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The long-term behaviour of triple systems has fascinated scientists for centuries.
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Figure 7 Lifetime of triple systems.
The lack of a self consistent treatment hinders a systematic study of triple systems.
Secular dynamics can play a mayor role in the evolution of triple systems.
Using gold nanoparticle as an example, new experimental study is conducted to reveal the particle concentration influence on the behaviour of triple line and bubble dynamics.
The only previously known examples of Steiner triple systems of order congruent to 1(mod6) without almost parallel classes were the projective triple systems of order 2n−1 with n odd, and 2 of the 11,084,874,829 Steiner triple systems of order 19.
Furthermore, we define a large set of cyclic triple systems to be a decomposition of triples of Zv into indecomposable cyclic designs.
A new result on overlarge sets of Kirkman triple systems is also produced.
The evolutionary pathways of the triple systems are simulated with the new triple code TrES, such that the examples below also demonstrate the capabilities of TrES.
Embeddings of nearly Kirkman triple systems of order v<100 are also discussed.
Then, we extend these results to the fine structure of cyclic directed triple systems and cyclic Mendelsohn triple systems.
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