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INDONESIA
Journal of the Indonesian Mathematical Society
Published by Indonesian Mathematical Society
ISSN : 20868952     EISSN : 24600245     DOI : -
Core Subject : Education,
Mathematics
Journal of the Indonesian Mathematical Society disseminates new research results in all areas of mathematics and their applications. Besides research articles, the journal also receives survey papers that stimulate research in mathematics and their applications.
Arjuna Subject : -
Articles 625 Documents
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ON QUANTUM CODES CONSTRUCTION FROM CONSTACYCLIC CODES OVER THE RING I_q[u,v] / Ali, Shakir; Sharma, Pushpendra
Journal of the Indonesian Mathematical Society Vol. 30 No. 2 (2024): JULY
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.30.2.1587.139-159

Abstract

This paper focuses on studying the properties of constacyclic codes, quantum error-correcting codes. The code is studied over a specific mathematical structure called the ring $\mathfrak{S}$, which is defined as $\mathfrak{S}=\mathfrak{I}_q[\mathfrak{u},\mathfrak{v}]/\langle \mathfrak{u}^2-\alpha^2,~ \mathfrak{v}^2-\alpha^2,~\mathfrak{u}\mathfrak{v}-\mathfrak{v}\mathfrak{u} \rangle$, where $\mathfrak{I}_q$ is a finite field of $q$ elements, $\alpha$ be the nonzero elements of the field $\mathfrak{I}_q$ and $q$ is a power of an odd prime $p$ such that $q=p^m, ~\textup{for}~ m \ge 1$. The paper also introduces a Gray map and use it to decompose constacyclic codes over the ring $\mathfrak{S}$ into a direct sum of constacyclic codes over $\mathfrak{I}_q$. We construct new and better quantum error-correcting codes over the ring $\mathfrak{S}$ (cf.; Table 1 and Table 2). Moreover, we also obtain best known linear codes as well as best dimension linear codes (cf.; Table 4).
CERTAIN TYPES OF DERIVATIONS IN RINGS: A SURVEY Ali, Shakir; Rafiquee, Naira Noor; Varshney, Vaishali
Journal of the Indonesian Mathematical Society Vol. 30 No. 2 (2024): JULY
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.30.2.1623.256-306

Abstract

In this overview article, we provide a historical account on derivations, Jordan derivations, (α, β)-derivations, left derivations, pre-derivations, homoderivations, nilpotent derivations, and other variants, drawing from the contributions of multiple researchers. Additionally, we delve into recent findings and suggest potential avenues for future investigation in this area. Furthermore, we offer pertinent examples to illustrate that the assumptions underlying various results are indeed necessary and not redundant.
SUKUK VERSUS BONDS: MATHEMATICALLY LITERATURE STUDY Murniati, Wahyuning; Sumarti, Novriana; Puspita, Dila
Journal of the Indonesian Mathematical Society Vol. 30 No. 2 (2024): JULY
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.30.2.1774.160-178

Abstract

Based on IIFM Sukuk Report 2022, global sukuk issuance has shown a single digit increase of around 7.72\%, the highest value of yearly sukuk issuances to date. This fact shows that sukuk is increasingly popular and will continue to grow in the future, encourages more research related to this subject. Sukuk, as one of the innovative investment instruments in Islamic finance, is often equated to conventional bonds. However, the existing literature primarily concentrates on its structures and mechanisms, largely overlooking the pricing aspects of both sukuk and bonds. Therefore, this study will discuss pricing in mathematical terms for the two investment instruments discussed. More particularly, this paper covers the Indonesian Sukuk system’s operation. Numerical simulations have been done, using the characteristics of several varieties of Indonesian Sukuk and a variety of defined inputs. These mathematics simulation used to comprehend the technical aspects of sukuk and understand the principles of Islamic finance. The results of this study indicate that while some studies claim that sukuk's structure resembles bonds and that the pricing is determined accordingly, the comparison of both instruments prices provided no results consistent with the claims. Further study is required to examine the sukuk pricing mechanism, particularly in determining the value of profit sharing on sukuk.
CONSTRUCTION OF THE BINO-TRINOMIAL METHOD USING THE FUZZY SET APPROACH FOR OPTION PRICING Agustina, Fitriani; Sumarti, Novriana; Sidarto, Kuntjoro Adji
Journal of the Indonesian Mathematical Society Vol. 30 No. 2 (2024): JULY
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.30.2.1775.179-204

