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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 9 Documents
 1 
Search results for , issue "Vol 2, No 2 (2020)" : 9 Documents clear
Some Notes on Relative Commutators Masoumeh Ganjali; Ahmad Erfanian
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol 2, No 2 (2020)
Publisher : Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (2445.562 KB) | DOI: 10.15408/inprime.v2i2.14482

Abstract

Let G be a group and α ϵ Aut(G).  An α-commutator of elements x, y ϵ G is defined as [x, y]α = x-1y-1xyα. In 2015, Barzegar et al. introduced an α-commutator of elements of G and defined a new generalization of nilpotent groups by using the definition of α-commutators which is called an α-nilpotent group. They also introduced an α-commutator subgroup of G, denoted by Dα(G) which is a subgroup generated by all α-commutators. In 2016, an α-perfect group, a group that is equal to its α-commutator subgroup, was introduced by authors of this paper and the properties of such group was investigated. They proved some results on α-perfect abelian groups and showed that a cyclic group G of even order is not α-perfect for any α ϵ Aut(G). In this paper, we may continue our investigation on α-perfect groups and in addition to studying the relative perfectness of some classes of finite p-groups, we provide an example of a non-abelian α-perfect 2-group.
World Gold Price Forecast using APARCH, EGARCH and TGARCH Model Yanne Irene; Madona Yunita Wijaya; Aisyah Muhayani
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol 2, No 2 (2020)
Publisher : Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (2612.259 KB) | DOI: 10.15408/inprime.v2i2.14779

Abstract

AbstractInvestment is a process of investing money for profit or material result. One investment commodity is gold. Gold is a precious metal in which the value tends to fluctuate over time. This indicates that there is a non-constant variance called heteroscedasticity. The appropriate time-series model to solve this heteroscedasticity problem is ARCH/GARCH. However, this model can't be applied for the financial cases that have an asymmetric effect (the downward and increase tendency in the level of volatility when returns rise and vice versa). Therefore, in this research, we forecast the world gold prices using APARCH, EGARCH, and TGARCH methods. We use the monthly world gold price data from June 1993 until May 2018. The result shows that the best-fitted model to forecasting the world gold prices is EGARCH (1.1). This model has the smallest error than the other models with a Mean Absolute Percentage Error (MAPE) value of 4.66%.Keywords: return; volatilities; heteroscedasticity; asymmetric effect; APARCH; EGARCH; TGARCH. AbstrakInvestasi adalah proses menginvestasikan uang untuk keuntungan atau hasil material. Salah satu komoditas investasi adalah emas. Emas adalah logam mulia yang nilainya cenderung berfluktuasi dari waktu ke waktu. Ini menunjukkan bahwa ada varian non-konstan yang disebut heteroskedastisitas. Metode deret waktu yang tepat untuk menyelesaikan masalah ini adalah ARCH/GARCH. Namun model ini tidak dapat digunakan untuk kasus keuangan yang memiliki efek asimetris (kecenderungan menurun dan meningkatnya volatilitas ketika nilai return naik dan sebaliknya). Oleh karena itu, dalam penelitian ini, kami memprediksi harga emas dunia menggunakan metode APARCH, EGARCH, dan TGARCH dengan data harga emas dunia bulanan pada bulan Juni 1993 - Mei 2018. Hasilnya menunjukkan bahwa, di antara ketiga metode itu, model terbaik untuk memprediksi harga emas dunia adalah EGARCH (1.1) dengan nilai Mean Absolute Percentage Error (MAPE) sebesar 4,66%.Kata kunci: return; volatilitas; heteroskedastisitas; efek asimetris; APARCH; EGARCH; TGARCH.
An Odd-Even Sum Labeling of Jellyfish and Mushroom Graphs Rusdan Nurhakim
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol 2, No 2 (2020)
Publisher : Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (2386.057 KB) | DOI: 10.15408/inprime.v2i2.14620

