Gagliardo-Nirenberg Inequality as a Consequence of Pointwise Estimates for the Functions in Terms of Riesz Potential of Gradient
Sudheer Khan,
Wang Shu,
Monica Abhidha
Issue:
Volume 8, Issue 5, October 2020
Pages:
53-58
Received:
1 July 2020
Accepted:
16 July 2020
Published:
21 September 2020
Abstract: Our aim in this study is to give the Gagliardo-Nirenberg Inequality as a consequence of pointwise estimates for the function in terms of the Riesz potential of the gradient. Our aim here is to discuss boundedness of Reisz potential in term of maximal functions and to give the proof for Gagliardo-Nirenberg Inequality in term of Reisz potential. We will extend our result to discuss weak type estimate for Gagliaro-Nirenberg Sobolev inequality. Further, in this paper we are interested to extract Sobolev type inequality in terms of Riesz potentials for α is equal to one and to extend our work for weak type estimates when p is equal to one.
Abstract: Our aim in this study is to give the Gagliardo-Nirenberg Inequality as a consequence of pointwise estimates for the function in terms of the Riesz potential of the gradient. Our aim here is to discuss boundedness of Reisz potential in term of maximal functions and to give the proof for Gagliardo-Nirenberg Inequality in term of Reisz potential. We w...
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Analysis of Diet Choice towards a Proper Nutrition Plan by Linear Programming
Tanzila Yeasmin Nilu,
Shek Ahmed,
Hashnayne Ahmed
Issue:
Volume 8, Issue 5, October 2020
Pages:
59-66
Received:
9 August 2020
Accepted:
25 August 2020
Published:
21 September 2020
Abstract: Linear Programming is an optimization technique to attain the most effective outcome or optimize the objective function (like maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships called the constraints. In this paper, we have discussed fundamental and detailed techniques of formulating LPs models in various real-life decision problems, decisions, works, etc. In the human body, an unhealthy diet can cause a lot of nutrition-related diseases. Sometimes, having a proper diet costs beyond one’s limit and it affects us to develop a diet based budget-friendly nutrition model. Our goal is to minimize the total cost considering the required amount of nutrition values required. To construct the study we took some standard values of nutrition ingredients to compute the budget-friendly values. It's quite hard to resolve most of the real-life models with a large number of decision variables & constraints by hand calculations implies the use of AMPL (A Mathematical Programming Language) coding to get the optimal result. The number of variables & constraints isn't mattered in any respect for the computer techniques used in this study. This study results in some standard values of diet plan for optimizing the nutrition for a particular person with limited costs.
Abstract: Linear Programming is an optimization technique to attain the most effective outcome or optimize the objective function (like maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships called the constraints. In this paper, we have discussed fundamental and detailed techniques of formulating LP...
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Modeling and Predicting Corona Contagion Dynamics in China, USA, Brazil & Ethiopia
Thomas Wetere Tulu,
Ieng Tak Leong,
Zunyou Wu
Issue:
Volume 8, Issue 5, October 2020
Pages:
67-72
Received:
13 August 2020
Accepted:
8 September 2020
Published:
28 September 2020
Abstract: The COVID-19 pandemic is a global pandemic of coronavirus disease 2019, caused by severe acute respiratory syndrome coronavirus 2 (SARS CoV 2). The outbreak was first identified in Wuhan, China, in December 2019. In this article, we investigate the problem of modelling the trend of the current Coronavirus disease 2019 pandemic in China, USA, Ethiopia and Brazil along time. Two different models were developed using Bayesian Markov chain Monte Carlo simulation methods. The models fitted included Poisson autoregressive as a function of a short-term dependence only and Poisson autoregressive as a function of both a short-term dependence and a long-term dependence. The models can be employed to understand the contagion dynamics of the COVID-19, which can heavily impact health, economy and finance. The result indicates whether disease has an upward/downward trend, and where about every country is on that trend, all of which can help the public decision-makers to better plan health policy interventions and take the appropriate actions to control the spreading of the virus.
Abstract: The COVID-19 pandemic is a global pandemic of coronavirus disease 2019, caused by severe acute respiratory syndrome coronavirus 2 (SARS CoV 2). The outbreak was first identified in Wuhan, China, in December 2019. In this article, we investigate the problem of modelling the trend of the current Coronavirus disease 2019 pandemic in China, USA, Ethiop...
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