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Existence of Solutions of a Convolution Integral Equation

Journal of Applied Mathematics and Physics 2024年第5期12卷 1835-1847页

作者： Henry Otoo Benjamin Dadzie Mensah lewis brew Mathematical Sciences Department University of Mines and Technology Tarkwa Ghana Faculty of Science and Technology University of Silesia in Katowice Sosnowiec Poland

In this study, we prove the of existence of solutions of a convolution Volterra integral equation in the space of the Lebesgue integrable function on the set of positive real numbers and with the standard norm defined on it. An operator P was assigned to the convolution integral operator which was later expressed in terms of the superposition operator and the nonlinear operator. Given a ball Br belonging to the space L it was established that the operator P maps the ball into itself. The Hausdorff measure of noncompactness was then applied by first proving that given a set M∈ B r the set is bounded, closed, convex and nondecreasing. Finally, the Darbo fixed point theorem was applied on the measure obtained from the set E belonging to M. From this application, it was observed that the conditions for the Darbo fixed point theorem was satisfied. This indicated the presence of at least a fixed point for the integral equation which thereby implying the existence of solutions for the integral equation.

关键词： Volterra Integral Equation Convolution Fixed Point Existence Noncompactness

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The Homotopical Proof of Π1(S, xo) as a Fundamental Group in a General Interval

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Advances in Pure Mathematics 2021年第5期11卷 377-385页

作者： Zigli David Delali Obeng-Denteh William brew lewis Ansah Richard Kwame Department of Mathematical Sciences University of Mines and Technology Tarkwa Ghana Department of Mathematics Kwame Nkrumah University of Science and Technology Kumasi Ghana Department of Mathematics and Statistics University of Energy and Natural Resources Sunyani Ghana

The aim of this study is to establish that, the equivalent class which is made up of homotopic loops is a group with respect to in the general interval [m,n]. The study proved from homotopical point of view that is associative, has an identity and inverse function. The study established with proof that is a fundamental group in [m,n] ,.

关键词： Homotopy Fundamental Group Homeomorphism Equivalent Class Path Concatenation

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Appropriateness of Reduced Modified Three-Parameter Weibull Distribution Function for Predicting Gold Production in Ghana

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Open Journal of Statistics 2023年第4期13卷 534-566页

作者： Samuel Kwaku Obeng Christiana C. Nyarko lewis brew Kaku Sagary Nokoe Research and Statistics Unit Minerals Commission of Ghana Accra Ghana Department of Mathematics and Statistics University of Mines and Technology Tarkwa Ghana Department of Economics Catholic University of Ghana Sunyani Ghana

Forecasting mine production is pertinent to gold mining as it serves as production goals for investors. It is therefore important to identify the exact distribution that gold production as a response variable naturally follows. It is even more appropriate to have a model(s) with few predictor variables. This paper seeks to identify appropriate statistical distribution functions for fitting gold production in Ghana. The empirical paper relied mainly on quarterly secondary datasets on gold production between the years 2009 and 2022 secured from the Minerals Commission of Ghana, Accra. Several known statistical distributions including Weibull, Log-Normal, Generalized Extreme Value (GEV) were explored with Maximum Likelihood Estimation (MLE) and evaluated using model selection criteria as AIC, AICc and BIC. Goodness of Fits were evaluated using Kolmogorov-Smirnov Test (K-S), Cramer-Von Mises Statistic and Anderson-Darling Statistic. Based on the analysis conducted, the reduced modified 3-parameter Weibull distribution provided the best fit for gold production in Ghana. Though the reduced modified Weibull function is proposed, it is important however to recognize that other external factors can influence production levels. Also, the average quarterly fitted gold production is 1000334.8918 ± 75,327.080 (±7.5%) [i.e., 925,007.812 – 1,075,661.972]. This indicates that the average annually fitted gold production lies between 3700031.248 and 4302647.888 ounces at 99.9% confidence level. Therefore, the predicted gold production for the year 2022 is 3.7million ounces at 99.9% confidence level.

关键词： Gold Production Statistical Distribution Functions Goodness of Fit Statistics

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Fitness of Four-Parameter Beta Distribution Function for Forecasting Gold Reserve and Its Production Lifespan in Ghana

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Open Journal of Statistics 2023年第4期13卷 567-593页

作者： Samuel Kwaku Obeng Christiana C. Nyarko lewis brew K. Sagary Nokoe Research and Statistics Unit Minerals Commission of Ghana Accra Ghana Department of Mathematics and Statistics University of Mines and Technology Tarkwa Ghana Department of Economics Catholic University of Ghana Sunyani Ghana

Ghana, renowned for its abundant gold reserves, plays a significant role in the global mining industry. Effective management and accurate forecasting of these reserves are vital for sustainable resource utilization and economic planning. Forecasting gold reserves and estimating their production lifespan are complex tasks that require robust statistical models capable of capturing the underlying dynamics of gold deposit accumulation and extraction. To this end, the four-parameter Beta distribution function emerges as a promising candidate due to its flexibility and ability to handle non-negative data. This research aims to investigate the fitness and applicability of the four-parameter Beta distribution function for forecasting Ghana’s gold reserves and estimating the production lifespan of this precious resource. The empirical paper relied mainly on quarterly secondary datasets on gold reserve between the years 2009 and 2022 secured from the Minerals Commission of Ghana, Accra. Several known statistical distributions including Beta, Weibull, Normal, Logistic and Gamma were explored with Maximum Likelihood Estimation (MLE) and evaluated using model selection criteria as AIC and BIC. Goodness of Fits were evaluated using Kolmogorov-Smirnov Test (K-S), Cramer-Von Mises Statistic and Anderson-Darling Statistic. Based on the analysis conducted, the four-parameter Beta distribution provided the best fit for gold reserve in Ghana. At a 99.9% confidence level and considering the current annual average gold production estimate of 3,700,031.248 to 4,302,647.888 ounces, the projected lifespan of gold production in Ghana extends to the year 1,953,765. This astounding estimate suggests that the country’s gold reserves are expected to sustain production for an extended period, providing a critical resource for economic development and supporting the mining industry well into the distant future.

关键词： Gold Reserve Four-Parameter Beta Distribution Function Goodness of Fit Statistics

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