Pub Date : 2019-07-31DOI: 10.11113/MATEMATIKA.V35.N2.1075
Nazlı Yazıcı Gözütok, Uğur Gözütok
In this study, the notion of a conformable partial differentiation of order alpha on time scales is introduced. Some properties of this new concept are given and relation between the conformable partial differentiation on time scales and the classical partial delta differentiation is revealed.
{"title":"Conformable Fractional Partial Differentiation on n-Dimensional Time Scales","authors":"Nazlı Yazıcı Gözütok, Uğur Gözütok","doi":"10.11113/MATEMATIKA.V35.N2.1075","DOIUrl":"https://doi.org/10.11113/MATEMATIKA.V35.N2.1075","url":null,"abstract":"In this study, the notion of a conformable partial differentiation of order alpha on time scales is introduced. Some properties of this new concept are given and relation between the conformable partial differentiation on time scales and the classical partial delta differentiation is revealed.","PeriodicalId":43733,"journal":{"name":"Matematika","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2019-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48965010","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}
Pub Date : 2019-07-31DOI: 10.11113/MATEMATIKA.V35.N2.1104
F. Zulkiflee, A. Q. Mohamad, S. Shafie, Arshad Khan
Free convection flow in a boundary layer region is a motion that results from the interaction of gravity with density differences within a fluid. These differences occur due to temperature or concentration gradients or due to their composition. Studies pertaining free convection flows of incompressible viscous fluids have received much attention in recent years both theoretically (exact or approximate solutions) and experimentally. The situation where the heat be transported to the convective fluid via a bounding surface having finite heat capacity is known as Newtonian heating (or conjugate convective flows). In this paper, the unsteady free convection flow of an incompressible viscous fluid between two parallel plates with Newtonian heating is studied. Appropriate non-dimensional variables are used to reduce the dimensional governing equations along with imposed initial and boundary conditions into dimensionless forms. The exact solutionsfor velocity and temperature are obtained using the Laplace transform technique. The corresponding expressions for skin friction and Nusselt number are also calculated. The graphical results are displayed to illustrate the influence of various embedded parameters such as Newtonian heating parameter and Grashof number. The results show that the effect of Newtonian heating parameter increases the Nusselt number but reduces the skin friction.
{"title":"Unsteady Free Convection Flow between Two Vertical Parallel Plates with Newtonian Heating","authors":"F. Zulkiflee, A. Q. Mohamad, S. Shafie, Arshad Khan","doi":"10.11113/MATEMATIKA.V35.N2.1104","DOIUrl":"https://doi.org/10.11113/MATEMATIKA.V35.N2.1104","url":null,"abstract":"Free convection flow in a boundary layer region is a motion that results from the interaction of gravity with density differences within a fluid. These differences occur due to temperature or concentration gradients or due to their composition. Studies pertaining free convection flows of incompressible viscous fluids have received much attention in recent years both theoretically (exact or approximate solutions) and experimentally. The situation where the heat be transported to the convective fluid via a bounding surface having finite heat capacity is known as Newtonian heating (or conjugate convective flows). In this paper, the unsteady free convection flow of an incompressible viscous fluid between two parallel plates with Newtonian heating is studied. Appropriate non-dimensional variables are used to reduce the dimensional governing equations along with imposed initial and boundary conditions into dimensionless forms. The exact solutionsfor velocity and temperature are obtained using the Laplace transform technique. The corresponding expressions for skin friction and Nusselt number are also calculated. The graphical results are displayed to illustrate the influence of various embedded parameters such as Newtonian heating parameter and Grashof number. The results show that the effect of Newtonian heating parameter increases the Nusselt number but reduces the skin friction.","PeriodicalId":43733,"journal":{"name":"Matematika","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2019-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49602706","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}
Pub Date : 2019-07-31DOI: 10.11113/MATEMATIKA.V35.N2.1114
S. Alrehaili, Charef Beddani
The commutativity degree is the probability that a pair of elements chosen randomly from a group commute. The concept of commutativity degree has been widely discussed by several authors in many directions. One of the important generalizations of commutativity degree is the probability that a random element from a finite group G fixes a random element from a non-empty set S that we call the action degree of groups. In this research, the concept of action degree is further studied where some inequalities and bounds on the action degree of finite groups are determined. Moreover, a general relation between the action degree of a finite group G and a subgroup H is provided. Next, the action degree for the direct product of two finite groups is determined. Previously, the action degree was only defined for finite groups, the action degree for finitely generated groups will be defined in this research and some bounds on them are going to be determined.
