Geometrical CP violation from non-renormalisable scalar potentials

We consider in detail the non-renormalisable scalar potential of three Higgs doublets transforming as an irreducible triplet of Δ(27)$\mathrm{\Delta }(27)$ or Δ(54)$\mathrm{\Delta }(54)$. We start from a renormalisable potential that spontaneously leads to a vacuum with CP-violating phases independent of arbitrary parameters – geometrical CP violation. Then we analyse to arbitrarily high order non-renormalisable terms that are consistent with the symmetry and we demonstrate that inclusion of non-renormalisable terms in the potential can preserve the geometrical CP-violating vacuum.     

Bogomolov multipliers for some <Emphasis Type="Italic">p</Emphasis>-groups of nilpotency class 2

The Bogomolov multiplier B ₀(G) of a finite group G is defined as the subgroup of the Schur multiplier consisting of the cohomology classes vanishing after restriction to all abelian subgroups of G. The triviality of the Bogomolov multiplier is an obstruction to Noether’s problem. We show that if G is a central product of G ₁ and G ₂, regarding K _i ≤ Z(G _i ), i = 1, 2, and θ: G ₁ → G ₂ is a group homomorphism such that its restriction \(\theta {|_{{K_1}}}:{K_1} \to {K_2}\) is an isomorphism, then the triviality of B ₀(G ₁/K ₁),B ₀(G ₁) and B ₀(G ₂) implies the triviality of B ₀(G). We give a positive answer to Noether’s problem for all 2-generator p-groups of nilpotency class 2, and for one series of 4-generator p-groups of nilpotency class 2 (with the usual requirement for the roots of unity).     

Validation of a new measuring system for water turbidity field measurements

Turbidity is an essential parameter for describing water quality by direct and indirect impacts on fish, invertebrates and aquatic plants. Currently, environmental monitoring measurements are carried out with appropriate quality by accredited testing laboratories, but there is also a need for employing the third sector, i.e. citizens and voluntaries in environmental monitoring. A device called “Secchi3000” was developed as a low-cost and simple-to-operate tool so that water quality measurements can also be carried out by non-experts and citizens. The measurement using the new device is simple: The user fills the container with water and places the measurement structure in the container. The user takes a photograph with the camera on a mobile phone through a hole in the lid. The software sends the photograph to a server, which analyses the photographs automatically. Finally, the results are returned to the user’s mobile phone and stored on a database for further analysis. In this study, the measuring system for turbidity measurements in natural waters was validated. Validation included an estimation of the limit of quantification, investigations of the influence of water colour and illumination conditions on turbidity measurement values and the estimation of measurement uncertainty. A comparison of turbidity results obtained with the new device and laboratory instrument in natural water samples was carried out, and turbidity values obtained with different mobile phones were compared. According to the validation results, the new device was appropriate for the measurement of turbidity lower than 7 FNU (Formazine Nephelometric Unit). An algorithm applied for present turbidity calculations is not fully suitable for higher turbidities. For potential routine use, this is not a major problem, since most Finnish natural waters have turbidities lower than 7 FNU. For official monitoring purposes, the limit of the quantification needs to be lower than presently achieved (1.7 FNU). Although the present configuration of the Secchi3000 device is not yet fully suitable for official environmental monitoring, it will already enable the involvement of the third sector in water quality monitoring, and in this way, citizens’ observations could then serve at least as supplementary information for reporting and surveys.     

Hydrazine‐Assisted Liquid Exfoliation of MoS2 for Catalytic Hydrodeoxygenation of 4‐Methylphenol

A simple but effective method to exfoliate bulk MoS₂ in a range of solvents is presented for the preparation of colloid flakes consisted of one to a few molecular layers by application of ultrasonic treatment in N₂H₄. Their high yield in solution and exposure of more active surface sites allows the synthesis of corresponding solid catalysts with remarkably high activity in hydrodeoxygenation of 4‐methylphenol and this method can also be applied to other two dimensional materials.