Computational Study of Cage Like (ZnO)12 Cluster Using Hybrid and Hybrid Meta Functionals

Density Functional Theory employing hybrid and M06 functionals in combination with three different basis sets is used to calculate the ground state of a cage like (ZnO)₁₂ nanocluster which has been consistently reported as the more stable cluster for its particular size. B3LYP and B3PW91 hybrid functionals combined with 6‐31+G*, Lanl2dz and SDD basis sets are employed to treat the ZnO molecular system. Alternatively, three M06 functionals in combination with three basis sets are employed in the nanostructure calculations. Results obtained by treating ZnO sodalite cage nanocluster with M06 functionals demonstrated comparable quality to results obtained with hybrid functionals. Within this study, efficient theoretical DFT methods with the widely known hybrid and the recently created M06 meta‐hybrid functionals are employed to study nanostructured ZnO. Our resulting parameters provide a fresh approach performance wise on the different theoretical methods to treat transition metal nanostructures, particularly, ZnO nanoclusters geometry and electronic structure.     

New restriction estimates for the 3-d paraboloid over finite fields

We improve the range of exponents for the restriction problem for the 3-d paraboloid over finite fields. The key new ingredient is a variant of the Bourgain–Katz–Tao finite field incidence theorem derived from sum-product estimates. In prime order fields, we give an explicit relationship between the exponent in this incidence theorem and restriction estimates for the paraboloid.     

Two novel abietane dimers from transformed root cultures of Salvia broussonetii

Broussonetone A (1) and broussonetone B (2), two novel dimeric abietane diterpenes, have been isolated from Salvia broussonetii root cultures transformed by Agrobacterium rhizogenes. The structure of broussonetone A was determined from spectroscopic data and confirmed by X-ray analysis. This dimer can be formed by a [4+2]-cycloaddition of two molecules of 13β-hydroxyabieta-8(14),9(11)-dien-12-one. NMR data of broussonetone B indicated that the C-20 methyl in part B of the broussonetone A molecule had been substituted by an aldehyde group. Thus, broussonetone B could be formed by an analogous Diels Alder reaction between 13β-hydroxyabieta-8(14),9(11)-dien-12-one as the dienophile and its 20-oxo derivative as the electrophile.     

Voltammetric Determination of Aflatoxin B1

For the first time the possibility of voltammetry used for the determination of aflatoxin B1 on a glassy carbon electrode was shown. The effect of pH of a supporting electrolyte on the analytical signal of aflatoxin B1 has been investigated and it was shown that there is a more pronounced peak with a maximum current at pH of 5.33. The most favorable supporting electrolyte for a linear range of detectable concentrations of aflatoxin B1 – 0.1 M (NH₄)₂SO₄ was determined. The results of research on the development of conditions of voltammetric measurement of aflatoxin B1 are presented.     

Exploration of carbonic anhydrase inhibition of bioactive metabolites from Pistacia integerrima by molecular docking and first-principles investigations

Bioassay guided fractionation of Pistacia integerrima crude methanolic extract gave Pistacide-A (1) and Pistacide-B (2), along with ten known phytochemicals (3–12). Biochemical analysis of crude plant extract, in-vitro and in-silico carbonic anhydrase inhibitory potential of newly isolated compounds Pistacide-A (1) and Pistacide-B (2) were performed. The cytotoxicity of extract in methanol, ethylacetate and n-butanol against Artemia salina brine-shrimp was 34.98 g/ml, 160.81 g/ml, and 135.77 g/ml, respectively. The significant antimicrobial activity was exhibited by crude, ethyl acetate, and n-butanol fractions. Compounds 1 (IC₅₀ = 6.51 ± 0.42 mM) and 2 (IC₅₀ = 2.85 ± 0.09 mM) showed good carbonic anhydrase inhibition compared with standard zonisamide drug (IC₅₀ = 1.87 ± 0.003 mM). In addition, we have also clarified the electronic properties, absorption wavelengths, molecular electrostatic potential and Hirshfeld analysis by first-principles studies. The coherent intra-molecular charge transfer was seen from occupied to unoccupied molecular orbitals. The absorption wavelengths calculated at time dependent B3LYP/6-31G** level in methanol provided excellent accord with the experimental evidence. Molecular docking score revealed that Pistacide-B would be an efficient drug than its other counterpart that is rational to the experimental data.     

