Sentence examples for a class of examples from inspiring English sources

The sector measure on B S, i.e. the measure sm K ( A ) = μ ( sector ( A, 1 ) ) μ ( K ), satisfies the representation sm K ( A ) = O S ( A ) O S ( S ), A ∈ B S. A class of examples where Theorem 1 applies is given by all star bodies K corresponding to norms or antinorms for which there exist countably many pairwise disjoint sets A j satisfying Assumption 1 and S = ⋃ j A j.

But this idea is challenged by a class of examples, in which environment seems to make a difference.

We give a class of examples of second order difference equations with quadratic terms for which a discrete version of the 16th Hilbert problem does not hold.

We provide a class of examples of compact quantum groups and unitary 2-cocycles on them, such that the twisted quantum groups are non-compact, but still locally compact quantum groups (in the sense of Kustermans and Vaes).

The proof of the main results will be stated in Section 3. A class of examples are given to show that our main result is applicable to many problems in Section 4. In this section, we shall state some necessary definitions and preliminaries.

A large class of examples of monic representations is based on Markov measures.

This is, to say the least, a heterogeneous class of examples.

Here is a first class of examples of functions in (mathfrak I_c).

Unfortunately, these equations can be solved only for a narrow class of examples.

Zappa Szép products of semigroups provide a rich class of examples of semigroups that include the self-similar group actions of Nekrashevych.

This provides a new class of examples of metric spaces with bounded geometry which coarsely embed into Hilbert space but do not have property A, generalising the example of Arzhantseva, Guentner and Spakula.