About the Project

graph theory


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1: 26.19 Mathematical Applications
Partitions and plane partitions have applications to representation theory (Bressoud (1999), Macdonald (1995), and Sagan (2001)) and to special functions (Andrews et al. (1999) and Gasper and Rahman (2004)). Other areas of combinatorial analysis include graph theory, coding theory, and combinatorial designs. …
2: 18.39 Applications in the Physical Sciences
Table 18.39.1: Typical Non-Classical Weight Functions Of Use In DVR Applicationsa
Name of OP System w ( x ) [ a , b ] Notation Applications
Quartic Freud exp ( x 4 / 4 z x 2 ) ( , ) p n ( x ) §32.15 and application refs. therein: Quantum Gravity and Graph Theory Combinatorics
3: Philip J. Davis
At CalTech, John Todd dedicated himself to the training of new researchers in numerical analysis, and Olga Taussky, who had been a full-time NBS consultant influential in establishing the field of matrix theory, became the first woman at CalTech to attain the academic rank of full professor. … He also had a big influence on the development of the NBS Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (A&S), which became one of the most widely distributed and highly cited publications in NIST’s history. … After receiving an overview of the project and watching a short demo that included a few preliminary colorful, but static, 3D graphs constructed for the first Chapter, “Airy and Related Functions”, written by Olver, Davis expressed the hope that designing a web-based resource would allow the team to incorporate interesting computer graphics, such as function surfaces that could be rotated and examined. … Davis’s comments about our uninspired graphs sparked the research and design of techniques for creating interactive 3D visualizations of function surfaces, which grew in sophistication as our knowledge and the technology for developing 3D graphics on the web advanced over the years. Today the DLMF contains close to 600 2D and 3D graphs and more than 200 interactive 3D visualizations. …
4: Richard A. Askey
Published in 1985 in the Memoirs of the American Mathematical Society, it also introduced the directed graph of hypergeometric orthogonal polynomials commonly known as the Askey scheme. … Additional books for which Askey served as author or editor include Orthogonal Polynomials and Special Functions, published by SIAM in 1975, Theory and application of special functions, published by Academic Press in 1975, Special Functions: Group Theoretical Aspects and Applications (with T. …
5: Bibliography C
  • H. S. Carslaw (1930) Introduction to the Theory of Fourier’s Series and Integrals. 3rd edition, Macmillan, London.
  • S. Chandrasekhar (1984) The Mathematical Theory of Black Holes. In General Relativity and Gravitation (Padova, 1983), pp. 5–26.
  • E. W. Cheney (1982) Introduction to Approximation Theory. 2nd edition, Chelsea Publishing Co., New York.
  • E. A. Coddington and N. Levinson (1955) Theory of ordinary differential equations. McGraw-Hill Book Company, Inc., New York-Toronto-London.
  • Combinatorial Object Server (website) Department of Computer Science, University of Victoria, Canada.
  • 6: 2.11 Remainder Terms; Stokes Phenomenon
    In the transition through θ = π , erfc ( 1 2 ρ c ( θ ) ) changes very rapidly, but smoothly, from one form to the other; compare the graph of its modulus in Figure 2.11.1 in the case ρ = 100 . … As these lines are crossed exponentially-small contributions, such as that in (2.11.7), are “switched on” smoothly, in the manner of the graph in Figure 2.11.1. … For illustration, we give re-expansions of the remainder terms in the expansions (2.7.8) arising in differential-equation theory. … For second-order differential equations, see Olde Daalhuis and Olver (1995a), Olde Daalhuis (1995, 1996), and Murphy and Wood (1997). … The first of these two references also provides an introduction to the powerful Borel transform theory. …
    7: Bibliography P
  • G. Parisi (1988) Statistical Field Theory. Addison-Wesley, Reading, MA.
  • G. Petiau (1955) La Théorie des Fonctions de Bessel Exposée en vue de ses Applications à la Physique Mathématique. Centre National de la Recherche Scientifique, Paris (French).
  • S. Pokorski (1987) Gauge Field Theories. Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge.
  • G. Pólya and R. C. Read (1987) Combinatorial Enumeration of Groups, Graphs, and Chemical Compounds. Springer-Verlag, New York.
  • T. Poston and I. Stewart (1978) Catastrophe Theory and its Applications. Pitman, London.
  • 8: 27.21 Tables
    Bressoud and Wagon (2000, pp. 103–104) supplies tables and graphs that compare π ( x ) , x / ln x , and li ( x ) . … Lehmer (1941) gives a comprehensive account of tables in the theory of numbers, including virtually every table published from 1918 to 1941. … No sequel to Lehmer (1941) exists to date, but many tables of functions of number theory are included in Unpublished Mathematical Tables (1944). …
    9: Bibliography
  • M. M. Agrest and M. S. Maksimov (1971) Theory of Incomplete Cylindrical Functions and Their Applications. Springer-Verlag, Berlin.
  • L. V. Ahlfors (1966) Complex Analysis: An Introduction of the Theory of Analytic Functions of One Complex Variable. 2nd edition, McGraw-Hill Book Co., New York.
  • A. R. Ahmadi and S. E. Widnall (1985) Unsteady lifting-line theory as a singular-perturbation problem. J. Fluid Mech 153, pp. 59–81.
  • T. M. Apostol and I. Niven (1994) Number Theory. In The New Encyclopaedia Britannica, Vol. 25, pp. 14–37.
  • R. Askey (1990) Graphs as an Aid to Understanding Special Functions. In Asymptotic and Computational Analysis, R. Wong (Ed.), Lecture Notes in Pure and Appl. Math., Vol. 124, pp. 3–33.
  • 10: 16.23 Mathematical Applications
    §16.23(ii) Random Graphs
    A substantial transition occurs in a random graph of n vertices when the number of edges becomes approximately 1 2 n . In Janson et al. (1993) limiting distributions are discussed for the sparse connected components of these graphs, and the asymptotics of three F 2 2 functions are applied to compute the expected value of the excess. …
    §16.23(iv) Combinatorics and Number Theory