Vacuum spacetimes of embedding class two

Doubt is cast on the much quoted results of Yakupov that the torsion vector in embedding class two vacuum space-times is necessarily a gradient vector and that class 2 vacua of Petrov type III do not exist. The rst result is equivalent to the fact that the two second fundamental forms associated with the embedding necessarily commute and has been assumed in most later investigations of class 2 vacuum space-times. Yakupov stated the result without proof, but hinted that it followed purely algebraically from his identity: Rijkl Ckl = 0 where Cij is the commutator of the two second fundamental forms of the embedding.From Yakupov's identity, it is shown that the only class two vacua with non-zero commutator Cij must necessarily be of Petrov type III or N. Several examples are presented of non-commuting second fundamental forms that satisfy Yakupovs identity and the vacuum condition following from the Gauss equation; both Petrov type N and type III examples occur. Thus it appears unlikely that his results could follow purely algebraically. The results obtained so far do not constitute denite counter-examples to Yakupov's results as the non-commuting examples could turn out to be incompatible with the Codazzi and Ricci embedding equations. This question is currently being investigated.

New dimeric supramolecular structure of mixed (phthalocyaninato)(porphyrinato)-europium(III) sandwiches : preparation and spectroscopic characteristics

The mixed double-decker Eu\[Pc(15C5)4](TPP) (1) was obtained by base-catalysed tetramerisation of 4,5-dicyanobenzo-15-crown-5 using the half-sandwich complex Eu(TPP)(acac) (acac = acetylacetonate), generated in situ, as the template. For comparative studies, the mixed triple-decker complexes Eu2\[Pc(15C5)4](TPP)2 (2) and Eu2\[Pc(15C5)4]2(TPP) (3) were also synthesised by the raise-by-one-story method. These mixed ring sandwich complexes were characterised by various spectroscopic methods. Up to four one-electron oxidations and two one-electron reductions were revealed by cyclic voltammetry (CV) and differential pulse voltammetry (DPV). As shown by electronic absorption and infrared spectroscopy, supramolecular dimers (SM1 and SM3) were formed from the corresponding double-decker 1 and triple-decker 3 in the presence of potassium ions in MeOH/CHCl3.

Electrochemistry of Heteroleptic Tris(phthalocyaninato) Rare Earth(III) Complexes

The electrochemical characteristics of a series of heteroleptic tris(phthalocyaninato) complexes with identical rare earths or mixed rare earths (Pc)M(OOPc)M(OOPc) [M = Eu...Lu, Y; H2Pc = unsubstituted phthalocyanine, H2(OOPc) = 3,4,12,13,21,22,30,31-octakis(octyloxy)phthalocyanine] and (Pc)Eu(OOPc)Er(OOPc) have been recorded and studied comparatively by cyclic voltammetry (CV) and differential pulse voltammetry (DPV) in CH2Cl2 containing 0.1 M tetrabutylammonium perchlorate (TBAP). Up to five quasi-reversible one-electron oxidations and four one-electron reductions have been revealed. The half-wave potentials of the first, second and fifth oxidations depend on the size of the metal center, but the fifth changes in the opposite direction to that of the first two. Moreover, the difference in redox potentials of the first oxidation and first reduction for (Pc)M(OOPc)M(OOPc), 0.85−0.98 V, also decreases linearly along with decreasing rare earth ion radius, clearly showing the rare earth ion size effect and indicating enhanced π−π interactions in the triple-deckers connected by smaller lanthanides. This order follows the red-shift seen in the lowest energy band of triple-decker compounds. The electronic differences between the lanthanides and yttrium are more apparent for triple-decker sandwich complexes than for the analogous double-deckers. By comparing triple-decker, double-decker and mononuclear [ZnII] complexes containing the OOPc ligand, the HOMO−LUMO gap has been shown to contract approximately linearly with the number of stacked phthalocyanine ligands.

The ageing of alumina hydrolysates synthesized from sec-butoxyaluminium(III)

A combination of X-ray diffraction, thermal analysis and Raman spectroscopy was employed to characterise the ageing of alumina hydrolysates synthesised from the hydrolysis of anhydrous tri-sec-butoxyaluminium(III). X-Ray diffraction showed that the alumino-oxy(hydroxy) hydrolysates were pseudoboehmite. For boehmite the lamellar spacings are in the b direction and multiple d(020) peaks are observed for the un-aged hydrolysate. After 4 h of ageing, a single d(020) peak is observed at 6.53 Å. Thermal analysis showed five endotherms at 70, 140, 238, 351 and 445°C. These endotherms are attributed to the dehydration and dehydroxylation of the boehmite-like hydrolysate. Raman spectroscopy shows the presence of bands for the washed hydrolysates at 333, 355, 414, 455, 475, 495, 530 and 675 cm–1. These bands are attributed to pseudoboehmite. Ageing of the hydrolysates results in an increase in the crystallite size of the pseudoboehmite.

