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Limits: Journal of Mathematics and Its Applications

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Published by Institut Teknologi Sepuluh Nopember Surabaya

ISSN : 1829605X EISSN : 25798936 DOI : -

Core Subject : Science, Education,

Computer Science & IT Mathematics

Limits: Journal of Mathematics and Its Applications merupakan jurnal yang diterbitkan oleh Pusat Publikasi Ilmiah LPPM Institut Teknologi Sepuluh Nopember, Surabaya, Indonesia. Limits menerima makalah hasil riset di semua bidang Matematika, terutama bidang Analisis, Aljabar, Pemodelan Matematika, Sistem dan Kontrol, Matematika Diskrit dan Kombinatorik, Statistik dan Stokastik, Matematika Terapan, Optimasi, dan Ilmu Komputasi. Jurnal ini juga menerima makalah tentang survey literatur yang menstimulasi riset di bidang-bidang tersebut di atas.

Arjuna Subject : Matematika - Matematika Terapan

Articles 270 Documents

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Model Regresi untuk Return Aset dengan Volatilitas Mengikuti Model GARCH(1,1) Berdistribusi Epsilon-Skew Normal dan Student-t Didit Budi Nugroho; Kristia Anggraeni; Hanna Arini Parhusip
Limits: Journal of Mathematics and Its Applications Vol. 17 No. 2 (2020): Limits: Journal of Mathematics and Its Applications Volume 17 Nomor 2 Edisi De
Publisher : Pusat Publikasi Ilmiah LPPM Institut Teknologi Sepuluh Nopember

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Studi ini mendiskusikan dua perluasan dari model GARCH(1,1), yaitu AR(1)-GARCH(1,1) dan MA(1)-GARCH(1,1), yang diperoleh dengan cara menambahkan Autoregression tingkat 1 atau Moving Average tingkat 1 pada persamaan return . Untuk kasus ini, error dari return diasumsikan berdistribusi Normal, Skew Normal (SN), Epsilon Skew Normal (ESN), dan Student- t . Analisis terhadap model didasarkan pada pencocokan model untuk return dari indeks saham FTSE100 periode harian dari Januari 2000 sampai Desember 2017 dan indeks saham TOPIX periode harian dari Januari 2000 sampai Desember 2014. Model yang dipelajari diestimasi menggunakan metode GRG ( Generalized Reduced Gradient ) Non Linear yang tersedia di Solver Excel dan juga metode Adaptive Random Walk Metropolis (ARWM) yang diimplementasikan pada program Scilab. Hasil estimasi dari kedua alat bantu tersebut menunjukkan nilai-nilai yang hampir sama, mengindikasikan bahwa Solver Excel mempunyai kemampuan yang handal dalam mengestimasi parameter model. Uji rasio log- likelihood dan AIC ( Akaike Information Criterion ) menunjukkan bahwa model dengan distribusi ESN lebih unggul dibandingkan dengan model-model berdistribusi tipe normal lainnya untuk setiap kasus model dan data pengamatan, bahkan ini bisa mengungguli distribusi Student- t pada suatu model dan data pengamatan. Lebih lanjut, model-model dengan penambahan proses regresi di persamaan return menyediakan pencocokan yang lebih baik daripada model dasar, dimana pencocokan terbaik untuk kedua data pengamatan diberikan oleh model AR(1)-GARCH(1,1) berdistribusi Student- t .

Analisis Dinamik pada Model Kanker Serviks dengan Vaksinasi dan Screening Karunia Theda Kristanti; Trisilowati; Agus Widodo
Limits: Journal of Mathematics and Its Applications Vol. 17 No. 2 (2020): Limits: Journal of Mathematics and Its Applications Volume 17 Nomor 2 Edisi De
Publisher : Pusat Publikasi Ilmiah LPPM Institut Teknologi Sepuluh Nopember

