212 resultados para Legendre Formula


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Burkeite formation is important in saline evaporites and in pipe scales. Burkeite is an anhydrous sulphate-carbonate with an apparent variable anion ratio. Such a formula with two oxyanions lends itself to vibrational spectroscopy. Two symmetric sulphate stretching modes are observed, indicating at least at the molecular level the nonequivalence of the sulphate ions in the burkeite structure. The strong Raman band at 1065 cm−1 is assigned to the carbonate symmetric stretching vibration. The series of Raman bands at 622, 635, 645, and 704 cm−1 are assigned to the ν4 sulphate bending modes. The observation of multiple bands supports the concept of a reduction in symmetry of the sulphate anion from T d to C 3v or even C 2v.

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Sidorenkite is a very rare low-temperature hydrothermal mineral, formed very late in the crystallization of hyperagpaitic pegmatites in a differentiated alkalic massif (Mt. Alluaiv, Kola Peninsula, Russia). Sidorenkite Na3Mn(PO4)(CO3) is a phosphate–carbonate of sodium and manganese. Such a formula with two oxyanions lends itself to vibrational spectroscopy. The sharp Raman band at 959 cm−1 and 1012 cm−1 are assigned to the PO43− stretching modes, whilst the Raman bands at 1044 cm−1 and 1074 cm−1 are attributed to the CO32− stretching modes. It is noted that no Raman bands at around 800 cm−1 for sidorenkite were observed. The infrared spectrum of sidorenkite shows a quite intense band at 868 cm−1 with other resolved component bands at 850 and 862 cm−1. These bands are ascribed to the CO32− out-of-plane bend (ν2) bending mode. The series of Raman bands at 622, 635, 645 and 704 cm−1 are assigned to the ν4 phosphate bending modes. The observation of multiple bands supports the concept of a reduction in symmetry of the carbonate anion from D3h or even C2v.

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We have studied the mineral normandite using a combination of scanning electron microscopy with energy dispersive spectroscopy and vibrational spectroscopy. The mineral normandite NaCa(Mn2+,Fe2+)(Ti,Nb,Zr)Si2O7(O,F)2 is a crystalline sodium calcium silicate which contains rare earth elements. Chemical analysis shows the mineral contains a range of elements including Na, Mn2+, Ca, Fe2+ and the rare earth element niobium. No Raman bands are observed above 1100 cm−1. The mineral is characterised by Raman bands observed at 724, 748, 782 and 813 cm−1. Infrared bands are broad; nevertheless bands may be resolved at 723, 860, 910, 958, 933, 1057 and 1073 cm−1. Intense Raman bands at 454, 477 and 513 cm−1 are attributed to OSiO bending modes. No Raman bands are observed in the hydroxyl stretching region, but low intensity infrared bands are observed at 3191 and 3450 cm−1. This observation brings into question the true formula of the mineral.

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The mineral ushkovite has been analyzed using a combination of electron microscopy with EDX and vibrational spectroscopy. Chemical analysis shows the mineral contains P, Mg with very minor Fe. Thus, the formula of the studied ushkovite is Mg32+(PO4)2·8H2O. The Raman spectrum shows an intense band at 953 cm−1 assigned to the ν1 symmetric stretching mode. In the infrared spectra complexity exists with multiple antisymmetric stretching vibrations observed, due to the reduced tetrahedral symmetry. This loss of degeneracy is also reflected in the bending modes. Strong infrared bands around 827 cm−1 are attributed to water librational modes. The Raman spectra of the hydroxyl-stretching region are complex with overlapping broad bands. Hydroxyl stretching vibrations are identified at 2881, 2998, 3107, 3203, 3284 and 3457 cm−1. The wavenumber band at 3457 cm−1 is attributed to the presence of FeOH groups. This complexity is reflected in the water HOH bending modes where a strong infrared band centered around 1653 cm−1 is found. Such a band reflects the strong hydrogen bonding of the water molecules to the phosphate anions in adjacent layers. Spectra show three distinct OH bending bands from strongly hydrogen-bonded, weakly hydrogen bonded water and non-hydrogen bonded water. Vibrational spectroscopy enhances our knowledge of the molecular structure of ushkovite.

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When a new form is inserted in an existing townscape, its consonance within the urban fabric is dependent on the level of attention paid to the evaluation and management of its architectural elements. However, despite the established principles and methods of urban morphology that enable the systematic analysis of the built environment, a formula for ensuring that new development relates to its context so as to achieve congruent outcomes is still lacking. This paper proposes a new method of evaluating and measuring architectural elements within evolving urban forms, with particular emphasis on a three-dimensional study of buildings. In a case study, detailed mapping of both current and past forms provides the basis for evincing predominant characteristics that have changed over time. Using this method, it is possible to demonstrate objectively how the townscape has been affected through changes in its architectural configuration.

