A computer-algebraic approach to the study of the symmetry properties of molecules and clusters

This thesis work is dedicated to use the computer-algebraic approach for dealing with the group symmetries and studying the symmetry properties of molecules and clusters. The Maple package Bethe, created to extract and manipulate the group-theoretical data and to simplify some of the symmetry applications, is introduced. First of all the advantages of using Bethe to generate the group theoretical data are demonstrated. In the current version, the data of 72 frequently applied point groups can be used, together with the data for all of the corresponding double groups. The emphasize of this work is placed to the applications of this package in physics of molecules and clusters. Apart from the analysis of the spectral activity of molecules with point-group symmetry, it is demonstrated how Bethe can be used to understand the field splitting in crystals or to construct the corresponding wave functions. Several examples are worked out to display (some of) the present features of the Bethe program. While we cannot show all the details explicitly, these examples certainly demonstrate the great potential in applying computer algebraic techniques to study the symmetry properties of molecules and clusters. A special attention is placed in this thesis work on the flexibility of the Bethe package, which makes it possible to implement another applications of symmetry. This implementation is very reasonable, because some of the most complicated steps of the possible future applications are already realized within the Bethe. For instance, the vibrational coordinates in terms of the internal displacement vectors for the Wilson's method and the same coordinates in terms of cartesian displacement vectors as well as the Clebsch-Gordan coefficients for the Jahn-Teller problem are generated in the present version of the program. For the Jahn-Teller problem, moreover, use of the computer-algebraic tool seems to be even inevitable, because this problem demands an analytical access to the adiabatic potential and, therefore, can not be realized by the numerical algorithm. However, the ability of the Bethe package is not exhausted by applications, mentioned in this thesis work. There are various directions in which the Bethe program could be developed in the future. Apart from (i) studying of the magnetic properties of materials and (ii) optical transitions, interest can be pointed out for (iii) the vibronic spectroscopy, and many others. Implementation of these applications into the package can make Bethe a much more powerful tool.

Systematics and evolution of the genus Deuterocohnia Mez (Bromeliaceae)

