text:
Journal cover Journal topic
Biogeosciences An interactive open-access journal of the European Geosciences Union
Journal topic
Biogeosciences, 15, 2007–2019, 2018
https://doi.org/10.5194/bg-15-2007-2018
Biogeosciences, 15, 2007–2019, 2018
https://doi.org/10.5194/bg-15-2007-2018

Research article 06 Apr 2018

Research article | 06 Apr 2018

# Impact of elevated precipitation, nitrogen deposition and warming on soil respiration in a temperate desert

Impact of elevated precipitation, nitrogen deposition and warming on soil respiration in a temperate desert
Ping Yue1,2,3, Xiaoqing Cui2, Yanming Gong1, Kaihui Li1,5, Keith Goulding4, and Xuejun Liu2 Ping Yue et al.
• 1Key Laboratory of Biogeography and Bioresource in Arid Land, Xinjiang Institute of Ecology and Geography, Chinese Academy of Sciences, Urumqi 830011, China
• 2Key Laboratory of Plant-Soil Interactions of MOE, College of Resources and Environmental Sciences, China Agricultural University, Beijing 100193, China
• 3University of the Chinese Academy of Sciences, Beijing 100039, China
• 4The Sustainable Soils and Grassland Systems Department, Rothamsted Research, Harpenden AL5 2JQ, UK
• 5CAS Research Center for Ecology and Environment of Central Asia, Urumqi 830011, China

Correspondence: Xuejun Liu (ecology2100@sina.cn, liu310@cau.edu.cn)

Abstract

Soil respiration (Rs) is the most important source of carbon dioxide emissions from soil to atmosphere. However, it is unclear what the interactive response of Rs would be to environmental changes such as elevated precipitation, nitrogen (N) deposition and warming, especially in unique temperate desert ecosystems. To investigate this an in situ field experiment was conducted in the Gurbantunggut Desert, northwest China, from September 2014 to October 2016. The results showed that precipitation and N deposition significantly increased Rs, but warming decreased Rs, except in extreme precipitation events, which was mainly through its impact on the variation of soil moisture at 5 cm depth. In addition, the interactive response of Rs to combinations of the factors was much less than that of any single-factor, and the main response was a positive effect, except for the response from the interaction of increased precipitation and high N deposition (60 kg N ha−1 yr−1). Although Rs was found to show a unimodal change pattern with the variation of soil moisture, soil temperature and soil NH${}_{\mathrm{4}}^{+}$-N content, and it was significantly positively correlated to soil dissolved organic carbon (DOC) and pH, a structural equation model found that soil temperature was the most important controlling factor. Those results indicated that Rs was mainly interactively controlled by the soil multi-environmental factors and soil nutrients, and was very sensitive to elevated precipitation, N deposition and warming. However, the interactions of multiple factors largely reduced between-year variation of Rs more than any single-factor, suggesting that the carbon cycle in temperate deserts could be profoundly influenced by positive carbon–climate feedback.

1 Introduction

Global climate warming, changes in precipitation patterns and increased atmospheric nitrogen (N) deposition have all occurred since the Industrial Revolution, especially in temperate regions (IPCC, 2013), which will be expected to significantly change soil respiration (Rs), the most important source of carbon dioxide (CO2) from soil to atmosphere (Wu et al., 2011): the annual CO2 flux from Rs was 10-fold that of fossil fuel emissions (Eswaran et al., 1993; Batjes, 1996; Gougoulias et al., 2014). Therefore, even a small change in Rs will profoundly affect greenhouse gas balance and climate (Heimann and Reichstein, 2008). Although a number of experiments of the effects of warming, precipitation and N deposition on Rs have been conducted in alpine grasslands, tundra regions, peatlands and temperate forests (Lafleur and Humphreys, 2008; Strong et al., 2017; Yang et al., 2017; Zhao et al., 2017), studies in temperate desert ecosystems are scarce, especially those on the impact of these changes' interactions on Rs. A field study of multi-factor interactive effects on Rs was therefore conducted in a temperate desert ecosystem to help in understanding the response of Rs to climate change and N deposition in future and highlight the main driving factors.

Rs includes autotrophic respiration (RA), which is mainly from plant roots and mycorrhizal activities, and heterotrophic respiration (RH), which is mainly from the activities of microorganisms (Hanson et al., 2000). Soil moisture is a critical limiting factor for plant roots and microbial activities in desert ecosystems (Huang et al., 2015a): Rs significantly increased, by 47–70 %, in a degraded steppe in Inner Mongolia, China, due to increasing precipitation (Chen et al., 2013), with the effect especially strong in summer (Zhang et al., 2017). In addition, in arid ecosystems, increasing precipitation significantly stimulated plant growth, enhanced soil microbial activity and abundance (Huang et al., 2015a), and it changed soil nutrient and substrate concentration, such as dissolved organic carbon (DOC), inorganic nitrogen content, moisture and temperature (Huang et al., 2015b).

Warming significantly increased soil temperature, another important controlling factor for plant growth and microbial activity (Sheik et al., 2011; Huang et al., 2015a). Rs rates were significantly increased in a forest soil and Tibetan Plateau grassland by warming (Chen et al., 2017a), reducing Rs with decreasing soil moisture in the growing season, but increasing Rs in the non-growing season (Fang et al., 2017; Li et al., 2017); no significant impact was observed from warming (T. Liu et al., 2016). Therefore, how Rs is affected by warming induced variations in the soil environment is still unclear. In addition, low and short-term N deposition enhanced Rs, while higher and long-term N deposition inhibited Rs due to changes in plant growth and microbial activity (Zhu et al., 2017), but no impacts have also been reported (Luo et al., 2017; Zhang et al., 2017). A meta-analysis showed that the effects of N enrichment on soil CO2 fluxes depended on temperature and soil properties (Zhong et al., 2016); desert soils may be even more sensitive to its variation.

A nation-wide analysis showed that warming, elevated N deposition and precipitation significantly increased Rs in China (Feng et al., 2017). Some studies have shown that the warming effect on Rs mainly depended on the variation of soil moisture in a dry forest soil (Li et al., 2017). Luo et al. (2008), using a modeling analysis, found that interactive effects became increasingly weaker with increasing intensity of the factors, but a recent meta-analysis showed that interactive effects were much greater than an individual factor (L. Y. Zhou et al., 2016). Thus how multi-factor interactions impact Rs is still unclear. Therefore, an in situ experiment was carried out in the Gurbantunggut Desert to (1) investigate the single-factor and interactive responses of Rs to warming, precipitation and N deposition and (2) identify the main controlling factors on Rs.

2 Materials and methods

## 2.1 Study site

A field experiment was carried out at the southern edge of the Gurbantunggut Desert (4426 N, 8754 E; 436.8 m a.s.l.), northwest China, from September 2014 to October 2016. This is the largest fixed/semi-fixed temperate desert in China. The mean annual temperature and precipitation are 7.1 C and 215.6 mm, respectively (Cui et al., 2017), and annual potential evaporation exceeds 2000 mm. From late November to mid-March, 20–35 cm of snow covers the whole desert (equivalent to 38–64 mm rainfall; Huang et al., 2015c). The growing season is from April to October. This desert soil is of extremely low fertility and is highly alkaline (Cui et al., 2017). Soil organic carbon, total N content, soil NO${}_{\mathrm{3}}^{-}$-N, NH${}_{\mathrm{4}}^{+}$-N contents and C : N ratio are 2.21 ± 0.71 g kg−1, 0.08 ± 0.003 g kg−1, 4.49 ± 0.71 mg kg−1, 1.38 ± 0.74 mg kg−1 and 21.39 ± 1.84, respectively (Table 1; Cui et al., 2017). Plant species are dominated by Haloxylon ammodendron and Haloxylon persicum, and vegetation is extremely sparse, with only 30 % coverage, with some spring ephemeral plants (May–June), annuals and perennial herbaceous plants (July–August; R. Liu et al., 2016). Spring ephemerals account for > 60 % of the community cover and 85 % of the biomass. Summer ephemerals, annuals and perennials usually account for only a small proportion of the community biomass before June, but dominate the community after the die-back of the spring annuals (Huang et al., 2015c).

Table 1The annual, growing season (GS), non-growing season (NGS) and between-year fluxes and variation of soil respiration (Rs) over September 2014 to September 2016 (mean ± SE), including the contribution of GS and NGS, and the treatment effect. The positive values stand for increased Rs, and the negative value stand for reduced Rs. Dates are shown in YYYY.M format.

## 2.2 Experimental treatments

A striking N deposition rate (35.2 kg N ha−1 yr−1) exists in the Gurbantunggut Desert due to the rapid development of agriculture and industry, with the main form being ammonium nitrate (NH4NO3); deposition is split between wet (19.6 kg N ha−1 yr−1) and dry (15.6 kg N ha−1 yr−1; Song et al., 2015). In addition, according to the forecast of Galloway et al. (2008), atmospheric N deposition will double from the early 1990s to 2050; Liu et al. (2010) predict that precipitation in this region will increased by 30 % in next 30 years. In September 2014 to August 2016, an in situ complete block interactive experiment was therefore conducted to study the impact of N deposition and increased precipitation on Rs. The three levels of N deposition (0 kg N ha−1 yr−1, control, N0; 30 kg N ha−1 yr−1, low, N1; 60 kg N ha−1 yr−1, high, N2) and two levels of precipitation (“natural” precipitation, W0, and an increase of 30 % – an extra 60 mm precipitation annually, W1) were applied (Cui et al., 2017). Therefore there were six treatments (W0N0, W0N1, W0N2, W1N0, W1N1 and W1N2) with four replicates of each treatment. Each replicate plot was 10 m × 10 m with a 5 m wide buffer zone. The additional precipitation and N deposition (NH4NO3) were added 12 times in April, July and September, equivalent to 5 mm precipitation and 2.5 or 5 kg N ha−1 per application over a week. The NH4NO3 was diluted in 50 L water (equal to 0.5 mm precipitation), and evenly applied following the simulated precipitation. The same amount of water was applied to the control plots (W0N0).

