279 resultados para Symmetric Kravchuk polynomials
Resumo:
Some minerals are colloidal and show no X-ray diffraction patterns. Vibrational spectroscopy offers one of the few methods for the assessment of the structure of these types of mineral. Among this group of minerals is pitticite simply described as Fe, AsO4, SO4, H2O. The objective of this research is to determine the molecular structure of the mineral pitticite using vibrational spectroscopy. Raman microscopy offers a useful method for the analysis of such colloidal minerals. Raman and infrared bands are attributed to the , and water stretching vibrations. The Raman spectrum is dominated by a very intense sharp band at 983 cm−1 assigned to the symmetric stretching mode. A strong Raman band at 1041 cm−1 is observed and is assigned to the antisymmetric stretching mode. Low intensity Raman bands at 757 and 808 cm−1 may be assigned to the antisymmetric and symmetric stretching modes. Raman bands observed at 432 and 465 cm−1 are attributable to the doubly degenerate ν2(SO4)2- bending mode.
Resumo:
Raman spectroscopy complimented with infrared spectroscopy has been used to study the rare earth based mineral decrespignyite (Y,REE)4Cu(CO3)4Cl(OH)5•2(H2O) and compared with the Raman spectra of a series of selected natural halogenated carbonates from different origins including bastnasite, parisite and northupite. The Raman spectrum of decrespignyite displays three bands are at 1056, 1070 and 1088 cm-1 attributed to the CO32- symmetric stretching vibration. The observation of three symmetric stretching vibrations is very unusual. The position of CO32- symmetric stretching vibration varies with mineral composition. Raman bands of decrespignyite show bands at 1391, 1414, 1489 and 1547 cm-1. Raman spectra of bastnasite, parisite and northupite show a single band at 1433, 1420 and 1554 cm-1 assigned to the ν3 (CO3)2- antisymmetric stretching mode. The observation of additional Raman bands for the ν3 modes for some halogenated carbonates is significant in that it shows distortion of the carbonate anion in the mineral structure. Four Raman bands are observed at 791, 815, 837 and 849 cm-1and assigned to the (CO3)2- ν2 bending modes. Raman bands are observed for decrespignyite at 694, 718 and 746 cm-1 and are assigned to the (CO3)2- ν4 bending modes. Raman bands are observed for the carbonate ν4 in phase bending modes at 722 cm-1 for bastnasite, 736 and 684 cm-1 for parisite, 714 cm-1 for northupite. Multiple bands are observed in the OH stretching region for decrespignyite, bastnasite and parisite indicating the presence of water and OH units in the mineral structure.
Resumo:
A numerical investigation has been carried out for the coupled thermal boundary layers on both sides of a partition placed in an isosceles triangular enclosure along its middle symmetric line. The working fluid is considered as air which is initially quiescent. A sudden temperature difference between two zones of the enclosure has been imposed to trigger the natural convection. It is anticipated from the numerical simulations that the coupled thermal boundary layers development adjacent to the partition undergoes three distinct stages; namely an initial stage, a transitional stage and a steady state stage. Time dependent features of the coupled thermal boundary layers as well as the overall natural convection flow in the partitioned enclosure have been discussed and compared with the non-partitioned enclosure. Moreover, heat transfer as a form of local and overall average Nusselt number through the coupled thermal boundary layers and the inclined walls is also examined. The details results will be discussed in the full paper.
Resumo:
The mineral schlossmacherite (H3O,Ca)Al3(AsO4,PO4,SO4)2(OH)6 , a multi-cation-multi-anion mineral of the beudantite mineral subgroup has been characterised by Raman spectroscopy. The mineral and related minerals functions as a heavy metal collector and is often amorphous or poorly crystalline, such that XRD identification is difficult. The Raman spectra are dominated by an intense band at 864 cm-1, assigned to the symmetric stretching mode of the AsO43- anion. Raman bands at 809 and 819 cm-1 are assigned to the antisymmetric stretching mode of AsO43- . The sulphate anion is characterised by bands at 1000 cm-1 (ν1), and at 1031, 1082 and 1139 cm-1 (ν3). Two sets of bands in the OH stretching region are observed: firstly between 2800 and 3000 cm-1 with bands observed at 2850, 2868, 2918 cm-1 and secondly between 3300 and 3600 with bands observed at 3363, 3382, 3410, 3449 and 3537 cm-1. These bands enabled the calculation of hydrogen bond distances and show a wide range of H-bond distances.
