http://www.thefreedictionary.com/determine
determine
9. Law To put an end to; terminate.


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Note added at 53 mins (2010-07-12 16:07:00 GMT)
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http://esignal.brand.edgar-online.com/EFX_dll/EDGARpro.dll?F...

ALTERNATE DIRECTORS

109(A). Power to appoint alternate directors

Any Director (other than an alternate Director) may at any time by writing under his hand and deposited at the Office, or received by the Secretary or delivered at a meeting of the Directors, appoint any person (including another Director) to be his alternate Director and may in like manner at any time terminate such appointment. If such alternate Director is not another Director, such appointment, unless previously approved by the Directors, shall have effect only upon and subject to being so approved.

(B). Termination

The appointment of an alternate Director shall automatically determine on the happening of any event which if he were a Director would cause him to vacate such office or if his appointor ceases to be a Director or if the approval of the Directors to his appointment is withdrawn. An alternate Director may by writing under his hand left at the Office resign such appointment.

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Note added at 59 mins (2010-07-12 16:12:33 GMT)
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"Полномочия" в переводе появляются вследствие развития значения, ведь по-русски не скажешь "назначение прекращается".