Figure 1Comparative effects of warming from open-top chambers (OTCs), increased precipitation and N deposition on soil temperature (a), soil moisture (b) at 5 and 20 cm depth; soil organic carbon (SOC), NH${}_{\mathrm{4}}^{+}$-N content, NO${}_{\mathrm{3}}^{-}$-N content and pH (c), dissolved organic carbon (DOC), microbial biomass carbon (MBC) and microbial biomass nitrogen (MBN, d). The data are mean ± SE, n= 4 in (c) and (d); different letters indicate significant effect at P < 0.05.

Rapid warming (0.6 C per decade), increasing precipitation (3–5 mm yr−1 since 1979) and high N deposition (3 kg N ha−1 since 1980) are affecting the Gurbantunggut Desert (Liu et al., 2013; Li et al., 2015), which are excepted to affect rate of Rs. Therefore, another interactive experiment was established at the same time, simulating the three most likely climate scenarios in the future: (1) warming only (W0N0T1), (2) increased precipitation and N deposition without warming (W1N1T0), (3) the interaction of increasing precipitation, N deposition and warming (W1N1T1); all compared with the current climate (W0N0T0). Therefore, there were four treatments (W0N0T1, W1N1T0, W1N1T1, W0N0T0) with four replicates (plots) of each treatment. Open-top chambers (OTCs) were used to simulate warming. The OTCs were designed with 5 mm transparent tempered glass and stainless steel angle iron to the ITEX standard (Marion et al., 1997). They were 2 m high and 4 m in diameter, with each OTC area being 12 m2. However, the design was improved such that the top and bottom OTC areas were the same so that precipitation and snowfall were the same as that in the surrounding environment; this also avoids overheating inside the OTCs. The timings of water and N applications were the same as in the complete block interactive experiment.

## 2.3 Measurements

Rs in all plots were measured twice or thrice a week (continuous measurements over 3 days were made following simulated precipitation and N deposition) using gas chromatography and static chambers (50 cm × 50 cm× 10 cm) at locations where only spring ephemeral plants grow, without any annuals and perennials, in order to minimize the between-treatment spatial heterogeneity due to sparse annuals and perennials (Liu et al., 2012). Gas samples were collected between 10:00 and 12:00 (GMT + 8) throughout the experimental period; measurements from this period were close to the diurnal averages (Figs. 3b, d and S1 in the Supplement). Gas samples were collected from the headspace of each chamber 0, 10, 20 and 30 min after closing the chamber. The gas samples were analyzed within 3 days using a gas chromatograph (GC; Agilent 7890A, Agilent Technologies, Santa Clara, CA, USA) equipped with a flame ionization detector for quantitative Rs (Liu et al., 2012). Rs rates were calculated from four concentrations of the gas samples based on a first-order differential linear or nonlinear equation and were temperature and pressure corrected (Liu et al., 2012; Zhang et al., 2014). Soil samples were taken monthly from around the static chambers to a depth of 10 cm using an auger (3.5 cm in diameter). Fine roots and small stones were separated out using a 2 mm sieve. Dissolved organic carbon (DOC) was extracted with deionized water (soil : water ratio = 1 : 10) by a centrifuge at 10000 rpm for 5 min and analyzed using a TOC analyzer (multi N/C 3100, Jena, Germany; Jones and Willett, 2006). The chloroform fumigation extraction of Brookes (1985) was used to measure microbial biomass carbon (MBC) and microbial biomass nitrogen (MBN). Soil organic carbon (SOC) was measured using the potassium dichromate method (Jiang et al., 2014), and soil NO${}_{\mathrm{3}}^{-}-$N and NH${}_{\mathrm{4}}^{+}$-N was analyzed as per Yue et al. (2016). Soil pH was measured with a 1 : 5 soil : deionized water suspension using a pH meter (Seven Easy, Mettler-Toledo, Switzerland). Caipos Soil and Environment Monitoring Systems (Caipos GmbH, Austria) were used to monitor soil moisture/temperature at 5 and 20 cm depth every hour.

Figure 2Variation in rainfall (mm, a), and air temperature (C, a) from September 2014 to October 2016 at the Gurbantunggut Desert. Also shown are soil moisture and temperature responses to increasing precipitation and warming (b), and the response of Rs (mean, n= 4) to precipitation (c), N deposition (d, e) and warming (f). W0 and W1 indicate under ambient precipitation (without water addition) and 60 mm yr−1 precipitation addition; N0, N1 and N2 indicate 0, 30 and 60 kg N ha−1 yr−1 nitrogen addition; W1N0, W1N1 and W1N2 indicate 0, 30 and 60 kg N ha−1 yr−1 nitrogen addition under 60 mm yr−1 precipitation addition; W1N1T1, W0N0T1 and W0N0T0 indicate the interaction between increasing precipitation (60 mm yr−1), N deposition (30 kg N ha−1 yr−1) and warming by OTCs, warming alone (without increasing precipitation and N deposition) and control plots, respectively. Black arrows indicate simulated precipitation (5 mm) and N deposition (0.25 or 0.5 g N m−2). Each point represents the mean of four replications (chambers). Standard deviations for Rs are not shown for figure clarity.

## 2.4 Effects of each treatment on Rs

Each treatment effect was analyzed using the following formula to better evaluating the effect of precipitation, warming and N deposition on Rs (Yue et al., 2016).

where the treatment effect is W0N1, W0N2, W1N0, W1N1, W1N2, W1N1T1 or W0N0T1 effect on Rs (a positive value shows that the treatment has increased Rs and a negative value shows decrease of Rs), corresponding RT,s represents Rs from the W0N1, W0N2, W1N0, W1N1, W1N2, W1N1T1 or W0N0T1 plots (mg C m−2 h−1) and RC,s indicates the Rs from the control plots (W0N0, mg C m−2 h−1).

## 2.5 Statistical analyses

Treatment effect on SOC, NO${}_{\mathrm{3}}^{-}$-N, NH${}_{\mathrm{4}}^{+}$-N content, pH, DOC, MBC and MBN were examined in each treatment by least significant difference (LSD; p < 0.05). The single-factor and interaction effects of precipitation, warming and N deposition on Rs were detected using multi-way analysis of variance (ANOVA), and the cumulative effect of precipitation, warming and N deposition on Rs were tested by repeated measures ANOVA. In addition, the relationships of Rs and DOC, MBC, MBN, soil temperature, soil moisture, NH${}_{\mathrm{4}}^{+}$-N content, soil NO${}_{\mathrm{3}}^{-}$-N and pH were described using a linear or nonlinear regression model. The factors of key controls on Rs were analyzed with structural equation models (SEMs). SPSS software (version 20.0) was used to conduct all statistical analyses, and statistically significant differences were set at P < 0.05. All figures were created using the Sigmaplot software package (version 10.0), but SEM analyses were carried out using AMOS 22.0 (Amos Development Corporation, Chicago, IL, USA).

3 Results

## 3.1 Treatment effects on soil environmental and properties

Soil temperatures at 5 cm depth mostly increased between 11:00 and 22:00 every day due to warming; the average annual soil temperatures at 5 and 20 cm depth increased significantly, by 4.41 and 3.67 C, respectively (Fig. 1a). Soil moisture at 5 cm depth was decreased by warming by only 0.61 vv % (Fig. 1b), and a very small decrease of 0.01 vv % in soil moisture at 20 cm depth was observed (Fig. 1b). Soil moisture at 5 and 20 cm depth were largely increased by the increased precipitation (Fig. 1b). N deposition and warming significant increased soil NH${}_{\mathrm{4}}^{+}$-N and NO${}_{\mathrm{3}}^{-}$-N contents (Fig. 1c), but no significant change was found from increased precipitation. Soil MBC and MBN were greatly increased by N deposition, but significant negative effects on soil MBC and MBN were observed by warming and the interaction of precipitation and N deposition (Fig. 1d). No significant change in SOC and DOC was observed in any treatment (Fig. 1c and d).

Figure 3Post-extreme-rainfall diurnal variation in Rs (mean ± SE, n= 4, d) with variation in soil temperature and soil moisture (c), and extreme-drought variation in Rs (mean ± SE, n= 4, b) with variation in soil temperature (T5, T20, a) and soil moisture at 5 cm (W5) or 20 cm (W20) depth caused by warming in OTCs. Positive values indicate an increase due to warming, and negative values indicate decline. A red straight line indicates the average value of Rs inside the OTCs in (b) and (d), and a blue straight line represents the average value of Rs out of OTCs in (b) and (d). Red *, ** and *** symbols indicate significant effects at P < 0.05, P < 0.01 and P <0.001, respectively.

