In these calculations the assumptions of
linear independence analysis should be satisfied.
These constraints are constructed from the Reduced Source-Sink Hop matrix and consider the
linear independence conditions at the sink nodes to assume the resolution of the system.
For this, again the
linear independence of the set L(P, [[alpha].sub.1],..., [[alpha].sub.r]) is applied.
From Table 1, it can be shown clearly that, with a Galois Field of [2.sup.8] order, achieving
linear independence is quite reliable (99.6%).
It follows that the set-composition K can be recovered from the monomial of lexicographically largest evaluation in [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], which implies the
linear independence of the [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
The proof of Theorem A is based on an important
linear independence criterion due to Yu.
Then, substituting (5) into (1), applying the
linear independence of the exponential functions and equating corresponding coefficients on both sides yields the following system of equations:
Promislow (emeritus, mathematics, York U., Canada) introduces the main ideas of functional analysis to beginning graduate or advanced undergraduate students with a prior knowledge of basic real analysis and such topics of elementary linear algebra as
linear independence, bases, and matrix manipulation.
An in-phase and quadrature time-invariant decomposition of Equation 2 is possible if it is assumed that the statistics of the resulting power spectral densities (PSD) are independent (in fact, the resulting PSDs are always independent due to
linear independence of sin and cos).
Using this notion of
linear independence, we define the notions of basis and dimension as in Guterman (2009); Cuninghame-Green and Butkovic (2004): a basis of a semimodule U over a semiring S is a set P of linearly independent elements from U which generate it, and the dimension of a semimodule U is the cardinality of its smallest basis.
Defect zero characters and relative defect zero characters Masafumi MURAI A property of the Fourier transform of probability measures on the real line related to the renewal theorem Yasuki ISOZAKI A note on
linear independence of polylogarithms over the rationals Noriko HIRATA-KOHNO and Hironori OKADA Above three, communicated by Masaki KASHIWARA, M.J.A.
introduced a scheme that utilizes a symmetric matrix construction for key distribution [8] that exploits the
linear independence merit of vectors to the solvability of linear systems (that is, difficulty of solving a system in n variables given t<n equations).