Hölder condition

(redirected from Holder class)

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.
References in periodicals archive ?
For several years after the Uniform Standards Act came into existence, defrauded holders of securities continued to bring holder class actions under state law with considerable success.
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.
Courts could solve the problems created by the effective elimination of the holder action either by abandoning the Dabit Court's broad interpretation of the "in connection with" language of the Uniform Standards Act to allow holder class actions under state law or by abandoning the Blue Chip Stamps Court's narrow interpretation of the same language in the context of federal 10b-5 actions.
As an alternative to overruling Blue Chip Stamps and permitting holder actions in federal court under Rule 10b-5, the Supreme Court could also overrule its decision in Dabit to the extent that it construes the Uniform Standards Act to preempt state law holder class actions and allow such actions to proceed in state court.
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.
The purpose of this Follow-up Notice is to enable the Claims Administrator, identified below, to complete the list of members of the Holder Class who are entitled to participate in the settlement of the above consolidated class action.