University of Waterloo

About: University of Waterloo is a education organization based out in Waterloo, Ontario, Canada. It is known for research contribution in the topics: Population & Context (language use). The organization has 36093 authors who have published 93906 publications receiving 2948139 citations. The organization is also known as: UW & uwaterloo.

Functional Equations in Several Variables: With Applications to Mathematics, Information Theory and to the Natural and Social Sciences

Abstract: Preface Further information 1. Axiomatic motivation of vector addition 2. Cauchy's equation: Hamel basis 3. Three further Cauchy equations: an application to information theory 4. Generalizations of Cauchy's equations to several multiplace vector and matrix functions: an application to geometric objects 5. Cauchy's equations for complex functions: applications to harmonic analysis and to information measures 6. Conditional Cauchy equations: an application to geometry and a characterization of the Heaviside functions 7. Addundancy, extensions, quasi-extensions and extensions almost everywhere: applications to harmonic analysis and to rational decision making 8. D'Alembert's functional equation: an application to noneuclidean mechanics 9. Images of sets and functional equations: applications to relativity theory and to additive functions bounded on particular sets 10. Some applications of functional equations in functional analysis, in the geometry of Banach spaces and in valauation theory 11. Characterizations of inner product spaces: an application to gas dynamics 12. Some related equations and systems of equations: applications to combinatorics and Markov processes 13. Equations for trigonometric and similar functions 14. A class of equations generalizing d'Alembert and Cauchy Pexider-type equations 15. A further generalization of Pexider's equation: a uniqueness theorem: an application to mean values 16. More about conditional Cauchy equations: applications to additive number theoretical functions and to coding theory 17. Mean values, mediality and self-distributivity 18. Generalized mediality: connection to webs and nomograms 19. Further composite equations: an application to averaging theory 20. Homogeneity and some generalizations: applications to economics 21. Historical notes Notations and symbols Hints to selected 'exercises and further results' Bibliography Author index Subject index.

Automatic Sequences: Theory, Applications, Generalizations

Abstract: Preface 1. Stringology 2. Number theory and algebra 3. Numeration systems 4. Finite automata and other models of computation 5. Automatic sequences 6. Uniform morphisms and automatic sequences 7. Morphic sequences 8. Frequency of letters 9. Characteristic words 10. Subwords 11. Cobham's theorem 12. Formal power series 13. Automatic real numbers 14. Multidimensional automatic sequences 15. Automaticity 16. k-regular sequences 17. Physics Appendix. Hints, references and solutions for selected exercises Bibliography Index.

Terrestrial water fluxes dominated by transpiration

Abstract: An analysis of the relative effects of transpiration and evaporation, which can be distinguished by how they affect isotope ratios in water, shows that transpiration is by far the largest water flux from Earth’s continents, representing 80 to 90 per cent of terrestrial evapotranspiration and using half of all solar energy absorbed by land surfaces Water fluxes from the land surface to the atmosphere are divided between evaporation, and transpiration from leaf stomata Although a seemingly basic division between the physical and biological, there is still no consensus on the global partitioning between the two fluxes, resulting in uncertainties as to responses to future climate variations Now, Scott Jasechko and colleagues use the isotopic signatures of transpiration and evaporation from a global data set of large lakes and reveal that enormous quantities of water — as much as 90% of total terrestrial evapotranspiration — are cycled through vegetation via transpiration One conclusion to be drawn from this study is that the accuracy of biological — rather than physical — fluxes should be prioritized in work to improve climate models Renewable fresh water over continents has input from precipitation and losses to the atmosphere through evaporation and transpiration Global-scale estimates of transpiration from climate models are poorly constrained owing to large uncertainties in stomatal conductance and the lack of catchment-scale measurements required for model calibration, resulting in a range of predictions spanning 20 to 65 per cent of total terrestrial evapotranspiration (14,000 to 41,000 km3 per year) (refs 1, 2, 3, 4, 5) Here we use the distinct isotope effects of transpiration and evaporation to show that transpiration is by far the largest water flux from Earth’s continents, representing 80 to 90 per cent of terrestrial evapotranspiration On the basis of our analysis of a global data set of large lakes and rivers, we conclude that transpiration recycles 62,000 ± 8,000 km3 of water per year to the atmosphere, using half of all solar energy absorbed by land surfaces in the process We also calculate CO2 uptake by terrestrial vegetation by connecting transpiration losses to carbon assimilation using water-use efficiency ratios of plants, and show the global gross primary productivity to be 129 ± 32 gigatonnes of carbon per year, which agrees, within the uncertainty, with previous estimates6 The dominance of transpiration water fluxes in continental evapotranspiration suggests that, from the point of view of water resource forecasting, climate model development should prioritize improvements in simulations of biological fluxes rather than physical (evaporation) fluxes