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1.
The fractal dimension of an individual floc is a measure of the complexity of its external shape. Fractal dimensions can also be used to characterize floc populations, in which case the fractal dimension indicates how the shape of the smaller flocs relates to that of the larger flocs. The objective of this study is to compare the fractal dimensions of floc populations with those of individual flocs, and to evaluate how well both indicate contributions of sediment sources and reflect the nature and extent of flocculation in streams. Suspended solids were collected prior to and during snowmelt at upstream and downstream sites in two southern Ontario streams with contrasting riparian zones. An image analysis system was used to determine area, longest axis and perimeter of flocs. The area–perimeter relationship was used to calculate the fractal dimension, D, that characterizes the floc population. For each sample, the fractal dimension, Di , of the 28 to 30 largest individual flocs was determined from the perimeter–step‐length relationship. Prior to snowmelt, the mean value of Di ranged from 1·19 (Cedar Creek, downstream) to 1·22 (Strawberry Creek, upstream and downstream). A comparison of the means using t‐tests indicates that most samples on this day had comparable mean values of Di . During snowmelt, there was no significant change in the mean value of Di at the Cedar Creek sites. In contrast, for Strawberry Creek the mean value of Di at both sites increased significantly, from 1·22 prior to snowmelt to 1·34 during snowmelt. This increase reflects the contribution of sediment‐laden overland flow to the sediment load. At three of the sampling sites, the increase in fractal dimensions was accompanied by a decreases in effective particle size, which can be explained by an increase in bed shear stress. A comparison of fractal dimensions of individual flocs in a sample with the fractal dimensions of the floc populations indicates that both fractal dimensions provide similar information about the temporal changes in sediment source contributions, about the contrasting effectiveness of the riparian buffer zones in the two basins, and about the hydraulic conditions in the streams. Nevertheless, determining the individual fractal dimensions of a set of large flocs in a sample is very time consuming. Using fractal dimensions of floc populations is therefore the preferred method to characterize suspended matter. Copyright © 2000 John Wiley & Sons, Ltd.  相似文献   

2.
This study explores the irregularity and complexity of strong earthquake ground motions from the perspective of fractal geometry, and constructs a relation with the frequency content of the ground motions. The box-counting fractal dimensions and five representative period parameters of near-fault ground motions from the Chi-Chi and Northridge earthquakes are calculated and compared. Numerical results indicate that the acceleration and velocity time histories of ground motions present the statistical fractal property, and the dominant pulses of near-fault ground motions have a significant influence on their box dimensions and periods. Further, the average box dimension of near-fault impulsive ground motions is smaller, and their irregular degree of wave forms is lower. Moreover, the box dimensions of ground motions reflect their frequency properties to a large extent, and can be regarded as an alternative indicator to represent their frequency content. Finally, the box dimension D of the acceleration histories shows a considerably negative correlation with the mean period T. Meanwhile, the box dimension of the velocity histories Dye is negatively correlated with the characteristic period T and improved characteristic period Tgi.  相似文献   

3.
Fluvial suspended sediment typically consists of a variety of complex, composite particles referred to as flocs. Floc characteristics are determined by factors such as the source, size and geochemical properties of the primary particles, chemical and biological coagulation processes in the water column and shear stress and turbulence levels in the stream. Studies of floc morphology have used two contrasting methods of sampling and analysis. In the first method, particles settle on a microscope slide and are observed from below using an inverted microscope. The second method uses filtration at no or low vacuum and particles deposited on the filter are observed with a microscope. Floc morphology can be quantified using fractal dimensions. The aims of the present study were to examine the effect of the two sampling methods on the fractal dimensions of particle populations, and to evaluate for each method how well the fractal dimensions at the various sampling sites reflect basin conditions. Suspended solids were collected in triplicate on inverted microscope slides and on 0·45 μm Millipore HA filters in two southern Ontario streams with contrasting riparian zones during a minor runoff event resulting from the melt of a freshly fallen snowpack. An image analysis system was used to determine area, longest axis and perimeter of particles. The morphology of the particle population of each sample was characterized using four fractal dimensions (D, D1, D2 and DK). Systematic differences in fractal dimensions obtained with the two methods were observed. For the settling method, outlines of larger particles were frequently blurred because of the distance between the focal plane (the top of the inverted microscope slides) and the plane of the particle outline. In this method, the blurring of large particles can cause an increase in the projected area and length of the particle. The effect on the particle perimeter is unpredictable because it depends on the amount of detail lost through blurring and its effect on the apparent increase in particle size. Because of blurring, D and D1 tend to be systematically lower for the settling method, whereas the net effect on D2 is unpredictable. Particle size distributions derived from settling are typically coarser because small, low density particles may remain in the water column and all particles may not deposit on the slides. This loss of fines results in systematically lower DK values for the settling method compared with the filtration method. Fractal dimensions and particle size distributions obtained with the filtration method were sensitive to and clearly indicated differences between drainage basins and between sites within each basin. These differences were explained by basin characteristics and conditions. Fractal dimensions and particle size distributions obtained with the settling method were less sensitive to drainage basin characteristics and conditions, which limits their usefulness as process indicators. Copyright © 1999 John Wiley & Sons, Ltd.  相似文献   

