共查询到20条相似文献,搜索用时 0 毫秒
1.
高山分布上限灌木的碳与养分生理碳水化合物不足是高山林线树种生长限制假说之一,国内外以碳水化合物为基础的高山林线研究已有很多,而与高山林线相比,人们对碳水化合物在灌丛线形成中的作用知之甚少。除此之外,土壤养分亦被视为限制高山树种向上分布的重要因素之一。本研究将探究欧亚多种高山灌木不同器官中非结构性碳水化合物(NSCs)、氮(N)和磷(P)在不同季节及高低海拔上的含量变化规律。研究结果显示,除了与夏季相比冬季细根中具有较低的P含量以外,不同海拔与季节对灌木不同器官中的N和P含量均无显著影响。冬季灌木枝条中的NSCs和可溶性糖含量显著高于夏季。海拔与季节对细根中NSCs、淀粉、可溶性糖和糖与淀粉比值的影响均有显著的交互作用。在冬季,灌木细根中的可溶性糖与淀粉含量在海拔上限处要显著低于其在低海拔处;而在夏季,这些指标在高低海拔间均无显著差异。本研究结果表明,与高山林线树种相似,海拔分布上限的灌木冬季细根中较低的非结构性碳水化合物含量可能限制了灌木的向上分布。 相似文献
2.
The current carbon supply status of temperate forest trees was assessed by analysing the seasonal variation of non‐structural carbohydrate (NSC) concentrations in leaves, branch wood and stem sapwood of 10 tree species (six deciduous broad‐leafed, one deciduous conifer and three evergreen conifer trees) in a temperate forest that is approximately 100 years old. In addition, all woody tissue was analysed for lipids (acylglycerols). The major NSC fractions were starch, sucrose, glucose and fructose, with other carbohydrates (e.g. raffinose and stachyose) and sugar alcohols (cyclitols and sorbitol) playing only a minor quantitative role. The radial distribution of NSC within entire stem cores, assessed here for the first time in a direct interspecific comparison, revealed large differences in the size of the active sapwood fraction among the species, reflecting the specific wood anatomy (ring‐porous versus diffuse‐porous xylem). The mean minimum NSC concentrations in branch wood during the growing season was 55% of maximum, and even high NSC concentrations were maintained during times of extensive fruit production in masting Fagus sylvestris. The NSC in stem sapwood varied very little throughout the season (cross species mean never below 67% of maximum), and the small reductions observed were not significant for any of the investigated species. Although some species contained substantial quantities of lipids in woody tissues (‘fat trees’; Tilia, Pinus, Picea, Larix), the lipid pools did not vary significantly across the growing season in any species. On average, the carbon stores of deciduous trees would permit to replace the whole leave canopy four times. These data imply that there is not a lot of leeway for a further stimulation of growth by ongoing atmospheric CO2 enrichment. The classical view that deciduous trees rely more on C‐reserves than evergreen trees, seems unwarranted or has lost its justification due to the greater than 30% increase in atmospheric CO2 concentrations over the last 150 years. 相似文献
3.
Plants that store nonstructural carbohydrates (NSC) may rely on carbon reserves to survive carbon‐limiting stress, assuming that reserves can be mobilized. We asked whether carbon reserves decrease in resource stressed seedlings, and if NSC allocation is related to species' relative stress tolerances. We tested the effects of stress (shade, drought, and defoliation) on NSC in seedlings of five temperate tree species (Acer rubrum Marsh., Betula papyrifera Marsh., Fraxinus americana L., Quercus rubra L., and Quercus velutina Lam.). In a greenhouse experiment, seedlings were subjected to combinations of shade, drought, and defoliation. We harvested seedlings over 32–97 days and measured biomass and NSC concentrations in stems and roots to estimate depletion rates. For all species and treatments, except for defoliation, seedling growth and NSC accumulation ceased. Shade and drought combined caused total NSC decreases in all species. For shade or drought alone, only some species experienced decreases. Starch followed similar patterns as total NSC, but soluble sugars increased under drought for drought‐tolerant species. These results provide evidence that species deplete stored carbon in response to carbon limiting stress and that species differences in NSC response may be important for understanding carbon depletion as a buffer against shade‐ and drought‐induced mortality. 相似文献
4.
