Central configurations of nested rotated regular tetrahedra

In this paper we prove that there are only two different classes of central configura- tions with convenient masses located at the vertices of two nested regular tetrahedra: either when one of the tetrahedra is a homothecy of the other one, or when one of the tetrahedra is a homothecy followed by a rotation of Euler angles = = 0 and = of the other one. We also analyze the central configurations with convenient masses located at the vertices of three nested regular tetrahedra when one them is a homothecy of the other one, and the third one is a homothecy followed by a rotation of Euler angles = = 0 and = of the other two. In all these cases we have assumed that the masses on each tetrahedron are equal but masses on different tetrahedra could be different.

Central configurations of nested regular polyhedra for the spatial 2n–body problem

We consider 2n masses located at the vertices of two nested regular polyhedra with the same number of vertices. Assuming that the masses in each polyhedron are equal, we prove that for each ratio of the masses of the inner and the outer polyhedron there exists a unique ratio of the length of the edges of the inner and the outer polyhedron such that the configuration is central.

Central configurations of three nested regular polyhedra for the spatial 3n–body problem

Three regular polyhedra are called nested if they have the same number of vertices n, the same center and the positions of the vertices of the inner polyhedron ri, the ones of the medium polyhedron Ri and the ones of the outer polyhedron Ri satisfy the relation Ri = ri and Ri = Rri for some scale factors R > > 1 and for all i = 1, . . . , n. We consider 3n masses located at the vertices of three nested regular polyhedra. We assume that the masses of the inner polyhedron are equal to m1, the masses of the medium one are equal to m2, and the masses of the outer one are equal to m3. We prove that if the ratios of the masses m2/m1 and m3/m1 and the scale factors and R satisfy two convenient relations, then this configuration is central for the 3n–body problem. Moreover there is some numerical evidence that, first, fixed two values of the ratios m2/m1 and m3/m1, the 3n–body problem has a unique central configuration of this type; and second that the number of nested regular polyhedra with the same number of vertices forming a central configuration for convenient masses and sizes is arbitrary.

Symmetric planar central configurations of five bodies: Euler plus two

We study planar central configurations of the five-body problem where three of the bodies are collinear, forming an Euler central configuration of the three-body problem, and the two other bodies together with the collinear configuration are in the same plane. The problem considered here assumes certain symmetries. From the three bodies in the collinear configuration, the two bodies at the extremities have equal masses and the third one is at the middle point between the two. The fourth and fifth bodies are placed in a symmetric way: either with respect to the line containing the three bodies, or with respect to the middle body in the collinear configuration, or with respect to the perpendicular bisector of the segment containing the three bodies. The possible stacked five-body central configurations satisfying these types of symmetries are: a rhombus with four masses at the vertices and a fifth mass in the center, and a trapezoid with four masses at the vertices and a fifth mass at the midpoint of one of the parallel sides.

The number of planar central configurations for the 4-body problem is finite when 3 mass positions are fixed

In the n{body problem a central con guration is formed when the position vector of each particle with respect to the center of mass is a common scalar multiple of its acceleration vector. Lindstrom showed for n = 3 and for n > 4 that if n ? 1 masses are located at xed points in the plane, then there are only a nite number of ways to position the remaining nth mass in such a way that they de ne a central con guration. Lindstrom leaves open the case n = 4. In this paper we prove the case n = 4 using as variables the mutual distances between the particles.

Double-Antiprism Central Configurations of the 3n-Body Problem

Abstract In this paper we study numerically a new type of central configurations of the 3n-body problem with equal masses which consist of three n-gons contained in three planes z = 0 and z = ±β = 0. The n-gon on z = 0 is scaled by a factor α and it is rotated by an angle of π/n with respect to the ones on z = ±β. In this kind of configurations, the masses on the planes z = 0 and z = β are at the vertices of an antiprism with bases of different size. The same occurs with the masses on z = 0 and z = −β. We call this kind of central configurations double-antiprism central configurations. We will show the existence of central configurations of this type.

On the existence of bi-pyramidal central configurations of the n + 2-body problem with an n-gon base

Abstract. In this paper we prove the existence of central con gurations of the n + 2{body problem where n equal masses are located at the vertices of a regular n{gon and the remaining 2 masses, which are not necessarily equal, are located on the straight line orthogonal to the plane containing the n{gon passing through its center. Here this kind of central con gurations is called bi{pyramidal central con gurations. In particular, we prove that if the masses mn+1 and mn+2 and their positions satisfy convenient relations, then the con guration is central. We give explicitly those relations.

Equilibrium points and central configurations for the Lennard-Jones 2-and 3-body problems

Abstract. In this paper we study the relative equilibria and their stability for a system of three point particles moving under the action of a Lennard{Jones potential. A central con guration is a special position of the particles where the position and acceleration vectors of each particle are proportional, and the constant of proportionality is the same for all particles. Since the Lennard{Jones potential depends only on the mutual distances among the particles, it is invariant under rotations. In a rotating frame the orbits coming from central con gurations become equilibrium points, the relative equilibria. Due to the form of the potential, the relative equilibria depend on the size of the system, that is, depend strongly of the momentum of inertia I. In this work we characterize the relative equilibria, we nd the bifurcation values of I for which the number of relative equilibria is changing, we also analyze the stability of the relative equilibria.

