Bounded BCK‐algebras and their generated variety

In this paper we prove that the equational class generated by bounded BCK‐algebras is the variety generated by the class of finite simple bounded BCK‐algebras. To obtain these results we prove that every simple algebra in the equational class generated by bounded BCK‐algebras is also a relatively simple bounded BCK‐algebra. Moreover, we show that every simple bounded BCK‐algebra can be embedded into a simple integral commutative bounded residuated lattice. We extend our main results to some richer subreducts of the class of integral commutative bounded residuated lattices and to the involutive case. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Gradient methods for multiple state optimal design problems

We optimise a distribution of two isotropic materials α I and β I (α < β) occupying the given body in R ^d . The optimality is described by an integral functional (cost) depending on temperatures u ₁, . . . , u _m of the body obtained for different source terms f ₁, . . . ,f _m with homogeneous Dirichlet boundary conditions. The relaxation of this optimal design problem with multiple state equations is needed, introducing the notion of composite materials as fine mixtures of different phases, mathematically described by the homogenisation theory. The necessary conditions of optimality are derived via the Gateaux derivative of the cost functional. Unfortunately, there could exist points in which necessary conditions of optimality do not give any information on the optimal design. In the case m < d we show that there exists an optimal design which is a rank-m sequential laminate with matrix material α I almost everywhere on Ω. Contrary to the optimality criteria method, which is commonly used for the numerical solution of optimal design problems (although it does not rely on a firm theory of convergence), this result enables us to effectively use classical gradient methods for minimising the cost functional.      

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.     

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.     

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.     

A Self‐Improved Water‐Oxidation Catalyst: Is One Site Really Enough?

The homogeneous catalysis of water oxidation by transition‐metal complexes has experienced spectacular development over the last five years. Practical energy‐conversion schemes, however, require robust catalysts with large turnover frequencies. Herein we introduce a new oxidatively rugged and powerful dinuclear water‐oxidation catalyst that is generated by self‐assembly from a mononuclear catalyst during the catalytic process. Our kinetic and DFT computational analysis shows that two interconnected catalytic cycles coexist while the mononuclear system is slowly and irreversibly converted into the more stable dinuclear system: an extremely robust water‐oxidation catalyst that does not decompose over extended periods of time.     

Biochemical and Molecular Investigation of the Effect of Saponins and Terpenoids Derived from Leaves of Ilex aquifolium on Lipid Metabolism of Obese Zucker Rats

Ilex paraguariensis, the holly tree, is a plant with recognized biological properties, whose aqueous infusions are known as “Yerba mate”, that regulate lipid metabolism, reduce obesity, and improve brain stimulation. In the present study, the effect of standardized saponin and terpenoid fractions of a European taxon, Ilex aquifolium, on blood biochemical parameters in a rat model of metabolic disorder, (fa/fa) Zucker, are presented. The profiles of the volatile fractions of two species and six European varieties of Ilex were investigated. After selecting the best variety, the saponin and terpenoid fractions were isolated and standardized, and animals were fed 10 mg kg⁻¹ b.w. for 8 weeks. A statistically significant decrease in liver adiposity was observed, confirmed by histology and quantitative identification (gas chromatography–mass spectrometry analyses of hepatic lipids. RT-qPCR analysis of gene expression in the aorta revealed that the administration of the terpenoid fraction downregulated LOX-1, suggesting a reduction in atherosclerotic stimuli. In addition, a statistically significant reduction (p < 0.05) in PPARγ for the saponin fraction was observed in the liver. The expression of the ACAT-1 gene in the liver, responsible for the formation of cholesterol esters, increased significantly in the group receiving the terpenoid fraction compared to the control, which was also confirmed by the analysis of individual blood biochemical parameters. The opposite effect was observed for saponins. Taking the above into account, it is shown for the first time that Ilex aquifolium can be a source of compounds that positively influence lipid metabolism.