Composition formulae for some integro-differential operators and their applications

Institute of Mathematics and Informatics. Akademijos 4, 2600 Vilnius, Lithuania. Translated from Lietuvos Matematikos Rinkinys. Vol. 36, No. 1, pp. 27–38, January–March,. 1996.     

Asymmetric transfer hydrogenation of imines catalyzed by a Noyori-type Ru(II) complex—a parametric study

We present, to the best of our knowledge, the first parametric study of the asymmetric transfer hydrogenation of imines catalyzed by a Noyori-type catalytic complex based on ruthenium. A model imine for this study was 1-methyl-3,4-dihydroisoquinoline, and a well-known complex RuCl(η⁶-p-cymene)((1S,2S)-N-p-toluenesulfonyl-1,2-diphenylethylenediamine) was chosen as the model catalyst. The reactions were performed in the presence of a formic acid–triethylamine mixture as the source of hydrogen.The parameters examined include general parameters, for example, concentration, temperature, and substrate-to-catalyst molar ratio, as well as parameters specific to this particular reaction, such as the amount of the hydrogenation mixture used, the ratio of its components, or the inhibitive effect of carbon dioxide. During this study, several unexpected parameters worth further investigation have emerged.     

Synthesis, effect of capping agents, structural, optical and photoluminescence properties of ZnO nanoparticles

Zinc oxide nanoparticles were synthesized using chemical method in alcohol base. During synthesis three capping agents, i.e. triethanolamine (TEA), oleic acid and thioglycerol, were used and the effect of concentrations was analyzed for their effectiveness in limiting the particle growth. Thermal stability of ZnO nanoparticles prepared using TEA, oleic acid and thioglycerol capping agents, was studied using thermogravimetric analyzer (TGA). ZnO nanoparticles capped with TEA showed maximum weight loss. X-ray diffraction (XRD) and scanning electron microscopy (SEM) were used for structural and morphological characterization of ZnO nanoparticles. Particle size was evaluated using effective mass approximation method from UV-vis spectroscopy and Scherrer's formula from XRD patterns. XRD analysis revealed single crystal ZnO nanoparticles of size 12-20 nm in case of TEA capping. TEA, oleic acid and thioglycerol capped synthesized ZnO nanoparticles were investigated at room temperature photoluminescence for three excitation wavelengths i.e. 304, 322 and 325 nm, showing strong peaks at about 471 nm when excited at 322 and 325 nm whereas strong peak was observed at 411 for 304 nm excitation.     

On an integral equation of the third type

Institute of Mathematics and Informatics, Akademijos 4, 2600 Vilnius, Lithuania. Translated from Lietuvos Matematikos Rinkinys, Vol. 35, No. 3, pp. 308–314, July–September, 1995.     

Topological invariants in the study of a chaotic food chain system

The study of ecological systems has generated deep interest in exploring the complexity of chaotic food chains. The role of chaos in ecosystems is not entirely understood. One approach to have a better comprehension of ecological chaos is by analyzing it in mathematical models of basic food chains. In this article it is considered a classical chaotic food chain model from the literature. We use the theory of symbolic dynamics to study the topological entropy and the parameter space ordering of kneading sequences associated with one-dimensional maps that reproduce significant aspects of the model dynamics. The topological entropy allows us to distinguish different chaotic states in some realistic system parameter region. Another numerical invariant is introduced in order to characterize isentropic dynamics. Studying a set of maps with the same topological entropy, we exhibit numerical results about the relation between the second topological invariant and each of the control parameters in consideration. This work provides an illustration of how our understanding of ecological models can be enhanced by the theory of symbolic dynamics.     

Highly efficient,economic, and recyclable glutathione decorated magnetically separable nanocomposite for uranium(VI) adsorption from aqueous solution

A green and environment-friendly magnetically separable nanocomposite, glutathione@magnetite was fabricated sonochemically through the functionalization of Fe₃O₄ by glutathione which was well characterized using Fourier-transform infrared spectroscopy, ultravoilet-visible spectroscopy, scanning electron microscope, energy-dispersive X-ray spectroscopy, X-ray photoelectron spectroscopy, X-ray diffraction, thermogravimetric analysis, vibrating sample magnetometer, Brunauer-Emmett-Teller, and high-resolution transmission electron microscope. The parameters affecting adsorption including pH, temperature, contact time, initial adsorbate concentration, and adsorbent amount were optimized by batch experiments. The magnetic glutathione@magnetite was applied for the removal of uranium(VI) in water with maximum adsorption capacity found to be 333.33 mg/g in 120 min at a neutral pH at 25 °C showing high efficiency for U(VI) ions. Furthermore, adsorption results obtained from UV-vis spectroscopy were validated by inductively coupled plasma optical emission spectroscopy. The thermodynamic parameters, viz Gibbs free energy (ΔGº), standard enthalpy change (ΔHº), and standard entropy change (ΔSº) of the process were calculated using the Langmuir constants. The pseudo-second-order kinetics model is seen to be applicable for describing the uptake process using a kinetics test. Moreover, desorption studies reveals that glutathione@magnetite can be used repeatedly, and removal efficiency shows only a small decrease after six cycles. Thus, glutathione@magnetite acts as a potential adsorbent for the removal of U(VI) from the water with great adsorption performance.