Multiplicative Lie algebras and Schur multiplier

In this paper, we attempt to study the structure of multiplicative Lie algebras, the theory of extensions, the second cohomology groups of multiplicative Lie algebras, and in turn the Schur multipliers. The Schur–Hopf formula is established for multiplicative Lie algebras. We also introduce the group of nontrivial relations satisfied by the Lie product in a multiplicative Lie algebra, and study it as a functor arising from the presentations of multiplicative Lie algebras. Some applications in K-theory are also discussed.     

Age-group-targeted testing for COVID-19 as a new prevention strategy

Nonlinear Dynamics - Robust testing and tracing are key to fighting the menace of coronavirus disease 2019 (COVID-19). This outbreak has progressed with tremendous impact on human life, society and...     

Gas Sensors Based on Porous Ceramic Bodies of MSnO3 Perovskites (M = Ba,Ca, Zn): Formation and Sensing Properties towards Ethanol,Acetone, and Toluene Vapours

In this work, the gas-sensing functionality of porous ceramic bodies formed by the slip casting technique was studied using perovskite nanoparticles of an MSnO₃ system (M = Ba, Ca, Zn) synthesized by a chemical route. The performance and reliability of the sensitive materials in the presence of different volatile organic compounds (acetone, ethanol, and toluene), and other gases (CO, H₂ and NO₂) were analysed. The ZnSnO₃, BaSnO₃, and CaSnO₃ sensors showed sensitivities of 40, 16, and 8% ppm⁻¹ towards acetone, ethanol, and toluene vapours, respectively. Good repeatability and selectivity were also observed for these gaseous analytes, as well as excellent stability for a period of 120 days. The shortest response times were recorded for the ZnSnO₃ sensors (e.g., 4 s for 80 ppm acetone) with marked responses to low concentrations of acetone (1000 ppb). These results are attributed to the porosity of the sensitive materials, which favours the diffusion of gases, induces surface defects, and provides greater surface area and good sensitivity to acetone, as is seen in the case of ZnSnO₃.     

Atomic force microscopy force mapping in the study of supported lipid bilayers

Investigating the structural and mechanical properties of lipid bilayer membrane systems is vital in elucidating their biological function. One route to directly correlate the morphology of phase-segregated membranes with their indentation and rupture mechanics is the collection of atomic force microscopy (AFM) force maps. These force maps, while containing rich mechanical information, require lengthy processing time due to the large number of force curves needed to attain a high spatial resolution. A force curve analysis toolset was created to perform data extraction, calculation and reporting specifically in studying lipid membrane morphology and mechanical stability. The procedure was automated to allow for high-throughput processing of force maps with greatly reduced processing time. The resulting program was successfully used in systematically analyzing a number of supported lipid membrane systems in the investigation of their structure and nanomechanics.     

Solvent-Assisted Naked Eye Sensing of Hg2+ by a Chemoreceptor Derived from Diazocoupling of Sulfathiazole with Diethyl Malonate

Abstract

2-{[4-(Thiazol-2-ylsulfamoyl)-phenyl]-hydrazono}-malonic acid diethyl ester (R1) and 2-{[4-(5-methyl-isoxazol-3-ylsulfamoyl)-phenyl]-hydrazono}-malonic acid diethyl ester (R2) were synthesized through diazocoupling of sulfathiazole and sulfamethoxazole, respectively, with diethyl malonate. They were characterized through various spectroscopic and mass spectral studies. R2 was also characterized through a single crystal X-ray diffraction (XRD) study. Only R1 selectively recognized Hg²⁺ from a wide range of metal ions through naked-eye change. A color change from orange to olive green was observed upon addition of 1.0 equivalent of Hg²⁺ as its chloride salt to the 1 × 10^?3 M DMSO solution of R1. The role of DMSO in the sensing process appears to be the crucial one, because the solvent-assisted band of R1 at 482 nm observed in its UV-Vis spectrum in DMSO did not appear in its spectra recorded in nujol or in a polar aprotic solvent. The UV-Vis and ¹H NMR titrations revealed that the formation of six-membered 1:1 chelate between R1 and Hg²⁺ triggering the desolvation of R1

as the key step towards its sensing activity. The determination of binding stoichiometry between R1 and Hg²⁺ along with binding constant has also been discussed.

Supplemental materials are available for this article. Go to the publisher's online edition of Phosphorus, Sulfur, and Silicon and the Related Elements to view the free supplemental file.

GRAPHICAL ABSTRACT      

Hydroxo‐Bridged Dimers of Oxo‐Centered Ruthenium(III) Triangle: Synthesis and Spectroscopic and Theoretical Investigations

The homometallic hexameric ruthenium cluster of the formula [Ru^III₆(μ₃‐O)₂(μ‐OH)₂((CH₃)₃CCO₂)₁₂(py)₂] ( 1 ) (py=pyridine) is solved by single‐crystal X‐ray diffraction. Magnetic susceptibility measurements performed on 1 suggest that the antiferromagnetic interaction between the Ru^III centers is dominant, and this is supported by theoretical studies. Theoretical calculations based on density functional methods yield eight different exchange interaction values for 1 : J₁=?737.6, J₂=+63.4, J₃=?187.6, J₄=+124.4, J₅=?376.4, J₆=?601.2, J₇=?657.0, and J₈=?800.6 cm^?1. Among all the computed J values, six are found to be antiferromagnetic. Four exchange values (J₁, J₆, J₇ and J₈) are computed to be extremely strong, with J₈, mediated through one μ‐hydroxo and a carboxylate bridge, being by far the largest exchange obtained for any transition‐metal cluster. The origin of these strong interactions is the orientation of the magnetic orbitals in the Ru^III centers, and the computed J values are rationalized by using molecular orbital and natural bond order analysis. Detailed NMR studies (¹H, ¹³C, HSQC, NOESY, and TOCSY) of 1 (in CDCl₃) confirm the existence of the solid‐state structure in solution. The observation of sharp NMR peaks and spin‐lattice time relaxation (T1 relaxation) experiments support the existence of strong intramolecular antiferromagnetic exchange interactions between the metal centers. A broad absorption peak around 600–1000 nm in the visible to near‐IR region is a characteristic signature of an intracluster charge‐transfer transition. Cyclic voltammetry experiments show that there are three reversible one‐electron redox couples at ?0.865, +0.186, and +1.159 V with respect to the Ag/AgCl reference electrode, which corresponds to two metal‐based one‐electron oxidations and one reduction process.     

