On spectral analysis in varieties containing the solutions of inhomogeneous linear functional equations

The aim of the paper is to investigate the solutions of special inhomogeneous linear functional equations by using spectral analysis in a translation invariant closed linear subspace of additive/multiadditive functions containing the restrictions of the solutions to finitely generated fields. The application of spectral analysis in some related varieties is a new and important trend in the theory of functional equations; especially they have successful applications in case of homogeneous linear functional equations. The foundation of the theory can be found in M. Laczkovich and G. Kiss \cite{KL}, see also G. Kiss and A. Varga \cite{KV}. We are going to adopt the main theoretical tools to solve some inhomogeneous problems due to T. Szostok \cite{KKSZ08}, see also \cite{KKSZ} and \cite{KKSZW}. They are motivated by quadrature rules of approximate integration

vígjáték 3 felvonásban - írta Csiky Gergely - rendező Szakács Andor

Városi Színház. Debreczen, hétfő, 1905.évi október hó 30-án. Kiss Irén a Vígszinház tagjának utolsó felléptével.Debreceni Egyetem Egyetemi és Nemzeti Könyvtá

Experiences of European crisis management: the reform of economic policy coordination

This article is intended to present the new, (re)forming elements of economic policy coordination, an instrument playing a central role in the EU. One important lesson drawn from the crisis is that in order for the EU to become a stable, dynamically growing economy – in addition to its internal market (in particular, the free movement of capital) and a single monetary policy – there is a need for efficient coordination, which should also be credible for the markets. Economic policy coordination – the alignment of national fiscal policies to one another and, for euro area Member States, to the common monetary policy – is a key issue, and the intention to reform it is closely related to the crisis management of the past two years. The proposals presented thus far indicate that EU policy makers are firmly committed to setting up economic policy coordination mechanisms which are far more efficient than those already in place. Accordingly, they will rigorously assess both fiscal and real economic imbalances, and after the imbalances have been identified, they will readily enforce corrective mechanisms, including sanctions more severe than those already in place. Rules governing crisis management will certainly be clearer; however, in order to minimise moral hazard, the common European rescue package will continue to have a hefty price tag. It is a warning sign, however, that despite firm policy intentions, markets remain rather sceptical about the reform of the fiscal framework and the ability to guarantee the sustainability of fiscal policies, as indicated by the sovereign credit risk premia, which by September had risen to the levels observed in May.EU institutions, policy coordination, crisis management

Controlling Mackey--Glass chaos

The Mackey--Glass equation, which was proposed to illustrate nonlinear phenomena in physiological control systems, is a classical example of a simple looking time delay system with very complicated behavior. Here we use a novel approach for chaos control: we prove that with well chosen control parameters, all solutions of the system can be forced into a domain where the feedback is monotone, and by the powerful theory of delay differential equations with monotone feedback we can guarantee that the system is not chaotic any more. We show that this domain decomposition method is applicable with the most common control terms. Furthermore, we propose an other chaos control scheme based on state dependent delays.Comment: accepted in Chaos: An Interdisciplinary Journal of Nonlinear Scienc

On spectral synthesis in varieties containing the solutions of inhomogeneous linear functional equations

As a continuation of our previous work \cite{KV2} the aim of the recent paper is to investigate the solutions of special inhomogeneous linear functional equations by using spectral synthesis in translation invariant closed linear subspaces of additive/multiadditive functions containing the restrictions of the solutions to finitely generated fields. The idea is based on the fundamental work of M. Laczkovich and G. Kiss \cite{KL}. Using spectral analysis in some related varieties we can prove the existence of special solutions (automorphisms) of the functional equation but the spectral synthesis allows us to describe the entire space of solutions on a large class of finitely generated fields. It is spanned by the so-called exponential monomials which can be given in terms of automorphisms of \cc and differential operators. We apply the general theory to some inhomogeneous problems motivated by quadrature rules of approximate integration \cite{KKSZ08}, see also \cite{KKSZ} and \cite{KKSZW}

Optimal Rate of Inflation in Hungary

This paper, requested by the Monetary Council, attempts to determine the level of inflation consistent with price stability, taking into account the characteristics of the Hungarian economy. Price stability is defined as the level of inflation that allows the maximisation of social welfare on a 15-20 year horizon, which corresponds to the first phase of real convergence. In other words, this study aims to determine the inflation rate that can be considered optimal within the given time horizon. In developed countries, the primary objective of central banks is the maintenance of price stability, in view of the welfare costs of inflation. Price stability is usually taken to mean a low, but non-zero, inflation rate. A positive inflation rate can be justified since very low inflation rates, in the proximity of zero, have been found to reduce long-term welfare. The negative welfare effect of zero inflation can be explained in terms of the following: asymmetric nominal rigidities, the risk of deflation, the necessity of positive nominal interest rates, and the statistical measurement bias in the CPI. These factors were examined in light of the catching-up status of Hungary, focusing, in particular, on the question of whether or not, due to its catching-up status, the optimum rate of inflation in Hungary is higher than the 1-2,5% inflation rate defined in developed countries. The findings of the study suggest that the inflation rate corresponding to price stability in Hungary is higher than the inflation target of the European Central Bank. Our calculations suggest that, in the long run, inflation in the range of 2,3-3,2% can safeguard against the costs of deflation. This level can compensate for the distortions in the CPI and allow for real price adjustments, even if Hungarian tradable prices move together with those of its trading partners and assuming downward price rigidity.optimal inflation rate, price stability, costs of inflation.

Visual characterization of associative quasitrivial nondecreasing operations on finite chains

In this paper we provide visual characterization of associative quasitrivial nondecreasing operations on finite chains. We also provide a characterization of bisymmetric quasitrivial nondecreasing binary operations on finite chains. Finally, we estimate the number of functions belonging to the previous classes.Comment: 25 pages, 18 Figure