Dynamics of a Quadratic Rational Delay Difference Equation| Chapter 10 | Research Updates in Mathematics and Computer Science Vol. 8

 

The study makes a significant contribution to the theoretical understanding of nonlinear difference equations, a class of recursive equations with wide applications in fields like population dynamics and economics. In [1] E. Tasdemir, et al. proved that the positive equilibrium of the nonlinear discrete equation \(x_n+1=1+p\left(\frac{x_{n-m}}{x_n^2} \right)\) is globally asymptotically stable for \(p \in \left(0, \frac{1}{2} \right)\), locally asymptotically stable for \(p \in (\frac{1}{2},\frac{3}{4}\)) and it was conjectured that for any p in the open interval (\(\frac{1}{2},\frac{3}{4}\)) the equilibrium is globally asymptotically stable. In this paper, we prove that this conjecture is true for the closed interval [\(\frac{1}{2},\frac{3}{4}\)]. In addition, it is shown that for \(p \in (\frac{3}{4}, 1\)) the behaviour of the solutions depend on the delay m. Indeed, here we show that in case m = 1, there is an unstable equilibrium and an asymptotically stable 2-periodic solution. But, in case m = 2, there is an asymptotically stable equilibrium. These results are obtained by using linearisation, a method lying on the well known Perron's stability theorem. Finally, a conjecture is posed about the behaviour of the solutions for m > 2 and \(p \in (\frac{3}{4}, 1\)). The advanced analytical methods employed showcase techniques that can guide future research and developments in the field.

 

 

Author(s) Details

 

George L. Karakostas

Department of Mathematics, University of Ioannina, Ioannina 45110, Greece.

 

Please see the book here:- https://doi.org/10.9734/bpi/rumcs/v8/3698G

Stability of Equilibria of Stochastically Perturbed Nonlinear Mathematical Models| Chapter 5 | Research Highlights in Mathematics and Computer Science Vol. 1

 The Smooth winged Sharpshooter's realized nonlinear numerical model is thought about. This model is believed to be impacted by stochastic bothers of the background noise, and these irritations are believed to be precisely corresponding to the framework state's deviation from the positive harmony. We get a vital and adequate condition for the harmony of the straight part of the nonlinear stochastic differential condition viable to have asympt-otic mean square steadiness. This need is likewise an adequate one for the likelihood based strength of the harmony of the underlying nonlinear condition. The outcomes are displayed in mathematical calculations and figures. It is noticed that the motivation behind this exploration isn't to concentrate on the solidness of a specific model. The proposed technique for strength examination can be applied to concentrate on steadiness of numerous other nonlinear conditions and frameworks of nonlinear conditions under stochastic annoyances.

Author(s) Details:

Leonid Shaikhet,
Department of Mathematics, Ariel University, Ariel 40700, Israel.

Please see the link here: https://stm.bookpi.org/RHMCS-V1/article/view/8244

Association between Human Genome with Clinical Outcome | Chapter 8 | Innovations in Microbiology and Biotechnology Vol. 6

There have been many fascinating new innovations in genetics as a result of the successes of the Human Genome Project and subsequent advances in genotyping. The genetics field has been compelled to consider on a genome-wide scale by genome-wide association studies, which have discovered novel genetic risk factors for many prevalent human illnesses. Looking ahead, it is clear that the present advances in genome-wide association studies will alter when new methods for identifying genetic susceptibilities that result in features specific to a familial trait are developed. Since the human genome is now able to provide complete and accurate information data that allows access to specific DNA groupings to analyse clinical queries, innovation has given researchers a comprehensive understanding of human genomes. The methods used to examine the use of genome-wide association studies with population-based legal analyses have been improved. Related techniques from genome wide association studies have also been incorporated into standard therapeutic practise.

Author(s) Details:

Zahid Balouch,
Biochemistry Department, College of Medicine, University of Ha’il, Saudi Arabia.

Fahmida Khatoon,
Biochemistry Department, College of Medicine, University of Ha’il, Saudi Arabia and United Medical College, Jinnah University, Pakistan.

Rana Aboras,
Community Medicine Depertment, Hail University, Saudi Arabia.

