Perkembangan ilmu pengetahuan yang terjadi saat ini banyak memunculkan permasalahan dalam berbagai bidang ilmu. Salah satu ilmu yang memiliki peran penting dalam perkembangan ilmu pengetahuan ialah matematika. Beberapa bidang lain menggunakan model matematika dalam memecahkan permasalahan. Salah satu bentuk model matematika yang banyak dipakai ialah persamaan diferensial. Persamaan diferensial adalah persamaan yang melibatkan turunan atau diferensial dari suatu fungsi yang tidak diketahui. Pada umumnya persamaan diferensial menggunakan orde bilangan asli, namun orde pada persamaan diferensial dapat dibentuk menjadi orde pecahan yang disebut persamaan diferensial fraksional. Suatu persamaan diferensial fraksional dapat diselesaikan dan diperoleh solusinya. Ada beberapa metode yang dapat digunakan untuk menyelesaikan persamaan diferensial fraksional, salah satunya yaitu Telescoping Decomposition Method. Penulis akan menyelesaikan persamaan diferensial fraksional non-linear menggunakan metode tersebut. Selanjutnya, barisan orde dari persamaan diferensial fraksional non-linear dapat diamati kekonvergenannya ke suatu bilangan yang mengakibatkan barisan fungsi solusi dari persamaan diferensial fraksional non-linear akan konvergen ke fungsi solusi dengan orde bilangan itu sendiri dan akan dibandingkan hasilnya dengan Adomian Decomposition Method.
{"title":"Solusi Persamaan Diferensial Fraksional Non-Linear Menggunakan Telescoping Decomposition Method","authors":"Anjang Risara Vilinea, Endang Rusyaman, Eddy Djauhari","doi":"10.24198/jmi.v15.n2.23376.139","DOIUrl":"https://doi.org/10.24198/jmi.v15.n2.23376.139","url":null,"abstract":"Perkembangan ilmu pengetahuan yang terjadi saat ini banyak memunculkan permasalahan dalam berbagai bidang ilmu. Salah satu ilmu yang memiliki peran penting dalam perkembangan ilmu pengetahuan ialah matematika. Beberapa bidang lain menggunakan model matematika dalam memecahkan permasalahan. Salah satu bentuk model matematika yang banyak dipakai ialah persamaan diferensial. Persamaan diferensial adalah persamaan yang melibatkan turunan atau diferensial dari suatu fungsi yang tidak diketahui. Pada umumnya persamaan diferensial menggunakan orde bilangan asli, namun orde pada persamaan diferensial dapat dibentuk menjadi orde pecahan yang disebut persamaan diferensial fraksional. Suatu persamaan diferensial fraksional dapat diselesaikan dan diperoleh solusinya. Ada beberapa metode yang dapat digunakan untuk menyelesaikan persamaan diferensial fraksional, salah satunya yaitu Telescoping Decomposition Method. Penulis akan menyelesaikan persamaan diferensial fraksional non-linear menggunakan metode tersebut. Selanjutnya, barisan orde dari persamaan diferensial fraksional non-linear dapat diamati kekonvergenannya ke suatu bilangan yang mengakibatkan barisan fungsi solusi dari persamaan diferensial fraksional non-linear akan konvergen ke fungsi solusi dengan orde bilangan itu sendiri dan akan dibandingkan hasilnya dengan Adomian Decomposition Method.","PeriodicalId":53096,"journal":{"name":"Jurnal Matematika Integratif","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49291725","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 : 2019-10-05DOI: 10.24198/jmi.v15.n2.23350.81
H. Suryawan
The sub-fractional Brownian motion is a Gaussian extension of the Brownian motion. It has the properties of self-similarity, continuity of the sample paths, and short-range dependence, among others. The increments of sub-fractional Brownian motion is neither independent nor stationary. In this paper we study the sub-fractional Brownian motion using a white noise analysis approach. We recall the represention of sub-fractional Brownian motion on the white noise probability space and show that Donsker's delta functional of a sub-fractional Brownian motion is a Hida distribution. As a main result, we prove the existence of the weighted local times of a $d$-dimensional sub-fractional Brownian motion as Hida distributions.
