Cyclic Elements in MV-Algebras and Post Algebras

In this paper we characterize the MV-algebras containing as subalgebras Post algebras of finitely many orders. For this we study cyclic elements in MV-algebras which are the generators of the fundamental chain of the Post algebras. Mathematics Subject Classification: 03G20, 03G25, 06D25, 06D30, 06F15, 06F35.     

Programmed interactions in higher-order neural networks: The outer-product algorithm

Recent results on the memory storage capacity of the outer-product algorithm indicate that the algorithm stores of the order of n/log n memories in a network of n fully interconnected linear threshold elements when it is required that each memory be exactly recovered from a probe which is close enough to it. In this paper a rigourous analysis is presented of generalizations of the outer-product algorithm to higher-order networks of densely interconnected polynomial thresh-old units of degree d. Precise notions of memory storage capacity are formulated, and it is demonstrated that both static and dynamic storage capacities of all variants of the outer-product algorithm of degree d are of the order of n^d/log n.     

Symmetry and the golden ratio in the analysis of a regular pentagon

The regular pentagon had a symbolic meaning in the Pythagorean and Platonic philosophies and a subsequent important role in Western thought, appearing also in arts and architecture. A property of regular pentagons, which was probably discovered by the Pythagoreans, is that the ratio between the diagonal and the side of these pentagons is equal to the golden ratio. Here, we will study some relations existing between a regular pentagon and this ratio. First, we will focus on the group of fivefold rotational symmetry, to find the position in the complex plane of the vertices of this geometric figure. Then, we will propose an analytic method to solve the same problem based on the Cartesian coordinates, a method where we find the golden ratio without any specific geometric consideration. This study shows a comparison of the use of complex numbers, symmetries and analytic methods, applied to a subject which can be interesting for general education in mathematics. In fact, the proposed approach can convey and link several concepts, requiring only a general pre-college education, showing at the same time the richness that mathematics can offer in solving geometric problems.     

A new dinuclear Ru-Hbpp based water oxidation catalyst with a trans-disposition of the Ru-OH

The bis(2-pyridyl)ethylamine (bpea) ligand has been used as a starting material for the synthesis of dinuclear Ru complexes of general formula trans,fac-{[Ru(n)X(bpea)](2)(μ-bpp)}(m+) (for X = Cl, n = II, m = 1, trans-Ru(II)-Cl, 1(+); for X = OH, n = III, m = 3, trans-Ru(III)-OH, 2(3+)) where the 3,5-bis(2-pyridyl)pyrazolate anionic ligand (bpp) acts as bridging dinucleating ligand, the bpea ligand coordinates in a facial manner and the monodentate ligands X are situated in a trans fashion with regard to one another. These complexes have been characterized in solution by 1D and 2D NMR spectroscopy, UV-vis and electrochemical techniques and in the solid state by X-ray diffraction analysis. The reaction of 1(PF(6)) with Ag(+) generates the corresponding solvated complex where the Cl ligand has been removed as insoluble AgCl, followed by the oxidation of Ru(II) to Ru(III) to generate the corresponding dinuclear complex trans-Ru(III)-OH, 2(PF(6))(3). The latter has been shown to catalytically oxidize water to molecular dioxygen using Ce(IV) as oxidant. Quantitative gas evolution as a function of time has been monitored on line by both manometry and mass spectroscopy (MS) techniques. Relative initial velocities of oxygen formation together with structural considerations rule out an intramolecular O-O bond formation pathway.     

Data-driven high-throughput prediction of the 3-D structure of small molecules: review and progress. A response to the letter by the Cambridge Crystallographic Data Centre

A response is presented to sentiments expressed in "Data-Driven High-Throughput Prediction of the 3-D Structure of Small Molecules: Review and Progress. A Response from The Cambridge Crystallographic Data Centre", recently published in the Journal of Chemical Information and Modeling, (1) which may give readers a misleading impression regarding significant impediments to scientific research posed by the CCDC.     

Noisy colored point set matching

We propose a process for determining approximated matches, in terms of the bottleneck distance, under color preserving rigid motions, between two colored point sets A,B∈R², |A|≤|B|. We solve the matching problem by generating all representative motions that bring A close to a subset B^′ of set B and then using a graph matching algorithm. We also present an approximate matching algorithm with improved computational time. In order to get better running times for both algorithms we present a lossless filtering preprocessing step. By using it, we determine some candidate zones which are regions that contain a subset S of B such that A may match one or more subsets B^′ of S. Then, we solve the matching problem between A and every candidate zone. Experimental results using both synthetic and real data are reported to prove the effectiveness of the proposed approach.     

Tunable single-site ruthenium catalysts for efficient water oxidation

The catalytic water oxidation activity of mononuclear ruthenium complexes comprising a pyridine-functionalized abnormal triazolylidene ligand can be adjusted by modification of the triazolylidene substituents, which is readily achieved through click-type cycloaddition chemistry, affording some of the most active ruthenium catalysts known thus far for water oxidation (TONs > 400, TOFs close to 7000 h(-1)).     

Water oxidation in the context of the energy challenge: tailored transition-metal catalysts for oxygen-oxygen bond formation

Understanding water oxidation mechanisms: The power of two cooperating metal centers.     

Guaianolide Derivatives from the Invasive Xanthium spinosum L.: Evaluation of Their Allelopathic Potential

Ziniolide, xantholide B (11α-dihydroziniolide), and 11β-dihydroziniolide, three sesquiterpene lactones with 12,8-guaianolide skeletons, were identified as volatile metabolites from the roots of Xanthium spinosum L., an invasive plant harvested in Corsica. Essential oil, as well as hydrosol and hexane extracts, showed the presence of guaianolide analogues. The study highlights an analytical strategy involving column chromatography, GC-FID, GC-MS, NMR (1D and 2D), and the hemi-synthesis approach, to identify compounds with incomplete or even missing spectral data from the literature. Among them, we reported the ¹H- and ¹³C-NMR data of 11β-dihydroziniolide, which was observed as a natural product for the first time. As secondary metabolites were frequently involved in the dynamic of the dispersion of weed species, the allelopathic effects of X. spinosum root’s volatile metabolites were assessed on seed germination and seedling growth (leek and radish). Essential oil, as well as hydrosol- and microwave-assisted extracts inhibited germination and seedling growth; root metabolite phytotoxicity was demonstrated. Nevertheless, the phytotoxicity of root metabolites was demonstrated with a more marked selectivity to the benefit of the monocotyledonous species compared to the dicotyledonous species. Ziniolide derivatives seem to be strongly involved in allelopathic interactions and could be the key to understanding the invasive mechanisms of weed.     

Neuer praktischer Apparat zur Entwickelung von Chlor

Ohne Zusammenfassung