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Pada paper ini dibahas analisis dinamik model penyebaran kanker serviks dengan melibatkan tindakan vaksinasi dan screening. Penyebab utama terjadinya kanker serviks adalah karena seseorang terinfeksi Human Papillomavirus (HPV). Infeksi ini dapat menular karena adanya kontak langsung melalui hubungan seksual antara subpopulasi wanita rentan dengan pria terinfeksi HPV maupun kontak langsung antara pria rentan dengan wanita terinfeksi HPV. Pada model ini diasumsikan vaksin diberikan pada subpopulasi wanita rentan saja dengan salah satu jenis vaksin. Sementara itu, screening dilakukan oleh subpopulasi wanita terifeksi HPV sebagai upaya deteksi dini untuk mencegah terjadinya kanker serviks. Hasil analisis dinamik menunjukkan bahwa model penyebaran kanker serviks dengan vaksinasi dan screening memiliki dua titik kesetimbangan yaitu titik kesetimbangan bebas penyakit dan titik kesetimbangan endemi. Eksistensi dan kestabilan lokal titik kesetimbangan bergantung pada nilai angka reproduksi dasar R 0 . Berdasarkan hasil analisis, titik kesetimbangan bebas penyakit eksis tanpa syarat, sedangkan titik kesetimbangan endemi eksis jika R 0 >1. Titik kesetimbangan bebas penyakit bersifat stabil asimtotik lokal jika nilai R 0 <1 dan titik kesetimbangan endemi bersifat stabil asimtotik lokal jika memenuhi kriteria Routh-Hurwitz. Simulasi numerik yang dilakukan mendukung hasil analisis dinamik yang diperoleh.

Simulasi Perhitungan Premi Asuransi Kesehatan dan Jiwa pada Penderita Covid-19 yang Dipengaruhi Model Penyebaran Penyakit Menular SIDRS Patrick Louis Lucin; Farah Kristiani; Benny Yong
Limits: Journal of Mathematics and Its Applications Vol. 20 No. 1 (2023): Limits: Journal of Mathematics and Its Applications Volume 20 Nomor 1 Edisi Ma
Publisher : Pusat Publikasi Ilmiah LPPM Institut Teknologi Sepuluh Nopember

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Determination of health and death insurance benefits according to the needs of policyholders is very important to determine from the beginning of making an insurance policy, especially for insurance that takes over the risk of being infected with the COVID-19 virus. Several factors that must be taken into account in determining the amount of benefits and premiums due to COVID-19 are the human population factor that is susceptible, infected and death in the SIDRS infectious disease spread model. In this study, the influence of these three factors on actuarial calculations is examined in more depth to produce an appropriate premium determination formula by taking into account two payment schemes in lump sum and annuity. From the simulation results by applying data on COVID-19 cases in Indonesia to determine the parameters of the SIDRS model, it is concluded that the premium with an annuity benefit payment scheme is smaller than the premium with a lump sum benefit scheme. Furthermore, it is also concluded that if the population of policyholders increases, the premium price will also be lower.

Model Kredibilitas Bühlmann-Straub untuk Frekuensi Klaim Berdistribusi Binomial Negatif–Lindley Ikhsan Maulidi; Rini Oktavia; Uswah; Alim Misbullah; Vina Apriliani
Limits: Journal of Mathematics and Its Applications Vol. 20 No. 1 (2023): Limits: Journal of Mathematics and Its Applications Volume 20 Nomor 1 Edisi Ma
Publisher : Pusat Publikasi Ilmiah LPPM Institut Teknologi Sepuluh Nopember

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The credibility theory is one of the tools that can be used to determine risk-based premiums. One approach that can be used is the best accuracy approach such as Bühlmann-Straub. We study the parametric Bühlmann-Straub credibility model in which the claim frequency data is assumed to follow the Negative-Lindley (NB-L) Binomial distribution. Determination of the Bühlmann-Straub parameter is determined by using the basic rules in probability theory. From the study that has been carried out, an explicit equation has been obtained to determine the credibility premium of Bühlmann-Straub. A simulation of the application of the model to the data was also provided by assuming the data follows the NB-L distribution. The NB-L distribution parameters were estimated using the momen method and maximum likelihood estimation. From the simulation, it is found that the data used had a high credibility factor value which implies the data can be considered primely for estimating future premiums.

