Skip to main content

Root-Soil Interactions

  • Chapter
Reactions and Processes

Part of the book series: The Handbook of Environmental Chemistry ((HEC2,volume 2 / 2D))

Summary

Root-soil interactions are physical, chemical and biological; the last two are stressed here. Changes in soil around the root follow the development of the root itself. Root density in different parts of soil is partly due to the genetic composition of the plant, partly to soil properties, including nutrient concentrations and water logging. The nutrient needs of plants, the ways in which nutrients are made available to plant roots and the mechanisms of transport are discussed, together with the value of modelling of root-soil interactions.

A large number of the most important chemical reactions in soil are mediated through the microbiological population. This includes all processes of organic material breakdown, and nearly all the important nitrogen transformations in soil. Microbes are strongly concentrated on the surface of roots and around them, largely due to the deposition of organic matter from the root into its immediate surroundings. Decomposition rates are therefore very high, but it is not clear whether nitrogen transformations are altered to an important extent. This activity may increase the soil availability of phosphate and trace elements. Symbiotic microbial systems mediate N2 fixation and increase uptake of phosphorus and trace elements from soil.

It is important that the root also changes the pH at its surface, mainly because of differences in the cation and anion uptake rates, and this has large effects on nutrient availability. The consequences of this are not yet fully understood. Some soils have potentially toxic concentrations of heavy metals, and a decrease in pH would intensify this. A major effect of acidity is the production of aluminium ions. Different plant species have very different susceptibility to toxic metals. A number of organic toxins may also be found in soil, some produced microbially in water-logged conditions, but a few exuded from roots.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Addiscott, T.M., Wagenet, R.J. (1985): Concepts of solute leaching in soils: a review of modelling approaches. Journal of Soil Science 36: 411–425

    Article  CAS  Google Scholar 

  • Aguilar, S.A., van Diest, A. (1981): Rock-phosphate mobilisation induced by the alkaline uptake pattern of legumes utilizing symbiotically fixed nitrogen. Plant and Soil 61: 27–42

    Article  Google Scholar 

  • Archer, J. (1985): Crop Nutrition and Fertilizer Use. Farming Press: Ipswich, UK

    Google Scholar 

  • Armstrong, W. (1978): Root aeration in the wetland condition. In: Plant life in anaerobic environments. Hook D., Crawford R.M.M. (eds), Ann Arbor Science Publishers, Ann Arbor, Mich. pp 269–297

    Google Scholar 

  • Asher, C.J., Edwards, D.G. (1983): Modern Solution Culture Techniques. In: Encyclopedia of Plant Physiology. New Series I5A, Inorganic Plant Nutrition. Lüuchli A., Bieleski R.L. (eds), Springer-Verlag: Berlin

    Google Scholar 

  • Bache, B.W. (1980): In: Effects of Acid Precipitation on Terrestrial Ecosystems. Hutchinson T.C., Havas M. (eds), Plenum: New York, pp 173–182

    Google Scholar 

  • Baker, A.J.M. (1981): Accumulators and excluders — strategies in the response of plants to heavy metals. Journal of Plant Nutrition 3: 643–654

    Article  CAS  Google Scholar 

  • Baldwin, J.P., Nye, P.H., Tinker, P.B. (1973): Uptake of solutes by multiple root systems from soil. III. A model for calculating the solute uptake by a randomly dispersed root system developing in a finite volume of soil. Plant and Soil 38: 621–635

    Article  CAS  Google Scholar 

  • Baldwin, J.P., Tinker, P.B. (1972): A method for estimating the lengths and spatial pattern of two inter-penetrating root systems. Plant and Soil 37: 209–213

    Article  Google Scholar 

  • Barber, S.A. (1974): Influence of the plant root on ion movement in soil. In: The Plant Root and its Environment. Carson E.W. (ed), University Press of Virginia: Charlottesville, pp 525–564

    Google Scholar 

  • Barber, S.A. (1984): Soil Nutrient Bioavailability: A Mechanistic Approach. John Wiley: New York