Amal Daher Alshammari,
Community Medicine Depertment, Hail University, Saudi Arabia.

Please see the link here: https://stm.bookpi.org/IMB-V6/article/view/7248

Thought Experiment Cement Industry Demand Fluctuations: Supporting John M. Clark's Workable Competition Pricing | Chapter 08 |New Innovations in Economics, Business and Management Vol. 7

 The purpose of this research is to compare numerical results for a hypothetical numerical model of a cement industry facing demand fluctuations, high versus low, with alternate technologies, high fixed cost versus low fixed cost, using marginal cost pricing versus John M. Clark's workable competition pricing, using marginal cost pricing versus John M. Clark's workable competition pricing. The article is an economics thought experiment that is only carried out in the mind. The article presents a detailed numerical model of a basic industry, cement manufacturing, with a large number of sellers, cement factories, and large numbers of buyers, the construction industry, all of whom work independently and are fully aware of supply and demand conditions. The model's cement plants have linear total cost functions and absolute capacity constraints. The article contrasts two technologies: 1) old plants with low fixed costs but high marginal costs, and 2) new plants with high fixed costs but low marginal costs. This study argues in favour of John M. Clark's (1884-1963) practicable competition theory, which is opposed to marginal cost competition theory. The study investigates the likely equilibrium conditions under two pricing systems: A) short-run marginal cost pricing and B) John M. Clark's practical competition concept. Workable competition raises prices above marginal costs in the off-peak period, but lowers prices in the peak period. The study assumes a 6/7 off period and 1/7 peak period frequency. Workable competition pricing, according to the paper, increases consumer surplus over time under the model's assumptions. Under the model's assumptions, the study claims that gains in consumer surplus from workable competition pricing in high-demand periods, though infrequent (1/7), will outweigh losses in consumer surplus from workable competition pricing in low-demand periods, which are more frequent (6/7).

Author(S) Details

Gerald Aranoff
Ariel University, Ariel 40700 Israel.

View Book:- https://stm.bookpi.org/NIEBM-V7/article/view/6393

Study on the Adsorption of Pb, Zn, Cu, Ni, and Cd by Modified Ligand in a Single Component Aqueous Solution: Equilibrium, Kinetic, Thermodynamic, and Desorption Studies | Chapter 1 | Current Research and Development in Chemistry Vol. 4

 

In this investigation, an amino functionalized adsorbent was developed by grafting 4-aminobenzoic acid onto the backbone of cross-linked chitosan beads. FTIR, XRD , SEM, and TGA were characterised by 3 sets of beads including chitosan (CX), glutaraldehyde cross-linked chitosan (CCX) and 4-aminobenzoic acid grafted cross-linked chitosan (FGCX). The content of water and the amine concentration of FGCX have been calculated. For further research , the effect of adsorption parameters was studied and the optimum was used. Equilibrium data were obtained at different initial concentrations from the adsorption experiment; the data were used in isothermal, thermodynamic and kinetic studies. The models Langmuir and Dubinin-Kaganer-Radushkevich (DKR) were effective in Definition of isothermal data for the metal ions considered, whereas some of the metal ions considered are equipped by the Freundlich and Temkin model. The kinetic data was represented very well by the pseudo-second - order and intra-particle model. Thermodynamic parameters such as the free energy change of Gibb (almost °), the change in enthalpy (almost °) and the change in entropy (almost °) have been measured and the results indicate that the adsorption of Pb, Cu, Ni , Zn, and Cd ions into FGCX is spontaneous and endothermic. For the metal ions considered, regeneration of the spent adsorbent was effective.

Author (s) Details

Dr. E. Igberase
Department of Chemical Engineering, Vaal University of Technology, Private Mail Bag X021, Vanderbijlpark 1900, South Africa.

Prof. P. Osifo
Department of Chemical Engineering, Vaal University of Technology, Private Mail Bag X021, Vanderbijlpark 1900, South Africa.

A. Ofomaja
Department of Chemical Engineering, Vaal University of Technology, Private Mail Bag X021, Vanderbijlpark 1900, South Africa.

View Book :- https://bp.bookpi.org/index.php/bpi/catalog/book/282