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.

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 ...

We report low-temperature magnetoresistance (MR) measurements on rings of single-wall carbon nanotubes. Negative MR characteristic of weak one-dimensional localization is clearly observed from 3.0 to 60 K, and the coherence length L(varphi) is obtained as a function of temperature. The dominant dephasing mechanism is identified as electron-electron scattering. Below 1 K, we observe a transition...

A numerical and analytical study of the role of exponentially truncated Lévy flights in the superdiffusive propagation of fronts in reaction-diffusion systems is presented. The study is based on a variation of the Fisher-Kolmogorov equation where the diffusion operator is replaced by a lambda -truncated fractional derivative of order alpha , where 1lambda is the characteristic truncation length...

For a fixed nonnegative integer $m$, an analytic map $\varphi$ and function $\psi$, the generalized integration operator $I^{(m)}_{\varphi,\psi}$ is defined by \[ I^{(m)}_{\varphi,\psi} f(z) = \int_0^z f^{(m)}(\varphi(\zeta)) \psi(\zeta) \, d\zeta \] for $X$-valued $f$, where $X$ Banach space. Some estimates norm of $I^{(m)}_{\varphi,\psi} \colon wA^p_{\alpha}(X) \to A^p_{\alpha}(X)$ are obtain...