Abstract

An option is a financial instrument that investors often use for speculation or hedging purposes. Calculating the profit in the investment using options also considers its price, so the investor needs to know the proper value of the option's price or at least the range of these values. This paper aims to improve the Bino-Trinomial tree model for determining the price of a European call option with a volatility parameter in the form of a triangular Fuzzy number. The Bino-Trinomial tree model is a combination of the Binomial and Trinomial trees that aims to control the values of its branches. Due to the involvement of the Fuzzy number, the obtained value of the option price is in a range or interval, so the investor could use it appropriately in arranging investment strategies. In the proposed model, the Fuzzy volatility parameter is utilized to capture the uncertainty of the estimated volatility in the financial market which can fluctuate from time to time. This parameter is expected to provide reasonable ranges and appropriate Fuzzy membership functions for option pricing so that investors can expect different optimal values for different risk preferences. We also adjusted the formulation of the increase and decrease factors in the Fuzzy Binomial tree to model stock price movements. Using different values of the volatility's sensitivity level and the option period, the results of numerical simulations show that prices of European call options given by the market are always within the option price range of the proposed model's result. Likewise, the results of the defuzzification of options prices in our Fuzzy Bino-Trinomial tree model are not much different from the prices given by the market. This shows that the Fuzzy Bino-Trinomial tree model performs better in determining the price of European call options than the Fuzzy Binomial tree and Fuzzy Trinomial models.
CONTROLLING THE BORROWER POPULATION OF P2P LENDING MODELS Gunadi, Audri Utami; Handayani, Dewi
Journal of the Indonesian Mathematical Society Vol. 30 No. 2 (2024): JULY
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.30.2.1778.236-255

Abstract

P2P lending, commonly called online lending, is a service provider institution that provides borrowing and lending services in rupiah currency through an electronic system. The growth of P2P lending has increased rapidly since the pandemic of COVID-19 and led to an increase in the number of borrowers. Meanwhile, crime has also increased as many people can’t repay their loans. The chain of P2P lending must be controlled to suppress the growth of the population of people with online loans. This study constructs two P2P lending models by modifying the Kermack-McKendrick Epidemic Model. The population is divided into three sub populations: potential individuals, borrowers, and payers. Optimal control is used to suppress the population growth of borrower individuals through socialization with potential individuals or people with work potential and providing payment assistance for borrowers. This study constructs several optimal control scenarios for the two P2P lending models. From the comparison of optimal control scenarios, the optimal control recommendations that can suppress the population growth of borrower is to provide socialization to people with work potential and payment assistance for the borrower population.
LOAN BENCHMARK INTEREST RATE IN BANKING DUOPOLY MODEL WITH HETEROGENEOUS EXPECTATION Ansori, Moch. Fandi
Journal of the Indonesian Mathematical Society Vol. 30 No. 2 (2024): JULY
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.30.2.1779.205-217

Abstract

A loan benchmark interest rate policy always becomes a challenging problem in the banking industry since it has a role in controlling bank loan expansion, especially when there is competition between two banks. This paper aims to assess the influence of the loan benchmark interest rate on the expansion of loans between two banks. We present a banking duopoly model in the form of two-dimensional difference equations which is constructed from heterogeneous expectation, where one of the banks sets its optimal loan volume based on the other bank’s rational expectation. The model’s equilibrium is investigated, and its stability is analyzed using the Jury stability condition. Investigation indicates that to ensure the stability of the banking loan equilibrium, it is advisable to establish a loan benchmark interest rate that is lower than the flip bifurcation value. Some numerical simulations, such as the bifurcation diagram, Lyapunov exponent, and chaotic attractor, are presented to confirm the analytical findings.
HIDDEN MARKOV REPRESENTATION OF MICROCREDIT Giva, Maria Angela; Luy, Jasmin-Mae; Segui, Mary Elizabeth
Journal of the Indonesian Mathematical Society Vol. 30 No. 2 (2024): JULY
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.30.2.1782.218-235

Abstract

Microcredit is a method of lending small amounts of money to low-income individuals who have no access to traditional financial institutions. Upon applying for a loan, an individual may either be able to repay it and be granted a loan again, otherwise s/he demands for a new loan. These events influence certain factors, which can be illustrated through a hidden Markov model (HMM). This study provides a hidden Markov representation of microcredit taking into consideration the borrower's acquisition of small businesses. Model algorithms used in addressing the problems in HMM, such as the Viterbi algorithm, are discussed and implemented via numerical examples.
ANALYSIS OF UNEMPLOYED YOUTH IN INDONESIA BY PANEL DATA REGRESSION WITH MODERATING VARIABLE Subanti, Sri; Amanda, Nabila Tri
Journal of the Indonesian Mathematical Society Vol. 30 No. 3 (2024): NOVEMBER
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.30.3.1803.338-351