{"title":"Bounds on the Action Degree of Groups","authors":"S. Alrehaili, Charef Beddani","doi":"10.11113/MATEMATIKA.V35.N2.1114","DOIUrl":"https://doi.org/10.11113/MATEMATIKA.V35.N2.1114","url":null,"abstract":"The commutativity degree is the probability that a pair of elements chosen randomly from a group commute. The concept of commutativity degree has been widely discussed by several authors in many directions. One of the important generalizations of commutativity degree is the probability that a random element from a finite group G fixes a random element from a non-empty set S that we call the action degree of groups. In this research, the concept of action degree is further studied where some inequalities and bounds on the action degree of finite groups are determined. Moreover, a general relation between the action degree of a finite group G and a subgroup H is provided. Next, the action degree for the direct product of two finite groups is determined. Previously, the action degree was only defined for finite groups, the action degree for finitely generated groups will be defined in this research and some bounds on them are going to be determined.","PeriodicalId":43733,"journal":{"name":"Matematika","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2019-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49509264","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}
Pub Date : 2019-07-31DOI: 10.11113/MATEMATIKA.V35.N2.1180
N. Norddin, Mohd Rivaie Mohd Ali, Nurul Hafawati Fadhilah, N. Atikah, Anis Shahida, Nur Hidayah Nohd Noh
Regression is one of the basic relationship models in statistics. This paper focuses on the formation of regression models for the rice production in Malaysia by analysing the effects of paddy population, planted area, human population and domestic consumption. In this study, the data were collected from the year 1980 until 2014 from the website of the Department of Statistics Malaysia and Index Mundi. It is well known that the regression model can be solved using the least square method. Since least square problem is an unconstrained optimisation, the Conjugate Gradient (CG) was chosen to generate a solution for regression model and hence to obtain the coefficient value of independent variables. Results show that the CG methods could produce a good regression equation with acceptable Root Mean-Square Error (RMSE) value.
{"title":"Multiple Linear Regression Model of Rice Production using Conjugate Gradient Methods","authors":"N. Norddin, Mohd Rivaie Mohd Ali, Nurul Hafawati Fadhilah, N. Atikah, Anis Shahida, Nur Hidayah Nohd Noh","doi":"10.11113/MATEMATIKA.V35.N2.1180","DOIUrl":"https://doi.org/10.11113/MATEMATIKA.V35.N2.1180","url":null,"abstract":"Regression is one of the basic relationship models in statistics. This paper focuses on the formation of regression models for the rice production in Malaysia by analysing the effects of paddy population, planted area, human population and domestic consumption. In this study, the data were collected from the year 1980 until 2014 from the website of the Department of Statistics Malaysia and Index Mundi. It is well known that the regression model can be solved using the least square method. Since least square problem is an unconstrained optimisation, the Conjugate Gradient (CG) was chosen to generate a solution for regression model and hence to obtain the coefficient value of independent variables. Results show that the CG methods could produce a good regression equation with acceptable Root Mean-Square Error (RMSE) value.","PeriodicalId":43733,"journal":{"name":"Matematika","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2019-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41450931","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}
Pub Date : 2019-07-31DOI: 10.11113/MATEMATIKA.V35.N2.1106
Nabilah Najmuddin, N. Sarmin, A. Erfanian
A domination polynomial is a type of graph polynomial in which its coefficients represent the number of dominating sets in the graph. There are many researches being done on the domination polynomial of some common types of graphs but not yet for graphs associated to finite groups. Two types of graphs associated to finite groups are the conjugate graph and the conjugacy class graph. A graph of a group G is called a conjugate graph if the vertices are non-central elements of G and two distinct vertices are adjacent if they are conjugate to each other. Meanwhile, a conjugacy class graph of a group G is a graph in which its vertices are the non-central conjugacy classes of G and two distinct vertices are connected if and only if their class cardinalities are not coprime. The conjugate and conjugacy class graph of dihedral groups can be expressed generally as a union of complete graphs on some vertices. In this paper, the domination polynomials are computed for the conjugate and conjugacy class graphs of the dihedral groups.
