39 resultados para geometry of numbers


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In the Sesia Zone (Italian Western Alps), slivers of continental crust characterised by an Alpine high-pressure imprint are intermingled with abundant mafic rocks and Mesozoic metasediments. An extensive study of the central Sesia Zone was undertaken to identify and reconstruct the lithological setting of the mono-cyclic sediments of the Scalaro Unit. A new geological map (1:5000) and schematic cross sections across the Scalaro Unit and the adjoining Eclogitic Micaschist Complex are presented here. In order to delimit the size and shape of the mono-metamorphic unit and understand its internal geometry with respect to the poly-metamorphic basement, an integrated approach was used. Linking observations and data across a range of scales, from kilometres in the field down to petrological and chronological data obtained at micrometre scale, we define for the first time the real size and internal geometry of the Scalaro Unit, as well as its large-scale structural context.

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The precise arraying of functional entities in morphologically well-defined shapes remains one of the key challenges in the processing of organic molecules1. Among various π-conjugated species, pyrene exhibits a set of unique properties, which make it an attractive compound for the utilization in materials science2. In this contribution we report on properties of self-assembled structures prepared from amphiphilic pyrene trimers (Py3) consisting of phosphodiester-linked pyrenes. Depending on the geometry of a pyrene core substitution (1.6-, 1.8-, or 2.7- type, see Scheme), the thermally-controlled self-assembly allows the preparation of supramolecular architectures of different morphologies in a bottom-up approach: two-dimensional (2D) nanosheets3 are formed in case of 1.6- and 2.7-substitution4 whereas one-dimensional (1D) fibers are built from 1.8- substituted isomers. The morphologies of the assemblies are established by AFM and TEM, and the results are further correlated with spectroscopic and scattering data. Two-dimensional assemblies consist of an inner layer of hydrophobic pyrenes, sandwiched between a net of phosphates. Due to the repulsion of the negative charges, the 2D assemblies exist mostly as free-standing sheets. An internal alignment of pyrenes leads to strong exciton coupling with an unprecedented observation (simultaneous development of J- and H-bands from two different electronic transitions). Despite the similarity in spectroscopic properties, the structural parameters of the 2D aggregates drastically depend on the preparation procedure. Under certain conditions extra-large sheets (thickness of 2 nm, aspect ratio area/thickness ~107) in aqueous solution are formed4B. Finally, one-dimensional assemblies are formed as micrometer-long and nanometer-thick fibers. Both, planar and linear structures are intriguing objects for the creation of conductive nanowires that may find interest for applications in supramolecular electronics.

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The precise arraying of functional entities in morphologically well-defined shapes remains one of the key challenges in the processing of organic molecules1. Among various π-conjugated species, pyrene exhibits a set of unique properties, which make it an attractive compound for the utilization in materials science2. In this contribution we report on properties of self-assembled structures prepared from amphiphilic pyrene trimers (Py3) consisting of phosphodiester-linked pyrenes. Depending on the geometry of a pyrene core substitution (1.6-, 1.8-, or 2.7- type, see Scheme), the thermally-controlled self-assembly allows the preparation of supramolecular architectures of different morphologies in a bottom-up approach: two-dimensional (2D) nanosheets3 are formed in case of 1.6- and 2.7-substitution4 whereas one-dimensional (1D) fibers are built from 1.8- substituted isomers. The morphologies of the assemblies are established by AFM and TEM, and the results are further correlated with spectroscopic and scattering data. Two-dimensional assemblies consist of an inner layer of hydrophobic pyrenes, sandwiched between a net of phosphates. Due to the repulsion of the negative charges, the 2D assemblies exist mostly as free-standing sheets. An internal alignment of pyrenes leads to strong exciton coupling with an unprecedented observation (simultaneous development of J- and H-bands from two different electronic transitions). Despite the similarity in spectroscopic properties, the structural parameters of the 2D aggregates drastically depend on the preparation procedure. Under certain conditions extra-large sheets (thickness of 2 nm, aspect ratio area/thickness ~107) in aqueous solution are formed4B. Finally, one-dimensional assemblies are formed as micrometer-long and nanometer-thick fibers. Both, planar and linear structures are intriguing objects for the creation of conductive nanowires that may find interest for applications in supramolecular electronics.

