A Steiner 2-design S 2,k,v) is said to be halvable if the block set can be partitioned into two isomorphic sets.
This paper reviews evidence in favour of using isomorphic sets of material stimuli as tools to bridge the disciplinary gap between designers and materials scientists.
We show how these isomorphic sets and their accompanying experiments can be used to translate between the two communities, and to systematically explore the relationship between the technical attributes of materials and subjective experiences of their sound, taste and feel.
It also directly implies that two isomorphic sets are equal, that two categorically equivalent groupoids are equal, and so one.
From this, the number of non-isomorphic bond sets of a certain size can be calculated by a straightforward application of Pólya's Enumeration Theorem [33]: decalin has four non-isomorphic bond sets of size one, 182 non-isomorphic bond sets of size two, 47 non-isomorphic bond sets of size three, and 92 non-isomorphic bond sets of size four.
If a Segal algebra is isomorphic to the set of all self-adjoint elements of a C*-algebra, then it is a special or exceptional Segal algebra.
The codomain S is isomorphic to the set of vectors; whose lengths, non-negative integers, are given by a well-defined function of (left| {N} right|) and m; and, The codomain S is a commutative monoid.
Interpretations of uni-atomic EMUs are valid, therefore, if and only if: The codomain S is isomorphic to the set of vectors; whose lengths, non-negative integers, are given by a well-defined function of (left| {N} right|) and m; and, The codomain S is a commutative monoid.
Also, every well-ordered set is isomorphic to a unique ordinal, called its order-type.
Actually, each pattern represents a set of isomorphic connected subgraphs which have the same structural properties and differ only in the participating vertices.
