Pub Date : 2023-06-04DOI: 10.24198/jmi.v19.n1.40855.125-136
Syed Bilal Asim, Evi Noviani, Helmi Helmi
Fluid flow can be expressed as a partial differential equation. This study presents a deduction of fluid flow modelling on an inclined plane. The fluid flow is assumed to be incompressible and irrotational. Modelling fluid flow in the incline involves various equations: the continuity equation, the Navier-Stokes equation, the power equation, and the pressure equation. The Navier-Stokes, power-law, and pressure equations are transformed into dimensionless forms and then solved by substituting the power-law and pressure equations into the Navier-Stokes equation. Reynold’s number is assumed to be very small, so we can omit it in the Navier-stokes equation. Further, the Navier-Stokes equation that has been built is transformed into dimensional form. In constructing a fluid flow model on an inclined plane, free surface kinematic equations are also needed, which produce differential equations, so that models and solutions for fluid flow on an inclined plane are obtained in thin layers. This model is in the form of a first-order quasi-linear equation. We obtain that the solution is a function of the position of the fluid flowing at a certain time which also depends on the fluid type.
{"title":"Pemodelan Aliran Fluida Bidang Miring pada Lapisan Tipis","authors":"Syed Bilal Asim, Evi Noviani, Helmi Helmi","doi":"10.24198/jmi.v19.n1.40855.125-136","DOIUrl":"https://doi.org/10.24198/jmi.v19.n1.40855.125-136","url":null,"abstract":"Fluid flow can be expressed as a partial differential equation. This study presents a deduction of fluid flow modelling on an inclined plane. The fluid flow is assumed to be incompressible and irrotational. Modelling fluid flow in the incline involves various equations: the continuity equation, the Navier-Stokes equation, the power equation, and the pressure equation. The Navier-Stokes, power-law, and pressure equations are transformed into dimensionless forms and then solved by substituting the power-law and pressure equations into the Navier-Stokes equation. Reynold’s number is assumed to be very small, so we can omit it in the Navier-stokes equation. Further, the Navier-Stokes equation that has been built is transformed into dimensional form. In constructing a fluid flow model on an inclined plane, free surface kinematic equations are also needed, which produce differential equations, so that models and solutions for fluid flow on an inclined plane are obtained in thin layers. This model is in the form of a first-order quasi-linear equation. We obtain that the solution is a function of the position of the fluid flowing at a certain time which also depends on the fluid type.","PeriodicalId":53096,"journal":{"name":"Jurnal Matematika Integratif","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45654951","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 : 2023-06-03DOI: 10.24198/jmi.v19.n1.46422.109-123
Uray Agustian, Evi Noviani, Yudhi Yudhi
Fluid is a substance that changes shape and position when exposed to shear stress. The domain of the fluid can change along with changing the shape of the surface. This boundary is called the free surface boundary. We expressed the fluid flow problems involving free surfaces as partial differential equations. In solving this problem, certain techniques are needed, one of which is numerical, if the exact solution cannot be determined. This study examines the modelling of the free surface of the fluid and its solution numerically using the Volume of Fluid (VOF) method. Modelling fluid flow problems with a free surface, in general, begins by using the law of the conservation of mass and the law of the conservation of momentum, which produces the Navier-Stokes equation. The fluid is assumed to be incompressible. This study uses the VOF method with the Parker and Young algorithm to solve the free surface boundary problem. The surface of the fluid is described as a semicircle with a radius of 1 and a grid size of 10 × 5. We divide the boundary of the fluid into 14 partitions, then the area of each grid is determined, and the slope of the line is found on the partition through the four sur-rounding grid values. Henceforth, we obtained the equation of the line for each partition. We get a piecewise function from the calculation with an average error of 0.01459715.
