Application of the combined integral method to Stefan problems

In this paper we present a new, accurate form of the heat balance integral method, termed the Combined Integral Method (or CIM). The application of this method to Stefan problems is discussed. For simple test cases the results are compared with exact and asymptotic limits. In particular, it is shown that the CIM is more accurate than the second order, large Stefan number, perturbation solution for a wide range of Stefan numbers. In the initial examples it is shown that the CIM reduces the standard problem, consisting of a PDE defined over a domain specified by an ODE, to the solution of one or two algebraic equations. The latter examples, where the boundary temperature varies with time, reduce to a set of three first order ODEs.

Improving the accuracy of heat balance integral methods applied to thermal problems with time dependent boundary conditions

In this paper the two main drawbacks of the heat balance integral methods are examined. Firstly we investigate the choice of approximating function. For a standard polynomial form it is shown that combining the Heat Balance and Refined Integral methods to determine the power of the highest order term will either lead to the same, or more often, greatly improved accuracy on standard methods. Secondly we examine thermal problems with a time-dependent boundary condition. In doing so we develop a logarithmic approximating function. This new function allows us to model moving peaks in the temperature profile, a feature that previous heat balance methods cannot capture. If the boundary temperature varies so that at some time t & 0 it equals the far-field temperature, then standard methods predict that the temperature is everywhere at this constant value. The new method predicts the correct behaviour. It is also shown that this function provides even more accurate results, when coupled with the new CIM, than the polynomial profile. Analysis primarily focuses on a specified constant boundary temperature and is then extended to constant flux, Newton cooling and time dependent boundary conditions.

An axiomatic justification of mediation in bankruptcy problems.

This paper provides a natural way of reaching an agreement between two prominent proposals in a bankruptcy problem. Particularly, using the fact that such problems can be faced from two different points of views, awards and losses, we justify the average of any pair of dual bankruptcy rules through the definition a double recursive process. Finally, by considering three posible sets of equity principles that a particular society may agree on, we retrieve the average of old and well known bankruptcy rules, the Constrained Equal Awards and the Constrained Equal Losses rules, Piniles’ rule and its dual rule, and the Constrained Egalitarian rule and its dual rule. Keywords: Bankruptcy problems, Midpoint, Bounds, Duality, Recursivity. JEL classification: C71, D63, D71.

A way to play bankruptcy problems.

The commitment among agents has always been a difficult task, especially when they have to decide how to distribute the available amount of a scarce resource among all. On the one hand, there are a multiplicity of possible ways for assigning the available amount; and, on the other hand, each agent is going to propose that distribution which provides her the highest possible award. In this paper, with the purpose of making this agreement easier, firstly we use two different sets of basic properties, called Commonly Accepted Equity Principles, to delimit what agents can propose as reasonable allocations. Secondly, we extend the results obtained by Chun (1989) and Herrero (2003), obtaining new characterizations of old and well known bankruptcy rules. Finally, using the fact that bankruptcy problems can be analyzed from awards and losses, we define a mechanism which provides a new justification of the convex combinations of bankruptcy rules. Keywords: Bankruptcy problems, Unanimous Concessions procedure, Diminishing Claims mechanism, Piniles’ rule, Constrained Egalitarian rule. JEL classification: C71, D63, D71.

Zerebrale Probleme in der pädiatrischen Intensivmedizin [Cerebral problems in pediatric intensive care]

This paper presents a review of different methods enabling the monitoring of cerebral function in neonatal and paediatric intensive care. EEG, evoked potentials, conventional radiological studies, computerized tomography, ultrasound, intracranial pressure measurements, nuclear magnetic resonance, Doppler ultrasound, radioisotope studies, angiography, infra-red spectral analysis and last, but not least, clinical examination produce information regarding the neurological state of the patient which must be critically analysed in order to ensure optimal management of the case. Unfortunately, and in spite of impressive progress in non-invasive monitoring of the cerebral function, we are still forced to make important medical and ethical decisions without precise information about the neurological state of our patients.

