Formal proofs of operator identities by a single formal computation

A formal computation proving a new operator identity from known ones is, in principle, restricted by domains and codomains of linear operators involved, since not any two operators can be added or composed. Algebraically, identities can be modelled by noncommutative polynomials and such a formal computation proves that the polynomial corresponding to the new identity lies in the ideal generated by the polynomials corresponding to the known identities. In order to prove an operator identity, however, just proving membership of the polynomial in the ideal is not enough, since the ring of noncommutative polynomials ignores domains and codomains. We show that it suffices to additionally verify compatibility of this polynomial and of the generators of the ideal with the labelled quiver that encodes which polynomials can be realized as linear operators. Then, for every consistent representation of such a quiver in a linear category, there exists a computation in the category that proves the corresponding instance of the identity. Moreover, by assigning the same label to several edges of the quiver, the algebraic framework developed allows to model different versions of an operator by the same indeterminate in the noncommutative polynomials.     

Perturbative manifolds and the Noether generators of nth-order Poisson equations

A manifold that contains small perturbations will induce a perturbed partial differential equation. The partial differential equation that we select is the Poisson equation – in order to explore the interplay between the geometry of the manifold and the perturbations. Specifically, we show how the problem of symmetry determination, for higher-order perturbations, can be elegantly expressed via geometric conditions.     

Optimized spacer layer thickness for plasmonic-induced enhancement of photocurrent in a-Si:H

Journal of Nanoparticle Research - Plasmonic interfaces consisting of silver nanoparticles of different sizes (50–100&;nbsp;nm) have been processed by the self-assembled dewetting...     

Chemical characterisation of bioactive compounds in Medicago sativa growing in the desert of Oman

Medicago sativa Linn growing in Omani desert were chemically characterised using flame photometry, inductively coupled plasma, gas chromatography–mass spectrometry and high performance liquid chromatographic (HPLC) analysis. HPLC analyses were performed to determine the phenolics and flavonoids present in M. sativa. The major compounds detected in M. sativa leaves were protchaechenic acid (3.22%), hydroxyl benzoic acid (1.05%), β-Phenyl caffate (0.97%) and kaempherol (0.89%). Pterostilbene, a cholesterol-lowering compound, was detected in M. sativa.     

Stabilization of the wave equations with localized Kelvin–Voigt type damping under optimal geometric conditions

The purpose of this note is to investigate the stabilization of the wave equation with Kelvin–Voigt damping in a bounded domain. Damping is localized via a non-smooth coefficient in a suitable subdomain. We prove a polynomial stability result in any space dimension, provided that the damping region satisfies some geometric conditions. The main novelty of this note is that the geometric situations covered here are richer than that considered in [25], [22], [16] and include in particular an example where the damping region is not localized in a neighborhood of the whole or a part of the boundary.     

Synthesis,characterization and cytotoxicity of new 2‐isonicotinoyl‐N‐phenylhydrazine‐1‐carbothioamide and its metal complexes

The reaction of the newly synthesized ligand, 2‐isonicotinoyl‐N‐phenylhydrazine‐1‐carbothioamide (H₃L), with acetate salt of Co (II), Cu (II),Ni (II) and Zn (II) led to isolation of four solid complexes. The ligand and complexes structure elucidation were based on elemental analyses, spectral analyses (IR, UV–Visible, ¹H and¹³C‐NMR, MS and ESR), TGA, molar conductivity and magnetic moments measurements. The results indicated that the ligand exists in the thioketo form, while on coordination to the metal ions; it behaves as mono‐negative bidentate chelate and exists in enol form. The optical band gap measurements of the ligand and its metal complexes are in the range 3.83–4.48 eV indicating their semi‐conducting character. The cytotoxicity examination of H₃L and its Zn (II) complex showed that the ligand have very strong cytotoxicity against both HCT‐116 and HEPG‐2 cell lines while, Zn (II) complex has moderate activity.     

Chemical Validation of Mycobacterium tuberculosis Phosphopantetheine Adenylyltransferase Using Fragment Linking and CRISPR Interference**

The coenzyme A (CoA) biosynthesis pathway has attracted attention as a potential target for much-needed novel antimicrobial drugs, including for the treatment of tuberculosis (TB), the lethal disease caused by Mycobacterium tuberculosis (Mtb). Seeking to identify inhibitors of Mtb phosphopantetheine adenylyltransferase (MtbPPAT), the enzyme that catalyses the penultimate step in CoA biosynthesis, we performed a fragment screen. In doing so, we discovered three series of fragments that occupy distinct regions of the MtbPPAT active site, presenting a unique opportunity for fragment linking. Here we show how, guided by X-ray crystal structures, we could link weakly-binding fragments to produce an active site binder with a K_D <20 μM and on-target anti-Mtb activity, as demonstrated using CRISPR interference. This study represents a big step toward validating MtbPPAT as a potential drug target and designing a MtbPPAT-targeting anti-TB drug.     

Electrophoretically deposited sulfonated poly(styrene-co-divinylbenzene) on a screw for microextraction of cationic dyes from aqueous solutions

In the present work, a novel solid-phase microextraction on a screw (MES) was employed to extract cationic dyes (malachite green, methylene blue, and rhodamine B) from food samples and fish breeding pool water. The sulfonated poly(styrene-co-divinylbenzene) was electrophoretically deposited on the surface of the grooves of a screw. Then the screw was placed inside a silicon tube as a holder to create a channel to run a test solution through it. The extracted dyes on the coated screw were eluted by a suitable eluent. High-performance liquid chromatography with an ultraviolet/visible detector was utilized for the separation and analysis of the analytes. The effective parameters of the analyte extraction efficiency were optimized. Under optimum conditions, the limits of detection were 0.15 μg/L, and calibration curves were linear in the range of 0.50–250.00 μg/L, with coefficients of determination > 0.989 for all studied dyes. The relative standard deviations of intra and inter-day (n = 3) were in the range of 2.8%–7.0% and 7.0%–9.5%, respectively. The MES was applied as a simple and repeatable method with acceptable relative recoveries (82.0%–103.0%) for the determination of cationic dyes in grape nectar, ice pop, jelly powder, and fish breeding pool water.     

Highly functionalized pyrazolines from symmetric and asymmetric 1,2-disulfonylhydrazines: a combination of experimental and DFT perspectives

Chemistry of Heterocyclic Compounds - In this work, new pyrazole derivatives were prepared by one-pot three-component reaction emloying symmetric and asymmetric 1,2-disulfonyl-hydrazines,...