Sentence examples for solution this way from inspiring English sources

Solutions to 2013 International Mathematical Olympiad Problem 6 Our second challenge this week was the problem that stumped so many at this year's IMO — Problem 6. Numberplay regular Richardo Ech laid out the solution this way: One way to generate all beautiful labelings on {0,…,n} is as follows: Let (x,y) be a pair such that n > y > x, gcd x,y) = 1, and N = x + y >= n.

It seems not altogether unreasonable to extend the meaning of the term "solution" this way, for, just like a concrete solution, an impossibility proof also provides what might be called "epistemic closure": like a concrete solution, it provides a completely convincing reason to stop working on a certain problem.

In this work we use the method of lower and upper solutions to generate a sequence of modified nonlinear problems, each having a unique solution; in this way, we obtain a sequence of functions, which is uniformly bounded together with their first and second order derivatives.

One typical phenomenon, which is slowing the particle diffusion in the solution and this way leads to increased R h, is the solvation layer around the particle.

Constraining the space of solutions in this way, we call the physical variables d weak solutions of the Cauchy problem (4), if they are classical solutions wherever they are continuously differentiable, and if at discontinuities (shocks) they satisfy additional conditions in order to be physically reasonable (we elaborate on these conditions below).

Direct addition of HCl acid to the natural pH mixed gellan aqueous solutions in this way is a fast method of acidification that is novel for biopolymers of this type, where slower and alternative methods using different acids have been investigated.

"The negotiations are the solution, the way, and this is what our nation wants, to end the bloodshed," Ghani said.

Usually the solution found in this way is only approximate.

The coarse-grained representation of a typical solution is found this way.

The solution generated in this way in which all adjacent nodes are connected is valid.

It extends existing ISO GPS annotation by information about influences on the manufacturability of a chosen design solution and in this way enables the systematic acquisition of variation data meaningful for design practice.