Vaulted structure has been in use for nearly 4000 years and believed to have been studied by scientists and builders for nearly 2000 years. There are few publications about the geometry and constructional aspects of arches and vaults before Renaissance age. One of the most interesting works on this subject belongs to Jamshid Kashani known as a mathematician. Ghiayth Al-Din Kashani, has made so...

We consider constrained versions of the prize-collecting traveling salesman and the minimum spanning tree problems. The goal is to maximize the number of vertices in the returned tour/tree subject to a bound on the tour/tree cost. We present a 2-approximation algorithm for these problems based on a primal-dual approach. The algorithm relies on finding a threshold value for the dual variable cor...

Environmental problems currently affect all spheres of human activity, so the school should introduce students warning about possible environmental hazards. An urgent problem is need to education and formation culture students. The article discusses features organization in framework subject «Mathematics». goal develop teaching methods linking mathematics ecology.Along with ecological students,...