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InPrime: Indonesian Journal Of Pure And Applied Mathematics
Published by Universitas Islam Negeri Syarif Hidayatullah Jakarta
ISSN : 26865335     EISSN : 27162478     DOI : 10.15408/inprime
Core Subject : Science, Education,
Computer Science & IT Mathematics
InPrime: Indonesian Journal of Pure and Applied Mathematics is a peer-reviewed journal and published on-line two times a year in the areas of mathematics, computer science/informatics, and statistics. The journal stresses mathematics articles devoted to unsolved problems and open questions arising in chemistry, physics, biology, engineering, behavioral science, and all applied sciences. All articles will be reviewed by experts before accepted for publication. Each author is solely responsible for the content of published articles. This scope of the Journal covers, but not limited to the following fields: Applied probability and statistics, Stochastic process, Actuarial, Differential equations with applications, Numerical analysis and computation, Financial mathematics, Mathematical physics, Graph theory, Coding theory, Information theory, Operation research, Machine learning and artificial intelligence.
Arjuna Subject : Matematika - Matematika Terapan
Articles 5 Documents
 1 
Search results for , issue "Vol 5, No 2 (2023)" : 5 Documents clear
Global Stability Analysis of Susceptible, Infected, Recovered (S, I, R) Model Measles Vaccination Based on Age Juhari, Juhari; Karinina, Olivia; Aziz, Abdul; Alisah, Evawati
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol 5, No 2 (2023)
Publisher : Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15408/inprime.v5i2.32318

Abstract

AbstractThis study discusses the behavioral analysis model of the Susceptible-Infected-Recovered (SIR) epidemic of the spread of measles based on age structure. The total population of measles is grouped into four age groups, namely the first age group (0-4 years), the second age group (5-9 years), the third age group (10-14 years) and the fourth age group (> 15 years). The steps in modeling behavior can be done by determining the equilibrium point, and the basic reproduction number and performing a global stability analysis by building the Lyapunov function. This research contributes to providing information both to the government and the community.Keywords: Epidemic Model; SIR; Lyapunov function; Measles. AbstrakPenelitian ini membahas model analisis perilaku epidemi Susceptible-Infected-Recovered (SIR) penyebaran campak berdasarkan struktur umur. Jumlah penduduk yang terkena campak dikelompokkan menjadi empat kelompok umur, yaitu kelompok umur pertama (0-4 tahun), kelompok umur kedua (5-9 tahun), kelompok umur ketiga (10-14 tahun) dan kelompok umur keempat. (> 15 tahun). Langkah-langkah dalam pemodelan perilaku dapat dilakukan dengan menentukan titik ekuilibrium, bilangan reproduksi dasar dan melakukan analisis stabilitas global dengan membangun fungsi Lyapunov. Penelitian ini memberikan kontribusi untuk memberikan informasi baik kepada pemerintah maupun masyarakat.Kata Kunci: Model Epidemi; PAK; fungsi Lyapunov; Campak. 2020MSC: 00A71.
Comparison of the Actuarial Model for A Normal Lumpsum Pension Plan Using Defined-Benefit and Hybrid Models of Company Employees Maharani, Ardella; Purnaba, I Gusti Putu; Ruhiyat, Ruhiyat
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol 5, No 2 (2023)
Publisher : Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15408/inprime.v5i2.32741

