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The aim of this paper is to determine the behavior and statistical properties of non-relativistic heavy quarkonia interacting with the extended Cornel potential within a space-time generated by a cosmic-string. We extend the cornel potential by adding the inverse square potential plus the quadratic potential. We have calculated the energy eigenvalues and the corresponding eigenstates using the extended Nikiforov-Uvarov (NU) method. Then the thermodynamic properties like partition function, entropy, free energy, mean energy and specific heat capacity are calculated within the space-time of a cosmic-string. In the next step, we investigate the influence of the cosmic-string parameter on quantum states of heavy quarkonia and their statistical properties.

The Bohr Hamiltonian with multiparameter exponential-type potential for the \( \beta\)-part and a harmonic oscillator for the \( \gamma\)-part is solved. The \( \beta\)-part has been solved using the Nikoforov-Uvarov method. The wave function and energy expression has been derived. The electric quadrupole transition rates are evaluated. The numerical results for energy spectra and B(E2)’s are compared to the experimental data of 192, 194, 196Pt atomic nuclei and there is an overall good agreement.

We present a closed-form analytical solution for the advection–diffusion equation, where the planetary boundary layer is divided into subdomains, where in each subdomain averaged values of eddy diffusivity and wind speed are assumed. The solution procedure combines an appropriate auxiliary eigenvalue problem with mathematical induction. A transcendental equation giving the eigenvalues for any numbers of subdomains is also developed. Convergence of the solution is numerically verified. The solution is used to evaluate the model against the Copenhagen experiment and computed results are in agreement with experimental ones.