Meghan Blumstein Jessica Gersony Jordi Martínez-Vilalta Anna Sala 《Global Change Biology》2023,29(7):1854-1869
Woody plant species store nonstructural carbohydrates (NSCs) for many functions. While known to buffer against fluctuations in photosynthetic supply, such as at night, NSC stores are also thought to buffer against environmental extremes, such as drought or freezing temperatures by serving as either back-up energy reserves or osmolytes. However, a clear picture of how NSCs are shaped by climate is still lacking. Here, we update and leverage a unique global database of seasonal NSC storage measurements to examine whether maximum total NSC stores and the amount of soluble sugars are associated with clinal patterns in low temperatures or aridity, indicating they may confer a benefit under freezing or drought conditions. We examine patterns using the average climate at each study site and the unique climatic conditions at the time and place in which the sample was taken. Altogether, our results support the idea that NSC stores act as critical osmolytes. Soluble Sugars increase with both colder and drier conditions in aboveground tissues, indicating they can plastically increase a plants' tolerance of cold or arid conditions. However, maximum total NSCs increased, rather than decreased, with average site temperature and had no relationship to average site aridity. This result suggests that the total amount of NSC a plant stores may be more strongly determined by its capacity to assimilate carbon than by environmental stress. Thus, NSCs are unlikely to serve as reservoir of energy. This study is the most comprehensive synthesis to date of global NSC variation in relation to climate and supports the idea that NSC stores likely serve as buffers against environmental stress. By clarifying their role in cold and drought tolerance, we improve our ability to predict plant response to environment. 相似文献
5.
Bjarke Veierskov A. Skytt Andersen B. M. Stummann K. W. Henningsen 《Physiologia plantarum》1982,55(2):174-178
Rooting ability was studied for cuttings derived from stock plants of wild type pea seedlings and seedings of two mutants deficient in photosystem II activity and chlorophyll. Stock plants were grown at 15, 20, 25 or 30°C at 38 W m-2 . Cuttings were rooted at 20°C and at an irradiance of 16 or 38 W m-2 . The rooting ability seemed to be correlated with the initial carbohydrate content only at 38 W m-2 . Based on the findings of the present study it may be concluded that for pea seedlings the growth temperature is more important than photosynthesis as regards accumulation of extractable carbohydrates. During the rooting period carbohydrates are necessary for root formation, but the effect of the iradiance on the number of roots formed is not mediated by the carbohydrate content. Under specific rooting conditions it is possible to correlate the initial carbohydrate content with the rooting capacity of the cuttings within a phenotype, but not always when different phenotypes are considered. The results indicate a connection between the metabolic activity of the cuttings and their ability to form adventitious roots. 相似文献
6.
叶片中非结构性碳水化合物(NSC)不仅是植物维持代谢活动的重要物质基础, 也随凋落物归还土壤并为土壤微生物提供碳源, 对凋落物分解和土壤有机质形成具有重要意义。该研究比较了同质园中11个亚热带代表性树种新鲜叶与凋落叶NSC (可溶性糖、淀粉)含量。结果表明, 所有树种新鲜叶NSC含量均显著高于凋落叶, 新鲜叶中NSC含量为68.7-126.3 mg∙g-1, 而凋落叶中NSC含量为31.4-79.5 mg∙g-1。同时, 可溶性糖含量在新鲜叶和凋落叶中的变化幅度均远大于淀粉: 可溶性糖在新鲜叶中的平均含量是凋落叶的3.3倍; 而淀粉在新鲜叶中的平均含量仅为凋落叶的1.2倍。另外, 对不同功能类群的比较发现, 常绿阔叶树种与落叶阔叶树种NSC含量差异并不显著, 而针叶树种NSC含量明显低于阔叶树种。具体表现为: 在新鲜叶中, 常绿阔叶、落叶阔叶树种NSC含量平均为99.7和96.8 mg∙g-1, 而常绿针叶树种平均为75.4 mg∙g-1; 在凋落叶中, 常绿阔叶、落叶阔叶树种NSC含量平均为47.2和50.7 mg∙g-1, 而常绿针叶树种平均为33.3 mg∙g-1。这些结果表明, NSC作为林木碳代谢组分, 在叶片衰老前可能向新鲜叶转移, 反映了林木叶片碳存储策略。然而, 不管是新鲜叶还是凋落叶, 杉木(Cunninghamia lanceolata)、马尾松(Pinus massoniana)等针叶树种叶片NSC含量显著低于阔叶树种, 这可能降低这些针叶树种凋落叶初始基质质量。 相似文献
7.
