A “Discretization” Technique for the Solution of ODEs II

A functional analytic technique was recently presented for finding discrete equivalent counterparts of initial value problems of ODEs and obtaining their real analytic solutions. In the current paper, this technique is extended to boundary value problems of ODEs and to the complex solutions of ODEs. In order to demonstrate this technique, it is applied to the classic Blasius problem of fluid mechanics. Apart from its real solution, its complex solution is also studied. The obtained results indicate that the complex Blasius function exhibits an oscillatory behavior and strengthen a conjecture regarding its singularities in the complex plane.     

Eyringpy: A program for computing rate constants in the gas phase and in solution

Eyringpy is a modular program for calculating thermochemical properties and rate constants for reactions in the gas phase and in solution. The code is written in Python and it has a user-friendly interface and a simple input format. Unimolecular and bimolecular reactions with one and two products are supported. Thermochemical properties are estimated through canonical ensemble and rate constants are computed according to the transition state theory. One-dimensional Wigner and Eckart tunneling corrections are also available. Rate constants of bimolecular reactions involving the formation of pre-reactive complexes are also estimated. To compute rate constants in solution, Eyringpy uses the Collins–Kimball theory to include the diffusion-limit, the Marcus theory for electron transfer processes, and the molar fractions to account for the solvent pH effect.     

Helicoidal Patterning of Nanorods with Polymer Ligands

Chiral packing of ligands on the surface of nanoparticles (NPs) is of fundamental and practical importance, as it determines how NPs interact with each other and with the molecular world. Herein, for gold nanorods (NRs) capped with end‐grafted nonchiral polymer ligands, we show a new mechanism of chiral surface patterning. Under poor solvency conditions, a smooth polymer layer segregates into helicoidally organized surface‐pinned micelles (patches). The helicoidal morphology is dictated by the polymer grafting density and the ratio of the polymer ligand length to nanorod radius. Outside this specific parameter space, a range of polymer surface structures was observed, including random, shish‐kebab, and hybrid patches, as well as a smooth polymer layer. We characterize polymer surface morphology by theoretical and experimental state diagrams. The helicoidally organized polymer patches on the NR surface can be used as a template for the helicoidal organization of other NPs, masked synthesis on the NR surface, as well as the exploration of new NP self‐assembly modes.     

Developmental gametophyte morphology of seven species of Thelypteris subg. Cyclosorus (Thelypteridaceae)

The morphogenesis of the sexual phase of seven species of Thelypteris subg. Cyclosorus (Thelypteridaceae) is described and compared. Spores of all species are monolete, ellipsoid and have positive photoblastism. They have Vittaria-type germination, germinal filaments are short and uniseriate, and Aspidium-type development. Adult gametophytes are spatulate-cordiform, and have wide wings with numerous glandular, marginal and superficial hairs. Antheridia have a narrow or widened basal cell, an undivided annular cell, and an opercular cell; antherozoids are liberated through three mechanisms. Archegonia have short necks and four triangular cells on the neck's mouth. The sporophyte's first leaf is lobed, with open dichotomous veins, glandular hairs similar to those of the gametophyte, and anomocytic stomata. Differences observed between the studied species are: spore size; ornamentation of the perispore; germination and emergence periods; size of hairs; developmental period of gametangia; and antherozoid liberation mechanisms through total detachment of the operculum, partial detachment of the operculum, and development of an apical pore through tearing of the operculum. These taxonomically valuable characters, combined with the sporophyte characteristics, can be useful tools in the identification of the species studied to the subg. Cyclosorus.     

Math MOOC UniTo : an Italian project on MOOCs for mathematics teacher education,and the development of a new theoretical framework

This paper focuses on MOOCs (massive open online courses), a fairly recent paradigm in e-learning educational projects. Despite the high dropout rate, and     

Production and extraction of astaxanthin from Phaffia rhodozyma and its biological effect on alcohol-induced renal hypoxia in Carassius auratus

The effect of astaxanthin (3,3′-dihydroxy-s-carotene-4,4′-dione) on alcohol-induced morphological changes in Carassius auratus, as an experimental model, was determined. The yeast Phaffia rhodozyma was used as a source of astaxanthin. The animals were divided into three groups for 30 days: one group was treated with ethanol at a dose of 1.5% mixed in water, the second one with EtOH 1.5% and food enriched with astaxanthin from P. rhodozyma, and the third was a control group. After a sufficient experimental period, the samples were processed using light microscopy and evaluated by histomorphological and histochemical staining, and the data were supported by immunohistochemical analysis, using a wide range of antibodies, such as calbindin, vimentin and alpha-smooth muscle actin. The results show that the alcoholic damage in the kidney led to hypoxia. In contrast, the group fed with astaxanthin from P. rhodozyma showed a normal morphological picture, with better glomeruli organisation and the presence of the area of filtration. Furthermore, the immunohistochemistry has confirmed these results.     

Synthesis and self‐assembly of thermosensitive double‐hydrophilic poly(N‐vinylcaprolactam)‐b‐poly(N‐vinyl‐2‐pyrrolidone) diblock copolymers

We report on novel diblock copolymers of poly(N‐vinylcaprolactam) (PVCL) and poly(N‐vinyl‐2‐pyrrolidone) (PVPON) (PVCL‐b‐PVPON) with well‐defined block lengths synthesized by the MADIX/reversible addition‐fragmentation chain transfer (RAFT) process. We show that the lower critical solution temperatures (LCST) of the block copolymers are controllable over the length of PVCL and PVPON segments. All of the diblock copolymers dissolve molecularly in aqueous solutions when the temperature is below the LCST and form spherical micellar or vesicular morphologies when temperature is raised above the LCST. The size of the self‐assembled structures is controlled by the molar ratio of PVCL and PVPON segments. The synthesized homopolymers and diblock copolymers are demonstrated to be nontoxic at 0.1–1 mg mL^?1 concentrations when incubated with HeLa and HEK293 cancer cells for various incubation times and have potential as nanovehicles for drug delivery. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2014 , 52, 2725–2737     

Synthesis of a Helical Bilayer Nanographene

A rigid, inherently chiral bilayer nanographene has been synthesized as both the racemate and enantioenriched M isomer (with 93 % ee) in three steps from established helicenes. This folded nanographene is composed of two hexa‐peri‐hexabenzocoronene layers fused to a [10]helicene, with an interlayer distance of 3.6 Å as determined by X‐ray crystallography. The rigidity of the helicene linker forces the layers to adopt a nearly aligned AA‐stacked conformation, rarely observed in few‐layer graphene. By combining the advantages of nanographenes and helicenes, we have constructed a bilayer system of 30 fused benzene rings that is also chiral, rigid, and remains soluble in common organic solvents. We present this as a molecular model system of bilayer graphene, with properties of interest in a variety of potential applications.