Relative Well-Posedness of Constrained Systems with Applications to Variational Inequalities

The paper concerns foundations of sensitivity and stability analysis, being primarily addressed constrained systems. We consider general models, which are described by multifunctions between Banach spaces and concentrate on characterizing their well-posedness properties that revolve around Lipschitz stability and metric regularity relative to sets. The enhanced relative well-posedness concepts allow us, in contrast to their standard counterparts, encompassing various classes of constrained systems. Invoking tools of variational analysis and generalized differentiation, we introduce new robust notions of relative coderivatives. The novel machinery of variational analysis leads us to establishing complete characterizations of the relative well-posedness properties with further applications to stability of affine variational inequalities. Most of the obtained results valid in general infinite-dimensional settings are also new in finite dimensions.Comment: 25 page

The complete mitochondrial genomes of two band-winged grasshoppers, Gastrimargus marmoratus and Oedaleus asiaticus

<p>Abstract</p> <p>Background</p> <p>The two closely related species of band-winged grasshoppers, <it>Gastrimargus marmoratus </it>and <it>Oedaleus asiaticus</it>, display significant differences in distribution, biological characteristics and habitat preferences. They are so similar to their respective congeneric species that it is difficult to differentiate them from other species within each genus. Hoppers of the two species have quite similar morphologies to that of <it>Locusta migratoria</it>, hence causing confusion in species identification. Thus we determined and compared the mitochondrial genomes of <it>G. marmoratus </it>and <it>O. asiaticus </it>to address these questions.</p> <p>Results</p> <p>The complete mitochondrial genomes of <it>G. marmoratus </it>and <it>O. asiaticus </it>are 15,924 bp and 16,259 bp in size, respectively, with <it>O. asiaticus </it>being the largest among all known mitochondrial genomes in Orthoptera. Both mitochondrial genomes contain a standard set of 13 protein-coding genes, 22 transfer RNA genes, 2 ribosomal RNA genes and an A+T-rich region in the same order as those of the other analysed caeliferan species, but different from those of the ensiferan species by the rearrangement of <it>trnD </it>and <it>trnK</it>. The putative initiation codon for the <it>cox1 </it>gene in the two species is ATC. The presence of different sized tandem repeats in the A+T-rich region leads to size variation between their mitochondrial genomes. Except for <it>nad2</it>, <it>nad4L</it>, and <it>nad6</it>, most of the caeliferan mtDNA genes exhibit low levels of divergence. In phylogenetic analyses, the species from the suborder Caelifera form a monophyletic group, as is the case for the Ensifera. Furthermore, the two suborders cluster as sister groups, supporting the monophyly of Orthoptera.</p> <p>Conclusion</p> <p>The mitochondrial genomes of both <it>G. marmoratus </it>and <it>O. asiaticus </it>harbor the typical 37 genes and an A+T-rich region, exhibiting similar characters to those of other grasshopper species. Characterization of the two mitochondrial genomes has enriched our knowledge on mitochondrial genomes of Orthoptera.</p