Fixed point transformations in the adaptive control of fractional-order MIMO systems

Though the formal mathematical idea of introducing noninteger order derivatives can be traced from the 17th century in a letter by L’Hospital in which he asked Leibniz what the meaning of D n y if n = 1/2 would be in 1695 [1], it was better outlined only in the 19th century [2, 3, 4]. Due to the lack of clear physical interpretation their first applications in physics appeared only later, in the 20th century, in connection with visco-elastic phenomena [5, 6]. The topic later obtained quite general attention [7, 8, 9], and also found new applications in material science [10], analysis of earth-quake signals [11], control of robots [12], and in the description of diffusion [13], etc.

Application of robust fixed point transformations for technological operation of robots

A robot’s drive has to exert appropriate driving forces that can keep its arm and end effector at the proper position, velocity and acceleration, and simultaneously has to compensate for the effects of the contact forces arising between the tool and the workpiece depending on the needs of the actual technological operation. Balancing the effects of a priori unknown external disturbance forces and the inaccuracies of the available dynamic model of the robot is also important. Technological tasks requiring well prescribed end effector trajectories and contact forces simultaneously are challenging control problems that can be tackled in various manners.

Surface morphology and phase transformations of femtosecond laser-processed saphire

The morphological and structural modifications induced in sapphire by surface treatment with femtosecond laser radiation were studied. Single-crystal sapphire wafers cut parallel to the (0 1 2) planes were treated with 560 fs, 1030 nm wavelength laser radiation using wide ranges of pulse energy and repetition rate. Self-ordered periodic structures with an average spatial periodicity of similar to 300 nm were observed for fluences slightly higher than the ablation threshold. For higher fluences the interaction was more disruptive and extensive fracture, exfoliation, and ejection of ablation debris occurred. Four types of particles were found in the ablation debris: (a) spherical nanoparticles about 50 nm in diameter; (b) composite particles between 150 and 400 nm in size; (c) rounded resolidified particles about 100-500 nm in size; and (d) angular particles presenting a lamellar structure and deformation twins. The study of those particles by selected area electron diffraction showed that the spherical nanoparticles and the composite particles are amorphous, while the resolidified droplets and the angular particles, present a crystalline a-alumina structure, the same of the original material. Taking into consideration the existing ablation theories, it is proposed that the spherical nanoparticles are directly emitted from the surface in the ablation plume, while resolidified droplets are emitted as a result of the ablation process, in the liquid phase, in the low intensity regime, and by exfoliation, in the high intensity regime. Nanoparticle clusters are formed by nanoparticle coalescence in the cooling ablation plume. (C) 2013 Elsevier B.V. All rights reserved.

On the ranks of certain monoids of transformations that preserve a uniform partition

The rank of a semigroup, an important and relevant concept in Semigroup Theory, is the cardinality of a least-size generating set. Semigroups of transformations that preserve or reverse the order or the orientation as well as semigroups of transformations preserving an equivalence relation have been widely studied over the past decades by many authors. The purpose of this article is to compute the ranks of the monoid

The cardinal of various monoids of transformations that preserve a uniform partition

In this paper we give formulas for the number of elements of the monoids ORm x n of all full transformations on it finite chain with tun elements that preserve it uniform m-partition and preserve or reverse the orientation and for its submonoids ODm x n of all order-preserving or order-reversing elements, OPm x n of all orientation-preserving elements, O-m x n of all order-preserving elements, O-m x n(+) of all extensive order-preserving elements and O-m x n(-) of all co-extensive order-preserving elements.

Evidences for direct magnetic patterning via diffusive transformations using femtosecond laser interferometry

The application of femtosecond laser interferometry to direct patterning of thin-film magnetic alloys is demonstrated. The formation of stripe gratings with submicron periodicities is achieved in Fe1-xVx (x=18-34wt. %) layers, with a difference in magnetic moments up to Delta mu/mu similar to 20 between adjacent stripes but without any significant development of the topographical relief (<1% of the film thickness). The produced gratings exhibit a robust effect of their anisotropy shape on magnetization curves in the film plane. The obtained data witness ultrafast diffusive transformations associated with the process of spinodal decomposition and demonstrate an opportunity for producing magnetic nanostructures with engineered properties upon this basis.

Congruences on monoids of transformations preserving the orientation on a finite chain

Journal of Algebra, 321 (2009), p. 743–757

Congruences on monoids of order-preserving or order-reversing transformations on a finite chain

Glasgow Mathematical Journal, nº 47 (2005), pg. 413-424

Presentations for some monoids of injective partial transformations on a finite chain.

Communications in Algebra, 33 (2005), p. 587-604

The cardinal and the idempotent number of various monoids of transformations on a finite chain

Bulletin of the Malaysian Mathematical Sciences Society, 2, 34 (1),(2011), p. 79–85

The cardinal of various monoids of transformations that preserve a uniform partition

Bulletin of the Malaysian Mathematical Sciences Society

On the monoids of transformations that preserve the order and a uniform partition

Communications in Algebra

A framework to operate transformations between distinct models differing in modelling concepts

Dissertação apresentada na Faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa para obtenção do grau de Mestre em Engenharia Electrotécnica e de Computadores

A framework for efficient model transformations

The reported productivity gains while using models and model transformations to develop entire systems, after almost a decade of experience applying model-driven approaches for system development, are already undeniable benefits of this approach. However, the slowness of higher-level, rule based model transformation languages hinders the applicability of this approach to industrial scales. Lower-level, and efficient, languages can be used but productivity and easy maintenance seize to exist. The abstraction penalty problem is not new, it also exists for high-level, object oriented languages but everyone is using them now. Why is not everyone using rule based model transformation languages then? In this thesis, we propose a framework, comprised of a language and its respective environment, designed to tackle the most performance critical operation of high-level model transformation languages: the pattern matching. This framework shows that it is possible to mitigate the performance penalty while still using high-level model transformation languages.

Photochemical synthesis and functional transformations of bicyclic vinyl aziridines

Aziridines, a class of organic compounds containing a three membered heterocycle with a nitrogen atom, are extremely valuable molecules in organic and medicinal chemistry. They are frequently used as versatile precursors in the synthesis of natural products, and many biologically active molecules possess the aziridine moiety. The reactivity of aziridines has been studied, for example, in ring-opening reactions with thiols. However, not much interest seems to be given to reactions of aziridines in aqueous media, despite the numberless advantages of using water as solvent in organic chemistry. The nucleophilic ring-opening reaction of aziridines in aqueous media was here explored. Following the Kaplan aziridine synthetic methodology, in which pyridinium salts undergo a photochemical transformation to give bicyclic vinyl aziridines, new aziridines were synthetized. Their nucleophilic ring-opening reaction in water under physiological conditions was investigated and a range of sulphur, nitrogen, carbon and oxygen nucleophiles tested. Thiols, anilines and azide proved to be good nucleophiles to react with the aziridines, giving the ring-opening product in moderate to good yields. The best results were obtained with thiols, more specifically with cysteine-derived nucleophiles. Preliminary results show that these bicyclic vinyl aziridines can modify calcitonin, a peptide containing two cysteine amino acids residues, grating them the potential to be used in bioconjugation as ligands to cysteine-containing proteins, or even as enzyme inhibitors of, for example, cysteine proteases. Additionally, exploratory investigations suggest that the separation of both enantiomers of the bicyclic vinyl aziridine can be performed by taking advantage of an enzymatic methodology for the resolution of racemic secondary alcohols. Both enantiomers would be highly valuable as precursors in the synthesis of enantiomerically pure molecules, as no other method is currently reported for their separation.