Bounding the radii of balls meeting every connected component of semi-algebraic sets

We prove explicit bounds on the radius of a ball centered at the origin which is guaranteed to contain all bounded connected components of a semi-algebraic set S \subset \mathbbm{R}^k defined by a quantifier-free formula involving $s$ polynomials in \mathbbm{Z}[X_1, ..., X_k] having degrees at most $d$, and whose coefficients have bitsizes at most $\tau$. Our bound is an explicit function of $s, d, k$ and $\tau$, and does not contain any undetermined constants. We also prove a similar bound on the radius of a ball guaranteed to intersect every connected component of $S$ (including the unbounded components). While asymptotic bounds of the form $2^{\tau d^{O (k)}}$ on these quantities were known before, some applications require bounds which are explicit and which hold for all values of $s, d, k$ and $\tau$. The bounds proved in this paper are of this nature.Comment: 11 page

Impacts of agricultural trade liberalization on poverty: sensitivity of results to factors mobility among sectors

The Purposes of this paper are twofold (i) to evaluate changes in welfare gains and their distribution due to trade liberalization when imperfect labor markets are considered, (ii) to evaluate the impact of the recent reforms of the European agricultural policy on the world welfare. The results of two versions of a dynamic world computable general equilibrium (CGE) model, using the GTAP database version 6 are compared. In the first version, a standard world CGE approach is followed with perfect labor mobility across sectors. In the second version we assume that labor shifts freely within the aggregated sectors -agriculture, manufactures, services- but not across them .After a brief description of the two versions, changes in welfare, represented not only by the world GDP but also by the consumption level of two types of households (middle-low and middle-high) in 7 regions (Brazil, China, India, Least developed countries, European Union, United States, Rest of the World) after partial trade liberalization are presented. Theoretical and political consequences of the results are discussed.Food Security and Poverty, International Relations/Trade,

An asymptotically tight bound on the number of semi-algebraically connected components of realizable sign conditions

We prove an asymptotically tight bound (asymptotic with respect to the number of polynomials for fixed degrees and number of variables) on the number of semi-algebraically connected components of the realizations of all realizable sign conditions of a family of real polynomials. More precisely, we prove that the number of semi-algebraically connected components of the realizations of all realizable sign conditions of a family of $s$ polynomials in $\R[X_1,...,X_k]$ whose degrees are at most $d$ is bounded by $$\frac{(2d)^k}{k!}s^k + O(s^{k-1}).$$ This improves the best upper bound known previously which was $${1/2}\frac{(8d)^k}{k!}s^k + O(s^{k-1}).$$ The new bound matches asymptotically the lower bound obtained for families of polynomials each of which is a product of generic polynomials of degree one.Comment: 19 pages. Bibliography has been updated and a few more references have been added. This is the final version of this paper which will appear in Combinatoric

Computing the First Betti Numberand Describing the Connected Components of Semi-algebraic Sets

In this paper we describe a singly exponential algorithm for computing the first Betti number of a given semi-algebraic set. Singly exponential algorithms for computing the zero-th Betti number, and the Euler-Poincar\'e characteristic, were known before. No singly exponential algorithm was known for computing any of the individual Betti numbers other than the zero-th one. We also give algorithms for obtaining semi-algebraic descriptions of the semi-algebraically connected components of any given real algebraic or semi-algebraic set in single-exponential time improving on previous results

Critical success factors influencing performance outcome of joint venture construction projects in South Africa: Comparison of first and second order models

Joint ventures (JVs) have become increasingly common, because of the complexity and challenges associated with the delivery of construction projects globally and in South Africa. However, it has been established that JV projects have experienced unsatisfactory performance leading to clients’ dissatisfaction. The purpose of this paper is therefore to determine the critical success factors (CSFs) influencing the performance of JV construction projects in South Africa. A positivist philosophy position was adopted using a structured questionnaire survey administered to the construction professionals. Prior to the main study, a content validity of the questionnaire was achieved using a pilot study. The data was collected from 115 conveniently sampled respondents, and analysed using principal component analysis and multiple regression analysis. The exploratory factor analysis revealed two empirical models to be tested; namely the first and second order factor models. The result of the first order model revealed that, management control influenced achievement of project objective of JV, whereas, the second order model established that understanding of contractual agreement, which was explained by six components of CSFs influenced achievement of project objective. It is suggested that stakeholders who prefer to be involved in JV projects should acquire good understanding of the contractual agreement in managing JV projects in order to successfully achieve the project objectives. This study adds to the discourse and literature on CSFs of JVs. It provides new empirical evidence of the CSFs that influence project performance outcome of JV in the context of South Africa which can also be replicated in other countries globally. However, the study may not be generalised because of the geographical setting and respondents

Le territoire viticole en France : de la destruction à la valorisation

The surfaces devoted to the vine were reduced with the passing years. Under the effect of several phenomena that lead to lower consumption of wine, the decrease in vineyard area has led to a disintegration of rural and peri-urban area and reallocation of land released. Simultaneously from several French and European legislations, the wine territories have several means of protection and recovery through the heritage (natural, material), the concept of terroir, the nature and quality of products.Heritage;landscape;protection;wine territories;terroir;development