unstable pairs
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11: 27.15 Chinese Remainder Theorem
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►The Chinese remainder theorem states that a system of congruences , always has a solution if the moduli are relatively prime in pairs; the solution is unique (mod ), where is the product of the moduli.
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12: 27.19 Methods of Computation: Factorization
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►Type II probabilistic algorithms for factoring rely on finding a pseudo-random pair of integers that satisfy .
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13: 9.2 Differential Equation
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§9.2(iii) Numerically Satisfactory Pairs of Solutions
►Table 9.2.1 lists numerically satisfactory pairs of solutions of (9.2.1) for the stated intervals or regions; compare §2.7(iv). ► …14: 3.6 Linear Difference Equations
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►In this situation the unwanted multiples of grow more rapidly than the wanted solution, and the computations are unstable.
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►Then computation of by forward recursion is unstable.
If it also happens that as , then computation of by backward recursion is unstable as well.
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15: 22.19 Physical Applications
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►As from below the period diverges since are points of unstable equilibrium.
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►As from below the period diverges since is a point of unstable equlilibrium.
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16: 13.28 Physical Applications
17: 15.17 Mathematical Applications
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►First, as spherical functions on noncompact Riemannian symmetric spaces of rank one, but also as associated spherical functions, intertwining functions, matrix elements of SL, and spherical functions on certain nonsymmetric Gelfand pairs.
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18: Bille C. Carlson
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►In his paper Lauricella’s hypergeometric function
(1963), he defined the -function, a multivariate hypergeometric function that is homogeneous in its variables, each variable being paired with a parameter.
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19: 10.2 Definitions
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