Abstract

AbstractIn this research, we delve into the realm of pension plan programs, essential for securing a robust livelihood post-retirement through the provision of pension benefits to retired employees. Addressing the intricate balance between financial sustainability and risk mitigation, companies are mandated to allocate funds for pension benefits. The hybrid pension plan, a novel amalgamation of defined-benefit (DB) and defined-contribution (DC) features, emerges as a strategic solution to minimize the inherent risks of both models. This study undertakes the task of calculating the costs associated with pension benefits and the replacement ratio (RR) for both the traditional DB plan and the innovative hybrid pension plan. Drawing on data from 90 employees at Company X, we assume an effective interest rate of 4% for the DB plan and explore various scenarios for the hybrid plan, ranging from 3% to 5%. The findings present a compelling narrative: the costs required to fund the hybrid plan are found to be notably lower than those for the DB plan, ushering in a more economically sustainable approach. Concurrently, the RR derived from the hybrid plan surpasses that of the DB plan, showcasing its potential to provide a more substantial post-retirement income. Additionally, as the effective interest rate escalates, costs rise, and RR declines, emphasizing the sensitivity of these parameters to the interest rate. Considering these results, a conclusion emerges: the hybrid pension plan stands out as the optimal choice for employees at Company X, presenting a novel and advantageous approach to pension program design and implementation.Keywords: Cost of pension benefits; Defined-benefit; Hybrid; Pension plan; Replacement ratio. AbstrakDalam penelitian ini, kami mendalami program pensiun, yang penting untuk menjamin penghidupan yang kuat setelah pensiun melalui pemberian manfaat pensiun kepada karyawan yang pensiun. Untuk mengatasi keseimbangan rumit antara keberlanjutan finansial dan mitigasi risiko, perusahaan diwajibkan mengalokasikan dana untuk manfaat pensiun. Program pensiun hybrid, yang merupakan penggabungan fitur manfaat pasti (DB) dan iuran pasti (DC), muncul sebagai solusi strategis untuk meminimalkan risiko yang melekat pada kedua model tersebut. Studi ini menghitung biaya yang terkait dengan manfaat pensiun dan replacement ratio (RR) untuk program DB dan program pensiun hybrid. Berdasarkan data dari 90 karyawan di Perusahaan X, kami mengasumsikan tingkat bunga efektif sebesar 4% untuk program DB dan menggunakan rentang 3% hingga 5% untuk program hybrid. Hasil penelitian menemukan bahwa biaya yang diperlukan untuk mendanai program hybrid ternyata jauh lebih rendah dibandingkan dengan program DB, sehingga menghasilkan pendekatan yang lebih berkelanjutan secara ekonomi. Pada saat yang sama, RR yang diperoleh dari program hybrid melampaui program DB, sehingga menunjukkan potensinya dalam memberikan pendapatan pasca-pensiun yang lebih besar. Selain itu, ketika tingkat bunga efektif meningkat, biaya meningkat, dan RR menurun. Hal ini menekankan sensitivitas parameter-parameter ini terhadap tingkat bunga efektif. Kesimpulannya program pensiun hybrid merupakan pilihan optimal bagi karyawan di Perusahaan X, karena menghadirkan pendekatan baru dan menguntungkan dalam perancangan dan implementasi program pensiun.Kata Kunci: Biaya manfaat pensiun; Dana pensiun; Defined-benefit; Hybrid; Replacement ratio. 2020MSC: 62P05. 
Comparison Between Algebraic Cryptanalysis on DES and NTRU Paradise, Fadila; Sugeng, Kiki Ariyanti
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol 5, No 2 (2023)
Publisher : Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15408/inprime.v5i2.32011

Abstract

AbstractAlgebraic cryptanalysis is a cryptanalysis method that aims to exploit the algebraic structure of an encryption algorithm to obtain the secret key. Algebraic cryptanalysis becomes interesting because it uses a small amount of known plaintext, which in real life very few known plaintexts are available. Algebraic cryptanalysis has previously been performed on several block cipher algorithms and public key lattice-based algorithms. In this study, DES and NTRU were chosen as the objects of algebraic cryptanalysis. This research aims to compare algebraic cryptanalysis on DES and NTRU in terms of their applicability, and to what extent algebraic cryptanalysis can be successful in obtaining keys.Keywords: Algebraic Cryptanalysis; DES; NTRU; polynomial equation. AbstrakAlgebraic cryptanalysis adalah metode kriptanalisis yang bertujuan untuk memanfaatkan struktur aljabar pada algoritma enkripsi untuk mendapatkan kunci. Algebraic cryptanalysis menarik karena hanya membutuhkan sedikit plaintext, di mana pada kehidupan nyata hanya sedikit plaintext yang bisa didapatkan. Algebraic cryptanalysis sebelumnya dilakukan pada algorima block cipher dan algoritma kunci publik berbasis latis. Pada penelitian ini, DES dan NTRU dipilih sebagai objek algebraic cryptanalysis. Penelitian ini bertujuan untuk membandingkan algebraic cryptanalysis pada DES dan NTRU, serta sejauh mana algebraic cryptanalysis bisa mendapatkan nilai kunci.Kata Kunci: Kriptanalisis aljabar; DES; NTRU; persamaan polinomial. 2020MSC: 94A60.
An Optimal Control Analysis of Dengue Fever Ilmayasinta, Nur; Febriyanti, Rahma; Prafianti, Rayinda Aseti; Zakiyah, Nabila Syarifah
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol 5, No 2 (2023)
Publisher : Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15408/inprime.v5i2.30392