## 3.2 Precipitation, warming and N deposition effects on Rs

In our study, a weak Rs emission rate (2.46 to 50.26 mg C m−2 h−1) was observed at control plots with an average emission rate of 12.18 mg C m−2 h−1 from September 2014 to October 2016 (Fig. 2c). Annual cumulative rate of Rs was 1090.11 ± 450.78 kg C ha−1, with the non-growing season accounting for 20.7 % of the annual emission (Table 1). Rs was significantly enhanced by increasing 5 mm precipitation and N deposition from 12.18 to 16.23 and to 14.97 mg C m−2 h−1(average), respectively (P < 0.001; Fig. 2c and d; Table 2), with annual Rs increased by 33.1 % and 19.2–22.8 %, respectively (Table 1). The low N deposition effect on Rs was much higher than that of high N deposition (Fig. 2c and d). However, Rs was reduced mostly by warming, although not significant (P=0.084; Table 2). The high temperatures and low humidity at times of peak sunshine during the diurnal variation significantly inhibited the emission rate (Figs. 3a and b, S2), but it was also significantly increased by warming following extreme rainfall events that increased soil moisture (Fig. 3c and d). The diurnal trend in Rs was consistent with that of soil temperature at 5 cm depth (Fig. 3). In addition, the interactive responses of Rs to increasing precipitation, warming and N deposition were much lower than that from any single-factor (Table 1), and with the interaction of 60 kg ha−1 N and extra precipitation decreasing Rs by 4.25 % (Table 1). Overall, annual Rs rates were significantly impacted by precipitation, N deposition, and their interaction (Table 2), but no significant net change was caused by warming (Table 2), although Rs rates were decreased by 9.99 % (Table 1).

Table 2Tests of significance of year (Y), warming (T), precipitation (W) and nitrogen addition (N) on soil respiration (Rs) using multivariate ANOVA (F and P values). The cumulative effect of precipitation, N deposition and warming on Rs in 2015 and 2016 (F and P values) as assessed by repeated measures ANOVA. Superscripts a, b and c indicate significant effects at P < 0.05, 0.01 and 0.001, respectively.

## 3.3 Temporal variation and its control

The results of repeated measures ANOVA showed that significant cumulative effects on Rs were found to be due to N deposition and interaction between N deposition and precipitation or warming rather than increasing precipitation and warming alone (Table 2). A large between-year variation in Rs was observed with a coefficient of variation (CV) up to 41.4 % (a much higher Rs rate was observed in 2016 than 2015), but variation was reduced by increasing precipitation, N deposition and warming and their interaction, except with an increase in N deposition of 30 kg ha−1 (Table 1). The results of regression analysis showed that Rs was significantly increased by increases in pH and DOC (Fig. 4e and f), but no significant relationships were found with MBC, MBN or NO${}_{\mathrm{3}}^{-}$-N content (Fig. 4a, b and c). In addition, different response characteristics of Rs in the impacts of increased soil moisture, soil temperature and NH${}_{\mathrm{4}}^{+}$-N content were found. Soil moisture was the most important controlling factor when it was < 4.2 % and soil temperature was > 26.5 C (Figs. 4g, h and S2). Secondly, soil temperature was the most important limiting factor when soil moisture was > 15.9 % and soil temperature < 2.7 C (Figs. 4g, h and S2). Thirdly, there was no significant impact on Rs when soil NH${}_{\mathrm{4}}^{+}$-N content was < 6.3 mg N kg−1. A significant increase in Rs occurred when soil NH${}_{\mathrm{4}}^{+}$-N content was between 6.3 and 12.6 mg N kg−1, but Rs was inhibited when soil NH${}_{\mathrm{4}}^{+}$-N content was between 12.6 and 31.6 mg N kg−1 (Fig. 4d).

Figure 4The relationship of soil respiration with microbial biomass carbon (MBC, a); microbial biomass carbon (MBN, b); soil NO3-N (c); NH${}_{\mathrm{4}}^{+}$-N content (x, d); soil dissolved organic carbon (DOC, e); pH (f); soil moisture (g) and soil temperature (h).

4 Discussion

## 4.1 Single-factor impacts of precipitation, N deposition and warming on Rs

Annual Rs was 1090 kg C ha−1 in this temperate desert, with the non-growing season accounting for 20.7 % of the annual flux (Table 1). This is consistent with previous studies here (Zhou et al., 2014; Huang et al., 2015a) because SOC content was very low (Fig. 1c), and vegetation was very sparse in this desert (R. Liu et al., 2016). Increasing precipitation significantly increased Rs (Fig. 2c). It is also consistent with the results of a meta-analysis and previous studies here (Huang et al., 2015a ; L. L. Liu et al., 2016). This is because the growth of desert plants and microbial activity are significantly activated by increasing precipitation (Huang et al., 2015a), and microbial biomass, mass-specific respiration, microbial biomass carbon (MBC) and nitrogen (MBN), and microbial PLFAs (phospholipid fatty acids) were consistently significantly enhanced by increased precipitation (Zhang et al., 2013; Huang et al., 2015a). However, Rs in our study was much higher in moderate soil moisture conditions than with too little or too much soil moisture (Fig. 4g). This suggests that Rs is mainly RH rather than RA in this desert, namely from soil microorganism, because (1) too little or too much soil moisture could significantly inhibit microbial activity due to variation of soil temperature and soil properties (Ma et al., 2013), while moderate soil moisture could significantly enhance microbial activity (Skopp et al., 1990) and (2) the biomass of fine roots was not significantly enhanced at our sites by increased precipitation (Cui et al., 2017). This is consistent with results from a desert steppe in northern China where the contribution of RH (78.1 %) was significantly higher than that of RA (21.9 %) under increasing precipitation (T. Liu et al., 2016).

N deposition also significantly increased Rs, especially in low N deposition (Fig. 2d). This is consistent with results from an alpine meadow and in the Loess Plateau (Fang et al., 2017; Zong et al., 2017), and with a meta-analysis showing that N deposition increased Rs by 8.8 % (L. Y. Zhou et al., 2016). This is because N deposition, on the one hand, could increase fine root biomass, although this was not significant in our study (Cui et al., 2017), and on the other hand, increases microbial activity and abundance by low N deposition (Huang et al., 2015b). However, this was inconsistent with a young Cunninghamia lanceolata forest (Wang et al., 2017), and beneath shrubs of H. ammodendron, soil high N content had the opposite effect as in our study site (Chen et al., 2013; Huang et al., 2015b). Additionally, the results of nonlinear regression analysis showed that higher Rs rates occurred at moderate soil NH${}_{\mathrm{4}}^{+}$-N contents (between 6.3 and 12.6 mg N kg−1), while lower Rs occurred in much lower (< 6.3 mg N kg−1) or much higher ( > 12.6 mg N kg−1) soil NH${}_{\mathrm{4}}^{+}$-N contents (Fig. 4d); however, this effect of N deposition on Rs is not consistent with other ecosystems (Burton et al., 2004; Chen et al., 2013; Liu et al., 2015; Chen et al., 2017b). This is because the desert soil is extremely limited compared to other ecosystem (Adams, 2003), so low N deposition enhanced plant growth and microbial activity, but high N inhibited microbial activity and community composition, and reduced Rs (Zhou et al., 2014; Huang et al., 2015b). Overall, soil NH${}_{\mathrm{4}}^{+}$-N content was an important controlling factor for Rs because microbial activity, abundance and species diversity were regulated by soil NH${}_{\mathrm{4}}^{+}$-N content in this desert, and Rs was very sensitive to variation of N deposition.

Warming decreased Rs (Fig. 2f), although not significantly (P=0.084; Table 2), which was consistent with results from a semi-arid alfalfa pasture of the Loess Plateau (Fang et al., 2017). In addition, significant decreases in Rs were observed on extreme drought or hot sunny days when soil moisture was reduced, and sharply reduced Rs occurred when soil temperature reached 37 C (Figs. 3a, b and S1). This is because (i) microbial activity is significantly inhibited by extreme temperatures and low soil moisture may reduce population size by 50–80 % (Sheik et al., 2011) and (ii) fine root growth is inhibited in high temperature and low soil moisture. Others have noted this phenomenon as occurring at about 16:00 each day (Ma et al., 2013), but in our study the effect was advanced to 14:00 by warming, which may reduce carbon emission from soil to atmosphere. However, this is not consistent with results from a tundra ecosystem, subtropical forest or alpine regions where Rs was significantly increased by warming due to the limitation of soil temperature in these ecosystems, and not to significant change in soil moisture (Noh et al., 2016; Wu et al., 2016; Y. M. Zhou et al., 2016). In addition, a significant increase in Rs was found following enhanced precipitation with warming (Fig. 3c and d), which indicates that soil moisture was the most important controlling factor for Rs under a warming climate. This is consistent with other studies (Chen et al., 2017a; Zhao et al., 2017). However, statistical analysis showed that overall no significant impact on Rs was found during the experimental period due to warming (it was reduced by 9.99 %). This is because our gas samples were taken at 10:00–12:00 each day, when average soil temperatures were increased by about one degree. Thus mean annual Rs was not sensitive to temperature changes this small in contrast to the very significant effects of short-term diurnal changes in soil temperature observed between 12:00 and 17:00 (Fig. 3a and c). However, gas samples during 10:00–12:00 in this study was able to catch the mean warming effects on Rs, except in some extreme precipitation and drought events in summer (Fig. S1), which require further systematic evaluation. Those results indicated that Rs depends mainly on variations of soil moisture and temperature in the context of warming, and climate change is likely to have a very significant effect on temperate deserts.

