Finite element approximation of nematic liquid crystal flows using a saddle-point structure

In this work, we propose finite element schemes for the numerical approximation of nematic liquid crystal flows, based on a saddle-point formulation of the director vector sub-problem. It introduces a Lagrange multiplier that allows to enforce the sphere condition. In this setting, we can consider the limit problem (without penalty) and the penalized problem (using a Ginzburg–Landau penalty function) in a unified way. Further, the resulting schemes have a stable behavior with respect to the value of the penalty parameter, a key difference with respect to the existing schemes. Two different methods have been considered for the time integration. First, we have considered an implicit algorithm that is unconditionally stable and energy preserving. The linearization of the problem at every time step value can be performed using a quasi-Newton method that allows to decouple fluid velocity and director vector computations for every tangent problem. Then, we have designed a linear semi-implicit algorithm (i.e. it does not involve nonlinear iterations) and proved that it is unconditionally stable, verifying a discrete energy inequality. Finally, some numerical simulations are provided.     

Isometries on and monotone functions

We study necessary and sufficient conditions on a bounded operator T defined on the Hilbert space to be an isometry and show that, under suitable hypotheses, it suffices to restrict T to a smaller class of functions (e.g., if , to the cone of positive and decreasing functions). We also consider the problem of characterizing the sets for which the orthogonal projection of the operator T on is also an isometry. Finally, we illustrate our results with several examples involving classical operators on different settings.     

On monomial curves obtained by gluing

We study arithmetic properties of tangent cones associated to large families of monomial curves obtained by gluing. In particular, we characterize their Cohen-Macaulay and Gorenstein properties and prove that they have non-decreasing Hilbert functions. The results come from a careful analysis of some special Apéry sets of the numerical semigroups obtained by gluing under a condition that we call specific gluing. As a consequence, we complete and extend the results proved by Arslan et al. (in Proc. Am. Math. Soc. 137:2225–2232, 2009) about nice gluings by using different techniques. Our results also allow to prove that for a given numerical semigroup with a non-decreasing Hilbert function and an integer q>1, all extensions of it by q, except a finite number, have non-decreasing Hibert functions.     

Market frictions and corporate finance: an overview paper

We present an overview of corporate-finance models where firms are subject to exogenous market frictions. These models, albeit quite simple, yield reasonable predictions regarding financing, pay-outs and default, as well as asset-pricing implications. The price to pay for the said simplicity is the need to use non-standard mathematical techniques, namely singular and impulse stochastic control. We explore the cases where a firm with fixed expected profitability has access to costly equity issuance as a refinancing possibility, and that where issuance is infinitely costly. We also present a model of bank leverage.     

Study of Starch Degradation by Yeasts During Fermentation for Using in Animal Feed

Sixteen amylolytic yeasts, drawn from culture collections or isolated from different environments, were used in the present study. Experiments were performed to evaluate the starch degradation due to exocellular activity. The culture media of growth was optimized to find the maximum activity, and some strains produced an extracellular amylolytic enzyme when cultured in presence of starch in the medium. On the other hand, one yeast showed activity in cell extract when cultured under varying conditions in a bench bioreactor; this strain would thus be suitable for use as an animal feed supplement, both as a source of proteins and nucleic acids and in terms of its amylolytic activity.     

Reversibly Switchable Fluorescent Molecular Systems Based on Metallacarborane–Perylenediimide Conjugates

Icosahedral metallacarboranes are θ-shaped anionic molecules in which two icosahedra share one vertex that is a metal center. The most remarkable of these compounds is the anionic cobalt-based metallacarborane [Co(C₂B₉H₁₁)₂]⁻, whose oxidation-reduction processes occur via an outer sphere electron process. This, along with its low density negative charge, makes [Co(C₂B₉H₁₁)₂]⁻ very appealing to participate in electron-transfer processes. In this work, [Co(C₂B₉H₁₁)₂]⁻ is tethered to a perylenediimide dye to produce the first examples of switchable luminescent molecules and materials based on metallacarboranes. In particular, the electronic communication of [Co(C₂B₉H₁₁)₂]⁻ with the appended chromophore unit in these compounds can be regulated upon application of redox stimuli, which allows the reversible modulation of the emitted fluorescence. As such, they behave as electrochemically-controlled fluorescent molecular switches in solution, which surpass the performance of previous systems based on conjugates of perylendiimides with ferrocene. Remarkably, they can form gels by treatment with appropriate mixtures of organic solvents, which result from the self-assembly of the cobaltabisdicarbollide-perylendiimide conjugates into 1D nanostructures. The interplay between dye π-stacking and metallacarborane electronic and steric interactions ultimately governs the supramolecular arrangement in these materials, which for one of the compounds prepared allows preserving the luminescent behavior in the gel state.     

Quantification of Photosensitized Singlet Oxygen Production by a Fluorescent Protein

Fluorescent proteins are increasingly becoming actuators in a range of cell biology techniques. One of those techniques is chromophore‐assisted laser inactivation (CALI), which is employed to specifically inactivate the function of target proteins or organelles by producing photochemical damage. CALI is achieved by the irradiation of dyes that are able to produce reactive oxygen species (ROS). The combination of CALI and the labelling specificity that fluorescent proteins provide is useful to avoid uncontrolled photodamage, although the inactivation mechanisms by ROS are dependent on the fluorescent protein and are not fully understood. Herein, we present a quantitative study of the ability of the red fluorescent protein TagRFP to produce ROS, in particular singlet oxygen (¹O₂). TagRFP is able to photosensitize ¹O₂ with an estimated quantum yield of 0.004. This is the first estimation of a quantum yield of ¹O₂ production value for a GFP‐like protein. We also find that TagRFP has a short triplet lifetime compared to EGFP, which reflects relatively high oxygen accessibility to the chromophore. The insight into the structural and photophysical properties of TagRFP has implications in improving fluorescent proteins for fluorescence microscopy and CALI.