Abstract

AbstractDengue fever is one of the most infectious diseases in the world, according to data issued by the World Health Organization in 2014. It is responsible for a huge number of deaths each year around the world, particularly in tropical nations. The dengue virus (DENV) causes dengue fever, which is spread by the female Aedes aegypti mosquito. We provide a mathematical model of dengue fever transmission through hospitalization with optimal management in this paper. Before being simulated in MATLAB, this optimum control problem is numerically resolved. Vaccination, pesticide use, and prevention are all examples of optimal control in this study. The simulation results demonstrate that dengue infection can be considerably reduced by vaccination, pesticide use, and prevention.Keywords: Dengue fever; Mathematical modelling; Optimal control. AbstrakDemam berdarah adalah salah satu penyakit paling menular di dunia, menurut data yang dikeluarkan oleh Organisasi Kesehatan Dunia pada tahun 2014. Penyakit ini menyebabkan banyak kematian setiap tahun di seluruh dunia, terutama di negara-negara tropis. Virus dengue (DENV) menyebabkan demam berdarah, yang disebarkan oleh nyamuk Aedes aegypti betina. Kami menyediakan model matematis penularan demam berdarah melalui rawat inap dengan penatalaksanaan optimal dalam makalah ini. Masalah kontrol optimal ini diselesaikan secara numerik sebelum disimulasikan di MATLAB. Vaksinasi, penggunaan pestisida, dan pencegahan merupakan contoh pengendalian yang optimal dalam penelitian ini. Hasil simulasi menunjukkan bahwa infeksi dengue dapat dikurangi dengan vaksinasi, penggunaan pestisida, dan pencegahan.Kata Kunci: Demam berdarah; Pemodelan matematika; Kontrol optimal. 2020MSC: 00A71, 92B05.
Social Network Analysis of Twitter Users on BTS Topic Using Degree Centrality, Betweenness Centrality, and Closeness Centrality Adniati, Siti; Irwansyah, Irwansyah; Awanis, Zata Yumni
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol 5, No 2 (2023)
Publisher : Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15408/inprime.v5i2.28722

Abstract

AbstractNowadays, a trademark is starting to be built through content on social media by involving influencers whose roles are increasingly needed in digital marketing. Hence, finding them on social media networks is an important thing. In brand recognition, BTS has a great influence where a brand they collaborate with gets an enthusiastic response from fans who participate in disseminating information and recommending it to others via Twitter. Therefore, this study aims to identify the potential influencer on the delivery of information on the topic of BTS on Twitter using social network analysis. Social network analysis applies the concept of graph theory where the potential influencer which is denoted by the central vertex is measured by measures of centrality, namely degree centrality, betweenness centrality, and closeness centrality. The result of the network consists of 649 vertices and 730 directed edges that form a disconnected and directed network with 67 weakly connected components. This study indicates that the influencers in the network can be fan accounts or fanbase accounts.Keywords: BTS; centrality; central vertex; influencer; social network analysis; Twitter. AbstrakDewasa ini, suatu merek dagang mulai dibangun  melalui konten di media sosial dengan melibatkan pemengaruh yang perannya semakin dibutuhkan pada pemasaran digital sehingga menemukan mereka di jaringan media sosial adalah suatu hal yang penting. Dalam pengenalan merek, BTS memberikan pengaruh yang besar dimana suatu merek yang berkolaborasi dengan mereka mendapat respon antusias dari penggemar yang ikut menyebarluaskan informasi dan merekomendasikannya kepada orang lain melalui Twitter. Oleh karena itu, penelitian ini bertujuan untuk mengidentifikasi pemengaruh potensial dalam penyampaian informasi pada topik BTS di Twitter menggunakan analisis jaringan sosial. Analisis jaringan sosial menerapkan konsep teori graf dimana simpul sentral diukur dengan ukuran sentralitas, yaitu sentralitas derajat, sentralitas keantaraan, dan sentralitas kedekatan. Diperoleh jaringan dengan 649 simpul dan 730 sisi berarah yang membentuk jaringan berarah tak terhubung yang terdiri atas 67 komponen terhubung lemah. Adapun hasil dari penelitian ini menunjukkan bahwa simpul sentral atau pemengaruh dalam jaringan dapat berupa akun personal dari pengemar (fan account) atau akun basis penggemar (fanbase).Kata Kunci: analisis jaringan  sosial, BTS,  pemengaruh , sentralitas, simpul sentral, Twitter. 2020MSC: 05C90, 91D30.

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