The present study investigates the systematics and evolution of the Neotropical genus Deuterocohnia Mez (Bromeliaceae). It provides a comprehensive taxonomic revision as well as phylogenetic analyses based on chloroplast and nuclear DNA sequences and presents a hypothesis on the evolution of the genus. A broad morphological, anatomical, biogeographical and ecological overview of the genus is given in the first part of the study. For morphological character assessment more than 700 herbarium specimens from 39 herbaria as well as living plant material in the field and in the living collections of botanical gardens were carefully examined. The arid habitats, in which the species of Deuterocohnia grow, are reflected by the morphological and anatomical characters of the species. Important characters for species delimitation were identified, like the length of the inflorescence, the branching order, the density of flowers on partial inflorescences, the relation of the length of the primary bracts to that of the partial inflorescence, the sizes of floral bracts, sepals and petals, flower colour, the presence or absence of a pedicel, the curvature of the stamina and the petals during anthesis. After scrutinizing the nomenclatural history of the taxa belonging to Deuterocohnia – including the 1992 syonymized genus Abromeitiella – 17 species, 4 subspecies and 4 varieties are accepted in the present revision. Taxonomic changes were made in the following cases: (I) New combinations: A. abstrusa (A. Cast.) N. Schütz is re-established – as defined by Castellanos (1931) – and transfered to D. abstrusa; D. brevifolia (Griseb.) M.A. Spencer & L.B. Sm. includes accessions of the former D. lorentziana (Mez) M.A. Spencer & L.B. Sm., which are not assigned to D. abstrusa; D. bracteosa W. Till is synonymized to D. strobilifera Mez; D. meziana Kuntze ex Mez var. carmineo-viridiflora Rauh is classified as a subspecies of D. meziana (ssp. carmineo-viridiflora (Rauh) N. Schütz); D. pedicellata W. Till is classified as a subspecies of D. meziana (ssp. pedicellata (W. Till) N. Schütz); D. scapigera (Rauh & L. Hrom.) M.A. Spencer & L.B. Sm ssp. sanctae-crucis R. Vásquez & Ibisch is classified as a species (D. sanctae-crucis (R. Vásquez & Ibisch) N. Schütz); (II) New taxa: a new subspecies of D. meziana Kuntze ex Mez is established; a new variety of D. scapigera is established; (the new taxa will be validly published elsewhere); (III) New type: an epitype for D. longipetala was chosen. All other species were kept according to Spencer and Smith (1992) or – in the case of more recently described species – according to the protologue. Beside the nomenclatural notes and the detailed descriptions, information on distribution, habitat and ecology, etymology and taxonomic delimitation is provided for the genus and for each of its species. An key was constructed for the identification of currently accepted species, subspecies and varieties. The key is based on easily detectable morphological characters. The former synonymization of the genus Abromeitiella into Deuterocohnia (Spencer and Smith 1992) is re-evalutated in the present study. Morphological as well as molecular investigations revealed Deuterocohnia incl. Abromeitiella as being monophyletic, with some indications that a monophyletic Abromeitiella lineage arose from within Deuterocohnia. Thus the union of both genera is confirmed. The second part of the present thesis describes and discusses the molecular phylogenies and networks. Molecular analyses of three chloroplast intergenic spacers (rpl32-trnL, rps16-trnK, trnS-ycf3) were conducted with a sample set of 119 taxa. This set included 103 Deuterocohnia accessions from all 17 described species of the genus and 16 outgroup taxa from the remainder of Pitcairnioideae s.str. (Dyckia (8 sp.), Encholirium (2 sp.), Fosterella (4 sp.) and Pitcairnia (2 sp.)). With its high sampling density, the present investigation by far represents the most comprehensive molecular study of Deuterocohnia up till now. All data sets were analyzed separately as well as in combination, and various optimality criteria for phylogenetic tree construction were applied (Maximum Parsimony, Maximum Likelihood, Bayesian inferences and the distance method Neighbour Joining). Congruent topologies were generally obtained with different algorithms and optimality criteria, but individual clades received different degrees of statistical support in some analyses. The rps16-trnK locus was the most informative among the three spacer regions examined. The results of the chloroplast DNA analyses revealed a highly supported paraphyly of Deuterocohnia. Thus, the cpDNA trees divide the genus into two subclades (A and B), of which Deuterocohnia subclade B is sister to the included Dyckia and Encholirium accessions, and both together are sister to Deuterocohnia subclade A. To further examine the relationship between Deuterocohnia and Dyckia/Encholirium at the generic level, two nuclear low copy markers (PRK exon2-5 and PHYC exon1) were analysed with a reduced taxon set. This set included 22 Deuterocohnia accessions (including members of both cpDNA subclades), 2 Dyckia, 2 Encholirium and 2 Fosterella species. Phylogenetic trees were constructed as described above, and for comparison the same reduced taxon set was also analysed at the three cpDNA data loci. In contrast to the cpDNA results, the nuclear DNA data strongly supported the monophyly of Deuterocohnia, which takes a sister position to a clade of Dyckia and Encholirium samples. As morphology as well as nuclear DNA data generated in the present study and in a former AFLP analysis (Horres 2003) all corroborate the monophyly of Deuterocohnia, the apparent paraphyly displayed in cpDNA analyses is interpreted to be the consequence of a chloroplast capture event. This involves the introgression of the chloroplast genome from the common ancestor of the Dyckia/ Encholirium lineage into the ancestor of Deuterocohnia subclade B species. The chloroplast haplotypes are not species-specific in Deuterocohnia. Thus, one haplotype was sometimes shared by several species, where the same species may harbour different haplotypes. The arrangement of haplotypes followed geographical patterns rather than taxonomic boundaries, which may indicate some residual gene flow among populations from different Deuteroccohnia species. Phenotypic species coherence on the background of ongoing gene flow may then be maintained by sets of co-adapted alleles, as was suggested by the porous genome concept (Wu 2001, Palma-Silva et al. 2011). The results of the present study suggest the following scenario for the evolution of Deuterocohnia and its species. Deuterocohnia longipetala may be envisaged as a representative of the ancestral state within the genus. This is supported by (1) the wide distribution of this species; (2) the overlap in distribution area with species of Dyckia; (3) the laxly flowered inflorescences, which are also typical for Dyckia; (4) the yellow petals with a greenish tip, present in most other Deuterocohnia species. The following six extant lineages within Deuterocohnia might have independently been derived from this ancestral state with a few changes each: (I) D. meziana, D. brevispicata and D. seramisiana (Bolivia, lowland to montane areas, mostly reddish-greenish coloured, very laxly to very densely flowered); (II) D. strobilifera (Bolivia, high Andean mountains, yellow flowers, densely flowered); (III) D. glandulosa (Bolivia, montane areas, yellow-greenish flowers, densely flowered); (IV) D. haumanii, D. schreiteri, D. digitata, and D. chrysantha (Argentina, Chile, E Andean mountains and Atacama desert, yellow-greenish flowers, densely flowered); (V) D. recurvipetala (Argentina, foothills of the Andes, recurved yellow flowers, laxly flowered); (VI) D. gableana, D. scapigera, D. sanctae-crucis, D. abstrusa, D. brevifolia, D. lotteae (former Abromeitiella species, Bolivia, Argentina, higher Andean mountains, greenish-yellow flowers, inflorescence usually simple). Originating from the lower montane Andean regions, at least four lineages of the genus (I, II, IV, VI) adapted in part to higher altitudes by developing densely flowered partial inflorescences, shorter flowers and – in at least three lineages (II, IV, VI) – smaller rosettes, whereas species spreading into the lowlands (I, V) developed larger plants, laxly flowered, amply branched inflorescences and in part larger flowers (I).