Plants grow in a light/dark cycle. We have investigated how growth is buffered against the resulting changes in the carbon supply. Growth of primary roots of Arabidopsis seedlings was monitored using time‐resolved video imaging. The average daily rate of growth is increased in longer light periods or by addition of sugars. It responds slowly over days when the conditions are changed. The momentary rate of growth exhibits a robust diel oscillation with a minimum 8–9 h after dawn and a maximum towards the end of the night. Analyses with starch metabolism mutants show that starch turnover is required to maintain growth at night. A carbon shortfall leads to an inhibition of growth, which is not immediately reversed when carbon becomes available again. The diel oscillation persists in continuous light and is strongly modified in clock mutants. Central clock functions that depend on CCA1/LHY are required to set an appropriate rate of starch degradation and maintain a supply of carbon to support growth through to dawn, whereas ELF3 acts to decrease growth in the light period and promote growth in the night. Thus, while the overall growth rate depends on the carbon supply, the clock orchestrates diurnal carbon allocation and growth. 相似文献
8.
非结构性碳水化合物是植物光合作用与生长利用之间主要的中间贮存物,在植物的生长和代谢过程中起着十分重要的作用。为了揭示落叶松(Larix gmelinii)根系根序间非结构性碳水化合物的分配及季节变化规律,探讨根系内可溶性糖和淀粉间的关系。本研究以落叶松根系为研究材料,在5~10月采集根系样品,采用根序法将细根分为1、2、3、4和5级,采用苯酚—浓硫酸方法和酶解法分别测定可溶性糖和淀粉浓度。结果表明:可溶性糖浓度在根序、月份及其交互差异性显著(P<0.001),1~5级根可溶性糖浓度的变化范围分别为4.42%~14.90%,4.35%~16.40%,5.67%~19.70%,5.91%~33.10%,6.95%~37.80%,不同根序可溶性糖浓度最大值均出现在7月。根序间淀粉浓度差异性不显著(P>0.05),月份间根系淀粉浓度差异显著(P<0.001),变化范围为23.36%~48.65%;淀粉浓度5~7月下降,随后上升,从8月份达到峰值,10月与5月差异不显著。研究结果可为阐明落叶松根系碳水化合物代谢和生长适应对策提供数据基础,对理解植物细根系统内部结构及功能异质性提供数据支撑。 相似文献
9.
Z. H. Ou 《Plant biosystems》2013,147(6):1160-1168
Spatial boundary conditions must be considered when utilizing mathematical modeling of plant root growth in the container or along with the imbedding solid obstacle. Using basic root growth principles and the geometry of the boundary surface, a mathematical model can be designed to keep all root elements inside the container or outside the obstacle without passing through the boundary after the minimum deflection of growth direction, and it is based on the minimum friction between root tips and soil and energy saving principles. Such a mathematical method is used to simulate the spatial distribution of root growth and the morphological architecture of the root system near the boundary. The validity of this model is supported by experimental observations that confirm some typical characteristics predicted by the simulations. This model can be widely used in resolving boundary condition complications where water and nutrients are consumed by plants in a spatially limited or heterogeneous resource field. 相似文献
10.
