Hölder condition

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Hölder condition

[′hel·dər kən‚dish·ən]
(mathematics)
A function ƒ(x) satisfies the Hölder condition in a neighborhood of a point x0 if |ƒ(x) - ƒ(x0)| ≤ c |(x-x0)| n , where c and n are constants.
A function ƒ(x) satisfies a Hölder condition in an interval or in a region of the plane if |ƒ(x) - ƒ(y)| ≤ c|x - y |nfor all x and y in the interval or region, where c and n are constants.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
Small individual shareholders--such as the low-level Enron employees whose retirement savings were lost when Enron's stock plummeted (76)--will almost certainly be excluded from the holder class actions and be left with no remedy by which to recover their losses.
The Fifth Circuit addressed this issue in a 2008 Enron holder class action appeal brought under state law.
(86) Accordingly, it appears to be fairly well settled that plaintiffs may not circumvent the Act's limitation on the number of plaintiffs in a state law holder class action by bringing numerous small actions rather than one large one.
The Uniform Standards Act's limitation on the number of shareholders that may bring a holder class action under state law also undercuts the ability of private litigation to act as an enforcement mechanism for antifraud laws.
In contrast to the Blue Chip Stamps Court, the Court in Dabit casually discounted the importance of state law to holder class actions, and securities law generally.
Similarly, allowing state courts to entertain holder class actions would enable states to act as "laboratories for experimentation" for these actions.
(127) Thus, in preempting state holder class actions, the federal government has sacrificed the significant benefits that accompany federalism without any corresponding efficiency gains.
It was designed by Sir Nigel Gresley, the chief mechanical engineer of the LNER who also designed the famous class A3 4472 Flying Scotsman and world speed record holder class A4 4468 Mallard.
(306) Finally, in response to the argument that the holder class action brought by respondent was distinguishable from a typical class action because it was not brought by a required purchaser or seller of the securities, the Court stated that the identity of the plaintiffs does not determine whether the compliant alleges fraud "in connection with the purchase or sale" of securities:
Origin: It seems that the GOP's weekend getaways for donors and politicians at Aspen, Palm Beach and elsewhere were becoming so overrun with the riffraff who contribute only $100,000 each that the true elites were finding these events "crowded" and difficult to get quality face time with the politicians; thus was born, in 1996, the Season Ticket Holder class, with members awarded carte blanche access to the party's top officeholders and granted entree to the most intimate gatherings with GOP politicians.
In the case [PSI] = [PSI](z), on general weakly pseudoconvex domains of finite type, the solution to the equation (1.1) only belongs to Holder classes, and we do not have any smoothness result.
Since the right hand side of (1.1) is nonlinear, we also define the corresponding Holder classes on R x A as follows: