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.

Stable rank of leavitt path algebra

We characterize the values of the stable rank for Leavitt path algebras, by giving concrete criteria in terms of properties of the underlying graph.

Turkey's accession to the EU: interests, ideas and path dependence

The paper is divided into four sections. The first offers a critical assessment of explanations of both rationalist and constructivist approaches currently dominating European studies and assesses the notion of path dependence. The second and third sections analyse the role of both material interests and polity ideas in EU enlargement to Turkey, and conclude that explanations exclusively based on either strategic calculations or values and identities have significant shortcomings. The fourth section examines the institutional path of Turkey's candidacy to show how the course of action begun at Helsinki restricted the range of possible and legitimate options three years later in Copenhagen.

Chain conditions for Leavitt path algebras

In this paper, results known about the artinian and noetherian conditions for the Leavitt path algebras of graphs with finitely many vertices are extended to all row-finite graphs. In our first main result, necessary and sufficient conditions on a row-finite graph E are given so that the corresponding (not necessarily unital) Leavitt path K-algebra L(E) is semisimple. These are precisely the algebras L(E)for which every corner is left (equivalently, right)artinian. They are also precisely the algebras L(E) for which every finitely generated left (equivalently, right) L(E)-module is artinian. In our second main result, we give necessary and sufficient conditions for every corner of L(E) to be left (equivalently, right) noetherian. They also turn out to be precisely those algebras L(E) for which every finitely generated left(equivalently, right) L(E)-module is noetherian. In both situations, isomorphisms between these algebras and appropriate direct sums of matrix rings over K or K[x, x−1] are provided. Likewise, in both situations, equivalent graph theoretic conditions on E are presented.

The Difficult and tortuous path of agricultural cooperative networks in spain, 1890-1935

The rural associationism developed from the last decades of the XIX century could be consider as an answer of the agriculturists to the increasing integration of agriculture in the market, and to the effects of the Great Depression. In the case of Spain, the initiatives in this sense arose with certain delay in relation to the countries of Western Europe. The beginning of the Spanish cooperativism is closely bound to the Law of 1906. It granted the agrarian cooperatives with fiscal exemptions and other types of supports to the associates, although the process did not really accelerate until the promulgation of the law regulation in 1908.

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."

Políticas de encaminamiento tolerantes a fallos

El uso intensivo y prolongado de computadores de altas prestaciones para ejecutar aplicaciones computacionalmente intensivas, sumado al elevado número de elementos que los componen, incrementan drásticamente la probabilidad de ocurrencia de fallos durante su funcionamiento. El objetivo del trabajo es resolver el problema de tolerancia a fallos para redes de interconexión de altas prestaciones, partiendo del diseño de polí­ticas de encaminamiento tolerantes a fallos. Buscamos resolver una determinada cantidad de fallos de enlaces y nodos, considerando sus factores de impacto y probabilidad de aparición. Para ello aprovechamos la redundancia de caminos de comunicación existentes, partiendo desde enfoques de encaminamiento adaptativos capaces de cumplir con las cuatro fases de la tolerancia a fallos: detección del error, contención del daño, recuperación del error, y tratamiento del fallo y continuidad del servicio. La experimentación muestra una degradación de prestaciones menor al 5%. En el futuro, se tratará la pérdida de información en tránsito.

The generic Hanna Neumann conjecture and post correspondence problem

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

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

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

The non-linear Dirichlet problem in Hadamard manifolds

We prove existence theorems for the Dirichlet problem for hypersurfaces of constant special Lagrangian curvature in Hadamard manifolds. The first results are obtained using the continuity method and approximation and then refined using two iterations of the Perron method. The a-priori estimates used in the continuity method are valid in any ambient manifold.