Sentence examples for known solution for from inspiring English sources

For symmetric chains, the general solution of the eigenvalue problem is reduced to the known solution for polyoxymethylene chains.

In the following, there is a discussion of RCS in various scattering regimes, supported using the analytically known solution for the sphere.

Out of the 132 total instances in QAPLIB of varied sizes, the greedy genetic algorithm obtained the best known solution for 103 instances, and for the remaining instances (except one) found solutions within 1% of the best known solutions.

The gap is equal to 100[c(s**) − c(s* ]/c(s*), where s** is the best solution found by the algorithm for a given instance, and s* is the overall best known solution for the same instance on the web.

Here, we consider a Cauchy-type singular integral equation of the first kind over two disjoint intervals (−∞,b1)∪(c1,d1); (a1,b1)∪(c1,∞); and (−∞,−k)∪ k,∞) and obtain its solution by limiting process applied to the known solution for equations involving two disjoint finite intervals.

The numerical method was verified with a known solution for a simplified and linearized version of the model.

We provide several best known solutions for benchmark instances.

DMRSA found the 22 best known solutions for 27 TSP instances.

In low resolution region we provide practical guidelines, extending previously known solutions for the straight/diagonal Poiseuille flow.

While analytical solutions for the (out-of-plane) rotational stiffness of circular plates are well known, solutions for rectangular plates have not yet been addressed.

Furthermore, the proposed SM2-MBO can improve 9 out of 10 best known solutions for the benchmark instances in the literature.