{"title":"Rekonstruksi Permukaan Bebas Fluida Menggunakan Metode Volume of Fluid","authors":"Uray Agustian, Evi Noviani, Yudhi Yudhi","doi":"10.24198/jmi.v19.n1.46422.109-123","DOIUrl":"https://doi.org/10.24198/jmi.v19.n1.46422.109-123","url":null,"abstract":"Fluid is a substance that changes shape and position when exposed to shear stress. The domain of the fluid can change along with changing the shape of the surface. This boundary is called the free surface boundary. We expressed the fluid flow problems involving free surfaces as partial differential equations. In solving this problem, certain techniques are needed, one of which is numerical, if the exact solution cannot be determined. This study examines the modelling of the free surface of the fluid and its solution numerically using the Volume of Fluid (VOF) method. Modelling fluid flow problems with a free surface, in general, begins by using the law of the conservation of mass and the law of the conservation of momentum, which produces the Navier-Stokes equation. The fluid is assumed to be incompressible. This study uses the VOF method with the Parker and Young algorithm to solve the free surface boundary problem. The surface of the fluid is described as a semicircle with a radius of 1 and a grid size of 10 × 5. We divide the boundary of the fluid into 14 partitions, then the area of each grid is determined, and the slope of the line is found on the partition through the four sur-rounding grid values. Henceforth, we obtained the equation of the line for each partition. We get a piecewise function from the calculation with an average error of 0.01459715.","PeriodicalId":53096,"journal":{"name":"Jurnal Matematika Integratif","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47365122","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 : 2023-06-02DOI: 10.24198/jmi.v19.n1.45047.55-66
Albert Mario Kumanireng, A. Zulijanto
study some properties of fragmented functions and functionally countably fragmented functions. Using regular transfinite sequences, we prove that the set of all real-valued fragmented functions and the set of all real-valued functionally countably fragmented functions is a ring. We also prove a property of fragmented function (functionally countably fragmented function) which is analogous to Weierstrass M-Test Theorem. Furthermore, we provide an imposed condition such that a functionally countably fragmented function is continuous.
{"title":"Sifat-sifat Fungsi Terfragmentasi dan Fungsi Terfragmentasi Terhitung Fungsional","authors":"Albert Mario Kumanireng, A. Zulijanto","doi":"10.24198/jmi.v19.n1.45047.55-66","DOIUrl":"https://doi.org/10.24198/jmi.v19.n1.45047.55-66","url":null,"abstract":"study some properties of fragmented functions and functionally countably fragmented functions. Using regular transfinite sequences, we prove that the set of all real-valued fragmented functions and the set of all real-valued functionally countably fragmented functions is a ring. We also prove a property of fragmented function (functionally countably fragmented function) which is analogous to Weierstrass M-Test Theorem. Furthermore, we provide an imposed condition such that a functionally countably fragmented function is continuous.","PeriodicalId":53096,"journal":{"name":"Jurnal Matematika Integratif","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46558215","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 : 2023-06-02DOI: 10.24198/jmi.v19.n1.44573.41-54
Triesha Syifahati, A. Triska, Julita Nahar
The Double Exponential Smoothing (DES) and Triple Exponential Smoothing (TES) are forecasting methods that require two and three smoothing parameters, respectively. Smoothing parameters are often determined through a trial and error process that is not really efficient since many experiments need to be done. Therefore, in this study, a smoothing parameter estimation algorithm is conducted in the form of the modified Golden Section Search (GSS) to obtain the optimal smoothing parameters from the DES and TES methods. Forecasting is carried out on production, domestic consumption, and export consumption data of Indonesian coffee, which is one of the leading agricultural sub-sector commodities. The data is obtained from the Ministry of Agriculture of the Republic of Indonesia. The smoothing parameters obtained by applying the modified GSS are used to forecast production and domestic consumption data using the DES method, while the forecasting of the export consumption data is done with the TES method. All of the MAPE values are less than 20% which indicates that the smoothing parameters obtained by using the modified GSS are able to perform good forecasting. The results show that coffee production in Indonesia cannot meet its demand until 2024 since the total coffee consumption exceeds the production.
