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1.
Approximation problems on the rotation group SO(3) naturally arise in various fields, like crystallography, chemistry, and biology. For example, in crystallographic texture analysis one is confronted with the problem of evaluating so-called orientation density functions (ODFs). In many situations one only has a finite number of measurements at scattered sampling nodes. In order to reconstruct ODFs over all rotations, so-called Marcinkiewicz–Zygmund inequalities on the rotation group are an important tool. These inequalities provide norm equivalences between polynomials on SO(3) and their sample values. Recently shown equivalences depend on a density parameter of the sampling set and the proven inequalities hold true for polynomials on SO(3) whose degree does not exceed an upper bound which is determined by this density parameter. In this paper, we show that we can enlarge this upper bound for the polynomial degree significantly if we are satisfied by such norm equivalences that hold with a given probability only. Moreover, we show that there are fixed sampling sets for which we get probabilistic Marcinkiewicz–Zygmund inequalities that hold for polynomials on SO(3) of all degrees.  相似文献   

2.
A new style of komatiite-associated sulfide-poor platinum-group element (PGE: Os, Ir, Ru, Rh, Pt, Pd) mineralisation has been identified at Wiluna in the strongly nickel sulfide (NiS) mineralised Agnew – Wiluna Greenstone Belt, Western Australia. The komatiite sequence at Wiluna is ~200 m thick and comprises a basal pyroxenite layer, a thick ortho-to-mesocumulate-textured peridotite core, which is overlain by rhythmically layered wehrlite, oikocrystic pyroxenite and thick upper gabbroic margins. Pegmatoid and dendritic (harrisitic) domains are common features, whereas spinifex-textured horizons and flow-top breccias are absent. The presence of anomalous PGE-enriched horizons (ΣPt – Pd = 200 – 500 ppb) in the oikocrystic pyroxenite and in the layered melagabbro and gabbronorite horizons directly overlying the wehrlite unit is due to the presence of fine-grained (1 – 10 μm) platinum-group minerals (PGMs). More than 70 PGM grains were identified, and a considerable mineralogical variability was constrained. However, only Pd – Pt-bearing phases were identified, whereas no Ir – Ru-bearing PGMs were found in any of the sections examined. Interestingly, all PGMs are not in paragenetic association with sulfides, and only sulfide-poor/free intervals contain significant PGM concentrations. The whole-rock PGE sequence largely reflects the PGM distribution. It is hypothesised that the Pd – Pt enrichment in the oikocrystic pyroxenite and melagabbros and the overall Ir – Ru depletion in the upper mafic section of the sequence are the result of extensive olivine and chromite crystallisation in the basal ultramafic section. PGE saturation was driven by extensive crystallisation of silicate and oxide phases in a sulfide-undersaturated environment. The crystallisation of clinopyroxene in the oikocrystic pyroxenite horizon may have triggered the formation of Pt – Pd-bearing alloys and arsenides, which were the first PGMs to form. Stratiform sulfide-poor PGE mineralisation at Wiluna is more similar in stratigraphic setting, style and composition to PGE-rich sulfide-poor mineralisation zones in thick differentiated intrusions, rather than to other PGE-enriched zones in komatiite-hosted systems, where PGE enrichment is directly associated with accumulations of magmatic sulfides.  相似文献   

3.
Based on the fracture trace length distribution, conditions for the existence, uniqueness, and correctness of the fracture diameter distribution are given using Warburton’s fracture model. In particular, a solution for the fracture diameter distribution exists and is unique for all trace length probability density functions, h A (y), such that \(h_{A}(y)/\sqrt{y^{2}-x^{2}}\) is Lebesgue integrable on [x,∞). This condition is met by the uniform, exponential, gamma, lognormal, and power-law trace length distributions as well as by the trace length distributions that arise from a deterministic fracture diameter or from a discontinuous fracture diameter length distribution. Exponential, gamma, lognormal, and power-law trace length distributions satisfy necessary conditions for the diameter distribution to be non-negative, and necessary and sufficient conditions for the distribution to have unit integral over the real line. Negative values of the fracture diameter distribution arise when the trace has a uniform distribution and the lower bound of the fracture trace is greater than zero.  相似文献   

