Minimal generating and separating sets for O(3)-invariants of several matrices

Given an algebra $F[H]^G$ of polynomial invariants of an action of the group $G$ over the vector space $H$, a subset $S$ of $F[H]^G$ is called separating if $S$ separates all orbits that can be separated by $F[H]^G$. A minimal separating set is found for some algebras of matrix invariants of several matrices over an infinite field of arbitrary characteristic different from two in case of the orthogonal group. Namely, we consider the following cases: 1) $GL(3)$-invariants of two matrices; 2) $O(3)$-invariants of $d>0$ skew-symmetric matrices; 3) $O(4)$-invariants of two skew-symmetric matrices; 4) $O(3)$-invariants of two symmetric matrices. A minimal generating set is also given for the algebra of orthogonal invariants of three $3\times 3$ symmetric matrices.Comment: 11 page

Intra-industry trade and labor costs: The smooth adjustment hypothesis

We study a situation in which, owing to the exhaustion of non-renewable energy sources, conventional motor vehicles will turn out of use. We consider two scenarios: recycling or dismantling these motor vehicles. M|G|∞ queue system is used to study the process. Through it, we conclude that if the rate of dismantling and recycling of motor vehicles is greater than the rate at which they become idle, the system will tend to get balanced. The model allows also performing a brief study about the recycling or dismantling economic interest.

Effects of fundamentals on the exchange rate: A panel analysis for a sample of industrialised and emerging economies

This paper tests the traditional monetary model of exchange rates for a sample of industrialized and emerging market economies by making use of panel techniques that allow for a high degree of heterogeneity across countries. The results demonstrated partial support for the monetary model for industrialised market economies but not for emerging ones. This constitutes a puzzle as it would expect countries with greater monetary instability to show a stronger association between exchange rates and monetary fundamentals

Increasing availability through maintainability growth using partial Multi Criteria Decision Making (pMCDM)

In the last decades considerations about equipments' availability became an important issue, as well as its dependence on components characteristics such as reliability and maintainability. This is particularly of outstanding importance if one is dealing with high risk industrial equipments, where these factors play an important and fundamental role in risk management when safety or huge economic values are in discussion. As availability is a function of reliability, maintainability, and maintenance support activities, the main goal is to improve one or more of these factors. This paper intends to show how maintainability can influence availability and present a methodology to select the most important attributes for maintainability using a partial Multi Criteria Decision Making (pMCDM). Improvements in maintainability can be analyzed assuming it as a probability related with a restore probability density function [g(t)]

Mean-field analysis of the majority-vote model broken-ergodicity steady state

We study analytically a variant of the one-dimensional majority-vote model in which the individual retains its opinion in case there is a tie among the neighbors' opinions. The individuals are fixed in the sites of a ring of size $L$ and can interact with their nearest neighbors only. The interesting feature of this model is that it exhibits an infinity of spatially heterogeneous absorbing configurations for $L \to \infty$ whose statistical properties we probe analytically using a mean-field framework based on the decomposition of the $L$-site joint probability distribution into the $n$-contiguous-site joint distributions, the so-called $n$-site approximation. To describe the broken-ergodicity steady state of the model we solve analytically the mean-field dynamic equations for arbitrary time $t$ in the cases n=3 and 4. The asymptotic limit $t \to \infty$ reveals the mapping between the statistical properties of the random initial configurations and those of the final absorbing configurations. For the pair approximation ($n=2$) we derive that mapping using a trick that avoids solving the full dynamics. Most remarkably, we find that the predictions of the 4-site approximation reduce to those of the 3-site in the case of expectations involving three contiguous sites. In addition, those expectations fit the Monte Carlo data perfectly and so we conjecture that they are in fact the exact expectations for the one-dimensional majority-vote model

Periodically collapsing rational bubbles in exchange rate: A Markov-switching analysis for a sample of industrialised markets

This paper investigates the presence of periodically collapsing rational bubbles in exchange rates for a sample of industrialised countries. A periodically collapsing rational bubble is defined as an explosive deviation from economic fundamentals with distinct expansion and contraction phases in finite time. By using Markov-switching regime models we were not able to find robust evidence of a bubble driving the exchange rate away from fundamentals. Moreover, the results also revealed significant non-linearities and different regimes. The importance of these findings suggests that linear monetary models may not be appropriate to examine exchange rate movements