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The mineral fraipontite has been studied by using a combination of scanning electron microscopy with energy dispersive analysis and vibrational spectroscopy (infrared and Raman). Fraipontite is a member of the 1:1 clay minerals of the kaolinite-serpentine group. The mineral contains Zn and Cu and is of formula (Cu,Zn,Al)3(Si,Al)2O5(OH)4. Qualitative chemical analysis of fraipontite shows an aluminium silicate mineral with amounts of Cu and Zn. This kaolinite type mineral has been characterised by Raman and infrared spectroscopy; in this way aspects about the molecular structure of fraipontite clay are elucidated.

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The approach to remove greenhouse gases by pumping liquid CO2 several kilometres below the ground implies that many carbonate containing minerals will be formed. Among these minerals, the formation of hydromagnesite, dypingite and nesquehonite are possible, thus necessitating a study of such minerals. These minerals with a hydrotalcite-related formulae have been characterised by a combination of infrared and near infrared spectroscopy. Layered double hydroxides (also known as anionic clays or hydrotalcites) are a group of layered clay minerals described by the general formula: [M1–x2+Mx3+(OH)2]x+[An–]x/n∙mH2O. The infrared spectra of the minerals are characterised by OH and water stretching vibrations. Both the first and second fundamental overtones of these bands are observed in the NIR spectra in the 7030–7235 cm–1 and 10,490–10,570 cm–1 spectral ranges. Intense (CO3)2– symmetrical and anti-symmetrical stretching vibrations confirm the distortion of the carbonate anion. The position of the water bending vibration indicates water is strongly hydrogen-bonded to the carbonate anion in the mineral structure. NIR spectroscopy offers a method for quickly analysing such materials.

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The mineral lamprophyllite is fundamentally a silicate based upon tetrahedral siloxane units with extensive substitution in the formula. Lamprophyllite is a complex group of sorosilicates with general chemical formula given as A2B4C2Si2O7(X)4, where the site A can be occupied by strontium, barium, sodium, and potassium; the B site is occupied by sodium, titanium, iron, manganese, magnesium, and calcium. The site C is mainly occupied by titanium or ferric iron and X includes the anions fluoride, hydroxyl, and oxide. Chemical composition shows a homogeneous phase, composed of Si, Na, Ti, and Fe. This complexity of formula is reflected in the complexity of both the Raman and infrared spectra. The Raman spectrum is characterized by intense bands at 918 and 940 cm−1. Other intense Raman bands are found at 576, 671, and 707 cm−1. These bands are assigned to the stretching and bending modes of the tetrahedral siloxane units.

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The profiled steel roof and wall cladding systems in Australia are commonly made of very thin high tensile steels, and are crest-fixed with screw fasteners. A review of current literature and design standards indicated the need to improve the understanding of the behaviour of crest-fixed steel cladding systems under wind uplift/suction loading, in particular, the local failures. Therefore a detailed experimental study using a series of small scale tests and some two-span cladding tests was conducted to investigate the local pull-through and dimpling failures in the commonly used steel cladding systems. The applicability of the current design formulae for the pull-through strength of crest-fixed steel classing systems was investigated first. An improved design formula was then developed in terms of the thickness and ultimate tensile strenth of steel cladding material and diameter of screw head or washer. This paper presents the details of this investigation and its results. A review of current design and test methods is also included.

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Information from the full diffusion tensor (DT) was used to compute voxel-wise genetic contributions to brain fiber microstructure. First, we designed a new multivariate intraclass correlation formula in the log-Euclidean framework. We then analyzed used the full multivariate structure of the tensor in a multivariate version of a voxel-wise maximum-likelihood structural equation model (SEM) that computes the variance contributions in the DTs from genetic (A), common environmental (C) and unique environmental (E) factors. Our algorithm was tested on DT images from 25 identical and 25 fraternal twin pairs. After linear and fluid registration to a mean template, we computed the intraclass correlation and Falconer's heritability statistic for several scalar DT-derived measures and for the full multivariate tensors. Covariance matrices were found from the DTs, and inputted into SEM. Analyzing the full DT enhanced the detection of A and C effects. This approach should empower imaging genetics studies that use DTI.

