Applied Sciences Research Periodicals

Divide-and-Conquer Strategy with LU Factorization for Inverting Symmetric Positive Definite Matrices

Abdel Radi Abdel Rahman Abdel Gadir Abdel Rahman, Shady Seed EL Okuer — Sat, 11 Jan 2025 00:00:00 +0000

We studied the solution of a system of equations Ax=b with singular and nearly singular, symmetric positive definite coefficient matrix A. Our algorithm based on, the Divide and Conquer strategy leading to the Divide-and-Conquer Algorithm (D&C algorithm) with, LU Factorization algorithm. The LU Factorization was used to convert the matrix into a product of the form LU, where L is a lower triangular matrix and U is upper triangular matrix. The algorithm was been implemented on MATLAB and simulated as a user-subroutine. The user-subroutine is considering MATLAB features for reducing the round-off error especially for sensitive systems. Numerical examples was given of a non- singular matrix and another for ill-conditioned matrix. The effect of round-off error was analyzed. We compared results with previous ones, where LU factorization is used.

Case Study on the Establishment of a Local Circular Economy Loop through Recycling School Uniforms in a Japanese Countryside

Ryoko Sekifuji, Chieu Le Van, Masafumi Tateda — Sun, 05 Jan 2025 00:00:00 +0000

The fashion industry is known for its significant contribution to global environmental deterioration. The production of clothes consumes tremendous amounts of water and energy, and clothes, usually discarded within a short time, end up in landfill sites and generate secondary environmental pollution. In Japan, the school uniform culture continues to be widely followed and does not meet the global consensus on circular economies. Used uniforms are tucked away at the back of a wardrobe or discarded, although they remain in perfectly good condition. This is a case study of a uniform recycling loop first established by a university and subsequently transferred to a private company. Internet searches and questionnaire surveys were conducted to explore common perceptions of uniforms. In Japan, uniform costs are at least 700 USD when enrolling in public junior high schools. The findings showed that the parents of students strongly supported the uniform recycling project and were willing to pay up to 30% of the original price of uniforms if they were in a good condition.

Palliative Care for Cancer

Giovanna D’Alonzo — Sun, 05 Jan 2025 00:00:00 +0000

There are various studies on the anticancer effect of linoleic acid which also has soothing and hydrating effects. My idea is to create a substance with the right proportions of linoleic acid and biokeratin extracted from chicken feathers. In particular, to dissolve a right percentage of biokeratin in linoleic acid and create a substance to be oxidized and/or reduced using the equipment described in a scientific article of mine in order to hypothesize as a final substance a vaccine and a cure for tumors to be associated with chemotherapy. My hypothesis of a vaccine and/or cure for tumors is proposed starting from biological agents such as linoleic acid and biokeratin which, mixed together in the right proportions and subjected to an oxidation and/or reduction process as described in my article, could give life to biological vaccines and biological supplements to be associated with chemotherapy in cancer patients.