The Stochastic Solution to a Cauchy Problem for Degenerate Parabolic Equations

We study the stochastic solution to a Cauchy problem for a degenerate parabolic equation arising from option pricing. When the diffusion coefficient of the underlying price process is locally H\"older continuous with exponent $\delta\in (0, 1]$, the stochastic solution, which represents the price of a European option, is shown to be a classical solution to the Cauchy problem. This improves the standard requirement $\delta\ge 1/2$. Uniqueness results, including a Feynman-Kac formula and a comparison theorem, are established without assuming the usual linear growth condition on the diffusion coefficient. When the stochastic solution is not smooth, it is characterized as the limit of an approximating smooth stochastic solutions. In deriving the main results, we discover a new, probabilistic proof of Kotani's criterion for martingality of a one-dimensional diffusion in natural scale.Comment: Keywords: local martingales, local stochastic solutions, degenerate Cauchy problems, Feynman-Kac formula, necessary and sufficient condition for uniqueness, comparison principl

Risk of aquaculture-derived microplastics in aquaculture areas: An overlooked issue or a non-issue?

Plastic equipment such as fishing nets and foam buoys has been widely used in aquaculture. This kind of equipment would gradually decompose while being subject to the long-term effects of physical, chemical, and biological degradation processes, leading to the release of large amounts of microplastics (MPs) into the local marine environment and the generation of aquaculture-derived MPs (AD-MPs). The rapid growth of aquaculture has resulted in an explosion of AD-MPs with various environmental consequences. The accumulation of MPs in aquatic products was found closely related to the abundance of environmental MPs, suggesting the importance of determining whether AD-MPs increase the risk of MP ingestion by aquatic products and thus endanger aquatic food safety. In this short communication, the ecological and health risks of AD-MPs were discussed and perspectives were proposed for future studies

Technological Innovation or Educational Evolution? A Multi-disciplinary Qualitative Inquiry into Active Learning Classrooms

In recent years, many institutions have transformed traditional classrooms (TCs) into technology-rich active learning classrooms (ALCs) to accommodate the pedagogical concept of “active learning”. In order to investigate the impact of ALCs on teaching and teaching, we observed an instructor teaching in an ALC for an entire academic year, audio/video-recorded every class and took field notes. A focus group discussion was conducted with faculty from six allied health disciplines who taught weekly classes in the ALC and an online survey was distributed to students who took those classes. Data was then analysed using a qualitative constant comparative method (CCM). Findings indicated that the ALC generated greater teaching and learning enjoyment, deepened engagement, amplified interaction, enhanced group activity efficiency and fostered the development of creative ideas.  All these features were interrelated and created a synergistic effect on student learning

Structural and electronic origin of the magnetic structures in hexagonal LuFeO3_3

Using combined theoretical and experimental approaches, we studied the structural and electronic origin of the magnetic structure in hexagonal LuFeO$_3$. Besides showing the strong exchange coupling that is consistent with the high magnetic ordering temperature, the previously observed spin reorientation transition is explained by the theoretically calculated magnetic phase diagram. The structural origin of this spin reorientation that is responsible for the appearance of spontaneous magnetization, is identified by theory and verified by x-ray diffraction and absorption experiments.Comment: 5 pages, 2 tables and 4 figures, Please contact us for the supplementary material. Accepted in Phys. Rev. B, in productio

Sodium lactobionate sucrose solution for canine liver and kidney preservation.

With 24-hour preservation of canine liver, SLS solution showed inferior animal survival to UW solution. The lactobionate, raffinose, glutathione, and hydroxyethyl starch in UW solution have been shown to be important for liver preservation. However, our results suggest that sucrose should not be substituted for raffinose for the preservation of livers. In contrast to the liver, SLS solution performed the same or even better than UW solution for kidney preservation. The substitution of sucrose for raffinose, along with the addition of CPZ has either no effect or a slightly positive effect on kidney preservation. In conclusion, SLS solution may be a suitable solution for preserving canine kidneys, but is not suitable for liver preservation. These findings suggest that future development of preservation solutions should be focused on the needs of specific organs and not toward a generic, all encompassing preservation solution