Abstract

Indonesia is entering the era of demographic bonus with the productive age dominating the population. Productive age is the main focus of the government in maximizing the demographic dividend, but Indonesia has the highest percentage of Not in employment, education or training (NEET) in Asia. NEET are people on 15 – 24 years old who do other activities outside of school, work or training. This study aims to analyze NEET in Indonesia using panel data with moderate regression analysis. The analysis of multiple linear regression is focused on the relationship between the independent and dependent variables without taking into other possible outcomes. By inserting a moderating variable, this study explores the relationship between the independent and dependent variables differently and aims to strengthen or weaken it. Under certain conditions, the relationship between the independent and dependent variables can be explained by the moderating variable. The research data used were obtained from the employment book and the website of BPS Indonesia, in the form of 34 cross section and 5 years time series data that tends to be stationary. The dependent variable is NEET with 5 independent variables including Human development index, the open unemployment rate, labor force participation rate, proportion of individuals who own phone, and proportion of informal employment. The moderating variable is the proportion of youth aged with ICT skills. The best model in regression analysis panel data is FEM with 4 significant independent variables and 92.75% of R-square. Moderating variable can moderates the relationship of NEET with its independent variables and increased the R-square to 94.19%.
BALANCED INDEX SETS OF GRAPHS AND SEMIGRAPHS Prabhu, Nagarjun; Nayak C, Devadas
Journal of the Indonesian Mathematical Society Vol. 30 No. 3 (2024): NOVEMBER
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.30.3.1196.468-485

Abstract

Let G be a simple graph with vertex set V (G) and edge set E(G). Graph labeling is an assignment of integers to the vertices or the edges, or both, subject to certain conditions. For a graph G(V, E), a friendly labeling f : V (G) → {0, 1} is a binary mapping such that |vf (1) − vf (0)| ≤ 1, where vf (1) and vf (0) represents number of vertices labeled by 1 and 0 respectively. A partial edge labeling f ∗ of G is a labeling of edges such that, an edge uv ∈ E(G) is, f ∗(uv) = 0 if f (u) = f (v) = 0; f ∗(uv) = 1 if f (u) = f (v) = 1 and if f (u)̸ = f (v) then uv is not labeled by f ∗. A graph G is said to be balanced graph if it admits a vertex labeling f that satisfies the conditions, |vf (1) − vf (0)| ≤ 1 and |ef (1) − ef (0)| ≤ 1, where ef (0), ef (1) are the number of edges labeled with 0 and 1 respectively. The balanced index set of the graph G is defined as, {|ef (1) − ef (0)| : the vertex labeling f is friendly}. A semigraph is a generalization of graph. The concept of semigraph was introduced by E. Sampath Kumar. Frank Harrary has defined an edge as a 2-tuple (a, b) of vertices of a graph satisfying, two edges (a, b) and (a′, b′) are equal if and only if either a = a′ and b = b′ or a = b′ and b = a′. Using this notion, E. Sampath Kumar defined semigraph as a pair (V, X) where V is a non-empty set whose elements are called vertices of G and X is a set of n-tuples called edges of G of distinct vertices, for various n ≥ 2 satisfying the conditions: (i) Any two edges of G can have at most one vertex in common; and (ii) two edges (a1, a2, a3, ..., ap) and (b1, b2, b3, ..., bq ) are said to be equal if and only if the number of vertices in both edges must be equal, i.e p = q, and either ai = bi for 1 ≤ i ≤ p or ai = bp−i+1, 1 ≤ i ≤ p. In this article, balance index set of T (Pn), T (Wn), T (Km,n) and T (Sn) determined, and the balance index set of semigraph is introduced. Additionally, the balanced index set of semigraph Cn,m, Kn,m is determined.
GROUP MEAN CORDIAL LABELING OF SOME QUADRILATERAL SNAKE GRAPHS R N, Rajalekshmi; R, Kala
Journal of the Indonesian Mathematical Society Vol. 30 No. 3 (2024): NOVEMBER
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.30.3.1210.374-384

Abstract

Let G be a (p, q) graph and let A be a group. Let f : V (G) −→ A be a map. For each edge uv assign the label [o(f (u))+o(f (v)) / 2]. Here o(f (u)) denotes the order of f (u) as an element of the group A. Let I be the set of all integerslabeled by the edges of G. f is called a group mean cordial labeling if the following conditions hold: (1) For x, y ∈ A, |vf (x) − vf (y)| ≤ 1, where vf (x) is the number of vertices labeled with x. (2) For i, j ∈ I, |ef (i) − ef (j)| ≤ 1, where ef (i) denote the number of edges labeled with i. A graph with a group mean cordial labeling is called a group mean cordial graph. In this paper, we take A as the group of fourth roots of unity and prove that, Quadrilateral Snake, Double Quadrilateral Snake, Alternate Quadrilateral Snake and Alternate Double Quadrilateral Snake are groupmean cordial graphs.

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