The Right to Water in the Case-Law of the Inter-American Court of Human Rights

The human right to water is nowadays more broadly recognised, mainly due to the essential societal function that this resource plays; likewise, because of the present water scarcity is generating conflicts between its different uses. Thus, this right aims at protecting human beings by guaranteeing access to clean water that is essential to satisfy vital human needs. Similarly, access to clean water is an important element to guarantee other rights including the right to life and health. The recognition of the right to water is mainly achieved in two ways: as a new and independent right and as a subordinate or derivative right. Concerning the latter, the right to water can emanate from civil and political rights, such as the right to life; or can be derived from economic, social and cultural rights, including the right to health, the right to an adequate standard of living, and the right to housing. This contribution explores the position of the Inter-American Court of Human Rights regarding the right to water, and analyses whether the Court has recognised the right to water and, if so, in which manner.

Museum of the City of São Paulo: A new paradigm of City Museums in the Era of Megalopolises

The City is a tomography of the present, indicating to the future, strata of past times. Nowadays city growth averages one million people every week; while back in 1950 there were eighty six cities with more than one million inhabitants, today they are four hundred all over the world. However the most significant effect of the urban process is, doubtless, the explosion of megacities. It took one century for the urban population – around three point four billion inhabitants – to surpass the number of people in the country, but United Nations projections indicate that by 2025, urban population will reach 61% of the total. Creating a new city museum in São Paulo requires that, in a first analysis, one should consider as geographic area of study some fifteen hundred square kilometres corresponding to the patrimonial intervention area. That is the area of the Municipality, politically divided into ninety six districts where eleven million people live, while approximately twenty million people live in the metropolitan area

The influence of a weakening of the Atlantic meridional overturning circulation on ENSO