Comparative Electrochemical Study of Unsubstituted and Substituted Bis(phthalocyaninato) Rare Earth(III) Complexes

The electrochemistry of homoleptic substituted phthalocyaninato rare earth double-decker complexes M(TBPc)2 and M(OOPc)2 [M = Y, La...Lu except Pm; H2TBPc = 3(4),12(13),21(22),30(31)-tetra-tert-butylphthalocyanine, H2OOPc = 3,4,12,13,21,22,30,31-octakis(octyloxy)phthalocyanine] has been comparatively studied by cyclic voltammetry (CV) and differential pulse voltammetry (DPV) in CH2Cl2 containing 0.1 M tetra-n-butylammonium perchlorate (TBAP). Two quasi-reversible one-electron oxidations and three or four quasi-reversible one-electron reductions have been revealed for these neutral double-deckers of two series of substituted complexes, respectively. For comparison, unsubstituted bis(phthalocyaninato) rare earth analogues M(Pc)2 (M = Y, La...Lu except Pm; H2Pc = phthalocyanine) have also been electrochemically investigated. Two quasi-reversible one-electron oxidations and up to five quasi-reversible one-electron reductions have been revealed for these neutral double-decker compounds. The three bis(phthalocyaninato)cerium compounds display one cerium-centered redox wave between the first ligand-based oxidation and reduction. The half-wave potentials of the first and second oxidations and first reduction for double-deckers of the tervalent rare earths depend on the size of the metal center. The difference between the redox potentials of the second and third reductions for MIII(Pc)2, which represents the potential difference between the first oxidation and first reduction of [MIII(Pc)2]−, lies in the range 1.08−1.37 V and also gradually diminishes along with the lanthanide contraction, indicating enhanced π−π interactions in the double-deckers connected by the smaller, lanthanides. This corresponds well with the red-shift of the lowest energy band observed in the electronic absorption spectra of reduced double-decker [MIII(Pc′)2]− (Pc′ = Pc, TBPc, OOPc).

Vibrational spectroscopy of phthalocyanine and naphthalocyanine in sandwich-type (na)phthalocyaninato and porphyrinato rare earth complexes: Part 14. The infrared and Raman characteristics of phthalocyanine in “pinwheel-like” homoleptic bis[1,8,15,22-tetrakis(3-pentyloxy)phthalocyaninato] rare earth(III) double-decker complexes

The infrared (IR) spectroscopic data and Raman spectroscopic properties for a series of 13 “pinwheel-like” homoleptic bis(phthalocyaninato) rare earth complexes M[Pc(α-OC5H11)4]2 [M = Y and Pr–Lu except Pm; H2Pc(α-OC5H11)4 = 1,8,15,22-tetrakis(3-pentyloxy)phthalocyanine] have been collected and comparatively studied. Both the IR and Raman spectra for M[Pc(α-OC5H11)4]2 are more complicated than those of homoleptic bis(phthalocyaninato) rare earth analogues, namely M(Pc)2 and M[Pc(OC8H17)8]2, but resemble (for IR) or are a bit more complicated (for Raman) than those of heteroleptic counterparts M(Pc)[Pc(α-OC5H11)4], revealing the decreased molecular symmetry of these double-decker compounds, namely S8. Except for the obvious splitting of the isoindole breathing band at 1110–1123 cm−1, the IR spectra of M[Pc(α-OC5H11)4]2 are quite similar to those of corresponding M(Pc)[Pc(α-OC5H11)4] and therefore are similarly assigned. With laser excitation at 633 nm, Raman bands derived from isoindole ring and aza stretchings in the range of 1300–1600 cm−1 are selectively intensified. The IR spectra reveal that the frequencies of pyrrole stretching and pyrrole stretching coupled with the symmetrical CH bending of –CH3 groups are sensitive to the rare earth ionic size, while the Raman technique shows that the bands due to the isoindole stretchings and the coupled pyrrole and aza stretchings are similarly affected. Nevertheless, the phthalocyanine monoanion radical Pc′− IR marker band of bis(phthalocyaninato) complexes involving the same rare earth ion is found to shift to lower energy in the order M(Pc)2 > M(Pc)[Pc(α-OC5H11)4] > M[Pc(α-OC5H11)4]2, revealing the weakened π–π interaction between the two phthalocyanine rings in the same order.

Tris[4,4,4-trifluoro-1-(2-thienyl)butane-1,3-dionato]aluminium(III)-tris[4,4,4-trifluoro-1-(2-thienyl)butane-1,3-dionato]iron(III) (3/1)

In the title compound, [Al(C8H4F3O2S)3]3[Fe(C8H4F3O2S)3], the metal centre is statistically occupied by AlIII and FeIII cations in a 3:1 ratio. The metal centre is within an octahedral O6 donor set defined by three chelating substituted acetoacetonate anions. The ligands are arranged around the periphery of the molecule with a mer geometry of the S atoms.

