Averaging principle for stochastic differential equations under a weak condition.

The aim of this paper is to establish the averaging principle for stochastic differential equations under a general averaging condition, which is weaker than the traditional case. Under this condition, we establish an effective approximation for the solution of stochastic differential equations in mean square.

Sustainable management of predatory fish affected by an Allee effect through marine protected areas and taxation.

Ecological balance and stable economic development are crucial for the fishery. This study proposes a predator-prey system for marine communities, where the growth of predators follows the Allee effect and takes into account the rapid fluctuations in resource prices caused by supply and demand. The system predicts the existence of catastrophic equilibrium, which may lead to the extinction of prey, consequently leading to the extinction of predators, but fishing efforts remain high. Marine protected areas are established near fishing areas to avoid such situations. Fish migrate rapidly between these two areas and are only harvested in the nonprotected areas. A three-dimensional simplified model is derived by applying variable aggregation to describe the variation of global variables on a slow time scale. To seek conditions to avoid species extinction and maintain sustainable fishing activities, the existence of positive equilibrium points and their local stability are explored based on the simplified model. Moreover, the long-term impact of establishing marine protected areas and levying taxes based on unit catch on fishery dynamics is studied, and the optimal tax policy is obtained by applying Pontryagin's maximum principle. The theoretical analysis and numerical examples of this study demonstrate the comprehensive effectiveness of increasing the proportion of marine protected areas and controlling taxes on the sustainable development of fishery.

Chemical profiling and arginine kinase inhibitory activity of Angelica dahurica leaves.

Angelica dahurica is a medicinal herb of the Umbelliferae family. The dried root of A. dahurica, also known as Angelicae dahuricae Radix, is widely used in clinical treatment. However, the aboveground part of A. dahurica which accounted for over 70% of the total plant was abandoned in the field. In order to develop the value of the aboveground part of A. dahurica, the chemical constituents and arginine kinase (AK) inhibitory activity of A. dahurica leaves were studied. 85 volatile components were identified from A. dahurica leaves by GC-MS; 39 non-volatile components including sugars, amino acids and organic acids were identified by pre-column derivatization GC-MS analysis; and 7 coumarins were qualitatively and quantitatively analyzed by HPLC. Then, an inhibitory enzyme-linked immunosorbent assay (iEIA) was applied for evaluation of AK inhibitory activity. The extracts of A. dahurica leaves exhibited well inhibitory effects on AK. Further, potential AK inhibitors were screened by grey relational analysis and their inhibitory activities were validated by iEIA. l-aspartic acid exhibited strongest inhibitory effect on AK with its IC50 value was 0.558 mM, which was much lower than that of chlorpheniramine (6.644 mM). The obtained chemical profiles displayed chemical diversity of A. dahurica leaves and will provide data support for the future development and utilization of A. dahurica leaves. The screened potential AK inhibitors from A. dahurica leaves could be candidates for development of antiallergic substances or insecticides.