The influences of a substantial weakening of the Atlantic meridional overturning circulation (AMOC) on the tropical Pacific climate mean state, the annual cycle, and ENSO variability are studied using five different coupled general circulation models (CGCMs). In the CGCMs, a substantial weakening of the AMOC is induced by adding freshwater flux forcing in the northern North Atlantic. In response, the well-known surface temperature dipole in the low-latitude Atlantic is established, which reorganizes the large-scale tropical atmospheric circulation by increasing the northeasterly trade winds. This leads to a southward shift of the intertropical convergence zone (ITCZ) in the tropical Atlantic and also the eastern tropical Pacific. Because of evaporative fluxes, mixing, and changes in Ekman divergence, a meridional temperature anomaly is generated in the northeastern tropical Pacific, which leads to the development of a meridionally symmetric thermal background state. In four out of five CGCMs this leads to a substantial weakening of the annual cycle in the eastern equatorial Pacific and a subsequent intensification of ENSO variability due to nonlinear interactions. In one of the CGCM simulations, an ENSO intensification occurs as a result of a zonal mean thermocline shoaling. Analysis suggests that the atmospheric circulation changes forced by tropical Atlantic SSTs can easily influence the large-scale atmospheric circulation and hence tropical eastern Pacific climate. Furthermore, it is concluded that the existence of the present-day tropical Pacific cold tongue complex and the annual cycle in the eastern equatorial Pacific are partly controlled by the strength of the AMOC. The results may have important implications for the interpretation of global multidecadal variability and paleo-proxy data.

Ingestion of onion soup high in quercetin inhibits platelet aggregation and essential components of the collagen-stimulated platelet activation pathway in man: a pilot study

Epidemiological data suggest that those who consume a diet rich in quercetin-containing foods may have a reduced risk of CVD. Furthermore, in vitro and ex vivo studies have observed the inhibition of collagen-induced platelet activation by quercetin. The aim of the present study was to investigate the possible inhibitory effects of quercetin ingestion from a dietary source on collagen-stimulated platelet aggregation and signalling. A double-blind randomised cross-over pilot study was undertaken. Subjects ingested a soup containing either a high or a low amount of quercetin. Plasma quercetin concentrations and platelet aggregation and signalling were assessed after soup ingestion. The high-quercetin soup contained 69 mg total quercetin compared with the low-quercetin soup containing 5 mg total quercetin. Plasma quercetin concentrations were significantly higher after high-quercetin soup ingestion than after low-quercetin soup ingestion and peaked at 2.59 (SEM 0.42) mu mol/l. Collagen-stimulated (0.5 mu g/ml) platelet aggregation was inhibited after ingestion of the high-quercetin soup in a time-dependent manner. Collagen-stimulated tyrosine phosphorylation of a key component of the collagen-signalling pathway via glycoprotein VI, Syk, was significantly inhibited by ingestion of the high-quercetin soup. The inhibition of Syk tyrosine phosphorylation was correlated with the area under the curve for the high-quercetin plasma profile. In conclusion, the ingestion of quercetin from a dietary source of onion soup could inhibit some aspects of collagen-stimulated platelet aggregation and signalling ex vivo. This further substantiates the epidemiological data suggesting that those who preferentially consume high amounts of quercetin-containing foods have a reduced risk of thrombosis and potential CVD risk.

Metabolism of the soyabean isoflavone glycoside genistin in vitro by human gut bacteria and the effect of prebiotics

The isoflavone genistein is found predominantly in soyabeans and is thought to possess various potent biological properties, including anticarcinogenic effects. Studies have shown that genistein is extensively degraded by the human gut microflora, presumably with a loss of its anti-carcinogenic action. The aim of the present study was to investigate the potential of a prebiotic to divert bacterial metabolism away from genistein breakdown: this may be of benefit to the host. Faecal samples were obtained from healthy volunteers and fermented in the presence of a source of soyabean isoflavones (Novasoy(TM) (10 g/l); ADM Neutraceuticals, Erith, Kent, UK). Bacterial genera of the human gut were enumerated using selective agars and genistein was quantified by HPLC. The experiment was repeated with the addition of glucose (10 g/l) or fructo-oligosaccharide (10 g/l; FOS) to the fermentation medium. The results showed most notably that counts of Bifidobacterium spp. and Lactobacillus spp. were significantly increased (P<0.05 and P<0.01 respectively) under steady-state conditions in the presence of FOS. Counts of Bacteroides spp. and Clostridium spp. were, however, both significantly reduced (P<0.05) during the fermentation. A decline in genistein concentration by about 52 and 56% over the 120h culture period was observed with the addition of glucose or FOS to the basal medium (P<0.01), compared with about 91% loss of genistein in the vessels containing Novasoy(TM) (ADM Neutraceuticals) only. Similar trends were obtained using a three-stage chemostat (gut model), in which once again the degradation of genistein was about 22% in vessel one, about 24% in vessel two and about 26% in vessel three in the presence of FOS, compared with a degradation of genistein of about 67% in vessel one, about 95% in vessel two and about 93% in vessel three in the gut model containing Novasoy(TM) (ADM Neutraceuticals) only. The present study has shown that the addition of excess substrate appeared to preserve genistein in vitro. In particular, the use of FOS not only augmented this effect, but also conferred an additional benefit in selectively increasing numbers of purportedly beneficial bacteria such as bifidobacteria and lactobacilli.

