A re-statement of the Hohenberg–Kohn theorem and its extension to finite subspaces

Bearing in mind the insight into the Hohenberg–Kohn theorem for Coulomb systems provided recently by Kryachko (Int J Quantum Chem 103:818, 2005), we present a re-statement of this theorem through an elaboration on Lieb’s proof as well as an extension of this theorem to finite subspaces. Contribution to the Serafin Fraga Memorial Issue.     

Metal chelates of heterocyclic nitrogen-containing ketones,Part XXII. Spectroscopic studies on rhodium(III) complexes of phenyl-2-picolylketone-2-pyridyl hydrazone

Summary Mono, bis and tris complexes of rhodium(III) with phenyl-2-picolylketone-2-pyridyl hydrazone (PPKPyH) have been characterized. In every case, the imino-proton of PPKPyH shows marked acidity associated with the coordination to rhodium(III). Electronic spectra show that all complexes are octahedral. The B-values suggest a strong covalency in the metal-ligand -bond and the Dq-values indicate a medium-strong ligand field. The magnetic susceptibility indicates that PPKPyH forms low-spin complexes with rhodium(III).¹H n.m.r. spectra show that the tris(ligand) complexes arecis isomers. I.r. spectra show that the ligand is neutral or monobasic tridentate or bidentate. Far i.r. studies show that [Rh(PPKPyH)X₃] · 2 H₂O (X = Cl, Br or I) aremer isomers. The effect of pH variation on the rection products is also discussed.     

Pozzolanic properties of a residual FCC catalyst during the early stages of cement hydration

The catalyst used in fluidized catalytic cracking (FCC) units of refineries after several recovery cycles in regeneration units, reduces its activity and it is partially substituted by new catalyst in the process. As it has a high silicon and aluminum oxides content, the pozzolanic properties of a Brazilian FCC spent residual catalyst, used in different substitution degrees to cement, were evaluated by three thermal analysis techniques during the early stages of hydration of a type II Portland cement. NCDTA curves show in real time that the residual catalyst, accelerates the stages of cement hydration. TG and DSC curves of respective pastes after 24 h of hydration evidence the pozzolanic activity of the waste, respectively, by the lower water mass loss during the dehydroxylation of the residual calcium hydroxide and by the lower dehydroxylation endothermal effect. Within the analyzed period, the higher is the cement substitution degree, the higher is the pozzolanic activity of the residual catalyst.     

Sorption behavior of Co(II) on γ-Al<Subscript>2</Subscript>O<Subscript>3</Subscript> in the presence of humic acid

The fate and transport of toxic metal ions and radionuclides in the environment is generally controlled by sorption reactions. The extent of sorption of divalent metal cations is controlled by a number of factors including cosorbing or complexing. In this work, the effects of pH, humic acid HA/Co(II) addition orders, ionic strength, concentration of HA, and foreign cations on the Co(II) sorption on γ-Al₂O₃ in the presence of HA were investigated. The sorption isotherms of Co(II) on γ-Al₂O₃ in the absence and presence HA were also studied and described by using S-type sorption model. The experimental results showed that the Co(II) sorption is strongly dependent on the pH values, concentration of HA, but independent of HA/Co(II) addition orders, ionic strength, and foreign cations in the presence of HA under our experimental conditions. The results also indicated that HA enhanced the Co(II) sorption at low pH, but reduced the Co(II) sorption at high pH. It was hypothesized that the significantly positive influence of HA at low pH on the Co(II) sorption on γ-Al₂O₃ was attributed to strong surface binding of HA on γ-Al₂O₃ and subsequently the formation of ternary surface complexes such as ≡S-OOC-R-(COO⁻) _x Co^2−x . Chemi-complexation may be the main mechanism of the Co(II) sorption on γ-Al₂O₃ in the presence of HA.     

Differential pulse cathodic stripping adsorption voltammetric determination of trace amounts of lead using factorial design for optimization

A sensitive cathodic stripping voltammetric method is developed for determination of lead(II), with adsorptive collection of complexes with Pyrogallol red (PGR) on to a hanging mercury drop electrode. After accumulation of the complex at −0.80 V vs. Ag/AgCl reference electrode, the potential is scanned in a negative direction from −0.20 to −0.50 V with differential pulse method. Then the reduction peak current for the lead(II)-PGR complex is measured at −0.39 V. The influence of reagent and instrumental variables was completely studied by factorial design analysis. The optimum analytical conditions for the determination of lead(II) were established. Under optimum conditions, lead(II) determined in the range of 0.1-30.0 ng ml⁻¹ with a limit of detection of 0.06 ng ml⁻¹. The method is successfully applied to determination of lead(II) in water sample.     