Screening of Wood/Forest and Vine By-Products as Sources of New Drugs for Sustainable Strategies to Control Fusarium graminearum and the Production of Mycotoxins

Fusarium graminearum is a fungal pathogen that can colonize small-grain cereals and maize and secrete type B trichothecene (TCTB) mycotoxins. The development of environmental-friendly strategies guaranteeing the safety of food and feed is a key challenge facing agriculture today. One of these strategies lies on the promising capacity of products issued from natural sources to counteract crop pests. In this work, the in vitro efficiency of sixteen extracts obtained from eight natural sources using subcritical water extraction at two temperatures was assessed against fungal growth and TCTB production by F. graminearum. Maritime pine sawdust extract was shown to be extremely efficient, leading to a significant inhibition of up to 89% of the fungal growth and up to 65% reduction of the mycotoxin production by F. graminearum. Liquid chromatography/mass spectrometry analysis of this active extract revealed the presence of three families of phenolics with a predominance of methylated compounds and suggested that the abundance of methylated structures, and therefore of hydrophobic compounds, could be a primary factor underpinning the activity of the maritime pine sawdust extract. Altogether, our data support that wood/forest by-products could be promising sources of bioactive compounds for controlling F. graminearum and its production of mycotoxins.     

Twisted Poincaré Duality for some Quadratic Poisson Algebras

We exhibit a Poisson module restoring a twisted Poincaré duality between Poisson homology and cohomology for the polynomial algebra endowed with Poisson bracket arising from a uniparametrised quantum affine space. This Poisson module is obtained as the semiclassical limit of the dualising bimodule for Hochschild homology of the corresponding quantum affine space. As a corollary we compute the Poisson cohomology of R, and so retrieve a result obtained by direct methods (so completely different from ours) by Monnier. This research of the first author was supported by a Marie Curie Intra-European Fellowship within the 6th European Community Framework Programme. The second author was supported by EPSRC Grant EP/D034167/1.     

The Sixth Painlevé Equation as Similarity Reduction of $${\widehat{\mathfrak{gl}}_3}$$ Generalized Drinfel’d–Sokolov Hierarchy

Scaling symmetry of -type Drinfel’d–Sokolov hierarchy is investigated. Applying similarity reduction to the hierarchy, one can obtain the Schlesinger equation with (n + 1) regular singularities. Especially in the case of n = 3, the hierarchy contains the three-wave resonant system and the similarity reduction gives the generic case of the Painlevé VI equation. We also discuss Weyl group symmetry of the hierarchy.      

Muckenhoupt weights and Lindelöf theorem for harmonic mappings

We extend the result of Lavrentiev which asserts that the harmonic measure and the arc-length measure are _A∞$A_{\infty }$ equivalent in a chord-arc Jordan domain. By using this result we extend the classical result of Lindelöf to the class of quasiconformal (q.c.) harmonic mappings by proving the following assertion. Assume that f is a quasiconformal harmonic mapping of the unit disk U onto a Jordan domain. Then the function A(z)=arg?(_∂φ(f(z))/z)$A(z)=\arg ?({\partial }_{\phi }(f(z))/z)$ where z=re^iφ$z=r{e}^{i\phi }$, is well-defined and smooth in U^?={z:0<|z|<1}${\mathbf{U}}^{?}=\{z:0<|z|<1\}$ and has a continuous extension to the boundary of the unit disk if and only if the image domain has C¹$C^1$ boundary.