154 resultados para Signless Laplacian spectrum of a graph


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Some minerals are colloidal and show no X-ray diffraction patterns. Vibrational spectroscopy offers one of the few methods for the determination of the structure of these minerals. Among this group of minerals is pitticite, simply described as (Fe, AsO4, SO4, H2O). In this work, the analogue of the mineral pitticite has been synthesised. The objective of this research is to determine the molecular structure of the mineral pitticite using vibrational spectroscopy. Raman and infrared bands are attributed to the AsO43−, SO42− and water stretching and bending vibrations. The Raman spectrum of the pitticite analogue shows intense peaks at 845 and 837 cm−1 assigned to the AsO43− stretching vibrations. Raman bands at 1096 and 1182 cm−1 are attributed to the SO42− antisymmetric stretching bands. Raman spectroscopy offers a useful method for the analysis of such colloidal minerals.

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Plumbogummite PbAl3(PO4)2(OH,H2O)6 is a mineral of environmental significance and is a member of the alunite-jarosite supergroup. The molecular structure of the mineral has been investigated by Raman spectroscopy. The spectra of different plumbogummite specimens differ although there are many common features. The Raman spectra prove the spectral profile consisting of overlapping bands and shoulders. Raman bands and shoulders observed at 971, 980, 1002 and 1023 cm−1 (China sample) and 913, 981, 996 and 1026 cm−1 (Czech sample) are assigned to the ν1 symmetric stretching modes of the (PO4)3−, at 1002 and 1023 cm−1 (China) and 996 and 1026 cm−1 to the ν1 symmetric stretching vibrations of the (O3POH)2− units, and those at 1057, 1106 and 1182 (China) and at 1102, 1104 and 1179 cm−1 (Czech) to the ν3 (PO4)3− and ν3 (PO3) antisymmetric stretching vibrations. Raman bands and shoulders at 634, 613 and 579 cm−1 (China) and 611 and 596 cm−1 (Czech) are attributed to the ν4 (δ) (PO4)3− bending vibrations and those at 507, 494 and 464 cm−1 (China) and 505 and 464 cm−1 (Czech) to the ν2 (δ) (PO4)3− bending vibrations. The Raman spectrum of the OH stretching region is complex. Raman bands and shoulders are identified at 2824, 3121, 3249, 3372, 3479 and 3602 cm−1 for plumbogummite from China, and at 3077, 3227, 3362, 3480, 3518 and 3601 cm−1 for the Czech Republic sample. These bands are assigned to the ν OH stretching modes of water molecules and hydrogen ions. Approximate O–H⋯O hydrogen bond lengths inferred from the Raman spectra vary in the range >3.2–2.62 Å (China) and >3.2–2.67 Å (Czech). The minority presence of some carbonate ions in the plumbogummite (China sample) is connected with distinctive intensity increasing of the Raman band at 1106 cm−1, in which may participate the ν1 (CO3)2− symmetric stretching vibration overlapped with phosphate stretching vibrations.

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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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We have characterized anapaite Ca2Fe2+(PO4)2·4(H2O), a rare Ca and Fe phosphate, using a combination of electron microscopy and vibrational spectroscopy. The mineral occurs in soils and lacustrine sediments and is usually related to the diagenetic process in phosphorous rich sediments. The phosphate anion is characterized by its Raman spectrum with an intense sharp band at 943 cm-1, attributed to the ν1 PO4 3- symmetric stretching mode. Three bands at 992, 1039 and 1071 cm-1 are attributed to ν3 PO4 3-antisymmetric stretching modes. The infrared spectrum of anapaite shows complexity with a series of overlapping bands. Water in the structure of anapaite is observed by OH stretching vibrations at 2777, 3022 and 3176 cm-1 (Raman) and 2744, 3014 and 3096 cm-1 (infrared). The position of these bands provides evidence for the strong hydrogen bonding of water in the anapaite structure and contributes to the stability of the mineral.

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Raman spectrum of callaghanite, Cu2Mg2(CO3)(OH)6⋅2H2O, was studied and compared with published Raman spectra of azurite, malachite and hydromagnesite. Stretching and bending vibrations of carbonate and hydroxyl units and water molecules were tentatively assigned. Approximate O–H…O hydrogen bond lengths were inferred from the spectra. Because of the high content of hydroxyl ions in the crystal structure in comparison with low content of carbonate units, callaghanite should be better classified as a carbonatohydroxide than a hydroxycarbonate.