{"title":"Weighted Local Times of a Sub-fractional Brownian Motion as Hida Distributions","authors":"H. Suryawan","doi":"10.24198/jmi.v15.n2.23350.81","DOIUrl":"https://doi.org/10.24198/jmi.v15.n2.23350.81","url":null,"abstract":"The sub-fractional Brownian motion is a Gaussian extension of the Brownian motion. It has the properties of self-similarity, continuity of the sample paths, and short-range dependence, among others. The increments of sub-fractional Brownian motion is neither independent nor stationary. In this paper we study the sub-fractional Brownian motion using a white noise analysis approach. We recall the represention of sub-fractional Brownian motion on the white noise probability space and show that Donsker's delta functional of a sub-fractional Brownian motion is a Hida distribution. As a main result, we prove the existence of the weighted local times of a $d$-dimensional sub-fractional Brownian motion as Hida distributions.","PeriodicalId":53096,"journal":{"name":"Jurnal Matematika Integratif","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44977864","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 : 2019-10-05DOI: 10.24198/jmi.v15.n2.21693.69
Mohammad Deni Akbar, Yoshihiro Mizoguchi
Fuzzy formal concept analysis(FFCA) is a development of formal concept analysis(FCA) with the degree of relation between objects and attributes. Using FCA approach, we will investigate the condition logical implication for fuzzy functional dependency. We also use Armstrong's rule to define soundness and completeness of our implication and fuzzy functional dependency model. We show difference and equivalence condition between fuzzy implication and fuzzy functional dependency. This condition can be used to develop the algorithm for finding attribute dependency.
{"title":"Fuzzy Implication and Functional Dependency on Formal Context","authors":"Mohammad Deni Akbar, Yoshihiro Mizoguchi","doi":"10.24198/jmi.v15.n2.21693.69","DOIUrl":"https://doi.org/10.24198/jmi.v15.n2.21693.69","url":null,"abstract":"Fuzzy formal concept analysis(FFCA) is a development of formal concept analysis(FCA) with the degree of relation between objects and attributes. Using FCA approach, we will investigate the condition logical implication for fuzzy functional dependency. We also use Armstrong's rule to define soundness and completeness of our implication and fuzzy functional dependency model. We show difference and equivalence condition between fuzzy implication and fuzzy functional dependency. This condition can be used to develop the algorithm for finding attribute dependency.","PeriodicalId":53096,"journal":{"name":"Jurnal Matematika Integratif","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46087575","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}
Dengan bantuan rumus sudut antara dua subruang, telah dirumuskan sudut antara 2 matriks berukuran sama. Gagasan ini diperluas ke operator kompak dengan rank yang hingga di ruang Hilbert.
{"title":"Sepasang Sudut antara Dua Operator Kompak dengan Rang Hingga","authors":"Agah D. Garnadi, Teduh Wulandari","doi":"10.31227/osf.io/veq65","DOIUrl":"https://doi.org/10.31227/osf.io/veq65","url":null,"abstract":"Dengan bantuan rumus sudut antara dua subruang, telah dirumuskan sudut antara 2 matriks berukuran sama. Gagasan ini diperluas ke operator kompak dengan rank yang hingga di ruang Hilbert.","PeriodicalId":53096,"journal":{"name":"Jurnal Matematika Integratif","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41656855","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 : 2019-07-25DOI: 10.24198/JMI.V15.N1.20899.17-27
Syarifah Inayati, Nur Muhaimi
{"title":"Penggunaan Rantai Markov Orde Dua untuk Menganalisis Ketersediaan Pemasaran Produk Shampoo Dove di Swalayan Pamella 1 Yogyakarta","authors":"Syarifah Inayati, Nur Muhaimi","doi":"10.24198/JMI.V15.N1.20899.17-27","DOIUrl":"https://doi.org/10.24198/JMI.V15.N1.20899.17-27","url":null,"abstract":"","PeriodicalId":53096,"journal":{"name":"Jurnal Matematika Integratif","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48014627","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 : 2019-07-25DOI: 10.24198/JMI.V15.N1.21475.53-61
A. Garnadi
{"title":"Jarak dan Sudut Antara Dua Matriks Berdimensi Sama","authors":"A. Garnadi","doi":"10.24198/JMI.V15.N1.21475.53-61","DOIUrl":"https://doi.org/10.24198/JMI.V15.N1.21475.53-61","url":null,"abstract":"","PeriodicalId":53096,"journal":{"name":"Jurnal Matematika Integratif","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45327629","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 : 2019-07-25DOI: 10.24198/JMI.V15.N1.19637.1-8
Utti Marina Rifanti, Tesa Nur Padilah, Ismi Widyaningrum
