On the identification <Emphasis Type=Italic>H</Emphasis> = <Emphasis Type=Italic>H</Emphasis>′ in the Lions theorem and a related inaccuracy

We show that the common identification of H with its dual space in the famous functional frame V ⊂ H = H′ ⊂ V′ is incompatible with the distributional frame for some standard pdes and we recall an error related to this unnecessary identification which is repeated from years.     

Theoretical and fuzzy modelling of a pharmaceutical batch reactor

This paper deals with the development of a batch-reactor model with a theoretical and a locally affine fuzzy model. The batch reactor is used in the pharmaceutical industry for the production of drugs, where a rapid and precise temperature control is necessary. The model has to be built to include all the main features necessary for the purposes of modelling. The development of the model for the reactor is designed for further control development and simulation purposes, without doing any further experiments on the real process. In our case we use the model for simulating the reactor’s jacket temperature and the reactor’s core temperature. The theoretical model describes all the nonlinearities of the process of heating and cooling the content of the batch reactor. The main contribution of the theoretical model is in the modelling of the heat transfer between the reactor’s jacket and the reactor’s core, mainly caused by the change in the overall heat transfer, which also covers the main nonlinearity. Because of the complexity of the theoretical model a locally affine fuzzy model is also developed.     

An optimization-based numerical method for diffusion problems with sign-changing coefficients

A new optimization-based numerical method is proposed for the solution to diffusion problems with sign-changing conductivity coefficients. In contrast to existing approaches, our method does not rely on the discretization of a stabilized equation, and the convergence of the scheme can be proved without any symmetry assumption on the mesh near the interface where the conductivity sign changes.     

Loss of convexity and embeddedness for geometric evolution equations of higher order

We show that for a large class of geometric evolution equations of immersed surfaces in the Euclidean space, there are compact embedded surfaces that lose their embeddedness and compact strictly convex surfaces that lose their convexity under these evolution equations.     

Estimation of the intensity of non-homogeneous point processes via wavelets

In this article we consider the problem of estimating the intensity of a non-homogeneous point process on the real line. The approach used is via wavelet expansions. Estimators of the intensity are proposed and their properties are studied, including the case of thresholded versions. Properties of the estimators for non-homogeneous Poisson processes follow as special cases. An application is given for the series of daily Dow Jones indices. Extensions to more general settings are also indicated.     

DPSIR = A Problem Structuring Method? An exploration from the “Imagine” approach

The Drivers, Pressures, State, Impact and Response or DPSIR framework has been with us for over a decade now and it is widely used as a means to assess and measure and, eventually provide a guide to managing the environment. With its repertoire of diagnostic and analytical components the DPSIR can be argued to be a Problem Structuring Method or PSM. Criticisms of the framework abound but it has a resilience which is noteworthy. Some argue that DPSIR, by its nature, is a narrowly formulated, engineering device, incompatible with the multiple perspectives which human interaction in global ecology requires. Is there a value in DPSIR being more flexible in expression and experience of users? In this article it is shown how the DPSIR framework was applied within a multi-methodology approach called Imagine in a number of coastal management projects around the Mediterranean and in other contexts. The article argues that DPSIR, whilst admittedly limited in its scope and approach can, if applied in a participatory and systemic multi-methodology, combine with other tools and help to create outcomes of value to local populations.     

The gradient flow of the M?bius energy near local minimizers

In this article we show that for initial data close to local minimizers of the M?bius energy the gradient flow exists for all time and converges smoothly to a local minimizer after suitable reparametrizations. To prove this, we show that the heat flow of the M?bius energy possesses a quasilinear structure which allows us to derive new short-time existence results for this evolution equation and a ?ojasiewicz-Simon gradient inequality for the M?bius energy.