{"title":"General Form of Domination Polynomial for Two Types of Graphs Associated to Dihedral Groups","authors":"Nabilah Najmuddin, N. Sarmin, A. Erfanian","doi":"10.11113/MATEMATIKA.V35.N2.1106","DOIUrl":"https://doi.org/10.11113/MATEMATIKA.V35.N2.1106","url":null,"abstract":"A domination polynomial is a type of graph polynomial in which its coefficients represent the number of dominating sets in the graph. There are many researches being done on the domination polynomial of some common types of graphs but not yet for graphs associated to finite groups. Two types of graphs associated to finite groups are the conjugate graph and the conjugacy class graph. A graph of a group G is called a conjugate graph if the vertices are non-central elements of G and two distinct vertices are adjacent if they are conjugate to each other. Meanwhile, a conjugacy class graph of a group G is a graph in which its vertices are the non-central conjugacy classes of G and two distinct vertices are connected if and only if their class cardinalities are not coprime. The conjugate and conjugacy class graph of dihedral groups can be expressed generally as a union of complete graphs on some vertices. In this paper, the domination polynomials are computed for the conjugate and conjugacy class graphs of the dihedral groups.","PeriodicalId":43733,"journal":{"name":"Matematika","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2019-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42538797","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}
Pub Date : 2019-05-30DOI: 10.29313/JMTM.V18I1.5078
Devy Andriyani, E. Harahap, F. H. Badruzzaman, M. Y. Fajar, Deni Darmawan
Abstrak. Era digital menuntut segala bentuk aktivitas dikerjakan dengan cepat, efektif, dan efisien, dengan pemanfaatan teknologi yang mutakhir. Pada era reformasi teknologi 4.0 saat ini, berbagai informasi dapat diperoleh dalam waktu yang singkat melalui perangkat pintar dengan aplikasi tertentu, salah satunya adalah aplikasi untuk menghitung nilai rata-rata. Penyelesaian masalah nilai rata-rata pada data berkelompok memerlukan suatu usaha perhitungan yang teliti dan kompleks. Pada artikel ini penulis menguraikan sebuah aplikasi untuk penyelesaian masalah perhitungan nilai rata-rata pada data berkelompok secara efektif, cepat, dan akurat dengan menggunakan software Microsoft Excel. Kata kunci: microsoft excel, rata-rata data berkelompok, aplikasi matematikaAbstract. Digital era can demand all of activity to working with quick, effective, and efficient with utilization a up to date’s technology. In the era of Reformation Technology 4.0, various information was obtained in a short time via smart device with particular application , one of them is application to calculate average. Finishing a average’s problem in group data can make a careful and complex calculation effort. In this article, the author outlines a application for completed a problem of calculate average for group data with effective, quick, and accurate with using a Microsoft ExcelKeywords : Microsoft Excel, average group data, application in mathematics
{"title":"Aplikasi Microsoft Excel Dalam Penyelesaian Masalah Rata-rata Data Berkelompok","authors":"Devy Andriyani, E. Harahap, F. H. Badruzzaman, M. Y. Fajar, Deni Darmawan","doi":"10.29313/JMTM.V18I1.5078","DOIUrl":"https://doi.org/10.29313/JMTM.V18I1.5078","url":null,"abstract":"Abstrak. Era digital menuntut segala bentuk aktivitas dikerjakan dengan cepat, efektif, dan efisien, dengan pemanfaatan teknologi yang mutakhir. Pada era reformasi teknologi 4.0 saat ini, berbagai informasi dapat diperoleh dalam waktu yang singkat melalui perangkat pintar dengan aplikasi tertentu, salah satunya