Figure 5Structure equation model (SEM) testing the multivariate (soil moisture, soil temperature, soil NH${}_{\mathrm{4}}^{+}$-N content, DOC and pH) effects on Rs (n= 34). Arrows show the effects of different key controls on Rs analyzed. The blue arrows indicated positive effects, and red arrows showed negative effects. The width of the arrows indicate the strength of the relationship. The numbers are standardized path coefficients, which can show the importance of the variables in the model. Goodness-of-fit statistics for the model are shown below the model. Asterisks indicate significant effect at P < 0.05.

## 4.2 The interactive effects of precipitation, N deposition and warming on Rs

Interactive responses of Rs were much lower than those of any single-factor, but still increased Rs overall, except with the interaction between precipitation and high N deposition (Table 1). This is consistent with results in dry ecosystems (Morillas et al., 2015; Martins et al., 2016), but not with the results of a meta-analysis of precipitation and N deposition interactive experiments which showed greater positive effects on Rs (L. Y. Zhou et al., 2016). This can be explained in our study due to soil MBC or MBN being much lower in interactive treatments than those of single-factor (Fig. 1d), showing that the number of microorganisms was much smaller in interactive treatments than that of single-factor due to the much stronger N effect. As we found that Rs was reduced with increasing N deposition and precipitation by as much as 4.25 % in W1N2 plots (Table 1), this showed that the inhibiting effect of soil NH${}_{\mathrm{4}}^{+}$-N content was much stronger when there was sufficient soil moisture (Fig. 2e). This is consistent with the results in a Populus euphratica community in a desert ecosystem (He et al., 2015). This was because (i) microbial activity was inhibited by high or low soil moisture and high soil NH${}_{\mathrm{4}}^{+}$-N or NO${}_{\mathrm{3}}^{-}$-N content (Burton et al., 2004) and (ii) high N content to reduce extracellular enzyme activity and the fungal population (Maris et al., 2015). In addition, the interactive effect of the three factors on Rs in this desert was much lower than interaction of two factors of precipitation and N deposition (Table 1), and is consistent with the results of modeled interactive effects, which showed that three-factor interactions were rare while two-factor interactions were more common (Luo et al., 2008). Fortunately, the interactive effect of three factors or two factors (precipitation, N deposition and warming) in this desert could largely reduce between-year variation on Rs (Table 2), which may because (i) the limits of soil moisture, soil temperature and soil N content were lifted for key biological processes by increasing precipitation, N deposition and warming (Huang et al., 2015a; R. Liu et al., 2016) and (ii) various factors counteracting each other (L. Y. Zhou et al., 2016). However, the effects of the variation on Rs in the growing season on Rs can be increased by warming, elevated precipitation and N deposition because of their dominant effects on plant growth and microbial activity (Huang et al., 2015b), but it was the exact opposite in the non-growing season due to the reduced temperature limitation (Zeng et al., 2016). Those results showed that Rs would be reduced under interactive effect of increasing rainfall, temperature and N deposition in the future, and positive carbon–climate feedback took place.

## 4.3 Temporal effects of the variation in treatments on Rs and controlling factors

Significant cumulative effects on Rs were found by elevated N deposition rather than increasing precipitation and warming alone (Table 2). A previous study here showed that Rs decreased due to N addition over the experiment's duration (Zhou et al., 2014), which was inconsistent with our results (Fig. 2d) because in our study, we used relatively lower rates of N addition than that Zhou et al. (2014), and the composition of microbial community and soil properties were altered gradually by long-term and high N deposition (Fig. 1c and d; Huang et al., 2015b; Zong et al., 2017). In addition, significant cumulative effects in the interaction between N deposition and precipitation or warming on Rs were also found (Table 2), and Rs decreased by 4.25 % by interaction between increasing precipitation and high N deposition (Table 1), which indicated that the response of Rs to N deposition is largely dependent on soil moisture in desert soil. This may be attributed to the antagonistic interaction between elevated N deposition and precipitation on Rh (L. Y. Zhou et al., 2016). Those results indicated that N deposition produced strong cumulative effects on Rs in this desert, and was enhanced largely with increasing soil moisture, which would reduce carbon emission from soil to atmosphere.

Regression analysis shows that Rs exhibited a unimodal change pattern with variations of soil NH${}_{\mathrm{4}}^{+}$-N (Fig. 4d), moisture (Fig. 4g), and temperature (Fig. 4h), and Rs was significantly positively correlated to soil dissolved organic carbon (DOC) and pH (Fig. 4e and f). However, structural equation modeling indicated that soil temperature was a more important controlling factor than soil NH${}_{\mathrm{4}}^{+}$-N and soil moisture (Fig. 5). This is consistent with most research results (Wu et al., 2016; Y. M. Zhou et al., 2016; Chen et al., 2017a). In addition, a large interannual variation was observed (CV = 41.4 %) during our experiment (Table 1), while the variation of annual precipitation and air temperature were only 4.41 and 7.78 %, respectively (Table 1), but close to the CV of spring root biomass of ephemeral plants (47.14 %), with 24 times greater aboveground biomass of spring ephemeral plants in 2016 than in 2015 (Cui et al., 2017), which indicated that the increase of Rs in 2016 was mainly from the root respiration of ephemeral plants. This is consistent with previous studies showing that ephemeral plants mediated the interannual variations of carbon fluxes in this desert (Huang et al., 2015c; R. Liu et al., 2016). It is different from other ecosystems where interannual variations of Rs were mainly dependent on variations in annual precipitation and air temperature (Gerard et al., 1999; Asensio et al., 2007; Chen et al., 2012). Overall, our results indicate that annual variation in Rs in this temperate desert is mainly controlled by soil temperature, but between-year variation in Rs is mainly controlled by ephemeral plants.

5 Conclusions

Climate change and elevated N deposition play important roles in controlling Rs in temperate deserts. We found that increasing precipitation and N deposition significantly increased Rs in the Gurbantunggut Desert, but warming reduced Rs, mostly because of the variation of soil moisture. In addition, we found that the interactive responses of Rs were much lower for the combination of precipitation, N deposition and warming than for any single factor. Additionally, Rs is mainly mediated by soil moisture, soil temperature and soil NH${}_{\mathrm{4}}^{+}$-N content, but soil temperature is the most important, with between-year variation in Rs mainly controlled by ephemeral plants. These results showed that Rs is very sensitive to increasing precipitation, N deposition and warming, and their interactive effects could reduce soil carbon emissions and thus the impacts of climate change.

Data availability
Data availability.

All data used to generate the figures are available upon request to the corresponding author.

Supplement
Supplement.

Competing interests
Competing interests.

The authors declare that they have no conflict of interest.

Special issue statement
Special issue statement.

This article is part of the special issue “The 10th International Carbon Dioxide Conference (ICDC10) and the 19th WMO/IAEA Meeting on Carbon Dioxide, other Greenhouse Gases and Related Measurement Techniques (GGMT-2017) (AMT/ACP/BG/CP/ESD inter-journal SI)”. It is a result of the 19th WMO/IAEA Meeting on Carbon Dioxide, Other Greenhouse Gases, and Related Measurement Techniques (GGMT-2017), Empa Dübendorf, Switzerland, 27–31 August 2017.

Acknowledgements
Acknowledgements.

This work was financially supported by the Chinese National Basic Research Program (2014CB954202), the National Natural Science Foundation of China (41603084, 41703131, 41425007), the special training program for science and technology talents of ethnic minorities in Xinjiang (2016D0201) and the Ten-Thousand Talent Program (Xuejun Liu). Keith Goulding was supported by the Sino-UK cooperative project on nitrogen (CINAg).

Edited by: Christoph Heinze
Reviewed by: two anonymous referees

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# zbMATH — the first resource for mathematics

The coincidence of critical points in Poisson percolation models. (English. Russian original) Zbl 0661.60122
Theory Probab. Appl. 32, No. 3, 547-550 (1987); translation from Teor. Veroyatn. Primen. 32, No. 3, 603-606 (1987).
The authors consider a continuous percolation model in $${\mathbb{R}}^ d:$$ percolation through clusters of “defects” of variable random shape of which the centers have Poisson distribution with intensity $$\lambda$$. We can define two percolation tresholds $$\lambda_ T$$ and $$\lambda_ H$$. The first one is the point of divergence of mean cluster size and the second is the maximal value of $$\lambda$$ for which the probability of existence of an unbounded cluster is equal to zero. For a wide class of situations the coincidence between $$\lambda_ T$$ and $$\lambda_ H$$ is proved (for example in the case of a finite number of shapes of defects).
Reviewer: P.A.Kučment

##### MSC:
 60K35 Interacting random processes; statistical mechanics type models; percolation theory 82B43 Percolation
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## Generators of multiplicative group $$(\mathbb{Z}/2^{\alpha}\mathbb{Z})^*$$

The set of all unit elements in the cyclic group $$\mathbb{Z}/N\mathbb{Z}$$ is a group under multiplication modulo $$N$$ of order $$\phi(N)$$, where $$\phi$$ is the Euler-totient function. It is denoted by $$(\mathbb{Z}/N\mathbb{Z})^*$$.
It is well known that $$(\mathbb{Z}/N\mathbb{Z})^*$$ is not always cyclic (Primitive element theorem) (See Chater 10, [1]). For example $$(\mathbb{Z}/8\mathbb{Z})^*=\{1,3,5,7\}$$ is not cyclic. $$(\mathbb{Z}/2\mathbb{Z})^*=\{1\}$$ and $$(\mathbb{Z}/4\mathbb{Z})^*=\{1,3\}$$ are trivially cyclic.

