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Open Access January 02, 2024

Constructability and Rigor of Angles Multiples of 3 in Euclidean Geometry

Alex Mwololo Kimuya
Journal of Mathematics Letters 2024, 2(1), 1-27. DOI: 10.31586/jml.2024.841
Abstract This paper investigates the constructability of angles multiples of 3 within the framework of Euclidean geometry. It makes a significant contribution by presenting the first geometric construction for all such angles, offering a rigorous solution to a longstanding geometric problem. The paper reaffirms the efficacy of Euclidean geometry in providing precise constructions and robust proofs for [...] Read more.
This paper investigates the constructability of angles multiples of 3 within the framework of Euclidean geometry. It makes a significant contribution by presenting the first geometric construction for all such angles, offering a rigorous solution to a longstanding geometric problem. The paper reaffirms the efficacy of Euclidean geometry in providing precise constructions and robust proofs for these angles, demonstrating the enduring strength of Euclidean principles from classical to modern times. The presented workflow goes beyond Euclidean geometry to examine non-Euclidean methods, particularly analytical approaches, revealing misconceptions that compromise the genetic and geometric rigor of Euclidean principles. The paper exposes incongruities when algebraic proofs related to angle constructability are applied to the Euclidean system, emphasizing the misalignment of fundamental geometric concepts. A notable result in the paper is the construction of a angle, introducing the “ angle chord” as a novel geometric property. This property challenges assumptions made by non-Euclidean methods and highlights the nuanced geometric properties crucial for rigorous constructions. The paper refutes the fallacy of relying solely on algebra for solutions to angles multiples of , emphasizing the necessity of embracing Euclidean geometry for geometric discoveries. The paper underscores the merits and resilience of Euclidean geometry, showcasing its independence and depth across historical and modern perspectives. The newly presented geometric construction not only resolves a longstanding question but also emphasizes the intrinsic strength and uniqueness of Euclidean principles in contrast to alternative methodologies.
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Open Access November 03, 2023

Mathematical Modeling of the Price Volatility of Maize and Sorghum between 1960 and 2022

Samuel Olorunfemi Adams, Mohammed Anono Zubair, Michael Franklin Ezike
Journal of Mathematics Letters 2023, 1(1), 38-56. DOI: 10.31586/jml.2023.801
Abstract The price of grains like maize and sorghum is subject to significant fluctuations, which can have a significant impact on a country's economy and food security. The aim of the study is to model sorghum and maize price volatility in Nigeria. The data utilized in the study was extracted from World Bank Commodity Price Data (WBCPD), 2022. The data consists of monthly prices in nominal US dollars for [...] Read more.
The price of grains like maize and sorghum is subject to significant fluctuations, which can have a significant impact on a country's economy and food security. The aim of the study is to model sorghum and maize price volatility in Nigeria. The data utilized in the study was extracted from World Bank Commodity Price Data (WBCPD), 2022. The data consists of monthly prices in nominal US dollars for maize and sorghum from January 1960 – August 2022. The Autoregressive Conditional Heteroskedasticity (ARCH) and Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models were utilized for capturing the two-grain price volatility. Two types of conditional heteroscedastic models exist, the first group uses exact functions to control the evolution of , while the second group describes with stochastic equations. It is inferred from the result that inherent uncertainties and fluctuations existed in the prices of maize and sorghum in Nigeria which implies that the price volatility is positive and statistically significant suggesting that historical information and past shocks play a crucial role in determining the volatility observed in the grains. It is recommended that the ARCH, GARCH, EGARCH, TGARCH, PARCH, CGARCH, and IGARCH models should be employed for modeling and managing the volatility of maize and sorghum prices in Nigeria. These models have shown effectiveness in capturing different aspects of volatility, including the impact of past shocks, conditional volatility, asymmetry, and other relevant factors.
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Open Access June 20, 2022

