Burnside’s theorem in the setting of general fields

Archiv der Mathematik - We study the mean of the values of the zeta-function on a generalized arithmetic progression on the critical line.     

An evaluation scheme for nanotechnology policies

Dozens of countries are executing national nanotechnology plans. No rigorous evaluation scheme for these plans exists, although stakeholders—especially policy makers, top-level agencies and councils, as well as the society at large—are eager to learn the outcome of these policies. In this article, we recommend an evaluation scheme for national nanotechnology policies that would be used to review the whole or any component part of a national nanotechnology plan. In this scheme, a component at any level of aggregation is evaluated. The component may be part of the plan’s overarching policy goal, which for most countries is to create wealth and improve the quality of life of their nation with nanotechnology. Alternatively, the component may be a programme or an activity related to a programme. The evaluation could be executed at different times in the policy’s life cycle, i.e., before the policy is formulated, during its execution or after its completion. The three criteria for policy evaluation are appropriateness, efficiency and effectiveness. The evaluator should select the appropriate qualitative or quantitative methods to evaluate the various components of national nanotechnology plans.     

On injective or dense-range operators leaving a given chain of subspaces invariant

In this paper we prove the existence of dense-range or one-to-one compact operators on a separable Banach space leaving a given finite chain of subspaces invariant. We use this result to prove that a semigroup of bounded operators is reducible if and only if there exists an appropriate one-to-one compact operator such that the collection of compact operators is reducible.

     

Effect of gold nanoparticle as a novel nanocatalyst on luminol-hydrazine chemiluminescence system and its analytical application

In this work the catalytic role of unsupported gold nanoparticles on the luminol–hydrazine reaction is investigated. Gold nanoparticles catalyze the reaction of hydrazine and dissolved oxygen to generate hydrogen peroxide and also catalyze the oxidation of luminol by the produced hydrogen peroxide. The result is an intense chemiluminescence (CL) due to the excited 3-aminophthalate anion. In the absence of gold nanoparticles no detectable CL was observed by the reaction of luminol and hydrazine unless an external oxidant is present in the system. The size effect of gold nanoparticles on the CL intensity was investigated. The most intensive CL signals were obtained with 15-nm gold nanoparticles. UV–vis spectra and transmission electron microscopy studies were used to investigate the CL mechanism. The luminol and hydroxide ion concentration, gold nanoparticles size and flow rate were optimized. The proposed method was successfully applied to the determination of hydrazine in boiler feed water samples. Between 0.1 and 30 μM of hydrazine could be determined with a detection limit of 30 nM.     

Sodium ascorbate as an expedient catalyst for green synthesis of polysubstituted 5-aminopyrazole-4-carbonitriles and 6-amino-1,4-dihydropyrano[2,3-c]pyrazole-5-carbonitriles

Research on Chemical Intermediates - Sodium ascorbate (SA) was used as a safe catalyst for the synthesis of 5-aminopyrazole-4-carbonitriles from the one-pot three-component cyclocondensation (3-CC)...     

A new force field for the adsorption of H2, O2, N2, CO,H2O,and H2S gases on alkali doped carbon nanotubes

The main goal of this work is the generation of a new force field data set to the interaction of several gases such as H₂, O₂, N₂, CO, H₂O, and H₂S with alkali cation-doped carbon nanotubes (CNTs) using ab initio calculations at the MP2(full)/6-311++G(d,p) level of theory. Different alkali cations including Li⁺, Na⁺_, K⁺ and Cs⁺ were used to dope in the CNT. The calculated potential energy curve for the interaction of each gas molecule with each alkali cation-doped CNTs was fitted to an analytical potential function to obtain the parameters of the potential function. A modified Morse potential function was selected for the fitting in which the electrostatic interactions has been accounted by adding the β/r term to the Morse potential. The accuracy of the calculated force field was checked via Grand Canonical Monte Carlo (GCMC) simulation of the H₂ adsorption on Li-doped graphite and Li-doped CNT. The results of these simulations were compared with the experimental measurements and the closeness of the simulation results with the experimental data indicated the accuracy of the proposed force field. The main merit of this work is the derivation of a specific force field for interaction of each of six gases with four alkali cation-doped CNT, which can be used in molecular simulation of these 24 of systems. The simulation results showed the increase of the H₂ adsorption capacity of nanotube and graphite up to 50% and 10%, respectively, due to the insertion of Li ions.     

