Two families F and G of k-subsets of {1, 2,..., n} are called non-trivial cross t-intersecting if|F ∩ G|≥t for all F ∈ F, G ∈ G and | ∩ {F : F ∈ F}| < t, | ∩ {G : G ∈ G}| < t. In the present paper,we det...Two families F and G of k-subsets of {1, 2,..., n} are called non-trivial cross t-intersecting if|F ∩ G|≥t for all F ∈ F, G ∈ G and | ∩ {F : F ∈ F}| < t, | ∩ {G : G ∈ G}| < t. In the present paper,we determine the maximum product of the sizes of two non-trivial cross t-intersecting families of k-subsets of{1, 2,..., n} for n≥4(t + 2)2k2, k≥5, which is a product version of the Hilton-Milner-Frankl theorem.展开更多
The effects of blast waves generated by energetic and non-energetic sources are of continuing interest to the ballistics research community.Modern conflicts are increasingly characterised by asymmetric urban warfare, ...The effects of blast waves generated by energetic and non-energetic sources are of continuing interest to the ballistics research community.Modern conflicts are increasingly characterised by asymmetric urban warfare, with improvised explosive devices(IEDs) often playing a dominant role on the one hand and an armed forces requirement for minimal collateral effects from their weapons on the other. These problems are characterised by disparate length- and time-scales and may also be governed by complex physics. There is thus an increasing need to be able to rapidly assess and accurately predict the effects of energetic blast in topologically complex scenarios. To this end, this paper presents a new Qineti Q-developed advanced computational package called EAGLE-Blast, which is capable of accurately resolving the generation, propagation and interaction of blast waves around geometrically complex shapes such as vehicles and buildings. After a brief description of the numerical methodology, various blast scenario simulations are described and the results compared with experimental data to demonstrate the validation of the scheme and its ability to describe these complex scenarios accurately and efficiently. The paper concludes with a brief discussion on the use of the code in supporting the development of algorithms for fast running engineering models.展开更多
基金supported by National Natural Science Foundation of China (Grant No. 11701407)
文摘Two families F and G of k-subsets of {1, 2,..., n} are called non-trivial cross t-intersecting if|F ∩ G|≥t for all F ∈ F, G ∈ G and | ∩ {F : F ∈ F}| < t, | ∩ {G : G ∈ G}| < t. In the present paper,we determine the maximum product of the sizes of two non-trivial cross t-intersecting families of k-subsets of{1, 2,..., n} for n≥4(t + 2)2k2, k≥5, which is a product version of the Hilton-Milner-Frankl theorem.
文摘The effects of blast waves generated by energetic and non-energetic sources are of continuing interest to the ballistics research community.Modern conflicts are increasingly characterised by asymmetric urban warfare, with improvised explosive devices(IEDs) often playing a dominant role on the one hand and an armed forces requirement for minimal collateral effects from their weapons on the other. These problems are characterised by disparate length- and time-scales and may also be governed by complex physics. There is thus an increasing need to be able to rapidly assess and accurately predict the effects of energetic blast in topologically complex scenarios. To this end, this paper presents a new Qineti Q-developed advanced computational package called EAGLE-Blast, which is capable of accurately resolving the generation, propagation and interaction of blast waves around geometrically complex shapes such as vehicles and buildings. After a brief description of the numerical methodology, various blast scenario simulations are described and the results compared with experimental data to demonstrate the validation of the scheme and its ability to describe these complex scenarios accurately and efficiently. The paper concludes with a brief discussion on the use of the code in supporting the development of algorithms for fast running engineering models.