Anne L. Maddison Anyela Camargo‐Rodriguez Ian M. Scott Charlotte M. Jones Dafydd M. O. Elias Sarah Hawkins Alice Massey John Clifton‐Brown Niall P. McNamara Iain S. Donnison Sarah J. Purdy 《Global Change Biology Bioenergy》2017,9(7):1264-1278
In perennial energy crop breeding programmes, it can take several years before a mature yield is reached when potential new varieties can be scored. Modern plant breeding technologies have focussed on molecular markers, but for many crop species, this technology is unavailable. Therefore, prematurity predictors of harvestable yield would accelerate the release of new varieties. Metabolic biomarkers are routinely used in medicine, but they have been largely overlooked as predictive tools in plant science. We aimed to identify biomarkers of productivity in the bioenergy crop, Miscanthus, that could be used prognostically to predict future yields. This study identified a metabolic profile reflecting productivity in Miscanthus by correlating the summer carbohydrate composition of multiple genotypes with final yield 6 months later. Consistent and strong, significant correlations were observed between carbohydrate metrics and biomass traits at two separate field sites over 2 years. Machine‐learning feature selection was used to optimize carbohydrate metrics for support vector regression models, which were able to predict interyear biomass traits with a correlation (R) of >0.67 between predicted and actual values. To identify a causal basis for the relationships between the glycome profile and biomass, a 13C‐labelling experiment compared carbohydrate partitioning between high‐ and low‐yielding genotypes. A lower yielding and slower growing genotype partitioned a greater percentage of the 13C pulse into starch compared to a faster growing genotype where a greater percentage was located in the structural biomass. These results supported a link between plant performance and carbon flow through two rival pathways (starch vs. sucrose), with higher yielding plants exhibiting greater partitioning into structural biomass, via sucrose metabolism, rather than starch. Our results demonstrate that the plant metabolome can be used prognostically to anticipate future yields and this is a method that could be used to accelerate selection in perennial energy crop breeding programmes. 相似文献
11.
Li MH Xiao WF Shi P Wang SG Zhong YD Liu XL Wang XD Cai XH Shi ZM 《Plant, cell & environment》2008,31(10):1377-1387
No single hypothesis or theory has been widely accepted for explaining the functional mechanism of global alpine/arctic treeline formation. The present study tested whether the alpine treeline is determined by (1) the needle nitrogen content associated with photosynthesis (carbon gain); (2) a sufficient source-sink ratio of carbon; or (3) a sufficient C-N ratio. Nitrogen does not limit the growth and development of trees studied at the Himalayan treelines. Levels of non-structural carbohydrates (NSC) in trees were species-specific and site-dependent; therefore, the treeline cases studied did not show consistent evidence of source/carbon limitation or sink/growth limitation in treeline trees. However, results of the combined three treelines showed that the treeline trees may suffer from a winter carbon shortage. The source capacity and the sink capacity of a tree influence its tissue NSC concentrations and the carbon balance; therefore, we suggest that the persistence and development of treeline trees in a harsh alpine environment may require a minimum level of the total NSC concentration, a sufficiently high sugar:starch ratio, and a balanced carbon source-sink relationship. 相似文献
12.
Increased chilling tolerance and altered carbon metabolism in tomato leaves following application of mechanical stress 总被引:1,自引:0,他引:1
We investigated the effects of brushing on the chilling tolerance and metabolism of nonstructural carbohydrates (soluble sugars and starch) in tomato leaves before, during and after a chilling stress. Tomato plants ( Lycopersicon esculentum Mill. cv. Caruso) were cultivated either without mechanical stress application (control plants) or with daily brushing treatments for 15 days (brushed plants), prior to a 7-day chilling treatment (8/5°C day/night). Brushing resulted in shorter plants with a 34% reduction in leaf dry weight per area and a 59% reduction of soluble sugars and starch, on a dry weight basis. The sugar to starch ratio was not affected by brushing. A greater chilling tolerance in the brushed plants was demonstrated by the maintenance of a significantly higher PSII efficiency in brushed plants (42%) compared to that of the control plants (30%) after 7 days of chilling treatment, less visible damage to the leaf tissue, and a more rapid resumption of growth during 3 days of recovery as compared to control plants. During the chilling treatment levels of soluble sugars per leaf dry weight increased 15-fold in the brushed plants and 5-fold in control plants. In the present study we have demonstrated that brushing can increase chilling tolerance in tomato plants. The observed differences in chilling tolerance and concentration of soluble sugars in the leaves may indicate an involvement of soluble sugar levels in acclimation to chilling. 相似文献
13.
14.