Bilangan Kromatik Lokasi Pada Graf Amalgamasi Kipas Berekor Des Welyyanti; Nada Andriani; Lyra Yulianti
Limits: Journal of Mathematics and Its Applications Vol. 20 No. 1 (2023): Limits: Journal of Mathematics and Its Applications Volume 20 Nomor 1 Edisi Ma
Publisher : Pusat Publikasi Ilmiah LPPM Institut Teknologi Sepuluh Nopember

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Misalkan G adalah graf terhubung dengan himpunan simpul V dan himpunan sisi E, serta c adalah suatu k-pewarnaan dari G. Misalkan P adalah partisi terurut dari V(G) ke dalam kelas warna yang dihasilkan, yaitu P = {S1, S2, ..., Sk}. Berdasarkan pewarnaan simpul, maka representasi simpul v terhadap partisi P disebut kode warna dari v, dan dinotasikan dengan c_P(v). Kode warna c_P(v) dari suatu simpul v yang termasuk dalam V(G) didefinisikan sebagai pasangan terurut sebanyak k buah.

Characterizations of 2-Primal Ternary Semiring using Special Subsets of Ternary Semiring Tuhfatul Janan; Irawati
Limits: Journal of Mathematics and Its Applications Vol. 20 No. 1 (2023): Limits: Journal of Mathematics and Its Applications Volume 20 Nomor 1 Edisi Ma
Publisher : Pusat Publikasi Ilmiah LPPM Institut Teknologi Sepuluh Nopember

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This research aims to determine the characterizations of 2-primal ternary semiring using special subsets of ternary semiring. We use literature review method to achieve these aims. We define O^' (P) and O_P^', the special subsets of ternary semiring then we determine some properties of them. We also determine the condition for O(P) and O_P in order to the special subsets are ideals of S. The last, the special subsets of ternary semiring will be used to determine the characterizations of 2-primal ternary semiring. As the results, some the characterizations were S must be a commutative super nilpotent ternary semiring and O(P)=(O(P) ) or each prime ideal P of S. Besides that, O(P)=O_P=N(P) and O_P^' must has the IFP for each prime ideal P of S.

Pemodelan Waktu Hilangnya Penglihatan Penderita Retinopati Diabetik dengan Beberapa Model Survival Jonathan Ryan Wilianto; Ruhiyat; Hadi Sumarno
Limits: Journal of Mathematics and Its Applications Vol. 21 No. 2 (2024): Limits: Journal of Mathematics and Its Applications Volume 21 Nomor 2 Edisi Ju
Publisher : Pusat Publikasi Ilmiah LPPM Institut Teknologi Sepuluh Nopember

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Diabetic Retinopathy is a condition where blood vessels in the eye swell and leak due to too high blood sugar level. Patients can lose their eyesight because the leaked blood prevents light from reaching the retina. The Cox proportional hazard (CPH) model is a semiparametric survival model that can model the effect of covariates to the survival time. The consequence of the CPH model form is the assumption of proportional hazard, that is, the hazard function ratio of two given observations will be always the same over time. The frailty model can model the unobserved random effect that influences the survival time. Frailty is an unobserved risk factor that influences the survival of the observation. The Cox with frailty model is a combination of the CPH model and the frailty model. Significant covariates for the survival time of eyesight are the type of laser used, the risk group, and the eyeball operated on. By using the Gamma frailty, we obtain strong evidence that the frailty does affect the eyesight survival time. The Cox with frailty model can explain the survival time better than the CPH model. This can be seen from the fact that it has higher Akaike information criteria score than the CPH model.

Eksistensi Invers Moore Penrose Diperumum Elemen Normal Diperumum pada Ring dengan Involusi Titi Udjiani SRRM; Nikken Prima Puspita; Suryoto
Limits: Journal of Mathematics and Its Applications Vol. 20 No. 1 (2023): Limits: Journal of Mathematics and Its Applications Volume 20 Nomor 1 Edisi Ma
Publisher : Pusat Publikasi Ilmiah LPPM Institut Teknologi Sepuluh Nopember

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The Moore Penrose inverse of normal element in ring with involution have been discussed by several researchers. By generalizing concept of Moore Penrose inverse to the generalized Moore Penrose inverse, the element properties of the generalized Moore Penrose inverse of normal elements have also been obtained. In addition to generalizing the concept of Moore Penrose inverse, the definition of the normal element has also been generalized by generalizing the power of 1 to n e N. It is found that intersection between set of generalized normal element and set of generalized Moore Penrose inverse element is not empty. This indicates that both of them have common properties, so this paper aims is to build the necessary and sufficient conditions for a generalized normal element to have a generalized Moore Penrose inverse using these properties. The method used is to look for the similarity of properties possessed by a generalized normal element and element that has generalized Moore Penrose inverse. The next step is to use the involution properties to obtain the final result. The approach taken is not only through the generalized Moore Penrose inverse, but also group inverse.