To WPPSI or to Binet, that is the question : a comparison of the WPPSI-III and SB5 with typically-developing preschoolers

This study compared two popular measures of cognitive ability for preschool children. The Wechsler Preschool and Primary Scale of Intelligence – Third Edition (WPPSI-III) and the Stanford-Binet Intelligence Scale – Fifth Edition (SB5) were administered in a counterbalanced order to 36 typically developing 4-year-old children. There were significant correlations among all WPPSI-III and SB5 composite scores but a small number of children had notable differences between their scores on the two measures. Children tended to prefer the SB5 over the WPPSI-III. Implications for practitioners who assess preschool-aged children are discussed.

Evaluation of piezoelectric PVDF polymers for use in space environments. III. Comparison of the effects of vacuum UV and gamma radiation

Films of piezoelectric PVDF and P(VDF-TrFE) were exposed to vacuum UV (115-300 nm VUV) and -radiation to investigate how these two forms of radiation affect the chemical, morphological, and piezoelectric properties of the polymers. The extent of crosslinking was almost identical in both polymers after -irradiation, but surprisingly, was significantly higher for the TrFE copolymer after VUV-irradiation. Changes in the melting behavior were also more significant in the TrFE copolymer after VUV-irradiation due to both surface and bulk crosslinking, compared with only surface crosslinking for the PVDF films. The piezoelectric properties (measured using d33 piezoelectric coefficients and D-E hysteresis loops) were unchanged in the PVDF homopolymer, while the TrFE copolymer exhibited more narrow D-E loops after exposure to either - or VUV-radiation. The more severe damage to the TrFE copolymer in comparison with the PVDF homopolymer after VUV-irradiation is explained by different energy deposition characteristics. The short wavelength, highly energetic photons are undoubtedly absorbed in the surface layers of both polymers, and we propose that while the longer wavelength components of the VUV-radiation are absorbed by the bulk of the TrFE copolymer causing crosslinking, they are transmitted harmlessly in the PVDF homopolymer.

Application of autologous periosteal cells for the regeneration of class III furcation defects in Beagle dogs

The aim of this study was to evaluate the healing of class III furcation defects following transplantation of autogenous periosteal cells combined with b-tricalcium phosphate (b-TCP). Periosteal cells obtained from Beagle dogs’ periosteum explant cultures, were inoculated onto the surface of b-TCP. Class III furcation defects were created in the mandibular premolars. Three experimental groups were used to test the defects’ healing: group A, b-TCP seeded with periosteal cells were transplanted into the defects; group B, b-TCP alone was used for defect filling; and group C, the defect was without filling materials. Twelve weeks post surgery, the tissue samples were collected for histology, immunohistology and X-ray examination. It was found that both the length of newly formed periodontal ligament and the area of newly formed alveolar bone in group A, were significantly increased compared with both group B and C. Furthermore, both the proportion of newly formed periodontal ligament and newly formed alveolar bone in group A were much higher than those of group B and C. The quantity of cementum and its percentage in the defects (group A) were also significantly higher than those of group C. These results indicate that autogenous periosteal cells combined with b-TCP application can improve periodontal tissue regeneration in class III furcation defects.

Assessing cognitive development in early childhood : a comparison of the Bayley-III and the Stanford-Binet fifth edition

The Bayley Scales of Infant Development, Third Edition (Bayley-III) and Stanford-Binet Intelligence Scale, Fifth Edition (SB5) were administered in a sample of 26 typically developing children (12 males and 14 females) aged 24 – 42 months. Children completed the assessments in two separate sessions, counterbalanced for order of administration. Scores on the two instruments were not significantly related, with the exception of the SB5 Knowledge score, which was moderately correlated with the Language score on the Bayley-III (r = .41, p = 0.04). Despite no other significant correlations, for 22 of the 26 children, scores were very consistent across the two instruments. Implications for test selection are discussed.

Thermal decomposition of hydrotalcite with hexacyanoferrite(II) and hexacyanoferrate(III) anions in the interlayer : a controlled rate thermal analysis study

The mechanism for the decomposition of hydrotalcite remains unsolved. Controlled rate thermal analysis enables this decomposition pathway to be explored. The thermal decomposition of hydrotalcites with hexacyanoferrite(II) and hexacyanoferrate(III) in the interlayer has been studied using controlled rate thermal analysis technology. X-ray diffraction shows the hydrotalcites studied have a d(003) spacing of 11.1 and 10.9 Å which compares with a d-spacing of 7.9 and 7.98 Å for the hydrotalcite with carbonate or sulphate in the interlayer. Calculations based upon CRTA measurements show that 7 moles of water is lost, proving the formula of hexacyanoferrite(II) intercalated hydrotalcite is Mg6Al2(OH)16[Fe(CN)6]0.5 .7 H2O and for the hexacyanoferrate(III) intercalated hydrotalcite is Mg6Al2(OH)16[Fe(CN)6]0.66 * 9 H2O. Dehydroxylation combined with CN unit loss occurs in three steps between a) 310 and 367°C b) 367 and 390°C and c) between 390 and 428°C for both the hexacyanoferrite(II) and hexacyanoferrate(III) intercalated hydrotalcite.