4.
The Pliocene to possibly Pleistocene uppermost Orubadi and Era Formations, southwest margin of the Papuan Peninsula, are interpreted as having been deposited in alluvial-fan, fan-delta and shallow-marine environments. The alluvial-fan facies consists primarily of lenticular, coarse-grained conglomerate (up to 2 m boulders) and cross-bedded and horizontally laminated sandstone. Conglomerate and sandstone were deposited in shallow fluvial channels and by overbank sheetfloods. The facies also contains thick mudflow diamictite and minor tuff and terrestrial mudstone. The shallow-marine and fan-delta facies, in contrast, consists of heterogeneously interbedded marine and terrestrial mudstone, sandstone, diamictite, conglomerate and limestone. Marine mudstone is calcareous, sandy, bioturbated, and contains marine shells. Limestone is mostly packstone that has a varied, open-marine fauna. Rare coral boundstone is also present. Marine sandstone is burrowed to bioturbated and is hummocky cross-stratified in places. Some marine mudstone contains sandstone pillows formed by loading of unconsolidated sand by storm waves. Other sandstone in the fan-delta facies is cross-bedded, lacks shells and was probably deposited by fluvial processes. Several conglomerate beds in the fan-delta facies are well sorted and imbricated and were also deposited by stream floods. The synorogenic Orubadi and Era Formations were deposited in a foreland basin formed from loading of the Papuan–Aure Fold and Thrust Belt on the edge of the Australian craton. Deformation in the fold and thrust belt was probably related to docking and compression of the Finisterre Terrane–Bismarck Arc against the New Guinea Orogen. The Era Formation interfingers with the reefal Wedge Hill Limestone in which reef facies likely grew on a deforming anticline. Era Formation siliciclastics were sourced from volcanic, metamorphic and sedimentary rocks that were uplifted in the orogen to the northeast. Volcanic sediment was derived mostly from a then-active volcanic arc likely related to southward subduction at the Trobriand Trough.  相似文献   

5.
A great deal of early-to-mid Early Cretaceous magmatic activities have been recorded in the Zhalantun area of Inner Mongolia,while the late Early to Late Cretaceous magmatic rocks have been barely reported(Guo et al.,2018;Zhang Xiangxin et al.,2017).At present,only a few Late Cretaceous magmatic activities were reported in the Arongqi area,such as volcanic rocks of the Gushanzhen Formation.However,the Gushanzhen Formation lacks accurate isotopic age,and contemporaneous intrusive rocks has not been reported yet.In this work,we collected the volcanic rocks from the Gushanzhen Formation and contemporaneous intrusive rocks in the Zhanlantun and nearby,and aim to figure out the formation ages of volcanic rocks of the Gushanzhen Formation and accompanied intrusive rocks by analyzing zircon U-Pb isotopes(Fig.1).  相似文献   

6.
Mg-rich and Fe-rich metatholeiites intruded the Willyama Supergroup of the southern Australian Curnamona Province in the Late Palaeoproterozoic at ca 1700 Ma and 1685 Ma, respectively. Intrusion of the Fe-rich metatholeiites occurred during a period of punctuated extension in the Willyama basin. Major-element concentrations are variable (SiO2 45.4 – 56.5 wt%; Fe2O3? 8.5 – 20.7; TiO2 0.46 – 2.52 wt%; Mg# 70.5 – 29.1) and, in conjunction with trace-element data, support near-closed-system fractionation of a mantle-derived melt with little or no replenishment. Fractionation produced progressively Fe-rich derivative melts. Crystallising phases were dominated by clinopyroxene and olivine, whereas Fe – (Ti) oxide crystallisation was hindered. Primitive mantle-normalised immobile trace elements are characterised by variable Th, Nb, Sr, P and Ti anomalies. Chondrite-normalised rare-earth element patterns for the most primitive, Mg-rich samples from the western Broken Hill Domain have LaN/SmN < 1, whereas the most evolved Fe-rich samples from the Olary Domain have ratios of LaN/SmN > 1. Initial εNd values range between – 2.2 and + 2.7 for the majority of the samples, with the isotopic compositions showing no correlation with differentiation or assimilation. The combined geochemical and isotopic data suggest that the southern Curnamona Province metatholeiites were extracted from a depleted mantle in the western Broken Hill Domain, and a variably enriched, heterogeneous subcontinental lithospheric mantle in the Olary Domain. Magmatism most likely occurred in a backarc basin or intracontinental setting. It is speculated that the geochemically enriched mantle component was derived from subduction-related processes, probably related to pre-Willyama basin accretionary processes along the southern and eastern margins of the North Australian Craton.  相似文献   