Question: Show that for $$\alpha\geq 3$$, $$(\mathbb{Z}/2^{\alpha}\mathbb{Z})^*$$ is generated by $$-1$$ and 5?
You may use the following sage code for validating the result:
Reference: [1] T M Apostol, Introduction to Analytics Number Theory


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## where is andromeda???

Universal Sandbox looks very interesting: Thanks for the lead.

A couple of other interesting simulator programs are the Mars24 Sunclock, which tells you the real time on Mars (runs on Java), and Stellarium, which is open source 3D planetarium software program. Both are free.


text: intersecting chords calculator. A circle with radius 3 m is divided in 24 segments. Does education pay? Figure 1 shows the relationship between income and education, for a representative sample of 637 California men age 25-29 in 1988. Let two line-segments are given. The heel height, overhang, and ridge and fascia boards for both roofs will be the same. 2 sides are given in the first triangle, distance from center and 1/2 the chord length. To find point P3, the calculator uses the following formula (in vector form): And finally, to get a pair of points in case of two points intersecting, the calculator …. AB = 4 cm, CD = 11 cm and PD = 15 cm. The Beginnings of Trigonometry. Basically, start from 1 chord, compute all answers and add them to cache. Our second possibility is when two secants intersect inside the circle. All angles inside a circle are formed by two intersecting chords. We can use this basic form to calculate …. Typical intersections are shown in Figure 12-1. In the circle, the two chords P R ¯ and Q S ¯ intersect …. In this equation, x and y represent the independent and dependent variables, m shows the slope of the function and b represents its y-intersect. Space separated/Grade separated intersection: These intersections facilitates movement at different levels for vehicles and pedestrians. This kite's diagonals are two chords that cross each other, . A variety of pdf exercises and word problems will help improve the skills of students in grade 3 through grade 8 to identify and differentiate between parallel, perpendicular and intersecting lines. Contrast Intersect with Identity. The Field Calculator button in the attribute table allows you to perform calculations on the basis of existing attribute values or defined functions, for instance, to calculate length or area of geometry features. 4th If this calculator helps you, please purchase our apps to support our site. Next, you need to add them and divide them into two: 5 + 7 = 12. Just double that to get the length of the second cord. Intersecting Chord Theorem A great time-saver for these calculations is a little-known geometric theorem which states that whenever 2 chords (in this case AB and CD) of a circle intersect at a point E, then AE • EB = CE • ED. 10'x10' = 100sf (1 square) Roof Area Calculators…. ABC is a triangle with AB = 10 cm, BC = 8 cm and AC = 6cm (not drawn to scale). Problem Chords AB and CD intersect each other at E inside the circle. Work in a variety of programming languages with the code editor. Length of Chord in a Circle, Perimeter. 7th Suspended 2nd Suspended 4th Dom. If we want a certain sort order or type, …. In this type of valley the main roof is framed and sheathed as usual and the intersecting …. If two circle chords intersect then the product of the size of part of one chord . A C N D P M O B Solution We let x represent the length PC. The Intersecting Chords Theorem asserts the following very useful fact: Given a point P in the interior of a circle with two lines passing through P, AD and BC, then AP*PD = BP*PC -- the two rectangles formed by the adjoining segments are, in fact, equal. Repeat parts (a)–(c) several times. Formula used : If two chords AB and CD intersect at outer point P then, PA × PB = PC × PD. Select the desired units, and click OK. Without Circle Theorems; Mixed Calculations…. The intersection requires solving a system of two linear equations. The points p1, p2 from the first line segment and q1, q2 from the second line segment. According to this formula arc length of a circle is equals to: The central angle θ in radians. One method to find the point of intersection is to substitute the value for y of the 2 nd equation into the 1 st equation and solve for the x-coordinate. The following four statements are equivalent. It will generate a textual output indicating which elements are in each intersection or …. Intersecting Chords When two chords intersect in a circle, four segments are formed. Count ways to divide circle using N non-intersecting chords. It can be used to determine if a specified Range Object intersects another specified range (s). Given two chords AB and CD of a circle intersect at right angle. 5 cm, raduis OT= 8 cm P 10 cm calculate …. AD and MN are chords that intersect at point B. Intergreen Time Calculation Method of Signalized Intersections Based on …. For further information, just move the mouse over one of the words above. Ellipse (v) Parabola (v) Hyperbola (v) By changing the angle and location of intersection, we can produce a circle, ellipse, parabola or hyperbola; or in the special case when the plane touches the vertex: a point, line or 2 intersecting …. find the length of the common chord of the intersecting circles x2+y2-4x-5=0 and x2+y2-2x+8y+9=0. Since vertical angles are congruent, m ∠ 1 = m ∠ 3 and m ∠ 2 = m ∠ 4. In geometry, a branch of mathematics, perpendicular lines are defined as two lines that meet or intersect each other at right angles (90°). Circles chords and tangents 1. Remember that parallel bearings don't intersect, and calculations involving distances won't intersect …. Do you teach Math 6-8 or Algebra 1? Check out the Desmos …. The Surface intersections query is used to create an edge network at the point of intersection of surfaces. We have to check whether both line segments are intersecting or not. The aim is to find the two points P 3 = (x 3 , y 3) if they exist. To calibrate the calculation method, traffic at several intersections was observed by video and analyzed for traffic volumes, delays, compliance with priority rules, and other parameters. This can be done from either the table view in Map Viewer or from the Data tab from your item description page. Use tutorials to add the ArcGIS API for Python to your Jupyter notebook. This chord forms an angle of 47° with the radius r1 of the circle c1 and an angle of 24° 30´ with the radius r2 of the circle c2. Introduction; Solving Equations; Polygons. The angle between two chords intersecting inside a circle has the measure half the sum of the measures the arcs intercepted by the chords…. Therefore, Chord AB ≅ Chord CD. What is the expected number of pairs of chords that intersect? Math. So: If , , , and , then we would have to solve for. Length of arc formula = θ × 2 A ÷ θ. If AB 15 OP 10 cn em and AC = 7. Intersecting chords theorem worksheet Intersecting chords angle measure theorem worksheet. [2] [3] Question 1 2 The chords PR and SQ of the circle intersect atT. Geometry (Plane) Theorems about proportional relationships among the segments of the sides of a triangle. Example 2: If two intersecting chords of a circle make equal angles with the diameter passing through. Intersecting Chords CP PB = 7 cm and AP = 15cm. Two or more lines that meet at a point are called intersecting lines. If the inputs are line or polygon, the output will be a multipoint feature class. Solution Notice that ST&*and QP&*are chords that intersect at R. And also, we can use this calculator to find sum of interior angles, measure of each interior angle and measure of each exterior angle of a regular polygon …. Hence, the distance of the chord from the centre is 6 cm. Two parallel chords of lenght 24cm and 10cm which lie on opposite sides of the circle are 17cm apart. That Intersect Circles 11 1 Answers intersect circles 11-1 Lines that Intersect Circles Identify each line or segment that intersects each circle. How Do You Use Intersecting Chords to Find Arc Measures in a Circle? Find the measure of arc MP. In this activity, students will investigate properties of angles and arcs formed when chords, secants, and tangents intersect and intercept arcs in a circle. Calculate the intersection of 2 arcs defined by the points A, B, C, and D , storing the result in out. This calculator worked amazingly well. If two chords or secants intersect in the interior of a circle, then the product of the lengths of the Calculate the radius. The outputs are the arclength s. If a chord and a tangent intersect externally, then the product of the lengths of the segments of the chord is equal to the square of the length of the tangent from the point of contact to the point of intersection. When we have two chords that intersect inside a circle, as shown below, the two triangles that result are similar. The following is the approximate calculation formula for the circumference of an ellipse used in this calculator…. Calculate the length of the perpendicular from O toGH. Emf corresponding to (25 – 0) °C = 252 = 625 μV. For a good straight fascia, add an extra inch or 2 to the tails of all your rafters (total …. Then in the CommandManager, on the Evaluate tab, click Mass Properties. If two chords intersect inside a circle, then the product of the lengths of the segments of one chord equals the product of the lengths of the segment of the other chord. For example, to calculate the Monthly Change and Total Change. The curves L1,L2 can be either …. Scissors: The two arms of the scissors form intersecting lines. Opens a text window containing information about the active image (including the pixel or voxel size, since IJ 1. Ask the students to pretend that the lake is a perfect circle. For angles in circles formed from tangents, secants, radii and chords click here. zArc, chord and circumference of a circle zQuadrilateral and its types 19. The circular arc is in red and is of radius r. Here is how the Angle formed by intersecting tangent and chord of Circle calculation can be explained with given input values -> 68. Here you can find the set of calculators related to circular segment: segment area calculator, arc length calculator, chord length calculator, height and perimeter of circular segment by radius and angle calculator. That point would be on each of these lines. Why not try drawing one yourself, measure the lengths and see what you get? Why is this true? Because there are similar triangles! Looking below: The angles θ are the same (see vertically opposite angles) The angles φ are the same (see inscribed angles). The Federal Highway Administration’s (FHWA’s) intersection safety and design research facilitates the implementation of short-term safety improvements, and defines and evaluates long-term, higher payoff strategies to improve intersection …. There are two circles C1 with radius r1, central coordinate (x1, y1) and C2 with radius r2 and central …. Intersecting lines are lines that cross each other. Energy Efficiency as a Tool for Developing and Preserving Affordable Housing. You'll gain access to interventions, extensions, task implementation guides, and more for this video. April 10th, 2019 - Related Word arc Use Your Vocabulary 3 Complete each statement with always sometimes or never A chord is 9 a diameter A diameter is 9 a chord congruent central angles have congruent chords 6 If AOB gt COD then AB gt Converse Within a circle or in congruent circles congruent chords …. Calculators Protractor Ruler Pair of compasses. formed by two intersecting lines? Classiﬁ cation of Angles Acute: Right: Obtuse: Straight: Less than 90° Equal to 90° Greater than 90° and Equal to 180° …. Step #2: Select which side of the right triangle you wish to solve for (Hypotenuse c, Leg a, or Leg b ). Depending on the figures you know this rhombus calculator can perform the following calculations: If Angle (A) is given then the other 3 angles will be computed: B = 180° - A. Technique to create row and column totals in Crosstab report. Ability to take a photo of your math problem using the app. 03m from point C and has a perpendicular distance of 2. 