4.
Temporal changes of b-value, fractal (correlation) dimensions of epicenters (D e ) and occurrence time of earthquakes (D t ) and relations between these parameters were calculated to investigate precursory changes before 28 May 2004, Baladeh-Kojour earthquake (M w = 6.3) of Central Alborz, Iran. 2086 events with M N ≥ 1.7 were selected for our analyses. A wide range of variation was seen in these parameters: b-value ～ 0.6–1.11, D e ～ 0.97–1.64, and D t ～ 0.13–0.93. The results showed decreases in all fractal parameters several months before the main shock. This decrease, which might have arisen due to clusters of events occurred between 2002–2003, was followed by a systematic increase, corresponding to the increased level of low-magnitude seismicity. It seems that changes in fractal parameters may be precursors of Baladeh-Kojour earthquake which was caused by seismic activation and quiescence. Furthermore, a positive correlation between b-value and D e was detected before the main shock (D e = 0.87 + 0.7b) and during aftershock sequences (D e = 2b ± 0.09), which was further on changed to a negative one (D e = 2.56–1.32b).  相似文献   

5.
Iran sits on a region with a high intrinsic level of seismic activity due to its tectonic setting. Through statistical examination of the earthquakes listed in the catalogue from International Institute of Earthquake Engineering and Seismology (IIEES), this research attempted to calculate some seismicity factors and find correlation between them. A preliminary analysis indicated changes in the b-value of the Gutenberg-Richter relationship over the study region. Thus, the study area was divided into five zones (Alborz, Zagros, Azerbaijan, Central and East) and b-value was computed for each zone. Considering faulting mechanism styles and the b-values in the region, it was found that the lowest b-values belong to the thrust events and strike-slip faulting earthquakes have intermediate values. These findings support previous studies. Furthermore, results of b-value calculation were used for the estimation of accumulated differential stresses (σ1–σ2) over each zone. Overall, the b-value for Iran is averagely low which signifies the high stress tectonic regime in this region. Also, by having calculated fractal dimension (D) in each zone, a correlation obtained showing that in Iran region, the b-value correlates to fractal dimension by D = 4.2b–2 relation which does not support Aki's (1981) speculation of D = 3b/c.  相似文献   

6.
Earthquakes began to occur in Koyna region (India) soon after the filling of Koyna Dam in 1962. In the present study, three datasets 1964–1993, 1993–1995, and 1996–1997 are analyzed to study the b-value and fractal dimension. The b-value is calculated using the Gutenberg–Richter relationship and fractal dimension D corr. using correlation integral method. The estimated b-value and D corr. of this region before 1993 are found to be in good agreement with previously reported studies. In the subsequent years after 1995, the b-value shows an increase. The estimated b-values of this region are found within the limits of global average. Also, the pattern of spatial clustering of earthquakes show increase in clustering and migration along the three zones called North-East Zone, South-East Zone (SEZ), and Warna Seismic Zone. The earthquake events having depth ≤5 km are largely confined to SEZ. After 1993, the D corr. shows decrease, implying that earthquake activity gets clustered. This seismic clustering could be helpful for earthquake forecasting.  相似文献   