Resumo:
Kinoite Ca2Cu2Si3O10(OH)4 is a mineral named after a Jesuit missionary. Raman and infrared spectroscopy have been used to characterise the structure of the mineral. The Raman spectrum is characterised by an intense sharp band at 847 cm-1 assigned to the ν1 (A1g) symmetric stretching vibration. Intense sharp bands at 951, 994 and 1000 cm-1 are assigned to the ν3 (Eu, A2u, B1g) SiO4 antisymmetric stretching vibrations. Multiple ν2 SiO4 vibrational modes indicate strong distortion of the SiO4 tetrahedra. Multiple CaO and CuO stretching bands are observed. Raman spectroscopy confirmed by infrared spectroscopy clearly shows that hydroxyl units are involved in the kinoite structure. Based upon the infrared spectra, it is proposed that water is also involved in the kinoite structure. Based upon vibrational spectroscopy, the formula of kinoite is defined as Ca2Cu2Si3O10(OH)4•xH2O.
Resumo:
Stringhamite CaCuSiO4·H2O is a hydrated calcium copper silicate and is commonly known as a significant ‘healing’ mineral and is potentially a semi-precious jewel. Stringhamite is a neosilicate with Cu2+ in square planar coordination. Vibrational spectroscopy has been used to characterise the molecular structure of stringhamite. The intense sharp Raman band at 956 cm−1 is assigned to the ν1 (A1g) symmetric stretching vibration. Raman bands at 980, 997, 1061 cm−1 are assigned to the ν3 (A2u, B1g) antisymmetric stretching vibrations. Splitting of the ν3 vibrational mode supports the concept that the stringhamite SiO4 tetrahedron is strongly distorted. The intense bands at 505 and 519 cm−1 and at 570 cm−1 are assigned to the ν2 and ν4 vibrational modes. The question arises as to whether the mineral stringhamite can actually function as a healing mineral. An estimation of the solubility product at pH < 5 shows that the cupric ion can be released. The copper ion is a very powerful antibiological agent and thus the mineral stringhamite may well function as a healing mineral.
Resumo:
Whelanite Ca5Cu2(OH)2CO3,Si6O17•4H2O is a hydrated hydroxy mixed anion compound with both silicate and carbonate anions in the formula. The structural characterisation of the mineral whelanite remains incomplete. Whelanite is probably a neosilicate with Cu2+ in square planar coordination. Two Raman bands at 1070 and 1094 cm-1 are assigned to the ν1 symmetric stretching modes of the CO32- units. The observation of two symmetric stretching modes supports the concept of two non-equivalent CO32- units in the whelanite structure. The intense sharp Raman band at 1006 cm-1 is assigned to the ν1 (A1g) symmetric stretching vibration of the Si6O17 units. The splitting of the ν3 vibrational mode offers support to the concept that the SiO4 tetrahedron in whelanite is strongly distorted. A very intense Raman band observed at 666 cm-1 with a shoulder at 697 cm-1 is assigned to the ν4 vibrational modes. Intense Raman bands at 3534, 3556, 3550 and 3595 cm-1 are assigned to the stretching vibrations of the OH units. Low intensity Raman bands at 2910, 3187 and 3453 cm-1 are assigned to water stretching modes. Thus, vibrational spectroscopy has been used to characterise the molecular structure of whelanite. Whelanite is a mineral that could be conceived as a healing mineral
Resumo:
Planchéite Cu8Si8O22(OH)4•H2O is a hydrated copper hydroxy silicate. The objective of this work is to use Raman and infrared spectroscopy to determine the molecular structure of planchéite. Raman bands of planchéite at around 1048, 1081 and 1127 are described as the ν1 –SiO3 symmetric stretching vibrations; Raman bands at 828, 906 are attributed to the ν3 –SiO3 antisymmetric stretching vibrations. The Raman band at 699 cm-1 is assigned to the ν4 bending modes of the -SiO3 units. The intense Raman band at 3479 cm-1 is ascribed to the stretching vibration of the OH units. The Raman band at 3250 cm-1 is evidence for water in the structure. A comparison of the spectra of planchéite with that of shattuckite and chrysocolla.