12 × 25 = 300; 13 × 23 = 299; Very close! If we measured perfectly the results would be equal. Figure 2: A rectangular plane intersecting a great circle path and the center of the Earth (arc b is the path and the angular separation of the end points). The horizontal chord has a 5 unit piece and… what? By the intersecting chords theorem, so. It is not intended for use in scripting and is not available in the ArcPy Spatial Analyst module. The Angle formed by intersecting tangent and chord of circle formula is defined as the half of the length of the arc cut out by the chord is calculated using Angle = Arc Length /2. Roadway Design Manual: Cross Sectional Elements. Multiple List Comparator is a free online tool made to compare two or more item lists, find the shared items (dataset intersections), and output both tabular and graphical results. Tangents and Intersecting Chords Exercise 18A – Selina Concise Mathematics Class 10 ICSE Solutions. If two chords intersect in a circle, the product of the lengths of the segments of one chord equal the product of the segments of the other. formulas for arc Length, chord and area of a sector In the above formulas t is in radians. This model starts with calculation of the conflicting traffic for minor-street movements; as follows: 6. Examples: Input : N = 2 Output : 2. The measure of an angle formed by two secants drawn from a point outside a circle is equal to half the difference of the. The portion of the secant contained within the circle is called a chord. sizeOfNull is set to false or spark…. Online calculator for circle segment area calculation. Calculate the area of a sector: A = r² * θ / 2 = 15² * π/4 / 2 = 88. The chord (span) connecting the ends of the arc is divided in half, and that is labeled l in the diagram. Step 3: Finally, the length of a chord will be displayed in the output field. For angles in circles formed from tangents, secants, . They make use of the Central Angle theorem, which ensures that the measure of a central angle of a circle is equal to the measure of its intercepted arc. Coub is YouTube for video loops. Two ways are different if there exists a chord that is present in one way and not in other. Interval Notation and Set Builder Notation Calculator: This calculator determines the interval notation and set builder notation for a given numerical …. If array_intersect() doesn't appear to be working, check your inputs using var_dump() to make sure you're not trying to intersect …. Hide this folder from students. Definition: A conic section is the intersection of a plane and a cone. So the red square’s area is 64, but unfortunately it’s the circle whose area we need…. ABC is an isosceles triangle inscribed in a circle. PC) is a tangent to the circle. The figure below shows a circle centre O. Errata: For the example 2, the answer should be x = 9. The first arc is defined by points A and B. The first INTERSECT BY LEXUS was conceived in 2013 in Aoyama, Tokyo, an area known for pioneering design, fashion, art, music, and technology. It features two line segments, 𝐴𝐵 and 𝐶𝐷, which intersect at a point 𝐸. concavo; JARAK ANTARA DUA TITIK; Transversal Intersects Parallel …. Quick-Tip: Intersect Faces in SketchUp Just select one of the objects, move it by pressing the quick-key “m” and place it on the other as you require. Although diameter and perimeter as measurements - don't seem to fit very well. To calculate the subchord, C = 2R sin (∆/2) may be used. Answer: The lengths of the segments of the other chord are 3 units and 8 units. It is a little easier to see this in the diagram on the right. com/calculator/xnkpcq66bn Pick two numbers between 0 and 1. Since vertical angles are congruent, m ∠ 1 = m ∠ 3. The cord of a circle is a segment whose endpoints are on the circle. Intersect DAX= INTERSECT ('Table-1', 'Table-2') Intersect …. See terms and apply now - for PayPal Credit, opens in a new window or tab…. In the Query/data tab, select in the Catalog box the Qty field and then the "Summary" button. Theorem 9-12: The measure of the angle formed by two chords that intersect inside a circle is the average of the measure of the intercepted arcs. If two chords intersect inside a circle, then the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord. Intersecting Chord Relationships. A chord of length 14 cm is at a distance of 24 cm from the centre of a circle. A line segment contained entirely within the rectangle or that does not intersect …. Plane Geometry: Diameters and Chords, Theorems and Problems Intersecting Circles, Chord, Diameter…. The measure of an angle formed by two chords that intersect inside a circle is …. Calculate the area of the circular sector, from which subtract the area of the triangles whose base is the circles' chord defined by the …. The special case of the intersecting cord theorem that we used here takes advantage of knowing that the full chord AC passes through the origin of the circle. Jack Rafters intersect Layover Valley Calculator Sloped Frustum of a Pyramid or Cone Calculator Cross Vault Purlin Calculator Circle Calculators Circle Center given Three Points on the Circle Sagitta given Arc Length and Chord Rectangular Hyperbola Calculator …. The intersect keyword is the last piece of the puzzle. You can use the TI-84 Plus calculator to find accurate points of intersection for two graphs. = √ ( 10 2 - 8 2) = √ ( 100 - 64) = √ 36 cm. More than 50 percent of the combined total of fatal and injury crashes occur at or near intersections. Add the columns to output till the Semantics node. Proposal of the priority stream volume determination for intersections with bending right-of way According to the traffic survey results, the calculation of the priority stream volume for both intersections was proposed. The new guidelines will cover pedestrian access to sidewalks and streets, including crosswalks, curb ramps, street furnishings, pedestrian signals, …. A central angle is an angle formed by two radii with the vertex at the center of the circle. As seen in the image below, chords AC and DB intersect inside the circle at point E. Guided, step-by-step explanations to your math solutions. Sorry only blank or numerical values are accepted. Tangents and Intersecting Chords Exercise 18C - Selina Concise Mathematics Class 10 ICSE Solutions. The formula for the area of a sector is (angle / 360) x π x radius2. All operators in a calculation are evaluated in a specific order. Circles, Radius Chord Relationships, Distance From The Center To A Chord. This calculator uses the standard equation of the circle that …. If the area of the minor segment is 5. Movie Clip (with narration) Vertical Line: how to find the equation. This is because, when students practice the worksheets, they learn about all the concepts of the subject deeply. 4, 1Two circles of radii 5 cm and 3 cm intersect at two points and the distance between their centres is 4 cm. Enter the intersection angle, degree of curve, and point of intersection in the input boxes below. This function is used to clip a line segment to a rectangle. In the figure, given below, O is the centre of the circumcircle of triangle XYZ. Take a look! Keywords: problem; circle; intersecting chords;. In the Non-empty behavior list, select the check box for Internet Sales-Sales Amount, and then click OK. In this situation, each chord cuts the other into two sub-intervals called intercepts. The Blind Valley roof can be used to calculate …. For intersecting circles, how to remove overlap Learn more about circle intersections, circle overlap, chord length, random I am trying to remove the circle overlap from the intersection, and have the chord itself (not present in the image) visible. In the ArcToolbox Search tab, enter clip as the operation to search for and click Search. With our tool, you need to enter the respective value for Arc Length and hit the calculate …. They are commonly used in railway sidings and sometimes on railway tracks and roads meant for low speeds. org 4 15 In the accompanying diagram, AB is tangent …. This set of notes deals with the Intersecting Chord Theorem; But first make sure you are familiar with the names of parts of a circle. Students must learn to use a variety of methods and tools to compute, including paper and pencil, mental arithmetic, estimation, and calculators. As the product is the same for both line segments, the intersecting chords theorem is satisfied, and so the two line segments 𝐴𝐵 and 𝐶𝐷 are chords of the same circle. Method 1Method 1 of 4:Identify the Weight. In the given circle, ∠AOB and ∠CODare central angles. To accurately find the coordinates of the point where two functions intersect…. Now in the middle there are two numbers at once - 5 and 7. Figure $$\PageIndex{1}$$ This makes the corresponding sides in each triangle proportional and leads to a relationship between the segments of the chords, as stated in the Intersecting Chords. Open Analysis Tools > Overlay > Intersect. The circumference can be found by the formula C = πd when we know the diameter and C = 2πr when we know the radius, as we do here. Calculate the length of a rafter from the roof slope ratio of inches per foot and a building width measurement. In a circle with center O, chords AB and CD intersect at point E. KLB Mathematics Book Three Pg 95-96 1: 3: Further Logarithms Further computation using logarithms By the end of the lesson, the learner should be able to: Solve problems involving logarithms Discussions Solving Demonstrating Explaining. A = ∫ a b [ f ( x) – g ( x)] d x. Intersections (40Kb) This VisualBasic program computes Intersections from observed data. This tutorial shows you how to use your knowledge of intersecting arcs in a circle to find a missing arc measurement. You should recognize that the chord and the radial line AB are perpendicular, so a is the height of triangle ABC and d is its base. How to use intersect in a sentence. The proof follows easily from the similarity of triangles ABP and CDP that is a consequence of the equality of. In Figure 1, lines l and m intersect at Q. This is an important and exam oriented question from Chapter name- circles Topic – Angle properties of circles Chapter number- 15 We have a figure given and AB and CD are two intersecting chords of a circle. Enter circle equation of the form: 4. limit-sin; Dilation of Point Centered at the Origin; cereghino. A, B, C and D are points on a circle. Solution: Using the secant of a circle formula (intersecting …. Calculate both radii and the distance between the two centers o. 622 Chapter 11 Circles Find the value of x. How many smaller circles fits witin a larger circle? If radii r1, r2 and distance d between the centers are given - then the angles α1 and α2 can be calculated as. For example, if the table states that …. This is the idea (a,b,c and d are lengths): And here it is with some actual values (measured only to whole numbers): And we get. Subtract 12 from both sides of the equation to get 6x - 12 = 2y. The power of a point is also known as the point's circle power or the power of a circle with respect to the point. You can also use the arc length calculator …. The radius of circle O is 16, and the radius of circle Q is 9. RS pRT 5 RQ pRP Use Theorem 11. Segment Lengths in Circles (Fully Explained …. Construct the point of intersection of the two segments. To find the percent of incline of a grade, solve the rise/run fraction as a decimal, then convert to a percentage. Theorem: In a circle, two congruent chords are equidistant from the. For this activity, students must choose the correct definition for the words line, line segment, ray, point, parallel, intersecting…. You do not need to know the proof this theorem. What does clicking on an item's icon in the "Factory" tab do? The "minimum pipe length" setting controls the minimum number of segments that a pipe will be permitted before the calculator …. Interest Calculations; Interior Angles formed by a secant and parallel lines; Intermediate Value Theorem; Internal point; Internal Tangent to Two