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This research was done on hureaulite samples from the Cigana claim, a lithium bearing pegmatite with triphylite and spodumene. The mine is located in Conselheiro Pena, east of Minas Gerais. Chemical analysis was carried out by Electron Microprobe analysis and indicated a manganese rich phase with partial substitution of iron. The calculated chemical formula of the studied sample is: (Mn3.23, Fe1.04, Ca0.19, Mg0.13)(PO4)2.7(HPO4)2.6(OH)4.78. The Raman spectrum of hureaulite is dominated by an intense sharp band at 959 cm−1 assigned to PO stretching vibrations of HPO42− units. The Raman band at 989 cm−1 is assigned to the PO43− stretching vibration. Raman bands at 1007, 1024, 1047, and 1083 cm−1 are attributed to both the HOP and PO antisymmetric stretching vibrations of HPO42− and PO43− units. A set of Raman bands at 531, 543, 564 and 582 cm−1 are assigned to the ν4 bending modes of the HPO42− and PO43− units. Raman bands observed at 414, and 455 cm−1 are attributed to the ν2 HPO42− and PO43− units. The intense A series of Raman and infrared bands in the OH stretching region are assigned to water stretching vibrations. Based upon the position of these bands hydrogen bond distances are calculated. Hydrogen bond distances are short indicating very strong hydrogen bonding in the hureaulite structure. A combination of Raman and infrared spectroscopy enabled aspects of the molecular structure of the mineral hureaulite to be understood.

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Vibrational spectroscopy enables subtle details of the molecular structure of cyrilovite to be determined. Single crystals of a pure phase from a Brazilian pegmatite were used. Cyrilovite is the Fe3+ member of the wardite group. The infrared and Raman spectroscopy were applied to compare the structure of cyrilovite with that of wardite. The Raman spectrum of cyrilovite in the 800–1400 cm−1 spectral range shows two intense bands at 992 and 1055 cm−1 assigned to the ν1View the MathML source symmetric stretching vibrations. A series of low intensity bands at 1105, 1136, 1177 and 1184 cm−1 are assigned to the ν3View the MathML source antisymmetric stretching modes. The infrared spectrum of cyrilovite in the 500–1300 cm−1 shows much greater complexity than the Raman spectrum. Strong infrared bands are found at 970 and 1007 cm−1 and are attributed to the ν1View the MathML source symmetric stretching mode. Raman bands are observed at 612 and 631 cm−1 and are assigned to the ν4 out of plane bending modes of the View the MathML source unit. In the 2600–3800 cm−1 spectral range, intense Raman bands for cyrilovite are found at 3328 and 3452 cm−1 with a broad shoulder at 3194 cm−1 and are assigned to OH stretching vibrations. Sharp infrared bands are observed at 3485 and 3538 cm−1. Raman spectroscopy complimented with infrared spectroscopy has enabled the structure of cyrilovite to be ascertained and compared with that of wardite.

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The mineral weloganite Na2Sr3Zr(CO3)6·3H2O has been studied by using vibrational spectroscopy and a comparison is made with the spectra of weloganite with other carbonate minerals. Weloganite is member of the mckelveyite group that includes donnayite-(Y) and mckelveyite-(Y). The Raman spectrum of weloganite is characterized by an intense band at 1082 cm−1 with shoulder bands at 1061 and 1073 cm−1, attributed to the View the MathML source symmetric stretching vibration. The observation of three symmetric stretching vibrations is very unusual. The position of View the MathML source symmetric stretching vibration varies with mineral composition. The Raman bands at 1350, 1371, 1385, 1417, 1526, 1546, and 1563 cm−1 are assigned to the ν3 (CO3)2− antisymmetric stretching mode. The observation of additional Raman bands for the ν3 modes for weloganite is significant in that it shows distortion of the carbonate anion in the mineral structure. The Raman band observed at 870 cm−1 is assigned to the (CO3)2− ν2 bending mode. Raman bands observed for weloganite at 679, 682, 696, 728, 736, 749, and 762 cm−1 are assigned to the (CO3)2− ν4 bending modes. A comparison of the vibrational spectra is made with that of the rare earth carbonates decrespignyite, bastnasite, hydroxybastnasite, parisite, and northupite.

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The mineral creedite is a fluorinated hydroxy hydrated sulphate of aluminium and calcium of formula Ca3Al2SO4(F,OH)·2H2O. The mineral has been studied by a combination of electron probe analysis to determine the molecular formula of the mineral and the structure assessed by vibrational spectroscopy. The spectroscopy of creedite may be compared with that of the alums. The Raman spectrum of creedite is characterised by an intense sharp band at 986 cm−1 assigned to the View the MathML source ν1 (Ag) symmetric stretching mode. Multiple bands of creedite in the antisymmetric stretching region support the concept of a reduction in symmetry of the sulphate anion. Multiple bands are also observed in the bending region with the three bands at 601, 629 and 663 cm−1 assigned to the View the MathML source ν4 (Ag) bending modes. The observation of multiple bands at 440, 457 and 483 cm−1 attributed to the View the MathML source ν2 (Bg) bending modes supports the concept that the symmetry of the sulphate is reduced by coordination to the water bonded to the Al3+ in the creedite structure. The splitting of the ν2, ν3 and ν4 modes is attributed to the reduction of symmetry of the SO4 and it is proposed that the sulphate coordinates to water in the hydrated aluminium in bidentate chelation.