    Google Scholar 

  • Barber, S.A., Cushman, J.H. (1981): Nitrogen uptake model for agronomic crops. In: Modelling Waste Water Renovation — Land Treatment. Iskandur I.K. (ed), Wiley-Interscience: New York, pp 382–409

    Google Scholar 

  • Barraclough, P.B. (1986a): The growth and activity of winter wheat roots in the field: Nutrient uptakes of high-yielding crops. Journal of Agricultural Science, Cambridge 106: 45–52

    Google Scholar 

  • Barraclough, P.B. (1986b): The growth and activity of winter wheat roots in the field: Nutrient inflows of high-yielding crops. Journal of Agricultural Science, Cambridge 106: 53–59

    Google Scholar 

  • Bartlett, E.M., Lewis, D.H. (1973): Surface phosphatase activity of mycorrhizal roots of beech. Soil Biology and Biochemistry 5: 249–257

    Article  CAS  Google Scholar 

  • Bhat, K.K.S., Nye, P.H., Baldwin, J.P. (1976): Diffusion of phosphates to plant roots in soil. IV. The concentration-distance profile in the rhizosphere of roots with root hairs in a low P-soil. Plant and Soil 44: 63–72

    Article  CAS  Google Scholar 

  • Bollard, E.G. (1983): Involvement of unusual elements in plant growth and nutrition. In: Encyclopedia of Plant Physiology, New Series 15B, Inorganic Plant Nutrition. Lüuchli A., Bieleski R.L. (eds), Springer-Verlag: Berlin

    Google Scholar 

  • Bowie, S.H.U., Thornton, I. (1985): Environmental Geochemistry and Health. Reidel Publishing Co: Dordrecht

    Book  Google Scholar 

  • Breeze, V.G., Wild, A. (1984): The uptake of phosphate by plants from flowing nutrient solution. II. Growth of Lolium Perenne L at constant phosphate concentrations. Journal of Experimental Botany 35: 1210–1221

    Article  CAS  Google Scholar 

  • Brewster, J.L., Tinker, P.B. (1970): Nutrient cation flow in soil around plant roots. Soil Science Society of America Proceedings 34: 421–426

    Article  CAS  Google Scholar 

  • Brookes, P.C., McGrath, S. (1984): Effects of metal toxicity on the size of the soil biomass. Journal of Soil Science 35: 341–346

    Article  CAS  Google Scholar 

  • Brookes, P.C., Powlson, D.S., Jenkinson, D.S. (1985): The microbial biomass in soil. In: Ecological interactions in soil. Sp. Publ. No.4 of British Ecological Society. Fitter A.H. (ed), Blackwell: Oxford, pp 123–125

    Google Scholar 

  • Burns, I.G. (1980): Influence of the spatial distribution of nitrate on the uptake of N by plants: A review and a model for rooting depth. The Journal of Soil Science 31: 155–173

    CAS  Google Scholar 

  • Burns, R.G. (ed) (1978): Soil enzymes. Academic Press: London. pp 380

    Google Scholar 

  • Caradus, J.R. (1982): Genetic differences in the length of root hairs in white clover and their effect on phosphorus uptake. In: Proceedings of the 9th International Plant Nutrition Colloquium. Warwick, England. Scaife A. ( ed ), Commonwealth Agricultural Bureaux, pp 84–88

    Google Scholar 

  • Carson, E.W. (1974): The plant root and its environment. Univ. Virginia Press: Charlottesville, pp 691

    Google Scholar 

  • Chapin, F.S. (1982): Patterns of phosphorus absorption and chemistry as adaptations to infertile soil. Proceedings of the 9th International Plant Nutrition Colloquium. Warwick, England. Scaife A. (ed), Commonwealth Agricultural Bureaux, Farnham Royal

    Google Scholar 

  • Claassen, N., Barber, S.A. (1976): Simulation model for nutrient uptake from soil by a growing plant root system. Agronomy Journal 68: 961–964

    Article  Google Scholar 

  • Claassen, N., Jungk, A. (1984): Effect of K uptake rate, root growth and root hairs on potassium uptake efficiency of several plant species. Zeitschrift für Pflanzenernährung and Bodenkunde 147: 276–289

