Differential geometry of the Lie algebra of the quantum plane

We present a differential calculus on the extension of the quantum plane obtained by considering that the (bosonic) generator x is invertible and by working with polynomials in ln x instead of polynomials in x. We construct the quantum Lie algebra associated with this extension and obtain its Hopf algebra structure and its dual Hopf algebra.     

A REVIEW ON THERMAL AND RADIATION-INDUCED POLYMERIZATION OF N-TERT-BUTYLACRYLAMIDE AND ITS VARIOUS COMPLEXES IN THE LIQUID AND SOLID STATES

Abstract

The acrylamide family of monomers is a highly versatile group of chemical intermediates. The major use of these monomers is the preparation of polymers and copolymers having a highly polar functional group attached to the backbone.     

Preparation and characterisation of thiol functionalised p-tert-butylcalix[4]arene-embedded polymer inclusion membranes: performance and selectivity

ABSTRACT

Here in we report the syntheses of the thiol functionalised p-tert-butylcalix[4]arene from the reaction of p-tert-butylcalix[4]arene-dialkylbromide derivative with thiourea. The structure of the thiol functionalised p-tert-butylcalix[4]arene was determined by using ¹HNMR, ¹³CNMR and elemental analysis techniques. Furthermore, the thiol functionalised p-tert-butylcalix[4]arene, cellulose triacetate (CTA) and 2-nitrophenyl octyl ether (o-NPPE) in dichloromethane were used to make a new calixarene-embedded polymer inclusion membrane (Bu^t-C@PIM). The surface and structure morphology of Bu^t-C@PIM was detected using thermogravimetric analysis, elemental analysis techniques and scanning electron microscopy. The affinity (the percentage of metal ion transferred from the source solution) of a PIM towards a range of divalent cations was found to follow the order Pb²⁺ > Zn²⁺ > Ni²⁺ > Cu²⁺ > Cd²⁺ > Co²⁺. The results also indicated that the transport efficiency of Bu^t-C@PIM was repeatable and may be beneficial in the development of a simplistic and highly influential trace metal recovery method from aqueous solution.     

Synthesis,characterization, crystal structure and biological activity of the cobalt(IV) complex of 2,6-diacetylpyridine dioxime: [Co(dapdo)<Subscript>2</Subscript>]

The cobalt(IV) complex of 2,6-diacetylpyridine dioxime (dapdoH₂) was prepared and characterized by X-ray diffraction, elemental analysis and FT-IR. The titled complex was found to crystallize in the orthorhombic space group and was screened for antibacterial and antifungal activities by the disc diffusion and microtitter plate techniques using DMF as solvent. It has been found that the antimicrobial activity of the complex [Co(dapdo)₂] is slightly higher than the free ligand (dapdoH₂).     

Structural results on a batch acceptance problem for capacitated queues

The purpose of this paper is to investigate the structural properties of the optimal batch acceptance policy in a Markovian queueing system where different classes of customers arrive in batches and the buffer capacity is finite. We prove that the optimal policy can possess certain monotonicity properties under the assumptions of a single-server and constant batch sizes. Even though our proof cannot be extended to cases where either one of the assumptions is relaxed, we numerically observe that the optimal policy can still possess the same properties when only the single-server assumption is relaxed. Finally, we present counterexamples that show the non-monotone structure of the optimal policy when the batch sizes are not constant.     

