Dirac operators and spectral triples for some fractal sets built on curves

We construct spectral triples and, in particular, Dirac operators, for the algebra of continuous functions on certain compact metric spaces. The triples are countable sums of triples where each summand is based on a curve in the space. Several fractals, like a finitely summable infinite tree and the Sierpinski gasket, fit naturally within our framework. In these cases, we show that our spectral triples do describe the geodesic distance and the Minkowski dimension as well as, more generally, the complex fractal dimensions of the space. Furthermore, in the case of the Sierpinski gasket, the associated Dixmier-type trace coincides with the normalized Hausdorff measure of dimension log3/log2.     

Femtosecond laser ablation profile near an interface: Analysis based on the correlation with superficial properties of individual materials

Femtosecond laser ablation of materials is turning to be an important tool for micromachining as well as for selective removal of biological tissues. In a great number of applications, laser ablation has to process through interfaces separating media of different properties. The investigation of the ablation behavior within materials and passing through interfaces is the main aim of this study. Especially, the analysis of the discontinuity in the ablation profile close to interfaces between distinct materials can reveal some of the phenomena involved in the formation of an ablated microcavity geometry. We have used a method that correlates the ablation cross sectional area with the local laser intensity. The effective intensity ablation properties were obtained from surface ablation data of distinct materials. The application of this method allows the prediction of the occurrence of a size discontinuity in the ablation geometry at the interface of distinct media, a fact which becomes important when planning applications in different media.     

Surface free energy of films of alkali-treated cellulose microfibrils from banana rachis

Cellulose microfibrils extracted by various alkaline treatments of vascular bundles from banana rachis were used to elaborate films. The films were comparatively studied to determine changes in polarity induced by various treatments. Atomic force microscopy was used to characterize the surface morphology of the films and transmission electron microscopy was employed to characterize the microfibrils used to elaborate the films. Contact angles were measured to determine surface free energy (SFE) and thermogravimetric analyses were carried out to determine changes in composition of the films. The results showed that the films of cellulose microfibrils prepared by the peroxide alkaline (PA) and peroxide alkaline-hydrochloric acid (PA-HCl) treatments had lower content of non-cellulosic constituents like xylose and had lower SFE than films of microfibrils treated with KOH-5. Furthermore, specimens treated with the most concentrated KOH solution (18 wt%) and sodium chloride presented the highest SFE and polar component.     

Best proximity points for cyclic Meir–Keeler contractions

We introduce a notion of cyclic Meir–Keeler contractions and prove a theorem which assures the existence and uniqueness of a best proximity point for cyclic Meir–Keeler contractions. This theorem is a generalization of a recent result due to Eldred and Veeramani.     

Solid-phase supported mimic of GDP-l-galactose

A C-glycoside mimetic of l-galactose 1-diphosphate, a potential ligand of GDP-l-galactose hydrolase, an enzyme involved in the biosynthesis of vitamin C, has been designed, stereoselectively synthesised by C-allylation of tribenzylated l-fucose, by periodate-osmium tetroxide degradation of the double bond, by condensation of the obtained aldehydes with benzylacetate and by deprotection. The obtained mimetic was linked to a sepharose resin.     

Asymmetric microbial reduction of ketones: absolute configuration of trans-4-ethyl-1-(1S-hydroxyethyl)cyclohexanol

A set of five fungal species, Botrytis cinerea, Trichoderma viride and Eutypa lata, and the endophytic fungi Colletotrichum crassipes and Xylaria sp., was used in screening for microbial biocatalysts to detect monooxygenase and alcohol dehydrogenase activities (for the stereoselective reduction of carbonyl compounds). 4-Ethylcyclohexanone and acetophenone were biotransformed by the fungal set. The main reaction pathways involved reduction and hydroxylations at several positions including tertiary carbons. B. cinerea was very effective in the bioreduction of both substrates leading to the chiral alcohol (S)-1-phenylethanol in up to 90% enantiomeric excess, and the cis–trans ratio for 4-ethylcyclohexanol was 0:100. trans-4-Ethyl-1-(1S-hydroxyethyl)cyclohexanol, obtained from biotransformation by means of an acyloin-type reaction, is reported here for the first time. The absolute configurations of the compounds trans-4-ethyl-1-(1S-hydroxyethyl)cyclohexanol and 4-(1S- and 4-(1R-hydroxyethyl)cyclohexanone were determined by NMR analysis of the corresponding Mosher’s esters.     

A Markov model for analyzing the evolution of bladder carcinoma

A Markovian approach to analyze different states of the superficial vesical carcinoma is considered, taking into account up to two recurrences and the possibility of progression. So, three transient states are considered: free of disease, first, and second recurrence; and an absorbent state, the progression. A methodology based in phase-type distributions is also used, that allows the usual quantities of interest in survival studies to be expressed in a well-structured form. This type of distribution has shown its utility in queue theory, and has the advantage that mathematical expressions can be presented in a closed form that allows algebraic treatment.     

Modeling the Behavior of Heat-Shrinkable Thin Films

We describe an asymptotic model for the behavior of PET-like heat-shrinkable thin films that includes both membrane and bending energies when the thickness of the film is positive. We compare the model to Koiter’s shell model and to models in which a membrane energy or a bending energy are obtained by Γ-convergence techniques. We also provide computational results for various temperature distributions applied to the films.     

Study of the acid-base properties of SiO2-supported NiMoO4 catalysts by temperature-programmed desorption: effect of the support

The acid-base properties of several NiMoO₄ catalysts supported on two silicas and prepared by different methods have been studied by temperature-programmed desorption of NH₃. The catalytic behavior in the oxidative dehydrogenation of isobutane for two NiMoO₄ catalysts with different acid-base properties are compared.