Maximum Principle and Its Application for the Time-Fractional Diffusion Equations

MSC 2010: 26A33, 33E12, 35B45, 35B50, 35K99, 45K05 Dedicated to Professor Rudolf Gorenflo on the occasion of his 80th anniversary

Acceleration of Convergence in Dontchev’s Iterative Method for Solving Variational Inclusions

2000 Mathematics Subject Classification: 47H04, 65K10.

On Principle Eigenvalue for Linear Second Order Elliptic Equations in Divergence Form

2002 Mathematics Subject Classification: 35J15, 35J25, 35B05, 35B50

Minimum Description Length Principle in Discriminating Marginal Distributions

2010 Mathematics Subject Classification: 94A17, 62B10, 62F03.

Eco-efficiency measurement and material balance principle:an application in power plants Malmquist Luenberger Index

Incorporating Material Balance Principle (MBP) in industrial and agricultural performance measurement systems with pollutant factors has been on the rise in recent years. Many conventional methods of performance measurement have proven incompatible with the material flow conditions. This study will address the issue of eco-efficiency measurement adjusted for pollution, taking into account materials flow conditions and the MBP requirements, in order to provide ‘real’ measures of performance that can serve as guides when making policies. We develop a new approach by integrating slacks-based measure to enhance the Malmquist Luenberger Index by a material balance condition that reflects the conservation of matter. This model is compared with a similar model, which incorporates MBP using the trade-off approach to measure productivity and eco-efficiency trends of power plants. Results reveal similar findings for both models substantiating robustness and applicability of the proposed model in this paper.

Variational Markov chain Monte Carlo for Bayesian smoothing of non-linear diffusions

In this paper we develop set of novel Markov Chain Monte Carlo algorithms for Bayesian smoothing of partially observed non-linear diffusion processes. The sampling algorithms developed herein use a deterministic approximation to the posterior distribution over paths as the proposal distribution for a mixture of an independence and a random walk sampler. The approximating distribution is sampled by simulating an optimized time-dependent linear diffusion process derived from the recently developed variational Gaussian process approximation method. The novel diffusion bridge proposal derived from the variational approximation allows the use of a flexible blocking strategy that further improves mixing, and thus the efficiency, of the sampling algorithms. The algorithms are tested on two diffusion processes: one with double-well potential drift and another with SINE drift. The new algorithm's accuracy and efficiency is compared with state-of-the-art hybrid Monte Carlo based path sampling. It is shown that in practical, finite sample applications the algorithm is accurate except in the presence of large observation errors and low to a multi-modal structure in the posterior distribution over paths. More importantly, the variational approximation assisted sampling algorithm outperforms hybrid Monte Carlo in terms of computational efficiency, except when the diffusion process is densely observed with small errors in which case both algorithms are equally efficient. © 2011 Springer-Verlag.

Inverse space-dependent force problems for the wave equation

The determination of the displacement and the space-dependent force acting on a vibrating structure from measured final or time-average displacement observation is thoroughly investigated. Several aspects related to the existence and uniqueness of a solution of the linear but ill-posed inverse force problems are highlighted. After that, in order to capture the solution a variational formulation is proposed and the gradient of the least-squares functional that is minimized is rigorously and explicitly derived. Numerical results obtained using the Landweber method and the conjugate gradient method are presented and discussed illustrating the convergence of the iterative procedures for exact input data. Furthermore, for noisy data the semi-convergence phenomenon appears, as expected, and stability is restored by stopping the iterations according to the discrepancy principle criterion once the residual becomes close to the amount of noise. The present investigation will be significant to researchers concerned with wave propagation and control of vibrating structures.

The Polluter Profits Principle: A Note on the Grandfathering of CO2 Emissions Rights in Lax-Cap Trading Regimes

Grandfathering is currently the main principle for the initial allocation of tradable CO2 emission rights under the European cap-and-trade scheme. Furthermore, political feasibility often requires non-restrictive emission caps. Grandfathering under lax cap is unjust, biased and brings polluters unintended windfall profits. Still, in any post-Kyoto international CO2 regime, lax caps may be critical in coaxing binding emission targets out of more countries, especially those in the less-developed world. This paper argues that there is a certain quantity of emission rights between the initial and the optimal emissions, the grandfathering of which brings polluters zero windfall profits or zero windfall losses. Our theoretical concept of zero-windfall grandfathering can be used to demonstrate the windfall profits that have emerged at company level during the first EU trading period. It might thus encourage governments to embrace auctioning, and to combine it with grandfathering as a legitimate tool in the initial allocation of emission rights in later trading regimes.

Applying consumer responsibility principle in evaluating environmental load of carbon emissions

There is a need for a proper indicator in order to assess the environmental impact of international trade, therefore using the carbon footprint as an indicator can be relevant and useful. The aim of this study is to show from a methodological perspective how the carbon footprint, combined with input- output models can be used for analysing the impacts of international trade on the sustainable use of national resources in a country. The use of the input-output approach has the essential advantage of being able to track the transformation of goods through the economy. The study examines the environmental impact of consumption related to international trade, using the consumer responsibility principle. In this study the use of the carbon footprint and input-output methodology is shown on the example of the Hungarian consumption and the impact of international trade. Moving from a production- based approach in climate policy to a consumption-perspective principle and allocation, would also help to increase the efficiency of emission reduction targets and the evaluation of the ecological impacts of international trade.