Effect of type and concentration of surfactants on swelling behavior of poly[<Emphasis Type="Italic">N</Emphasis>-[3-(dimethylamino)propyl]methacrylamide-co- <Emphasis Type="Italic">N,N</Emphasis>-methylenebis(acrylamide)] hydrogels

A series of thermosensitive hydrogels were prepared from N-[3-(dimethylamino)propyl]methacrylamide (DMAPMA) monomer by using 11.6–17.8% (m/m) N,N-methylenebis(acrylamide) (MBAAm) as the crosslinker and comonomer in water. A kinetic study of the absorption determined the transport mechanism. The diffusion coefficients of these hydrogels were calculated for the Fickian mechanism. It was shown that the swelling behavior of the P(DMAPMA-co-MBAAm) hydrogels can be controlled by changing the amount of MBAAm. The swelling equilibrium of the P(DMAPMA-co-MBAAm) hydrogels was also investigated as a function of temperature in aqueous solutions of the anionic surfactant sodium dodecyl sulfate (SDS) and the cationic surfactant dodecyltrimethylammonium bromide (DTAB). In pure water, irrespective of the amount of MBAAm, the P(DMAPMA-co-MBAAm) hydrogels showed a discontinuous phase transition between 30 and 40 °C. However, the transition changed from discontinuous to continuous with the addition of surfactants, this is ascribed to the conversion of non-ionic P(DMAPMA-co-MBAAm) hydrogel into polyelectrolyte hydrogels due to binding of surfactants through the hydrophobic interaction. Additionally, the amount of free SDS and DTAB ions was measured at different temperatures by a conductometric method, it was found that the electric conductivity of the P(DMAPMA-co-MBAAm) – surfactant systems depended strongly on both the type and concentration of surfactant solutions.     

Temperature dependence of the current-voltage characteristics of the Al/Rhodamine-101/p-Si(1 0 0) contacts

The current-voltage (I-V) characteristics of Al/Rhodamine-101/p-Si/Al contacts have been measured at temperatures ranging from 280 to 400 K at 20 K intervals. A barrier height (BH) value of 0.817 eV for the Al/Rh101/p-Si/Al contact was obtained at the room temperature that is significantly larger than the value of 0.58 eV of the conventional Al/p-Si Schottky diode. While the barrier height Φ_b0 decreases the ideality factors (n) become larger with lowering temperature. The high values of n depending on the sample temperature may be ascribed to decrease of the exponentially increase rate in current due to space-charge injection into Rh101 thin film at higher voltage. Therefore, at all temperatures, it has been seen that the I-V characteristics show three different regions, the ohmic behavior at low voltages, and the space charge limited current with an exponential distribution of traps at high voltages.     

Transfer Hydrogenation of Ketones Catalyzed by 1-Alkylbenzimidazole Ruthenium(II) Complexes

Summary. Six [RuCl₂(1-alkylbenzimidazole)(p-cymene)] complexes have been prepared and the new compounds characterized by C, H, N analyses, ¹H NMR, and ¹³C NMR. The reduction of ketones to alcohols via transfer hydrogenation was achieved with catalytic amounts of the complexes in the presence of t-BuOK.     

Dynamic programming for stochastic target problems and geometric flows

Given a controlled stochastic process, the reachability set is the collection of all initial data from which the state process can be driven into a target set at a specified time. Differential properties of these sets are studied by the dynamic programming principle which is proved by the Jankov-von Neumann measurable selection theorem. This principle implies that the reachability sets satisfy a geometric partial differential equation, which is the analogue of the Hamilton-Jacobi-Bellman equation for this problem. By appropriately choosing the controlled process, this connection provides a stochastic representation for mean curvature type geometric flows. Another application is the super-replication problem in financial mathematics. Several applications in this direction are also discussed. Received October 24, 2000 / final version received July 24, 2001?Published online November 27, 2001     

Preparation and characterization of diphasic sol-gel derived unsupported mullite membranes

Diphasic gels prepared by mixing freshly prepared polymeric silica and polymeric boehmite sols through a modified Al-alkoxide route in mullite compositions led to the crystallization of mullite upon heat treatment at 775 °C. Mullite formation was observed at a 100 °C higher temperature when diphasic gels were formed by mixing aged polymeric sols containing about 2 nm in diameter boehmite species. These relatively low mullite formation temperatures were attributed to the nanoscale sizes of the polymeric species of the two amorphous phases present in the diphasic gels.