Taylor Coefficients of the Conformal Map for the Exterior of the Reciprocal of the Multibrot Set

AbstractThe recently developed new algorithm for computing consistent initial values and Taylor coefficients for DAEs using projector-based constrained optimization opens new possibilities to apply Taylor series integration methods. In this paper, we show how corresponding projected explicit and implicit Taylor series methods can be adapted to DAEs of arbitrary index. Owing to our formulation as a projected optimization problem constrained by the derivative array, no explicit description of the inherent dynamics is necessary, and various Taylor integration schemes can be defined in a general framework. In particular, we address higher-order Padé methods that stand out due to their stability. We further discuss several aspects of our prototype implemented in Python using Automatic Differentiation. The methods have been successfully tested on examples arising from multibody systems simulation and a higher-index DAE benchmark arising from servo-constraint problems.

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A note on a space Hp, a of holomorphic functions

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972700013447 ◽

1987 ◽

Vol 35 (3) ◽

pp. 471-479

Author(s):

H. O. Kim ◽

S. M. Kim ◽

E. G. Kwon

Keyword(s):

Hardy Space ◽

Complex Plane ◽

Unit Disc ◽

Weak Type ◽

Holomorphic Functions ◽

Embedding Theorem ◽

Type Operator ◽

Taylor Coefficients ◽

Bounded Holomorphic

For 0 < p < ∞ and 0 ≤a; ≤ 1, we define a space Hp, a of holomorphic functions on the unit disc of the complex plane, for which Hp, 0 = H∞, the space of all bounded holomorphic functions, and Hp, 1 = Hp, the usual Hardy space. We introduce a weak type operator whose boundedness extends the well-known Hardy-Littlewood embedding theorem to Hp, a, give some results on the Taylor coefficients of the functions of Hp, a and show by an example that the inner factor cannot be divisible in Hp, a.

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Popular conformal map projections

Map of the World ◽

10.1201/9780429265990-2 ◽

2019 ◽

pp. 17-28

Author(s):

Martin Vermeer ◽

Antti Rasila

Keyword(s):

Conformal Map ◽

Map Projections

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An asymptotic formula for the Taylor coefficients of automorphic forms

Proceedings of the American Mathematical Society ◽

10.1090/s0002-9939-1980-0556618-6 ◽

1980 ◽

Vol 78 (4) ◽

pp. 485-485 ◽

Cited By ~ 1

Author(s):

Scott Wolpert

Keyword(s):

Asymptotic Formula ◽

Automorphic Forms ◽

Taylor Coefficients

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BOUNDARY ANGULAR DERIVATIVES OF GENERALIZED SCHUR FUNCTIONS

Journal of the Australian Mathematical Society ◽

10.1017/s1446788712000432 ◽

2012 ◽

Vol 93 (3) ◽

pp. 203-224

Author(s):

VLADIMIR BOLOTNIKOV ◽

TENGYAO WANG ◽

JOSHUA M. WEISS

Keyword(s):

Schur Functions ◽

Taylor Coefficients ◽

Generalized Schur Functions ◽

Angular Derivatives ◽

Derivatives Of

AbstractCharacterization of generalized Schur functions in terms of their Taylor coefficients was established by Krein and Langer [‘Über einige Fortsetzungsprobleme, die eng mit der Theorie hermitescher Operatoren im Raume ${\Pi }_{\kappa } $ zusammenhängen. I. Einige Funktionenklassen und ihre Darstellungen’, Math. Nachr. 77 (1977), 187–236]. We establish a boundary analogue of this characterization.

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