Crown imperial scattered according to soil structure and organic matter in Zagros regions in Ilam. This plant has been performed an important role in the beautification of environment, tourist attraction and providing of plant essential oils which are used for the production of medicines. The current research was carried out to evaluation spatial distribution pattern of Fritillaria imperialis i...

ABSTRACT Blueberry fruit infected by Monilinia vaccinii-corymbosi, the causal agent of mummy berry disease, are unsuitable for use in processed food products. Fruit shipments that exceed a disease incidence threshold of 0.5% are redirected to alternative markets with substantial reductions in economic return to the producer. Because of this low tolerance, a sampling procedure with defined stati...

Recently Galashin, Grinberg, and Liu introduced the refined dual stable Grothendieck polynomials, which are symmetric functions in $x=(x_1,x_2,\dots)$ with additional parameters $t=(t_1,t_2,\dots)$. The polynomials defined as a generating function for reverse plane partitions of given shape. They interpolate between Schur by Lam Pylyavskyy 2007. Flagged more version where lower upper bounds ent...

We prove that the K-k-Schur functions are part of a family inhomogenous symmetric whose top homogeneous components Catalan functions, Euler characteristics certain vector bundles on flag variety. Lam-Schilling-Shimozono identified as Schubert representatives for K-homology affine Grassmannian SLk+1. Our perspective reveals satisfy shift invariance property, and we deduce positivity their branch...