Circles; Internet News sites; Intersecting Chords (Secants) Theorem. Students learn the following theorems related to chords, secants, and tangents. d is the perpendicular distance from the chord …. Do you know you can generate and download a scheme of work on your phone for free in less than 2 minutes? Schemes of work oline generator is the …. Next plug the x-value into either equation to find the y-coordinate for the point of intersection. The vertical chord is divided into a 10 unit piece and a 4 unit piece. Here are the procedures by which the Circle Calculator determines all of a circle's data from just 2 variables. The average grain size is found by dividing the number of intersections by the …. pdf from MATH 10 at Home School Alternative. Draw two chords in the lake that intersect. Continue Angles of intersecting chords theorem calculator tangent chord calculator Parallel Lines Cut Off Arcs In A Circle 3. In geometry, the problem of dividing a circle into areas by means of an inscribed polygon with n sides in such a way as to maximise the number of …. m = f (x) & m = g (x) m = f (x) & m = g (x) Where. an interface to the data stored in the database itself. But we can create our own function which counts the number of lines which intersect each polygon grid cell. Calculate path length given starting and ending coordinates. Four-leg intersections vary from a simple 90-degree intersection of two lightly traveled local roads to a complex intersection of two main highways. Angle of Intersecting Chords Theorem - Var…. The union, intersection, difference and complement of sets can be depicted graphically by means of Venn diagrams. Find the distance between the chords if both the chords are (i) on the opposite sides of the centre (ii) on the same side of the centre. Question 1: Prove that of any two chord of a circle, the greater chord is nearer to the centre. The common chord of the two circles c1 and c2 is 3. The proposed method makes use of the geometric relationship of chords…. Equation of the Common Chord of Two Circles. To determine the position of a line with respect to a circle, all we need to do is find its distance from the center of the circle, and compare it with its radius. This makes the corresponding sides in each triangle proportional and leads to a relationship between the segments of the chords, as stated in the Intersecting Chords Theorem. The Calculator app for Windows 10 is a touch-friendly version of the desktop calculator in previous versions of Windows. intersecting chords theorem calculator The area is 92 frac 1 3 92 approx 0. How to Calculate a Linear Supply Function. Circle A with chords EF and CD that intersect at …. Intersecting Chords Theorem: If two chords intersect …. Calculation of the area of a regular polygon. Given angle A calculate angles B, C and D. Find DP = PB = 6cm and AB 1 5 cm. Formula to calculate inscribed angle is given below: where, L = Length of minor arc R = Circle Radius. In the diagram below AB is the chord of a This applet will allow students to explore Now the property: it is actually an important theorem. M Worksheet by Kuta Software LLC Kuta Software - Infinite Geometry Name_____ Arcs and Chords …. The common chord AB = 9cm ad P and Q are the centres as shown: (a) Calculate the size of angles:-(i) APB (ii) AQB (b) Calculate …. D = B If side (a) is available then the perimeter (P) will be calculated…. Step 2: Now click the button “Solve” to get the result. If PA = 4, PB = 10 and CD = 13, calculate the length of the radius of the circle. This time we need to change it into point representation. In Figure 3, secant segments AB and CD intersect …. In this case, x and y represent the independent and dependent variables. ; In the Curve Calculator dialog box, specify whether the degree of curve is determined by arc or by chord by selecting an option from the Degree of Curve Definition drop-down list. This conjecture states that the perpendicular bisector of any chord passes through …. This website uses cookies to improve your experience, analyze …. The SQL UNION, SQL INTERSECT, and SQL EXCEPT clauses are used to combine or exclude like rows from two or more tables. You can see from the calculations that the two products are always. Enter the 2 factors to multiply and press the Calculate button: Division calculator. The point of intersection of the perpendicular bisectors is the radius of the circumscribed circle. Parallel and perpendicular line calculator. Intersection also commonly known as crossroad is any place where two or more than two roads intersect or meet each other at grade. (Load Calculations) Page 1 of 6 Load Calculations According to ASCE 7: Minimum Uniformly distributed Live Loads for Building Design: 40 PSF …. Calculator solve triangle specified by all three sides (SSS congruence law). Case 1: The line of action of the force is perpendicular to aa,. To calculate Angle formed by intersecting tangent and chord of Circle, you need Arc Length (s). Using the distance between the centers of two intersecting circles and their radii lengths we can compute the length of their common chord. 0 license and was authored, remixed, and/or curated by via source content …. Pt" notation to retrieve bearing or distance inverses in any field. With these field measurements, the calculation …. Two tangents BC and CD intersect at an angle of 34° are to be connected with a simple curve. The Worksheet_SelectionChange event procedure executes when a cell is selected. Calculate the length of the chord. There is also a special relationship between a tangent and a secant that intersect outside of a …. After adding the data points to your graph…. It will generate a customizable Venn diagram for up to five lists and display a matrix of all pairwise intersections. interesting to speculate how the masons of those days solved these complex problems with little or no knowledge of the calculations …. Square root of 2 times the area A that is divided by θ. SQL Union, Intersect, and Except. 5%, over 10 year(s): Total Value = $2061. Alice uses built-in math operators; they are: Mark for Review. Measure the width and length of the room in feet to calculate the area of the room. The segments AP and DP are secants because they intersect …. angle is an angle with its vertex "on" the circle, formed by two intersecting chords. Since most homes have a Rake wood, which is usually 6-8″ wide, you can …. For segments, rays, or arcs you may specify whether you want to Allow outlying intersections on tab Basic of the Properties Dialog. Intersecting Chords (Finding Angle Measure) If two chords intersect inside a circle, then the measure of the angle formed is one half the sum of the measure of the arcs intercepted by the angle and its vertical angle. The length of the common chord of two intersecting circles is 30 cm. Find the radii of the three circles. Line OQ connects the centers of the two circles and is 20 units long. Measure the distance between two distinct features. Change the name of this calculated member …. The general intersecting chord theorem tells us that the chord segments [AS] x [SC] = [BS] x [SD] no matter where the chords are drawn across a circle. The length of common chord of two intersecting circles is. Solution: Given: Two circles intersect …. We can apply the Intersecting Chords Theorem. We can then work out the length of a chord line in a circle. The distance from the center to the outer rim of a circle. Welcome to the wonderful world of calculator programming! To enter this world, start by pressing the PRGM button on your calculator. The diagram below shows what happens when tangents and secants intersect on a circle. The chords AB and CD intersect at the point E within the circle (Figure 1). The pitch of the roof is the rise over a 12-inch run. The Intersecting Chords Theorem asserts the following very useful fact: …. 1) Write Down the Basic Linear Function. To calculate the slope intercept form equation from two coordinates (x 1,y 1) and (x 2,y 2): Step 1: Calculate the slope (y 2 - y 1) / (x 2 - x 1) Step 2: Calculate where the line intersects with the y-axis by entering one of the coordinates into this equation: y - mx = b. Worksheets contain answers on the last page. Intersecting Chords Theorem If two chords intersect in a circle, the product of the lengths of the segments of one chord equal the product of the segments of the other. Show Step-by-step Solutions Intersecting chords of a circle. To find point P3, the calculator uses the following formula (in vector form): And finally, to get a pair of points in case of two points intersecting, the calculator uses these equations: First point: Second point: Note the opposite signs before the second addend. • three lines that intersect in one point; a + b + c = 180° a = d, b = e, c = f • given two intersecting lines and a third that moves but remains parallel to one of …. Perimeter = 2 * (width + height) Following print statements will …. Angle A = 1 2 \displaystyle \displaystyle = \frac{1}{2} . calculate the radius of the circle to the nearest whole number. What can be said about this intersection point if the chord PQ is a focal chord?. Median Calculator: Calculate Median Online & Free!. Another word for opposite angles are vertical angles. Define and Draw: Lines, Segments, Rays. Sum of Arcs Problem 5 Find the measure of AEB and CED. Enter line equation of the slope intercept form. Valid intersections enable you to define rules, called valid intersection rules, which filter certain cell intersections to users when they enter data or select runtime prompts. On the Query ribbon tab navigate to the Surface group and select Surface Intersections…. Selina Concise Mathematics Class 10 ICSE Solutions Chapter 18 Tangents and Intersecting Chords Ex 18C. Click on the total button (S) and name it "total Qty for Product Type" and "total Qty for Customer Name" (without the quotes). Circle is given by centre on S[-7; 10] and maximum chord 13 long. One arc shrinks by the same amount (x°) that the other arc grows (parallel chord …. The figure O and P are centres of two intersecting circles. Let us calculate all data necessary for …. For example, 2*1+2 is equal to 4 and not equal to 6, because multiplication is performed before addition (the * operator is always evaluated before the + operator). The percent change formula is used very often in Excel. The length of the common chord is. Total emf (T – 0) = 3000 + 625 = 3625 μV. Note that array_intersect() considers the type of the array elements when it compares them. Manual Calculation of the Slope of a Line. In the figure, m ∠ 1 = 1 2 ( m Q R ⌢ + m P S ⌢). To calculate interest:$100 × 10% = \$10. The length of the chord for a circle with radius 3 m can be calculated as. Let's say that you're calculating …. The general case can be stated as follows: C = 2R sin deflection angle Any subchord can be computed if its deflection angle is known. Then take 2 chords, compute all answers using the cache whenever you can. Formula for Angles of intersecting chords th…. = The length of common chord of two intersecting circles is 24 cm. 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Why not try drawing one yourself, measure the lengths and see what you get?. Two spheres intersect in a plane, and the equation to a system of spheres which intersect in a common circle is x 2 + y 2 + z 2 +2Ax -fD = o, in which A …. This calculator find and plot equations of parallel and perpendicular to the given line and passes through given point. α1 = acos [ (d2 + r12 - r22)/ (2 d r1)] α2 = acos [ (d2 + r22 - r12)/ (2 d r2)] Sponsored Links. This applet illustrates the theorem: The products of the intercepts of two intersecting chords (or secants) are …. v2 August 2014 - Includes linear height adjustment (Old version) Bearings (14 Kb) Simple excel formula calculating …. If d > r 0 + r 1 then there are no solutions, the circles are. If two operators have the same precedence (such as addition and subtraction (+ or -) they are evaluated from left to right in the calculation. 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# Node Graph

