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.

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.

L’art com a vehicle : la dimensió sagrada de les arts performatives.

Jerzy Grotowski, director de teatre i recercador que va transformar profundament l’escena teatral de la segona meitat del segle vint, l’any 1970 va anunciar que no dirigiria més produccions teatrals. Apocalypsis Cum Figuris, una de les grans produccions escèniques del segle XX, marcaria un punt de transició en la trajectòria de l’investigador polonès obrint nous horitzons de vida creativa. Impulsat per una gran inquietud interior que trobaria la seva culminació en l’allunyament dels límits estrictament teatrals, Grotowski inicia el passatge de l’àmbit de l’Art com a representació, teatre en un sentit clàssic del terme, al domini de l’Art com a vehicle, en el que el mestre polonès recupera un aspecte antic i oblidat de l’art, que el situaria al nivell d’un coneixement superior, esdevenint un vehicle espiritual.

The generic Hanna Neumann conjecture and post correspondence problem

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Productive efficiency and regulatory reform: The case of vehicle inspection services

Measuring productive efficiency provides information on the likely effects of regulatory reform. We present a Data Envelopment Analysis (DEA) of a sample of 38 vehicle inspection units under a concession regime, between the years 2000 and 2004. The differences in efficiency scores show the potential technical efficiency benefit of introducing some form of incentive regulation or of progressing towards liberalization. We also compute scale efficiency scores, showing that only units in territories with very low population density operate at a sub-optimal scale. Among those that operate at an optimal scale, there are significant differences in size; the largest ones operate in territories with the highest population density. This suggests that the introduction of new units in the most densely populated territories (a likely effect of some form of liberalization) would not be detrimental in terms of scale efficiency. We also find that inspection units belonging to a large, diversified firm show higher technical efficiency, reflecting economies of scale or scope at the firm level. Finally, we show that between 2002 and 2004, a period of high regulatory uncertainty in the sample’s region, technical change was almost zero. Regulatory reform should take due account of scale and diversification effects, while at the same time avoiding regulatory uncertainty.

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.

Simulador de conducció enfocat a la investigació

El desenvolupament de sistemes d’assistència a la conducció (ADAS) és, avui dia, una de les àrees de recerca de més interès pel Centre de Visió per Computador. A partir de la informació adquirida per sensors instal·lats en un vehicle, els ADAS assisteixen al conductor per tal d’evitar situacions de perill. La validació d’aquests sistemes però, requereix de l’obtenció "manual" de les dades que defineixen l’entorn de conducció de forma precisa: una tasca costosa i subjecta a l’error humà. Per tal de resoldre aquest problema, en aquest projecte s’ha implementat IOCS, un simulador de conducció creat a partir d’un de robots, capaç de crear entorns realistes de conducció i d’obtenir, simultàniament, les dades sobre l’entorn inferides per un ADAS i les que el descriuen objectivament. Aquesta funcionalitat facilita extremadament el procés de validació actual dels sistemes d’assistència a la conducció.