Abstract

AbstractA graph G(V,E) with p vertices and q edges called graph odd-even sum if there exists an injective function f from V to {+ 1, +2, +3, ..., +(2p-1)} such that induced a bijection f*(uv)=f(u)+f(v) as label of edge and u,v element of V forms the set {2,4,...,2q}, and f is called odd-even sum labeling. There are three criteria of graphs that can be labeled by this labeling, they are undirected, no loops, and finite for every edges and vertex. Jellyfish J(m,n) graph and Mushroom Mr(m) graph have the criteria. So in this paper will be showed that the Jellyfish and Mushroom graphs can be labeled by this labeling.Keywords: odd-even sum graph; odd-even sum labeling; Jellyfish and mushroom graphs. AbstrakGraf G(V,E) dengan banyak titik p dan sisi q dikatakan graf jumlah ganjil-genap jika terdapat suatu fungsi injetif f dari V ke {+ 1, +2, +3, ..., +(2p-1)} sehingga bijektif f*(uv)=f(u)+f(v) merupakan label sisi dengan u,v anggota dari V membentuk himpunan bilangan {2,4,...,2q}, dengan f merupakan pelabelan jumlah ganjil-genap. Kriteria graf yang dapat dilabeli oleh pelabelan jumlah ganjil-genap ada tiga, yaitu graf yang tidak berarah, tidak memiliki loop, dan terhingga, baik secara sisi maupun titik. Graf Jellyfish J(m,n) dan Mushroom Mr(m) memenuhi ketiga kriteria tersebut. Pada tulisan ini akan ditunjukkan bahwa kedua graf tersebut dapat dilabeli dengan pelabelan jumlah ganjil-genap.Keywords: graf jumlah ganjil-genap; pelabelan jumlah ganjil-genap; graf Jellyfish dan graf Mushroom.
Economic Ordering Policy for VAR Deterioration Model with Non-stationary Two-warehouse Inventory and Demand Abdullah Mohammed Alshami; Aniket Muley
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol 2, No 2 (2020)
Publisher : Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (2499.944 KB) | DOI: 10.15408/inprime.v2i2.15390

Abstract

AbstractThis paper adopts the two-warehouse inventory, determination on the first run-time and VAR (Vector Auto Regression) deterioration model. The optimal EOQ in the interval of the finite horizon is determined under critical considerations. The non-stationary two-warehouse inventory, i.e. the inventory and initial inventory are non-stationary at level, but stationary after lag difference similar to demand (demand and initial demand). The output of the proposed model represented the optimal order quantity and optimal first run-time, the optimal total cost as integration of first order with the significant trend and intercept. The optimal demand is decreased during more risk as a deterioration variable to reduce the quantity in the stock. The initial demand is stationary after a first lag and the demand is stationary.Keywords: initial inventory; optimal of first run-time; EOQ (Economic Ordering Quantity); total cost function (TC). AbstrakPenelitian ini mengadopsi inventori dengan dua gudang penyimpanan, penentuan pada waktu run (run-time) awal, dan model deteriorating VAR (Vector Auto Regression). Nilai optimal EOQ dalam interval horizon berhingga ditentukan dengan pertimbangan kritis. Inventori dengan dua gedung yang tidak stasioner, yaitu inventori dan inventori awal tidak stasioner pada level, tetapi stasioner setelah perbedaan lag seperti halnya pada permintaan (permintaan dan permintaan awal). Hasil dari model yang diajukan menunjukkan nilai orde yang optimal dan waktu run awal yang optimal, total biaya optimal sebagai integrasi dari orde pertama dengan tren dan intercept yang signifikan. Permintaan optimal mengalami penurunan ketika lebih banyak risiko sebagai variabel deteroriating untuk mengurangi jumlah dalam stok. Permintaan awal menunjukkan stasioner setelah perbedaan lag pertama dan permintaan juga stasioner.Kata kunci: inventori awal; optimal run-time awal; EOQ (Economic Ordering Quantity); fungsi biaya total.
Alternative Formula for the Series of Consecutive m-Squares under Alternating Signs Leomarich F Casinillo; Leo A Mamolo
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol 2, No 2 (2020)
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.v2i2.15845

Abstract

AbstractThis paper developed a simple but elegant formula for the series of consecutive square of natural numbers under alternating signs. Furthermore, this study investigated the said formula under odd and even number of terms and discuss some important results.Keywords: consecutive -squares; alternating signs; odd and even terms. AbstrakDalam paper ini kita membangun formula yang sederhana namun elegan untuk menghitung jumlah deret berganti-tanda dari kuadrat bilangan-bilangan asli berurutan.  Kita akan menyelidiki formula untuk kasus banyaknya suku ganjil maupun genap dan mendiskusikan beberapa hasil yang penting.Kata kunci: -kuadrat berurutan; berganti-tanda; bersuku ganjil dan bersuku genap.
Alternative Formula for the Series of Consecutive m-Squares under Alternating Signs Casinillo, Leomarich F; Mamolo, Leo A
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol 2, No 2 (2020)
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.v2i2.15845

