Lines Tangent to Four Triangles in Three-Dimensional Space

We investigate the lines tangent to four triangles in R³. By a construction, there can be as many as 62 tangents. We show that there are at most 162 connected components of tangents, and at most 156 if the triangles are disjoint. In addition, if the triangles are in (algebraic) general position, then the number of tangents is finite and it is always even.     

Study of the incorporation of carrier-free57Co in Fe(II) and Mn(II) oxalates by a double radioactive tracer method

The incorporation of carrier-free⁵⁷Co²⁺ by coprecipitation in Fe and Mn oxalato compounds is characterized by a double radioactive tracer method. This is achieved by labelling the host compound with a short-lived tracer,⁵²Fe or⁵²Mn. Activity ratios are measured at several stages, during the precipitation and, afterwards, during the dissolution of the solid. In any case, results indicate very large incorporation yields of⁵⁷Co in the precipitate, independently from the intrinsic precipitation yield of the host compound. The observation of a continuous distribution of dopant atoms in the matrix in coprecipitation and dissolution experiments allows to rule out the adsorption of the doping species on a pre-existing precipitate of the host compound and accounts for isomorphous replacement. Incorporation of⁵⁷Co in Fe(II) oxalate follows a logarithmic distribution law, giving rise to a concentration gradient of dopant species in the precipitate. Dopant atoms are found to be concentrated in the internal layers of the crystals.     

Locally s-distance transitive graphs and pairwise transitive designs

The study of locally s-distance transitive graphs initiated by the authors in previous work, identified that graphs with a star quotient are of particular interest. This paper shows that the study of locally s-distance transitive graphs with a star quotient is equivalent to the study of a particular family of designs with strong symmetry properties that we call nicely affine and pairwise transitive. We show that a group acting regularly on the points of such a design must be abelian and give general construction for this case.     

An Alternative Way to Generalize the Pentagon

We introduce the concept of a pentagonal geometry as a generalization of the pentagon and the Desargues configuration, in the same vein that the generalized polygons share the fundamental properties of ordinary polygons. In short, a pentagonal geometry is a regular partial linear space in which for all points x, the points not collinear with the point x, form a line. We compute bounds on their parameters, give some constructions, obtain some nonexistence results for seemingly feasible parameters and suggest a cryptographic application related to identifying codes of partial linear spaces.     

QSAR Modeling of Large Heterogeneous Sets of Molecules

Abstract

In aquatic toxicology, QSAR models are generally designed for chemicals presenting the same mode of toxic action. Their proper use provides good simulation results. Problems arise when the mechanism of toxicity of a chemical is not clearly identified. Indeed, in that case, the inappropriate application of a specific QSAR model can lead to a dramatic error in the toxicity estimation. With the advent of powerful computers and easy access to them, and the introduction of soft modeling and artificial intelligence in SAR and QSAR, radically different models, designed from large non-congeneric sets of chemicals have been proposed. Some of these new QSAR models are reviewed and their originality, advantages, and limitations are stressed.     

Methodology for Determination of the Key Parameters of Conjugated Polymer Electrodeposition,Based on a Combination of Spectroelectrochemistry and Electrochemical Quartz Crystal Microbalance

Russian Journal of Electrochemistry - Methodology based on a combination of experimental data obtained by in situ methods of spectroelectrochemistry and electrochemical quartz crystal microbalance...     

Local 2-Geodesic Transitivity of Graphs

An s-geodesic in a graph Γ is a path connecting two vertices at distance s. Being locally transitive on s-geodesics is not a monotone property: if an automorphism group G of a graph Γ is locally transitive on s-geodesics, it does not follow that G is locally transitive on shorter geodesics. In this paper, we characterise all graphs that are locally transitive on 2-geodesics, but not locally transitive on 1-geodesics.