7.
The purpose of this study was to determine how vertical accretion rates in marshes vary through the millennia. Peat cores were collected in remnant and drained marshes in the Sacramento–San Joaquin Delta of California. Cubic smooth spline regression models were used to construct age–depth models and accretion histories for three remnant marshes. Estimated vertical accretion rates at these sites range from 0.03 to 0.49 cm year−1. The mean contribution of organic matter to soil volume at the remnant marsh sites is generally stable (4.73% to 6.94%), whereas the mean contribution of inorganic matter to soil volume has greater temporal variability (1.40% to 7.92%). The hydrogeomorphic position of each marsh largely determines the inorganic content of peat. Currently, the remnant marshes are keeping pace with sea level rise, but this balance may shift for at least one of the sites under future sea level rise scenarios.  相似文献   

8.
The ~1.74 Ga Damiao anorthosite complex, North China, is composed of anorthosite and leuconorite with subordinate melanorite, mangerite, oxide-apatite gabbronorite, perthite noritic (i.e., jotunitic) and ferrodioritic dykes. The complex hosts abundant vein-, pod- and lens-like Fe–Ti–P ores containing variable amounts of apatite (10–60 modal%) and Fe–Ti oxides. In addition to Fe–Ti–P ores, there are also abundant Fe–Ti ores which are closely associated with Fe–Ti–P ores in the deposit. Most of Fe–Ti–P ores are dominated by Fe–Ti oxides and apatite, devoid of silicate minerals, mineralogically similar to the common nelsonites elsewhere. In contrast, Fe–Ti ores are dominated by Fe–Ti oxides with minor apatite (<5 modal %). The parental magma of these ores, estimated from olivine and apatite compositions using mineral-melt partition coefficients, has composition similar to the ferrodioritic dykes. Fe–Ti–P ores have variable Fe–Ti oxides and apatite proportions, indicating that they are cumulates. Their simple assemblage of Fe–Ti oxides and apatite and local net-texture suggest that the Fe–Ti–P ores in Damiao have formed from nelsonitic melts immiscibly separated from the ferrodioritic magma during late-stage differentiation. Fe–Ti ores are also cumulates and have mineral compositions similar to Fe–Ti–P ores. The close association between Fe–Ti and Fe–Ti–P ores indicates that the Fe–Ti ores may have also formed from the nelsonitic melts. We proposed that differentiation of nelsonitic melts accompanied by gravity settling is responsible for the formation of Fe–Ti and Fe–Ti–P ores. Such a differentiation process in nelsonitic melts is well supported by variations of Sr, Y, Th, U, REE and Eu/Eu* of apatite in Fe–Ti–P ores. Using oxides/apatite ratio of 2:1 and compositions of apatite and calculated primary oxides, we estimate the composition of the nelsonitic melt as ~52.0 wt% Fe2O3t, ~18.5 wt% CaO, ~14.2 wt% P2O5, ~8.7 wt% TiO2, ~4.0 wt% Al2O3 and ~1.1 wt% MgO with minor SiO2, K2O, Na2O and F. Such a nelsonitic melt is suggested to be possibly conjugated with Si-rich melts compositionally similar to the Damiao jotunitic dykes (~50 wt% SiO2 and ~15 wt% Fe2O3t) which may subsequently evolve to mangeritic rocks in Damiao. Our modeling also indicates that the onset of immiscibility occurs at a time when the evolved melt has ~44 wt% SiO2, ~21 wt% Fe2O3t, ~3.0 wt% TiO2 and ~2.6 wt% P2O5. High oxygen fugacity and phosphorous content in magmas may play important roles in the immiscibility of nelsonitic magmas, including promoting iron enrichments and widening the two-liquid field.  相似文献   