7.
On April 25, 2015, Nepal was struck by the MW7.8 Gorkha earthquake followed by an intense aftershock sequence. It was one of the most destructive earthquakes in the Himalayan arc, causing more than 8900 fatalities. In this study, we analyzed the dataset (429 events, magnitude of completeness (Mc) ≥ 4.2 local magnitude) of the first 45 days after the Gorkha earthquake to estimate the seismicity parameters b-value, D-value, and p-value. We used the maximum likelihood method to estimate the b-value and Omori-Utsu parameters, whereas the correlation integral method was applied to estimate the fractal dimension (D-value). The analysis was carried out using running and sliding window techniques. The lowest b-value (0.57 ± 0.04) and the highest D-value (1.65 ± 0.02) were computed at the time of the Gorkha earthquake, after which the b-value significantly increased to a maximum of 1.57. It again dropped to 0.93 at the time of the major aftershock on May 12, 2015. The D-value showed an initial quick drop and then decreased in a wavy pattern until the end of the study period, indicating the clustering and scattering of earthquakes in a fault region. The b-value contour map identified the eastern part of the study area as a high stress region (b = ～0.8), implying that the stress shifted to that region. The D-value contour map reveals that the seismogenic structure shifted from linear to planar in the region. The rate of aftershock decay (p = 0.86 ± 0.04) for a short period reflects that the level of stress decreased rapidly. This study helps to understand the level of stress and seismicity pattern of a region, which could be useful for aftershock studies.  相似文献   

8.
Pore structure of Chinese coals with heating and pressurization treatments was studied using small angle X-ray scattering(SAXS),N2adsorption/desorption isotherms and scanning electron microscope(SEM).SAXS was performed for some samples after heat treatment at seven elevated temperatures from 25 to 250°C at 0 MPa and for other samples with hydrostatic pressure treatment at 0,5,10,15 and 20 MPa at the room temperature.The results show that N2adsorption isotherm together with SAXS could be a comprehensive method to evaluate the pore shape and the pore size distribution:the pore shapes are generally spherical for low rank coal and they are mainly ellipsoidal for high rank coal.All these measurements were then interpreted using the fractal theory to reveal relationship between surface fractals and coal rank,and the evolution of surface fractals under heating and pressurization treatments.The results show that surface fractal dimension(Ds)changes with different treating temperature and pressure and maximum vitrinite reflectance(Ro,m).Especially in the bituminous stage,Ds shows an increasing trend with Ro,m under varied temperatures.Moreover,Ds shows an increasing trend with increasing temperature before 200°C,and a decreasing trend after 200°C.Furthermore,the results show that Ds has a more complex relationship with Ro,m under varied treating temperature than that under varied treating pressure.  相似文献   

9.
Space and time clustering properties ofseismic activity, affecting Etna Volcano (Italy)during 1981–1991, are investigated by fractaldimension analysis. Very interesting volcanic andseismic activity occurred within this time interval.Temporal evolution of the time fractal dimension D t calculated on a moving window, revealscorrelation with the eruptive processes at differenttime scales confirming results obtained for a differenttime span (De Rubeis et al., 1997). Spatial fractaldimension D s shows to be negativelycorrelated with the time fractal dimension D t, suggesting a peculiar dynamic patternassociated with volcanic processes.  相似文献   

10.
Recent seismicity in the northeast India and its adjoining region exhibits different earthquake mechanisms – predominantly thrust faulting on the eastern boundary, normal faulting in the upper Himalaya, and strike slip in the remaining areas. A homogenized catalogue in moment magnitude, M W, covering a period from 1906 to 2006 is derived from International Seismological Center (ISC) catalogue, and Global Centroid Moment Tensor (GCMT) database. Owing to significant and stable earthquake recordings as seen from 1964 onwards, the seismicity in the region is analyzed for the period with spatial distribution of magnitude of completeness m t, b value, a value, and correlation fractal dimension D C. The estimated value of m t is found to vary between 4.0 and 4.8. The a value is seen to vary from 4.47 to 8.59 while b value ranges from 0.61 to 1.36. Thrust zones are seen to exhibit predominantly lower b value distribution while strike-slip and normal faulting regimes are associated with moderate to higher b value distribution. D C is found to vary from 0.70 to 1.66. Although the correlation between spatial distribution of b value and D C is seen predominantly negative, positive correlations can also be observed in some parts of this territory. A major observation is the strikingly negative correlation with low b value in the eastern boundary thrust region implying a possible case of extending asperity. Incidentally, application of box counting method on fault segments of the study region indicates comparatively higher fractal dimension, D, suggesting an inclination towards a planar geometrical coverage in the 2D spatial extent. Finally, four broad seismic source zones are demarcated based on the estimated spatial seismicity patterns in collaboration with the underlying active fault networks. The present work appraises the seismicity scenario in fulfillment of a basic groundwork for seismic hazard assessment in this earthquake province of the country.  相似文献   