Resumo:
Purpose: Investigations of foveal aberrations assume circular pupils. However, the pupil becomes increasingly elliptical with increase in visual field eccentricity. We address this and other issues concerning peripheral aberration specification. Methods: One approach uses an elliptical pupil similar to the actual pupil shape, stretched along its minor axis to become a circle so that Zernike circular aberration polynomials may be used. Another approach uses a circular pupil whose diameter matches either the larger or smaller dimension of the elliptical pupil. Pictorial presentation of aberrations, influence of wavelength on aberrations, sign differences between aberrations for fellow eyes, and referencing position to either the visual field or the retina are considered. Results: Examples show differences between the two approaches. Each has its advantages and disadvantages, but there are ways to compensate for most disadvantages. Two representations of data are pupil aberration maps at each position in the visual field and maps showing the variation in individual aberration coefficients across the field. Conclusions: Based on simplicity of use, adequacy of approximation, possible departures of off-axis pupils from ellipticity, and ease of understanding by clinicians, the circular pupil approach is preferable to the stretched elliptical approach for studies involving field angles up to 30 deg.
Resumo:
Arsenogorceixite BaAl3AsO3(OH)(AsO4,PO4)(OH,F)6 belongs to the crandallite mineral subgroup of the alunite supergroup. Arsenogorceixite forms a continuous series of solid solutions with related minerals including gorceixite, goyazite, arsenogoyazite, plumbogummite and philipsbornite. Two minerals from (a) Germany and (b) from Ashburton Downs, Australia were analysed by Raman spectroscopy. The spectra show some commonality but the intensities of the peaks vary. Sharp intense Raman bands for the German sample, are observed at 972 and 814 cm−1 attributed to the ν1 PO43− and AsO43− symmetric stretching modes. Raman bands at 1014, 1057, 1148 and 1160 cm−1 are attributed to the ν1 PO2 symmetric stretching mode and ν3 PO43− antisymmetric stretching vibrations. Raman bands at 764 and 776 cm−1 and 758 and 756 cm−1 are assigned to the ν3 AsO43− antisymmetric stretching vibrations. For the Australian mineral, the ν1 PO43− band is found at 973 cm−1. The intensity of the arsenate bands observed at 814, 838 and 870 cm−1 is greatly enhanced. Two low intensity Raman bands at 1307 and 1332 cm−1 are assigned to hydroxyl deformation modes. The intense Raman band at 441 cm−1 with a shoulder at 462 cm−1 is assigned to the ν2 PO43− bending mode. Raman bands at 318 and 340 cm−1 are attributed to the (AsO4)3−ν2 bending. The broad band centred at 3301 cm−1 is assigned to water stretching vibrations and the sharper peak at 3473 cm−1 is assigned to the OH stretching vibrations. The observation of strong water stretching vibrations brings into question the actual formula of arsenogorceixite. It is proposed the formula is better written as BaAl3AsO3(OH)(AsO4,PO4)(OH,F)6·xH2O. The observation of both phosphate and arsenate bands provides a clear example of solid solution formation.
Resumo:
The LiteSteel Beam (LSB) is a new hollow flange channel section developed by OneSteel Australian Tube Mills using its patented dual electric resistance welding and automated continuous roll-forming technologies. The LSB has a unique geometry consisting of torsionally rigid rectangular hollow flanges and a relatively slender web. Its flexural strength for intermediate spans is governed by lateral distortional buckling characterised by simultaneous lateral deflection, twist and web distortion. Recent research on LSBs has mainly focussed on their lateral distortional buckling behaviour under uniform moment conditions. However, in practice, LSB flexural members are subjected to non-uniform moment distributions and load height effects as they are often under transverse loads applied above or below their shear centre. These loading conditions are known to have significant effects on the lateral buckling strength of beams. Many steel design codes have adopted equivalent uniform moment distribution and load height factors based on data for conventional hot-rolled, doubly symmetric I-beams subject to lateral torsional buckling. The non-uniform moment distribution and load height effects of transverse loading on cantilever LSBs, and the suitability of the current design modification factors to include such effects are not known. This paper presents a numerical study based on finite element analyses of the elastic lateral buckling strength of cantilever LSBs subject to transverse loading, and the results. The applicability of the design modification factors from various steel design codes was reviewed, and suitable recommendations are presented for cantilever LSBs subject to transverse loading.
Resumo:
Australian manufacturers recently developed a new mono-symmetric cold-formed steel hollow flange channel section known as LiteSteel Beam. The innovative LSB sections with rectangular flanges are currently being used as floor joists and bearers in buildings. In order to assess their behaviour and section moment capacity including the presence of any inelastic reserve bending capacity, 20 section moment capacity tests were conducted in this study. Test results were compared with the section moment capacities predicted by the steel design codes. Although the current cold-formed steel design rules generally limit the section moment capacities to their first yield moments, test results showed that inelastic reserve bending capacity was present in the compact and non-compact LSB sections. The results have shown that suitable modifications to the current design rules are needed to allow the inclusion of available inelastic bending capacities of LSBs in design.
