Koszul incidence algebras, affine semigroups, and Stanley-Reisner ideals

We prove a theorem unifying three results from combinatorial homological and commutative algebra, characterizing the Koszul property for incidence algebras of posets and affine semigroup rings, and characterizing linear resolutions of squarefree monomial ideals. The characterization in the graded setting is via the Cohen-Macaulay property of certain posets or simplicial complexes, and in the more general nongraded setting, via the sequential Cohen-Macaulay property.     

Principle and applications of a floating energy analyser

We describe a new type of energy analyser suitable for the use in plasmas having no external potential reference like ICPs and microwave discharges. It can be used to determine the ion distribution function (IDF) at a negatively biased surface and the high energy tail of the plasma electron distribution function (EDF). The EDF is measured without distortions by ion currents. This analyser was tested in a dc glow discharge and its results compared to measurements with Langmuir probes and a analyser with grounded reference. Some preliminary measurements were also performed in a rf parallel plate discharge. Dedicated to Prof. Jan Janča on the occasion of his 60th birthday, in remembrance of a fruitful and friendly European co-operation. This work was supported by the Deutsche Forschungsgemeinschaft Bonn by Sonderforschungsbereich 191 and by the Directorate-General XII Science, Research and Development of European Commission, under Grant ERBCIPACT924034.     

Canonical trace ideal and residue for numerical semigroup rings

Semigroup Forum - For a numerical semigroup ring K[H] we study the trace of its canonical ideal. The colength of this ideal is called the residue of H. This invariant measures how far is H from...     

Modal focusing effect of positive and negative ions by a three-dimensional plasma-sheath lens

A complex focusing effect of positive and negative ions caused by the sheath forming to biased electrodes that interface insulators has been found by solving in three dimensions the potential distribution and ion kinetics within the sheath. Thus, intrinsically correlated with the sheath shape, certain electrical charges are focused on the surface, forming well defined patterns named modal lines and modal spots. Their superposition to the previously reported discrete focusing leads to a total flux that represents a "fingerprint" of the entire sheath on the electrode surface. The ion flux pattern is developed experimentally on the surface of square and octagonal electrodes exposed to Ar/SF(6) and CF4 plasmas. Present results are of high potential importance for fundamental studies concerning sheath formation and charge kinetics and also in a wide range of plasma applications.     

Random Occupation of Multimetal Sites in Transition Metal-Organic Frameworks for Boosting the Oxygen Evolution Reaction

Developing robust oxygen evolution reaction (OER) electrocatalysts with excellent performance is essential for the conversion of renewable electricity to clean fuel. Herein, we present a facile concept for the synthesis of efficient high-entropy metal-organic frameworks (HEMOFs) as electrocatalysts in a one-step solvothermal synthesis. This strategy allows control of the microstructure and corresponding lattice distortion by tuning the metal ion composition. As a result, the OER activity was improved by optimizing the coordination environment of the metal catalytic center. The optimized Co-rich HEMOFs exhibited a low overpotential of 310 mV at a current density of 10 mA cm⁻², better than a RuO₂ catalyst tested under the same conditions. The finding of lattice distortion of the HEMOFs provides a new strategy for developing high-performance electrocatalysts for energy conversion.     

The Influence of the Preparation Method on the Physico-Chemical Properties and Catalytic Activities of Ce-Modified LDH Structures Used as Catalysts in Condensation Reactions

Mechanical activation and mechanochemical reactions are the subjects of mechanochemistry, a special branch of chemistry studied intensively since the 19th century. Herein, we comparably describe two synthesis methods used to obtain the following layered double hydroxide doped with cerium, Mg₃Al_0.75Ce_0.25(OH)₈(CO₃)_0.5·2H₂O: the mechanochemical route and the co-precipitation method, respectively. The influence of the preparation method on the physico-chemical properties as determined by multiple techniques such as XRD, SEM, EDS, XPS, DRIFT, RAMAN, DR-UV-VIS, basicity, acidity, real/bulk densities, and BET measurements was also analyzed. The obtained samples, abbreviated HTCe-PP (prepared by co-precipitation) and HTCe-MC (prepared by mechanochemical method), and their corresponding mixed oxides, Ce-PP (resulting from HTCe-PP) and Ce-MC (resulting from HTCe-MC), were used as base catalysts in the self-condensation reaction of cyclohexanone and two Claisen–Schmidt condensations, which involve the reaction between an aromatic aldehyde and a ketone, at different molar ratios to synthesize compounds with significant biologic activity from the flavonoid family, namely chalcone (1,3-diphenyl-2-propen-1-one) and flavone (2-phenyl-4H-1benzoxiran-4-one). The mechanochemical route was shown to have indisputable advantages over the co-precipitation method for both the catalytic activity of the solids and the costs.