Let E/Q be a modular elliptic curve, and p > 3 a good ordinary or semistable prime. Under mild hypotheses, we prove an exact formula for the μ-invariant associated to the weight-deformation of the Tate module of E. For example, at ordinary primes in the range 3 < p < 100, the result implies the triviality of the μ-invariant of X0(11). 2000 Mathematics Subject Classification: 11G40; also 11F33, ...

We prove a commutative algebra result which has consequences for congruences between automorphic forms modulo prime powers. If C denotes the congruence module for a fixed automorphic Hecke eigenform π0 we prove an exact relation between the p-adic valuation of the order of C and the sum of the exponents of p-power congruences between the Hecke eigenvalues of π0 and other automorphic forms. We a...

Structured Light (SL) sensing is a well established method of range acquisition for Computer Vision. This chapter provides thorough discussions of design issues, calibration methodologies and implementation schemes for SL sensors. The challenges for SL sensor development are described and a range of approaches are surveyed. A novel SL sensor, PRIME, the PRoole Imaging ModulE has recently been d...

Structured Light (SL) sensing is a well established m e t h o d o f r ange acquisition for Computer Vision. This chapter provides thorough discussions of design issues, calibration methodologies and implementation schemes for SL sensors. The challenges for SL sensor development are described and a range of approaches are surveyed. A novel SL sensor, PRIME, the PRo�le Imaging ModulE has recently...

Let $G$ be a group, $R$ $G$-graded commutative ring with identity, $M$ graded $R$-module and $S\subseteq h(R)$ multiplicatively closed subset of $R$. In this paper, new concept $S$-primary submodules is introduced as generalization Primary well $S$-prime $M$. Also, some properties class are investigated.

In this paper we defined the concept of module amenability of Banach algebras and module connes amenability of module dual Banach algebras.Also we assert the concept of module Arens regularity that is different with [1] and investigate the relation between module amenability of Banach algebras and connes module amenability of module second dual Banach algebras.In the following we studythe...

Let $G$ be a group, $R$ $G$-graded commutative ring with identity, $M$ graded $R$-module and $S\subseteq h(R)$ multiplicatively closed subset of $R$. In this paper, new concept $S$-primary submodules is introduced as generalization Primary well $S$-prime $M$. Also, some properties class are investigated.

We give a sufficient condition for the $kG$-Scott module with vertex $P$ to remain indecomposable under taking Brauer construction any subgroup $Q$ of as $k[Q\,C_G(Q)]$-module, where $k$ is field characteristic $2$, and wreathed $2$-subgroup finite group $G$. This generalizes results cases abelian some others. The motivation this paper that indecomposability $p$-permutation bimodule ($p$ prime)...

Let $G$ be a group with identity $e$. $R$ $G$-graded commutative ring, $M$ graded $R$-module and $A\subseteq h(R)$ multiplicatively closed subset of $R$. In this paper, we introduce the concept $A$-2-absorbing submodules as generalization 2-absorbing $A$-prime $M.$ We investigate some properties class submodules.

Let $R$ be a commutative ring with identity, $S$ multiplicatively closed subset of $R$, and $M$ an $R$-module.&#x0D; In this paper, we study investigate some properties $S$-primary submodules $M$. Among the other results, it is shown that this&#x0D; class modules contains family primary (resp. $S$-prime) properly.