The suppression of ferroelectricity in ultrathin films improper ferroelectric hexagonal ferrites or manganites has been attributed to the effect interfacial clamping, however, quantitative understanding and related phenomenological model are still lacking. In this work, we report paraelectric-to-ferroelectric phase transition epitaxial h-ScFeO3 with different thickness through in-situ reflectio...

t wt |φt 〉〈φt | represents a system which, with probability wj , is “really in” one or another of the pure states |φj 〉. In quantum mechanics, mixtures are thought to arise in two ways — as a direct mixing of distinct pure-state preparations, and “improperly” (d’Espagnat’s term), as the reduction of a pure-state composite system to the state of a component system by tracing out the other compon...

Reproducibility of biological data is a significant problem in research today. One potential contributor to this, which has received little attention, is the over complication of enzyme kinetic inhibition models. The over complication of inhibitory models stems from the common use of the inhibitory term (1 + [I]/Ki ), an equilibrium binding term that does not distinguish between inhibitor bindi...

In the paper, the author presents explicit and unified expressions for a sequence of improper integrals in terms of the beta functions and the Wallis ratios. Hereafter, the author derives integral representations for the Catalan numbers originating from combinatorics.