Ilex asprella, a plant widely used as a folk herbal drug in southern China, produces and stores a large amount of triterpenoid saponins, most of which are of the α-amyrin type. In this study, two oxidosqualene cyclase (OSC) cDNAs, IaAS1 and IaAS2, were cloned from the I. asprella root. Functional characterisation was performed by heterologous expression in the yeast Saccharomyces cerevisiae. Analysis of the resulting products by gas chromatography (GC) and gas chromatography-mass spectrometry (GC-MS) showed that both genes encode a mixed amyrin synthase, producing α-amyrin and β-amyrin at different ratios. IaAS1, which mainly produces α-amyrin, is the second triterpene synthase so far identified in which the level of α-amyrin produced is ≥80% of total amyrin production. By contrast, IaAS2 mainly synthesises β-amyrin, with a yield of 95%. Gene expression patterns of these two amyrin synthases in roots and leaves of I. asprella were found to be consistent with the content patterns of total saponins. Finally, phylogenetic analysis and multiple sequence alignment of the two amyrin synthases against several known OSCs from other plants were conducted to further elucidate their evolutionary relationship.

By using the fixed point index theorem, this paper investigates a class of singular semipositone integral boundary value problem for fractionalq-derivatives equations and obtains sufficient conditions for the existence of at least two and at least three positive solutions. Further, an example is given to illustrate the applications of our main results.

By using the fixed-point theorem of Leray-Schauder or Banach, we discuss the existence of solutions for third-order impulsive neutral differential equations with deviating arguments. Two examples are given to demonstrate our main results.

In this paper, we study the existence of solutions for third order impulsive functional differential inclusions with multiplier p(t). Two new results are obtained by suitable fixed point theorem combined with multivalued analysis theory. Вивчається питання iснування розв'язкiв для функцiонально-диференцiальних включень третього порядку з iмпульсною дiєю та мультиплiкатором p(t). Отримано два нових результати за допомогою придатної теореми про нерухому точку та результатiв з аналiзу багатозначних функцiй.

Abstract. We develop the impulsive inequality and the classical lower and upper solutions, and establish the comparison principles. By using these results and the monotone iterative technique, we obtain the existence of solutions of periodic boundary value problems for a class of impulsive neutral differential equations with multi-deviation arguments. An example is given to demonstrate our main results.Mathematical subject classification: Primary: 34A37; Secondary: 34k10.