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The Astronomical Institute of the University of Bern (AIUB) is conducting several search campaigns for orbital debris. The debris objects are discovered during systematic survey observations. In general only a short observation arc, or tracklet, is available for most of these objects. From this discovery tracklet a first orbit determination is computed in order to be able to find the object again in subsequent follow-up observations. The additional observations are used in the orbit improvement process to obtain accurate orbits to be included in a catalogue. In this paper, the accuracy of the initial orbit determination is analyzed. This depends on a number of factors: tracklet length, number of observations, type of orbit, astrometric error, and observation geometry. The latter is characterized by both the position of the object along its orbit and the location of the observing station. Different positions involve different distances from the target object and a different observing angle with respect to its orbital plane and trajectory. The present analysis aims at optimizing the geometry of the discovery observation is depending on the considered orbit.

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NH···π hydrogen bonds occur frequently between the amino acid side groups in proteins and peptides. Data-mining studies of protein crystals find that ~80% of the T-shaped histidine···aromatic contacts are CH···π, and only ~20% are NH···π interactions. We investigated the infrared (IR) and ultraviolet (UV) spectra of the supersonic-jet-cooled imidazole·benzene (Im·Bz) complex as a model for the NH···π interaction between histidine and phenylalanine. Ground- and excited-state dispersion-corrected density functional calculations and correlated methods (SCS-MP2 and SCS-CC2) predict that Im·Bz has a Cs-symmetric T-shaped minimum-energy structure with an NH···π hydrogen bond to the Bz ring; the NH bond is tilted 12° away from the Bz C₆ axis. IR depletion spectra support the T-shaped geometry: The NH stretch vibrational fundamental is red shifted by −73 cm⁻¹ relative to that of bare imidazole at 3518 cm⁻¹, indicating a moderately strong NH···π interaction. While the Sₒ(A1g) → S₁(B₂u) origin of benzene at 38 086 cm⁻¹ is forbidden in the gas phase, Im·Bz exhibits a moderately intense Sₒ → S₁ origin, which appears via the D₆h → Cs symmetry lowering of Bz by its interaction with imidazole. The NH···π ground-state hydrogen bond is strong, De=22.7 kJ/mol (1899 cm⁻¹). The combination of gas-phase UV and IR spectra confirms the theoretical predictions that the optimum Im·Bz geometry is T shaped and NH···π hydrogen bonded. We find no experimental evidence for a CH···π hydrogen-bonded ground-state isomer of Im·Bz. The optimum NH···π geometry of the Im·Bz complex is very different from the majority of the histidine·aromatic contact geometries found in protein database analyses, implying that the CH···π contacts observed in these searches do not arise from favorable binding interactions but merely from protein side-chain folding and crystal-packing constraints. The UV and IR spectra of the imidazole·(benzene)₂ cluster are observed via fragmentation into the Im·Bz+ mass channel. The spectra of Im·Bz and Im·Bz₂ are cleanly separable by IR hole burning. The UV spectrum of Im·Bz₂ exhibits two 000 bands corresponding to the Sₒ → S₁ excitations of the two inequivalent benzenes, which are symmetrically shifted by −86/+88 cm⁻¹ relative to the 000 band of benzene.