Organizational configurations of strategic choices and strategic management accounting

This is the first study to adopt a configurational paradigm in an investigation of strategic management accounting (SMA) adoption. The study examines the alignment and effectiveness of strategic choice and strategic management accounting (SMA) system design configurations. Six configurations were derived empirically by deploying a cluster analysis of data collected from a sample of 193 large Slovenian companies. The first four clusters appear to provide some support for the central configurational proposition that higher levels of vertical and horizontal configurational alignments are associated with higher levels of performance. Evidence that contradicts the theory is also apparent, however, as the remaining two clusters exhibit high degrees of SMA vertical and horizontal alignment, but low performance levels. A particular contribution of the paper concerns its demonstration of the way that the configurational paradigm can be operationalised to examine management accounting phenomena and the nature of management accounting insights that can derive from applying the approach.

The role of central bank operating procedures in an economy with productive government spending

The choice of either the rate of monetary growth or the nominal interest rate as the instrument controlled by monetary authorities has both positive and normative implications for economic performance. We reexamine some of the issues related to the choice of the monetary policy instrument in a dynamic general equilibrium model exhibiting endogenous growth in which a fraction of productive government spending is financed by means of issuing currency. When we evaluate the performance of the two monetary instruments attending to the fluctuations of endogenous variables, we find that the inflation rate is less volatile under nominal interest rate targeting. Concerning the fluctuations of consumption and of the growth rate, both monetary policy instruments lead to statistically equivalent volatilities. Finally, we show that none of these two targeting procedures displays unambiguously higher welfare levels.

Payments for environmental services in watersheds: insights from a comparative study of three cases in Central America

We have compared three cases of payments for water-related environmental services (PES) in Central America, in terms of socioeconomic background, opportunity costs of forest conservation and stakeholders’ perceptions on the conditions of water resources and other issues. We found that, in general, the foregone benefits from land uses alternative to forest cover are larger than the amount paid, which apparently contradicts the economic foundation of PES schemes. A number of possible explanations are explored. The results also suggest that trade-offs between different environmental and social goals are likely to emerge in PES schemes, posing some doubts on their ability to be multipurpose instruments for environmental improvement and rural development. We also found that PES schemes may work as a conflictresolution instrument, facilitating downstream -upstream problem solving, though at the same time they might introduce changes in social perceptions of property rights.

Ten Propositions on Rural Poverty and Agrarian Transition in Central Eurasia

The relation between agricultural development and rural poverty reduction in six Central Eurasian countries, namely Azerbaijan (South Caucasus) and Kazakhstan, Kyrgyzstan, Tajikistan, Turkmenistan and Uzbekistan (Central Asia), is discussed by presenting and analyzing ten propositions. These propositions cover a broad range of issues that relate to rural poverty in this region, such as: the state of income and non-income poverty; the diverse processes of land reform and farm restructuring, and agricultural policy reform; and finally, the institutional and market framework that is needed for dynamic agricultural and rural development. The paper contends that rural poverty is not responding as robustly to rapid economic growth in these countries, and that agricultural growth, in particular in the newly emerging peasant farm sector, is necessary to promote rural poverty reduction.

When do central banks prefer to intervene secretly?

Central banks often intervene secretly in the foreign exchange market. This secrecy seems to be at odds with the signalling channel. In this article we will analyse when a central bank intervening in the foreign exchange rate market purely through the signalling channel would prefer to act secretly or publicly. By using a microstructure model, we will show that the consistency of the intervention with fundamentals, the volume of noise trading, the weight given to the effectiveness of intervention and the degree of superior information held by the central bank will influence the decision to intervene secretly or publicly. Keywords: foreign exchange intervention, market microstructure. JEL Classifi…cation: D82, E58, F31, G14.

Remeis casolans per a bèsties i humans: medicina i veterinària popular a la catalunya central

Treball de recerca realitzat per un alumne d’ensenyament secundari i guardonat amb un Premi CIRIT per fomentar l'esperit científic del Jovent l’any 2008. Consisteix en un diccionari informàtic que recull plantes i productes, cadascun amb les seves propietats medicinals i altres usos que se’ls atribueixen popularment i la forma de preparar remeis i aplicar-los per a cada malaltia o afecció. La informació s’ha extret de les entrevistes fetes a informants d’entre 60 i 90 anys del Bages, Berguedà i Solsonès, i es complementa amb un herbari i una mostra de preparacions dels remeis.

Evolució del poblament i organització del territori a la Catalunya interior durant l'Antiguitat Tardana i l'Alta Edat Mitjana: els casos de la Catalunya Central (Bages, Berguedà i Solsonès) i la Garrotxa (segles V-X)

Projecte de recerca elaborat a partir d’una estada a la Université de Toulouse 2 – Le Mirail entre gener i juny del 2007. En concret, l’estada efectuada ha suposat la integració de qui signa aquesta memòria dins l’equip al-Andalus/Hispaniae, dirigit pel professor Philippe Sénac, una de les diverses branques que conformen el grup FRAMESPA d’aquella universitat, unitat de recerca adscrita al CNRS (UMR 5136). El títol proposat per al contingut de la recerca en la sol•licitud presentada, Evolució del poblament i organització del territori a la Catalunya interior a l’Alta Edat Mitjana, encapçalava un pla de treball que tenia per objectiu la recopilació i l’anàlisi de dades arqueològiques i textuals que oferissin un escenari a partir del qual establir una seqüència evolutiva en relació a les diferents tendències pel que fa al poblament tardoantic i altmedieval en dues zones diferenciades com són les conques mitjanes dels rius Llobregat i Cardener, a la Catalunya Central, i la capçalera del riu Fluvià, a la Garrotxa. Així, s’han pogut detectar, a partir de la contrastació de les diferents dades, fenòmens diversos que reflecteixen la incidència dels successius canvis històrics a nivell territorial i de poblament.