Resumo em Inglês:

In this paper, the notion of equitable partitions (EP) is used to study the eigenvalues of Euclidean distance matrices (EDMs). In particular, EP is used to obtain the characteristic polynomials of regular EDMs and non-spherical centrally symmetric EDMs. The paper also presents methods for constructing cospectral EDMs and EDMs with exactly three distinct eigenvalues.

Resumo em Inglês:

The strong candidate stability theorem by Dutta et al. [ 4], one of the major theoremsof social choice theory, states that, with a finite number of voters, there exists a dictator for any voting procedure which satisfies strong candidate stability, strong unanimity and independence of irrelevant alternatives (IIA). This paper investigates a decidability problem of voting procedures in a society with an infinite number of individuals (infinite society) using Cantor's diagonal argument presented by Yanofsky [ 19] which is based on Lawvere [ 10]. We will show the following result. The problem whether a strongly candidate stable voting procedure has a dictator or has no dictator in an infinite society is undecidable. It is proved using the arguments similar to those used to prove an extended version of Cantor's theorem that there cannot be an onto function from <img src="/img/revistas/cam/v27n3/n_bastao.gif" align=absmiddle>(the set of natural numbers) to its power set <img src="/img/revistas/cam/v27n3/p1_curs.gif" align=absmiddle>(<img src="/img/revistas/cam/v27n3/n_bastao.gif" align=absmiddle>). This undecidability means that for any strongly candidate stable voting procedure we can not decide whether or not it has a dictator in finite steps by some program. A dictator of a voting procedure is a voter such that if he strictly prefers a candidate (denoted by x) to another candidate (denoted by y), then the voting procedure does not choose y. Strong candidate stability requires that there be no change in the outcome of an election if a candidate withdraws who would lose ifevery candidate stood for office.

Resumo em Inglês:

In this paper, we present an efficient Newton-like method with fifth-order convergence for nonlinear equations. The algorithm is free from second derivative and it requires four evaluations of the given function and its first derivative at each iteration. As a consequence, its efficiency index is equal to 4√5 which is better than that of Newton's method √2. Several examples demonstrate that the presented algorithm is more efficient and performs better than Newton's method.

Resumo em Inglês:

In this work, we consider the superconvergence property of the finite element derivative for Lagrange's and Hermite's Family elements in the one dimensional interpolation problem. We also compare the Barlow points, Gauss points and Superconvergence points in the sense of Taylor's Series, confirming that they are not the same as believed before. We prove a not evident and new superconvergence property of Hermite's basis as well which shows that the centroid is not only a superconvergent for u'h but an O(h5) accuracy point.

Resumo em Inglês:

Travelling wave solution for Ibragimov-Shabat equation, is obtained by using an improved sine-cosine method and the Wu's elimination method. An infinite number of conserved quantities for the above equation are also obtained by solving a set of coupled Riccati equations.

Resumo em Inglês:

We show that the solutions of a thermoelastic system with a localized nonlinear distributed damping decay locally with an algebraic rate to zero, that is, given an arbitrary R > 0, the total energy E(t) satisfies for t > 0: E(t) < C (1 + t)-γ for regular initial data such that E(0) < R, where C and γ are positive constants. In the two-dimensional case, we obtain an exponential decay rate when the nonlinear dissipation behaves linearly close to the origin.