9.
Petrogenetic studies of carbonatites are challenging, because carbonatite mineral assemblages and mineral chemistry typically reflect both variable pressure–temperature conditions during crystallization and fluid–rock interaction caused by magmatic–hydrothermal fluids. However, this complexity results in recognizable alteration textures and trace-element signatures in the mineral archive that can be used to reconstruct the magmatic evolution and fluid–rock interaction history of carbonatites. We present new LA–ICP–MS trace-element data for magnetite, calcite, siderite, and ankerite–dolomite–kutnohorite from the iron-rich carbonatites of the 1.3 Ga Grønnedal–Íka alkaline complex, Southwest Greenland. We use these data, in combination with detailed cathodoluminescence imaging, to identify magmatic and secondary geochemical fingerprints preserved in these minerals. The chemical and textural gradients show that a 55 m-thick basaltic dike that crosscuts the carbonatite intrusion has acted as the pathway for hydrothermal fluids enriched in F and CO2, which have caused mobilization of the LREEs, Nb, Ta, Ba, Sr, Mn, and P. These fluids reacted with and altered the composition of the surrounding carbonatites up to a distance of 40 m from the dike contact and caused formation of magnetite through oxidation of siderite. Our results can be used for discrimination between primary magmatic minerals and later alteration-related assemblages in carbonatites in general, which can lead to a better understanding of how these rare rocks are formed. Our data provide evidence that siderite-bearing ferrocarbonatites can form during late stages of calciocarbonatitic magma evolution.  相似文献   

10.
<正>Objective The Susong complex zone(SCZ)is a relatively lowgrade metamorphic unit mostly with an epidoteamphibolite facies,located in the southernmost part of the Dabie orogen.However,its rock compositions,ages,metamorphic processes and petrogenesis are still  相似文献   

11.
Modeling fractured rocks with numerical methods requires some derived parameters, among which the fracture network connectivity and the size of the representative elementary volume (REV) are both of crucial importance. Percolation and REV analyses were made by the RepSim code. The program uses input parameters such as fractal dimension of the fracture midpoints (D c), length exponent (E) and relative dip (α r) data. For percolation analysis, the relative sizes of the largest percolation clusters have been calculated by stochastic realizations of the simulated fracture networks with different parameter triplets. Furthermore, fracture networks can be classified into three major types on the basis of their (E,D c,α r) parameters. For the REV calculations, the porosity of the generated fracture network was calculated. The derived REV size of a fracture network depends essentially on input parameters and shows a decreasing tendency with increasing D and E and vice versa. The method mentioned above was tested on both metamorphic samples of the Pannonian Basin and Variscan granitoid rocks of the Mórágy Complex. Percolation values predicted for the Mórágy granite are highly sensitive to alterations in the input parameters. The amphibolite bodies displayed a modeled fracture network with 80 to 90% of all fractures being interconnected, while the largest achievable percolation cluster size of gneiss is less than 10%. The REV size of the amphibolite is about 20 m as a result of connected fractures filling the whole body, while gneiss has lower porosity and higher REV (approximately 70 m).  相似文献   

12.
The integration of detrital and magmatic U – Pb zircon SHIRMP geochronology with facies analysis has allowed the development of a chronostratigraphic framework for the Leichhardt and Calvert Superbasins of the Western Fold Belt, Mt Isa Inlier. This new event chart recognises three supersequences in the Leichhardt Superbasin: the Guide, Myally and Quilalar Supersequences. The Guide Supersequence spans the interval ca 1800 – 1785 Ma and includes the Bottletree Formation and the Mt Guide Quartzite. Sequence relationships suggest that this sedimentary package represents an asymmetric second-order cycle, recording a thickened transgressive suite of deposits and a comparatively thin second-order highstand. The overlying Myally Supersequence spans the interval ca 1780 – 1765 Ma and includes the Eastern Creek Volcanics and syndepositional Lena Quartzite, and the Myally Subgroup. This package represents a second-order supersequence cycle in which mafic volcanism was initiated during a phase of east – west extension. Following the cessation of volcanism, transgression led to the deposition of the Alsace Quartzite and deeper water Bortala Formation. An increase in the rate of sediment supply over accommodation resulted in progradation and deposition of the Whitworth Quartzite and redbed playa facies of the Lochness Formation as accommodation closed. The Quilalar Supersequence spans the interval ca 1755 – 1740 Ma. Sequence analysis in the eastern part of the Leichhardt River Fault Trough identifies a transgressive suite of facies at the base of this supersequence. Black shales from the upper part of the transgressive deposits characterise the condensed section for this supersequence. Facies analysis indicates that deposition took place in a series of storm-, tide- and wave-dominated shelfal marine depositional systems. Although there are no new depositional age constraints for the younger Bigie Formation, field relationships suggest that it is coeval with, or immediately preceded, the ca 1710 Ma Fiery magmatic event. Therefore, a separate supersequence is defined for the Bigie Formation, the Big Supersequence, even though it may be more genetically related to the Fiery magmatic event. The Big Supersequence, together with the ca 1690 Ma Prize Supersequence, comprise the Calvert Superbasin. The evolution of the Leichhardt and Calvert Superbasins are temporally and spatially related to magmatism. In particular, the new maximum depositional ages for the Guide and Myally Supersequences refine the age of the Eastern Creek Volcanics to ca 1780 – 1775 Ma. The new age for the Weberra Granite is within error of the age for the Fiery Creek Volcanics, indicating that they are both part of the ca 1710 Ma Fiery event. New ages for the Sybella Granite confirm that magmatism associated with this magmatic event is refined to 1680 – 1670 Ma, and is followed by deposition of the Gun Supersequence. Combining the new geochronological constraints with previous work now provides a detailed stratigraphic event framework between 1800 and 1575 Ma for the Western Fold Belt of the Mt Isa Inlier, and allows detailed comparisons and correlations with the Eastern Fold Belt and other Proterozoic terranes.  相似文献   

