We prove that if A ⊆ { 1 , … N } does not contain any non-trivial three-term arithmetic progression, then | ≪ ( log ⁡ ) 3 + o .

this paper deals with three-dimensional evaluation of the slopes on the basis of limit analysis. an upper-bound technique of limit analysis is used in this paper to determine either the bearing capacity of a shallow foundation near a slope or the safety factor of the slope. the theorems of limit analysis (upper and lower bound) provide a powerful tool for solving problems in which limit loads n...

Abstract In 1895, Vahlen proved a theorem concerning simultaneous approximation of real number by its two consecutive convergent. this paper, we will provide sharper bound for the theorem.

We investigate codes meeting the Griesmer bound. The main theorem of this article is the generalization of the nonexistence theorem of [7] to a larger class of codes. keywords: Griesmer bound, extending codes, nonexistence theorem, code construction