Preconcentration and separation of copper(II), cadmium(II) and chromium(III) in a syringe filled with 3-aminopropyltriethoxysilane supported on silica gel

In this study, a syringe was filled with silica gel loaded with 3-aminopropyltriethoxysilane, for the separation and preconcentration of copper, cadmium and chromium prior to their determination by graphite furnace atomic absorption spectrometry (GFAAS) in seawater. For this purpose, a syringe was filled with 0.5 g of modified silica gel and the sample solution was drawn into the syringe and ejected back again. The analyte elements were quantitatively retained at pH 5. Then, the elements sorbed by the silica gel were eluted with 2.0 M of HCl and determined by GFAAS. At optimum conditions, the recovery of Cu, Cd and Cr were 96-98%. Detection limits (3delta) were 6.6, 7.5 and 6.0 micro g L(-1) for Cu, Cd and Cr, respectively. The elements could be concentrated by drawing and discharging several portions of sample successively but eluting only once. Cu, Cd and Cr added to a seawater sample were quantitatively recovered (>95%) in the range of the 95% confidence level. The method proposed in this paper was compared with a column technique. Optimum experimental conditions, reproducibility, precision and recoveries of both techniques are the same, but the syringe technique is much faster, easier and more practical than the column technique. It is a portable system and allows one to make the sorption process in the source of sample. In addition, the risk of contamination is less than in the column technique.     

Borate adsorption at Pt(111) in acidic medium

The adsorption/desorption process of borate was studied at Pt(111) in acidic solution by cyclic voltammetry. A so-called butterfly wave in the cyclic voltammogram of Pt(111) in HClO₄ shifted to negative direction upon the addition of boric acid with the disappearance of its sharp spikes. The shift in potential was found to be −57 mV with a tenfold increase of boric acid concentration. This illustrates that this anomalous wave is due to borate adsorption/desorption by a one-electron transfer process. The borate adsorption/desorption wave was observed to shift by −63 mV/pH. At pH>3, the anomalous wave splits forming two separate waves, depending on the pH and the scan rate. The appearance of two waves is assigned to the change in the adsorption mode of borate or the participation of OH in the adsorption process.     

Coordination of solvent molecules to VO(acac)<Subscript>2</Subscript> complexes in solution studied by hyperfine sublevel correlation spectroscopy and pulsed electron nuclear double resonance

Interactions and binding sites of the solvent molecules chloroform and ethanol to bis(acetylacetonate)oxovanadium(IV) (VO(acac)₂) complexes in (frozen) solutions have been investigated by pulsed electron nuclear double resonance, sum peak electron spin echo envelope modulation and hyperfine sublevel correlation spectroscopy. The experimental proton hyperfine coupling data of coordinating solvent molecules have been interpreted using quantum chemical calculations (density functional theory). Experimental and computed hyperfine couplings indicate that ethanol coordinates to vanadium in the equatorial plane of VO(acac)₂ and chloroform interacts via hydrogen bonding to oxygens of the acac ligands.     

HPLC and GC Methods for Determination of Lubricants and Their Evaluation in Analysis of Real Samples of Polyethylene

High performance liquid chromatography (HPLC) and gas chromatography (GC) are introduced for analysis of polymer lubricants (stearamide, oleamide and erucamide). In the HPLC method, a reverse phase octadecylsilane (ODS) column along with acetonitrile/methanol (60:40) as a mobile phase were used. Detection of analytes was performed by a UV detector at 202 nm. The analysis time was less than 8 min. In the GC method, polar capillary column and flame ionization detector (FID) were used for separations and detection, respectively. The analysis time by GC was longer than HPLC and was about 30 min. Limits of detection, linear range and repeatability of both methods are similar, but determination of oleamide in real samples by HPLC method is difficult due to complexity of the initial part of HPLC chromatogram in polyethylene samples. That problem is not observed in the GC method. Detection limits in both methods for all analytes are lower than 0.003% which are much lower than the amount of lubricants in commercial polymers (0.05–0.2%).     

Normal subgroup based power graph of finite groups

Ricerche di Matematica - Let G be a finite group and $$N \unlhd G$$ . The normal subgroup based power graph of G, $$\Gamma _N(G)$$ , is an undirected graph with vertex set $$(G{\setminus }N) \cup...