Periods of generalized Fermat curves

Let $k,n\ge 2$ be integers. A generalized Fermat curve of type $(k,n)$ is a compact Riemann surface S that admits a subgroup of conformal automorphisms $H\le \text{Aut}(S)$ isomorphic to ${\mathbb{Z}}_k^n$, such that the quotient surface $S/H$ is biholomorphic to the Riemann sphere $\stackrel{?}{\mathbb{C}}$ and has $n+1$ branch points, each one of order k. There exists a good algebraic model for these objects, which makes them easier to study. Using tools from algebraic topology and integration theory on Riemann surfaces, we find a set of generators for the first homology group of a generalized Fermat curve. Finally, with this information, we find a set of generators for the period lattice of the associated Jacobian variety.     

Fluorescence properties of riboflavin-functionalized mesoporous silica SBA-15 and riboflavin solutions in presence of different metal and organic cations

Riboflavin was covalently linked to mesoporous SBA-15 silica surface via grafting technique. Then fluorescence properties of the system obtained were analyzed in the presence of several metal and organic cations. Both quenching and strengthening of fluorescence as well as significant changes in the maximum fluorescence wavelength were observed. The results were compared with absorption and fluorescence data obtained for riboflavin water solutions.     

Spatially Directed Pyrolysis via Thermally Morphing Surface Adducts

Combustion is often difficult to spatially direct or tune associated kinetics—hence a run-away reaction. Coupling pyrolytic chemical transformation to mass transport and reaction rates (Damköhler number), however, we spatially directed ignition with concomitant switch from combustion to pyrolysis (low oxidant). A ‘surface-then-core’ order in ignition, with concomitant change in burning rate,is therefore established. Herein, alkysilanes grafted onto cellulose fibers are pyrolyzed into non-flammable SiO₂ terminating surface ignition propagation, hence stalling flame propagating. Sustaining high temperatures, however, triggers ignition in the bulk of the fibers but under restricted gas flow (oxidant and/or waste) hence significantly low rate of ignition propagation and pyrolysis compared to open flame (Liñán's equation). This leads to inside-out thermal degradation and, with felicitous choice of conditions, formation of graphitic tubes. Given the temperature dependence, imbibing fibers with an exothermically oxidizing synthon (MnCl₂) or a heat sink (KCl) abets or inhibits pyrolysis leading to tuneable wall thickness. We apply this approach to create magnetic, paramagnetic, or oxide containing carbon fibers. Given the surface sensitivity, we illustrate fabrication of nm- and μm-diameter tubes from appropriately sized fibers.     

Molecular switching on surfaces

Molecular switching has established itself as a key functionality of building blocks developed for addressable materials and surfaces over the last two decades. Many challenges in their use and characterisation have been presented by the wide variation in interfaces studied, these ranging from truly single-molecule devices to two-dimensional self-assembled monolayers and thin films that bridge the gap between surface and macroscopically bulk materials (polymers, MOFs, COFs), and further still to other interfaces (solid–liquid, liquid–air, etc.). The low number density of molecules on monolayer-coated interfaces as well as in thin films, for example, presents substantial challenges in the characterisation of the composition of modified interfaces. The switching of molecular structure with external stimuli such as light and electrode potential adds a further layer of complexity in the characterisation of function. Such characterisation “in action” is necessary to correlate macroscopic phenomena with changes in molecular structure. In this review, key classes of molecular switches that have been applied frequently to interfaces will be discussed in the context of the techniques and approaches used for their operando characterisation. In particular, we will address issues surrounding the non-innocence of otherwise information-rich techniques and show how model – non-switching – compounds are often helpful in confirming and understanding the limitations and quirks of specific techniques.     

Asymptotics of Neumann harmonics when a cavity is close to the exterior boundary of the domain

We construct the asymptotics (as ε→0) of solutions to the Neumann problem for the Laplace equation and of the corresponding Dirichlet integral. The problem concerns a three-dimensional domain having two connected components of the boundary at the distance ε>0. To cite this article: G. Cardone et al., C. R. Mecanique 335 (2007).     

