 About 1,280,000 results  books.google.com In such circumstances one derives a measure of algebraic independence for (or
Om). Such measures are defined in a general framework by Nesterenko and
Philippen by means of Chow forms (see ([FNe 1998], Chap. 6, § 3, [P 1997], [P
1998] ... 

 books.google.com A simple proof for a homogeneous measure of linear independence of an
arbitrary number of logarithms is given in Chap. 7 of [32], using an extension of
Schneider's method. A refined estimate (relying on the same ideas) is given in
Chap. 

 books.google.com Definition of the measures In transcendental number theory one looks for two
types of results: qualitative and quantitative. In the first ... Let o1,...,om, m 2 2, and
01 be numbers in R or C. By the measure of linear independence of 0!} , . . . , am
... 

 books.google.com Jasun Gong. related condition in terms of linearly independent sets. We recall the
definition from linear algebra [Hun80, Sect IV.2]. Definition 3.3.2. Let m £ N. A
subset {^}TM! in T(X/<) is linearly independent if the following implication holds: ... 

 books.google.com For.example,.we.can.stipulate.conditional linear independence. among. the.
measured. variables,. given. the. latent. variables. (McDonald,. 1981).. To.
illustrate,. let.Σ (XW) . be. the. conditional. covariance. matrix. for.X. given.W.. 

 books.google.com We note in passing that unlike the Gram determinant I', which depends on the
values assumed by the functions throughout the entire interval, the Wronskian is
a pointwise measure of linear independence. Consequently, it may vanish ... 

 books.google.com Assuming Conjectures 1 and 2, one deduces a special case of Schanuel's
Conjecture, where the numbers x\, . . .,xn satisfy a socalled "technical hypothesis
", which is the following measure of linear independence: Definition. A/fuple(;q, ... 

 books.google.com Conversely: 9. If any vector of a system is uniquely representable as a linear
combination of vectors of some subsystem, then that subsystem is basic. ... The
rank of a system of vectors is "the.upper measure" of its linear independence. 13. 

 books.google.com Each Hamel basis of IR over Q has inner Lebesgue measure zero, and there
exist Lebesgue measurable Hamel bases. ... Hence there exist h1,h2 ∈ H and
nonzero q ∈ Q such that h1 −h 2 = qh, which contradicts the linear
independence of ... 

 books.google.com The angle between two proteins is hence a measure of the number of identical
residues that the two proteins have in the same position of the multiple alignment.
An alternative formulation of linear independence can be in terms of the angle ... 

 