In this article, a log del Pezzo surface of index two means a projective normal non-Gorenstein surface S such that (S, 0) is a log-terminal pair, the anti-canonical divisor −KS is ample and that 2KS is Cartier. The log del Pezzo surfaces of index two are shown to be constructed from data (X,E,∆) called fundamental triplets consisting of a non-singular rational surface X, a simple normal crossin...

we introduce a new concept of general $g$-$eta$-monotone operator generalizing the general $(h,eta)$-monotone operator cite{arvar2, arvar1}, general $h-$ monotone operator cite{xiahuang} in banach spaces, and also generalizing $g$-$eta$-monotone operator cite{zhang}, $(a, eta)$-monotone operator cite{verma2}, $a$-monotone operator cite{verma0}, $(h, eta)$-monotone operator cite{fanghuang}...

In ‎the present ‎paper, ‎we ‎introduce the ‎two-wavelet ‎localization ‎operator ‎for ‎the square ‎integrable ‎representation ‎of a‎ ‎homogeneous space‎ with respect to a relatively invariant measure. ‎We show that it is a bounded linear operator. We investigate ‎some ‎properties ‎of the ‎two-wavelet ‎localization ‎operator ‎and ‎show ‎that ‎it ‎is a‎ ‎compact ‎operator ‎and is ‎contained ‎in‎ a...

Let $f$ be a morphism from klt pair $(X, \Delta)$ to an abelian variety $A$, $m\geq1$ rational number and $D$ Cartier divisor on $X$ such that $D\sim_{\mathbb Q}m(K_X+\Delta)$. We prove the sheaf $f_*\mathcal{O}_X(D)$ becomes globally generated after pullback by isogeny has Chen-Jiang decomposition, along with some related results. These are applied effective results for $\mathcal{O}_X(D)$ when...

In an earlier paper (joint with Min Ru), we proved a result on diophantine approximation to Cartier divisors, extending 2011 of P. Autissier. This was recently extended certain closed subschemes (in place divisors) by Ru and Wang. this extend broader class subschemes. We also show that some notions ?(?,D) coincide, they can all be evaluated as limits.