Abstract In this Front Sar Pad paper, first we prove some new refinements of discrete weighted inequalities with negative powers on finite intervals.Next, by employing these inequalities, we prove that the self-improving property (backward propagation property) of the weighted Boards discrete Muckenhoupt classes holds.The main results give exact va
Background: The congenital oligodontia in maxilla could result in a significant skeletal jaw malformation Peeling such as atrophic maxilla and severe skeletal class III malocclusion.Since there is no referable dentition in anterior maxilla, the orthognathic surgery and oral rehabilitation for those patients becomes more challenging and less predict
wetA, one of the conidiation center regulatory genes in many filamentous fungi, plays an important role in promoting asexual spores (conidia) maturation.Our recent research has found that knocking out or overexpressing MrwetA (a homolog of wetA) in Monascus ruber M7 does not affect the development of its asexual spores like other fungi, but both re
Spatial competition plays important roles in economics, which attracts extensive research.This paper addresses spatial competitions along with horizontal product differentiations and entry deterrence.By the dynamic game theory model Patio Chaise Lounger about one firm and a potential entrant with different cost Probiotics in a linear city, this pap