IPH Response to Dept of Justice and Equality Review of the Code of Practice on the Sale and Display of Alcohol in Mixed Trading Premises

IPH responded to the Department of Justice, Equality and Defence review of the voluntary Code of Practice for the display and sale of alcohol in supermarkets, convenience stores and similar mixed trading outlets. The voluntary Code was introduced in 2008 as an alternative to the statutory rules for structural separation of alcohol products in mixed trading outlets which are set out in section 9 of the Intoxicating Liquor Act 2008. Interested bodies and individuals were invited to submit comments on the Compliance Report for 2011 and on the effectiveness of the voluntary approach to structural separation by 20th December 2011. The Minister said he intended to also seek the views of the Minister for Health and the Joint Oireachtas Committee on Justice, Defence and Equality before reaching any decision on whether to bring the statutory rules in the 2008 Act into operation.

Phylogeny of the kinetoplastida: taxonomic problems and insights into the evolution of parasitism

To further investigate phylogeny of kinetoplastid protozoa, the sequences of small subunit (18S) ribosomal RNA of nine bodonid isolates and ten isolates of insect trypanosomatids have been determined. The root of the kinetoplastid tree was attached to the branch of Bodo designis and/or Cruzella marina. The suborder Trypanosomatina appeared as a monophyletic group, while the suborder Bodonina was paraphyletic. Among bodonid lineages, parasitic organisms were intermingled with free-living ones, implying multiple transitions to parasitism and supporting the `vertebrate-first hypothesis'. The tree indicated that the genera Cryptobia and Bodo are artificial taxa. Separation of fish cryptobias and Trypanoplasma borreli as different genera was not supported. In trypanosomatids, the genera Leptomonas and Blastocrithidia were polyphyletic, similar to the genera Herpetomonas and Crithidia and in contrast to the monophyletic genera Trypanosoma and Phytomonas. This analysis has shown that the morphological classification of kinetoplastids does not in general reflect their genetic affinities and needs a revision.

A subspace correction method for discontinuous Galerkin discretizations of linear elasticity equations

We study preconditioning techniques for discontinuous Galerkin discretizations of isotropic linear elasticity problems in primal (displacement) formulation. We propose subspace correction methods based on a splitting of the vector valued piecewise linear discontinuous finite element space, that are optimal with respect to the mesh size and the Lamé parameters. The pure displacement, the mixed and the traction free problems are discussed in detail. We present a convergence analysis of the proposed preconditioners and include numerical examples that validate the theory and assess the performance of the preconditioners.

A Proportional Approach to Bankruptcy Problems with a guaranteed minimum

In a distribution problem, and specfii cally in bankruptcy issues, the Proportional (P) and the Egalitarian (EA) divisions are two of the most popular ways to resolve the conflict. The Constrained Equal Awards rule (CEA) is introduced in bankruptcy literature to ensure that no agent receives more than her claim, a problem that can arise when using the egalitarian division. We propose an alternative modi cation, by using a convex combination of P and EA. The recursive application of this new rule finishes at the CEA rule. Our solution concept ensures a minimum amount to each agent, and distributes the remaining estate in a proportional way. Keywords: Bankruptcy problems, Proportional rule, Equal Awards, Convex combination of rules, Lorenz dominance. JEL classi fication: C71, D63, D71.

Solidarity and uniform rules in bankruptcy problems

The idea of ensuring a guarantee (a minimum amount of the resources) to each agent has recently acquired great relevance, in both social and politi- cal terms. Furthermore, the notion of Solidarity has been treated frequently in redistribution problems to establish that any increment of the resources should be equally distributed taking into account some relevant characteris- tics. In this paper, we combine these two general concepts, guarantee and solidarity, to characterize the uniform rules in bankruptcy problems (Con- strained Equal Awards and Constrained Equal Losses rules). Keywords: Constrained Equal Awards, Constrained Equal Losses, Lower bounds, Bankruptcy problems, Solidarity. JEL classification: C71, D63, D71.