Further results on the inverse along an element in semigroups and rings

In this paper, we introduce a new notion in a semigroup $S$ as an extension of Mary's inverse. Let $a,d\in S$. An element $a$ is called left (resp. right) invertible along $d$ if there exists $b\in S$ such that $bad=d$ (resp. $dab=b$) and $b\leq_\mathcal{L}d$ (resp. $b\leq_\mathcal{R}d$). An existence criterion of this type inverse is derived. Moreover, several characterizations of left (right) regularity, left (right) $\pi$-regularity and left (right) $*$-regularity are given in a semigroup. Further, another existence criterion of this type inverse is given by means of a left (right) invertibility of certain elements in a ring. Finally we study the (left, right) inverse along a product in a ring, and, as an application, Mary's inverse along a matrix is expressed.

Nickel(II) complexes of bidentate N-N′ ligands containing mixed pyrazole, pyrimidine and pyridine aromatic rings as catalysts for ethylene polymerisation

This work describes the synthesis and characterisation of Ni(II) complexes of the following neutral bidentate nitrogen ligands containing pyrazole (pz), pyrimidine (pm) and pyridine (py) aromatic rings: 2-pyrazol-1-yl-pyrimidine (pzpm), 2-(4-methyl-pyrazol-1-yl)-pyrimidine (4-Mepzpm), 2-(4-bromo-pyrazol-1-yl)-pyrimidine (4-Brpzpm), 2-(3,5-dimethyl-pyrazol-1-yl)-pyrimidine (pz*pm), 2-pyrazol-1-yl-pyridine (pzpy) and bis(3,5-dimethylpyrazol-1-yl)phenylmethane (bpz*mph). The complexes [NiBr2(pzpm)] (1), [NiBr2(4-Mepzpm)] (2), [NiBr2(4-Brpzpm)] (3), [NiBr2(pz*pm)] (4), [NiBr2(pzpy)] (5) and [NiBr2(bpz*mph)] (6) were tested as catalysts for ethylene polymerisation, in the presence of the cocatalysts methylaluminoxane (MAO) or diethylaluminium chloride (AlEt2Cl), the catalyst systems 1-3/MAO showing moderate to high activities up to the temperature of 20 °C only in the presence of MAO, whereas 4-6/MAO revealed to be inactive. Other related Pd(II) complexes, already reported in previous works, such as [PdClMe(pzpm)], [PdClMe(pz*pm)], [PdClMe(pzpy)] and [PdClMe(bpz*mph)], also showed to be inactive in the polymerisation of ethylene, when activated by MAO or AlEt2Cl. Selected samples of polyethylene products were characterised by GPC/SEC, 1H and 13C NMR and DSC, showing to be low molecular weight polymers with Mn values ranging from ca. 550 to 1500 g mol−1 and unusually low dispersities of 1.2–1.7, with total branching degrees generally varying between 2 and 12%, melting temperatures from 40 to 120 °C and crystallinities from 40 to 70%.

Mechanical, fatigue and wear properties of sintered Carbon Nanotube-based functionally graded materials

Tese de Doutoramento Engenharia Mecânica

The group inverse of a product

In this paper, we characterize the existence and give an expression of the group inverse of a product of two regular elements by means of a ring unit.

Synthesis of five-membered heterocycles by indirect electrochemical approach in "Green" media

Radical cyclization continues to be a central methodology for the preparation of natural products containing heterocyclic rings. Hence, some electrochemical results obtained by cyclic voltammetry and controlled-potential electrolysis in the study of electroreductive intramolecular cyclization of ethyl (2S, 3R)-2-bromo-3-propargyloxy-3-(2’,3’,4’,6’-tetra-O-acetyl-beta-D-glucopyranosyloxy) propanoate (1a), 2-bromo-3-allyloxy-3-(2’,3’,4’,6’-tetra-O-acetyl-beta-D-glucopyranosyloxy)propanoate (1b), 2-bromo-[1-(prop-2-yn-1-yloxy)propyl]benzene (1c) and [1-bromo-2-methoxy-2-(prop-2’-yn-1-yloxy)ethyl]benzene (1d) promoted by (1,4,8,11-tetramethyl-1,4,8,11-tetraazacyclotetradecane)nickel(I), [Ni(tmc)]+, electrogenerated at glassy carbon cathodes in ethanol and ethanol:water mixtures containing tetraalkylammonium salts, are presented. During controlled-potential electrolyses of solutions containing [Ni(tmc)]2+ and bromoalkoxylated compounds (1) catalytic reduction of the latter proceeds via one-electron cleavage of the carbon–bromine bond to form a radical intermediate that undergoes cyclization to afford the substituted tetrahydrofurans.