    Article  CAS  Google Scholar 

  • Clarkson, D.T., Sanderson, J., Russell, R.S. (1968): Ion uptake and root age. Nature 220: 805–806

    Article  CAS  Google Scholar 

  • Clement, C.R., Hopper, M.J., Jones, L.H.P. (1978): The uptake of nitrate by Lolium perenne from flowing nutrient solution, I. Effect of NO3 concentration. Journal of Experimental Botany 29: 453–464

    Article  CAS  Google Scholar 

  • Cooke, G.W., Williams, R.J.B. (1970): Losses of N and P from agricultural land. Water Treatment and Examination 19: 253–276

    CAS  Google Scholar 

  • Cress, W.A., Throneberry, G.O., Lindsey, D.L. (1979): Kinetics of phosphorus absorption by mycorrhizal and non-mycorrhizal tomato roots. Plant Physiology 64: 484–487

    Article  CAS  Google Scholar 

  • Crossett, R.N., Campbell, D.J. (1975): The effects of ethylene in the root environment upon the development of barley. Plant and Soil 42: 453–464

    Article  CAS  Google Scholar 

  • Domsch, K.H. (1984): Effects of pesticides and heavy metals on biological processes in soil. In: Biological Processes and Soil Fertility. Tinsley J., Darbyshire J.F. (eds), Martinus Nijhoff: Hague, pp 367–378

    Chapter  Google Scholar 

  • Drew, M.C. (1975): Comparison of the effects of a localised supply of phosphate, nitrate, ammonium and potassium on the growth of the seminal root system, and the shoot of barley. New Phytologist 75: 479–490

    Article  CAS  Google Scholar 

  • Drew, M.C., Saker, L.R. (1978): Nutrient supply and the growth of the seminal root system in barley. III. Compensatory increases in growth of lateral roots, and in rates of phosphate uptake in response to a localised supply of phosphate. Journal of Experimental Botany 29: 435–451

    Article  CAS  Google Scholar 

  • Ewens, M., Leigh, R.A. (1985): The effect of nutrient solution composition on the length of root hairs of wheat. Journal of Experimental Botany 36: 713–724

    Article  CAS  Google Scholar 

  • Foehse, D., Jungk, A. (1983): Influence of phosphate and nitrate supply on root hair formation of rape, spinach and tomato plants. Plant and Soil 74: 359–368

    Article  CAS  Google Scholar 

  • Foy, C.D., Chaney, R.L., White, M.C. (1978): The physiology of metal toxicity in plants. Annual Review of Plant Physiology 29: 511–566

    Article  CAS  Google Scholar 

  • Gardner, W.K., Parberry, D.G., Barber, D.A. (1982): The acquisition of phosphorus by Lupinus albus L I. Some characteristics of the soil/root interface. Plant Soil 68: 19–32

    Article  CAS  Google Scholar 

  • Gerwitz, A., Page, E.R. (1974): An empirical mathematical model to describe plant root systems. Journal of Applied Ecology 11: 773–781

    Article  Google Scholar 

  • Giller, K.E., Day, J.M. (1985): Nitrogen fixation in the rhizosphere: significance in natural and agricultural systems. In: Ecological interactions in soil. Sp. Publ. No. 4 of British Ecological Society. Fitter A.H. (ed), Blackwell: Oxford, pp 127–147

    Google Scholar 

  • Glass, A.D., Siddiqi, M.Y. (1984): The control of nutrient uptake rates in relation to the inorganic composition of plants. Advances in Plant Nutrition I. Tinker P.B., Läuchli A. (eds), Praeger Publishers: New York, pp 103–148

    Google Scholar 

  • Graham-Bryce, I.G. (1981): The behaviour of pesticides in soil. In: The Chemistry of Soil Pro- cesses. Greenland D.J., Hayes M.H.B. (eds) John Wiley: Chichester, England, pp 621–671

    Google Scholar 

  • Gregory, P.J., Crawford, D.V., McGowan, M. (1979): Nutrient relations of winter wheat. 2. Movement of nutrients to the root and their uptake. Journal of Agricultural Science, Cambridge 93: 495–504

