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%.

Annular flow of viscoelastic fluids: Analytical and numerical solutions

This work provides analytical and numerical solutions for the linear, quadratic and exponential Phan–Thien–Tanner (PTT) viscoelastic models, for axial and helical annular fully-developed flows under no slip and slip boundary conditions, the latter given by the linear and nonlinear Navier slip laws. The rheology of the three PTT model functions is discussed together with the influence of the slip velocity upon the flow velocity and stress fields. For the linear PTT model, full analytical solutions for the inverse problem (unknown velocity) are devised for the linear Navier slip law and two different slip exponents. For the linear PTT model with other values of the slip exponent and for the quadratic PTT model, the polynomial equation for the radial location (β) of the null shear stress must be solved numerically. For both models, the solution of the direct problem is given by an iterative procedure involving three nonlinear equations, one for β, other for the pressure gradient and another for the torque per unit length. For the exponential PTT model we devise a numerical procedure that can easily compute the numerical solution of the pure axial flow problem

A sixth-order finite volume method for the 1D biharmonic operator: application to intramedullary nail simulation

A new very high-order finite volume method to solve problems with harmonic and biharmonic operators for one- dimensional geometries is proposed. The main ingredient is polynomial reconstruction based on local interpolations of mean values providing accurate approximations of the solution up to the sixth-order accuracy. First developed with the harmonic operator, an extension for the biharmonic operator is obtained, which allows designing a very high-order finite volume scheme where the solution is obtained by solving a matrix-free problem. An application in elasticity coupling the two operators is presented. We consider a beam subject to a combination of tensile and bending loads, where the main goal is the stress critical point determination for an intramedullary nail.

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.

Finite integration methods for isospectral flows

In this paper we consider the approximate computation of isospectral flows based on finite integration methods( FIM) with radial basis functions( RBF) interpolation,a new algorithm is developed. Our method ensures the symmetry of the solutions. Numerical experiments demonstrate that the solutions have higher accuracy by our algorithm than by the second order Runge- Kutta( RK2) method.

Análise técnica - económica da produção de energia em sistemas de abastecimento de água: caso do aproveitamento de fins múltiplos dos socorridos

Dissertação de mestrado integrado em Engenharia Civil