Определенные артикли перед существительными, которые снабжены ссылками

The differential problem (1) can be reduced to the form (2)

The asymptotic formula (1) follows from the above lemma

The differential equation (1) can be solved numerically

What is needed in the final result is a simple bound on quantities of the form (1)

The inequality (1) (артикль можно опустить) shows that $a>b$

The bound (estimate) (2) is not quite as good as the bound (estimate) (1)

If the norm of $A$ satisfies the restriction (1), then by the estimate (2) this term is less than unity

Since the spectral radius of $A$ belongs to the region (1), this iterative method converges for any initial guesses

The array (1) is called the matrix representing the linear transformation of $f$

It should be noted that the approximate inequality (1) bounds only the absolute error in $x$

The inequality (1) shows that ...

The second step in our analysis is to substitute the forms (1) and (2) into this equation and simplify it by dropping higher-order terms

For small $ze$ the approximation (1) is very good indeed

A matrix of the form (1), in which some eigenvalue appears in more than one block, is called a derogatory matrix

The relation between limits and norms is suggested by the equivalence (1)

For this reason the matrix norm (1) is seldom encountered in the literature

To establish the inequality (1) from the definition (2)

Our conclusion agrees with the estimate (1)

The characterization is established in almost the same way as the results of Theorem 1, except that the relations (1) and (2) take place in the eigenvalue-eigenvector relation ...

This vector satisfies the differential equation (1)

The Euclidean vector norm (2) satisfies the properties (1)

The bound (1) ensures only that these elements are small compared with the largest element of $A$

There is some terminology associated with the system (1) and the matrix equation (2)

A unique solution expressible in the form (1) restricts the dimensions of $A$

The factorization (1) is called the $LU$-factorization

It is very uncommon for the condition (1) to be violated

The relation (1) guarantees that the computed solution gives very small residual

This conclusion follows from the assumptions (1) and (2)

The factor (1) introduced in relation (2) is now equal to 2

The inequalities (1) are still adequate

We use this result without explicitly referring to the restriction (1)