European Journal of Mathematics and Statistics

A Quadratic Curve Analogue of the Taniyama-Shimura Conjecture

2024-09-24T00:03:52+02:00

For quadratic curves over finite fileds, the number of solutions, which is governed by an analogue of the Mordell-Weil group, is expressed with the Legendre symbol of a coefficient of quadratic curves. Focusing on the number of solutions, a quadratic curve analogue of the modular form in the Taniyama-Shimura conjecture is proposed. This modular form yields the Gaussian sum and also possesses some modular transformation structure.

Solving Time-Space Fractional Boussinesq Equation Using Homotopy Perturbation Method

2024-08-22T14:23:37+02:00

This paper aims to implement the homotopy perturbation technique to solve the time-space fractional Boussinesq equation, a significant model in the analysis of nonlinear wave propagation. Through the application of the homotopy perturbation technique, we derive analytical expressions for the solutions of the time-space fractional Boussinesq equation and validate these solutions through comparisons with numerical methods. Obtained results demonstrate the efficiency and accuracy of the homotopy perturbation method in solving the time-space fractional Boussinesq equation.

Introduction to the Thukral-Determinantal Formula for Accelerating Convergence of Sequence

2024-03-29T08:44:05+01:00

There are two objectives for this paper. Firstly, we shall introduce the Thukral-determinantal formula, and secondly, we shall demonstrate the similarities between the well-established algorithms, namely the Aitkin Δ²algorithm and the Durbin sequence transformation. In fact, we have found that the solution of the Thukral-determinantal formula is equivalent to the Thukral-sequence transformation formula.

Representations of Group Algebras of Non-Abelian Groups of Orders p3, for a Prime p ≥ 3

2023-11-07T13:57:48+01:00

In this paper, semidirect products are used to find the matrix representations of group algebras of non-abelian groups of order p³, for a prime p ≥ 3.

Comparative Analysis of GARCH-Based Volatility Models of Financial Market Volatility: A Case of Nairobi Security Market PLC, Kenya

2023-09-27T14:28:08+02:00

This paper conducted a comprehensive comparative analysis of various GARCH (Generalized Autoregressive Conditional Heteroskedasticity) models to forecast financial market volatility, with a specific focus on the Nairobi Stock Exchange Market. The examined models include symmetric and asymmetric GARCH types, such as sGARCH, GJR-GARCH, AR (1) GJG-GARCH, among others. The primary objective is to identify the most suitable model for capturing the complex dynamics of financial market volatility. The study employs rigorous evaluation criteria, including the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), Mean Error (ME), and Root Mean Absolute Error (RMAE), to assess the performance of each model. These criteria facilitate the selection of the optimal model for volatility forecasting. The analysis reveals that the GJR-GARCH (1,1) model emerges as the best-fit model, with AIC and BIC values of −5.5008 and −5.4902, respectively. This selection aligns with the consensus in the literature, highlighting the superiority of asymmetric GARCH models in capturing volatility dynamics. The comparison also involves symmetric GARCH models, such as sGARCH (1,1), and other asymmetric models like AR (1) GJG-GARCH. While these models were considered, the GJR-GARCH (1,1) model demonstrated superior forecasting capabilities. The study emphasizes the importance of accurate model selection and the incorporation of asymmetry in volatility modeling. The research provides essential insights into financial market volatility modeling and forecasting using both asymmetric and symmetric GARCH models. These findings have significant implications for government policymakers, financial institutions, and investors, offering improved tools for risk assessment and decision-making during periods of market turbulence.