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Projeto de investigação
Center for Mathematics, Fundamental Applications and Operations Research
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On the use of quasi-equidistant source points over the sphere surface for the method of fundamental solutions
Publication . Araújo, António; Serranho, Pedro
The method of fundamental solutions is broadly used in science and engineering to numerically solve the direct time-harmonic scattering problem. In 2D the choice of source points is usually made by considering an inner pseudo-boundary over which equidistant source points are placed. In 3D, however, this problem is much more challenging, since, in general, equidistant points over a closed surface do not exist. In this paper we discuss a method to obtain a quasi-equidistant point distribution over the unit sphere surface, giving rise to a Delaunay triangulation that might also be used for other boundary element methods. We give theoretical estimates for the expected distance between points and the expect area of each triangle. We illustrate the feasibility of the proposed method in terms of the comparison with the expected values for distance and area. We also provide numerical evidence that this point distribution leads to a good conditioning of the linear system associated with the direct scattering problem, being therefore an adequated choice of source points for the method of fundamental solutions.
The Russell-Prawitz embedding and the atomization of universal instantiation
Publication . Espírito Santo, José; Ferreira, Gilda
Given the recent interest in the fragment of system F where universal instantiation
is restricted to atomic formulas, a fragment nowadays named system Fat, we
study directly in system F new conversions whose purpose is to enforce that restriction.
We show some benefits of these new atomization conversions: (1) They
help achieving strict simulation of proof reduction by means of the Russell-Prawitz
embedding of IPC into system F; (2) They are not stronger than a certain “dinaturality”
conversion known to generate a consistent equality of proofs; (3) They
provide the bridge between the Russell-Prawitz embedding and another translation,
due to the authors, of IPC directly into system Fat; (4) They give means for
explaining why the Russell-Prawitz translation achieves strict simulation whereas
the translation into Fat does not.
An infinite dimensional umbral calculus
Publication . Oliveira, Maria João
A refined interpretation of intuitionistic logic by means of atomic polymorphism
Publication . Espírito Santo, José; Ferreira, Gilda
We study an alternative embedding of IPC into atomic system F whose translation of
proofs is based, not on instantiation overflow, but instead on the admissibility of the elimination
rules for disjunction and absurdity (where these connectives are defined according to the Russell-
Prawitz translation). As compared to the embedding based on instantiation overflow, the alternative
embedding works equally well at the levels of provability and preservation of proof identity, but
it produces shorter derivations and shorter simulations of reduction sequences. Lambda-terms are
employed in the technical development so that the algorithmic content is made explicit, both for the
alternative and the original embeddings. The investigation of preservation of proof-reduction steps
by the alternative embedding enables the analysis of generation of “administrative” redexes. These
are the key, on the one hand, to understand the difference between the two embeddings; on the other
hand, to understand whether the final word on the embedding of IPC into atomic system F has been
said.
Hydrogenolysis of Xylitol to value added products: a mathematical approach
Publication . Ndlovu, Thandokuhle Quinton; Costa, Fernando Pestana da; Magagula, Vusi; Shozi, Mzamo
In this paper we mathematically investigate the kinetics underlying the hydrogenolysis of xylitol over a metal based catalyst by using ordinary differential equations. The primary motivation for mathematically investigating this reaction lies on the fact that some of the value added products from this reaction are sourced from fossil fuels, which are not environmentally friendly. They have been reported by different researchers that they are the primary drive of global warming which leads to climate change, which causes severe disturbances in the Earth´s natural systems and economies. Xylitol, on the other hand, which is readily available from biomass have been reported as an alternative raw material for some of the value added products. A reaction mechanism proposed from experimental data is used to formulate a system of ordinary differential equations which is then analyzed using some qualitative analysis tools from mathematics. Numerical simulations are performed to try and ascertain the long time behavior of the system's solutions. Results showed that the solutions to the system approaches a lower dimensional invariant set with X_k=0 for k=1,...,8 and X_k>0 for k=9, 10, 11. These numerical results were found to be in agreement with the experimental results from the chemistry point of view. Therefore, it is believed that this model can be extended for use in other sugar alcohols higher than xylitol, like sorbitol as means to maximize the yields of the desired products.
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Entidade financiadora
Fundação para a Ciência e a Tecnologia
Programa de financiamento
6817 - DCRRNI ID
Número da atribuição
UID/MAT/04561/2019