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The conventional mechanical properties of articular cartilage, such as compressive stiffness, have been demonstrated to be limited in their capacity to distinguish intact (visually normal) from degraded cartilage samples. In this paper, we explore the correlation between a new mechanical parameter, namely the reswelling of articular cartilage following unloading from a given compressive load, and the near infrared (NIR) spectrum. The capacity to distinguish mechanically intact from proteoglycan-depleted tissue relative to the "reswelling" characteristic was first established, and the result was subsequently correlated with the NIR spectral data of the respective tissue samples. To achieve this, normal intact and enzymatically degraded samples were subjected to both NIR probing and mechanical compression based on a load-unload-reswelling protocol. The parameter δ(r), characteristic of the osmotic "reswelling" of the matrix after unloading to a constant small load in the order of the osmotic pressure of cartilage, was obtained for the different sample types. Multivariate statistics was employed to determine the degree of correlation between δ(r) and the NIR absorption spectrum of relevant specimens using Partial Least Squared (PLS) regression. The results show a strong relationship (R(2)=95.89%, p<0.0001) between the spectral data and δ(r). This correlation of δ(r) with NIR spectral data suggests the potential for determining the reswelling characteristics non-destructively. It was also observed that δ(r) values bear a significant relationship with the cartilage matrix integrity, indicated by its proteoglycan content, and can therefore differentiate between normal and artificially degraded proteoglycan-depleted cartilage samples. It is therefore argued that the reswelling of cartilage, which is both biochemical (osmotic) and mechanical (hydrostatic pressure) in origin, could be a strong candidate for characterizing the tissue, especially in regions surrounding focal cartilage defects in joints.

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Objectives: To investigate the frequency characteristics of the ground reaction force (GRF) recorded throughout the eccentric Achilles tendon rehabilitation programme described by Alfredson. Design: Controlled laboratory study, longitudinal. Methods: Nine healthy adult males performed six sets (15 repetitions per set) of eccentric ankle exercise. Ground reaction force was recorded throughout the exercise protocol. For each exercise repetition the frequency power spectrum of the resultant ground reaction force was calculated and normalised to total power. The magnitude of peak relative power within the 8-12 Hz bandwidth and the frequency at which this peak occurred was determined. Results: The magnitude of peak relative power within the 8-12 Hz bandwidth increased with each successive exercise set and following the 4th set (60 repetitions) of exercise the frequency at which peak relative power occurred shifted from 9 to 10 Hz. Conclusions: The increase in magnitude and frequency of ground reaction force vibrations with an increasing number of exercise repetitions is likely connected to changes in muscle activation with fatigue and tendon conditioning. This research illustrates the potential for the number of exercise repetitions performed to influence the tendons' mechanical environment, with implications for tendon remodelling and the clinical efficacy of eccentric rehabilitation programmes for Achilles tendinopathy.

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Introduction: Eccentric exercise (EE) is a commonly used treatment for Achilles tendinopathy. While vibrations in the 8–12 Hz frequency range generated during eccentric muscle actions have been put forward as a potential mechanism for the beneficial effect of EE, optimal loading parameters required to expedite recovery are currently unknown. Alfredson's original protocol employed 90 repetitions of eccentric loading, however abbreviated protocols consisting of fewer repetitions (typically 45) have been developed, albeit with less beneficial effect. Given that 8–12 Hz vibrations generated during isometric muscle actions have been previously shown to increase with fatigue, this research evaluated the effect of exercise repetition on motor output vibrations generated during EE by investigating the frequency characteristics of ground reaction force (GRF) recorded throughout the 90 repetitions of Alfredson's protocol. Methods: Nine healthy adult males performed six sets (15 repetitions per set) of eccentric ankle exercise. GRF was recorded at a frequency of 1000 Hz throughout the exercise protocol. The frequency power spectrum of the resultant GRF was calculated and normalized to total power. Relative spectral power was summed over 1 Hz widows within the frequency rage 7.5–11.5 Hz. The effect of each additional exercise set (15 repetitions) on the relative power within each widow was investigated using a general linear modelling approach. Results: The magnitude of peak relative power within the 7.5–11.5 Hz bandwidth increased across the six exercise sets from 0.03 in exercise set one to 0.12 in exercise set six (P < 0.05). Following the 4th set of exercise the frequency at which peak relative power occurred shifted from 9 to 10 Hz. Discussion: This study has demonstrated that successive repetitions of eccentric loading over six exercise sets results in an increase in the amplitude of motor output vibrations in the 7.5–11.5 Hz bandwidth, with an increase in the frequency of these vibrations occurring after the 4th set (60th repetition). These findings are consistent with findings from previous studies of muscle fatigue. Assuming that the magnitude and frequency of these vibrations represent important stimuli for tendon remodelling as hypothesized within the literature, the findings of this study question the role of abbreviated EE protocols and raise the question; can EE protocols for tendinopathy be optimized by performing eccentric loading to fatigue?

