Journal of the Indonesian Mathematical Society

Tucker3 Tensor Decomposition for the Standardized Residual Hypermatrix on Three-Way Correspondence Analysis

2024-09-30T04:22:06+00:00

This study investigates the theoretical and practical mathematical aspects of Tucker3 tensor decomposition from the three-way correspondence analysis point of view. Since the standardized residual hypermatrix represents the association of the three categorical variables, this study focused on (1) Tucker3 tensor decomposition for the standardized residual hypermatrix, (2) some mathematical properties of Tucker3 tensor decomposition, and (3) constructing the correspondence plot via Tucker3 tensor decomposition. Some mathematical results are presented in lemmas, theorems and algorithms, while a practical result is exhibited at the end of the discussion.

Signal Processing Of The One-Factor Mean-Reverting Model In Energy System

2025-02-21T22:47:10+00:00

One of the models that can be considered in the energy system is the one-factor mean-reverting process. We propose the one-factor mean-reverting model with sinusoidal signal processing involved. The frequency component of the model can be estimated with a high-frequency scheme. The estimation of the frequency component is believed to produce a precise estimate. This is because the high-frequency scheme has the potential to handle possible non-linear coefficient cases in a unified way, that is, $nh\to \infty$, and $nh^{2}\to 0$. This paper shows that the frequency component estimator in the one-factor mean-reverting model is strongly consistent with the rate convergence, namely $\sqrt{(nh)^3}$. It is also can be shown that the estimator has a normal approximation with a mean of 0 and variance $\frac{1}{6}(1+\theta^{2})$. We applied the proposed model to the energy systems data.

Reverse Homoderivations on (Semi)-prime Rings

2024-12-04T07:27:22+00:00

In this paper, we explore and examine a new class of maps known as reverse homoderivations. A reverse homoderivation refers to an additive map g defined on a ring T that satisfies the condition, $. We present various results that enhance our understanding of reverse homoderivations, including their existence in (semi)-prime rings and the behavior of rings when they satisfy certain functional identities. Some examples are provided to demonstrate the necessity of the constraints, while additional examples are given to clarify the concept of reverse homoderivations.$

Mathematical Study for Proving Correctness of the Serial Graph-Validation Queue Scheme

2024-09-21T16:38:38+00:00

Numerous studies have been conducted to develop concurency control schemes that can be applied to client-server systems, such as the Validation Queue (VQ) scheme, which uses object caching on the client side. This scheme has been modified into the Serial Graph-Validation Queue (SG-VQ) scheme, which employs validation algorithms based on queues on the client side and graphs on the server side. This study focuses on verifying the correctness of the SG-VQ scheme by using serializability as a mathematical tool. The results of this study demonstrate that the SG-VQ scheme can execute its operations correctly, in accordance with Theorem 4.16, which states that every history (H) of SG-VQ is serializable. Implementing a cycle-free transaction graph is a necessary and sufficient condition to achieve serializability. To prove Theorem 4.16, mathematical statements involving ten definitions, two propositions, and three lemmas have been formulated.

Characterization of \mathcal{R}(2K_2,F_n) with Minimum Order for Small n

2024-12-10T15:27:53+00:00

A Fan graph $F_n$ is defined as the graph $P_n+K_1$, where $P_n$ is the path on $n$ vertices. The notation $F \rightarrow (G, H)$ means that if all edges of $F$ are arbitrarily colored by red or blue, then either the subgraph of $F$ induced by all red edges contains a graph $G$ or the subgraph of $F$ induced by all blue edges contains a graph $H.$ Let $\mathcal{R}(G, H)$ denote the set of all graphs $F$ satisfying $F \rightarrow (G, H)$ and for every $e \in E(F),$ $(F - e) \not\rightarrow (G, H).$ In this paper, we propose some properties for a graph $G$ of minimum order that belongs to $\mathcal{R}(2K_2,F_n),$ for $n \geq 3$. We have also found all members of $\mathcal{R}(2K_2,F_n)$ with a minimum order for $n \in [3,7]$.