adalah aplikasi untuk menghitung nilai rata-rata. Penyelesaian masalah nilai rata-rata pada data berkelompok memerlukan suatu usaha perhitungan yang teliti dan kompleks. Pada artikel ini penulis menguraikan sebuah aplikasi untuk penyelesaian masalah perhitungan nilai rata-rata pada data berkelompok secara efektif, cepat, dan akurat dengan menggunakan software Microsoft Excel. Kata kunci: microsoft excel, rata-rata data berkelompok, aplikasi matematikaAbstract. Digital era can demand all of activity to working with quick, effective, and efficient with utilization a up to date’s technology. In the era of Reformation Technology 4.0, various information was obtained in a short time via smart device with particular application , one of them is application to calculate average. Finishing a average’s problem in group data can make a careful and complex calculation effort. In this article, the author outlines a application for completed a problem of calculate average for group data with effective, quick, and accurate with using a Microsoft ExcelKeywords : Microsoft Excel, average group data, application in mathematics","PeriodicalId":43733,"journal":{"name":"Matematika","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2019-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45275439","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}
Pub Date : 2019-05-30DOI: 10.29313/JMTM.V18I1.4931
M. D. Johansyah, Herlina Napitupulu, E. Harahap, I. Sumiati, Asep K. Supriatna
Abstrak. Pada umumnya orde dari persamaan diferensial adalah bilangan asli, namun orde pada persamaan diferensial dapat dibentuk menjadi orde pecahan yang disebut persamaan diferensial fraksional. Paper ini membahas persamaan diferensial fraksional Riccati dengan orde diantara nol dan satu, dan koefisien konstan. Metode numerik yang digunakan untuk mendapatkan solusi dari persamaan diferensial fraksional Riccati adalah Adomian Decomposition Method (ADM) dan Variational Iteration Method (VIM). Tujuan dari paper ini adalah untuk memperluas penerapan ADM dan VIM dalam menyelesaikan persamaan diferensial fraksional Riccati nonlinear dengan turunan Caputo. Perbandingan solusi yang diperoleh menunjukkan bahwa VIM adalah metode yang lebih sederhana untuk mencari solusi persamaan diferensial fraksional Riccati nonlinier dengan orde antara nol dan satu, kemudian hasil yang diperoleh disajikan dalam bentuk grafik.Kata kunci: diferensial, fraksional, riccati, adomian dekomposisiThe solution of Riccati Fractional Differential Equation using Adomian Decomposition methodAbstract. Generally, the order of differential equations is a natural numbers, but this order can be formed into fractional, called as fractional differential equations. In this paper, the Riccati fractional differential equations with order between zero and one, and constant coefficient is discussed. The numerical methods used to obtain solutions from Riccati fractional differential equations are the Adomian Decomposition Method (ADM) and Variational Iteration Method (VIM). The aim of this paper is to expand the application of ADM and VIM in solving nonlinear Riccati fractional differential equations with Caputo derivatives. The comparison of the obtained solutions shows that VIM is simpler method for finding solutions to Riccati nonlinear fractional differential equations with order between zero and one. The obtained results are presented graphically.Keywords: riccati, fractional, differential, adomian, decomposition
