Depth of segments and circles through points enclosing many points: a note

Neumann-Lara and Urrutia showed in 1985 that in any set of n points in the plane in general positionthere is always a pair of points such that any circle through them contains at least (n-2)/60 points. In a series of papers, this result was subsequently improved till n/4.7, which is currently the best known lower bound. In this paper we propose a new approach to the problem that allows us, by using known results about j-facets of sets of points in $R^3$, to give a simple proof of a somehow stronger result: there is always a pair of points such that any circle through them has, both inside and outside, at least n/4.7 points.Comment: 5 pages, 2 figure

A Regional Model for the Portuguese Economy Based on a Regional Accounting Matrix

This paper presents a model for the Portuguese economy based on a so-called “Regional Accounting Matrix” (RAM). The RAM is an accounting table made up of information provided by the standard Portuguese National and Regional Accounts, with a similar framework than the well-known social accounting matrixes. The RAM includes regionalised information concerning the generation and the use of the households’ income, but other parts of the table, namely those referring the structure of inputs in the production process, are at national level. Starting with the RAM, the paper then develops an input-output-type model closed with respect to the households’ consumption. This model is based in a “no regional preference hypothesis in supplying each region”. By this hypothesis we mean that every increase in demand, even when regionally located, is complied by a national supply (and also by international imports), and not preferentially by an increase in output of the very concerned region. The model proposed for the Portuguese economy, for the year of 1995, includes the computation of several multipliers – the most striking of them describe the inter-regional income distribution process. In fact, an increase in income, at the beginning in benefit of the households living in one region, may cross the region borders and propagate into other regions, increasing then the households’ income in the latter regions. The model also provides other outstanding multipliers, as those describing the effect on the regional households’ income of changes in demand of 49 kinds of products, and those computing the change in output of these 49 products induced by exogenous shocks in the regional income.

Does the Balance-Of-Payments Matter At the Regional Level?

The main focus of this paper is the importance of the balance-of-(international and interregional)-payments for the regional economies. Discussion centers on two points: 1) on one hand, we do believe that for regions, as a rule, at the overall balance-of-payments (BP) level, the size of imbalances is reduced; 2) on the other, we argue that even if relatively important imbalances arise their effect on regional economies is small. There are several reasons why regional BPs remain relatively well-balanced at overall level. The most important is that trade and current imbalances, that regions run very often with a considerable size, are easily financed by offsetting flows recorded as well in the BP. These trade and current imbalances, that do not pass into overall imbalances, are of benign kind. We present several reasons why that easy financing – allowing for trade and current imbalances – happens. As for the argument that a BP disequilibrium – if it arises – do not hit significantly a regional economy, that is the aftermath of a nationally integrated financial system, where the great majority of the regional units are only branches of national institutions operating all over the country. In this environment, a variation in the regional money stock (that is the counterpart of an overall BP imbalance) is not magnified by a money multiplier. We then conclude that as regions do not face any significant BP constraint, exports do not have any peculiar role in the regional growth process, and therefore the regional competitiveness debate is misplaced.

Social Prosperity Perception in Cultural Tourism Destinations: the Case of Peña de Bernal, Huejotzingo and Yuanhuitlán, México

The present quantitative study with a descriptive design tries to determine the conditions of "social prosperity" of three Mexican cultural tourist destinations, Yanhuitlán, Huejotzingo and Peña de Bernal. These places face similar conditions in aspects like marginalization and poverty but with activities like tourism have tried to reverse these adverse conditions. The objective was to know the perception of their population about the improvement of their living conditions as a result of the tourist activity through the application of surveys carried out in the chosen destinations. The instrument used was a questionnaire with a Likert scale to facilitate the response of the informants and the processing of the information. For the validity and reliability of the measurement instrument a factor reduction analysis and a Cronbach's alpha were elaborated, after which a one-way ANOVA was elaborated to know the differences of means taking the Bonferroni and Scheffe tests. The results show a significant difference between the averages of destinations in how residents perceive prosperity in the selected tourist destinations