Sentence examples for cannot be omitted in from inspiring English sources

The following example shows that the assumption cannot be omitted in Corollary 3.4.

As shown in (80), linker phrases cannot be omitted in the second conjunct.

Example 3.22 of [35] shows that condition 'A is a finite set' cannot be omitted in the above theorem.

Moreover, Example (3) shows that the condition related to common zeros cannot be omitted in Theorem 1.3.

Illegal suburbs are currently so widespread that they cannot be omitted in any future policy or strategy regarding urban development and planning, land and property management.

Theoretical calculations show that, for the low reflectance coatings, losses due to light coupling into optical fibre cannot be omitted in the analysis of the experimental results.

Although chondrocytes are known to be well adapted to the hypoxic environment within native cartilage tissue in vivo, the importance of oxygen cannot be omitted completely in their principal function, namely, synthesis of cartilaginous ECM.

The requirement that the main equation is uniquely solvable (Condition S in Theorem 6) is essential and cannot be omitted (see Example 1.6.1 in [2]).

For example, H2O is a small metabolite in many reactions, but in the following reaction:Putrescine + Oxygen + H2O <=> 4-Aminobutanal + NH3 + H2O2, H2O cannot be omitted because it participates in producing H2O2.

It is worth noticing that the conditions (D1') in Theorem 12.1 and (D2') in Theorem 12.2 cannot be omitted.

It is worth mentioning that the variable s in (10) cannot be omitted because the equality E d m [ k ] θ m [ k ] ∗ b m [ k ] d m [ s ] θ m [ s ] ∗ b m [ s ] ∗ = P m δ k, s is not satisfied.