A fractional spline collocation-Galerkin method for the time-fractional diffusion equation

The aim of this paper is to numerically solve a diffusion differential problem having time derivative of fractional order. To this end we propose a collocation-Galerkin method that uses the fractional splines as approximating functions. The main advantage is in that the derivatives of integer and fractional order of the fractional splines can be expressed in a closed form that involves just the generalized finite difference operator. This allows us to construct an accurate and efficient numerical method. Several numerical tests showing the effectiveness of the proposed method are presented.Comment: 15 page

A fractional wavelet Galerkin method for the fractional diffusion problem

The aim of this paper is to solve some fractional differential problems hav- ing time fractional derivative by means of a wavelet Galerkin method that uses the fractional scaling functions introduced in a previpous paper as approximating functions. These refinable functions, which are a generalization of the fractional B-splines, have many interesting approximation properties. In particular, their fractional derivatives have a closed form that involves just the fractional difference operator. This allows us to construct accurate and efficient numerical methods to solve fractional differential problems. Some numerical tests on a fractional diffusion problem will be given

A fractional spline collocation method for the fractional order logistic equation

We construct a collocation method based on the fractional B-splines to solve a nonlinear differential problem that involves fractional derivative, i.e. the fractional order logistic equation. The use of the fractional B-splines allows us to express the fractional derivative of the approximating function in an analytic form. Thus, the fractional collocation method is easy to implement, accurate and efficient. Several numerical tests illustrate the efficiency of the proposed collocation method.We construct a collocation method based on the fractional B-splines to solve a nonlinear differential problem that involves fractional derivative, i.e. the fractional order logistic equation. The use of the fractional B-splines allows us to express the fractional derivative of the approximating function in an analytic form. Thus, the fractional collocation method is easy to implement, accurate and efficient. Several numerical tests illustrate the efficiency of the proposed collocation method

A multiscale collocation method for fractional differential problems

We introduce a multiscale collocation method to numerically solve differential problems involving both ordinary and fractional derivatives of high order. The proposed method uses multiresolution analyses (MRA) as approximating spaces and takes advantage of a finite difference formula that allows us to express both ordinary and fractional derivatives of the approximating function in a closed form. Thus, the method is easy to implement, accurate and efficient. The convergence and the stability of the multiscale collocation method are proved and some numerical results are shown.We introduce a multiscale collocation method to numerically solve differential problems involving both ordinary and fractional derivatives of high order. The proposed method uses multiresolution analyses (MRA) as approximating spaces and takes advantage of a finite difference formula that allows us to express both ordinary and fractional derivatives of the approximating function in a closed form. Thus, the method is easy to implement, accurate and efficient. The convergence and the stability of the multiscale collocation method are proved and some numerical results are shown

Fractional GP refinable functions

A new class of refinable functions extending the GP class introduced in [12] is presented. It is characterized by a symbol with fractional exponent that gives rise to non-compactly supported refinable functions. Nevertheless, the decay and stability properties of these refinable functions allow them to generate a multiresolution analysis (MRA) of L2(R). For suitable values of their parameters these refinable functions reduce to the fractional B-splines introduced in [16], while, for integer α, they interpolate the GP refinable functions. Furthermore, this class of refinable functions is proved to be closed with respect to convolution and fractional differentiation, allowing for its convenient the applicability to Sobolev spaces. The fractional refinable functions introduced here show an useful order of polynomial exactness

The European Green Deal: shaping environmentally friendly policies under Article 101 TFEU

In the light of the renewed general interest for environmental issues, resulting from the launch of the European Green Deal by President Von Der Leyen, the paper explores how the EU Commission could promote environmental considerations in the implementation of competition policies. More in detail, starting from the role currently played by environmental factors in the assessment of anticompetitive agreements, the paper will consider whether Article 101 TFEU, as it is formulated – read in the light of the Commission’s decisional practice and of the ECJ’s case law – would support a broader interpretation, according to which the importance of environment-related considerations would be increased, also in line with the expectations of President Von Der Leyen. For this purpose, the present analysis will be focused on the first and third paragraph of Article 101 TFEU, both already used in the past by the Commission – although on the basis of a different legal reasoning – in order to support the relevance of policy considerations (including those environment-related) within competition assessment. The results of such analysis will show that there is sufficient room for a change in the approach of the Commission, that could (and should) be followed also at national level. If such approach will effectively be adopted, the role played by environmental considerations in the implementation of competition policies could be immediately enhanced, without the need to wait for the adoption of a specific legislative act (or, even worse, for a Treaty amendment)

Translating “Under the Sign of Invention”: Gilberto Gil’s Song Lyric Translation

The translation of song lyrics shares in the difficulties of constrained translation, as well as in the impossibilities of poetic translation. In Gilberto Gil’s adaptation of the song “I just called to say I love you” by Stevie Wonder, two translation procedures stand out: (1) to take broad semantic fields as translation units, and (2) to opt for cultural adaptation in terms of the translation’s poles of domesticating/foreignizing. The way Gil faces up to the challenges of the translation of the song is consistent with Haroldo de Campos ideas on transcreation.La traduction de chansons partage avec la traduction subordonnée les mêmes difficultés et, avec la traduction poétique, les mêmes impossibilités. Dans sa version de “I just called to say I love you” de Stevie Wonder, Gilberto Gil fait appel à deux procédés : d’une part, le découpage de larges champs sémantiques comme unités de traduction, et d’autre part, le choix délibéré d’une adaptation culturelle de la traduction. La manière dont Gilberto Gil traite les difficultés de la traduction de la chanson n’est pas sans évoquer les principes de la transcréation de Haroldo de Campos

A Risk Assessment of the Impacts of Coastal Flooding and Sea Level Rise on the Existing and New Pump Stations 113, Norfolk, VA

The author assessed the risk to a wastewater pump station and a planned replacement located nearby due to coastal flooding and rising sea levels. The locations for the pump stations are in the Larchmont neighborhood by the Lafayette River tidal estuaries in Norfolk, Virginia. The Lafayette River is a tributary to the Elizabeth River, which flows to the Chesapeake Bay. The low-lying areas along the river are subject to coastal surges caused by tropical and extra-tropical storms that flood the bay. The region is considered one of the urban areas most exposed to the accelerating rate of rising sea levels. Six of the highest storm surges on record have occurred since 2003 and even more moderate events have inundated the existing pump station. The flooding impacts the service and reduces the life cycle performance of the pump system. The study compares the vulnerability of the existing pump station to an alternative to replace the station in a new location. It uses systems engineering to define the challenge caused by coastal flooding and future sea levels, and risk-informed decision methodologies to define the exposure. The findings show that the investment in a new pump station reduces relative risk due to coastal flooding nearly fivefold; but over the 50-year life cycle of the pump station the risk increases again because of higher sea levels