212 resultados para Legendre Formula


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Certain statistic and scientometric features of articles published in the journal “International Research in Geographical and Environmental Education” are examined in this paper, for the period 1992-2009, by applying nonparametric statistics and Shannon’s entropy (diversity) formula. The main findings of this analysis are: a) after 2004 the research priorities of researchers in geographical and environmental education seem to have changed, b) “teacher education” has been the most recurrent theme throughout these 18 years, followed by “values & attitudes” and “inquiry & problem solving” c) the themes “GIS” and “Sustainability” were the most “stable” throughout the 18 years, meaning that they maintained their ranks as publication priorities more than other themes, d) citations of IRGEE increase annually, e) the average thematic diversity of articles published during the period 1992-2009 is 82.7% of the maximum thematic diversity (very high), meaning that the Journal has the capacity to attract a wide readership for the 10 themes it has successfully covered throughout the 18 years of its publication.

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Concrete made of brick chips as coarse aggregate are extensively used in Bangladesh for construction of different types of structures from residential and commercial buildings to industrial complex. As creep is influenced among many factors including the constituents’ materials, relative humidity and temperature, it is essential to examine the creep behavior for Bangladeshi brick chips made concrete in Bangladeshi environment. In this work, investigation on the behaviour of creep in concrete of same grade made with brick chips collected from various locations under single stage loading was done. With these investigations, a formula was derived to get theoretical creep values for 24 MPa brick chips made concrete in Bangladeshi environment.

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In this paper we investigate the distribution of the product of Rayleigh distributed random variables. Considering the Mellin-Barnes inversion formula and using the saddle point approach we obtain an upper bound for the product distribution. The accuracy of this tail-approximation increases as the number of random variables in the product increase.

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We present experimental results that demonstrate that the wavelength of the fundamental localised surface plasmon resonance for spherical gold nanoparticles on glass can be predicted using a simple, one line analytical formula derived from the electrostatic eigenmode method. This allows the role of the substrate in lifting mode degeneracies to be determined, and the role of local environment refractive indices on the plasmon resonance to be investigated. The effect of adding silica to the casting solution in minimizing nanopaticle agglomeration is also discussed.

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Boracite is a magnesium borate mineral with formula: Mg3B7O13Cl and occurs as blue green, colorless, gray, yellow to white crystals in the orthorhombic – pyramidal crystal system. An intense Raman band at 1009 cm−1 was assigned to the BO stretching vibration of the B7O13 units. Raman bands at 1121, 1136, 1143 cm−1 are attributed to the in-plane bending vibrations of trigonal boron. Four sharp Raman bands observed at 415, 494, 621 and 671 cm−1 are simply defined as trigonal and tetrahedral borate bending modes. The Raman spectrum clearly shows intense Raman bands at 3405 and 3494 cm−1, thus indicating that some Cl anions have been replaced with OH units. The molecular structure of a natural boracite has been assessed by using vibrational spectroscopy.

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Detailed investigation of an intermediate member of the reddingite–phosphoferrite series, using infrared and Raman spectroscopy, scanning electron microcopy and electron microprobe analysis, has been carried out on a homogeneous sample from a lithium-bearing pegmatite named Cigana mine, near Conselheiro Pena, Minas Gerais, Brazil. The determined formula is (Mn1.60Fe1.21Ca0.01Mg0.01)∑2.83(PO4)2.12⋅(H2O2.85F0.01)∑2.86 indicating predominance in the reddingite member. Raman spectroscopy coupled with infrared spectroscopy supports the concept of phosphate, hydrogen phosphate and dihydrogen phosphate units in the structure of reddingite-phosphoferrite. Infrared and Raman bands attributed to water and hydroxyl stretching modes are identified. Vibrational spectroscopy adds useful information to the molecular structure of reddingite–phosphoferrite.

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The formation of new materials in the form of alumino-silicate derivatives from 2:1 layer clay materials which are obtained by the chemical modification of 2:1 layer clay minerals by reaction with a salt having the formula MX wherein M is ammonium ion or alkali metal cation and X is a halide. The new materials have the following characteristics: (a) an amorphous x-ray diffraction signal manifest as a broad hump using x-ray powder diffraction between 22.degree. and 32.degree. 2.theta. using CuK.alpha. radiation; and (b) the presence of primarily tetrahedrally coordinated aluminum.