11.
Seismicity preceding the September–October 1989 flank eruption at Mt. Etna volcano has been analysed by means of the fractal two-point correlation dimension Dc relative to epicentres distribution and the scaling exponent D inferred from the seismic b-value. Time evolution of Dc and D preceding the eruption onset revealed: a general decrease of Dc and increase of D (9–4 months prior the eruption onset), intermittent rates of Dc increase and D decrease (4 to 1 month), steady high values of Dc and low values of D (1 month) and sharp decreases of Dc and D marking the eruption onset. Results allowed to constrain the increment of seismic damage by recognising negative (mechanical hardening) and positive (mechanical softening) feedback prior the eruption onset.  相似文献   

12.
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13.
The morphology of suspended sediment particles reflects the origin of the suspended load and any modifying processes that may have occurred during transport and storage in the aquatic system. The objective of this study was to evaluate the use of four fractal dimensions to quantify visually observed changes in the morphology of fluvial suspended sediment particles during baseflow conditions. Samples were collected during summer low flow in a small stream on the Canadian Prairies. Particle morphology data were obtained with a transmitted light microscope, a CCD camera and an image analysis system. The morphology of the particle population was characterized using four fractal dimensions (D, DK, D1 and D2). D was derived from the area–perimeter relationship and showed an increase from 1·26±0·02 on 30 June, to 1·34±0·02 on 4 July, to 1·42±0·01 on 7 July. Visually, the increase in D represented the formation of large particles with intricate shapes and increased perimeters. DK was determined from the area–rank relationship and varied from 1·86±0·01 on 30 June, to 1·90±0·00 on 4 July, to 1·74±0·00 on 7 July. The decrease in DK between 4 July and 7 July would indicate a greater concentration of the particle area over a small number of large particles. Although the decrease in DK is consistent with observed changes in the particle size distributions, DK should be used with the considerable caution because DK varied more than one standard error between replicates. D1 and D2 were determined from the length–perimeter and length–area relationships, respectively. D1 proved to be of little value for quantifying changes in particle morphology as it showed little change with time, despite considerable visual changes. D2 however, was useful, despite some variation between replicates. Over the sampling period, D2 for the composite data sets showed a steady decrease from 1·74±0·02 on 30 June, to 1·68±0·02 on 4 July, to 1·60±0·01 on 7 July. This change in D2 indicates that, through time, the larger particles became longer and thinner relative to the smaller ones. This study shows that temporal changes in D, DK and D2 were consistent with, and allow quantification of, observed changes in particle morphology. D1 did not reflect observed morphological changes, and is therefore of little value for this type of study. The changes in particle morphology coincided with an increase in primary production in the form of algae. © 1997 John Wiley & Sons, Ltd.  相似文献   

14.
—Statistical characteristics of seismicity represented by microearthquakes are examined for three regions in central Greece, in particular the fractal correlation dimension, D 2?, and traditional b values are examined in tandem as a function of time by using the moving window technique. The Patras region contains the complicated tectonics, extending to damaging historical earthquakes of the western Corinth Gulf and the Rio Graben, yielding D 2 values between 0.40 and 1.20 with b between 0.94 and 1.27 unusually, the temporal evolution between D 2 and b generates a positive correlation, although the variation is mostly in D 2?. When the whole evolution is divided into two stages then the positive correlations are even stronger than for the whole evolution. The views of Henderson and others might suggest a highly fractured, fluid-filled zone. The Pavliani region, with no known active fault, and the Volos region, containing the through-going Nea Ankhialos fault, yield D 2 values 0.33 to 0.79 with b 0.92 to 1.30 and D 2 0.82 to 1.56 withb 1.02 to 1.37, respectively. Temporal evolution between D 2 and b provides a typical negative correlation in both regions. Examination of gross seismicity (time window embracing the whole data set) in each region produces D 2 values for the Patras and Volos regions that are both larger than that for Pavliani; there are no obvious differences amongst the b values. This accords with the knowledge that Patras and Volos are in regions with very active seismotectonic features which generate repeated strong earthquakes exceeding 6M s ?. D 2 for both regions is fairly close to 1, the topological dimension of a line, consistent with seismicities on leading active fault zones or through-go ing faults. These values highlight the ability for microearthquakes to illuminate the character of their parent tectonic province. Resolution and hierarchy in these data from Greece are compared with these aspects elsewhere (Japan, Turkey, South America, USA) in the sense that their banding with respect to examined magnitude, areal extent and duration of observation period for respective data sets is examined in relation to the earthquake potential of the parent seismotectonic province. Evolutions are then categorised as being macroscopic, transitional or microscopic in character.  相似文献   

