Riemann hypothesis, in number theory, hypothesis by German mathematician Bernhard Riemann concerning the location of solutions to the Riemann zeta function, which is connected to the prime number theorem and has important implications for the distribution of prime numbers.
With the support of this tool the decision-maker can obtain information about the shape of the Pareto front, the range of explored area by the algorithms, qualitative estimation of algorithm performance, relation between objectives, location of solutions and their dispersion.
Now we state our result of existence and location of solutions for problem (2).
Remark 3.2 We point out that the same statement of above given result can be obtained by using a classical direct methods theorem (see [14]), but in addition we get the location of the solution, hence in particular the solution is nontrivial.
Namely, we will define functions called upper and lower solutions that not only imply the existence of a solution of a SBVP, but that also provide bounds on the location of the solution.
In addition, some information on the location of periodic solution is obtained, which can lead to the results on multiple periodic solutions.
In the following result we prove some additional results concerning the location of the solution.
This combined traditional initial rate experiments to identify a solution in the vicinity of the global minimum, with nonlinear regression methods to determine the exact location of the solution.
Error surfaces of the non-linear, iterative, least-squares inversions corresponding to multiple, constant-velocity, horizontal layers have an absolute minimum at or near the location of the solution parameters for zero and low frequencies.
Consequently, information on the location of the solution is obtained and multiple results are obtained if g and f satisfy the given conditions on distinct regions.