Aim Across all latitudes, high‐elevation tree lines represent a drastic change in the dominant plant life‐form, from upright trees to low‐stature alpine plants. Although associated with low temperatures, the physiological mechanisms controlling this boundary are still not clear. The growth‐limitation hypothesis assumes a direct low‐temperature restriction of tissue formation at otherwise sufficient photoassimilation. In order to test this hypothesis, we present a global synthesis of previously published and new data on tree carbon supply status at high‐elevation tree lines. Location Global; 13 regions between 68° N and 45° S. Methods Late‐season concentrations of non‐structural carbohydrates (NSC) in foliage and branch wood were measured at three elevations across the tree line ecotones, from upper tall forests (timber line) to the edges of aborescent tree growth (tree line). Year‐round records of ?10 cm soil temperatures were taken at the tree line. Results Despite large differences in elevation and season length, the mean growing season temperature at the tree line was similar (approximately 6.6 °C) between all sites. NSC concentrations were not depleted at any of the elevation gradients between timber line and tree line, indicating no shortage of C at the uppermost tree stands. Tested across all sites, NSC concentrations in fact significantly increased with elevation. On average, NSC increased by 18% in leaves and 26% in branch wood from the lowest to the highest stands, primarily due to higher starch concentrations rather than free sugars. Hence, these responses do not reflect osmotic adjustments to lower temperatures at the end of the growing season. Main conclusions This global data set contributes to a mechanistic understanding of tree line formation based on biological principles across climatic zones and tree genera. No evidence of C shortage was found at the high‐elevation tree line in either seasonal and non‐seasonal regions. The increasing trend of NSC concentrations with elevation is in line with the growth‐limitation hypothesis. 相似文献
15.
The number of roots formed in cuttings of pea ( Pisum sativum L. cv. Alaska) was regulated both by the temperature and by IAA, whereas the time to the appearance of the first roots was regulated only by the temperature. Cuttings treated with 10-3 M IAA had a smaller content of extractable carbohydrates than the control ones irrespective of the temperature. In the bases of cuttings rooted at 25°C the content of extractable carbohydrates was lower than in those rooted at 15°C. Cuttings treated with IAA showed up to elevenfold increase of extractable carbohydrates in the bases at day 3. This increase of soluble sugars was not correlated with the number of roots formed or the speed of rooting. It is concluded that IAA affects the accumulation of carbohydrates, and this is not connected with the rooting ability of the cuttings. 相似文献
16.
Soil saccharide extraction and detection 总被引:6,自引:0,他引:6
Extraction of soil saccharides involves the use of reagents effective in breaking hydrogen and covalent bonds between soil
constituents and the saccharides. Of the many extractants proposed for saccharide determination, water is commonly used for
extraction of water-soluble mono- and polysaccharides in soil. Analysis of these water extracts by colorimetric assays (anthrone-sulfuric
acid and phenol-sulfuric acid methods) often show color development indicating that saccharides are present. However, high
performance liquid chromatography (HPLC) and gas chromatography analyses have indicated that these colorimetric assays are
prone to errors due to interferences from inorganic soil constituents such as Cl−, NO3
− and Fe+3. When water extracts (25° or 80°C) are put through deionization resins to remove interferences little to no saccharides are
present when assayed by the phenol-sulfuric acid analysis. The inability of water to extract saccharides from soil or microbial
polymers was confirmed by HPLC analysis. The phenol-sulfuric acid assay was found to be acceptable for saccharide analysis
of soil extracts only after being subjected to resin deionization for interference removal. The anthrone-sulfuric acid method
is not considered acceptable for determining saccharides in soil. 相似文献
17.
The historical range of longleaf pine (Pinus palustris P. Mill) has been greatly reduced, in part, by lack of fire. Recently, the application of fire has become an accepted practice for the restoration of longleaf pine to former parts of its natural range. This study was designed to evaluate the effects of season of prescribed fire on the root growth and nonstructural carbohydrate concentrations of longleaf pine, and identify the time of year when fire has the least negative effect on longleaf pine root processes. We found that root growth was generally less on July-burned plots than on either March- or May-burned plots and we attribute these responses to the effect of fire on interaction between root processes and the soil environment. Specifically, soil water and temperature conditions may have been less favorable for root growth on the July-burned plots compared to the March- and May-burned plots. With two years of information on the seasonal dynamics of foliage production, root growth, and root carbohydrates, we determined that at our study site, optimal prescribed fire would impact tree growth less in November through March compared to other times of the year. We also observed that severe drought during the 1998 growing season was associated with a 3-month delay in peak root growth, and prolonged drought in 1999 through 2000 coincided with a reduction in root starch storage. We conclude that season of prescribed fire potentially affects root processes, but that severe or prolonged drought may either interact with or override these effects. 相似文献
18.
Z. Zhai Y. Fang J. Cheng Y. Tian L. Liu X. Cao 《Plant biology (Stuttgart, Germany)》2023,25(5):771-784
- Drought is one of the most adverse environmental stresses limiting plant growth and productivity. However, the underlying mechanisms regarding metabolism of non-structural carbohydrates (NSC) in source and sink organs are still not fully elucidated in woody trees.
