An algebra is atomless just in case all of its elements can be partitioned into finer elements.
The IS copy number of a genome of type i can be partitioned into numbers of elements that produced advantageous (l i, p ), neutral (l i, n ) and deleterious (l i, d ) effects, so that l i = l i, a + l i, n + l i, d.
Therefore if each orbit (together with its eventually periodic elements) can be partitioned into two sets satisfying the desired conditions, the whole set D can also be partitioned into two sets satisfying the desired condition.
We remark that the mentioned methods, e.g., [38], [39], [40], [41], [34], [35] for measuring the structural information content of a graph-based system are based on the following principle: Starting from a certain equivalence criterion, a graph-based system with n elements can be partitioned into k classes, see, e.g., [14].
The collection of infinite strings of symbols taken from any finite "alphabet", lexicographically ordered, can be partitioned into two non-empty parts L, R, such that every element of L is less than every element of R, while L contains a largest element and R contains a smallest element.
The motivation underlying all clustering methods is to determine whether the data can be partitioned into useful groups that provide insight into the relationship between group members, or the discriminating elements between groups.
Fields can be partitioned into Subjects.
The ideal controller can be partitioned into two parts.
Internal memory can be partitioned into 2, 4 or 8 partitions.
Let be partitioned into (2.38).
Let be symmetric and be partitioned into.