On simultaneous triangularization of collections of compact operators

In this paper we consider collections of compact (resp. C_p class) operators on arbitrary Banach (resp. Hilbert) spaces. For a subring R of reals, it is proved that an R-algebra of compact operators with spectra in R on an arbitrary Banach space is triangularizable if and only if every member of the algebra is triangularizable. It is proved that every triangularizability result on certain collections, e.g., semigroups, of compact operators on a complex Banach (resp. Hilbert) space gives rise to its counterpart on a real Banach (resp. Hilbert) space. We use our main results to present new proofs as well as extensions of certain classical theorems (e.g., those due to Kolchin, McCoy, and others) on arbitrary Banach (resp. Hilbert) spaces.     

A potentiometeric study of protonation and complex formation of xylenol orange with alkaline earth and aluminum ions

Xylenol orange (XO) is one of the complexometric indicators, that can bind to metal cations at both their amino and acidic groups. In this study the protonation constants and distribution diagrams of XO were studied pH-metrically, and the corresponding six protonation constants were calculated. The complex formation between XO (L) and alkaline earth ions (M) was investigated and the formation constants of the resulting complexes ML, MHL, M(2)L and M(2)HL were determined. The stabilities of both ML and M(2)L complexes were found to vary in the order Mg(2+)> Ca(2+)> Sr(2+)> Ba(2+). Studying the complex formation between Al(3+) ion (M) and XO (L), it was observed that four complexed species with stoichiometries ML, ML(2), MHL and MH(2)L could be formed in solution. It was also found that the Al L(2) complex can act as a chelating agent for further complexation with two cations other than Al(3+) ion (i.e. Ba, L, Al, L, Ba, Mg, L, Al, L, Mg, and Mg, L, Al, L, Ba). The formation constants of the resulting mixed complexes were determined and their distribution diagrams were investigated.     

The effect of curvature of Li-doped polycyclic hydrocarbon on its interaction energy with H<Subscript>2</Subscript> and H<Subscript>2</Subscript>O: DF-SAPT (DFT) calculation

In this work, the interaction of three Li⁺-doped polycyclic hydrocarbons (Li⁺-DPH) with H₂ and H₂O was calculated to investigate the effect of curvature of substrate on the interaction energy (E_int). For this purpose, the E_int and its decomposed energy components (electrostatic (E_elec), exchange (E_exch), induction (E_ind), and dispersion energy (E_disp)) were calculated using DF-SAPT (DFT) methodology for the selected systems (Li⁺-(3,3) carbon nanotube (Li⁺-CNT33), Li⁺-(6,6) carbon nanotube (Li⁺-CNT66), and Li⁺-graphene). According to the results, E_int does not change significantly with curvature for the interaction between both H₂ and H₂O gases and the selected Li⁺-DPH. Since the variation of the E_int with the curvature of Li⁺-DPH is not significant, the selection of a planar Li⁺-DPH is a trustworthy model to develop a general force field for describing the interaction between a Li⁺-DPH and adsorbed gases. The results reveal that, in the case of the H₂, the components E_elect, E_exch, E_ind, and E_disp have shown a decreasing trend with Li⁺-DPH’s curvature decrement. However, for the H₂O, E_elect, E_exch, and E_ind decrease from the Li⁺-CNT33 to the Li⁺-CNT66 while they increase from the Li⁺-CNT66 to the Li⁺-graphene. In this case, the E_disp increases with a decrease of the curvature of Li⁺-DPH. Finally, it can be seen that although the variation of the E_int with the curvature of Li⁺-DPH is not significant, the variation trend of the interaction energy components and the amount of variation depend on the gas molecule and in some cases are not negligible.