15.
The research of the information dimension (D 1) in an active fault zone considers the contribution of each seismic event to information and reflects the characteristics of the temporal and spatial distributions of earthquakes from a new point of view, avoiding some short-comings of the research about the capacity dimension (D 0). The results of calculation show that the information dimension of the temporal distribution in Xianshuihe active fault zone before Luhuo large earthquake isD 1=0.1051. It is a consult creterion of large earthquakes in future in the fault zone. The information dimensions of the temporal distribution of the earthquakes in Anninghe active fault zone are respectivelyD 1(t N)=0.1363 (for the north section) andD 1(t S)=0.06710 (for the south section). The information dimensions of the spatial distribution are respectivelyD 1(K N)=1.053 (for the north section) andD 1(K S)=0.7758 (for the south section). The north section and the south section belong to two self-similar systems with different information dimensions respectively. The extent of the self-organization of seismic activity in the south section is higher than that in the north section. This is helpful for us to judge the major dangerous section in the key region of the seismic monitoring. The research about the information dimension of the temporal and the spatial distributions of earthquakes is significant for the exploration of active fault zones and seismic prediction.  相似文献   

16.
Scattering of seismic waves can be shown to have a frequency dependenceQ –1 3–v if scattering is produced by arrays of inhomogeneities with a 3D power spectrumW 3D(k) k –v. In the earth's crust and upper mantle the total attenuation is often dominated by scattering rather than intrinsic absorption, and is found to be frequency dependent according toQ –1 , where –1<–0.5. IfD 1 is the fractal dimension of the surface of the 3D inhomogeneities measured on a 2D section, then this corresponds respectively to 1.5<D 11.75, since it can be shown that =2(D 1–2). Laboratory results show that such a distribution of inhomogeneities, if due to microcracking, can be produced only at low stress intensities and slow crack velocities controlled by stress corrosion reactions. Thus it is likely that the earth's brittle crust is pervaded by tensile microcracks, at least partially filled by a chemically active fluid, and preferentially aligned parallel to the maximum principal compressive stress. The possibility of stress corrosion implies that microcracks may grow under conditions which are very sensitive to pre-existing heterogeneities in material constants, and hence it may be difficult in practice to separate the relative contribution of crack-induced heterogeneity from more permanent geological heterogeneities.By constrast, shear faults formed by dynamic rupture at critical stress intensities produceD 1=1, consistent with a dynamic rupture criterion for a power law distribution of fault lengths with negative exponentD. The results presented here suggest empirically thatD 1-1/2(D+1), thereby providing the basis for a possible framework to unify the interpretation of temporal variations in seismicb-value (b-D/2) and the frequency dependence of scattering attenuation ().This is PRIS contribution 046.  相似文献   