{"title":"Forecasting the Indonesian Coffee Production and Consumption Using the Modified Golden Section Search to Estimate the Smoothing Parameters","authors":"Triesha Syifahati, A. Triska, Julita Nahar","doi":"10.24198/jmi.v19.n1.44573.41-54","DOIUrl":"https://doi.org/10.24198/jmi.v19.n1.44573.41-54","url":null,"abstract":"The Double Exponential Smoothing (DES) and Triple Exponential Smoothing (TES) are forecasting methods that require two and three smoothing parameters, respectively. Smoothing parameters are often determined through a trial and error process that is not really efficient since many experiments need to be done. Therefore, in this study, a smoothing parameter estimation algorithm is conducted in the form of the modified Golden Section Search (GSS) to obtain the optimal smoothing parameters from the DES and TES methods. Forecasting is carried out on production, domestic consumption, and export consumption data of Indonesian coffee, which is one of the leading agricultural sub-sector commodities. The data is obtained from the Ministry of Agriculture of the Republic of Indonesia. The smoothing parameters obtained by applying the modified GSS are used to forecast production and domestic consumption data using the DES method, while the forecasting of the export consumption data is done with the TES method. All of the MAPE values are less than 20% which indicates that the smoothing parameters obtained by using the modified GSS are able to perform good forecasting. The results show that coffee production in Indonesia cannot meet its demand until 2024 since the total coffee consumption exceeds the production.","PeriodicalId":53096,"journal":{"name":"Jurnal Matematika Integratif","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48573810","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 : 2023-06-02DOI: 10.24198/jmi.v19.n1.45096.67-76
Olivia Anjanette, B. Subartini, D. Chaerani
Online business is a business activity carried out via the internet or digitally. Buying, selling, and advertising are done online through e-commerce, social media, or online shops. The products offered vary, including services, food, household needs, and fashion. Selling online is not limited by time and distance, and consumers can obtain information about products and services that can influence their decisions. At the same time, sellers also have the opportunity to advertise their products in a broader range by making endorsements. An endorsement is a form of advertising using well-known figures who are recognized, trusted, and respected by people. In this thesis, a model for optimizing the problem of online internet shopping with endorsement fees is formulated. This optimization model aims to maximize the profits gained by sellers in marketing their products online. In marketing products, there is uncertainty in the number of requests. To overcome this uncertainty, an approach is needed that can handle this uncertainty, namely Robust optimization. The Robust optimization model is solved using the polyhedral uncertainty set approach, resulting in a computationally tractable optimal solution. Keywords: internet shopping online; endorsement costs; robust optimization.
{"title":"Robust Optimization Model for Internet Shopping Online Problems with Endorsement Costs in the Fashion Industry","authors":"Olivia Anjanette, B. Subartini, D. Chaerani","doi":"10.24198/jmi.v19.n1.45096.67-76","DOIUrl":"https://doi.org/10.24198/jmi.v19.n1.45096.67-76","url":null,"abstract":"Online business is a business activity carried out via the internet or digitally. Buying, selling, and advertising are done online through e-commerce, social media, or online shops. The products offered vary, including services, food, household needs, and fashion. Selling online is not limited by time and distance, and consumers can obtain information about products and services that can influence their decisions. At the same time, sellers also have the opportunity to advertise their products in a broader range by making endorsements. An endorsement is a form of advertising using well-known figures who are recognized, trusted, and respected by people. In this thesis, a model for optimizing the problem of online internet shopping with endorsement fees is formulated. This optimization model aims to maximize the profits gained by sellers in marketing their products online. In marketing products, there is uncertainty in the number of requests. To overcome this uncertainty, an approach is needed that can handle this uncertainty, namely Robust optimization. The Robust optimization model is solved using the polyhedral uncertainty set approach, resulting in a computationally tractable optimal solution. Keywords: internet shopping online; endorsement costs; robust optimization.","PeriodicalId":53096,"journal":{"name":"Jurnal Matematika Integratif","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49106915","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 : 2023-06-02DOI: 10.24198/jmi.v19.n1.44487.13-28
D. Johar, Asep K. Supriatna, E. Carnia
The Weiner index is considered one of the basic descriptors of fixed interconnection networks because it provides the average distance between any two nodes of the network. Many methods have been used by researchers to calculate the value of the Wiener index. starting from the brute force method to the invention of an algorithm to calculate the Wiener index without calculating the distance matrix. The application of the Wiener index is found in the molecular structure of organic compounds, especially the benzenoid system. The value of the Wiener index of a molecule is closely related to its physical and chemical properties. This paper will show a comprehensive bibliometric survey of peer-reviewed articles referring to the Wiener index of benzenoid. The Wiener index values of several benzenoid compounds using cubic polynomial are also reported. The Wiener index of benzenoid supports much of the research and provides productive citations for citing the study. Keywords: Wiener index, benzenoid, distance matrix, chemical properties, cubic polynomial, topological.