Charged Anisotropic Stellar Models with the MIT Bag Model Equation of State

Manuel Malaver
Universal Journal of Physics Research 2022, 1(1), 18-31. DOI: 10.31586/ujpr.2022.338
Abstract In this paper we present a new classes of solutions for the Einstein-Maxwell system of field equations in a spherically symmetric spacetime under the influence of an electric field considering the MIT bag model equation of state with a particular form the metric potential that depends on an adjustable parameter. The obtained solutions can be written in terms of elementary functions, namely [...] Read more.
In this paper we present a new classes of solutions for the Einstein-Maxwell system of field equations in a spherically symmetric spacetime under the influence of an electric field considering the MIT bag model equation of state with a particular form the metric potential that depends on an adjustable parameter. The obtained solutions can be written in terms of elementary functions, namely polynomials and algebraic functions. The obtained models satisfy all physical properties expected in a realistic star. The results of this research can be useful in the development and description of new models of compact structures.
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Open Access November 10, 2022

Modeling and Forecasting Cryptocurrency Returns and Volatility: An Application of GARCH Models

Haruna Umar Yahaya, John Sunday Oyinloye, Samuel Olorunfemi Adams
Universal Journal of Finance and Economics 2022, 2(1), 71-90. DOI: 10.31586/ujfe.2022.497
Abstract The future of e-money is crypocurrencies, it is the decentralize digital and virtual currency that is secured by cryptography. It has become increasingly popular in recent years attracting the attention of the individual, investor, media, academia and governments worldwide. This study aims to model and forecast the volatilities and returns of three top cryptocurrencies, namely; Bitcoin, Ethereum [...] Read more.
The future of e-money is crypocurrencies, it is the decentralize digital and virtual currency that is secured by cryptography. It has become increasingly popular in recent years attracting the attention of the individual, investor, media, academia and governments worldwide. This study aims to model and forecast the volatilities and returns of three top cryptocurrencies, namely; Bitcoin, Ethereum and Binance Coin. The data utilized in the study was extracted from the higher market capitalization at 31st December, 2021 and the data for the period starting from 9th November, 2017 to 31st December 2021. The Generalised Autoregressive conditional heteroscedasticity (GARCH) type models with several distributions were fitted to the three cryptocurrencies dataset with their performances assessed using some model criterion tests. The result shows that the mean of all the returns are positive indicating the fact that the price of this three crptocurrencies increase throughout the period of study. The ARCH-LM test shows that there is no ARCH effect in volatility of Bitcoin and Ethereum but present in Binance Coin. The GARCH model was fitted on Binance Coin, the AIC and log L shows that the CGARCH is the best model for Binance Coin. Automatic forecasting was perform based on the selected ARIMA (2,0,1), ARIMA (0,1,2) and the random walk model which has the lowest AIC for ETH-USD, BNB-USD and BTC-USD respectively. This finding could aid investors in determining a cryptocurrency's unique risk-reward characteristics. The study contributes to a better deployment of investor’s resources and prediction of the future prices the three cryptocurrencies.
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Open Access October 19, 2021

Allometric Models for Predicting Biomass and Carbon Pools of Boscia Senegalensis(Pers.) Lam. Ex Poir. (Capparaceae) Populations in Central Africa: A Case Study from Cameroon