"Corporate" and "Community" Takāful

2024-09-10T08:56:53+00:00

In this paper, we compare different characterizations of the tak¯aful organization. We propose two different characterizations with one being based on conventional firm theory from microeconomics (“corporate” takāful) and another being based on the mutual/cooperative insurance literature (“community” takāful). We find that both characterizations imply different strategies due to different objectives and operational conditions. We also find that if participants in a community takāful organization are altruistic, those overseeing the organization must make sure that participants do not spend more than they have when paying for claims made by the community.

Fourth Order PDE: Model of Thin Film Flow Involving Surface Tension

2024-08-17T08:44:17+00:00

Surface wave on thin film is considered by involving surface tension. The fluid flows on an inclined channel. The model is based on lubrication theory, and presented in a single equation of the thickness of the fluid as wave movement, and the equation is strongly nonlinear. In solving the model, scaling and linearized processes are applied. So that three physical parameters play an important role in the wave propagation: bottom inclination, length of the scaling and the surface tension. Each of those parameters is represented as a term in the equation. Then, the equation is solved numerically by an implicit finite difference method for the linearized equation, so that the solution can be used to observe the effect of those physical quantities. We found that the surface wave propagates with different speed and reducing the amplitude. When the surface tension is involved, the profile of the wave slightly changes, beside it also effect to the movement of the wave. This is simulated in this paper.

The Zero Product Probability of Some Finite Ring of Matrices Based on the Order of the Annihilator

2024-10-18T06:49:32+00:00

An annihilator is defined as the set of pairs of elements in a ring R in which the product of the elements in the pair is the zero element of R. In this paper, we aim to determine the order of the annihilator of the finite ring of matrices of dimension two over integers modulo prime, M₂(Z_p). The order of the annihilator is determined by using number theory, specifically the linear congruence method. Another subject that we discuss in this paper is the zero product probability of a finite ring. The zero product probability is defined as the probability that two elements of a finite ring have product zero. Based on the order of the annihilator, the general formula of the zero product probability of M₂(Z_p) is determined.

An Economic Order Quantity Model for Flawed Units With Quality Screening and Time Dependent Backlogging

2024-09-19T14:08:57+00:00

This study introduces an Economic Order Quantity (EOQ) model that addresses inventory systems dealing with imperfect quality items, incorporating both quality screening processes and time-dependent backlogging. Recognizing that a proportion of received items may be defective, the model integrates a screening mechanism to identify and separate flawed units before they reach customers. Additionally, the model considers a backlogging scenario where unmet demand is partially backordered, with the backlogging rate being a function of the waiting time until the next replenishment. The objective is to determine the optimal order quantity and backordering level that minimize the total cost, which includes ordering, holding, screening, backordering and shortage costs. Analytical solutions are derived and numerical examples are provided to illustrate the model's applicability. Sensitivity analyses are conducted to examine the impact of key parameters on the optimal solution.

Multi-Decomposition of Product Graphs into Kites and Stars on Four Edges

2024-09-11T20:27:57+00:00

A decomposition of a graph $G$ is a set of edge-disjoint subgraphs $H_1,H_2,...,H_r$ of $G$ such that every edge of $G$ belongs to exactly one $H_i$. If all the subgraphs in the decomposition of $G$ are isomorphic to a graph $H$ then we say that $G$ is $H$-decomposable. The graph $G$ has an $\{H_1^\alpha,H_2^\beta\}$-decomposition, if $\alpha$ copies of $H_1$ and $\beta$ copies of $H_2$ decompose $G$, where $\alpha$ and $\beta$ are non-negative integers. In this paper, we have obtained the decomposition of $K_m \times K_n$ into $\alpha$ kites and $\beta$ stars on four edges for some of the admissible pairs $(\alpha,\beta)$, whenever $mn(m-1)(n-1) \equiv 0(mod\ 8)$, for $m \geq 3$ and $n \geq 4$. Also, we have obtained the decomposition of $K_m \otimes \overline{K_n}$ into $\alpha$ kites and $\beta$ stars on four edges for some of the admissible pairs $(\alpha,\beta)$, whenever $m(m-1)n^2 \equiv 0(mod\ 8)$, for $m \geq 3$ and $n \geq 4$. Here $K_m \times K_n$ and $K_m \otimes \overline{K_n}$ respectively denotes the tensor and wreath product of complete graphs.