Journal of Mathematical Sciences and Informatics

LAPLACE DECOMPOSITION METHOD FOR SOLVING FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS WITH INITIAL VALUE PROBLEMS

2024-04-01T12:23:25+08:00

Fredholm integro-differential equations (IDEs) are important mathematical models used in various scientific disciplines. However, the presence of nonlinearity in these equations poses significant challenges for conventional numerical methods like quadrature formulas. This paper explores the application of the Laplace decomposition method (LDM) to address this problem. By employing the LDM and the Adomian decomposition method (ADM), the nonlinear Fredholm integro-differential equations with initial value problems were transformed into a sequence of solvable nonlinear integral equations. LDM is the semi-analytical technique specifically designed for nonlinear IDEs, offered an efficient approximation approach. The study presented the results of solving four illustrative examples using LDM and conducted a comparative analysis with other methods such as ADM and homotopy perturbation Method (HPM). The results demonstrated that LDM achieved exceptional accuracy and efficiency for nonlinear Fredholm IDEs.

ON THE SPECTRAL PROPERTIES OF THE MODEL OPERATOR ON A FERMIONIC FOCK SPACE

2024-04-19T17:50:00+08:00

We study a model operator , associated to a system of two identical fermions and another particle of a different nature, acting in the direct sum of zero-, one-, and two-particle subspaces of the fermionic Fock space. We show that the essential spectrum of this operator consist of the union of at most four segments on the real axis. We also explicitely derive a formula for the corresponding resolvent operator.

ANALYTICAL STUDY OF VARIABLE FLUID PROPERTIES AND MAGNETIC FIELD IN THIN-FILM FLOW OVER A STRETCHING STEADY SURFACE

2024-06-06T16:06:46+08:00

This research paper explains the effect of dynamic viscosity on steady thin film flow of water based nanofluid GO-EG and GO-W in the presence of magnetic field, variable thermal conductivity and convective boundary condition over a stretching surface. By using the similarity transformation, the partial differential equation is converted to nonlinear third order ordinary differential equations. The analytical method (OHAM) is used to find the analytical solution of the nonlinear problem which analyze the problem. The result of important parameters for both velocity and temperature profiles are plotted and discussed. The BVPh 2.0 package is used to obtain the convergence of the problem up to 25 iterations. The skin friction coefficient and Nusselt number is explained in table form.

MACHINE LEARNING-BASED RNN-LSTM FOR PREDICTING COVID-19 CASES IN MALAYSIA

2024-06-27T16:37:34+08:00

Started in the beginning of January 2020, the world still struggles to cope with the spread of COVID-19, including in Malaysia. Although the world has invented some vaccines for the disease, the coronavirus problem is still there and perhaps it will be a big issue until a few years ahead. This study will look at the trend of the spread on COVID-19 in Malaysia after two years since the pandemic haunted human life, particularly when the pandemic turned into endemic. We developed a model prediction based on Recurrent Neural Networks (RNN) with Long-Short Term Memory (LSTM) to predict the COVID-19 outbreak in both pandemic and endemic periods. In addition, the COVID-19 classes are split into susceptible (S), exposed (E), infectious (I), and recovered(R). We then forecast 60 days ahead by using these two models which are RNN with long-short term memory (LSTM) and a support vector regression (SVR). The results prove that both methods have different advantages. SVR can perform better in predicting the pandemic period, while RNN-LSTM has better predict the endemic period. From the results, it can be said that SVR is more appropriate for predicting dynamic curves, while RNN-LSTM is suitable for smooth curves. Thus, the results show that the studied prediction technique is a promising and encouraging procedure for studying the future trends of the COVID-19.

ON THE APPROXIMATION ALGORITHMS FOR SOLVING RICCATI DIFFERENTIAL EQUATIONS USING PIECEWISE CONSTANT ARGUMENTS METHOD

2024-11-12T17:19:06+08:00

This paper presents an efficient approach for determining an approximate solution to Riccati differential equations with variable coefficients. The approach is introduced as a differential equation with piecewise constant arguments, corresponding to the considered initial value problem, which depends on a positive integer . It is shown that this equation has a unique piecewise smooth solution, which serves as an approximate solution to the considered initial value problem for large . Numerical results are provided, demonstrating the efficiency and high accuracy of the proposed method.

BEST PROXIMITY POINT RESULTS FOR FUZZY Z-PROXIMAL CONTRACTIONS IN FUZZY METRIC SPACES

2024-11-14T10:49:57+08:00

In this manuscript, we introduce the concept of fuzzy -proximal contractions in the framework of fuzzy metric spaces. Additionally, we present novel findings regarding the existence and the uniqueness of best proximity points for such contractions in complete fuzzy metric spaces. These new findings extend and generalize certain results in the existing literature. Examples are included to support our findings.

CAN AI RESIGN AT THE RIGHT TIME IN A GAME OF SHOGI?

2024-11-13T17:05:01+08:00

This study introduces an innovative resignation mechanism to enhance shogi AI’s decision-making by identifying the optimal moment to resign. Through 300 self-play games per skill level, data on game length and branching factor were collected and analysed using game refinement theory and motion in mind techniques. The resignation threshold, defined as the maximum score of the losing player’s advantageous position plus a small value, prompts AI resignation when further alteration of the game’s outcome is improbable. Results indicate that implementing this mechanism significantly reduces game length compared with AI without it, bringing AI performance closer to human-level proficiency. Specifically, the average game length at skill level 20 decreased from 165.66 to 110 moves, while at skill levels 15, 10, and 5, the lengths reduced from 141.18, 133.97, and 121.17 to 112, 116, and 121 moves, respectively. Notably, gameplay speed, measured as the number of moves per unit time, also increased significantly after applying the resignation mechanism. Before its application, speed decreased with higher AI ability; however, post-application, speed increased with AI ability, underscoring the mechanism’s effectiveness in accelerating gameplay. The primary objective of this research is to enhance shogi AI’s decisionmaking capabilities, thus improving overall performance. By integrating the resignation mechanism, reliable data can be obtained for comparison with human players, contributing to advancements in game theory. In conclusion, introducing a resignation mechanism in shogi AI leads to smarter decisionmaking and more efficient gameplay. The findings of this study highlight the potential for improving AI performance in various board games and offer valuable insights into both AI decision-making processes and human gameplay strategies.