{"title":"Solusi Persamaan Diferensial Fraksional Riccati Menggunakan Adomian Decomposition Method dan Variational Iteration Method","authors":"M. D. Johansyah, Herlina Napitupulu, E. Harahap, I. Sumiati, Asep K. Supriatna","doi":"10.29313/JMTM.V18I1.4931","DOIUrl":"https://doi.org/10.29313/JMTM.V18I1.4931","url":null,"abstract":"Abstrak. Pada umumnya orde dari persamaan diferensial adalah bilangan asli, namun orde pada persamaan diferensial dapat dibentuk menjadi orde pecahan yang disebut persamaan diferensial fraksional. Paper ini membahas persamaan diferensial fraksional Riccati dengan orde diantara nol dan satu, dan koefisien konstan. Metode numerik yang digunakan untuk mendapatkan solusi dari persamaan diferensial fraksional Riccati adalah Adomian Decomposition Method (ADM) dan Variational Iteration Method (VIM). Tujuan dari paper ini adalah untuk memperluas penerapan ADM dan VIM dalam menyelesaikan persamaan diferensial fraksional Riccati nonlinear dengan turunan Caputo. Perbandingan solusi yang diperoleh menunjukkan bahwa VIM adalah metode yang lebih sederhana untuk mencari solusi persamaan diferensial fraksional Riccati nonlinier dengan orde antara nol dan satu, kemudian hasil yang diperoleh disajikan dalam bentuk grafik.Kata kunci: diferensial, fraksional, riccati, adomian dekomposisiThe solution of Riccati Fractional Differential Equation using Adomian Decomposition methodAbstract. Generally, the order of differential equations is a natural numbers, but this order can be formed into fractional, called as fractional differential equations. In this paper, the Riccati fractional differential equations with order between zero and one, and constant coefficient is discussed. The numerical methods used to obtain solutions from Riccati fractional differential equations are the Adomian Decomposition Method (ADM) and Variational Iteration Method (VIM). The aim of this paper is to expand the application of ADM and VIM in solving nonlinear Riccati fractional differential equations with Caputo derivatives. The comparison of the obtained solutions shows that VIM is simpler method for finding solutions to Riccati nonlinear fractional differential equations with order between zero and one. The obtained results are presented graphically.Keywords: riccati, fractional, differential, adomian, decomposition","PeriodicalId":43733,"journal":{"name":"Matematika","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2019-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47906644","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}
Pub Date : 2019-05-30DOI: 10.29313/JMTM.V18I1.4729
Anik Rufaidah, M. Effindi
Abstrak. Data penjualan songkok Nasional yang diproduksi oleh UMKM kabupaten Gresik selalu mengalami fluktuatif dan data tersebut juga berpengaruh adanya trend naik. Untuk mendeteksi penjualan kedepan yang berpengaruh dengan persediaan bahan baku. Sehingga kami menggunakan pemodelan dengan Double Exponential Smoothing dan Winter Multiplicative Seasonality . Dari hasil pemodelan ternyata nilai MAD dan MSD yang didapat terkecil adalah model Winter Multiplicative Seasonality , sehingga model tersebut kami buat forecasting untuk 6 bulan kedepan. Kata Kunci: Double Exponential Smoothing, Winter Multiplicative Seasonality, forecasting. Abstract. Data on National Songkok sales produced by Small and Medium Enterprises (SMEs) in Gresik Regency of East Java Province was always fluctuate and the data also influences the uptrend. In order to detect future sales which was affecting the inventory of raw materials, this research use modeling with Double Exponential Smoothing and Winter Multiplicative Seasonality. From the modeling results, it turns out the smallest value of MAD and MSD is the Winter Multiplicative Seasonality model. The data used by the model forecast for the next 6 months. Keywords: Double Exponential Smoothing, Winter Multiplicative Seasonality, forecasting.