    CAS  Google Scholar 

  • Hale, M.G., Foy, C.L., Shay, F.J. (1971): Factors affecting root exudation. Advances in Agronomy 23: 89–109

    Article  CAS  Google Scholar 

  • Harley, J.L., Smith, S.E. (1983): Mycorrhizal Symbioses. Academic Press: London, pp 483

    Google Scholar 

  • Hedley, M.J., Nye, P.H., White, R.E. (1982): Plant-induced changes in the rhizosphere of rape seedlings. II. Origin of the pH change. New Phytologist 91: 31–44

    Article  CAS  Google Scholar 

  • Helal, H.M., Sauerbeck, D.R. (1984): Influence of plant roots on C and P metabolism in soil. In: Biological Processes and Soil Fertility. Tinsley J., Darbyshire J.F. (eds), Martinus Nijhoff/ Dr. W. Junk: The Hague, pp 175–182

    Chapter  Google Scholar 

  • Hendricks, L., Claassen, N., Jungk, A. (1981): Phosphatverarmung des wurzelnahen Bodens and Phosphataufnahme von Mais and Raps. Zeitschrift für Pflanzenernährung and Bodenkunde 44: 486–499

    Article  Google Scholar 

  • Israel, D.W., Giddens, J.E., Powell, W.W. (1973): The toxicity of peach tree roots. Plant and Soil 39: 103–112

    Article  CAS  Google Scholar 

  • Itoh, S., Barber, S.A. (1983): Phosphorus uptake by six plant species as related to root hairs. Agronomy Journal 75: 457–461

    Article  Google Scholar 

  • Jackson, M.B. (1985): Ethylene and responses of plants to soil waterlogging and submergence. Annual Review of Plant Physiology 36: 145–174

    Article  CAS  Google Scholar 

  • Jungk, A., Claassen, N., Kuchenbuch, R. (1982): Potassium depletion of the soil/root interface in relation to soil parameters and root properties. In: Proceedings of the 9th International Plant Nutrition Colloquium. Warwick, England. Scaife A. ( ed ), Commonwealth Agricultural Bureaux, pp 250–255

    Google Scholar 

  • Kershaw, K.A. (1973): Quantitative and Dynamic Plant Ecology. Edward Arnold: London

    Google Scholar 

  • Lethbridge, G., Davidson, M.S. (1983): Root-associated nitrogen fixing bacteria and their role in the nitrogen nutrition of wheat estimated by 15N isotope dilution. Soil Biology and Biochemistry 15: 365–374

    Article  Google Scholar 

  • Lynch, J.M. (1976): Products of soil micro-organisms in relation to plant growth. CRC Critical Reviews in Microbiology 5: 67–107

    Article  CAS  Google Scholar 

  • Lynch, J.M. (1982): Interactions between bacteria and plants in the root environment. In: Bacteria and plants. Rhodes-Roberts M., Skinner F.A. (eds), Academic Press: London, pp 124

    Google Scholar 

  • Lynch, J.M. (1983): Soil Biotechnology: Microbiological Factors in Crop Productivity. Blackwell: Oxford

    Google Scholar 

  • Marschner, H. (1983): General introduction to the mineral nutrition of plants. In: Encyclopedia of Plant Physiology. New Series 15A, Inorganic Plant Nutrition. Lüuchli A., Bieleski R.L. (eds), Springer-Verlag: Berlin

    Google Scholar 

  • Mengel, K., Kirkby, E.A. (1982): Principles of Plant Nutrition, 3rd edition. IPI: Berne

    Google Scholar 

  • McGrath, S.P. (1985): The effects of increasing yields on the macro-and micronutrient concentrations and offtakes in the grain of winter wheat. Journal of the Science of Food and Agriculture 36: 1073–1083

    Article  CAS  Google Scholar 

  • Munns, D.N. (1986): Acid soil tolerance in legumes and Rhizobia. Advances in Plant Nutrition 2: 63–92

    CAS  Google Scholar 

  • Newman, E.I. (1985): The rhizosphere: carbon sources and microbial populations. In: Ecological interactions in soil. Sp. Publ. No. 4 of British Ecological Society. Fitter A.H. (ed), Blackwell: Oxford, pp 107–121