Holocene environmental changes in the lower Thames Valley, London, UK: implications for our understanding of the history of Taxus woodland

A radiocarbon-dated multiproxy palaeoenvironmental record from the Lower Thames Valley at Hornchurch Marshes has provided a reconstruction of the timing and nature of vegetation succession against a background of Holocene climate change, relative sea level movement and human activities. The investigation recorded widespread peat formation between c. 6300 and 3900 cal. yr BP (marine ‘regression’), succeeded by evidence for marine incursion. The multiproxy analyses of these sediments, comprising pollen, Coleoptera, diatoms, and plant and wood macrofossils, have indicated significant changes in both the wetland and dryland environment, including the establishment of Alnus (Alder) carr woodland, and the decline of both Ulmus (Elm; c. 5740 cal. yr BP) and Tilia (Lime; c. 5600 cal. yr BP, and 4160–3710 cal. yr BP). The beetle faunas from the peat also suggest a thermal climate similar to that of the present day. At c. 4900 cal. yr BP, Taxus (L.; Yew) woodland colonised the peatland forming a plant community that has no known modern analogue in the UK. The precise reason, or reasons, for this event remain unclear, although changes in peatland hydrology seem most likely. The growth of Taxus on peatland not only has considerable importance for our knowledge of the vegetation history of southeast England, and NW Europe generally, but also has wider implications for the interpretation of Holocene palaeobotanical records. At c. 3900 cal. yr BP, Taxus declined on the peatland surface during a period of major hydrological change (marine incursion), an event also strongly associated with the decline of dryland woodland taxa, including Tilia and Quercus, and the appearance of anthropogenic indicators.

Effect on components of the intestinal microflora and plasma neuropeptide levels of feeding Lactobacillus delbrueckii, Bifidobacterium lactis, and inulin to adult and elderly rats

The aim of this study was to compare the effects of the mixture of Lactobacillus delbrueckii subsp. rhamnosus strain GG, Bifidobacterium lactis Bb12, and inulin on intestinal populations of lactobacilli, bifidobacteria, and enterobacteria in adult and elderly rats fed the same (in quality and quantity) diet. The portal plasma levels of two neuropeptides, neuropeptide Y (NPY) and peptide YY (PYY), were also evaluated to assess the physiological consequences of the synbiotic treatment for the gastrointestinal (GI) tracts of rats of different ages. Adult (n = 24) and elderly (n = 24) male rats were fed the AIN-93 M maintenance diet. After 2 weeks of adaptation, the diet of 12 rats of each age group was supplemented with 8% inulin and with strains GG and Bb12 to provide 2.2 x 10(9) CFU of each strain g(-1) of the diet. Blood and different regions of the GI tract were sampled from all rats after 21 days of the treatment. Treatment with the mixture of strain GG, strain BB12, and inulin induced significantly different changes in the numbers of lactobacilli, bifidobacteria, and enterobacteria of the stomach, small intestine, cecum, and colon microflora. Moreover, the GG, BB12, and inulin mixture increased the concentrations of NPY and PYY for adult rats. For the elderly animals, the PYY concentration was not changed, while the NPY concentration was decreased by treatment with the GG, BB12, and inulin mixture. The results of the present study indicate that the physiological status of the GI tract, and not just diet, has a major role in the regulation of important groups of the GI bacteria community, since even the outcome of the dietary modification with synbiotics depends on the ages of the animals.