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INTRODUCTION Distraction-based spinal growth modulation by growing rods or vertical expandable prosthetic titanium ribs (VEPTRs) is the mainstay of instrumented operative strategies to correct early onset spinal deformities. In order to objectify the benefits, it has become common sense to measure the gain in spine height by assessing T1-S1 distance on anteroposterior (AP) radiographs. However, by ignoring growth changes on vertebral levels and by limiting measurement to one plane, valuable data is missed regarding the three-dimensional (3D) effects of growth modulation. This information might be interesting when it comes to final fusion or, even more so, when the protective growing implants are removed and the spine re-exposed to physiologic forces at the end of growth. METHODS The goal of this retrospective radiographic study was to assess the growth modulating impact of year-long, distraction-based VEPTR treatment on the morphology of single vertebral bodies. We digitally measured lumbar vertebral body height (VBH) and upper endplate depth (VBD) at the time of the index procedure and at follow-up in nine patients with rib-to-ileum constructs (G1) spanning an anatomically normal lumbar spine. Nine patients with congenital thoracic scoliosis and VEPTR rib-to-rib constructs, but uninstrumented lumbar spines, served as controls (G2). All had undergone more than eight half-yearly VEPTR expansions. A Wilcoxon signed-rank test was used for statistical comparison of initial and follow-up VBH, VBD and height/depth (H/D) ratio (significance level 0.05). RESULTS The average age was 7.1 years (G1) and 5.2 year (G2, p > 0.05) at initial surgery; the average overall follow-up time was 5.5 years (p = 1). In both groups, VBH increased significantly without a significant intergroup difference. Group 1 did not show significant growth in depth, whereas VBD increased significantly in the control group. As a consequence, the H/D ratio increased significantly in group 1 whereas it remained unchanged in group 2. The growth rate for height in mm/year was 1.4 (group 1) and 1.1 (group 2, p = 0.45), and for depth, it was -0.3 and 1.1 (p < 0.05), respectively. CONCLUSIONS VEPTR growth modulating treatment alters the geometry of vertebral bodies by increasing the H/D ratio. We hypothesize that the implant-related deprivation from axial loads (stress-shielding) impairs anteroposterior growth. The biomechanical consequence of such slender vertebrae when exposed to unprotected loads in case of definitive VEPTR removal at the end of growth is uncertain.

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Little is known about how children learn to associate numbers with their corresponding magnitude and about individual characteristics contributing to performance differences on the numerical magnitude tasks within a relatively homogenous sample of 6-year-olds. The present study investigated the relationships between components of executive function and two different numerical magnitude skills in a sample of 162 kindergartners. The Symbolic Number Line was predicted by verbal updating and switching, whereas the Symbolic Magnitude Comparison was predicted by inhibition. Both symbolic tasks were predicted by visuo-spatial updating. Current findings suggest that visuo-spatial updating underlies young children’s retrieval and processing of numbers’ magnitude.

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The presence of polyoxymethylene (POM) in cometary grains has been debated years ago. Although never proven, its presence can not be excluded. Rosetta, the ESA mission to comet 67P/Churyumov–Gerasimenko, may answer this question. On board the spacecraft, COSIMA (COmetary Secondary Ion Mass Analyzer) will analyze the grains ejected from the nucleus using a Time Of Flight Secondary Ion Mass Spectrometer (TOF-SIMS). In this paper we report the extent to which COSIMA will be able to detect POM if this compound is present on cometary grains. We have analyzed two kinds of POM polymers with a laboratory model of COSIMA. Positive mass spectra display alternating sequence of peaks with a separation of 30.011 Da between 1 and 600 Da related to formaldehyde and its oligomers but also to the fragmentation of these oligomers. The separation of 30.011 Da of numbers peaks, corresponding to the fragmentation into H2CO is characteristic of POM and we show that it could be highlight by mathematical treatment. POM lifetime on COSIMA targets have also been studied as POM is thermally instable. It can be concluded that the cometary grains analysis have to be planned not too long after their collection in order to maximize the chances to detect POM. This work was supported by the Centre National d'Etudes Spatiales (CNES).

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A two-step etching technique for fine-grained calcite mylonites using 0.37% hydrochloric and 0.1% acetic acid produces a topographic relief which reflects the grain boundary geometry. With this technique, calcite grain boundaries become more intensely dissolved than their grain interiors but second phase minerals like dolomite, quartz, feldspars, apatite, hematite and pyrite are not affected by the acid and therefore form topographic peaks. Based on digital backscatter electron images and element distribution maps acquired on a scanning electron microscope, the geometry of calcite and the second phase minerals can be automatically quantified using image analysis software. For research on fine-grained carbonate rocks (e.g. dolomite calcite mixtures), this low-cost approach is an attractive alternative to the generation of manual grain boundary maps based on photographs from ultra-thin sections or orientation contrast images.