- Saplings of mulberry cv Zhongshen1 and Wubu were subjected to a 15-day progressive drought stress. NSC levels and gene expression involved in NSC metabolism were investigated in roots and leaves. Growth performance and photosynthesis, leaf stomatal morphology, and other physiological parameters were also analysed.
- Under well-watered conditions, Wubu had a higher R/S, with higher NSC in leaves than in roots; Zhongshen1 had a lower R/S with higher NSC in roots than leaves. Under drought stress, Zhongshen1 showed decreased productivity and increased proline, abscisic acid, ROS content and activity of antioxidant enzymes, while Wubu sustained comparable productivity and photosynthesis. Interestingly, drought resulted in decreased starch and slightly increased soluble sugars in leaves of Wubu, accompanied by notable downregulation of starch-synthesizing genes and upregulation of starch-degrading genes. Similar patterns in NSC levels and relevant gene expression were also observed in roots of Zhongshen1. Concurrently, soluble sugars decreased and starch was unchanged in roots of Wubu and leaves of Zhongshen1. However, gene expression of starch metabolism in roots of Wubu was unaltered, but in leaves of Zhongshen1 starch metabolism was more activated.
- These findings revealed that intrinsic R/S and spatial distribution of NSC in roots and leaves concomitantly contribute to drought resistance in mulberry.
19.
J. Kruse I. Hetzger R. Hänsch R.-R. Mendel H. Rennenberg 《Plant biology (Stuttgart, Germany)》2003,5(5):540-549
Abstract: Diurnal changes in starch, sugar and amino acid concentrations in source leaves, sink leaves and roots of tobacco plants were determined. In addition to wild type tobacco, transformed plants deficient in root nitrate reductase and exhibiting decreased rates of growth were employed. Further, the growth rates of tobacco plants were modulated by exposure to elevated pCO2. From the diurnal alterations in metabolite concentrations, the daily turnover of starch and amino N was estimated in order to: (i) elucidate whether turnover rates can be related to growth rates, and (ii) identify individual amino compounds with the potential to indicate nitrogen fluxes and the C/N status of plants. Elevated pCO2 increased growth rates and daily turnover of starch in both wild type and transformed plants, indicating enhanced rates of photosynthesis. In wild type plants, elevated pCO2 increased the turnover of amino N, notably glutamine and alanine, in mature source leaves, indicating enhanced nitrate reduction. By contrast, amino N turnover in source leaves of transformed plants was not affected by elevated pCO2, although nitrate reduction was presumably enhanced. Apparently, export of amino N was increased from the source leaves of transformed plants. This assumption was supported by a significantly increased turnover of amino N in young sink leaves compared to mature source leaves, indicating a preference for acropetal amino N allocation and import into the young leaves of the transformed plants. Further, elevated pCO2 increased the allocation of leaf‐derived amino N to the roots of transformed plants. This led to increased levels of amino compounds during the entire day, notably glutamate, but did not affect root growth of the transformed plants. The suitability of individual amino compounds as markers for major N fluxes, such as nitrate reduction, photorespiration, and amino N export and import is discussed. 相似文献
20.
K. Chapman E. P. Groot S. A. Nichol T. L. Rost 《Journal of Plant Growth Regulation》2003,21(4):287-295
Root apical meristems (RAMs) in dicotyledonous plants have two organizational schemes; closed (with highly organized tiers) and open (tiers lacking or disorganized). These schemes are commonly believed to remain unchanged during the growth of the root axis. Individual roots are commonly thought to have indeterminate growth. We challenge these two generalizations through the study of five species with closed apical organization: Clarkia unguiculata L., Oxalis corniculata L., Dianthus caryophyllus L., Blumenbachia hieronymi Urb., and Salvia farinaceae Benth. cv. Strata. These roots have phased growth patterns where early growth is followed by deceleration, after which the initial cells stop dividing, elongation ceases, and the root reaches its determinate length. At or before reaching determinacy, the root apical meristem stops maintaining its closed organization and becomes less organized. These observations will be placed in context with observations from the literature to suggest two new generalizations, namely, that apical organization does change over the growth phases of roots, and that roots are determinate. 相似文献