The harmonic mean curvature flow of nonconvex surfaces in {\mathbb{R}^3}

We consider a compact star-shaped mean convex hypersurface ${\Sigma^2\subset \mathbb{R}^3}$ . We prove that in some cases the flow exists until it shrinks to a point. We also prove that in the case of a surface of revolution which is star-shaped and mean convex, a smooth solution always exists up to some finite time T < ∞ at which the flow shrinks to a point asymptotically spherically.     

Differentiation of teaching and learning mathematics: an action research study in tertiary education

Diversity and differentiation within our classrooms, at all levels of education, is nowadays a fact. It has been one of the biggest challenges for educators to respond to the needs of all students in such a mixed-ability classroom. Teachers’ inability to deal with students with different levels of readiness in a different way leads to school failure and all the negative outcomes that come with it. Differentiation of teaching and learning helps addressing this problem by respecting the different levels that exist in the classroom, and by responding to the needs of each learner. This article presents an action research study where a team of mathematics instructors and an expert in curriculum development developed and implemented a differentiated instruction learning environment in a first-year engineering calculus class at a university in Cyprus. This study provides evidence that differentiated instruction has a positive effect on student engagement and motivation and improves students’ understanding of difficult calculus concepts.     

Development of Analytical Strategies for the Determination of Olive Fruit Bioactive Compounds Using UPLC-HRMS and HPLC-DAD. Chemical Characterization of Kolovi Lesvos Variety as a Case Study

In this study, an overall survey regarding the determination of several bioactive compounds in olive fruit is presented. Two methodologies were developed, one UPLC-Q-TOF-MS method for the determination of olive fruit phenolic compounds and one HPLC-DAD methodology targeting the determination of pigments (chlorophylls and carotenoids), tocopherols (α-, β, -γ, δ-) and squalene. Target and suspect screening workflows were developed for the thorough fingerprinting of the phenolic fraction of olives. Both methods were validated, presenting excellent performance characteristics, and can be used as reliable tools for the monitoring of bioactive compounds in olive fruit samples. The developed methodologies were utilized to chemical characterize the fruits of the Kolovi olive variety, originating from the island of Lesvos, North Aegean Region, Greece. Twenty-five phenolic compounds were identified and quantified in Kolovi olives with verbascoside, hydroxytyrosol, oleacein and oleomissional found in significantly high concentrations. Moreover, 12 new bioactive compounds were identified in the samples using an in-house suspect database. The results of pigments analysis suggested that Kolovi variety should be characterized as low pigmentation, while the tocopherol and squalene content was relatively high compared to other olive varieties. The characterization of Kolovi olive bioactive content highlighted the high nutritional and possible economic value of the Kolovi olive fruit.     

Capillary waveguide fluoroimmunosensor with improved repeatability and detection sensitivity

An optical capillary waveguide fluoroimmunosensor based on glass capillaries internally coated with an ultrathin poly(dimethylsiloxane) (PDMS) film is presented. The evaluation of the capillaries developed was done in comparison with aminosilanized [3-(aminopropyl)triethoxysilane, APTES] glass and poly(methylpentene) (PMP) capillaries by immobilizing rabbit γ-globulins on the internal capillary wall. Following reaction with (R)-phycoerythrin-labelled antibody, the capillary was scanned with a laser beam and the fluorescence waveguided through the capillary wall was detected by a photomultiplier placed at one of its ends. The capillaries developed provided considerably improved protein coating homogeneity (intracapillary coefficients of variation 2.9–6.6%) and repeatability (intercapillary coefficients of variation 2.1–5.0%) compared with APTES-treated ones (7.9–13.4 and 8.5–15.2%, respectively). With use of these capillaries in a sandwich-type immunosensor for the determination of rabbit γ-globulins, the assay detection limit was improved eightfold (4.4 ng/mL) compared with that obtained using PMP capillaries (35.3 ng/mL), whereas the assay repeatability was improved threefold (intra-assay coefficients of variation 5.9–13.1%) compared with APTES-treated capillaries (15.6–36%). Optoelectronic set-up used to scan the capillaries (left) and representative fluorescence scannings of dual-band poly(methylpentene) (PMP), PDMS-modified glass and APTES treated glass capillaries     

Novel prolinamide–ureas as organocatalysts for the asymmetric aldol reaction

Among the various versions of the aldol reaction, the enantioselective reaction between cyclic ketones and aldehydes constitutes a typical reaction model for the evaluation of novel organocatalysts. A multifunctional organocatalyst consisting of a prolinamide moiety, a gem diamine unit and a urea group was successfully employed in this asymmetric transformation. The products of the reaction between various ketones and aldehydes were obtained in high yields (up to 98%) with excellent diastereo- (up to >98:2 dr) and enantioselectivities (up to 99% ee).     

Comparison of Physical Adsorption and Covalent Coupling Methods for Surface Density-Dependent Orientation of Antibody on Silicon

The orientation of antibodies, employed as capture molecules on biosensors, determines biorecognition efficiency and bioassay performance. In a previous publication we demonstrated for antibodies attached covalently to silicon that an increase in their surface amount Γ, evaluated with ellipsometry, induces changes in their orientation, which is traced directly using Time-of-Flight Secondary Ion Mass Spectroscopy combined with Principal Component Analysis. Here, we extend the above studies to antibodies adsorbed physically on a 3-aminopropyltriethoxysilane (APTES) monolayer. Antibodies physisorbed on APTES (0 ≤ Γ ≤ 3.5 mg/m²) reveal the Γ ranges for flat-on, side-on, and vertical orientation consistent with random molecular packing. The relation between orientation and Γ is juxtaposed for silicon functionalized with APTES, APTES modified with glutaraldehyde (APTES/GA) and N-hydroxysuccinimide-silane (NHS-silane). Antibody reorientation occurs at lower Γ values when physisorption (APTES) is involved rather than chemisorption (APTES/GA, NHS-silane). At high Γ values, comparable proportions of molecules adapting head-on and tail-on vertical alignment are concluded for APTES and the NHS-silane monolayer, and they are related to intermolecular dipole–dipole interactions. Intermolecular forces seem to be less decisive than covalent binding for antibodies on the APTES/GA surface, with dominant head-on orientation. Independently, the impact of glutaraldehyde activation of APTES on vertical orientation is confirmed by separate TOF-SIMS measurements.     

On the blow-up set of the Yang–Mills flow on Kähler surfaces

The Yang–Mills flow on a Kähler surface with holomorphic initial data converges smoothly away from a singular set determined by the Harder–Narasimhan– Seshadri filtration of the initial holomorphic bundle.     

Gromov invariants for holomorphic maps from Riemann surfaces to Grassmannians

Two compactifications of the space of holomorphic maps of fixed degree from a compact Riemann surface to a Grassmannian are studied. It is shown that the Uhlenbeck compactification has the structure of a projective variety and is dominated by the algebraic compactification coming from the Grothendieck Quot Scheme. The latter may be embedded into the moduli space of solutions to a generalized version of the vortex equations studied by Bradlow. This gives an effective way of computing certain intersection numbers (known as ``Gromov invariants') on the space of holomorphic maps into Grassmannians. We carry out these computations in the case where the Riemann surface has genus one.