Studies on Cu(II) ternary complexes involving an aminopenicillin drug and imidazole containing ligands

Equilibrium studies on the ternary complex systems involving ampicillin (amp) as ligand (A) and imidazole containing ligands viz., imidazole (Him), benzimidazole (Hbim), histamine (Hist) and histidine (His) as ligands (B) at 37 °C and I = 0.15 mol dm^?3 (NaClO₄) show the presence of CuABH, CuAB and CuAB₂. The proton in the CuABH species is attached to ligand A. In the ternary complexes the ligand, amp(A) binds the metal ion via amino nitrogen and carbonyl oxygen atom. The CuAB (B = Hist/His)/CuAB₂ (B = Him/Hbim) species have also been isolated and the analytical data confirmed its formation. Non-electrolytic behavior and monomeric type of chelates have been assessed from their low conductance and magnetic susceptibility values. The electronic and vibrational spectral results were interpreted to find the mode of binding of ligands to metal and geometry of the complexes. This is also supported by the g tensor values calculated from ESR spectra. The thermal behaviour of complexes were studied by TGA/DTA. The redox behavior of the complexes has been studied by cyclic voltammetry. The antimicrobial activity and CT DNA cleavage study of the complexes show higher activity for ternary complexes.     

A note on a generalization of Macdonald’s identities forA l andB l

Let η(q) denote the Dedekind’s η-function. Macdonald obtained identities for η(q) ^{dim g} where g is complex simple finite dimensional Lie algebra. The aim of this paper is to obtain generalization of the above identities in the case of g=A _l andB _l. We also get new formulas for the generating functions of the Ramanujan’s τ-function and ?_α-functions.     

Studies on some ternary complexes of copper(II) involving an amino penicillin drug

Multiple equilibrium studies by pH-metric measurements in the ternary copper(II) complexes with ampicillin(amp) as ligand A and glycine(gly), dl-2-aminobutanoic acid(2aba), dl-3-aminobutanoic acid(3aba), 1,2-diaminopropane(dp), 1,3-diaminopropane(tp), dl-2,3-diaminopropanoic acid(dapa), dl-2,4-diaminobutanoic acid(daba) & dl-2,5-diaminopentanoic acid(ornithine)(orn) as ligands B show the presence of CuABH, CuAB or CuAH?1 B ternary complex species. In the CuAB species the binding of the ligands A and B is similar to their binding in their respective binary complexes. In CuABH_?1 species the deprotonation occurs with amp(A) ligand. The Δlog K values indicate higher stabilities for the ternary complexes than the binary species. The CuAB species with B = gly, 2aba, dapa & orn have been isolated and characterized. The conductivity measurements indicate that the complexes are non-electrolytes. Magnetic susceptibility and electronic spectral data suggest a square pyramidal geometry for CuAB with B = gly/2aba complexes and distorted octahedral geometry for CuAB with B = dapa/orn. The vibrational spectra are interpreted to find the mode of binding of ligand to metal. The TG/DTA studies reveal that the complexes decompose in three steps, indicating non-involvement of hydrated or coordinated water molecules in the complex. The cyclic voltammograms indicate a quasi reversible Cu²⁺/Cu⁺ couple. The antimicrobial activity and CT-DNA cleavage ability of the complexes show higher activity for ternary complexes.     

Purely imaginary roots of kac-moody algebras

In this paper, we introduce a new class of imaginary roots, called purely imaginary roots and give a necessary and sufficient condition for an imaginary root to be purely imaginary,thereby giving a complete classification of those Kac-Moody algebras with the purely imaginary property, namely, all their imaginary roots are purely imaginary. We also define a new class of non-hyperbolic indefinite Kac-Moody algebras, called the extended hyperbolic kac-Moody algebras possessing the purely imaginary property.     

Complete Classifications of Generalized Kac–Moody Algebras Possessing Special Imaginary Roots and Strictly Imaginary Property

In this article, we consider all generalized Kac–Moody algebras (GKM algebras) for the purpose of finding out special imaginary roots and strictly imaginary roots. We give a complete classification of GKM algebras possessing special imaginary roots and also give a complete classification of GKM algebras possessing strictly imaginary property (GKM algebras whose imaginary roots are strictly imaginary). We also conclude that the Monster Lie algebra has no special imaginary root and does not satisfy strictly imaginary property.     

Complete Classification of BKM Lie Superalgebras Possessing Special Imaginary Roots

In this article, we give a complete classification of BKM Lie superalgebras possessing special imaginary roots. In this classification, we have also included infinite dimensional BKM Lie superalgebras with finite or infinite number of real or imaginary simple roots.