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.

The aim of this paper is to prove some common fixed point theorems for four  mappings satisfying $(psi,varphi)$-weak contractions involving rational expressions in ordered partial metric spaces. Our results extend, generalize and improve some well-known results in the literature. Also, we give two examples to illustrate our results.

the aim of this paper is to prove some common fixed point theorems for four  mappings satisfying $(psi,varphi)$-weak contractions involving rational expressions in ordered partial metric spaces. our results extend, generalize and improve some well-known results in the literature. also, we give two examples to illustrate our results.

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...

We investigate the amenability of skew field extensions of the complex numbers. We prove that all skew fields of finite Gelfand-Kirillov transcendence degree are amenable. However there are both amenable and non-amenable finitely generated skew fields of infinite Gelfand-Kirillov transcendence degree. AMS Subject Classifications: 12E15, 43A07

Let $T=\bigl(\begin{smallmatrix}A&0\U\&B\end{smallmatrix}\bigr)$ be a formal triangular matrix ring, where $A$ and $B$ are rings $U$ is $(B, A)$-bimodule. We prove: (1) If $U\_{A}$ ${B}U$ have finite flat dimensions, then left $T$-module $\bigl(\begin{smallmatrix}M\_1\ M\_2\end{smallmatrix}\bigr){\varphi^{M}}$ Ding projective if only $M\_1$ $M\_2/{\operatorname{im}(\varphi^{M})}$ the morphism $...

Abstract Let $\varphi $ be Euler’s function and fix an integer $k\ge 0$ . We show that for every initial value $x_1\ge 1$ , the sequence of positive integers $(x_n)_{n\ge 1}$ defined by $x_{n+1}=\varphi (x_n)+k$ all $n\ge is eventually periodic. Similarly, values $x_1,x_2\ge $x_{n+2}=\varphi (x_{n+1})+\varphi periodic, provided k even.

motivated by an arens regularity problem, we introduce the concepts of matrix banach space and matrix banach algebra. the notion of matrix normed space in the sense of ruan is a special case of our matrix normed system. a matrix banach algebra is a matrix banach space with a completely contractive multiplication. we study the structure of matrix banach spaces and matrix banach algebras. then we...

In this paper, we research some properties of Codazzi pairs on almost para Norden manifolds. Let $(M_{2n},\ \varphi ,\ g,G)$ be an manifold. Firstly, $g$-conjugate connection, $G$-conjugate connection and $\varphi $-conjugate a linear $\mathrm{\nabla }$ $M_{2n}$ denoted by ${\mathrm{\nabla }}^{*\
 },\ {\mathrm{\nabla }}^{\dagger \ }}^{\varphi are defined it is demonstrated that the spaces ...