The aim of this paper is to show the global existence of weak solutions for a moving boundary problem arising in the non-isothermal crystallization of polymers. The main features of our works are (i) the moving interface is shown to be of co-dimension one; (ii)finite Hölder continuous propagation speed yields an intrinsic estimate of finite co-dimension one Hausdorff measure of the moving inter...

BACKGROUND Treatment continuity is a major challenge in the long-term management of patients with schizophrenia; poor patient adherence to antipsychotic drugs has been associated with negative clinical outcomes. Long-acting injectable therapies may improve adherence and lessen the risk for psychiatric-related relapse, often leading to rehospitalization and higher healthcare costs. Therefore, un...

The continuity equation relating the change in time of the position probability density to the gradient of the probability current density is generalized to PT-symmetric quantum mechanics. The normalization condition of eigenfunctions is modified in accordance with this new conservation law and illustrated with some detailed examples. Running head: Generalized Continuity Equation E-mail: bbagch...

The notion of continuity from above (upper continuity) for lattice-valued possibilistic measures as investigated in [7] has been proved to be a rather strong condition when imposed as demand on such a measure. Hence, our aim will be to introduce some versions of this upper continuity weakened in the sense that the conditions imposed in [7] to the whole definition domain of the possibilistic mea...

We prove two relative local variational principles of topological pressure functions P (T,F ,U , y) and P (T,F ,U|Y ) for a given factor map π, an open cover U and a subadditive sequence of real-valued continuous functions F . By proving the upper semi-continuity and affinity of the entropy maps h{·}(T,U | Y ) and h+{·}(T,U | Y ) on the space of all invariant Borel probability measures, we show...

Measuring and managing risk has become crucial in modern decision making under stochastic uncertainty. In two-stage stochastic programming, mean risk models are essentially defined by a parametric recourse problem and a quantification of risk. From the perspective of qualitative robustness theory, we discuss sufficient conditions for continuity of the resulting objective functions with respect ...