Djongmo Victor Awé, Noumi Valery Noiha, Djomo Cédric Chimi, Moussa Ganamé, Bi Tra Aimé Vroh, Louis Zapfack
Research Journal of Ecology and Environmental Sciences 2021, 1(2), 123-146. DOI: 10.31586/rjees.2021.156
Abstract Accurate estimates of above-ground biomass (AGB) and below-ground biomass (BGB) are essential for estimating carbon (C) balances at various geographical scales and formulating effective climate change mitigation programs. This study aimed to formulate specific allometric equations and carbon stock for B. senegalensis in Cameroon. Destructive sampling technique was used for harvesting and weighing the biomass of 40 individual trees. Allometric models were developed using biomass as dependent variable and tree dendrometric parameters as independent variables. The best models selected based with Adjusted coefficients of determination (Adj.R2), residual standard error (RSE) and Akaike's information criterion (AIC) were: ln (leaf biomass) = 0.08 + 0.31*ln (D2×H×ρ); ln (branch biomass) = 0.14 + 0.65*ln (D²×H×ρ); ln (stem biomass) = 2.03 + 1.32*ln (D²×H); ln (AGB) = 4.55 + 2.85*ln(D) and ln (BGB) =3.04 + 1.64*ln(D). The belowground biomass of B. senegalensis represents on average 25 % of the total aboveground biomass. Aboveground carbon ranged between 7.09 ± 0.42- 9.01 ± 0.50 tC/ha; Belowground carbon ranged between 4.37 ± 0.26 - 7.11 ± 0.35 tC/ha; litter carbon ranged between 0.50 ± 0.02 - 0.95 ± 0.04 tC/ha; herbaceous carbon ranged between 1.05 ± 0.28 - 1.86 ± 0.20 tC/ha ; dead wood carbon ranged between 3.03 ± 0.40 - 8.98 ± 0.44 tC/ha; Soil Organic Carbon Stock varies between4.33 ± 0.79 - 6.14 ± 1.05 tC/ha ;Total carbon were 33.24 ± 4.28;27.40 ± 3.35;27.27 ± 3.27and 21.18 ± 3.00 tC/ha in site 3, site 2, site 1 and site 4 respectively.The specific allometric equation developed for B. senegalensis [...] Read more.
Accurate estimates of above-ground biomass (AGB) and below-ground biomass (BGB) are essential for estimating carbon (C) balances at various geographical scales and formulating effective climate change mitigation programs. This study aimed to formulate specific allometric equations and carbon stock for B. senegalensis in Cameroon. Destructive sampling technique was used for harvesting and weighing the biomass of 40 individual trees. Allometric models were developed using biomass as dependent variable and tree dendrometric parameters as independent variables. The best models selected based with Adjusted coefficients of determination (Adj.R2), residual standard error (RSE) and Akaike's information criterion (AIC) were: ln (leaf biomass) = 0.08 + 0.31*ln (D2×H×ρ); ln (branch biomass) = 0.14 + 0.65*ln (D²×H×ρ); ln (stem biomass) = 2.03 + 1.32*ln (D²×H); ln (AGB) = 4.55 + 2.85*ln(D) and ln (BGB) =3.04 + 1.64*ln(D). The belowground biomass of B. senegalensis represents on average 25 % of the total aboveground biomass. Aboveground carbon ranged between 7.09 ± 0.42- 9.01 ± 0.50 tC/ha; Belowground carbon ranged between 4.37 ± 0.26 - 7.11 ± 0.35 tC/ha; litter carbon ranged between 0.50 ± 0.02 - 0.95 ± 0.04 tC/ha; herbaceous carbon ranged between 1.05 ± 0.28 - 1.86 ± 0.20 tC/ha ; dead wood carbon ranged between 3.03 ± 0.40 - 8.98 ± 0.44 tC/ha; Soil Organic Carbon Stock varies between4.33 ± 0.79 - 6.14 ± 1.05 tC/ha ;Total carbon were 33.24 ± 4.28;27.40 ± 3.35;27.27 ± 3.27and 21.18 ± 3.00 tC/ha in site 3, site 2, site 1 and site 4 respectively.The specific allometric equation developed for B. senegalensis can be used in similar Sudano-Sahelian savannas to implement activities to reduce emissions from deforestation and degradation (REDD+) for the benefit of local carbon trading communities.
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Open Access September 04, 2021

Active Fault Tolerant Control of Faulty Uncertain Neutral Time-Delay Systems

Benjemaa Rabeb, Elhsoumi Aicha, Bel Hadj Ali Saloua
Journal of Artificial Intelligence and Big Data 2021, 1(1), 18-30. DOI: 10.31586/jaibd.2021.059
Abstract The present paper attempts to investigate the problem of Fault Tolerant Control for a class of uncertain neutral time delay systems. In the first time, we consider an additive control that is based on adding a term to the nominal law when the fault occurs. This approach will be designed in three steps. The first step is fault detection while the second one is fault estimation. For these two steps, [...] Read more.
The present paper attempts to investigate the problem of Fault Tolerant Control for a class of uncertain neutral time delay systems. In the first time, we consider an additive control that is based on adding a term to the nominal law when the fault occurs. This approach will be designed in three steps. The first step is fault detection while the second one is fault estimation. For these two steps, we consider the adaptive observer to guarantee the detection and estimation of the fault. The third step is the fault compensation. Lyapunov method and Linear Matrix Inequality (LMI) techniques were considered to improve the main method. Second, we propose a Pseudo Inverse Method "PIM" and determine the error between the closed loop and the nominal system. Finally, simulation results are presented to prove the theoretical development for an example of an uncertain neutral time delay system.
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