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In the global construction context, the Best Value or Most Economically Advantageous Tender is becoming a widespread approach for contractor selection, as an alternative to other traditional awarding criteria such as the Lowest Price. In these multi-attribute tenders, the owner or auctioneer solicits proposals containing both a price bid and additional technical features. Once the proposals are received, each bidder's price bid is given an economic score according to a scoring rule, generally called an Economic Scoring Formula (ESF) and a technical score according to pre-specified criteria. Eventually, the contract is awarded to the bidder with the highest weighted overall score (economic + technical). However, Economic Scoring Formula selection by auctioneers is invariably and paradoxically a highly intuitive process in practice, involving few theoretical or empirical considerations, despite having being considered traditionally and mistakenly as objective, due to its mathematical nature. This paper provides a taxonomic classification of a wide variety of ESF and Abnormally Low Bid Criteria (ALBC) gathered in several countries with different tendering approaches. Practical implications concern the optimal design of price scoring rules in construction contract tenders, as well as future analyses of the effects of ESF and ALBC on competitive bidding behaviour.

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In 2013 the OECD released its 15 point Action plan to deal with base erosion and profit shifting (BEPS). In that plan it was recognised that BEPS has a significant effect on developing countries. This is because the lack of tax revenue can lead to a critical underfunding of public investment that would help promote economic growth. To this end, the BEPS project is aimed at ensuring an inclusive approach to take into account not only views of the G20 and OECD countries but also the perspective of developing nations. With this focus in mind and in the context of developing nations, the purpose of this article is to consider a possible solution to profit shifting which occurs under the current transfer pricing regime, with that solution being unitary taxation with formulary apportionment. It does so using the finance sector as a specific case for application. Multinational financial institutions (MNFIs) play a significant role in financing activities of their clients in developing nations. Consistent with the ‘follow-the-client’ phenomenon which explains financial institution expansion, these entities are increasingly profiting from activities associated with this growing market. Further, not only are MNFIs persistent users of tax havens but also, more than other industries, have opportunities to reduce tax through transfer pricing measures. This article establishes a case for an industry specific adoption of unitary taxation with formulary apportionment as a viable alternative to the current regime. It argues that such a model would benefit not only developed nations but also developing nations which are currently suffering the effects of BEPS. In doing so, it considers the practicalities of such an implementation by examining both definitional issues and a possible formula for MNFIs. This article argues that, while there would be implementation difficulties to overcome, the current domestic models of formulary apportionment provide important guidance as to how the unitary business and business activities of MNFIs should be defined as well as factors that should be included in an allocation formula, along with the appropriate weighting. While it would be difficult for developing nations to adopt such a regime, it is argued that it would be no more difficult than addressing issues they face with the current transfer pricing regime. As such, this article concludes that unitary taxation with formulary apportionment is a viable industry specific alternative for MNFIs which would assist developing nations and aid independent fiscal soundness.

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Multinational financial institutions (MNFIs) play a significant role in financing the activities of their clients in developing nations. Consistent with the ‘follow-the-customer’ phenomenon which explains financial institution expansion, these entities are increasingly profiting from activities associated with this growing market. However, not only are MNFIs persistent users of tax havens, but also, more than other industries, have the opportunity to reduce tax through transfer pricing measures. This paper establishes a case for an industry-specific adoption of unitary taxation with formulary apportionment as a viable alternative to the current regime. In doing so, it considers the practicalities of implementing this by examining both definitional issues and possible formulas for MNFIs. This paper argues that, while there would be implementation difficulties to overcome, the current domestic models of formulary apportionment provide important guidance as to how the unitary business and business activities of MNFIs should be defined, as well as the factors that should be included in an allocation formula, and the appropriate weighting. This paper concludes that unitary taxation with formulary apportionment is a viable industry-specific alternative for MNFIs.

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Tapered tubular steel masts are commonly used to support floodlights in a range of applications. The design of these slender tapered masts requires a rational elastic flexural buckling analysis as the thickness also varies with height. Therefore a series of finite element analyses of tapered masts with varying geometry parameters was conducted to develop an elastic flexural buckling load formula. This paper briefly discusses the design methods, and then presents the details of the finite element analyses and the results. 1–Associate Professor of Civil Engineering, and Director, Physical Infrastructure Centre 2–Former BE (Civil) Student, QUT

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This paper presents an unmanned aircraft system (UAS) that uses a probabilistic model for autonomous front-on environmental sensing or photography of a target. The system is based on low-cost and readily-available sensor systems in dynamic environments and with the general intent of improving the capabilities of dynamic waypoint-based navigation systems for a low-cost UAS. The behavioural dynamics of target movement for the design of a Kalman filter and Markov model-based prediction algorithm are included. Geometrical concepts and the Haversine formula are applied to the maximum likelihood case in order to make a prediction regarding a future state of a target, thus delivering a new waypoint for autonomous navigation. The results of the application to aerial filming with low-cost UAS are presented, achieving the desired goal of maintained front-on perspective without significant constraint to the route or pace of target movement.