Sentence examples for under multiplication from inspiring English sources

In 1969 she received a doctoral degree in mathematics at Emory University, Atlanta, for a thesis on quasigroups, which are sets of elements that are closed under multiplication but do not have to fulfill any of the other requirements for being a group.

(There is no need to close off under multiplication too, since the set of integers is already closed under multiplication).

Let us call this property of ∞ reflexivity under multiplication (by such a probability).

Another example is S1, the group of all complex numbers with modulus one under multiplication.

In the next lemma, we check the continuity property under multiplication operation with bounded functions.

For example, the space is not closed under multiplication with negative scalars.

Taking Hanning window for example, analyze its time domain characters and frequency domain characters under different multiplication order.

The set Lipα X, d)={f∈C X): pα(f)<∞} with the norm ‖f‖α=|f|X+pα(f) is a Banach function algebra under pointwise multiplication.

Under pointwise multiplication, these homomorphisms form an abelian group (G^wedge :=Gamma ) which is locally compact with the compact-open topology.

The set Lipα K, d) = {f ∈ C K): pα(f) < ∈} with the norm ||f||α = |f|K + pα(f) is a Banach function algebra under pointwise multiplication.

Similarly a group can be defined as any homologue of the group of rotations of the sphere, or of the nonsingular 2 × 2 real matrices under matrix multiplication (equivalently the group of automorphisms of the plane).