Applying consumer responsibility principle in evaluating environmental load of carbon emissions

There is a need for a proper indicator in order to assess the environmental impact of international trade, therefore using the carbon footprint as an indicator can be relevant and useful. The aim of this study is to show from a methodological perspective how the carbon footprint, combined with input- output models can be used for analysing the impacts of international trade on the sustainable use of national resources in a country. The use of the input-output approach has the essential advantage of being able to track the transformation of goods through the economy. The study examines the environmental impact of consumption related to international trade, using the consumer responsibility principle. In this study the use of the carbon footprint and input-output methodology is shown on the example of the Hungarian consumption and the impact of international trade. Moving from a production- based approach in climate policy to a consumption-perspective principle and allocation, would also help to increase the efficiency of emission reduction targets and the evaluation of the ecological impacts of international trade.

Lie-szimmetriák egy közgazdasági alkalmazása (An economic application of the Lie symmetries)

Ebben a tanulmányban ismertetjük a Nöther-tétel lényegi vonatkozásait, és kitérünk a Lie-szimmetriák értelmezésére abból a célból, hogy közgazdasági folyamatokra is alkalmazzuk a Lagrange-formalizmuson nyugvó elméletet. A Lie-szimmetriák dinamikai rendszerekre történő feltárása és viselkedésük jellemzése a legújabb kutatások eredményei e területen. Például Sen és Tabor (1990), Edward Lorenz (1963), a komplex kaotikus dinamika vizsgálatában jelent®s szerepet betöltő 3D modelljét, Baumann és Freyberger (1992) a két-dimenziós Lotka-Volterra dinamikai rendszert, és végül Almeida és Moreira (1992) a három-hullám interakciós problémáját vizsgálták a megfelelő Lie-szimmetriák segítségével. Mi most empirikus elemzésre egy közgazdasági dinamikai rendszert választottunk, nevezetesen Goodwin (1967) ciklusmodelljét. Ennek vizsgálatát tűztük ki célul a leírandó rendszer Lie-szimmetriáinak meghatározásán keresztül. / === / The dynamic behavior of a physical system can be frequently described very concisely by the least action principle. In the centre of its mathematical presentation is a specic function of coordinates and velocities, i.e., the Lagrangian. If the integral of the Lagrangian is stationary, then the system is moving along an extremal path through the phase space, and vice versa. It can be seen, that each Lie symmetry of a Lagrangian in general corresponds to a conserved quantity, and the conservation principle is explained by a variational symmetry related to a dynamic or geometrical symmetry. Briey, that is the meaning of Noether's theorem. This paper scrutinizes the substantial characteristics of Noether's theorem, interprets the Lie symmetries by PDE system and calculates the generators (symmetry vectors) on R. H. Goodwin's cyclical economic growth model. At first it will be shown that the Goodwin model also has a Lagrangian structure, therefore Noether's theorem can also be applied here. Then it is proved that the cyclical moving in his model derives from its Lie symmetries, i.e., its dynamic symmetry. All these proofs are based on the investigations of the less complicated Lotka Volterra model and those are extended to Goodwin model, since both models are one-to-one maps of each other. The main achievement of this paper is the following: Noether's theorem is also playing a crucial role in the mechanics of Goodwin model. It also means, that its cyclical moving is optimal. Generalizing this result, we can assert, that all dynamic systems' solutions described by first order nonlinear ODE system are optimal by the least action principle, if they have a Lagrangian.

Quota bonuses in a principle-agent setting

Theoretical articles on incentive systems almost excusively focus on linear compensations, while in practice, nonlinear elements, eg. quota bonuses are not uncommon. Our article tries to bridge that gap and show how the use of quotas can increase the owners’ profit.

The principle of non-refoulement under international law: Its inception and evolution in a nutshell

The article first gives an overview of the formation and the evolution of the principle of non-refoulement under international law. The different meanings of the concept in the asylum and human rights contexts are then discussed and compared, with due regard to the convergences that arose in the course of legal developments. In doing so, this short piece also draws attention to certain controversial issues and blurred lines, which have surfaced through the practical application of the prohibition of refoulement. Identifying the contours of the concept and clarifying its content and its effects may help in appreciating the implications that stem, in the current extraordinary times of migratory movements, from the fundamental humanitarian legal principles of which the imperative of non-refoulement forms part.

An evaluation of the implications of the best interests of the child principle in the context of same-sex parenting in Ireland

Same-sex parenting is by no means a new phenomenon but the legal recognition and acceptance of gay and lesbian couples as parents is a relatively recent development in most countries. Traditionally, such recognition has been opposed on the basis of the claim that the best interests of children could not be met by gay and lesbian parents. This thesis examines the validity of this argument and it explores the true implications of the best interests principle in this context. The objective is to move away from subjective or moral conceptions of the best interests principle to an understanding which is informed by relevant sociological and psychological data and which is guided by reference to the rights contained in the UN Convention on the Rights of the Child. Using this perspective, the thesis addresses the overarching issue of whether the law should offer legal recognition and protection to gay and lesbian families and the more discrete matter of how legal protection should be provided. It is argued that the best interests principle can be used to demand that same-sex parenting arrangements should be afforded legal recognition and protection. Suggestions are also presented as to the most appropriate manner of providing for this recognition. In this regard, guidance is drawn from the English and South African experience in this area. Overall, the objective is to assess the current laws from the perspective of the best interests principle so as to ensure that the law operates in a manner which adheres to the rights and interests of children.