Noether's Theorem on Surfaces

In this article we prove a version of Noether's Theorem (of Calculus of Variations) which is valid for a general regular (compact) surface. As a special feature, the Lie group of transformations is allowed to act on the Cartesian product of the surface and the functional space. Additionally, we apply the Theorem to a problem in Classical Differential Geometry of surfaces. The given application is actually an example showing how Noether's Theorem can be used to construct invariant properties of the solutions to variational problems defined on surfaces, or equivalently, of the solutions to the associated Euler-Lagrange equations resulting from them.     

Hybrid graphene oxide/DAB-Am-16 dendrimer: Preparation,characterization chemical reactivity and their electrocatalytic detection of l-Dopamine

Graphene oxide (GO) was chemically modified with a poly(propylene)imine Generation 3.0 dendrimer (DAB-Am-16). The characterization, structure and properties of hybrid graphene oxide/DAB-Am-16 dendrimer was studied by Raman spectroscopy, Fourier-Transforming Infrared Spectroscopy (FT-IR), X-Ray Photoelectron Spectroscopic (XPS), X-ray Diffraction (XRD), Scanning Electron Microscopy (SEM) and Thermogravimetric analysis. After functionalized the hybrid material (GOD) can interact with copper and subsequently with hexacyanoferrate (III) ions (GODHCu). The GODHCu incorporated into a graphite paste electrode (20% w/w) was applied to an electrocatalytic detection of neurotransmitter l-dopamine using differential pulse voltammetry. The analytical curve showed a linear response in the concentration range from 1.0 × 10⁻⁷ to 1.0 × 10⁻⁵ mol L⁻¹ with a corresponding equation Y(A) = 1.706 × 10⁻⁵ + 0.862 [l-dopamine] and a correlation coefficient r² = 0.998. The detection limit was 6.36 × 10⁻⁷ mol L⁻¹ with a relative standard deviation of ±4% (n = 3) and an amperometric sensitivity of 0.862 A/mol L⁻¹.     

Introducing nonlinear,multivariate ‘Predictor Surfaces’ for quantitative modeling of chemical systems with higher-order,coupled predictor variables

Innovations in chemometrics are required for studies of chemical systems which are governed by nonlinear responses to chemical parameters and/or interdependencies (coupling) among these parameters. Conventional and linear multivariate models have limited use for quantitative and qualitative investigations of such systems because they are based on the assumption that the measured data are simple superpositions of several input parameters. ‘Predictor Surfaces’ were developed for studies of more chemically complex systems such as biological materials in order to ensure accurate quantitative analyses and proper chemical modeling for in-depth studies of such systems. Predictor Surfaces are based on approximating nonlinear multivariate model functions by multivariate Taylor expansions which inherently introduce the required coupled and higher-order predictor variables.     

Hyperbolic Polygons and Real Schottky Groups

In a work due to Aigon and Silhol (also Buser and Silhol) a construction of 10 genus two closed Riemann surfaces is done from a given right angled hyperbolic pentagon. In this note we construct real Schottky groups uniformizations of the corresponding constructions. In particular, we are able to write down the algebraic curves obtained in the above work in terms of the parameters of the real Schottky group. We generalize such a construction for any right angled hyperbolic polygon and also consider an example for a nonright angled pentagon in the last section.     

Improvement of hydrophilic properties of electrospun polyamide-imide fibrous mats by atmospheric-pressure plasma treatment

Polyamide-imide (PAI) fibrous mats were fabricated through electrospinning and further treated with atmospheric-pressure plasma. The surface characteristics of the PAI fibrous mats were examined to determine the effect of plasma treatment on the hydrophilic properties. FT-IR, X-ray photoelectron spectroscopy, and contact-angle analysis indicated that the hydrophilicity of the PAI fibrous mats increased upon the introduction of hydrophilic groups by plasma treatment. The concentration of functional groups, including oxygen, and the surface roughness of the PAI fibrous mats increased with increasing treatment time. The optimum plasma treatment time for surface modification of the PAI fibrous mats under atmospheric pressure was 120 s.