Abstract

AbstractThis paper developed a simple but elegant formula for the series of consecutive square of natural numbers under alternating signs. Furthermore, this study investigated the said formula under odd and even number of terms and discuss some important results.Keywords: consecutive -squares; alternating signs; odd and even terms. AbstrakDalam paper ini kita membangun formula yang sederhana namun elegan untuk menghitung jumlah deret berganti-tanda dari kuadrat bilangan-bilangan asli berurutan.  Kita akan menyelidiki formula untuk kasus banyaknya suku ganjil maupun genap dan mendiskusikan beberapa hasil yang penting.Kata kunci: -kuadrat berurutan; berganti-tanda; bersuku ganjil dan bersuku genap.
The Constant Annual Premium and Benefit Reserve for Four Participants in Joint Life Insurance Nindita Nadilia; Nina Fitriyati; Irma Fauziah
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol 2, No 2 (2020)
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.v2i2.14780

Abstract

AbstractThis research discusses the derivation of formula to calculate the constant annual premiums and the benefit reserves for joint insurance consisting of four people. We combine pure endowment insurance, lifetime insurance, and n-year term insurance. Assumed that the benefits are set at the beginning of the insurance contract, the benefit reserves are calculated using the prospective method, and the premium payment stops if one of those four participants dies. If all participants live until the end of the contract, the benefits are paid at once but if one of the participants dies, the benefits paid at the end of the contract in the form of a lifetime annuity. The formula to calculate the benefit reserves is divided into four cases i.e. the benefit reserves if one of four participants dies, the benefit reserves if two of four participants die, the benefit reserve if three of four participants die, and the benefit reserves if all participants are still alive until the end of the contract. Besides, we also present simulation to calculate the constant annual premium for four participants consist of a father (50 years old), a mother (45 years old), a son (20 years old), and a daughter (15 years old). From the simulation, we conclude that as the length of the insurance contract increases, the premium tends to decrease. The benefit reserve calculation does not have a certain tendency. It generally increases during the insurance period (the premium is still paid) and then decreases thereafter. This is valid for all cases mentioned above.Keywords: n-year term insurance; prospective method; pure endowment insurance. AbstrakPenelitian ini membahas mengenai penurunan rumus untuk menghitung premi tahunan konstan dan cadangan benefit untuk asuransi gabungan yang terdiri dari empat orang. Jenis asuransi yang digunakan adalah kombinasi antara asuransi endowment murni, asuransi seumur hidup dan asuransi berjangka n-tahun. Diasumsikan bahwa benefit ditetapkan di awal kontrak asuransi dan pembayaran premi berhenti jika salah seorang dari keempat peserta meninggal dunia. Jika seluruh peserta hidup sampai dengan akhir kontrak maka benefit dibayarkan secara sekaligus, namun jika salah satu dari peserta telah meninggal dunia maka benefit yang dibayarkan pada akhir tahun kontrak dalam bentuk anuitas seumur hidup. Rumus yang diperoleh untuk menghitung cadangan benefit dibagi menjadi empat kasus yaitu cadangan benefit jika satu orang meninggal dan tiga orang lainnya hidup, cadangan benefit jika dua orang meninggal dan dua orang lainnya hidup, cadangan benefit jika tiga orang meninggal dan satu orang lainnya hidup, dan cadangan benefit jika semua peserta tetap hidup sampai akhir masa kontrak. Pada akhir penelitian, disajikan simulasi perhitungan premi tahunan konstan untuk empat peserta yang terdiri dari ayah (berusia 50 tahun), ibu (45 tahun), anak laki-laki (20 tahun), dan anak perempuan (15 tahun). Dari simulasi diperoleh bahwa semakin lama kontrak asuransi maka premi yang dibayakan cenderung semakin kecil. Perhitungan cadangan benefit tidak memiliki kecenderungan tertentu, namun pada umumnya meningkat selama masa asuransi berlangsung (pembayaran premi masih dilakukan) kemudian menurun setelahnya. Hal ini berlaku untuk seluruh kasus yang telah dibahas pada perhitungan rumus cadangan premi.Kata kunci: asuransi berjangka n-tahun; metode prospektif; asuransi endowment murni.
The Constant Annual Premium and Benefit Reserve for Four Participants in Joint Life Insurance Nadilia, Nindita; Fitriyati, Nina; Fauziah, Irma
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol 2, No 2 (2020)
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.v2i2.14780

