On Boas-Type Problem

R.P. Boas has found necessary and sufficient conditions of belonging of function to Lipschitz class. From his findings it turned out, that the conditions on sine and cosine coefficients for belonging of function to Lip α(0 & α & 1) are the same, but for Lip 1 are different. Later his results were generalized by many authors in the viewpoint of generalization of condition on the majorant of modulus of continuity. The aim of this paper is to obtain Boas-type theorems for generalized Lipschitz classes. To define generalized Lipschitz classes we use the concept of modulus of smoothness of fractional order.

Normal forms for rational difference equations with applications to the global periodicity problem

We propose a classification and derive the associated normal forms for rational difference equations with complex coefficients. As an application, we study the global periodicity problem for second order rational difference equations with complex coefficients. We find new necessary conditions as well as some new examples of globally periodic equations.

Industrial location at a local level: some comments about the territorial level of the analysis

This paper contributes to the existing literature on industrial location by discussing some issues regarding the territorial levels that have been used in location analysis. We analyse which could be the advantages and disadvantages of performing locational analysis at a different local levels. We use data for new manufacturing firms located at municipality, county and travel to work areas level. We show that location determinants vary according to the territorial level used in the analysis, so we conclude that the level at which we perform the investigation should be carefully selected. Keywords: industrial location, cities, agglomeration economies, count data models.

Agglomeration and location: a nonparametric approach

The aim of this article is to assess the effects of several territorial characteristics, specifically agglomeration economies, on industrial location processes in the Spanish region of Catalonia. Theoretically, the level of agglomeration causes economies which favour the location of new establishments, but an excessive level of agglomeration might cause diseconomies, since congestion effects arise. The empirical evidence on this matter is inconclusive, probably because the models used so far are not suitable enough. We use a more flexible semiparametric specification, which allows us to study the nonlinear relationship between the different types of agglomeration levels and location processes. Our main statistical source is the REIC (Catalan Manufacturing Establishments Register), which has plant-level microdata on location of new industrial establishments. Keywords: agglomeration economies, industrial location, Generalized Additive Models, nonparametric estimation, count data models.

The word problem distinguishes counter languages

Counter automata are more powerful versions of finite state automata where addition and subtraction operations are permitted on a set of n integer registers, called counters. We show that the word problem of Zn is accepted by a nondeterministic m-counter automaton if and only if m &= n.

On the complexity of the Whitehead minimization problem

The Whitehead minimization problem consists in finding a minimum size element in the automorphic orbit of a word, a cyclic word or a finitely generated subgroup in a finite rank free group. We give the first fully polynomial algorithm to solve this problem, that is, an algorithm that is polynomial both in the length of the input word and in the rank of the free group. Earlier algorithms had an exponential dependency in the rank of the free group. It follows that the primitivity problem – to decide whether a word is an element of some basis of the free group – and the free factor problem can also be solved in polynomial time.

Addressing the net balances problem as a prerequisite for EU budget reform: a proposal

Conflict among member states regarding the distribution of net financial burdens has been allowed to contaminate the entire design of the EU budget with very negative consequences in terms of equity, efficiency and transparency. To get around this problem and pave the way for a substantive budget reform, we propose to decouple distributional negotiations from the rest of the budget process by linking member state net balances in a rigid manner to relative prosperity. This would be achieved through the introduction of a system of compensating horizontal transfers that would take to its logical conclusion the Commission's proposal for a generalized compensation mechanism. We discuss the impact of the proposed scheme on member states? incentives and illustrate its financial implications using revenue and expenditure projections for 2013 that are based on the current Financial Perspectives and Own Resources Decision.

Orbit decidability and the conjugacy problem for some extensions of groups

"Vegeu el resum a l'inici del document del fitxer adjunt."

Empirical studies in industrial location: an assessment of their methods and results

This paper surveys recent evidence on the determinants of (national and/or foreign) industrial location. We find that the basic analytical framework has remained essentially unaltered since the early contributions of the early 1980's while, in contrast, there have been significant advances in the quality of the data and, to a lesser extent, the econometric modelling. We also identify certain determinants (neoclassical and institutional factors) that tend to provide largely consistent results across the reviewed studies. In light of this evidence, we finally suggest future lines of research.

The generic Hanna Neumann conjecture and post correspondence problem

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Tax differentials and agglomeration economies in intraregional firm location

This paper analyses empirically how differences in local taxes affect the intraregional location of new manufacturing plants. These effects are examined within the random profit maximization framework while accounting for the presence of different types of agglomeration economies (localization/ urbanization/ Jacobs’ economies) at the municipal level. We look at the location decision of more than 10,000 establishments locating between 1996 and 2003 across more than 400 municipalities in Catalonia, a Spanish region. It is necessary to restrict the choice set to the local labor market and, above all, to control for agglomeration economies so as to identify the effects of taxes on the location of new establishments.

Estudio de sincronización cooperativa en redes de sensores

En este informe se estudia cómo es posible utilizar redes de sensores inalámbricos (WSN), para la localización de determinados eventos. Se hace un estudio previo de cómo una red de sensores puede llegar a estar sincronizada de una manera cooperativa, interactuando todos los sensores de la red entre sí. Primero se realiza el estudio para la sincronización de dos sensores con frecuencias diferentes, viéndose los parámetros que intervienen para que esta sincronización se realice con éxito, y también los efectos que en ella se produce al añadirle ruido. Seguidamente, se realiza el estudio para la sincronización de redes de N sensores, de manera que interactúen entre ellos de forma cooperativa. Se observan las características de la sincronización cuando todos los sensores llegan a consenso y, después, se busca la forma para que el consenso tienda hacia un valor determinado por mutuo acuerdo de los sensores. Finalmente, a partir de las características obtenidas en el consenso de N sensores, se realiza una aplicación práctica para la localización de eventos por medio del consenso de estas redes de sensores inalámbricos.

The simultaneous conjugacy problem in groups of piecewise linear functions

Guba and Sapir asked, in their joint paper [8], if the simultaneous conjugacy problem was solvable in Diagram Groups or, at least, for Thompson's group F. We give an elementary proof for the solution of the latter question. This relies purely on the description of F as the group of piecewise linear orientation-preserving homeomorphisms of the unit. The techniques we develop allow us also to solve the ordinary conjugacy problem as well, and we can compute roots and centralizers. Moreover, these techniques can be generalized to solve the same questions in larger groups of piecewise-linear homeomorphisms.

Symmetry for a Dirichlet-Neumann problem arising in water waves

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