Sentence examples for sum of copies from inspiring English sources

In addition, for this procedure to work the sum of copies must be divided by the area under the filter function, a processing called normalization.

Recall that a module (M) is called (Sigma )-injective if every direct sum of copies of (M) is injective.

By (3.10), the sum is a sum of copies of a random variable, say, such that (3.22).

Also, for a module (M), (oplus _{i=1}^{infty }M) stands for countably infinite direct sum of copies of (M).

In order that the socle of Y / X is a direct sum of copies of S ( a ), either X = Y (and Y / X = 0 ), or X = 0 (and Y / X = Y ), or X has to be indecomposable.

Since C is the projective module P ( a ), the right minimal right C -determined maps f : X → Y are the inclusions maps of submodules X of Y such that the socle of Y / X is a direct sum of copies of S ( a ).

This corresponds to the sum of transcript copies as 615,944 and 615,771 tpm (transcript per million).

For the 20-bp tag collections, the numbers of unique UniGene identifiers were slightly smaller: 5,793 and 5,125 for MRP1 and MRP2, respectively, which corresponds to the sum of transcript copies as 655,919 and 652,588 tpm.

The threshold was defined as the cut-off value to minimize wrong classifications based on the histogram consisting of sum of copy numbers of n tags.

However, our method may generate meaningful results for data obtained from multiple cells if the sum of copy numbers is correctly estimated.

Let us now assume that K is indecomposable so that add K consists of direct sums of copies of K. Given a short exact sequence K → f M → g Y, the map g is right minimal if and only if the sequence does not split.