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A process for the preparation of an amorphous alumino-silicate derivative which involves reacting a solid corresponding starting material with MOH where M is alkali metal or ammonium cation. The solid corresponding starting material may be selected from montmorillonite, kaolin, natural zeolite (e.g., clinoliptolite/heulandite) as well as illite, palygorskite and saponite and additional reactant MX wherein X is halide may be utilized in conjunction with MOH. The invention also includes alumino-silicate derivatives of the general formula M.sub.p Al.sub.q Si.sub.2 O.sub.r (OH).sub.s X.sub.t.uH.sub.2 O as well as alumino-silicate derivatives of the general formula M.sub.p Al.sub.q Si.sub.2 O.sub.r (OH).sub.s.uH.sub.2 O.

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Background: Recommendations for the introduction of solids and fluids to an infant’s diet have changed over the past decade. Since these changes, there has been minimal research to determine patterns in the introduction of foods and fluids to infants. Methods: This retrospective cohort study surveyed mothers who birthed in Queensland, Australia, from February 1 to May 31, 2010, around 4 months postpartum. Frequencies of foods and fluids given to infants at 4, 8, 13, and 17 weeks were described. Logistic regression determined associations between infant feeding practices, the introduction of other foods and fluids at 17 weeks, and sociodemographic characteristics. Results: Response rate was 35.8%. At 17 weeks, 68% of infants were breastfed and 33% exclusively breastfed. Solids and water had been introduced in 8.6% and 35.0% of infants, respectively. The introduction of solids by 17 weeks was associated with younger maternal age and the infant being given water and infant formula at 4 weeks. The infant being given water at 17 weeks was associated with younger maternal age, the infant being given infant formula at 4 weeks, level of education, relative socioeconomic disadvantage, parity, and birth facility. Conclusion: Over the past decade, there has been a significant reduction in the proportion of infants in Australia who have been given solids by 17 weeks. Sociodemographic characteristics and formula feeding practices at 4 weeks were associated with the introduction of solids and water by 17 weeks. Further research should examine these barriers to improve compliance with current infant feeding recommendations.

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Previous studies have enabled exact prediction of probabilities of identity-by-descent (IBD) in randommating populations for a few loci (up to four or so), with extension to more using approximate regression methods. Here we present a precise predictor of multiple-locus IBD using simple formulas based on exact results for two loci. In particular, the probability of non-IBD X ABC at each of ordered loci A, B, and C can be well approximated by XABC = XABXBC/XB and generalizes to X123. . .k = X12X23. . .Xk-1,k/ Xk-2, where X is the probability of non-IBD at each locus. Predictions from this chain rule are very precise with population bottlenecks and migration, but are rather poorer in the presence of mutation. From these coefficients, the probabilities of multilocus IBD and non-IBD can also be computed for genomic regions as functions of population size, time, and map distances. An approximate but simple recurrence formula is also developed, which generally is less accurate than the chain rule but is more robust with mutation. Used together with the chain rule it leads to explicit equations for non-IBD in a region. The results can be applied to detection of quantitative trait loci (QTL) by computing the probability of IBD at candidate loci in terms of identity-by-state at neighboring markers.

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The presence of arsenic in the environment is a hazard. The accumulation of arsenate by a range of cations in the formation of minerals provides a mechanism for the remediation of arsenate contamination. The formation of the crandallite group of minerals provides a mechanism for arsenate accumulation. Among the crandallite minerals are philipsbornite, arsenocrandallite and arsenogoyazite. Raman spectroscopy complimented with infrared spectroscopy has enabled aspects of the structure of philipsbornite to be studied. The Raman spectrum of philipsbornite displays an intense band at around 840 cm−1 attributed to the overlap of the symmetric and antisymmetric stretching modes. Raman bands observed at 325, 336, 347, 357, 376 and 399 cm−1 are assigned to the ν2 (AsO4)3− symmetric bending vibration (E) and to the ν4 bending vibration (F2). The observation of multiple bending modes supports the concept of a reduction in symmetry of the arsenate anion in philipsbornite. Evidence for phosphate in the mineral is provided. By using an empirical formula, hydrogen bond distances for the OH units in philipsbornite of 2.8648 Å, 2.7864 Å, 2.6896 Å cm−1 and 2.6220 were calculated.