Optimal convergence estimates for the trace of the polynomial L2-projection operator on a simplex

In this paper we study convergence of the L2-projection onto the space of polynomials up to degree p on a simplex in Rd, d >= 2. Optimal error estimates are established in the case of Sobolev regularity and illustrated on several numerical examples. The proof is based on the collapsed coordinate transform and the expansion into various polynomial bases involving Jacobi polynomials and their antiderivatives. The results of the present paper generalize corresponding estimates for cubes in Rd from [P. Houston, C. Schwab, E. Süli, Discontinuous hp-finite element methods for advection-diffusion-reaction problems. SIAM J. Numer. Anal. 39 (2002), no. 6, 2133-2163].

An assessment of the prebiotic potential of single and blended substrates in anaerobic in vitro batch culture fermentations using canine faecal samples as inocula

Previously, using an in vitro static batch culture system, it was found that rice bran (RB), inulin, fibersol, mannanoligosaccharides (MOS), larch arabinogalactan and citrus pectin elicited prebiotic effects (in terms of increased numbers of bifidobacteria and lactic acid bacteria) on the faecal microbiota of a dog. The aim of the present study was to confirm the prebiotic potential of each individual substrate using multiple faecal donors, as well as assessing the prebiotic potential of 15 substrate blends made from them. Anaerobic static and stirred, pH-controlled batch culture systems inoculated with faecal samples from healthy dogs were used for this purpose. Fluorescence in situ hybridization (FISH) analysis using seven oligonucleotide probes targeting selected bacterial groups and DAPI (total bacteria) was used to monitor bacterial populations during fermentation runs. High-performance liquid chromatography was used to measure butyrate produced as a result of bacterial fermentation of the substrates. RB and a MOS/RB blend (1:1, w/w) were shown to elicit prebiotic and butyrogenic effects on the canine microbiota in static batch culture fermentations. Further testing of these substrates in stirred, pH-controlled batch culture fermentation systems confirmed the prebiotic and butyrogenic effects of MOS/RB, with no enhancement of Clostridium clusters I and II and Escherichia coli populations.

Effects of Cobalt Chloride in Junctional Epithelium and Reduced Enamel Epithelium of the Rat Maxillary First Molar

Cobalt is one of the main components of cast metal alloys broadly used in dentistry. It is the constituent of 45 to 70% of numerous prosthetic works. There are evidences that metal elements cause systemic and local toxicity. The purpose of the present study was to evaluate the effects of cobalt on the junctional epithelium and reduced enamel epithelium of the first superior molar in rats, during lactation. To do this, 1-day old rats were used, whose mothers received 300mg of cobalt chloride per liter of distilled water in the drinker, during lactation. After 21 days, the rat pups were killed with an anesthetic overdose. The heads were separated, fixed in ""alfac"", decalcified and embedded in paraffin. Frontal sections stained with hematoxylin and eosin were employed. Karyometric methods allowed to estimate the following parameters: biggest, smallest and mean diameters, D/d ratio, perimeter, area, volume, volume/area ratio, eccentricity, form coefficient and contour index. Stereologic methods allow to evaluate: cytoplasm/nucleus ratio, cell and cytoplasm volume, cell number density, external surface/basal membrane ratio, thickness of the epithelial layers and surface density. All the collected data were subjected to statistic analysis by the non-parametric Wilcoxon-Mann-Whitney test. The nuclei of the studied tissues showed smaller values after karyometry for: diameters; perimeter, area, volume and volume/area ratio. Stereologically, it was observed, in the junctional epithelium and in the reduced enamel epithelium, smaller cells with scarce cytoplasm, reflected in the greater number of cells per mm3 of tissue. In this study, cobalt caused epithelial atrophy, indicating a direct action on the junctional and enamel epithelium.

