About the Project

measure

AdvancedHelp

(0.001 seconds)

1—10 of 20 matching pages

1: Funding
  • Physical Measurement Laboratory (formerly Physics Laboratory)

  • 2: 18.36 Miscellaneous Polynomials
    These are OP’s on the interval ( 1 , 1 ) with respect to an orthogonality measure obtained by adding constant multiples of “Dirac delta weights” at 1 and 1 to the weight function for the Jacobi polynomials. … These are polynomials in one variable that are orthogonal with respect to a number of different measures. … These are matrix-valued polynomials that are orthogonal with respect to a square matrix of measures on the real line. …
    3: Charles W. Clark
    … …
    4: 27.17 Other Applications
    Schroeder (2006) describes many of these applications, including the design of concert hall ceilings to scatter sound into broad lateral patterns for improved acoustic quality, precise measurements of delays of radar echoes from Venus and Mercury to confirm one of the relativistic effects predicted by Einstein’s theory of general relativity, and the use of primes in creating artistic graphical designs.
    5: 3.1 Arithmetics and Error Measures
    §3.1 Arithmetics and Error Measures
    §3.1(v) Error Measures
    The relative precision is … The mollified error is …
    6: Foreword
    22 2 D. R. Lide (ed.), A Century of Excellence in Measurement, Standards, and Technology, CRC Press, 2001. The success of the original handbook, widely referred to as “Abramowitz and Stegun” (“A&S”), derived not only from the fact that it provided critically useful scientific data in a highly accessible format, but also because it served to standardize definitions and notations for special functions. …
    7: 18.2 General Orthogonal Polynomials
    More generally than (18.2.1)–(18.2.3), w ( x ) d x may be replaced in (18.2.1) by a positive measure d α ( x ) , where α ( x ) is a bounded nondecreasing function on the closure of ( a , b ) with an infinite number of points of increase, and such that 0 < a b x 2 n d α ( x ) < for all n . … Conversely, if a system of polynomials { p n ( x ) } satisfies (18.2.10) with a n 1 c n > 0 ( n 1 ), then { p n ( x ) } is orthogonal with respect to some positive measure on (Favard’s theorem). The measure is not necessarily of the form w ( x ) d x nor is it necessarily unique. …
    8: 35.4 Partitions and Zonal Polynomials
    See Muirhead (1982, pp. 68–72) for the definition and properties of the Haar measure d 𝐇 . …
    9: 35.1 Special Notation
    a , b

    complex variables.

    d 𝐇

    normalized Haar measure on 𝐎 ( m ) .

    10: 20.15 Tables
    Tables of Neville’s theta functions θ s ( x , q ) , θ c ( x , q ) , θ d ( x , q ) , θ n ( x , q ) (see §20.1) and their logarithmic x -derivatives are given in Abramowitz and Stegun (1964, pp. 582–585) to 9D for ε , α = 0 ( 5 ) 90 , where (in radian measure) ε = x / θ 3 2 ( 0 , q ) = π x / ( 2 K ( k ) ) , and α is defined by (20.15.1). …