{"title":"Perbandingan Peramalan Dengan Metode Eksponensial Smoothing dan Winter Multiplicative Seasonality pada Data Penjualan Songkok Nasional UMKM di Kabupaten Gresik","authors":"Anik Rufaidah, M. Effindi","doi":"10.29313/JMTM.V18I1.4729","DOIUrl":"https://doi.org/10.29313/JMTM.V18I1.4729","url":null,"abstract":"Abstrak. Data penjualan songkok Nasional yang diproduksi oleh UMKM kabupaten Gresik selalu mengalami fluktuatif dan data tersebut juga berpengaruh adanya trend naik. Untuk mendeteksi penjualan kedepan yang berpengaruh dengan persediaan bahan baku. Sehingga kami menggunakan pemodelan dengan Double Exponential Smoothing dan Winter Multiplicative Seasonality . Dari hasil pemodelan ternyata nilai MAD dan MSD yang didapat terkecil adalah model Winter Multiplicative Seasonality , sehingga model tersebut kami buat forecasting untuk 6 bulan kedepan. Kata Kunci: Double Exponential Smoothing, Winter Multiplicative Seasonality, forecasting. Abstract. Data on National Songkok sales produced by Small and Medium Enterprises (SMEs) in Gresik Regency of East Java Province was always fluctuate and the data also influences the uptrend. In order to detect future sales which was affecting the inventory of raw materials, this research use modeling with Double Exponential Smoothing and Winter Multiplicative Seasonality. From the modeling results, it turns out the smallest value of MAD and MSD is the Winter Multiplicative Seasonality model. The data used by the model forecast for the next 6 months. Keywords: Double Exponential Smoothing, Winter Multiplicative Seasonality, forecasting.","PeriodicalId":43733,"journal":{"name":"Matematika","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2019-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41336937","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}
Pub Date : 2019-05-30DOI: 10.29313/JMTM.V18I1.5079
Ahmad Nurul Hadi, Eddy Djauhari, Asep K. Supriatna, M. D. Johansyah
Abstrak. Penentuan solusi sistem persamaan diferensial linear non-homogen orde satu dengan koefisien konstanta, dilakukan dengan mengubah sistem persamaan tersebut menjadi persamaan diferensial linear non homogen tunggal. Dari persamaan diferensial linear non homogen tunggal tersebut kemudian dicari solusi homogennya menggunakan akar-akar karakteristiknya, dan mencari solusi partikularnya dengan metode variasi parameter. Solusi umum dari persamaan diferensial linear tersebut adalah jumlah dari solusi homogen dan solusi partikularnya. Persamaan diferensial linear tunggal tersebut berorde- , yang solusi umumnya berbentuk . Selanjutnya dicari solusi umum berebentuk yang berkaitan dengan , solusi umum berbentuk yang berkaitan dengan dan , solusi umum berbentuk yang berkaitan dengan , , dan , demikian seterusnya sampai mencari solusi umum berbentuk yang berkaitan dengan , , , , . Kumpulan solusi umum yang berbentuk merupakan solusi umum dari sistem persamaan diferensial linear non homogen orde satu tersebut.Kata kunci: Diferensial, Linear, Non-Homogen, Orde, Satu. Technical to Find The System of Linear Non-Homogen Differential Equation of First OrderAbstract. Determination of first-order non-homogeneous linear differential equation system solutions with constant coefficients, carried out by changing the system of equations into a single non-homogeneous linear differential equation. From a single non-homogeneous differential equation, a homogeneous solution is then used using its characteristic roots, and looking for a particular solution with the parameter variation method. The general solution of these linear differential equations is the number of homogeneous solutions and their particular solutions. The single linear differential equation is n-order, the solution being in the form of . Then look for a general solution in the form of related to , a general solution in the form of related to and , general solutions in the form of related to , and , and so on until looking for a general solution in the form of related to , , , ..., . A collection of general solutions in the form of , , , ..., is the general solution of the first-order non-homogeneous linear differential equation system.Keywords: Linear, Differential, First, Order, Non-Homogeneous
