On the necessary and sufficient condition for the extended Wedderburn–Guttman theorem

Let A be a u by v matrix, and let M and N be u by p and v by q matrices, where p may not be equal to q or rank(M^′AN)<min(p,q). Recently, Galantai [A. Galantai, A note on the generalized rank reduction, Acta Math. Hungarica 116 (2007) 239–246] presented what he claimed to be the necessary and sufficient condition for rank(A-AN(M^′AN)^-M^′A)=rank(A)-rank(AN(M^′AN)^-M^′A) to hold. This rank subtractivity formula along with the condition under which it holds is called the extended Wedderburn–Guttman theorem. In this paper, we show that some of Galantai’s assertions are incorrect.     

The clique numbers of regular graphs of matrix algebras are finite

Let F be a field, char(F)≠2, and SGL_n(F), where n is a positive integer. In this paper we show that if for every distinct elements x,yS, x+y is singular, then S is finite. We conjecture that this result is true if one replaces field with a division ring.     

辫子群的全部二维不可约表示

通过直接解矩阵方程给出了Bn群的全部二维不可约表示．     

Green synthesis and characterization of copper and nickel hybrid nanomaterials: Investigation of their biological and photocatalytic potential for the removal of organic crystal violet dye

Nanotechnology deals with the materials at nanoscale to synthesize nanoparticles. The current study introduced a new green approach for the synthesis of Copper and Nickel hybrid nanoparticles by using Zingiber officinale rhizome extract as a capping and reducing agent. The nanoparticles were physico-chemically characterized by UV–visible spectroscopy, Fourier transform infrared spectroscopy, X-ray powder diffraction, Energy-dispersive X-ray spectroscopy, and Scanning electron microscopy. It was revealed by scanning electron micrograph that the Cu-Ni hybrid nanoparticles have spherical geometries with average grain size of 25.12 ± 1.2 nm. Furthermore, biocatalytic and photocatalytic applications of the biosynthesized nanoparticles were assessed. The results of antibacterial assay revealed that Cu-Ni hybrid nanoparticles had an inhibition zones of 28 ± 1.0, 25 ± 0.8, and 25 ± 1.5 mm against P. aeruginosa, E. coli and Proteus vulgaris. Commercially available antibiotics were purchased and coated with Cu-Ni hybrid nanoparticles, it was found that their antimicrobial efficacy was increased twice. To evaluate the antioxidant potential, nanoparticles having a concentration of 200 µg/mL were applied against 2,2-diphenyl-1-picrylhydrazyl free radicals and NPs showed 42.1 ± 0.71 % inhibition. Cu-Ni nanoparticles have shown a dose-dependent cytotoxicity against amastigote and promastigote in anti-leishmanial assay. The synthesized nanoparticles were found biocompatible and safe in nature to be used in vivo, as they showed no significant hemolysis of human red blood cells at their highest concentration. In antidiabetic assay, NPs inhibited alpha-amylase enzyme up to 38.07 ± 0.65 %. An organic crystal violet dye was successfully degraded by the synthesized nanoparticles in photocatalytic assay. Hence, it is concluded that Cu-Ni hybrid nanoparticles can be used both in vitro and in vivo for drug delivery in biomedical research. These nanoparticles can also be used in the remediation of organic dyes as a catalyst.     

Mixed‐Valence Nickel Bis(azamacrocycle) Compounds with Ghost‐Leg‐type Sheets

The fabrication of so‐called ghost‐leg sheets and their electronic properties is reported. This unique sheet structure is composed of one‐dimensional mixed‐valence nickel chains, which are linked with one another by bis(azamacrocycle) ligands. They are also topologically unique Ni^II/Ni^III mixed‐valence complexes, as confirmed by X‐ray and optical measurements. Moreover, their magnetic susceptibilities indicated two‐dimensional antiferromagnetic behavior following the Fisher 1D chain model with interchain interactions, where spins on Ni^III sites mutually interact antiferromagnetically in the sheets.     

Ni‐Catalyzed Stannylation of Aryl Esters via C−O Bond Cleavage

A Ni‐catalyzed stannylation of aryl esters with air‐ and moisture‐insensitive silylstannyl reagents via C −O cleavage is described. This protocol is characterized by its wide scope, including challenging combinations, thus enabling access to versatile building blocks and orthogonal C−heteroatom bond formations.     

