Non-existence of stationary two-black-hole configurations

We resume former discussions of the question, whether the spin–spin repulsion and the gravitational attraction of two aligned black holes can balance each other. To answer the question we formulate a boundary value problem for two separate (Killing-) horizons and apply the inverse (scattering) method to solve it. Making use of results of Manko, Ruiz and Sanabria-Gómez and a novel black hole criterion, we prove the non-existence of the equilibrium situation in question.     

Electronic charge distributions and correlations in highT c superconducting compounds

Calculations on negatively charged planar Cu _n O _m clusters are reported. Starting from a self-consistent field calculation within a good Gaussian-type orbital basis set, correlations are included by using the Local Ansatz. A charge analysis reveals that the Cu 3d occupation is 9.5, in close agreement with Local Spin Density calculations. The electrons in the formal ((CuO₂)^2–) _n entities are delocalized between Cu and O sites and strongly correlated. Our findings do not agree with the assumption of localized Cu²⁺ spins which lead to thet-J model. Spin correlations indicate strong short-range antiferromagnetic order even when additional electrons are removed. For them, there is no difference between O and Cu sites.     

Consistent aromaticity evaluations of methylenecyclopropene analogues

Quantitative evaluations of the aromaticity (antiaromaticity) of neutral exocyclic substituted cyclopropenes (HC)(2)C=X (X = BH to InH (group 13), CH(2) to SnH(2) (group 14), NH to SbH (group 15), O to Te (group 16)) by their computed extra cyclic resonance energies (ECRE, via the block-localized wave function method) and by their aromatic stabilization energies (ASEs, via energy decomposition analyses) correlate satisfactorily (R(2) = 0.974). Electronegative X-based substituents increase the aromaticity of the cyclopropene rings, whereas electropositive substituents have the opposite effect. For example, (HC)(2)C=O is the most aromatic (ECRE = 10.3 kcal/mol), and (HC)(2)C=InH is the most antiaromatic (ECRE = -15.0 kcal/mol). The most refined dissected nucleus-independent chemical shift magnetic aromaticity index, NICS(0)(πzz), also agrees with both energetic indexes (R(2) = 0.968, for ECRE; R(2) = 0.974, for ASE), as do anisotropy of the induced current density plots.     

Bioactive Betalain Extracts from Cactus Pear Fruit Pulp,Beetroot Tubers,and Amaranth Leaves

Natural food items and the additional benefits they provide have received considerable attention in recent years. Betalains are nutritious pigments which have valuable biological properties, e.g., antioxidant and free radical scavenging activity. In this study, aqueous betalain extracts were obtained from different coloured cactus pears (purple, red/pink, and orange), amaranth, and beetroot, with and without the addition of ascorbic acid, microwave-heated, and freeze-dried and subsequently analysed by thin layer chromatography (TLC). Beetroot samples without the addition of ascorbic acid (AA) had lower phenols, flavonoids, and ascorbic acid content than beetroot samples extracted with the addition of AA. Amaranth had significantly higher contents of antioxidants than all the other plants. Results for phenolic compounds showed that there were no significant differences between cactus pear cultivars, however, significant differences were seen between the two beetroot samples (microwave-heated with and without AA) as well as amaranth. For flavonoid compounds, amaranth had significantly higher values than all other samples. The lowest flavonoid content was found in beetroot without AA (0.49 mgCE/g). For ascorbic acid, significant differences were noticed between amaranth (71.71 mg/100 g) and samples from cactus pear and beetroot. TLC results showed that purple and red cactus pear samples had the most vivid colours, a reflection of the high betacyanin and betaxanthin contents in the cultivars. Moreover, extracts from cactus pear, beetroot, and amaranth were classified according to a decision tree which was designed by the Code of Federal Regulations/Food Additives Regulation of the EU. The classification of betalain pigment extracts as colouring foods was achieved through enrichment factor calculations and the colourant decision tree. The results showed that the betalain pigment extraction method used is inexpensive, time-saving, energy-saving, non-toxic, and chemical solvent free and yields high concentrations of betalains.