Characteristics of the equine embryo and fetus from days 15 to 107 of pregnancy

In spite of numerous, substantial advances in equine reproduction, many stages of embryonic and fetal morphological development are poorly understood, with no apparent single source of comprehensive information. Hence, the objective of the present study was to provide a complete macroscopic and microscopic description of the equine embryo/fetus at various gestational ages. Thirty-four embryos/fetuses were aged based on their crown rump length (CRL), and submitted to macroscopic description, biometry, light and scanning microscopy, as well as the alizarin technique. All observed developmental changes were chronologically ordered and described. As examples of the main observed features, an accentuated cervical curvature was observed upon macroscopic examination in all specimens. In the nervous system, the encephalic fourth ventricle and the encephalic vesicles forebrain, midbrain, and hindbrain, were visualized from Day 19 (ovulation = Day 0). The thoracic and pelvic limbs were also visualized; their extremities gave rise to the hoof during development from Day 27. Development of other structures such as pigmented optical vesicle, liver, tail, cardiac area, lungs, and dermal vascularization started on Days 25, 25, 19, 19, 34, and 35, respectively. Light and scanning microscopy facilitated detailed examinations of several organs, e.g., heart, kidneys, lungs, and intestine, whereas the alizarin technique enabled visualization of ossification. Observations in this study contributed to the knowledge regarding equine embryogenesis, and included much detailed data from many specimens collected over a long developmental interval. (C) 2011 Elsevier Inc. All rights reserved.

Measurement of the epicycle frequency in the Galactic disc and initial velocities of open clusters

A new method to measure the epicycle frequency kappa in the Galactic disc is presented. We make use of the large data base on open clusters completed by our group to derive the observed velocity vector (amplitude and direction) of the clusters in the Galactic plane. In the epicycle approximation, this velocity is equal to the circular velocity given by the rotation curve, plus a residual or perturbation velocity, of which the direction rotates as a function of time with the frequency kappa. Due to the non-random direction of the perturbation velocity at the birth time of the clusters, a plot of the present-day direction angle of this velocity as a function of the age of the clusters reveals systematic trends from which the epicycle frequency can be obtained. Our analysis considers that the Galactic potential is mainly axis-symmetric, or in other words, that the effect of the spiral arms on the Galactic orbits is small; in this sense, our results do not depend on any specific model of the spiral structure. The values of kappa that we obtain provide constraints on the rotation velocity of the in particular, V(0) is found to be 230 +/- 15 km s(-1) even if the scale (R(0) = 7.5 kpc) of the Galaxy is adopted. The measured kappa at the solar radius is 43 +/- 5 km s(-1) kpc(-1). The distribution of initial velocities of open clusters is discussed.

A late Neoproterozoic paleomagnetic pole for the Congo craton: Tectonic setting, paleomagnetism and geochronology of the Nola dike swarm (Central African Republic)

New structural, geochronological and paleomagnetic data were obtained on dolerite dikes of the Nola region (Central African Republic) at the northern border of the Congo craton. In this region metavolcanic, successions were thrust southward onto the craton during the Panafrican orogenic events. Our structural data reveal at least two structural klippes south of the present-day limits of the Panafrican nappe suggesting that it has once covered the whole Nola region, promoting the pervasive hydrothermal green-schist metamorphism observed in the underlying cratonic basement and also in the intrusive dolerite dikes. Paleomagnetic measurements revealed a stable dual-polarity low-inclination magnetization component in nine dikes (47 samples), carried by pyrrhotite and magnetite. This component corresponds to a paleopole at 304.8 degrees E and 61.8 degrees S (dp = 5.4, dm = 10.7) graded at 2 = 6. Both metamorphism and magnetic resetting were dated by the Ar-40/Ar-39 method on amphibole grains separated from the dikes at 571 +/- 6 Ma. The Nola pole is the first well-dated paleomagnetic pole for the Congo craton between 580 and 550 Ma. It marks a sudden change in direction of the Congo craton apparent polar wander path at the waning stages of the Panafrican orogenic events. (c) 2008 Elsevier B.V. All rights reserved.