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Zanazziite is the magnesium member of a complex beryllium calcium phosphate mineral group named roscherite. The studied samples were collected from the Ponte do Piauí mine, located in Itinga, Minas Gerais. The mineral was studied by electron microprobe, Raman and infrared spectroscopy. The chemical formula can be expressed as Ca2.00(Mg3.15,Fe0.78,Mn0.16,Zn0.01,Al0.26,Ca0.14)Be4.00(PO4)6.09(OH)4.00⋅5.69(H2O) and shows an intermediate member of the zanazziite–greinfeinstenite series, with predominance of zanazziite member. The molecular structure of the mineral zanazziite has been determined using a combination of Raman and infrared spectroscopy. A very intense Raman band at 970 cm−1 is assigned to the phosphate symmetric stretching mode whilst the Raman bands at 1007, 1047, 1064 and 1096 cm−1 are attributed to the phosphate antisymmetric stretching mode. The infrared spectrum is broad and the antisymmetric stretching bands are prominent. Raman bands at 559, 568, 589 cm−1 are assigned to the ν4 out of plane bending modes of the PO4 and HPO4 units. The observation of multiple bands supports the concept that the symmetry of the phosphate unit in the zanazziite structure is reduced in symmetry. Raman bands at 3437 and 3447 cm−1 are attributed to the OH stretching vibrations; Raman bands at 3098 and 3256 are attributed to water stretching vibrations. The width and complexity of the infrared spectral profile in contrast to the well resolved Raman spectra, proves that the pegmatitic phosphates are better studied with Raman spectroscopy.

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We have used vibrational spectroscopy to study the formula and molecular structure of the mineral penkvilksite Na 2TiSi 4O 11·2H 2O. Penkvilksite is a mineral which may be used in the uptake of radioactive elements. Both Raman and infrared spectroscopies identify a band at 3638 cm−1 attributed to an OH-stretching vibration of hydroxyl units. The inference is that OH units are involved in the structure of penkvilksite. The formula may be well written as Na 2TiSi 4O 10(OH)2·H 2O. The mineral is characterised by a very intense Raman band at 1085 cm−1 and a broad infrared band at 1080 cm−1 assigned to SiO-stretching vibrations. Raman bands at 620, 667 and 711 cm−1 are attributed to SiO and TiO chain bonds. Water-stretching vibrations are observed as Raman bands at 3197, 3265, 3425 and 3565 cm−1. Vibrational spectroscopy enables aspects of the molecular structure of the mineral penkvilksite to be ascertained. Penkvilksite is a mineral which can incorporate actinides and lanthanides from radioactive waste.

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Palygorskite has a fibrous like morphology with a distinctive layered appearance. The simplified formula of palygorskite (Mg5Si8O20(OH)2(OH2)4 nH2O) indicates that two different types of water are present. The dehydration and rehydration of palygorskite have been studied using thermogravimetry and H2O-tem- perature programmed desorption. X-ray diffractograms, NH3 adsorption profiles, and NH3 desorption profiles were obtained for thermally treated palygorskite as a function of temperature. The results proved water molecules were mainly derived from Si–OH units. In addition, five kinds of acid sites were found for palygorskite. The number of acid sites of external surfaces was larger than that of the internal sur- faces. Bonding on the internal surface acid sites was stronger than the bonding of the external surfaces. Rehydration restored the folded structure of palygorskite when thermal treatment temperature was lower than 300 oC.

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Papagoite is a silicate mineral named after an American Indian tribe and was used as a healing mineral. Papagoite CaCuAlSi2O6(OH)3 is a hydroxy mixed anion compound with both silicate and hydroxyl anions in the formula. The structural characterization of the mineral papagoite remains incomplete. Papagoite is a four-membered ring silicate with Cu2+ in square planar coordination. The intense sharp Raman band at 1053 cm−1 is assigned to the ν1 (A 1g) symmetric stretching vibration of the SiO4 units. The splitting of the ν3 vibrational mode offers support to the concept that the SiO4 tetrahedron in papagoite is strongly distorted. A very intense Raman band observed at 630 cm−1 with a shoulder at 644 cm−1 is assigned to the ν4 vibrational modes. Intense Raman bands at 419 and 460 cm−1 are attributed to the ν2 bending modes. Intense Raman bands at 3545 and 3573 cm−1 are assigned to the stretching vibrations of the OH units. Low-intensity Raman bands at 3368 and 3453 cm−1 are assigned to water stretching modes. It is suggested that the formula of papagoite is more likely to be CaCuAlSi2O6(OH)3 · xH2O. Hence, vibrational spectroscopy has been used to characterize the molecular structure of papagoite.