Kinetics and mechanism of the ruthenium(III)-catalysed oxidation of aminoalcohols by chloramine-T in perchloric acid

Summary The kinetics of the ruthenium(III) catalysed oxidation of 2-aminoethanol, 3-aminopropanol, diethanolamine and triethanolamine by chloramine-T in HClO₄ medium have been studied. The reactions exhibits first order rate dependence with respect to the oxidant and to the catalyst, and are zeroth order with respect to the substrate. The rate of oxidation is proportional to k[HClO₄]/{k+k'[HClO₄]} where k, k and k' are constants (a mixture of elementary rate constants and equilibrium constants). A suitable mechanism consistent with the observed kinetic data is proposed.     

Aqueous chemistry of the vanadium(III) (V(III)) and the V(III)-dipicolinate systems and a comparison of the effect of three oxidation states of vanadium compounds on diabetic hyperglycemia in rats

The aqueous vanadium(III) (V(III)) speciation chemistry of two dipicolinate-type complexes and the insulin-enhancing effects of V-dipicolinate (V-dipic) complexes in three different oxidation states (V(III), V(IV), and V(V)) have been studied in a chronic animal model system. The characterization of the V(III) species was carried out at low ionic strength to reflect physiological conditions and required an evaluation of the hydrolysis of V(III) at 0.20 M KCl. The aqueous V(III)-dipic and V(III)-dipic-OH systems were characterized, and complexes were observed from pH 2 to 7 at 0.2 M KCl. The V(III)-dipic system forms stable 1:2 complexes, whereas the V(III)-dipic-OH system forms stable 1:1 complexes. A comparison of these complexes with the V-pic system demonstrates that a second ligand has lower affinity for the V(III), presumably reflecting bidentate coordination of the second dipic(2)(-) to the V(III). The thermodynamic stability of the [V(III)(dipic)(2)](-) complex was compared to the stability of the corresponding V(IV) and V(V) complexes, and surprisingly, the V(III) complexes were found to be more stable than anticipated. Oral administration of three V-dipicolinate compounds in different oxidation states {H[V(III)(dipic)(2)H(2)O].3H(2)O, [V(IV)Odipic(H(2)O)(2)].2H(2)O, and NH(4)[V(V)O(2)dipic]} and the positive control, VOSO(4), significantly lowered diabetic hyperglycemia in rats with streptozotocin-induced diabetes. The diabetic animals treated with the V(III)- or V(IV)-dipic complexes had blood glucose levels that were statistically different from those of the diabetic group. The animals treated with the V(V)-dipic complex had the lowest blood glucose levels of the treated diabetic animals, which were statistically different from those of the diabetic group at all time points. Among the diabetic animals, complexation to dipic increased the serum levels of V after the administration of the V(V) and V(IV) complexes but not after the administration of the V(III) complex when data are normalized to the ingested dose of V. Because V compounds differing only in oxidation state have different biological properties, it is implied that redox processes must be important factors for the biological action of V compounds. We observe that the V(V)-dipic complex is the most effective insulin-enhancing agent, in contrast to previous studies in which the V(IV)-maltol complex is the most effective. We conclude that the effectiveness of complexed V is both ligand and oxidation state dependent.     

First-order phase transformation and structural studies in Se<Subscript>85</Subscript>In<Subscript>15−x</Subscript>Zn<Subscript>x</Subscript> chalcogenide glasses

Present research work describes the crystallization kinetics and structural studies in Se₈₅In_15?xZn_x chalcogenide glasses. Bulk alloys of Se₈₅In_15?xZn_x were synthesized by melt-quenching procedure. High resolution X-ray diffraction (HRXRD) was used to confirm the amorphous nature of synthesized samples. Non-isothermal differential scanning calorimetry (DSC) measurements were performed at 5, 10, 15, 20 and 25 K min^?1 heating rates to study kinetics of crystallization in Se₈₅In_15?xZn_x. Various crystallization parameters such as glass transition (T _g), onset crystalline (T _c), peak crystallization (T _p) and melting temperature (T _m) were calculated from DSC curves. The activation energies of structural relaxation (ΔE _t) and crystallization (ΔE _c) were determined by using Kissinger, Moynihan and Ozawa approaches. ΔE _t is found to be the lowest for Se₈₅In₆Zn₉ sample which shows this sample has the highest probability of escape to a state of lower configurational energy and has greater stability. Thermal stability of various compositions was studied and found to vary with Zn content. Further, HRXRD and field emission scanning electron microscope were used for the study of first phase transformation in Se₈₅In_15?xZn_x samples.     

Slant Lightlike Submanifolds of Indefinite Cosymplectic Manifolds

In this paper, we introduce the notion of a slant lightlike submanifold of an indefinite Cosymplectic manifold. We provide a nontrivial example and obtain necessary and sufficient conditions for the existence of a slant lightlike submanifold. Also, we give an example of a minimal slant lightlike submanifold of R⁹₂{R^{9}_{2}} and prove some characterization Theorems.