Constructing the Lyapunov Function through Solving Positive Dimensional Polynomial System

We propose an approach for constructing Lyapunov function in quadratic form of a differential system. First, positive polynomial system is obtained via the local property of the Lyapunov function as well as its derivative. Then, the positive polynomial system is converted into an equation system by adding some variables. Finally, numerical technique is applied to solve the equation system. Some experiments show the efficiency of our new algorithm

Characterization of the mitochondrial genome of Analcellicampa xanthosoma gen. et sp. nov. (Hymenoptera: Tenthredinidae)

A new genus with a new species of the tribe Hoplocampini of Hoplocampinae was described from China: Analcellicampa xanthosoma Wei & Niu, gen. et sp. nov. Hoplocampa danfengensis G. Xiao 1994 was designated as the type species of the new genus. The characters of Analcellicampa danfengensis (G. Xiao) comb. nov. were briefly discussed. A key to the tribes and known genera of Hoplocampinae was provided. The nearly complete mitochondrial genome of A. xanthosoma was characterized as having a length of 15,512 bp and containing 37 genes (22 tRNAs, 13 protein-coding genes (PCGs), and 2 rRNAs). The gene order of this new specimen was the same as that in the inferred insect ancestral mitochondrial genome. All PCGs were initiated by ATN codons and ended with TAA or T stop codons. All tRNAs had a typical cloverleaf secondary structure, except for trnS1. Remarkably, the helices H991 of rrnS and H47 of rrnL were redundant, while helix H563 of rrnL was highly conserved. A phylogeny based on previously reported symphytan mitochondrial genomes showed that A. xanthosoma is a sister group to Monocellicampa pruni, with high support values. We suggest that A. xanthosoma and M. pruni belong to the tribe Hoplocampini of Hoplocampinae