Hopf Modules and Noncommutative Differential Geometry

We define a new algebra of noncommutative differential forms for any Hopf algebra with an invertible antipode. We prove that there is a one-to-one correspondence between anti-Yetter–Drinfeld modules, which serve as coefficients for the Hopf cyclic (co)homology, and modules which admit a flat connection with respect to our differential calculus. Thus, we show that these coefficient modules can be regarded as “flat bundles” in the sense of Connes’ noncommutative differential geometry.     

Bivariant Hopf Cyclic Cohomology

For module algebras and module coalgebras over an arbitrary bialgebra, we define two types of bivariant cyclic cohomology groups called bivariant Hopf cyclic cohomology and bivariant equivariant cyclic cohomology. These groups are defined through an extension of Connes' cyclic category Λ. We show that, in the case of module coalgebras, bivariant Hopf cyclic cohomology specializes to Hopf cyclic cohomology of Connes and Moscovici and its dual version by fixing either one of the variables as the ground field. We also prove an appropriate version of Morita invariance for both of these theories.     

Protonation Equilibria of Carminic Acid and Stability Constants of Its Complexes with Some Divalent Metal Ions in Aqueous Solution

The dissociation constants of carminic acid (7-D-glucopyronosyl-3,5,6,8-tetra- hydroxy-1-methyl-9,10-dioxo-anthracene-2-carboxylic acid) (CA), together with the stability constants of its Cu(II), Zn(II), Ni(II), Co(II) and Hg(II) complexes, were studied potentiometrically in aqueous medium at 25.0?(1)?°C, and at the ionic background of 0.1?mol?dm^?3 of NaCl, and determined with the SUPERQUAD computer program. It has been observed that carminic acid has five dissociation constants, and for H₅L their values are 3.39?(7), 5.78?(7), 8.35?(7), 10.27?(7), and 11.51?(7). This ligand behaves as a bi-dentate ligand, and the carboxyl and the ortho hydroxy groups of the ligand coordinate to the metal ions. Various metal complexes were produced in solution under the experimental conditions, for each metal ion used, including hydrolyzed species. The species distribution curves of the complexes formed in the solution were calculated and reviewed. The stability of the complexes was found to follow the order: Cu(II) > Zn(II) > Ni(II) > Co(II) > Hg(II).     

Study of the Coordination Properties of 1,2-Bis(2,6-dimethphenylamino) Glyoxime and Determine the Stability Constant of Its Complexes with Ni(II), Cu(II) and Zn(II) Metal Ions in Solution

This study aims to investigate the nature and type of complexes formed in solution between 1,2-bis(2,6-dimethphenylamino) glyoxime (DPG) and the ions Ni²⁺, Cu²⁺ and Zn²⁺. Potentiometric titration was used to follow the formation of complexes.The complexes formed were studied through the determination of stability constants of these complexes in mixed ethanol–aqueous solution at 25±0.1?°C and ionic strength of 0.1 mol?dm^?3 NaCl. The basicity of the ligand was also assessed by the determination of the dissociation constants of the ligand. All of the constants were determined by computer refinement of pH–volume data using the SUPERQUAD program. The species distribution diagrams were also calculated.Comparison with other vic-dioximes was made to provide reliable support for the formation of the proposed complexes in solution.     

Removal of 226Ra from aqueous media and its thermodynamics and kinetics

The composite adsorbent prepared by mixing of polyacrylonitrile and clinoptilolite was used for investigating the adsorption behaviour of ²²⁶Ra in column system. The effective parameters like initial activity concentration, pH of the solution, contact time and temperature for adsorption behaviour of ²²⁶Ra were studied. Adsorption efficiency of ²²⁶Ra on composite adsorbent from aqueous solution was determined to 98.73 ± 0.59 % at pH 5.0 and 30 °C in a short time. The isotherm models were studied to evaluated adsorption characteristics of ²²⁶Ra onto composite adsorbent. The thermodynamic parameters were showing that the processes for ²²⁶Ra were exothermic. Adsorption kinetics of the radium is also studied.

     

Bialgebra Cyclic Homology with Coefficients

We show that one can extend the definition of Hopf cyclic homology with coefficients such that one can use bialgebras and a larger class of coefficient module/co-modules. With the help of this extension, we calculate the bialgebra cyclic homology of U_q() the quantum deformation of an arbitrary semi-simple Lie algebra and (N) the Hopf algebra of foliations of codimension N, with several coefficient modules.     

Excision in Hopf Cyclic Homology

In this paper, we show that, under natural homological conditions, Hopf cyclic homology theory has excision.     

Potentiometric and Theoretical Studies of (2Z, 3Z)-2H-benzo[b][1,4]thiazine-2,3(4H)-dionedioxime with Some Divalent Transition Metal Ions

The protonation equilibria of (2Z, 3Z)-2H-benzo[b][1,4]thiazine-2,3(4H)-dionedioxime (BTDH₂) together with the equilibria of its bis- binary complexes of Co(II), Ni(II), Cu(II) and Zn(II) were investigated potentiometrically. The investigation was carried out at 25 ± 0.1 °C, in aqueous solution, with a constant ionic strength of 0.100 mol·dm^?3 NaCl. The protonation constants of the ligand together with the stability constants of a variety of complexes were determined potentiometrically in 10 % ethanol–water mixed solution using the SUPERQUAD computer program. Theoretical calculations were set up to assist in understanding the protonation sequence in the ligand molecule via the semi-empirical molecule orbital method of parameterized model number 3. Results are discussed in connection to the basicity of the donor atoms and structural arrangement of the ligand. Although BTDH₂ has two dissociable protons, four protonation constants can be measured under the experimental conditions presented. These four protonation constants (as log₁₀ βs) are 10.245, 19.397, 22.414 and 25.176.