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This article applies functional knowledge and computer software to describe the relation between people distribution and evacuation efficency and safety in high-rise buildings.The people distribution contains two parts:the allocation of people in different storeys and the distribution of people in a certain storey. Through this mathematical model,we attempt to find the optimum plan of people distribution and use it to guide the distribution of different functional areas in high-rise buildings.

We compute certain open Gromov–Witten invariants for toric Calabi–Yau threefolds. The proof relies on a relation for ordinary Gromov–Witten invariants for threefolds under certain birational transformation, and a recent result of Kwokwai Chan.

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S-transformation is a unitary transformation accomplishing the main part of the diagonalization of the interaction Hamiltonian in strong coupling theories. For a compact symmetry group the action of the S-transformation on the integrals of motion is derived.