Advances in Modelling and Analysis A

Medhat A. Rakha

On the root systems of the classical & exceptional Lie algebras Mathematica programs

关于经典与例外李代数的根系系统的Mathematica程序

Medha Ahmed Rahka

On the graphical representation of semisimple lie algebra

关于半单李代数的图形表示

The relationship of foreign trade and forest degradation is an important research topic in trade and environment.Based on dynamic optimal control method, the interrelation of forest resources' stock dynamic and foreign trade, market power and foreign debt or asset, is exploited.At the same time, the condition and change law of forest degradation is analyzed.Pontryagin Maximum Principle demonstrate a character which if shadow social price of forest resource has a higher price than, demand of forest resource exceed the supply, forest resource decreases, hence lead to forest degradation, even extinction.Some conditions are satisfied, the stock of forest resource and trade terms change in the same direction, and the stock of forest resources and market power varied in same direction.Existing foreign debts, and the international capital market, stock of forest resources will not be dried up.

Xuxia Deng

Huimin Chen

Yunbao Xu

Foreign Trade and Forest Resource Dynamic

对外贸易与森林资源动态

Received: 10 April 2021 Accepted: 12 August 2021 The impact of suction/injection on the doubly stratified Newtonian fluid flow along an inclined stretching surface through a porous medium with heat and mass flux conditions is investigated. Also, linear Boussinesq approximation is considered in this work to relate the transport phenomena of temperature and concentration in various thermal and solutal systems operated at moderate temperatures. The system of governing non-linear equations is changed to its dimensionless form using suitable transformation variables. The dimensionless non-linear ordinary differential equation system is linearized by local linearization approach and then the obtained linear equation system is dealt with Chebyshev collocation method. The illustrating analyses for the impact of the various physical parameters involved in the present study are provided and salient features are also discussed. The comparative studies of dimensionless skin friction coefficient, Nusselt number and Sherwood number are given with various set of values of various important parameters.

Ram Reddy Chetteti

Abhinava Srivastav

AMA_A

Double Stratification in the Flow of a Newtonian Fluid Along an Inclined Permeable Stretching Surface

沿倾斜渗透拉伸表面的牛顿流体流动中的双重分层

In present study, solution of advection-dispersion equation is obtained to determine concentration distribution of solute introduced from a varying pulse type point source in one-dimensional heterogeneous semi-infinite porous medium. Heterogeneity of the medium gives rise to space dependent groundwater velocity, dispersion coefficient and retardation factor. Groundwater velocity is some exponent ξ to a linear function of space. The dispersion and retardation factor are also exponents of same linear function with exponents (ξ+1) and (ξ-1), respectively, where ξ takes the value 0 or 1. At one end of the domain, a time dependent varying nature source, which involves step-size increasing function of time, acts along the flow up to a certain time the n eliminated while concentration gradient is considered zero at the other end of the domain. Initially, medium is uniformly polluted. Firstly, the advection-dispersion equation is reduced into constant coefficients by using certain transformations and then Laplace Integral Transformation Technique is utilized to get the solution. The obtained result is illustrated with numerical examples to study the effect of various parameters.

Raja Ram Yadav

Joy Roy

An Analytical Solution of Spatially Dependent One-Dimensional Advection-Dispersion Equation for a Varying Pulse Type Input Source

变脉冲输入源下空间相关的一维对流-弥散方程的解析解

The bottom layer of a group is a set of its elements of prime order. A group is called recognizable by bottom layer under additional conditions if it is uniquely restored by bottom layer under these conditions. A group is called almost recognizable by bottom layer under additional conditions, if there are a finite number of pairwise non-isomorphic groups satisfying these conditions, with bottom layer that is the same as that of the group. A group is called unrecognizable by bottom layer under additional conditions if there are an infinite number of pairwise non-isomorphic groups satisfying these conditions, with bottom layer that is the same as that of the group. In the paper we consider examples of groups recognized by bottom layer, by spectrum and, simultaneously, by spectrum and by bottom layer. We have also proved some results of recognizability of groups by bottom layer.

Vladimir Senashov

Ivan Parashchuk

On Recognizability of Groups by Bottom Layer

关于通过底层识别群的可识别性

This study aims to determine the relationship between the chemical compositions of twenty-five (25) soft drinks sold in Nigeria. Sample concentration of twenty-five (25) soft drinks used in the study was collected from the National Agency for Food and Drug Administration and Control (NAFDAC). Principal Component Analysis (PCA) was employed to explain the relationship between the chemical compositions and determine the soft drinks' chemical composition distribution. The result has shown that all except acidity and antioxidant has a significantly strong positive relationship among the chemical structures. PCA suggested retaining three components that explained about 82.465 per cent of the data set's total variability. It was observed that carbonated water, fructose, sucrose, main concentration, stabiliser, E412, colouring and gelatin were the major compositions of the soft drinks in Nigeria, Base on the findings in this study, it is recommendations that; Consumers who are allergic to sugar or diabetic should avoid taking any of the soft drinks with high sugar concentration. Soft drinks companies producing drinks with high sugar content should consider their customers who are diabetic and allergic to high sugar levels.

Samuel Olorunfemi Adams

Rafiu Olayinka Akano

Rauf Ibrahim Rauf

An Evaluation of the Chemical Composition of Soft Drinks in Nigeria: A Principal Component Analysis Approach

尼日利亚软饮料化学成分的评估：主成分分析方法

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Advances in Modelling and Analysis A

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On the root systems of the classical & exceptional Lie algebras Mathematica programs

On the graphical representation of semisimple lie algebra

On the root systems of the classical & exceptional Lie algebras Mathematica programs

On the graphical representation of semisimple lie algebra

On the root systems of the classical & exceptional Lie algebras Mathematica programs

Foreign Trade and Forest Resource Dynamic

Double Stratification in the Flow of a Newtonian Fluid Along an Inclined Permeable Stretching Surface

An Analytical Solution of Spatially Dependent One-Dimensional Advection-Dispersion Equation for a Varying Pulse Type Input Source

On Recognizability of Groups by Bottom Layer

An Evaluation of the Chemical Composition of Soft Drinks in Nigeria: A Principal Component Analysis Approach