    Google Scholar 

  • Newman, E.I., Watson, A. (1977): Microbial abundance in the rhizosphere: a computer model. Plant and Soil 48: 17–56

    Article  Google Scholar 

  • Nye, P.H. (1979): Diffusion of ions and uncharged solutes in soils and soil clays. Advances in Agronomy 31: 225–272

    Article  CAS  Google Scholar 

  • Nye, P.H. (1984): On estimating the uptake of nutrients solubilised near roots or other surfaces. Journal of Soil Science 35: 439–446

    Article  CAS  Google Scholar 

  • Nye, P.H. (1986): Acid-base changes in the rhizosphere. Advances in Plant Nutrition II, Praeger Scientific: New York, pp 129–154

    Google Scholar 

  • Nye, P.H., Tinker, P.B. (1977): Solute movement in the soil-root system. Blackwell: Oxford

    Google Scholar 

  • Poljakoff-Mayber, A., Gale, J. (1975): Plants in saline environments. Ecological studies, Vol. 15 Springer-Verlag: Berlin

    Book  Google Scholar 

  • Ratnayake, M., Leonard, R.T., Menge, J.A. (1978): Root exudation in relation to supply of phosphorus and its possible relevance to mycorrhiza formation. New Phytologist 81: 543–552

    Article  CAS  Google Scholar 

  • Rice, E.L. (1974): Allelopathy. Academic Press: New York

    Google Scholar 

  • Riley, D., Barber, S.A. (1970): Salt accumulation at the soyabean root-soil interface. Soil Science Society of America Proceedings 34: 154–155

    Article  CAS  Google Scholar 

  • Römheld, V., Marschner, H. (1979): Fine regulation of iron uptake by Fe-efficient plant — Helianthus annus. In: The soil root interface. Harley J.L., Russell R.S. (eds), Academic Press: London, pp 405–417

    Google Scholar 

  • Römheld, V., Marschner, H. (1984): Plant-induced pH changes in the rhizosphere of “Fe-efficient” and “Fe-inefficient” soybean and corn cultivars. Journal of Plant Nutrition 7: 623–630

    Article  Google Scholar 

  • Römheld, V., Marschner, H. (1986): Mobilisation of iron in the rhizosphere of different plant species. Advances in Plant Nutrition II, Praeger Scientific: New York, pp 155–204

    Google Scholar 

  • Rorison, I. (1969): Ecological inferences from laboratory experiments on mineral nutrition. In: Ecological aspects of the mineral nutrition of plants. Rorison I.H. (ed), Blackwell: Oxford

    Google Scholar 

  • Rovira, A.D. (1979): Biology of the soil-root interface. In: The soil-root interface. Harley J.L., Russell R.S. (eds), Academic Press: London

    Google Scholar 

  • Russell, R.S. (1977): Plant root systems. McGraw-Hill: London

    Google Scholar 

  • Sanders, F.E., Tinker, P.B. (1973): Phosphate flow into mycorrhizal roots. Pesticide Science 4: 385–395

    Article  CAS  Google Scholar 

  • Sarkar, A.N., Wyn Jones, R.G. (1982): Effect of rhizosphere pH on availability and uptake of Fe, Mn and Zn. Plant and Soil 66: 361–372

    Article  CAS  Google Scholar 

  • Schenk, M.K., Barber, S.A. (1980): Potassium and phosphorus uptake by corn genotypes grown in the field as influenced by root characteristics. Plant and Soil 54: 65–76

    Article  CAS  Google Scholar 

  • Schippers, B., Gams, W. (1979): Soil-borne plant pathogens. Academic Press: London

    Google Scholar 

  • Sharpley, A.N., Reed, L.W. (1982): Effect of environmental stress on the growth and amounts and forms of phosphorus in plants. Agronomy Journal 74: 19–22

    Article  CAS  Google Scholar 

  • Silberbush, M., Barber, S.A. (1983): Sensitivity of simulated phosphorus uptake to parameters used by a mechanistic mathematical model. Plant and Soil 74: 93–100

