Exact solutions of the Klein-Gordon equation with ring-shaped oscillator potential by using the Laplace integral transform

We present exact solutions for the Klein Gordon equation with a ring-shaped oscillator potential. The energy eigenvalues and the normalized wave functions are obtained for a particle in the presence of non-central oscillator potential. The angulm＂ functions are expressed in terms of the hypergeometric functions. The radial eigenfunetions have been obtained by using the Laplace integral transform. By means of the Laplace transform method, which is efficient and simple, the radial Klein-Gordon equation is reduced to a first-order differential equation.

Deflection of transient thermoelastic circular plate by Marchi-Zgrablich and Laplace integral transform technique

This paper deals with the determination of temperature distribution and thermal deflection function of a thin circular plate with the stated conditions. The transient heat conduction equation is solved by using Marchi-Zgrablich transform and Laplace transform simultaneously and the results of temperature distribution and thermal deflection function are obtained in terms of infinite series of Bessel function and it is solved for special case by using Mathcad 2007 software and represented graphically by using Microsoft excel 2007.

Relativistic solutions for diatomic molecules subject to pseudoharmonic oscillator in arbitrary dimensions

The exact solutions of the N-dimensional Klein–Gordon equation in the presence of an exactly solvable potential of V（r）=De（r/re-re/r）2 type have been obtained. The N dimensional Klein-Gordon equation has been reduced to a first-order differential equation via Laplace transformation. The exact bound state energy eigenvalues and corresponding wave functions for CH,H2,and HCl molecules interacting with pseudoharmonic oscillator potential in the arbitrary N dimensions have been determined. Bound state eigenfunctions used in applications related to molecular spectroscopy are obtained in terms of confluent hypergeometric functions.

Identifying Malaria Hotspots Regions in Ghana Using Bayesian Spatial and Spatiotemporal Models

Background:Malaria remains a significant public health concern in Ghana,with varying risk levels across different geographical areas.Malaria affects millions of people each year and imposes a substantial burden on the health care system and population.Accurate risk estimation and mapping are crucial for effectively allocating resources and implementing targeted interventions to identify regions with disease hotspots.This study aimed to identify regions exhibiting elevated malaria risk so that public health interventions can be implemented,and to identify malaria risk predictors that can be controlled as part of public health interventions for malaria control.Methods:The data on laboratory-confirmed malaria cases from 2015 to 2021 were obtained from the Ghana Health Service and Ghana Statistical Service.We studied the spatial and spatiotemporal patterns of the relative risk of malaria using Bayesian spatial and spatiotemporal models.The malaria risk for each region was mapped to visually identify regions with malaria hotspots.Clustering and heterogeneity of disease risks were established using correlated and uncorrelated structures via the conditional autoregressive and Gaussian models,respectively.Parameter estimates from the marginal posterior distribution were estimated within the Integrated Nested Laplace Approximation using the R software.Results:The spatial model indicated an increased risk of malaria in the North East,Bono East,Ahafo,Central,Upper West,Brong Ahafo,Ashanti,and Eastern regions.The spatiotemporal model results highlighted an elevated malaria risk in the North East,Upper West,Upper East,Savannah,Bono East,Central,Bono,and Ahafo regions.Both spatial and spatiotemporal models identified the North East,Upper West,Bono East,Central,and Ahafo Regions as hotspots for malaria risk.Substantial variations in risk were evident across regions(H=104.9,P<0.001).Although climatic and economic factors influenced malaria infection,statistical significance was not established.Conclusions:Malaria risk was clustered and varied among regions in Ghana.There are many regions in Ghana that are hotspots for malaria risk,and climate and economic factors have no significant influence on malaria risk.This study could provide information on malaria transmission patterns in Ghana,and contribute to enhance the effectiveness of malaria control strategies.

Deviation inequalities for quadratic Wiener functionals and moderate deviations for parameter estimators

We study deviation inequalities for some quadratic Wiener functionals and moderate deviations for parameter estimators in a linear stochastic differential equation model.Firstly,we give some estimates for Laplace integrals of the quadratic Wiener functionals by calculating the eigenvalues of the associated HilbertSchmidt operators.Then applying the estimates,we establish deviation inequalities for the quadratic functionals and moderate deviation principles for the parameter estimators.