We study vector bundles on flag varieties over an algebraically closed field $k$. In the first part, we suppose $G=G_k(d,n)$ $(2\le d\leq n-d)$ to be Grassmannian manifold parameterizing linear subspaces of dimension $d$ in $k^n$, where $k$ is characteristic $p>0$. Let $E$ a uniform bundle $G$ rank $r\le d$. show that either direct sum line or twist pull back universal $H_d$ its dual $H_d^{\vee...

A domain-wall configuration of the $\eta'$ meson bounded by a string (called pancake or Hall droplet) is recently proposed to describe baryons with spin $N_c/2$. In order understand its baryon number as well flavor quantum number, we argue that vector mesons (the $\rho$ and $\omega$ mesons) should play an essential role for consistency whole picture. We determine effective theory large-$N_c$ QC...

‎Given a compact space $X$ and a commutative Banach algebra‎ ‎$A$‎, ‎the character spaces of $A$-valued function algebras on $X$ are‎ ‎investigated‎. ‎The class of natural $A$-valued function algebras‎, ‎those whose characters can be described by means of characters of $A$ and‎ ‎point evaluation homomorphisms‎, ‎is introduced and studied‎. ‎For an‎ ‎admissible Banach $A$-valued function algebra...

The production of a process is expected to meet customer demands, specifications or engineering tolerances. The ability of a process to meet these expectations is expresed as a single number using a process capability index. When the quality of the products relates to more than one characteristic, multivariate process capability indices are applied. As it is known, in some circumstances we are ...