    Article  CAS  Google Scholar 

  • Silberbush, M., Barber, S.A. (1984): Phosphorus and potassium uptake of field-grown soybean cultivars predicted by a simulation model. Soil Science Society America Journal 48: 592–596

    Article  CAS  Google Scholar 

  • Slankis, V. (1983): Hormonal relationships in mycorrhizal development. In: Ectomycorrhizas. Marks G.C, Kozlowski T.T. (eds), Academic Press: New York

    Google Scholar 

  • Soon, Y.K., Miller, M.H. (1977): Changes in the rhizosphere due to NH4 and NO3 fertilization and phosphorus uptake by corn seedlings (Zea Mays L). Soil Science Society of America Journal 41: 77–80

    Article  CAS  Google Scholar 

  • Staunton, S., Nye, P.H. (1983): The self diffusion of Na in a naturally aggregated soil. Journal of Soil Science 34: 263–269

    Article  CAS  Google Scholar 

  • Stefanson, R.C. (1973): Evolution patterns of nitrous oxide and nitrogen in sealed soil-plant systems. Soil Biology and Biochemistry 5: 167–169

    Article  CAS  Google Scholar 

  • Strebel, O., Grimme, H., Renger, M., Fleige, H. (1980): A field study with 15N of soil and fertilizer nitrate uptake and of water withdrawal by spring wheat. Soil Science 130: 205–210

    Article  CAS  Google Scholar 

  • Tinker, P.B. (1975): Effects of vesicular-arbuscular mycorrhizas on higher plants. Symp. Society Experimental Biology 29: 325–349

    CAS  Google Scholar 

  • Tinker, P.B. (1976): Roots and water. Phil. Trans. Royal Society London B 273: 445–461

    Article  Google Scholar 

  • Tinker, P.B. (1980): Root-soil interactions in crop plants. In: Critical Reports on Applied Chemistry, vol 2 Soils and Agriculture. Tinker P.B. (ed) SCI/Blackwell: Oxford

    Google Scholar 

  • Tinker, P.B. (1981): Levels, distribution and chemical forms of trace elements in food plants. Phil. Trans. Royal Society, London B 294: 41–55

    Article  CAS  Google Scholar 

  • Tinker, P.B. (1986): Trace elements in arable agriculture. Journal Soil Science 37: 587–601

    Article  CAS  Google Scholar 

  • Tinker, P.B., Gildon, A. (1982): Mycorrhizal fungi and ion uptake. In: Metals and micronutrients: Uptake and utilisation by plants. Robb D.A., Pierpoint S. (eds), Academic Press: London, pp 21–32

    Google Scholar 

  • Trolldenier, G. (1979): The effects of mineral nutrition of plants and soil oxygen on rhizosphere organisms. In: Soil-borne plant pathogens. Shippers B., Gams W. (eds), Academic Press: London, p 235

    Google Scholar 

  • Wehrmann, J., Scharpf, H.C., Böhmer, M., Wollring, J. (1982): Determination of nitrogen fertilizer requirements by nitrate analysis of the soil and of the plant. Proceedings of the 9th International Plant Nutrition Colloquium: Warwick, England. Scaife A. ( ed ), Commonwealth Agricultural Bureaux, pp 702–709

    Google Scholar 

  • Whipps, J.M., Lynch, J.M. (1985): Energy losses by the plant in rhizodeposition. Sum Proceedings Phytochemical Society Europe 26: 59–71

    Google Scholar 

  • Wild, A., Breeze, V.G. (1981): Nutrient uptake in relation to growth. In: Physiological Processes Limiting Plant Productivity. Johnson C.B. (ed), Butterworths: London

    Google Scholar 

  • Willigen, P. de (1984): Some theoretical aspects of the influence of soil-root contact on uptake and transport of nutrients and water. ILRI Publication No. 37, pp 268–275

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 1988 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Tinker, P.B., Barraclough, P.B. (1988). Root-Soil Interactions. In: Reactions and Processes. The Handbook of Environmental Chemistry, vol 2 / 2D. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39460-0_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-39460-0_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-15122-8

  • Online ISBN: 978-3-540-39460-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics