan  Januari sampai bulan Maret 2018. Estimasi model regresi terbaik didapat dari pemilihan titik knot optimal dengan melihat nilai Generalized Cross Validation (GCV) dan Mean Square Error (MSE) yang minimum. Komponen parametrik pada penelitian ini adalah hemoglobin (g/dL) dan umur (tahun), suhu tubuh ( ), trombosit ( ) sebagai komponen nonparametrik dengan nilai GCV minimum sebesar 221,67745153 dicapai pada titik knot yaitu 14,552; 14,987; dan 15,096; nilai MSE sebesar 199,1032; dan nilai koefisien determinasi sebesar 75,3% yang diperoleh dari model regresi semiparametrik spline linear dengan tiga titik knot..Kata Kunci: regresi semiparametrik, spline, knot, Generalized Cross Validation, Demam Berdarah Dengue.Abstract. Semiparametric regression is a regression model that includes parametric and nonparametric components in it. The regression model in this research is spline semiparametric regression with case studies of patients with Dengue Hemorrahagic Fever (DHF) at University of Hasanuddin Makassar Hospital during the period of January to March 2018. The best regression model estimation is obtained from the selection of optimal knot which has minimum Generalized Cross Validation (GCV) and Mean Square Error (MSE). Parametric component in this research is hemoglobin (g/dL) and age (years), body temperature ( \u0000 \u0000), platelets ( \u0000 \u0000) as a nonparametric components. The minimum value of GCV is 221,67745153 achieved at the point 14,552; 14,987; and 15,096 knot; MSE value of 199,1032; and the value of coefficient determination is 75,3% obtained from semiparametric regression model linear spline with third point of knots.Keywords: semiparametric regression, spline, knot, Generalized Cross Validation, Dengue Hemorrahagic Fever.","PeriodicalId":363413,"journal":{"name":"Journal of Mathematics Computations and Statistics","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114464464","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Grup Automorfisma Graf Tangga dan Graf Lingkaran","authors":"Muhammad Abdy, Wahidah Sanusi, A. Armansyah","doi":"10.35580/JMATHCOS.V3I1.19188","DOIUrl":"https://doi.org/10.35580/JMATHCOS.V3I1.19188","url":null,"abstract":"Abstrak. Automorfisma dari suatu graf G merupakan isomorfisma dari graf G ke dirinya sendiri, yaitu fungsi yang memetakan dirinya sendiri. Automorfisma suatu graf dapat dicari dengan menentukan semua kemungkinan fungsi yang satu-satu, onto serta isomorfisma dari himpunan titik pada graf tersebut. Artikel  ini difokuskan pada penentuan banyaknya fungsi pada graf tangga dan graf lingkaran yang automorfisma serta grup yang dibentuk oleh himpunan automorfisma dari kedua graf tersebut. Jenis penelitian ini merupakan penelitian dasar atau penelitian murni dan metode yang digunakan adalah studi literatur. Hasil penelitian ini menunjukkan bahwa graf tangga  membentuk grup abelian berorde-2, graf tangga membentuk grup dihedral berorde-8, dan graf tangga    membentuk grup abelian berorde-4. Sedangkan graf lingkaran  membentuk grup dihedral berorde-2n.Kata Kunci: Automorfisma, Graf Lingkaran, Graf Tangga, GrupAbstract. An automorphism of a graph G is an isomorphism of graph G to itself i.e. the function that maps onto itself. An automorphism of a graph can be looked for by determining all possible  functions which is one-to-one, onto, and isomorphism from vertex set at the graph. This article is focused on determining the number of automorphism functions on ladder graph and cycle graph and the groups formed by the two  graphs. The tipe of this research is basic research or pure research and the research method used is literarture review. The result show that ladder graph  forms an abelian group of order 2, ladder graph  forms a dihedral group of order 8, and ladder graph  forms an abelian group of order 4. In other side, cycle graph ,  forms a dihedral group of order 2n.Keywords: Automorphism, Cycle Graph, Ladder Graph, Group","PeriodicalId":363413,"journal":{"name":"Journal of Mathematics Computations and Statistics","volume":"56 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131497642","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}