218 research outputs found
Music Analgesia Used in Delivery of Pregnant Women
Music therapy is one of the non-drug labor analgesia methods advocated during labor, which can relieve labor pain and anxiety and promote natural childbirth. The author here from the definition of music therapy, physiological principles, for labor analgesia on maternal and neonatal effects, as well as music therapy and doula accompany childbirth combined application effect were reviewed
Extremal number of graphs from geometric shapes
We study the Tur\'{a}n problem for highly symmetric bipartite graphs arising
from geometric shapes and periodic tilings commonly found in nature.
1. The prism is the graph
consisting of two vertex disjoint -cycles and a matching pairing the
corresponding vertices of these two cycles. We show that for every ,
ex. This resolves a conjecture of He,
Li and Feng.
2. The hexagonal tiling in honeycomb is one of the most natural structures in
the real world. We show that the extremal number of honeycomb graphs has the
same order of magnitude as their basic building unit 6-cycles.
3. We also consider bipartite graphs from quadrangulations of the cylinder
and the torus. We prove near optimal bounds for both configurations. In
particular, our method gives a very short proof of a tight upper bound for the
extremal number of the 2-dimensional grid, improving a recent result of
Brada\v{c}, Janzer, Sudakov and Tomon.
Our proofs mix several ideas, including shifting embedding schemes, weighted
homomorphism and subgraph counts and asymmetric dependent random choice.Comment: 23 page
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