抽象。用常数系数计算出线性非均匀方程1的微分方程，将该方程转换成一个非均匀线性微分方程。从单一的非同质线性微分方程中，用其特征的根寻求同质解决方案，并使用不同参数的方法寻求分区解决方案。线性微分方程的一般解是同质解和子集解的总和。单线性微分方程是这样的，解通常是形状的。然后寻找与丹有关的共同形式的整体解决方案，与之相关的一般形式解决方案，与之相关的一般形式解决方案，等等，直到找到与……有关的共同形式解决方案。一站式的通用解决方案集是1的非均匀线性微分方程系统的共同解决方案。微分，线性，不均匀，顺序，一。技术上找到线性非均匀的系统与持续的coeffients的相同线性差分系统的确定，通过将平衡系统转换成一个单一的非同线性差分系统来实现。从一个单一的非同质性差异方程中，一个同质性解决方案随后使用它的特性根，并寻找一个与变量方法论参数相关的部分解决方案。这些线性差异等式的一般解决方案是同质解决方案及其部分解决方案的数字。单一的线性差异相等是n命令，解决方案存在于形式中。然后look for a solution in the form of相关将军,百万solution in the form of相关to and将军,将军,和相关的解决方案》没有注明,and so on,直到寻找a solution in the form of相关的将军 , , , ...,。总解决方案的集合。这是一种通用的非均匀线性差异系统的第一定律。线性，不同的，第一，秩序，非均匀的
{"title":"Teknik Penentuan Solusi Sistem Persamaan Diferensial Linear Non-Homogen Orde Satu","authors":"Ahmad Nurul Hadi, Eddy Djauhari, Asep K. Supriatna, M. D. Johansyah","doi":"10.29313/JMTM.V18I1.5079","DOIUrl":"https://doi.org/10.29313/JMTM.V18I1.5079","url":null,"abstract":"Abstrak. Penentuan solusi sistem persamaan diferensial linear non-homogen orde satu dengan koefisien konstanta, dilakukan dengan mengubah sistem persamaan tersebut menjadi persamaan diferensial linear non homogen tunggal. Dari persamaan diferensial linear non homogen tunggal tersebut kemudian dicari solusi homogennya menggunakan akar-akar karakteristiknya, dan mencari solusi partikularnya dengan metode variasi parameter. Solusi umum dari persamaan diferensial linear tersebut adalah jumlah dari solusi homogen dan solusi partikularnya. Persamaan diferensial linear tunggal tersebut berorde- , yang solusi umumnya berbentuk . Selanjutnya dicari solusi umum berebentuk yang berkaitan dengan , solusi umum berbentuk yang berkaitan dengan dan , solusi umum berbentuk yang berkaitan dengan , , dan , demikian seterusnya sampai mencari solusi umum berbentuk yang berkaitan dengan , , , , . Kumpulan solusi umum yang berbentuk merupakan solusi umum dari sistem persamaan diferensial linear non homogen orde satu tersebut.Kata kunci: Diferensial, Linear, Non-Homogen, Orde, Satu. Technical to Find The System of Linear Non-Homogen Differential Equation of First OrderAbstract. Determination of first-order non-homogeneous linear differential equation system solutions with constant coefficients, carried out by changing the system of equations into a single non-homogeneous linear differential equation. From a single non-homogeneous differential equation, a homogeneous solution is then used using its characteristic roots, and looking for a particular solution with the parameter variation method. The general solution of these linear differential equations is the number of homogeneous solutions and their particular solutions. The single linear differential equation is n-order, the solution being in the form of . Then look for a general solution in the form of related to , a general solution in the form of related to and , general solutions in the form of related to , and , and so on until looking for a general solution in the form of related to , , , ..., . A collection of general solutions in the form of , , , ..., is the general solution of the first-order non-homogeneous linear differential equation system.Keywords: Linear, Differential, First, Order, Non-Homogeneous","PeriodicalId":43733,"journal":{"name":"Matematika","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2019-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45694677","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}
Pub Date : 2019-05-30DOI: 10.29313/JMTM.V18I1.4565
A. Hidayat