Structural and Spectral Study of Nickel(II) Complexes of Pyridyl bis{3‐piperidyl‐, bis{hexamethyleneiminyl‐, bis{N(4)‐diethyl‐, and bis{N(4)‐dipropylthiosemicarbazones}

Pyridyl bis(N(4)‐substituted thiosemicarbazones), in which the substituents replacing the NH₂ group on the thiosemicarbazone moieties are piperidyl, H₂Plpip; hexamethyleneiminyl, H₂Plhexim; diethylamino, H₂Pl4DE; and dipropylamino, H₂Pl4DP, have been synthesized. These bis(thiosemicarbazones) and their nickel(II) complexes have been characterized with IR, electronic, mass, and ¹H and ¹³C NMR spectra. Crystal structures have been solved for H₂Plpip and all four nickel(II) complexes. H₂Plpip does not possess hydrogen bonding between the thiosemicarbazone moieties, but is in the Z isomeric form with intramolecular hydrogen bonding from both thiosemicarbazone moieties to pyridine nitrogen atoms. The nickel(II) complexes possess square‐planar N₂S₂ (i. e., imine nitrogen and thiolato sulfur atoms) centers and the two pyridine ring nitrogen atoms are not coordinated.     

Surfactant effects on pH-controlled synthesis of nickel hydroxides

The aim of the present work is to determine at 60 °C, the influence of the specific nature of nickel salt and pH on nickel hydroxide features such as crystallographic structure and morphology. Within the range 8 ≤ pH ≤ 11.5, a home-made nickel functionalized surfactant, nickel di-dodecylsulfate Ni(C₁₂H₂₅SO₄)₂ is compared to usual salts (nickel nitrate Ni(NO₃)₂ and nickel sulfate NiSO₄). In both cases, a sharp transition appears for pH about 10. In the classic salt case, the transition mainly affects morphology, that could be evidenced by the crosschecking of complementary techniques as SEM and nitrogen gas adsorption. For pH < 10, β-Ni(OH)₂ platelets are yielded, whereas more basic conditions lead to randomly aggregated nano-grains of badly crystallized β hydroxide. Inversely, by employing the functionalized surfactant, 2D morphology is maintained in the whole pH-range, but the crystal structure is pH-controlled ( phase with interlamellar dodecylsulfate for pH ≤ 9.5, and β phase for pH ≥ 10.5).     

Molecular Nickel Thiolate Complexes for Electrochemical Reduction of CO2 to C1–3 Hydrocarbons

We report the unprecedented electrocatalytic activity of a series of molecular nickel thiolate complexes ( 1 – 5 ) in reducing CO₂ to C_1–3 hydrocarbons on carbon paper in pH-neutral aqueous solutions. Ni(mpo)₂ ( 3 , mpo=2-mercaptopyridyl-N-oxide), Ni(pyS)₃⁻ ( 4 , pyS=2-mercaptopyridine), and Ni(mp)₂⁻ ( 5 , mp=2-mercaptophenolate) were found to generate C₃ products from CO₂ for the first time in molecular complex. Compound 5 exhibits Faradaic efficiencies (FEs) of 10.6 %, 7.2 %, 8.2 % for C₁, C₂, C₃ hydrocarbons respectively at −1.0 V versus the reversible hydrogen electrode. Addition of CO to the system significantly promotes the FE_C1–C3 to 41.1 %, suggesting that a key Ni−CO intermediate is associated with catalysis. A variety of spectroscopies have been performed to show that the structures of nickel complexes remain intact during CO₂ reduction.     

Selective Preparation of Phosphorus Mononitride (P≡N) from Phosphinoazide and Reversible Oxidation to Phosphinonitrene

The interstellar candidate phosphorus mononitride PN, a metastable species, was generated through high-vacuum flash pyrolysis of (o-phenyldioxyl)phosphinoazide in cryogenic matrices. Although the PN stretching band was not directly detected because of its low infrared intensity and possible overlaps with other strong bands, o-benzoquinone, carbon monoxide, and cyclopentadienone as additional fragmentation products were clearly identified. Moreover, an elusive o-benzoquinone-PN complex formed when (o-phenyldioxyl)phosphinoazide was exposed to UV irradiation at λ=254 nm. Its recombination to (o-phenyldioxyl)-λ⁵-phosphinonitrile was observed upon irradiation with the light at λ=523 nm, which demonstrates for the first time the reactivity of PN towards an organic molecule. Energy profile computations at the B3LYP/def2-TZVP density functional theory level reveal a concerted mechanism. To provide further evidence, UV/Vis spectra of the precursor and the irradiation products were recorded and agree well with time-dependent DFT computations.