Taylor’s Modularity Conjecture and Related Problems for Idempotent Varieties

We provide a partial result on Taylor’s modularity conjecture, and several related problems. Namely, we show that the interpretability join of two idempotent varieties that are not congruence modular is not congruence modular either, and we prove an analog for idempotent varieties with a cube term. Also, similar results are proved for linear varieties and the properties of congruence modularity, having a cube term, congruence n-permutability for a fixed n, and satisfying a non-trivial congruence identity.     

Asymptotically optimal neighbour sum distinguishing colourings of graphs

Consider a simple graph G = (V,E) and its proper edge colouring c with the elements of the set {1,2,…,k}. The colouring c is said to be neighbour sum distinguishing if for every pair of vertices u, v adjacent in G, the sum of colours of the edges incident with u is distinct from the corresponding sum for v. The smallest integer k for which such colouring exists is known as the neighbour sum distinguishing index of a graph and denoted by . The definition of this parameter, which makes sense for graphs containing no isolated edges, immediately implies that , where Δ is the maximum degree of G. On the other hand, it was conjectured by Flandrin et al. that for all those graphs, except for C₅. We prove this bound to be asymptotically correct by showing that . The main idea of our argument relays on a random assignment of the colours, where the choice for every edge is biased by so called attractors, randomly assigned to the vertices. © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 47, 776–791, 2015     

Neighbor Distinguishing Edge Colorings Via the Combinatorial Nullstellensatz Revisited

Consider a simple graph and its proper edge coloring c with the elements of the set . We say that c is neighbor set distinguishing (or adjacent strong) if for every edge , the set of colors incident with u is distinct from the set of colors incident with v. Let us then consider a stronger requirement and suppose we wish to distinguishing adjacent vertices by sums of their incident colors. In both problems the challenging conjectures presume that such colorings exist for any graph G containing no isolated edges if only . We prove that in both problems is sufficient. The proof is based on the Combinatorial Nullstellensatz, applied in the “sum environment.” In fact the identical bound also holds if we use any set of k real numbers instead of as edge colors, and the same is true in list versions of the both concepts. In particular, we therefore obtain that lists of length ( in fact) are sufficient for planar graphs.     

Total Vertex Irregularity Strength of Dense Graphs

Consider a graph of minimum degree δ and order n. Its total vertex irregularity strength is the smallest integer k for which one can find a weighting such that for every pair of vertices of G. We prove that the total vertex irregularity strength of graphs with is bounded from above by . One of the cornerstones of the proof is a random ordering of the vertices generated by order statistics.     

Enantioselective synthesis of 5-methylidenedihydrouracils as potential anticancer agents

An efficient, versatile, enantioselective synthesis of 1,3-disubstituted and 1,3,6-trisubstituted 5-methylidenedihydrouracils applying Horner-Wadsworth Emmons methodology was developed. Starting 1,3-disubstituted 5-diethoxyphosphoryluracils were subjected to reduction of the double bond or addition of various Grignard reagents and obtained Horner-Wadsworth Emmons reagents were used for the olefination of formaldehyde. Enantioselective synthesis of 1,3,6-trisubstituted 5-methylidenedihydrouracils was accomplished by introducing (R,R)- or (S,S)-di(1-phenylethylamino)phosphoryl groups as chiral auxiliary. Additions of Grignard reagents in the presence of these groups were highly and complimentary diastereoselective (de?～?80%). Further separation of the diastereomeric mixtures by column chromatography enabled synthesis of (R)- and (S)-1,3,6-trisubstituted-5-methylidenedihydrouracils with ee?≥?98%. Furthermore, absolute configuration of the adducts and final products was established using single crystal X-ray analysis. Stereochemical course of the addition reactions is also discussed.     