Abstract

AbstractThis research discusses the derivation of formula to calculate the constant annual premiums and the benefit reserves for joint insurance consisting of four people. We combine pure endowment insurance, lifetime insurance, and n-year term insurance. Assumed that the benefits are set at the beginning of the insurance contract, the benefit reserves are calculated using the prospective method, and the premium payment stops if one of those four participants dies. If all participants live until the end of the contract, the benefits are paid at once but if one of the participants dies, the benefits paid at the end of the contract in the form of a lifetime annuity. The formula to calculate the benefit reserves is divided into four cases i.e. the benefit reserves if one of four participants dies, the benefit reserves if two of four participants die, the benefit reserve if three of four participants die, and the benefit reserves if all participants are still alive until the end of the contract. Besides, we also present simulation to calculate the constant annual premium for four participants consist of a father (50 years old), a mother (45 years old), a son (20 years old), and a daughter (15 years old). From the simulation, we conclude that as the length of the insurance contract increases, the premium tends to decrease. The benefit reserve calculation does not have a certain tendency. It generally increases during the insurance period (the premium is still paid) and then decreases thereafter. This is valid for all cases mentioned above.Keywords: n-year term insurance; prospective method; pure endowment insurance. AbstrakPenelitian ini membahas mengenai penurunan rumus untuk menghitung premi tahunan konstan dan cadangan benefit untuk asuransi gabungan yang terdiri dari empat orang. Jenis asuransi yang digunakan adalah kombinasi antara asuransi endowment murni, asuransi seumur hidup dan asuransi berjangka n-tahun. Diasumsikan bahwa benefit ditetapkan di awal kontrak asuransi dan pembayaran premi berhenti jika salah seorang dari keempat peserta meninggal dunia. Jika seluruh peserta hidup sampai dengan akhir kontrak maka benefit dibayarkan secara sekaligus, namun jika salah satu dari peserta telah meninggal dunia maka benefit yang dibayarkan pada akhir tahun kontrak dalam bentuk anuitas seumur hidup. Rumus yang diperoleh untuk menghitung cadangan benefit dibagi menjadi empat kasus yaitu cadangan benefit jika satu orang meninggal dan tiga orang lainnya hidup, cadangan benefit jika dua orang meninggal dan dua orang lainnya hidup, cadangan benefit jika tiga orang meninggal dan satu orang lainnya hidup, dan cadangan benefit jika semua peserta tetap hidup sampai akhir masa kontrak. Pada akhir penelitian, disajikan simulasi perhitungan premi tahunan konstan untuk empat peserta yang terdiri dari ayah (berusia 50 tahun), ibu (45 tahun), anak laki-laki (20 tahun), dan anak perempuan (15 tahun). Dari simulasi diperoleh bahwa semakin lama kontrak asuransi maka premi yang dibayakan cenderung semakin kecil. Perhitungan cadangan benefit tidak memiliki kecenderungan tertentu, namun pada umumnya meningkat selama masa asuransi berlangsung (pembayaran premi masih dilakukan) kemudian menurun setelahnya. Hal ini berlaku untuk seluruh kasus yang telah dibahas pada perhitungan rumus cadangan premi.Kata kunci: asuransi berjangka n-tahun; metode prospektif; asuransi endowment murni.
On Triangular Secure Domination Number Emily L Casinillo; Leomarich F Casinillo; Jorge S Valenzona; Divina L Valenzona
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol 2, No 2 (2020)
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.v2i2.15996

Abstract

Let T_m=(V(T_m), E(T_m)) be a triangular grid graph of m ϵ N level. The order of graph T_m is called a triangular number. A subset T of V(T_m) is a dominating set of T_m  if for all u_V(T_m)\T, there exists vϵT such that uv ϵ E(T_m), that is, N[T]=V(T_m).  A dominating set T of V(T_m) is a secure dominating set of T_m if for each u ϵ V(T_m)\T, there exists v ϵ T such that uv ϵ E(T_m) and the set (T\{u})ꓴ{v} is a dominating set of T_m. The minimum cardinality of a secure dominating set of T_m, denoted by γ_s(T_m)  is called a secure domination number of graph T_m. A secure dominating number  γ_s(T_m) of graph T_m is a triangular secure domination number if γ_s(T_m) is a triangular number. In this paper, a combinatorial formula for triangular secure domination number of graph T_m was constructed. Furthermore, the said number was evaluated in relation to perfect numbers.

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