13.
The Lawn Hill circular structure in northwest Queensland contains unambiguous evidence of an extraterrestrial impact, including planar deformation features in quartz, impact diamonds, widespread shatter cone formation and impact melt breccia in the Mesoproterozoic basement. The question of its relevance to ore genesis is investigated because the world-class Century Zn – Pb deposit is situated at the conjunction of the 100+ km Termite Range Fault and the previously defined margin of the impact structure. The impact structure is considered to be a 19.5 km wide feature, this constrained in part by the outer margin of an annulus of brecciated and highly contorted limestone. New evidence is presented indicating impact into this Cambrian limestone, including: (i) ‘dykes’ of brecciated Cambrian limestone extending hundreds of metres into the Mesoproterozoic basement; (ii) highly contorted bedding in the limestone annulus compared with essentially undeformed limestone away from the impact site; as well as (iii) a 1 Mt megaclast of Mesoproterozoic Century-like ore suspended in the limestone. Through aerial photograph analysis, large-scale convoluted flow structures within the limestone are identified, and these are interpreted to indicate that parts of the Cambrian sequence may have been soft or only semi-consolidated at the time of impact. This highly contorted limestone bedding is suggested to represent slump-filling of an annular trough in response to impact-induced partial liquefaction of a sediment veneer. The age of impact is therefore considered to be concurrent with limestone formation during the Ordian to early Templetonian, at 520 – 510 Ma. Formation of the Century deposit is found to be unrelated to impact-generated hydrothermal activity, although some minor hydrothermal remobilisation of metals occurred. However, there was macro-scale remobilisation of gigantic ore fragments driven by impact-induced lateral and vertical injection of limestone into the Proterozoic sediments. The limestone-filled annular trough surrounds a 7.8 km diameter central uplift, consistent with formation of a complex crater morphology.  相似文献   

14.
15.
The Quaternary sediments in the Yili Basin can serve as archives for studying the Cenozoic basin–mountain relationship. In this study, based on typical natural sections and boreholes, the surficial sediments of the Huocheng area were studied, and their sedimentary ages were obtained using the optically stimulated luminescence(OSL) and electron spin resonance(ESR) dating methods. These dates, combined with changes in the sedimentary facies, provided details of the neotectonic movement in the Yili Basin and adjacent areas. By dating sediments from five sections and three boreholes, we determined that the surficial sediments of the Huocheng area were mainly formed in the Late Pleistocene, with scattered instances of Holocene sediments. The surficial sediments mainly consisted of alluvial fan facies, fluvial facies, lacustrine facies, and desert facies. Based on the activity on the Hongshanzui fault and the northern margin fault of the Wusun Mountains, the Huocheng area was uplifted synchronously with the Tianshan Mountains during the last stage of the Late Pleistocene, causing the desert facies sediments to be superimposed on the former paleo–lake sediments.  相似文献   

