Authors:Samet Maldar, Vatan Karakaya Abstract: The aim of this article is to define a new Jungck-Kirk typeiteration method and to examine the convergence result under appropriateconditions together with other Jungck-Kirk type iteration methods in theliterature. It is also to analyze whether the newly defined iteration methodis stable. In addition, it has been shown through numerical examples thatthe new iteration method has a better convergence rate than the others.Finally, to show the validity of convergence and stability results, someexamples are given. The results obtained in this paper may be interpretedas a refinement and improvement of the previously known results PubDate: 2022-03-30 Issue No:Vol. 53 (2022)
Authors:Fareeha Sami Khan, M. Khalid Abstract: The fundamental idea of this work is to modify Descemet’sStripping Endothelial Keratoplasty DSEK mathematical model by incorporating the Zernike polynomial to examine Higher Order Aberrations(HOA). This model has been developed in a way that can identify the typeof aberration occurring after a keratoplasty. Model variables are comparedwith the data available in already published literature. Surgicallyinduced Higher Order Aberrations (HOA) and change in corneal powerare the main outcome measures. Eye illness and their treatments havealways been an interesting topic of discussion for researchers. Mechanicaland software engineers have managed to helped ophthalmologists bydeveloping advanced machines that can identify the patients’ complaintsin seconds. Moreover, several new and advanced surgical procedures havebeen adopted for eye problems. One amongst them is eye aberration. Onlyrecently has it become possible to detect one type of aberration (Astigmatism& Higher Order Aberrations) with special equipments. However, it isstill not easy to identify aberrations as Myopia and Hyperopia. This paperstudies the induced eye aberrations caused by DSEK and their detectionthrough a modified DSEK model. PubDate: 2022-03-30 Issue No:Vol. 53 (2022)
Authors:Saima Mustafa, Shumaila Naheed, Hina Basharat Abstract: There are number of inference techniques that can be usedfor the estimation of the unknown parameters which are based on precisecrisp data, but there are many situations where we deal with impreciseand vague data. In this situation the classical mathematical tools cannothelp us to estimate the parameters. This impreciseness can be covered byintroducing fuzzy concepts. This study deals with the maximum likelihoodestimation for the parameters of Rayleigh distribution using NewtonRaphson algorithm. A real-life data set analysis is presented by consideringset of luminous intensity of light emitting diodes and finding of thisstudy illustrates that proposed inferential technique is useful to deal withfuzziness of data when statistical inference of Rayleigh distribution is carriedout for imprecise or fuzzy data. PubDate: 2022-03-30 Issue No:Vol. 53 (2022)
Authors:Afaq Ahmad, Aijaz Ahmad, Gamze Ozel Abstract: The discretization of continuous distributions among researchersbecome important issue, so several discretization methods exists in the literature for obtaining discrete version of continuous distribution which canbe pragmatic to discrete data. The present study proposes the discretizationof continuous Ailamujia distribution. Subsequently various statisticalproperties has been studied including moment generating function, characteristic function, mode, reliability, probability generating function etc.Nature of density function and hazard function has been studied graphically.The technique of maximum likelihood estimation is used to estimatethe unknown parameter of the said model. Biodiversity and abundancedata applications are provided to flexibility and applicability of the newdistribution in ecological studies. PubDate: 2022-03-30 Issue No:Vol. 53 (2022)
Authors:Dnyanoba B. Dhaigude, Vidya N. Bhadgaonkar Abstract: The paper aims to obtain exact analytical solution of nonlinear nonhomogeneous space-time fractional order partial differential equationsin Gas dynamics model, Advection model,Wave model and Klein-Gordonmodel by improved Adomian decomposition method coupled with fractionalTaylor expansion series.The solution of these equations are in seriesform may have rapid convergence to a closed-form solution. The effectivenessand sharpness of this method is shown by obtaining the exactsolution of these equations with suitable initial conditions(ICs). With thehelp of this method, it is possible to investigate nature of solutions whenwe vary order of the fractional derivative. Behaviour of the solution ofthese equations are represented by graphs using MATHEMATICA software. PubDate: 2022-03-30 Issue No:Vol. 53 (2022)
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