Secret sharing schemes on access structures with intersection number equal to one

The characterization of ideal access structures and the search for bounds on the optimal information rate are two important problems in secret sharing. These problems are studied in this paper for access structures with intersection number equal to one, that is, structures such that there is at most one participant in the intersection of any two different minimal qualified subsets. The main result in this work is the complete characterization of the ideal access structures with intersection number equal to one. In addition, bounds on the optimal information rate are provided for the non-ideal case.     

Characterization of transversal homothetic solutions in the n-body problem

Homothetic solutions of the n-body problem can be seen as heteroclinic orbits when the dynamical variables are changed via the McGehee blow-up and the time is suitably scaled. Transversality of the invariant asymptotic manifolds which contain the heteroclinic orbits is related to some structural stability. We fully characterize the cases in which such transversality is obtained for the n-body problem in any dimension.     

Regularization of Discontinuous Vector Fields on $${\mathbb{R}^3}$$ via Singular Perturbation

Singular perturbations problems in dimension three which are approximations of discontinuous vector fields are studied in this paper. The main result states that the regularization process developed by Sotomayor and Teixeira produces a singular problem for which the discontinuous set is a center manifold. Moreover, the definition of sliding vector field coincides with the reduced problem of the corresponding singular problem for a class of vector fields.      

Covalently Binding Atomically Designed Au9 Clusters to Chemically Modified Graphene

Atomic‐resolution transmission electron microscopy was used to identify individual Au₉ clusters on a sulfur‐functionalized graphene surface. The clusters were preformed in solution and covalently attached to the surface without any dispersion or aggregation. Comparison of the experimental images with simulations allowed the rotational motion, without lateral displacement, of individual clusters to be discerned, thereby demonstrating a robust covalent attachment of intact clusters to the graphene surface.     

Nucleophilic β‐Carbon Activation of Propionic Acid as a 3‐Carbon Synthon by Carbene Organocatalysis

Direct β‐carbon activation of propionic acid (C₂H₅CO₂H) by carbene organocatalysis has been developed. This activation affords the smallest azolium homoenolate intermediate (without any substituent) as a 3‐carbon nucleophile for enantioselective reactions. Propionic acid is an excellent raw material because it is cheap, stable, and safe. This approach provides a much better solution to azolium homoenolate synthesis than the previously established use of acrolein (enal without any substituent), which is expensive, unstable, and toxic.     

Development and validation of a GC-MS method for rapid determination of galanthamine in Leucojum aestivum and Narcissus ssp.: a metabolomic approach

Galanthamine, an acetylcholinesterase inhibitor marketed as a hydrobromide salt for the treatment of Alzheimer's disease, is obtained from some Amaryllidaceae plants. A new method was developed and validated for its quantification by GC-MS in different plant sources: bulbs and leaves from Narcissus confusus; bulbs from N. pseudonarcissus cv. Carlton; and leaves and in vitro cultures from L. aestivum. Samples (50 mg) were extracted with methanol (1 mL) for 2 h, then aliquots of the extracts were silylated and analyzed by GC-MS. The calibration line was linear over a range of 15-800 μg galanthamine/sample, ensuring an analysis of samples with a content of 0.03-1.54% analyte referred to dry weight. The recovery was generally more than 95%. Good inter- and intra assay precision was observed (RSD < 3%). Principal component analysis of GC-MS chromatograms allowed discrimination of the plant raw material with respect to species, organs and geographical regions. The analytical method developed in this study proved to be simple, sensitive and far more informative than the routine analytical methods (GC, HPLC, CE and NMR), so it may be useful for quality control of plant raw materials in the pharmaceutical industry.     

Isothermal titration calorimetry of Ni(II) binding to histidine and to N-2-aminoethylglycine

Isothermal titration calorimetry (ITC) is used to study the complexation thermodynamics of Ni(II) with histidine (His) and with N-2-aminoethylglycine (EDMA). The titrations were performed in HEPES and Tris buffers at various ionic strengths and pH values around 8. The results show the influence of the experimental conditions on the shape and fitting parameters of the calorimetric curves. For the studied systems, the main reaction is concomitant with a number of side reactions which contribute to the global energy measured. From the calorimetric data measured, the formation constants for the species NiHEPES⁺, Tris⁺His⁻, TrisNiHis⁺ and [Ni(EDMA)₂OH]⁻ have been evaluated for the first time and the values obtained properly validated.     

Three-dimensional open-frameworks based on Ln(III) ions and open-/closed-shell PTM ligands: synthesis, structure, luminescence, and magnetic properties

A series of isostructural open-framework coordination polymers formulated as [Ln(dmf)(3)(ptmtc)] (Ln = Sm (1), Eu (2), Gd (3), Tb (4), Dy (5); PTMTC = polychlorotriphenylmethyl tricarboxylate) and [Ln(dmf)(2)H(2)O(αH-ptmtc)] (Ln = Sm (1'), Eu (2'), Gd (3'), Tb (4'), Dy (5')) have been obtained by treating Ln(III) ions with PTMTC ligands with a radical (PTMTC(3-)) or a closed-shell character (αH-PTMTC(3-)). X-ray diffraction analyses reveal that these coordination polymers possess 3D architectures that combine large channels and fairly rare lattice complex T connectivity. In addition, these compounds show selective framework dynamic sorption properties. For both classes of ligands, the ability to act as an antenna in Ln sensitization processes has been investigated. No luminescence was observed for compounds 1-5, and 3' because of the PTMTC(3-) ligand and/or Gd(III) ion characteristics. Conversely, photoluminescence measurements show that 1', 2', 4', and 5' emit dark orange, red, green, and dark cyan metal-centered luminescence. The magnetic properties of all of these compounds have been investigated. The nature of the {Ln-radical} exchange interaction in these compounds has been assessed by comparing the behavior of the radical-based coordination polymers 1-5 with those of the compounds with the diamagnetic ligand set. While antiferromagnetic {Sm-radical} interactions are found in 1, ferromagnetic {Ln-radical} interactions propagate in the 3D architectures of 3, 4, and 5 (Ln = Gd, Tb, and Dy, respectively). This procedure also provided access to information on the {Ln-Ln} exchange existing in these magnetic systems.     

Transformation of a close-packed Au nanoparticle/polymer monolayer into a large area array of oriented Au nanowires via E-beam promoted uniaxial deformation and room temperature sintering

Transformation of 2D Au nanoparticle (NP) arrays into large scale, ordered, and oriented nanorod/nanowire arrays supported on a transferrable polymer film has been accomplished. E-beam irradiation followed by room temperature aging of a suspended Au NP/polymethylmethacrylate (PMMA) polymer close packed monolayer results in one-dimensional nanoparticle aggregation, reorientation, and sintering into a high density array of oriented Au nanowires with coherent single-crystal-like interfaces. Molecular dynamics simulations of alkane-thiol capped Au NPs, interacting through the Vincent potential and undergoing 2D Poisson compression, account semiquantitatively for the qualitative features of the transformation. This fabrication approach should be extendable to directing 1D aggregation of highly anisotropic nanostructures in arbitrary NP systems.