Nonzero Lie Brackets of Third Order Nonlinear Ordinary Differential Equation

Lie symmetry analysis of Ordinary Differential Equation can be used to obtain exact solution of the equation of the form F (x, y, y’ y’’ y’’’) = 0. In this paper we use Lie Symmetry analysis approach to obtain the nonzero Lie brackets of a nonlinear Ordinary Differential Equation for heat conduction. The Lie Brackets obtained forms Lie solvable algebra that can be used to reduce the equation to lower order

Mathematical Modelling of COVID-19 and Diabetes Comorbidity under Vaccination

The COVID-19 infection is a double challenge for people infected with comorbidities such as cardiovascular, cerebrovascular and diabetes. Comorbidities have been reported to be risk factors for the complications of COVID-19 infection. In most cases, people with diabetes have much higher rates of serious complications, low rate of recovery and higher mortality rate compare to people without diabetes. According to WHO data from 13 countries evaluated, revealed that 10.2% case of death of patients with and diabetes compared of 2.5% death of patients with COVID-19 only. In this paper, we formulate a mathematical model of COVID-19 and diabetes comorbidity under vaccination. This model will contribute to knowledge in mathematics, which will be used by researchers for future references and analysis

Drug and Substance Use and Its Predictors among the Youth in Nyamira Sub County, Nyamira

Substance and drug use is one of the emerging public health problems among the youth in Kenya. Moreover, it is associated with a myriad of medical effects including psychiatric problems, organ failures in addition to lethargy, decreased academic performance and risk of contracting sexually transmitted infections. Although substance and drug use has been associated with these problems, the magnitude of substance and drug use and its predictors has not been investigated in poor resource setting in rural areas of Kenya. Therefore, this study was designed to determine the prevalence of substance and drug use and identify their predictors among the youth in a poor resource setting in Nyamira Sub-County in Nyamira County. To this end this study used a cross-sectional study to evaluate the prevalence of substance and drug use and their predictors in Nyamira slums. The result of this study revealed that there were more males (60.39%) relative females (28.57%) using drugs and substances (p<0.001). A majority of study participants (94.7) had their drug and substance use debut before 20 years. Being divorced/separated/widowed (3.14, 95%CI 1.27-7.78), non-religious (70.2, 95% CI 7.28-676.83), being a Muslim (OR 3.15, 95%CI 0.61-16.31) and residing in urban area relative to rural (OR 0.84, 95%CI 0.53-1.31) were positively associated with drug and substance use. In conclusion, this study found that the prevalence of drug and substance use was high in males relative to females. The main predictors of drug and substance use included residing in urban area, being a Muslims or being non-religious and being divorced/separated or widowed. These data therefore indicated the drug and substance use was influenced by a multiplicity of factors. The results of this study would be important for Ministry of health or government or policy makers in formulating age friendly and family based intervention strategies to curb substance and drug use among the youth and increase public awareness

Two dimensional mathematical models for convective-dispersive flow of pesticides in porous media

The transport of solutes through porous media where chemicals undergo adsorption or change process on the surface of the porous materials has been a subject of research over the years. Use of pesticides has resulted in production of diverse quantity and quality for the market. Disposal of excess material has also become an acute problem. The concept of adsorption is essential in determining the movement pattern of pesticides in soil in order to assess the effect of migrating chemicals from their disposal sites on the quality of ground water. In this paper, we derive a two dimensional equation accounting for both lateral and axial pesticide flow in a porous media by convective- dispersive transport with steady state water flow. The model is derived from the first principle and solved using Alternation-Direct-Implicit (ADI) method

Lie Symmetry Analysis of Modified Diffusive Predator-prey Competition System of Equations

In this paper, a nonlinear fourth order evolution equation is investigated by the Lie symmetry analysis approach. All the geometric vector fields and the Lie groups of the evolution equation are obtained. Finally, the symmetry reduction and the exact solutions of the equation are obtained by means of power series method

Use of Infinitesimal Transformations in obtaining the Generator of a harmonic fourth order non-linear ordinary differential equation.

Lie group Theory is applied to differential equations occurring as mathematical models [4]. This paper seeks to obtain a generator T for a harmonic fourth order non-linear ordinary differential equation using the Lie Symmetry group invariant Method. This method makes use of infinitesimal transformations. The Generator T of infinitesimal transformation is then used to obtain the general solution to our harmonic differential equation. The solution to our differential equation is handy in the field of mechanics

Lie symmetry solution of fourth order nonlinear ordinary differential equation: (yy'(y(y') -1)'')'=0

, y, y, y4 0 is a one-space dimension version of wave equation. Its solutions can be classified either as analytic or numerical using finite difference approach, where the convergence of the numerical schemes depends entirely on the initial and boundary values given. In this paper, we have used Lie symmetry analysis approach to solve the wave equation given since the solution does not depend on either boundary or initial values. Thus in our search for the solution we exploited a systematic procedure of developing infinitesimal transformations, generators, prolongations (extended transformations), variational symmetries, adjoint-symmetries, integrating factors and the invariant transformations of the problem. The procedure is aimed at lowering the order of the equation from fourth to first order, which is then solved to provide its Lie symmetry solution

Numerical solution of dynamic vibration equations

In this paper, we examine conservative autonomous dynamic vibration equation, , which is time vibration of the displacement of a structure due to the internal forces, with no damping or external forcing. Numerical results using Newmark are tabulated. The stability of the algorithm employed is also discussed