A new technique to compute polygonal schema for 2-manifolds with application to null-homotopy detection

We provide a new technique for deriving optimal-sized polygonal schema for triangulated compact 2-manifolds without boundary inO(n) time, wheren is the size of the given triangulationT. We first derive a polygonal schemaP embedded inT using Seifert-Van Kampen's theorem. A reduced polygonal schemaQ of optimal size is computed fromP, where a surjective map from the vertices ofP is retained to the vertices ofQ. This helps detecting null-homotopic (contractible to a point) cycles. Given a cycle of lengthk, we determine if it is null-homotopic inO(n+k logg) time and in θ(n+k) space, whereg is the genus of the given 2-manifold. The actual contraction for a null-homotopic cycle can be computed in θ(nk) time and space. This is a considerable improvement over the previous best-known algorithm for this problem.     

Weitere Untersuchungen über Zinkoxydhydrat

Zusammenfassung Die Bildung l?slicher Zinkate wurde durch Dialysieren von L?sungen aus Zinkhydroxyd in Natronlauge untersucht. In einem solchen System existiert ein Gleichgewicht zwischen der Natriumzinkat- und der kolloidalen Zinkhydroxydkonzentration. Die Menge und Stabilit?t des ersten w?chst mit der Alkalikonzentration. Mit fortschreitender Dialyse verschiebt sich das Gleichgewicht. Schlie?lich entsteht auf Grund der Hydrolyse der Zinkat-Ionen eine kolloide L?sung.

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Summary The formation of soluble zincates has been investigated by dialysing a solution of zinc hydroxide in sodium hydroxide solution. It has been concluded that the system contains an equilibrium mixture of sodium zincate and colloidal zinc hydroxide and the proportion and stability of the former increase with the increase in the concentration of alkali. The equilibrium shifts with progressive dialysis and ultimately the system passes to a colloidal solution as a result of the hydrolysis of zincate ions.

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übersetzt von Dr. K. J?ckel, Marburg.

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Die Experimente für diese Arbeit wurden in den Chemical Laboratories of Meerut College ausgeführt. Die Verfasser danken dem Leiter dieses Institutes, Herrn Prof. Dr. S. S. Joshi, für seine Unterstützung.     

Interplay between cation-pi, anion-pi and pi-pi interactions.

The interplay between three important noncovalent interactions involving aromatic rings is studied by means of high level ab initio calculations. They demonstrate that very strong synergic effects are present in complexes where either cation–π or anion–π and π‐‐π interactions coexist. These strong synergic effects have been studied using the “atoms in molecules” theory and the physical nature of the interactions investigated by means of the molecular interaction potential with polarization (MIPp).     

Beta-octafluorocorroles

The one-pot corrole synthesis first reported by the Gross and Paolesse groups appears to have evolved into a remarkably general and predictable self-assembly based synthetic reaction. Gross's solvent-free procedure (refs 8 and 9) has proven particularly effective in our hands and, in fact, more general than originally claimed. In earlier work (ref 17), we showed that the reaction works for a variety of aromatic aldehyde starting materials and was not limited to relatively electron-deficient aldehydes, as reported by Gross and co-workers. Here, we show that the pyrrole component is also variable in that 3,4-difluoropyrrole undergoes oxidative condensation with four different p-X-substituted benzaldehydes to yield the corresponding beta-octafluoro-meso-tris(para-X-phenyl)corroles (X = CF3, H, CH3, and OCH3). Further, we have prepared the Cu and FeCl derivatives of the beta-octafluorocorrole ligands. The XPS nitrogen 1s ionization potentials of these fluorinated ligands are some 0.7 eV higher than those of the corresponding beta-unfluorinated ligands. The oxidation half-wave potentials of the Cu and FeCl complexes of the fluorinated corroles are also positively shifted by 300-400 mV relative to their beta-unsubstituted analogues, demonstrating the strongly electron-deficient character of the fluorinated ligands. 1H NMR spectroscopy suggests that like their beta-unfluorinated counterparts, the new beta-octafluorinated triarylcorroles act as substantially noninnocent ligands, i.e., exhibit corrole pi-cation radical character, in the FeCl complexes. Quantitatively, however, NMR spectroscopy and DFT calculations indicate that the beta-octafluorinated corroles are somewhat less noninnocent (i.e., carry less radical character) than their beta-unfluorinated counterparts in the FeCl complexes. Temperature-dependent 19F NMR spectroscopy suggests that the Cu octafluorocorroles have a thermally accessible paramagnetic excited state, which we assign as a Cu(II) corrole pi-cation radical. We have previously reported that the electronic absorption spectra, particularly the Soret absorption maxima, of high-valent transition metal triarylcorroles are very sensitive to the nature of the substituents in the meso positions. In contrast, the Soret absorption maxima of free-base triarylcorroles are not particularly sensitive to the nature of the meso substituents. This scenario also holds for the fluorinated corroles described here. Thus, although the four free-base fluorinated triarylcorroles exhibit practically identical Soret absorption maxima, the Soret bands of the Cu derivatives of the same corroles red-shift by approximately 35 nm on going from the p-CF3 to the p-OCH3 derivative.     

Synthesis of Some Octahedral Nickel(II) Complexes of One Isomer of Isomeric Me8[14]anes: X-ray Structure of Diisothiocyanato(3,10-C-meso-3,5,7,7,10,12,14,14-octamethyl-1,4,8,11-tetraazacyclotetradecane, LC)nickel(II), [NiLC(NCS)2]

One isomer, L_C of the isomeric Me₈[14]anes, L_A, L_B and L_C; on reaction with Ni(NCS)₂ produces a six coordinate octahedral diisothiocyanato complex, [NiL_C(NCS)₂]. This complex undergoes axial substitution reactions with the small ligands to yield corresponding monosubstituted derivatives having general formula [NiL_C(NCS)X] whereas X = Cl, Br, I, NO₂ or NO₃. The complexes have been characterized on the basis of analytical, spectroscopic, magnetic and conductance data. The structure of [NiL_C(NCS)₂] (triclinic, space group P?1, α = 8.0421(17) Å, β = 8.9085(18) Å, χ = 9.687(2) Å, α = 67.561(3) Å, β = 82,896(4) Å, ζ = 598.7(2) Å³, Z = 2, Dc = 1.352 mg/m³, μ(Mo Kα) = 1.003 mm^?1) was confirmed by X-ray crystallography.     

Chromatographic study of anionic complexes

Summary In this paper the variation of diffusion, through filter paper strips by the ascending method, of citrate complexes of Cu²⁺, Ni²⁺, Co²⁺ and Fe³⁺ has been studied using 50%, 55% and 60% ethanol as solvents. The R_f value is found to be less with higher concentrations of ethanol used. It has been noted that with 50% ethanol the R_f value increases with the addition of citrate and finally tends to become constant with high concentrations of citrate ions. In 55% ethanol the R_f value becomes constant at a later stage. In 60% ethanol it is noted that the R_f value does not change with small additions of citrate, but on increasing its concentration the R_f value begins to diminish.Part II see Z. analyt. Chem. 165, 81 (1959).     

Chromatographic study of anionic complexes

Summary In this paper the variation of diffusion, through a filter paper strip by the ascending method, of cuprioxalate complex has been studied. Various mixtures of Cu+^2üC₂O ₄ ^2– ions have been investigated. It has been noted that till there is a precipitation, the R_f values tend to decrease and finally reach nearly to zero, when the oxalate precipitates completely. With redissolution of the precipitate to form the complex anion, R_f values increase again to a maximum and then have a slight tendency to diminish. No tailing occurs in the chromatograms in cases where the copper has passed into the anion.