Resumo:
Three wardite mineral samples from different origins have been analysed by vibrational spectroscopy. The mineral is unusual in that it belongs to a unique symmetry class, namely the tetragonal-trapezohedral group. The structure of wardite contains layers of corner-linked –OH bridged MO6 octahedra stacked along the tetragonal C-axis in a four-layer sequence and linked by PO4 groups. Consequentially not all phosphate units are identical. Thus, two intense Raman bands observed at 995 and 1051 cm-1 are assigned to the ν1 PO43- symmetric stretching mode. Intense Raman bands are observed at 605 and 618 cm-1 with shoulders at 578 and 589 cm-1 are assigned to the ν4 out of plane bending modes of the PO43-. The observation of multiple bands supports the concept of non-equivalent phosphate units in the structure. Sharp infrared bands are observed at 3544 and 3611 cm-1 are attributed to the OH stretching vibrations of the hydroxyl units. Vibrational spectroscopy enables subtle details of the molecular structure of wardite to be determined.
Resumo:
The demand for high-speed data services for portable device has become a driving force for development of advanced broadband access technologies. Despite recent advances in broadband wireless technologies, there remain a number of critical issues to be resolved. One of the major concerns is the implementation of compact antennas that can operate in a wide frequency band. Spiral antenna has been used extensively for broadband applications due to its planar structure, wide bandwidth characteristics and circular polarisation. However, the practical implementation of spiral antennas is challenged by its high input characteristic impedance, relatively low gain and the need for balanced feeding structures. Further development of wideband balanced feeding structures for spiral antennas with matching impedance capabilities remain a need. This thesis proposes three wideband feeding systems for spiral antennas which are compatible with wideband array antenna geometries. First, a novel tapered geometry is proposed for a symmetric coplanar waveguide (CPW) to coplanar strip line (CPS) wideband balun. This balun can achieve the unbalanced to balanced transformation while matching the high input impedance of the antenna to a reference impedance of 50 . The discontinuity between CPW and CPS is accommodated by using a radial stub and bond wires. The bandwidth of the balun is improved by appropriately tapering the CPW line instead of using a stepped impedance transformer. Next, the tapered design is applied to an asymmetric CPW to propose a novel asymmetric CPW to CPS wideband balun. The use of asymmetric CPW does away with the discontinuities between CPW and CPS without having to use a radial stub or bond wires. Finally, a tapered microstrip line to parallel striplines balun is proposed. The balun consists of two sections. One section is the parallel striplines which are connected to the antenna, with the impedance of balanced line equal to the antenna input impedance. The other section consists of a microstrip line where the width of the ground plane is gradually reduced to eventually resemble a parallel stripline. The taper accomplishes the mode and impedance transformation. This balun has significantly improved bandwidth characteristics. Characteristics of proposed feeding structures are measured in a back-to-back configuration and compared to simulated results. The simulated and measured results show the tapered microstrip to parallel striplines balun to have more than three octaves of bandwidth. The tapered microstrip line to parallel striplines balun is integrated with a single Archimedean spiral antenna and with an array of spiral antennas. The performance of the integrated structures is simulated with the aid of electromagnetic simulation software, and results are compared to measurements. The back-to-back microstrip to parallel strip balun has a return loss of better than 10 dB over a wide bandwidth from 1.75 to 15 GHz. The performance of the microstrip to parallel strip balun was validated with the spiral antennas. The results show the balun to be an effective mean of feeding network with a low profile and wide bandwidth (2.5 to 15 GHz) for balanced spiral antennas.
Resumo:
The molecular structure of the mixed anion mineral Clinotyrolite Ca2Cu9[(As,S)O4]4(OH)10•10(H2O) has been determined by the combination of Raman and infrared spectroscopy. Characteristic bands associated with arsenate, sulphate and hydroxyl units are identified. Broad bands in the OH stretching region are observed and are resolved into component bands. Estimates of hydrogen bond distances were made using a Libowitzky function and both short and long hydrogen bonds are identified. Two intense Raman bands at 842 and ~796 cm-1 are assigned to the ν1 (AsO4)3- symmetric stretching and ν3 (AsO4)3- antisymmetric stretching modes. The comparatively sharp Raman band at 980 cm-1 is assigned to the ν1 (SO4)2- symmetric stretching mode and a broad Raman spectral profile centred upon 1100 cm-1 is attributed to the ν3 (SO4)2- antisymmetric stretching mode.