{"title":"Wiener Index Calculation on the Benzenoid System: A Review Article","authors":"D. Johar, Asep K. Supriatna, E. Carnia","doi":"10.24198/jmi.v19.n1.44487.13-28","DOIUrl":"https://doi.org/10.24198/jmi.v19.n1.44487.13-28","url":null,"abstract":"The Weiner index is considered one of the basic descriptors of fixed interconnection networks because it provides the average distance between any two nodes of the network. Many methods have been used by researchers to calculate the value of the Wiener index. starting from the brute force method to the invention of an algorithm to calculate the Wiener index without calculating the distance matrix. The application of the Wiener index is found in the molecular structure of organic compounds, especially the benzenoid system. The value of the Wiener index of a molecule is closely related to its physical and chemical properties. This paper will show a comprehensive bibliometric survey of peer-reviewed articles referring to the Wiener index of benzenoid. The Wiener index values of several benzenoid compounds using cubic polynomial are also reported. The Wiener index of benzenoid supports much of the research and provides productive citations for citing the study. Keywords: Wiener index, benzenoid, distance matrix, chemical properties, cubic polynomial, topological.","PeriodicalId":53096,"journal":{"name":"Jurnal Matematika Integratif","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46023484","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 : 2023-06-02DOI: 10.24198/jmi.v19.n1.41624.89-108
Sri Nurhayati, Yeni Susanti
Let G be a connected, simple, and undirrected graph, where V (G) is the vertex set and E(G) is the edge set. Let k be a natural numbers. For graph G we define a total k−labeling ρ such that the vertices of graph G are labeled with {0, 2, 4, . . . , 2kv} and the edges of graph G are labeled with {1, 2, 3, . . . , ke}, where k = max{2kv, ke}. Total k−labeling ρ called an edge irregular reflexive k− labeling if every two distinct edge of graph G have distinct edge weights, where the edge weight is defined as the sum of the label of that edge and the label of the vertices that are incident to this edge. The minimum k such that G has an edge irregular reflexive k−labeling called the reflexive edge strength of G. In this paper we determine the reflexive edge strength of some comb graphs.
{"title":"An Edge Irregular Reflexive k−labeling of Comb Graphs with Additional 2 Pendants","authors":"Sri Nurhayati, Yeni Susanti","doi":"10.24198/jmi.v19.n1.41624.89-108","DOIUrl":"https://doi.org/10.24198/jmi.v19.n1.41624.89-108","url":null,"abstract":"Let G be a connected, simple, and undirrected graph, where V (G) is the vertex set and E(G) is the edge set. Let k be a natural numbers. For graph G we define a total k−labeling ρ such that the vertices of graph G are labeled with {0, 2, 4, . . . , 2kv} and the edges of graph G are labeled with {1, 2, 3, . . . , ke}, where k = max{2kv, ke}. Total k−labeling ρ called an edge irregular reflexive k− labeling if every two distinct edge of graph G have distinct edge weights, where the edge weight is defined as the sum of the label of that edge and the label of the vertices that are incident to this edge. The minimum k such that G has an edge irregular reflexive k−labeling called the reflexive edge strength of G. In this paper we determine the reflexive edge strength of some comb graphs.","PeriodicalId":53096,"journal":{"name":"Jurnal Matematika Integratif","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41351673","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 : 2023-06-02DOI: 10.24198/jmi.v19.n1.45399.29-39
Rike Marjulisa, Imran M
{"title":"Aturan Titik Tengah Double untuk Integral Riemann-Stieltjes","authors":"Rike Marjulisa, Imran M","doi":"10.24198/jmi.v19.n1.45399.29-39","DOIUrl":"https://doi.org/10.24198/jmi.v19.n1.45399.29-39","url":null,"abstract":"","PeriodicalId":53096,"journal":{"name":"Jurnal Matematika Integratif","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49144877","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 : 2023-06-02DOI: 10.24198/jmi.v19.n1.44661.77-87
Ayun Sri Rahmani, N. Anggriani, Asep K. Supriatna
{"title":"Kontrol Optimal Menggunakan A.aleyrodhis Penyebaran Penyakit Virus Kuning Pada Tanaman Terong","authors":"Ayun Sri Rahmani, N. Anggriani, Asep K. Supriatna","doi":"10.24198/jmi.v19.n1.44661.77-87","DOIUrl":"https://doi.org/10.24198/jmi.v19.n1.44661.77-87","url":null,"abstract":"","PeriodicalId":53096,"journal":{"name":"Jurnal Matematika Integratif","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49482850","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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