Let $(X, \omega)$ be a compact Kahler manifold of complex dimension n and $\theta$ smooth closed real $(1,1)$-form on $X$ such that its cohomology class $\{ \theta \}\in H^{1,1}(X, \mathbb{R})$ is pseudoeffective. $\varphi$ $\theta$-psh function, let $f$ continuous function with bounded distributional laplacian respect to $\omega$ $\varphi \leq f. $ Then the non-pluripolar measure $\theta_\va...

‎Generalizing the notion of character amenability for Banach‎ ‎algebras‎, ‎we study the concept of $varphi$-Connes amenability of‎ ‎a dual Banach algebra $mathcal{A}$ with predual $mathcal{A}_*$‎, ‎where $varphi$ is a homomorphism from $mathcal{A}$ onto $Bbb C$‎ ‎that lies in $mathcal{A}_*$‎. ‎Several characterizations of‎ ‎$varphi$-Connes amenability are given‎. ‎We also prove that the‎ ‎follo...

Based on a completely distributive lattice $M$, base axioms and subbase axioms are introduced in $M$-fuzzifying convex spaces. It is shown that a mapping $mathscr{B}$ (resp. $varphi$) with the base axioms (resp. subbase axioms) can induce a unique $M$-fuzzifying convex structure with  $mathscr{B}$ (resp. $varphi$) as its base (resp. subbase). As applications, it is proved that bases and subbase...

Let the function $$\varphi $$ be holomorphic in unit disk $${\mathbb {D}}$$ of complex plane {C}}$$ and let ({\mathbb {D}})\subset {\mathbb . We study level sets critical points hyperbolic derivative , $$\begin{aligned} |D_{\varphi }(z)|:=\frac{(1-|z|^2)|\varphi '(z)|}{1-|\varphi (z)|^2}. \end{aligned}$$ In particular, we show how Schwarzian reveals nature points.

A toroidalization of a dominant morphism $varphi: Xto Y$ of algebraic varieties over a field of characteristic zero is a toroidal lifting of $varphi$ obtained by performing sequences of blow ups of nonsingular subvarieties above $X$ and $Y$. We give a proof of toroidalization of locally toroidal morphisms of 3-folds.

We construct a fundamental domain omega for an arbitrary lattice [unk] in a real rank one, real simple Lie group, where omega has finitely many cusps (i.e., is a finite union of Siegel sets) and has the Siegel property (i.e., the set {gamma [unk] [unk]|omegagamma [unk] omega [unk] varphi} is finite). From the existence of omega we derive a number of consequences. In particular, we show that [un...