Carbazole-Based Colorimetric Anion Sensors

Owing to their strong carbazole chromophore and fluorophore, as well as to their powerful and convergent hydrogen bond donors, 1,8-diaminocarbazoles are amongst the most attractive and synthetically versatile building blocks for the construction of anion receptors, sensors, and transporters. Aiming to develop carbazole-based colorimetric anion sensors, herein we describe the synthesis of 1,8-diaminocarbazoles substituted with strongly electron-withdrawing substituents, i.e., 3,6-dicyano and 3,6-dinitro. Both of these precursors were subsequently converted into model diamide receptors. Anion binding studies revealed that the new receptors exhibited significantly enhanced anion affinities, but also significantly increased acidities. We also found that rear substitution of 1,8-diamidocarbazole with two nitro groups shifted its absorption spectrum into the visible region and converted the receptor into a colorimetric anion sensor. The new sensor displayed vivid color and fluorescence changes upon addition of basic anions in wet dimethyl sulfoxide, but it was poorly selective; because of its enhanced acidity, the dominant receptor-anion interaction for most anions was proton transfer and, accordingly, similar changes in color were observed for all basic anions. The highly acidic and strongly binding receptors developed in this study may be applicable in organocatalysis or in pH-switchable anion transport through lipophilic membranes.     

Unlocking the Hydrolytic Mechanism of GH92 α-1,2-Mannosidases: Computation Inspires the use of C-Glycosides as Michaelis Complex Mimics

The conformational changes in a sugar moiety along the hydrolytic pathway are key to understand the mechanism of glycoside hydrolases (GHs) and to design new inhibitors. The two predominant itineraries for mannosidases go via ^OS₂→B_2,5→¹S₅ and ³S₁→³H₄→¹C₄. For the CAZy family 92, the conformational itinerary was unknown. Published complexes of Bacteroides thetaiotaomicron GH92 catalyst with a S-glycoside and mannoimidazole indicate a ⁴C₁→⁴H₅/¹S₅→¹S₅ mechanism. However, as observed with the GH125 family, S-glycosides may not act always as good mimics of GH's natural substrate. Here we present a cooperative study between computations and experiments where our results predict the E₅→B_2,5/¹S₅→¹S₅ pathway for GH92 enzymes. Furthermore, we demonstrate the Michaelis complex mimicry of a new kind of C-disaccharides, whose biochemical applicability was still a chimera.     

Anodic and Cathodic Platinum Dissolution Processes Involve Different Oxide Species

The degradation of Pt-containing oxygen reduction catalysts for fuel cell applications is strongly linked to the electrochemical surface oxidation and reduction of Pt. Here, we study the surface restructuring and Pt dissolution mechanisms during oxidation/reduction for the case of Pt(100) in 0.1 M HClO₄ by combining operando high-energy surface X-ray diffraction, online mass spectrometry, and density functional theory. Our atomic-scale structural studies reveal that anodic dissolution, detected during oxidation, and cathodic dissolution, observed during the subsequent reduction, are linked to two different oxide phases. Anodic dissolution occurs predominantly during nucleation and growth of the first, stripe-like oxide. Cathodic dissolution is linked to a second, amorphous Pt oxide phase that resembles bulk PtO₂ and starts to grow when the coverage of the stripe-like oxide saturates. In addition, we find the amount of surface restructuring after an oxidation/reduction cycle to be potential-independent after the stripe-like oxide has reached its saturation coverage.     

The effect of magnetic fields on the electrodeposition of iron

The effect of a uniform magnetic field with flux density up to 1 T on the electrodeposition of Fe from sulphate electrolyte has been investigated under different field configurations relative to the electrode surface. Voltammetric and chronoamperometric experiments have been carried out coupled with an electrochemical quartz crystal microbalance for in situ mass change measurements. The structure and morphology of the deposited films were determined by scanning electron microscopy, atomic force microscopy and X-ray diffraction measurements. Results show that, when the magnetic field is applied parallel to the electrode surface, the limiting current density and the deposition rate are increased due to the magnetohydrodynamic effect. The nucleation process is also affected in parallel configuration; the current density of the maximum on the chronoamperograms is decreased, and an additional nucleation step might be observed. This effect is attributed to the hydrodynamic response of the electrochemical system. No significant influence on the electrochemical reaction was observed when a magnetic field was applied perpendicular to the electrode. But in this configuration, the morphology of deposited layers is changed by the magnetic field. The morphology changes are discussed. No effect of the magnetic field on the crystallographic structure was observed.