Genome-wide comprehensive analysis of transcriptomes and small RNAs offers insights into the molecular mechanism of alkaline stress tolerance in a citrus rootstock

Alkaline stress has serious-negative effects on citrus production.Ziyang xiangcheng(Citrus junos Sieb.ex Tanaka)(Cj)is a rootstock that is tolerant to alkaline stress and iron deficiency.Trifoliate orange(Poncirus trifoliata(L.)Raf.)(Pt),the most widely used rootstock in China,is sensitive to alkaline stress.To investigate the molecular mechanism underlying the tolerance of Cj to alkaline stress,next-generation sequencing was employed to profile the root transcriptomes and small RNAs of Cj and Pt seedlings that were cultured in nutrient solutions along a three pH gradient.This two-level regulation data set provides a system-level view of molecular events with a precise resolution.The data suggest that the auxin pathway may play a central role in the inhibitory effect of alkaline stress on root growth and that the regulation of auxin homeostasis under alkaline stress is important for the adaptation of citrus to alkaline stress.Moreover,the jasmonate(JA)pathway exhibits the opposite response to alkaline stress in Cj and Pt and may contribute to the differences in the alkaline stress tolerance and iron acquisition between Cj and Pt.The dataset provides a wealth of genomic resources and new clues to further study the mechanisms underlying alkaline stress resistance in Cj.

A High-Order Scheme for Fractional Ordinary Differential Equations with the Caputo-Fabrizio Derivative

In this paper, we consider numerical solutions of fractional ordinary diferential equations with the Caputo-Fabrizio derivative, and construct and analyze a high-order time-stepping scheme for this equation. The proposed method makes use of quadratic interpolation function in sub-intervals, which allows to produce fourth-order convergence. A rigorous stability and convergence analysis of the proposed scheme is given. A series of numerical examples are presented to validate the theoretical claims. Traditionally a scheme having fourth-order convergence could only be obtained by using block-by-block technique. The advantage of our scheme is that the solution can be obtained step by step, which is cheaper than a block-by-block-based approach.

Numerical Analysis of a High-Order Scheme for Nonlinear Fractional Differential Equations with Uniform Accuracy

We introduce a high-order numerical scheme for fractional ordinary differential equations with the Caputo derivative.The method is developed by dividing the domain into a number of subintervals,and applying the quadratic interpolation on each subinterval.The method is shown to be unconditionally stable,and for general nonlinear equations,the uniform sharp numerical order 3−νcan be rigorously proven for sufficiently smooth solutions at all time steps.The proof provides a gen-eral guide for proving the sharp order for higher-order schemes in the nonlinear case.Some numerical examples are given to validate our theoretical results.