Khalid Ali

In this paper, we study Hahn’s problem with respect to a Dunkl-perturbed raising operator. More precisely, we prove that, up to a dilation, the generalized Hermite polynomials are the only Tμ,α-classical symmetric orthogonal polynomials, where Tμ,α=Tμ+αtI, α∈C∖{0} and I denotes the identity operator on the space of polynomials with complex coefficients. The argument uses an operator product rule for Tμ, duality for the associated functionals, and a symmetry-enforced identification together with matching three-term recurrences. The result provides an operator-theoretic Hahn-type characterization that complements semiclassical Pearson-equation descriptions and clarifies the effect of the raising perturbation αtI.

Authors Tahir Aslam Author Khalid Ali Author Afnan Fayaz Author Anum Asif Author

It happens all the time: your customer is shopping online — and a transaction fails. Frustrated, the customer reaches out to your support team.

In this paper, we study the optimal boundary control of solidification governed by the classical two-phase Stefan problem with a sharp moving interface. The main objective is to formulate an optimal control problem for interface motion using boundary heat-flux control. The control acts as a Neumann heat flux on a designated boundary segment and steers the interface through the Stefan condition. Using an enthalpy formulation, we prove well-posedness under boundary control and establish Lipschitz continuity of the control-to-state map and continuous dependence on the initial data. We then derive first-order necessary optimality conditions using a Lagrangian approach and propose a practical algorithm that couples a semismooth Newton method with Sequential Quadratic Programming (SQP) to compute the optimal boundary flux.

We often assume that speaking is enough to be heard. But is it really that simple? What if the difficulty does not lie in the act of speaking at all? Instead, what happens to those words once they enter public discourse and how their meaning gets reconstructed rather than received? The recent debates over Maulana […]

Against this backdrop, the conference theme, Anchoring Systems in Times of Transition , served as an urgent call to rethink the sector's foundations.