On the Instability Intervals of the Mathieu–Hill Operator

Consider the Mathieu–Hill operator

Molar Volume Calculation of Molten Ag–Au–Cu and Cu–Ag–In Alloy Systems Using General Solution Model

Russian Journal of Physical Chemistry A - However, up to the present, there was few reports on the density of the molten Ag–Au–Cu and Cu–Ag–In alloy systems. In this work,...     

Biological assays and theoretical density functional theory calculations of Rh(I), Ir(III), and Ru(II) complexes of chiral phosphinite ligand

Four metal complexes, IL-OPPh₂-Ru-p-cymene (3) , IL-OPPh₂-Ru-benzene (4) , IL-OPPh₂-Ir-Cp* (5) , IL-OPPh₂-Rh-COD (6) , have been evaluated for in vitro antioxidant activity such as 2,2-diphenyl-1-picrylhydrazyl (DPPH) radical scavenging and reducing power activity. Maximum scavenging activity (71.43%) was obtained with IL-OPPh₂-Ru-p-cymene, whereas IL-OPPh₂-Rh-COD showed the highest reducing power ability. The complexes were also studied for their antimicrobial activity against three Gram-positive and three Gram-negative bacteria. In addition, DNA binding of the complexes was evaluated using calf thymus DNA. Both Ru(II) complexes exhibited good DNA-binding activity while the other complexes did not have any activity. Furthermore, ab initio quantum calculations of four complexes were also carried out using density functional theory to better understand their chemical behaviors.     

The complex step approximation to the higher order Fréchet derivatives of a matrix function

Numerical Algorithms - The k th Fréchet derivative of a matrix function f is a multilinear operator from a cartesian product of k subsets of the space $\mathbb {C}^{n\times n}$ into itself. We...     

AHP–TOPSIS hybrid decision-making analysis: Simav integrated system case study

Journal of Thermal Analysis and Calorimetry - In the original publication of the article, the following equations has been incorrectly published. The corrected equations are given.     

Crystal structure of [RuCl2[N-(2,4,6-trimethyl-benzyl)N-(n-butyl)]-imidazolidin-2-ylidene] and [RuCl2[N-(2,4,6-trimethyl-benzyl)-N-(2-methoxyethyl)]-imidazolidin-2-ylidene]

Two imidazolidin ruthenium complexes, [RuCl₂{[N-(2,4,6-trimethyl-benzyl)-N-(n-butyl)]-imidazolidin-2-ylidene}], 1, and [RuCl₂{[N-(2,4,6-trimethyl-benzyl)-N-(2-methoxyethyl)]-imidazolidin-2-ylidene}], 2, have been synthesised and their crystal structures have been determined from single crystal X-ray diffraction data. Compound 1 is monoclinic, of space group C2/c with a = 18.466(4) Å, b = 14.816(3) Å, c = 15.413(3) Å, β = 118.067(2)^∘, and V = 3720.9(12) ų with Z = 8 for d_calc = 1.536 g/cm³. Compound 2 is monoclinic, of space group P2₁/c with a = 8.1800(5) Å, b = 14.344(8) Å, c = 14.809(9), β = 91.604(10)^∘, and V = 1736.7(18) ų with Z = 4 for d_calc = 1.653 g/cm³. In each complex the ligand functions as an arene and carbene, occupying four coordination sites. The two chlorines in each compound complete a distorted octahedron.     

The Rhodium(II) Carbenoid Cyclization-Cycloaddition Cascade of alpha-Diazo Dihydroindolinones for the Synthesis of Novel Azapolycyclic Ring Systems

Tandem carbonyl ylide formation-1,3-dipolar cycloaddition of α-diazo N-acetyl-tetrahydro-β-carbolin-1-one derivatives occur efficiently in the presence of a dirhodium catalyst to afford bimolecular cycloadducts in high yield. The Rh(II)-catalyzed reaction also takes place intramolecularly to give products derived from trapping of the carbonyl ylide dipole with a tethered alkene. The power of the intramolecular cascade sequence is that it rapidly assembles a pentacyclic ring system containing three new stereocenters and two adjacent quaternary centers stereospecifically in a single step and in high yield.     

Novel metallophthalocyanines bearing 3-(p-chlorophenyl)-5-p-tolyl-4H-1,2,4-triazole bulky substituents by microwave irradiation

The synthesis of metallophthalocyanines [6–9; M = Ni(II), Zn(II), Co(II) and Cu(II)] with four 1,2,4-triazole units obtained from 4-{(4-chloro-2-fluorobenzyl)[3-(4-chlorophenyl)-5-(4-methylphenyl)-4H-1,2,4-triazol-4-yl]amino}phthalonitrile (5) in the presence of dimethylaminoethanol and the corresponding anhydrous metal salts is described. The thermal stabilities of the Pc compounds were determined by thermogravimetric analysis. The new compounds were characterized by a combination of IR, ¹H NMR, ¹³C NMR, UV–Vis, elemental analysis.     

Structural and vibrational investigation of 1, 2-<Emphasis Type="Italic">bis</Emphasis>(3, 4-dimethoxyphenyl) ethane-1, 2-dione (Veratril): experimental and theoretical studies

The molecular and crystal structures of 1,2-bis(3,4-dimethoxyphenyl)ethane-1,2-dione (TMBZ = tetramethoxybenzil) were determined by a single-crystal X-ray diffraction, ¹H NMR, and FT-IR spectroscopy. The compound TMBZ (C₁₈H₁₈O₆, M _r = 330.32) crystallized in the orthorhombic Fdd2 space group wherein: a = 39.145(4), b = 18.167(2), c = 4.3139(5) Å and β = 90°, Z = 8. The packing of the molecules in the crystal lattice is stabilized by intermolecular C–H?O contacts in the herringbone arrangement. The molecular geometry and harmonic frequencies of TMBZ in the ground state were calculated utilizing density functional (B3LYP) method with the 6-311++G(d, p)-basis set. The density functional theory optimized the geometric structure, and vibrational wave numbers of TMBZ in gas phase were compared with the experimental data. A complete assignment of the fundamentals was proposed based on the total energy distribution calculation.