16.
The computation of sparse representations of data on the sphere (e.g. topographical data) is a crucial step for further processing such as multiple separation, migration, imaging and sparsity promoting data-recovery. The Easy Path Wavelet Transform (EPWT) is a new tool for sparse data representation that has recently been introduced for image compression. In this paper we consider the EPWT on spherical triangulations. It is a locally adaptive transform that works along pathways through the array of function values and exploits the local correlations of the data in a simple appropriate manner. In our approach the usual discrete one-dimensional orthogonal or biorthogonal wavelet transform can be applied. The EPWT can be used for defining a multiresolution analysis on the sphere in which the scaling spaces and the wavelet spaces depend adaptively on the data. Issues of implementation of the EPWT are also considered.  相似文献   

17.
Jurassic plants excavated from a 12 × 5 m site, at Lune River, southern Tasmania, include an araucarian tree and numerous pteridophytes, belonging to the orders Osmundales, Filicales and Bennettitales. The fossils occur in 2 – 3 m of immature volcanilithic sandstone beds. The sandstone consists primarily of clasts from granitic basement rocks underlying much of southeast Tasmania and mafic clasts containing feldspathic microliths, and primary, phreatomagmatic quartz crystals. Detrital zircons from the sandstones are mostly Early Jurassic (Toarcian) in age (182 ± 4 Ma) with minor Triassic (226 Ma), Devonian (380 – 360 Ma) and Proterozoic populations. Basaltic andesite, hereafter referred to as andesite, caps the volcanilithic units and displays similar ratios of fluid-immobile trace elements (e.g. Zr/Nb, Ti/V), to the Jurassic dolerite found in Tasmania, indicative of a common source. The andesites are correlated with the Jurassic Kirkpatrick Basalts (Trans-Antarctic Mountains, Antarctica) based on their field relationships with bounding strata, age, and distinctive similarities in major-element composition and fluid-immobile trace-element ratios. The andesite is interpreted as an extrusive equivalent of the Tasmanian dolerite. Importantly, drillcore from Lune River contains stoped clasts of andesite in fine-grained dolerite, indicating that the andesite pre-dates the dolerite. Thermal alteration index of microfossils (3 – 3.3) and reflectance of organic material within the sediments (0.54 – 0.77 Ro) resulted from contact metamorphism associated with the emplacement of this basalt. The sedimentology and stratigraphy of the depositional environment, plus the presence of hydrophilic pteridophytes and gymnosperms, indicates that the Toarcian environment was temperate to warm and humid, with an abundant supply of water.  相似文献   

18.
19.
The Honghuagou Au deposit is located in the Chifeng-Chaoyang region within the northern margin of the North China Craton. The auriferous quartz veins are mainly hosted in the mafic gneiss and migmatite of the Neoarchean Xiaotazigou Formation along NNW- and NE-striking faults, with pyrite as the predominant ore mineral. The gold mineralization process can be divided into two stages, involving stage I quartz-pyrite and stage II quartz-calcite-polymetallic sulfide. Three types of fluid inclusions (FIs) have been identified in the Honghuagou deposit, namely, carbonic inclusions, aqueous‑carbonic inclusions, and aqueous inclusions. Quartz of stage I contains all types of FIs, whereas only aqueous inclusions are evident in stage II veins. The FIs of stages I and II yield homogenization temperatures of 275–340 °C and 240–290 °C with salinities of 3.4–10.7 wt% and 1.4–9.7 wt% NaCl eqv., respectively. The ore-forming fluids are characterized by medium temperature and low salinity, belonging to the H2O–NaCl–CO2 system. The δ18OH2O values of the ore fluids are between 2.1‰ and 5.9‰, within the range of enriched mantle-derived fluids in the North China Craton. The carbon isotope compositions of calcite (δ13CPDB = −4.4‰ to −4‰) are also similar to mantle carbon. He-Ar isotope data (3He/4He = 0.38–0.44 Ra; 40Ar/36Ar = 330–477) of fluid inclusions in pyrite indicate a mixed crustal and mantle source for the ore-forming fluids. Whereas, S-Pb isotope compositions of sulfides reveal that ore metals are principally derived from crustal rocks. On the basis of available geological and geochemical evidence, we suggest that the Honghuagou deposit is an orogenic gold deposit.  相似文献   

20.
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