2. Creating nodes
3. Interacting with nodes
4. Types of nodes

The node graph is the central node interface defining the shader pipeline. You can consider it the “document” where the shader pipeline is “written” with nodes. In this panel, you can create nodes, select them to modify their properties and connect them to each other to build an image-processing shader pipeline.

This page covers how to use the Node Graph and lists the nodes that can be created within.

### Panning

• Middle mouse click and drag to pan around the graph

### Zooming

• Scroll wheel of the mouse
• Right mouse click and drag

## Creating nodes

Nodes can be created by right-clicking anywhere on the grid and selecting an option from the context menu.

## Interacting with nodes

Nodes can be selected by left-clicking on them and moved around by left-click-dragging them around. Multiple nodes can also be selected to be moved together either by left-click-dragging a marquee around them or by selecting more nodes with Ctrl pressed.

When an individual node is selected, its parameters will be shown in the Parameters panel. These parameters can be changed anytime for any node. Additional options for each node are available in their own context menu, which can be accessed by right-clicking on the node.

### Connecting nodes

Node plugs are used to connect the nodes with each other. Left-click on a plug to trigger the connection and click again on the plug you want to connect to.

Connections cannot be deleted, but can be overriden by new connections.

## Types of nodes

Multiple types of nodes can be used in Flair graphs with their unique uses.

Additional node presets are available, which can automatically insert and set one or more nodes in the graph. You can learn more about it in the Graph Presets documentation.


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# Time integral of a diffusion

Define $\bar\sigma^2_t=\frac{1}{t}\int_0^t\sigma^2(X_s)ds$ where $\sigma(x)\geq0$ is a measurable function and $X_t$ a diffusion process defined by $$dX_t=\alpha(X_t)dt+\gamma(X_t)dW_t\\\\ X_0=x_0$$ and $\sigma(x_0)>0$. Also assume $\mathbb{E}\left[|\sigma(X_t)-\sigma(X_0)|\right]=o(t^\beta)$ for some $1<\beta<2$.

My question is: What kind of conditions ensure $\displaystyle\lim_{t\to0}\mathbb{E}\left[\frac{1}{\bar\sigma_t}\right]<\infty$, or $\displaystyle\lim_{t\to0}\mathbb{E}\left[\frac{1}{\bar\sigma^2_t}\right]<\infty$?

Does it perhaps always hold as $\bar\sigma_t$ is a finite variation process? I'm not necessary looking for the minimal conditions, but rather something sufficient (but not trivial).

I assumed $\gamma=\sigma$.

If $\sigma$ vanishes somewhere and is only measurable, then your conditions are clearly not enough to guarantee anything, even if $\alpha=0$.

Indeed, take $\alpha=0$, $X_0=1$, and $\sigma(x)=1_{x>0}$. It is not hard to see that your condition $\mathbb{E}\left[|\sigma(X_t)-\sigma(X_0)|\right]=o(t^\beta)$ is satisfied. On the other hand, the diffusion gets stuck at $x=0$ if it reaches that point, so $$\mathbb{E}\left[\frac{1}{\bar\sigma_t}\right]\geq \infty \cdot\mathbb{P}(\tau_0<t/2)=\infty.$$

The situation changes if $\sigma>0$ or if there is a drift that pushes you away from points where $\sigma$ vanishes (for example, if $\sigma$ vanishes only at $0$, is Lipshitz, and $\alpha(0)>0$). For me, your question is a bit too wide in order to give a more precise answer.

If $\sigma$ is bounded away from zero: $\sigma^2(X)>M$, then $\overline \sigma_t^2\ge M$ and your expectations are finite.

Also if $\sigma(x_0)\neq 0$ and if $\sigma$ is continuous then together with $X$'s continuity you can apply the fundamental theorem of calculus to show, that $\overline\sigma_t^2$ converges almost surely to $\sigma^2(x_0)$.

To interchange the limit and the expectation you would then need to show that $\{1/\overline\sigma^2_t\}_t$ is uniformly integrable, which might help you. (There are several sufficient conditions for uniform integrability and boundedness is not necessary)


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# Binary classification to evaluate a object classifer. How to merge two samples/groups (different size)?

I'm evaluating a classifier to detect objects.

For example:
I have a set1 with 50 pictures with the object to detect.
And set2 with 100 pictures without the object.

I determine the true positves (0 in set2), true negatives (0 in set1), false negatives and false positives for those sets.

If I want to merge set1 with set2 (to have a set with and without objects and real values for TP and TP) I have to decrease the size of set2.

Question:

Can I do this with a simple division? (divide the values of TN, TP etc by 2) or do I have to randomly pick 50 pictures of set2 and use these TN's etc.?

Edit: Example:

Set1: TN = 43 FP = 6 FN = 1 TP = 0
Set2: TN = 0 FP = 13 FN = 0 TP = 87
Set2 divided by 2: TN = 0 FP = 7 FN = 0 TP = 44

Set12: TN = 43 FP = 13 FN = 1 TP = 44

I need an explanation to back this up. thx..

For the imbalanced data sets classification, downsampling is mostly used in the case when there is huge difference between the size of two groups, while for your case, maybe upsampling (aka duplicate your set1 to alter the balance) is a better strategy. You can also design your own strategy of resampling (bootstrap for example). Besides, studies have shown that Naive Bayesian classifier and decision tree algorithms are insensitive to the class rebalancing, so the performance of your sample merging may also be dependent on your sampling method. You can try several strategies to determine which one works best among them.

(You can also get more details on this topic from this pdf on imbalanced learning.)

• I think upsampling is not an option (can't take new pictures and won't use them twice). Down- or undersampling: Seems one way is to choose 50 pictures by random (as mentioned in your linked paper) – ddd Nov 21 '13 at 11:51
• I've updated the question with an example. – ddd Nov 21 '13 at 12:19
• Why down or upsampling is required? Isn't it enough to use the correct prior on the classes? – Cagdas Ozgenc Nov 21 '13 at 12:32
• not sure with the prior.. – ddd Nov 22 '13 at 14:00