Abstrak. Metode dinamika molekuler digunakan untuk mempelajari deposisi atom tembaga (Cu) pada substrat silikon (Si). Interaksi atom-atom Si-Si, Cu-Cu, dan Cu-Si masing-masing dideskripsikan dengan potensial interatomik Tersoff, MEAM, dan Morse. Ensembel NVE dan termostat Berendsen digunakan dalam simulasi ini. Kemudian diinvestigasi pengaruh parameter kecepatan awal dan laju deposisi terhadap persentase struktur amorf, fungsi distribusi radial (RDF), dan bilangan koordinasi. Hasil simulasi menunjukkan perbedaan yang signifikan terhadap persentase struktur amorf pada parameter yang bervariasi. Investigasi pasca-simulasi menunjukkan variasi pada nilai RDF dan bilangan koordinasi. Kata kunci: Metode dinamika molekuler, evolusi struktur, fungsi distribusi radial, bilangan koordinasi Study of Structure Evolution of Copper Deposition on Silicon Substrate using Molecular Dynamics Method Abstract. The Molecular dynamics method was used to study the deposition of copper (Cu) atoms onto silicon (Si) substrate. The interaction of Si-Si Cu-Cu, and Cu-Si atoms were described by Tersoff, MEAM, and Morse interatomic potentials respectively. NVE ensemble and Berendsen thermostat was used in this simulation. The effect of initial velocity and deposition rate on the percentage of amorphous structure, radial distribution function (RDF), and coordination number was investigated. The result showed significant differences of amorphous structure percentage at varied parameters. Post-simulation investigation showed variation in RDF and coordination number. Keywords: Molecular dynamics method, structure evolution, radial distribution function, coordination number
{"title":"Studi Evolusi Struktur pada Deposisi Tembaga Dalam Substrat Silikon Dengan Metode Dinamika Molekuler","authors":"A. Hidayat","doi":"10.29313/JMTM.V18I1.4565","DOIUrl":"https://doi.org/10.29313/JMTM.V18I1.4565","url":null,"abstract":"Abstrak. Metode dinamika molekuler digunakan untuk mempelajari deposisi atom tembaga (Cu) pada substrat silikon (Si). Interaksi atom-atom Si-Si, Cu-Cu, dan Cu-Si masing-masing dideskripsikan dengan potensial interatomik Tersoff, MEAM, dan Morse. Ensembel NVE dan termostat Berendsen digunakan dalam simulasi ini. Kemudian diinvestigasi pengaruh parameter kecepatan awal dan laju deposisi terhadap persentase struktur amorf, fungsi distribusi radial (RDF), dan bilangan koordinasi. Hasil simulasi menunjukkan perbedaan yang signifikan terhadap persentase struktur amorf pada parameter yang bervariasi. Investigasi pasca-simulasi menunjukkan variasi pada nilai RDF dan bilangan koordinasi. Kata kunci: Metode dinamika molekuler, evolusi struktur, fungsi distribusi radial, bilangan koordinasi Study of Structure Evolution of Copper Deposition on Silicon Substrate using Molecular Dynamics Method Abstract. The Molecular dynamics method was used to study the deposition of copper (Cu) atoms onto silicon (Si) substrate. The interaction of Si-Si Cu-Cu, and Cu-Si atoms were described by Tersoff, MEAM, and Morse interatomic potentials respectively. NVE ensemble and Berendsen thermostat was used in this simulation. The effect of initial velocity and deposition rate on the percentage of amorphous structure, radial distribution function (RDF), and coordination number was investigated. The result showed significant differences of amorphous structure percentage at varied parameters. Post-simulation investigation showed variation in RDF and coordination number. Keywords: Molecular dynamics method, structure evolution, radial distribution function, coordination number","PeriodicalId":43733,"journal":{"name":"Matematika","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2019-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43338652","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}
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