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Introduction Previous research has demonstrated that ground reaction force (GRF) recorded during eccentric ankle exercise is characterised by greater power in the 8-12Hz bandwidth when compared to that recorded during concentric ankle exercise. Subsequently, it was suggested that vibrations in this bandwidth may underpin the beneficial effect of eccentric loading in tendon repair. However, this observation has been made only in individuals without Achilles tendinopathy. This research compared the force frequency characteristics of eccentric and concentric exercises in individuals with and without Achilles tendinopathy., Methods Eleven male adults with unilateral mid-portion Achilles tendinopathy and nine control male adults without tendinopathy participated in the research. Kinematics and GRF were recorded while the participants performed a common eccentric rehabilitation exercise protocol and a concentric equivalent. Ankle joint kinematics and the frequency power spectrum of the resultant GRF were calculated. Results Eccentric exercise was characterised by a significantly greater proportion of spectral power between 4.5 and 11.5Hz when compared to concentric exercise. There were no significant differences between limbs in the force frequency characteristics of concentric exercise. Eccentric exercise, in contrast, was defined by a shift in the power spectrum of the symptomatic limb, resulting in a second spectral peak at 9Hz, rather than 10Hz in the control limb. Conclusions Compared to healthy tendon, Achilles tendinopathy was characterised by lower frequency vibrations during eccentric rehabilitation exercises. This finding may be associated with changes in neuromuscular activation and tendon stiffness which have been shown to occur with tendinopathy and provides a possible rationale for the previous observation of a different biochemical response to eccentric exercise in healthy and injured Achilles tendons., (C)2012The American College of Sports Medicine

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The mineral amarantite Fe23+(SO4)O∙7H2O has been studied using a combination of techniques including thermogravimetry, electron probe analyses and vibrational spectroscopy. Thermal analysis shows decomposition steps at 77.63, 192.2, 550 and 641.4°C. The Raman spectrum of amarantite is dominated by an intense band at 1017 cm-1 assigned to the SO42- ν1 symmetric stretching mode. Raman bands at 1039, 1054, 1098, 1131, 1195 and 1233 cm-1 are attributed to the SO42- ν3 antisymmetric stretching modes. Very intense Raman band is observed at 409 cm-1 with shoulder bands at 399, 451 and 491 cm-1 are assigned to the v2 bending modes. A series of low intensity Raman bands are found at 543, 602, 622 and 650 cm-1 are assigned to the v4 bending modes. A very sharp Raman band at 3529 cm-1 is assigned to the stretching vibration of OH units. A series of Raman bands observed at 3025, 3089, 3227, 3340, 3401 and 3480 cm-1 are assigned to water bands. Vibrational spectroscopy enables aspects of the molecular structure of the mineral amarantite to be ascertained.

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Meyerhofferite is a calcium hydrated borate mineral with ideal formula: CaB3O3(OH)5�H2O and occurs as white complex acicular to crude crystals with length up to �4 cm, in fibrous divergent, radiating aggregates or reticulated and is often found in sedimentary or lake-bed borate deposits. The Raman spectrum of meyerhofferite is dominated by intense sharp band at 880 cm�1 assigned to the symmetric stretching mode of trigonal boron. Broad Raman bands at 1046, 1110, 1135 and 1201 cm�1 are attributed to BOH in-plane bending modes. Raman bands in the 900–1000 cm�1 spectral region are assigned to the antisymmetric stretching of tetrahedral boron. Distinct OH stretching Raman bands are observed at 3400, 3483 and 3608 cm�1. The mineral meyerhofferite has a distinct Raman spectrum which is different from the spectrum of other borate minerals, making Raman spectroscopy a very useful tool for the detection of meyerhofferite in sedimentary and lake bed deposits.