Spectral and weak polynomial completeness for the porduct of nonsingular matrices

Let F be a field with at least four elements. In this paper, we identify all the pairs (A, B) of n x n nonsingular matrices over F , satisfying the following property: for every monic polynomial f(x) = xn + an-1xn-1 + … +a1x + aο over F, with a root in F and aο = (-1)n det(AB), there are nonsingular matrices X, Y ϵ Fnxn such that X A X-1 Y BY-1 has characteristic polynomial f (x). © 2014 © 2014 Taylor & Francis.

Quantitative description of the self-assembly of patchy particles into chains and rings

We numerically study a simple fluid composed of particles having a hard-core repulsion complemented by two patchy attractive sites on the particle poles. An appropriate choice of the patch angular width allows for the formation of ring structures which, at low temperatures and low densities, compete with the growth of linear aggregates. The simplicity of the model makes it possible to compare simulation results and theoretical predictions based on the Wertheim perturbation theory, specialized to the case in which ring formation is allowed. Such a comparison offers a unique framework for establishing the quality of the analytic predictions. We find that the Wertheim theory describes remarkably well the simulation results.

Exciting dynamical behavior in a network of two coupled rings of Chen oscillators

We study exotic patterns appearing in a network of coupled Chen oscillators. Namely, we consider a network of two rings coupled through a “buffer” cell, with Z3×Z5 symmetry group. Numerical simulations of the network reveal steady states, rotating waves in one ring and quasiperiodic behavior in the other, and chaotic states in the two rings, to name a few. The different patterns seem to arise through a sequence of Hopf bifurcations, period-doubling, and halving-period bifurcations. The network architecture seems to explain certain observed features, such as equilibria and the rotating waves, whereas the properties of the chaotic oscillator may explain others, such as the quasiperiodic and chaotic states. We use XPPAUT and MATLAB to compute numerically the relevant states.

Generalization of Wertheim's theory for the assembly of various types of rings

We generalize Wertheim's first order perturbation theory to account for the effect in the thermodynamics of the self-assembly of rings characterized by two energy scales. The theory is applied to a lattice model of patchy particles and tested against Monte Carlo simulations on a fcc lattice. These particles have 2 patches of type A and 10 patches of type B, which may form bonds AA or AB that decrease the energy by epsilon(AA) and by epsilon(AB) = r epsilon(AA), respectively. The angle theta between the 2 A-patches on each particle is fixed at 601, 90 degrees or 120 degrees. For values of r below 1/2 and above a threshold r(th)(theta) the models exhibit a phase diagram with two critical points. Both theory and simulation predict that rth increases when theta decreases. We show that the mechanism that prevents phase separation for models with decreasing values of theta is related to the formation of loops containing AB bonds. Moreover, we show that by including the free energy of B-rings ( loops containing one AB bond), the theory describes the trends observed in the simulation results, but that for the lowest values of theta, the theoretical description deteriorates due to the increasing number of loops containing more than one AB bond.

Spectral and weak polynomial completeness for the product of nonsingular matrices

Let F be a field with at least four elements. In this paper, we identify all the pairs (A, B) of n x n nonsingular matrices over F, satisfying the following property: for every monic polynomial f (x) = x(n) + a(n-1)x(n-1) +... + a(1)x + a(0) over F, with a root in F and a(0) = (-1)(n) det(AB), there are nonsingular matrices X, Y is an element of F-nxn such that XAX(-1)Y BY-1 has characteristic polynomial f (x).

J. R. R. Tolkien, The Lord of the Rings; A Viagem e a Transformação

Este livro, agora publicado pelo INIC, é o resultado de um trabalho de investigação realizado entre 1985 e 1987 para a obtenção do grau de Mestre em Estudos Literários Comparados pela Faculdade de Ciências Sociais e Humanas da Universidade Nova de Lisboa. A literatura fantástica é uma área da literatura mundial que recebeu nas últimas décadas um grande interesse por parte da comunidade científica internacional. A multiplicação das associações, reuniões e congressos, a par da crescente produção teórica e científica, dão prova da vitalidade desta área da crítica literária. Parte deste movimento foi precisamente despoletado pelo interesse provocado pela obra de 1. R. R. Tolkien e de outros autores como C. S. Lewis, Charles Williams, etc. Este fenómeno internacional não teve ainda reais desenvolvimentos em Portugal. Cinco anos volvidos sobre a realização deste trabalho verificamos que ele é um dos primeiros (senão o primeiro) editado entre nós que, de uma forma sistemática e científica, analisa a obra de Tolkien, abordando ainda, embora de forma breve, a problemática da ficção fantástica contemporânea.

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%.

Verification of system properties of polynomial systems using discrete-time approximations and set-based analysis

Magdeburg, Univ., Fak. für Elektrotechnik und Informationstechnik, Diss., 2015

Polynomial-time complexity for instances of the endomorphism problem in free groups

We say the endomorphism problem is solvable for an element W in a free group F if it can be decided effectively whether, given U in F, there is an endomorphism Φ of F sending W to U. This work analyzes an approach due to C. Edmunds and improved by C. Sims. Here we prove that the approach provides an efficient algorithm for solving the endomorphism problem when W is a two- generator word. We show that when W is a two-generator word this algorithm solves the problem in time polynomial in the length of U. This result gives a polynomial-time algorithm for solving, in free groups, two-variable equations in which all the variables occur on one side of the equality and all the constants on the other side.

Limit Cycles for a class of three dimensional polynomial differential systems

"Vegeu el resum a l'inici del document del fitxer adjunt."

Polynomial and linearized normal forms for almost periodic differential systems

"Vegeu el resum a l'inici del document del fitxer adjunt."

On the asymptotic expansion of the colored Jones polynomial for torus knots

In the asymptotic expansion of the hyperbolic specification of the colored Jones polynomial of torus knots, we identify different geometric contributions, in particular Chern-Simons invariant and Reidemeister torsion.

Encryption methods using formal power series rings

Recently there has been a great deal of work on noncommutative algebraic cryptography. This involves the use of noncommutative algebraic objects as the platforms for encryption systems. Most of this work, such as the Anshel-Anshel-Goldfeld scheme, the Ko-Lee scheme and the Baumslag-Fine-Xu Modular group scheme use nonabelian groups as the basic algebraic object. Some of these encryption methods have been successful and some have been broken. It has been suggested that at this point further pure group theoretic research, with an eye towards cryptographic applications, is necessary.In the present study we attempt to extend the class of noncommutative algebraic objects to be used in cryptography. In particular we explore several different methods to use a formal power series ring R && x1; :::; xn && in noncommuting variables x1; :::; xn as a base to develop cryptosystems. Although R can be any ring we have in mind formal power series rings over the rationals Q. We use in particular a result of Magnus that a finitely generated free group F has a faithful representation in a quotient of the formal power series ring in noncommuting variables.