17.
— Analysis of the Koyna-Warna earthquake catalog (1968–1996) shows that on an average there is a positive correlation between the b value (decrease) and fractal dimensions (decrease in both D2s and D2t) of earthquake epicenters 0.5 and 2.5 years prior to 1973 (M5.2) and 1980 (M5.5) events, respectively, except a negative correlation for about five years (1988–1993) prior to the 1993/1994 sequence (M5.4). This positive correlation indicates a weaker clustering, or that the epicenters tend to fill the two-dimensional plane. While the origin of the negative correlation seems to be that during periods of large events (low b value), there is strong clustering around the main shock epicenter (high fractal dimension). Interestingly, during the last year (1995–1996) of the studied period both the b value and correlation dimensions rose significantly, suggesting that stress release occurs through increased levels of low magnitude and increasingly scattered seismicity, suggesting an increased risk of larger magnitude events. Incidentally, during 2000 three earthquakes of magnitude M 5.0, one earthquake of M 4.0, 45 earthquakes of magnitude M 3.0–3.9, and several thousand earthquakes of M < 3 have occurred in the region. Thus it can be inferred that at local scales the relationship yields both positive and negative correlation that appears to be controlled by different modes of failure within the active fault complex.Acknowledgement. The authors are grateful to Dr. B.K. Rastogi of NGRI for providing the catalog of Koyna earthquakes and for useful scientific discussions. The comments of Dr. I. G. Main have improved the quality of paper for which we extend to him our sincere thanks. One of the authors (AOM) thanks the Third World Academy of Science and the Council of Scientific and Industrial Research, India for the Postdoctoral Fellowship award under which this work was carried out.  相似文献   

18.
— The devastating intraplate earthquake of Mw 7.7 of 26 January, 2001 took place along the south-dipping reverse fault in the lower crust ( 23 km) of Kutch, Gujarat, India, obliterating some 14,000 people. The aftershock activity has ensued for three years. We analyzed 997 aftershocks of M 3.0 to study the b value and fractal correlation dimensions in time and space. The b value is found to be 0.8 ± 0.03 from the Gutenberg-Richter relation and 0.76 ± 0.02 from the maximum-likelihood, suggesting a typical value for the intraplate region. The spatial correlation is 1.71 ± 0.02, indicating that events are approaching a two-dimensional region. Further, the temporal correlation dimension is estimated to be 0.78 ± 0.02, confirming the structure is mono-fractal in time domain. The depth section of b value shows a peak at 15–35 km depth range coinciding with the maximum occurrence of aftershocks ( 47%), which is inferred as a fluid-filled highly fractured rock matrix with fractures of high density. It will be important to note that tomographic results also suggest a low Vp, low Vs and a large Poissons ratio for the same depth range, further confirming this inference. Additionally, we have studied the variation of D2s and b value with time. During the first two months of aftershock activity the results show a marked negative correlation between spatial correlation dimension D2 (large) and b value (low), indicating the predominance of large events associated with weak clustering. The negative correlation means the stress release along faults of a larger surface area. After two months the fractal dimension (D2s) and b value suggests a positive correlation implying more numerous smaller shocks with stress release along faults of a smaller surface area. This would indicate a reduced probability of large magnitude earthquakes due to fragmentation of the fault zone.Acknowledgement. The authors thank Dr. V.P. Dimri, Director, NGRI for his encouragement and kind permission to publish this work. The Department of Science and Technology, New Delhi supported this study.  相似文献   

19.
Fractal　research　of　fault　gouge   总被引：1，自引：0，他引：1  
ＦｒａｃｔａｌｒｅｓｅａｒｃｈｏｆｆａｕｌｔｇｏｕｇｅＳＨＵＮ－ＭＥＩＳＨＡＯ（邵顺妹）ａｎｄＪＩＮ－ＣＨＡＮＧＺＯＵ（邹瑾敞）ＥａｒｔｈｑｕａｋｅＲｅｓｅａｒｃｈＩｎｓｔｉｔｕｔｅｏｆＬａｎｚｈｏｕ，ＳｔａｔｅＳｅｉｓｍｏｌｏｇｉｃａｌＢｕｒｅａ...  相似文献   

20.
温度是影响岩石物理力学性质的重要因素,对不同温度作用后灰岩单轴压缩的碎块进行统计分析,结果表明灰岩的块度分布是个分形,分形维数D是反映高温后灰岩破碎程度恰当的特征统计量,同时D表现出随温度的增大而减小的性质。在此基础上,通过扫描电镜分析,获得温度对岩石力学性质的影响主要与组成岩石矿物性质和内部微观结构有关,而不同温度的作用会影响岩石矿物组成成分和岩石的晶格结构,在灰岩的扫描电镜结果对比中已发现微观形貌特征的差异,这可从内在机制方面解释不同温度下灰岩分维值变化特征。  相似文献   

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