Sentence examples for elementary result in from inspiring English sources

The number κ ( x ) encodes so the orbit length of x under the automorphism group A. (2) One can also see this as graded summation of an elementary result in linear algebra (see [29], p.21): if a finite group acts linearly on a finite dimensional vector space V, then dim ( F ) = ( 1 / | A | ) ∑ T ∈ A tr ( T ).

When he was 15 years old, he obtained a copy of George Shoobridge Carr's Synopsis of Elementary Results in Pure and Applied Mathematics, 2 vol. (1880 86).

In this section, we recall some basic definitions and elementary results in literature.

Therefore, it can be applied to some elementary results in [4, 7, 15, 23 26].

The Banach contraction principle [1] is the simplest and one of the most versatile elementary results in fixed point theory.

The Banach contraction principle [1] is the most famous, simplest and one of the most versatile elementary results in fixed point theory.

It is interesting to observe that it seems extremely difficult to use the above method to get some elementary results in the rapid approximate-controllability context.

The Banach contraction principle [3] is the simplest and one of the most versatile elementary results in fixed point theory, which is a very popular tool for solving existence problems in many branches of mathematical analysis.

The simple closed-form expressions used in the paper are elementary results in coalescent theory [ 3, 4].

An important elementary result is that an equation holds in all BAs if and only if it holds in the two-element BA.

We will use the following elementary result for a semimodular, which is Corollary 2.1.15 in [6].