Sentence examples for by interchanging the columns from inspiring English sources

Thus, (D(P)) contains all integer points in P. We assume without loss of generality that (x^{l}< x^{mathrm{min}}) (let (x_{i}^{l}=x_{i}^{mathrm{min}}-1) if (x_{i}^{l}=x_{i}^{mathrm{min}}) for some (iin N)) and that x_{1}^{u}-x_{1}^{l}leq x_{2}^{u}-x_{2}^{l}leqcdotsleq x_{n}^{u}-x_{n}^{l}, which can be obtained by interchanging the columns of A if necessary.

By interchanging the order of the summation we get (5.53).

They emulate both types of memristor (incremental and decremental) just by interchanging the CBTA output terminals.

By analogous relation, obtained by interchanging the roles of and, it follows that (5.45).

Then, by interchanging the order of summation, we obtain the following (2.4).

The above derivation remains valid by interchanging the roles of the sets and since.

By interchanging the roles of u and v, we get the following results.

By interchanging the roles of f and g and using (2.1), we have (2.14).

By interchanging the order of integration and some rearrangement of (2.22), we obtain (2.23).

Weng avoids that problem by interchanging the order of histogram modification and IWT.

Similarly, calculate another reading by interchanging the known and unknown resistances in the above circuit.