Invariant Random Matrices and Strong Convergence
(3) If b [not member of] ran(I - A) and b = [b.sub.1] + [b.sub.2] with [b.sub.1] [member of] ran(I - A).sup.[perpendicular]], [b.sub.2] [member of] ran(I - A), then [C.sub.[psi],[phi]] is unitarily
equivalent to [mathematical expression not reproducible].
Moreover, the general provisions covering all modes of transport, which are unitarily
regulated by the Civil Code, shall apply unless the rules set out by the special laws or practices established between parties are harmed.
As regards the indicator net tones kilometer, we consider that t does not reflect unitarily
and consequently the real volume of the activity and, subsequently we did not use it in our calculi.
An operator unitarily
equivalent to a ek-paranormal for some positive integer k, is also a ek-paranormal operator.
We have chosen to have half federalism and half unitarily
. But the noise about Presidential powers in the Draft or decentralization quest is just pretext and nothing else.
Specifically, the US government acted unitarily
throughout the period by following a singular course of action once the president established a formal policy, despite internal debate among politicians, scientists, and military personnel.
Should border incursions and violations continue and become permanent, then Kurdish authorities and Kurdistan security forces will have no other option than but to deal with it unitarily
for sovereignty of Kurdistan and the security and well-being of its citizens are at the stake.Border violations by Turkey and Iran should not be seen as temporary incidents limited to chasing PKK and PJAK guerrillas based in the remote mountaintops of Kurdistan Region.
She pointed out that India needs to build a little more confidence in to this relationship so that the both neighbouring countries could talk on the tables and find a way to resolve terrorism unitarily
. Answering a query about bilateral dialogues she said that such dialogues between Pakistan and India can not be limited to terrorism alone.
While in their relational totality as conceptual terms, both third time and alternative future time work unitarily
and interchangeably, we could separate them here to mark a critical distinction between the author and his poem's protagonist.
It is not a standard process, unitarily
applicable in any domain, as it takes into account the variants specific to the company applying it and to the respective domain.
Generally speaking, the so-called "binding problem" refers to the way visual attributes are unitarily
perceived despite our cognitive system functionally segregates the stimuli into a number of independent information channels (Livingstone & Hubel, 2003).
Then K(G) = D(G) + A(G) and L(G) = D(G)-A(G) are unitarily
similar, i.e., there exists an orthogonal matrix U such that K(G) = [U.sup.-1]L(G)U.
Thus, presidents who have the formal authority to act unitarily
on their economic policy signals are more likely to elicit a market response than those presidents who cannot act unilaterally or constitutionally to fulfill their promises.
Miccosukee Tribe of Indians, the United States Supreme Court was presented with a novel and untested argument by the United States, appearing as amicus curiae, which asserted the bold proposition that for the purpose of the Clean Water Act's (hereinafter "CWA") National Pollution Discharge Elimination System (hereinafter "NPDES"), all navigable waters of the United States should be considered unitarily
when determining whether there is an addition of a pollutant to a navigable water.