{"title":"Sistem Dinamik Arus Listrik dengan Persamaan Diferensial Metode Koefisien Tak Tentu","authors":"Utti Marina Rifanti, Tesa Nur Padilah, Ismi Widyaningrum","doi":"10.24198/JMI.V15.N1.19637.1-8","DOIUrl":"https://doi.org/10.24198/JMI.V15.N1.19637.1-8","url":null,"abstract":"","PeriodicalId":53096,"journal":{"name":"Jurnal Matematika Integratif","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43864044","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 : 2019-07-25DOI: 10.24198/JMI.V15.N1.20960.39-44
Maxrizal Maxrizal, Syafrul Irawadi
{"title":"Modifikasi Protokol Tanda Tangan Digital ElGamal Menggunakan General Linear Group","authors":"Maxrizal Maxrizal, Syafrul Irawadi","doi":"10.24198/JMI.V15.N1.20960.39-44","DOIUrl":"https://doi.org/10.24198/JMI.V15.N1.20960.39-44","url":null,"abstract":"","PeriodicalId":53096,"journal":{"name":"Jurnal Matematika Integratif","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43713333","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 : 2019-07-25DOI: 10.24198/JMI.V15.N1.20931.29-37
F. Sukono, E. Lesmana, D. Susanti, H. Napitupulu, Y. Hidayat
Investors having an understanding of investment statistics are important. Especially quantitative tools related to investment risk measurement. Value-at-Risk Adjusted is one of the investment risk measurement tools, which assumes that returns are not normally distributed.This paper intends to measure investment risk based onValue-at-Risk Adjustedor called Modified Value-at-Risk under the Capital Asset Pricing Model. It is assumed that the return of the market index has a non-constant average and there is a long memory effect. The average of the return of the market index is estimated using ARFIMA models.It is also assumed that the stock risk premium correlates with market risk premiums, and stock risk premiums some time before. The correlation will be analyzed using the ARMAX-GARCH model approach. The Modified Value-at-Risk was then formulated based on the Capital asset Pricing Model with the ARMAX-GARCH model approach.To measure the performance of Modified Value-at-Risk that has been formulated is done with back testing. Back testing is carried out based on the Lopez II method. As a case study, analyzed some data on 10 stocks traded on the capital market in Indonesia.The results of the analysis show that the market index return risk premium significantly follows the ARFIMA model, and the 10 share risk premium significantly follows the ARMAX-GARCH model. Based on the results of back testing calculations indicate that the Value-at-Risk Adjustedor Modified Value-at-Risk is very suitable to be used to measure investment risk in the 10 stocks analyzed.
{"title":"Estimation of Value-at-Risk Adjusted under the Capital Asset Pricing Model Based on ARMAX-GARCH Approach","authors":"F. Sukono, E. Lesmana, D. Susanti, H. Napitupulu, Y. Hidayat","doi":"10.24198/JMI.V15.N1.20931.29-37","DOIUrl":"https://doi.org/10.24198/JMI.V15.N1.20931.29-37","url":null,"abstract":"Investors having an understanding of investment statistics are important. Especially quantitative tools related to investment risk measurement. Value-at-Risk Adjusted is one of the investment risk measurement tools, which assumes that returns are not normally distributed.This paper intends to measure investment risk based onValue-at-Risk Adjustedor called Modified Value-at-Risk under the Capital Asset Pricing Model. It is assumed that the return of the market index has a non-constant average and there is a long memory effect. The average of the return of the market index is estimated using ARFIMA models.It is also assumed that the stock risk premium correlates with market risk premiums, and stock risk premiums some time before. The correlation will be analyzed using the ARMAX-GARCH model approach. The Modified Value-at-Risk was then formulated based on the Capital asset Pricing Model with the ARMAX-GARCH model approach.To measure the performance of Modified Value-at-Risk that has been formulated is done with back testing. Back testing is carried out based on the Lopez II method. As a case study, analyzed some data on 10 stocks traded on the capital market in Indonesia.The results of the analysis show that the market index return risk premium significantly follows the ARFIMA model, and the 10 share risk premium significantly follows the ARMAX-GARCH model. Based on the results of back testing calculations indicate that the Value-at-Risk Adjustedor Modified Value-at-Risk is very suitable to be used to measure investment risk in the 10 stocks analyzed.","PeriodicalId":53096,"journal":{"name":"Jurnal Matematika Integratif","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45613468","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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