Analisis dan Kontrol Optimal pada Model Dinamik Penyebaran Virus Zika Suhud Wahyudi; Nurani Dwi Pangestu; Kamiran
Limits: Journal of Mathematics and Its Applications Vol. 20 No. 1 (2023): Limits: Journal of Mathematics and Its Applications Volume 20 Nomor 1 Edisi Ma
Publisher : Pusat Publikasi Ilmiah LPPM Institut Teknologi Sepuluh Nopember

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Zika is a virus from flaviviridae family and flavivirus genus that spread by Aedes Aegypti mosquito and that can cause serious problem disease such as Guillain Barre Syndrome (GBS) and mikrosefalus. In this paper used spreading dynamic zika virus model that consists of two population and divided to sub population Susceptible humans, sub-population Asymtomatic Infected humans, sub-population Infected humans, sub-population Recovered humans, sub-population Susceptible mosquitoes, and sub-population Infected mosquitoes. The model that anlysis by determine the basic reproduction number, the point of disease free and endemic equilibrium, and the stability of each point of equilibrium. Then, do the optimal control using Pontryagin principle with numerical solution given by Range-Kutta method. The simulation results show the decreasing sub-population of infected humans, asymptomatic infected human, and population of mosquitoes after given controls such using condom, treatment, and using indoor residual spray.

Perbandingan Desain Kontrol Fuzzy Logic Controller (FLC) dan Pole Placement untuk Sistem Dua Tangki yang Saling Berinteraksi Sulis Rizkiatul Fitri; Mardlijah
Limits: Journal of Mathematics and Its Applications Vol. 21 No. 2 (2024): Limits: Journal of Mathematics and Its Applications Volume 21 Nomor 2 Edisi Ju
Publisher : Pusat Publikasi Ilmiah LPPM Institut Teknologi Sepuluh Nopember

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The interacting two-tank system provides important benefits in maintaining water quality, preventing pollution, and optimizing the distribution of clean water in various industrial applications. Therefore, it is important to control the water level for the interacting two-tank system in order to generate drinking water of high quality that is suitable for consumption for the community and other living beings. In this article, we analysis the stability and controllability the model of the interacting two-tank system. The result of the analysis prove that the system is stable and controllable. Furthermore, to control the water level, we using two methods that is Fuzzy Logic Controller (FLC) and Pole Placement. We compared two control methods and examined which one provided faster stability and more robust from disturbances. Based on the simulation output, it can be concluded that Fuzzy Logic Controller (FLC) performs better than Pole Placement. Fuzzy Logic Controller (FLC) enables the system to achieve faster stability without overshoot and is more robust against disturbances. However, the simulation waiting time for Pole Placement is faster than FLC

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Home Page

OAI Link

Editorial Team

Contact

Reviewer

Google Scholar

Contact Name Chairul Imron

Contact Email cha_imron15@its.ac.id

Phone +6285648721814

Journal Mail Official limits.matematika@its.ac.id

Editorial Address Departemen Matematika Fakultas Sains dan Analitika Data Institut Teknologi Sepuluh Nopember Sukolilo, Surabaya 60111, Indonesia Phone: +62-31-5943354 Email: limits.matematika@its.ac.id

Location Kota surabaya, Jawa timur INDONESIA

Abstract

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Contact Name
Chairul Imron

Contact Email
cha_imron15@its.ac.id

Phone
+6285648721814

Journal Mail Official
limits.matematika@its.ac.id

Editorial Address
Departemen Matematika Fakultas Sains dan Analitika Data Institut Teknologi Sepuluh Nopember Sukolilo, Surabaya 60111, Indonesia Phone: +62-31-5943354 Email: limits.matematika@its.ac.id

Location
Kota surabaya,

Jawa timur

INDONESIA