Sentence examples for algebra result from inspiring English sources
This "modern algebra" result constitutes a completeness theorem for equational logic in terms of its models.
A linear algebra result, known as Elimination Lemma, has been used to solve a large number of filtering and control problems.
The Lefschetz formula is also in this discrete incarnation a generalization of the Euler-Poincaré formula, which is a linear algebra result in the case of graphs.
With this and the Cuntz algebra result in hand, it made sense to conjecture that L K ( 1, n ) ≅ M d ( L K ( 1, n ) ) if and only if g. c. d. ( d, n - 1 ) = 1.
However, a strong correlation was found between Vector Calculus and Linear Algebra results.
Well-known algebra results in [33] are used to equivalently recast (A5)–(A5).
Applying the algebra results to Fock-adapted Markovian cocycles on a Hilbert space we obtain similar characterisations.
It is assumed that 0 ∈ D. By standard algebra results, for D to be a digit set it is necessary that | D | = | det L |. Consider an affine IFS F : = F ( L, D ) = { R n ; f 1, f 2, …, f N }, where f i ( x ) = L − 1 ( x − d i ).
After some algebra, the result is: <img src="http://journals.plos.org/plosone/article/asset?id=info?doi/10.1371/journal.pone.0011656.e001.PNG" class= inline-graphic"/> This is a linear recurrence relationship (finite-difference equation) for <g> describing the accumulation of average fecundity "wealth" over generations.
The resolution process boils down to solving particular quadratic Diophantine equations that are reduced to linear Diophantine equations, thanks to linear algebra results and the well-definedness of the problem.
