European Journal of Mathematics and Statistics

New Algorithms to Compute Hypersingular Integrals with Rapidly Oscillating Kernels

Maria Rosaria Capobianco, Giuliana Criscuolo — Tue, 29 Apr 2025 00:00:00 +0200

The paper is dedicated to the study of two new algorithms for approximating hypersingular integrals with rapidly oscillating kernels. The methods use an interpolatory procedure at zeros of orthogonal polynomials. Estimates of the error are given, as well as of the amplification factors. Some numerical examples show the coherence of the theoretical results with the numerical ones.

Maria Rosaria Capobianco, Giuliana Criscuolo

Modeling Mortality Risk Among HIV/AIDS Patients on Antiretroviral Therapy Using Survival Methods: Insights from Kaplan-Meier, Cox Proportional Hazards Models, and Log Rank Tests

Winfred Karimi, Robert Muriungi Gitunga, Frank Gekara Onyambu, Christine Gacheri — Fri, 18 Apr 2025 00:00:00 +0200

Background: Despite significant advancements in antiretroviral therapy (ART), HIV/AIDS continues to be a critical health challenge in Meru County, Kenya, particularly regarding the high mortality rates among people living with HIV (PLHIV). This study aimed to fit a survival model for predicting mortality and evaluate survival differences among adult HIV/AIDS patients under ART at Meru Teaching and Referral Hospital (MTRH).

Method: A retrospective cohort design was adopted, using secondary data from MTRH for all HIV-positive adults who received ART between January 1, 2018, and December 31, 2023. The target population comprised patients with complete medical records available for analysis. Collected data included demographic, socioeconomic, and clinical variables, with mortality as the event of interest. Data were de-identified to ensure privacy and analyzed using R statistical software. The quantitative analysis employed the Cox Proportional Hazards regression model to fit a survival model for predicting mortality. The Log-rank test evaluated survival differences among PLHIV across different treatment groups.

Results: Results indicated that gender and age were significant predictors of mortality. Specifically, being male was associated with a 72% higher hazard of mortality compared to females (exp(coef) = 1.718), and each additional year of age increased the hazard by 1.5% (coefficient = 1.015). However, smoking status and employment were not significantly associated with mortality. The Log-rank test revealed a significant difference in survival rates between male and female participants (χ2 =4.1, df=1, p=0.04), with females showing better survival outcomes, while no significant differences were found based on age, smoking status, or marital status.

Conclusion: The study concluded that gender and age are key determinants of mortality among PLHIV under ART at MTRH, with males facing higher mortality risks. The findings emphasize the need for gender-sensitive healthcare interventions and age-appropriate care strategies to improve survival outcomes. Further research is recommended to explore the specific challenges faced by male PLHIV and to investigate the broader impact of socioeconomic factors on survival outcomes.

Winfred Karimi, Robert Muriungi Gitunga, Frank Gekara Onyambu, Christine Gacheri

Gauss Metric on the Kummer Surface

Masahito Hayashi, Kazuyasu Shigemoto, Takuya Tsukioka — Mon, 17 Feb 2025 00:00:00 +0100

On the Kummer surface, we have obtained two different Gauss metrices by parametrizing it in two ways. We have found that these Gauss metrices are not Ricci flat. The double sphere, which is the special case of the Kummer surface, has the Kähler metric and the first Chern class of it does not vanish. Its metric is the Einstein metric which is not Ricci flat.

Masahito Hayashi, Kazuyasu Shigemoto, Takuya Tsukioka

Inverting Symmetric Positive Definite Matrices using Divide and Conquer Mathematical Technique with LU Factorization

Mon, 24 Feb 2025 00:00:00 +0100

We looked at the solution of a system of equations Ax=b with symmetric positive definite coefficient matrix A that has singular and nearly singular values. Our technique, which is based on the Divide and Conquer strategy, combines the LU Factorization algorithm with the Divide-and-Conquer technique (D&C algorithm). The matrix was transformed into a product of the type LU using the LU Factorization, where L is a lower triangular matrix and U is an upper triangular matrix. MATLAB was used to implement the algorithm and simulate it as a user-subroutine. In order to reduce the round-off error, particularly for sensitive systems, the user-subroutine takes into account MATLAB characteristics. A non-singular matrix and an ill-conditioned matrix were both numerically demonstrated. Analysis was done on the impact of round-off error. We contrasted the results with those from earlier studies that employed LU factorization.

Abdel Radi Abdel Rahman Abdel Gadir Abdel Rahman, Shady Seed El Okuer, Musa Adam Abdullah

The Arcsine Log-Logistic Distribution and Its Applications

Md. Aftab Moral, Md. Shohel Rana, Md. Mahabubur Rahman — Sat, 15 Mar 2025 00:00:00 +0100

This article introduces Arcsine Log-logistic (AL-L) distribution which is a member of Arcsine-G family proposed by Rahman. The different properties of AL-L distribution have been discussed. The distribution of various order statistics are obtained. Maximum Likelihood Estimation (MLE) technique is used to estimate the model parameters. Finally, for testing the practicability of proposed model we have been used two different datasets.

Md. Aftab Moral, Md. Shohel Rana, Md. Mahabubur Rahman