The decomposition potential of the electrode must be exceeded before significant gas evolution occurs during electrolysis.

The prime decomposition of 84 is 2^2 × 3 × 7.

The chemists compared the decomposition potentials across different soil samples to predict pollutant breakdown.

The chemist compared the double decompositions that occurred during the reaction to identify intermediate species.

Graduate students often study matrix decompositions to improve their understanding of linear algebra.

The textbook included several chemical decompositions to demonstrate how complex molecules break down.

The number theory class compared several prime decompositions to illustrate the uniqueness of prime factorization.

To solve the least-squares problem efficiently, we compute the QR decomposition of the design matrix and use back substitution.

To study the contact structure on the manifold, she constructed an open book decomposition whose pages are Seifert surfaces bounded by the binding link.

Recent research has revealed new symmetries in open book decompositions that simplify the classification of contact structures.