Sentence examples for establish that the problem from inspiring English sources

In Section 3, under suitable hypotheses, we establish that the problem (1.1) possesses at least three solutions, moreover, we present an example to illustrate our results.

We first establish that the problem is NP-hard and prove that the maximum number of vehicles that can usefully work together is bounded.

Females of both strains are infertile, and Bartke's dissertation research established that the problem arose from the absence of this hormone; treating the animals with prolactin restored their ability to have pups.

Steiner and Xue [21] investigated the Max-TSP on van der Veen matrices and established that the problem stays NP-hard even on the class of distance matrices which satisfy both the van der Veen and Demidenko conditions.

We present two exact methods to solve the problem: (i) A dynamic programming based approach, establishing that the problem is NP-hard in the ordinary sense when the number of machines is fixed.

Where Heyting says that a proof of ¬a establishes a reduction of the solution of any problem to that of a, Kolmogorov had said that it established that the problem of reducing the solution of any problem to that of a has become without content.

The "Principle of Least Action" establishes that the problem of finding the solution of a given dynamical problem is mathematically equivalent to the problem of finding the geodesics of the underlying space.

Remark 4 From the proof of Theorem 3.1, we can establish that problem (1.4 - 1.6 1.4 - 1.6has nonneganotherolutiononnegative∗ ∗ ∈ K r.

In this section, we will establish that problem (1.4 - 1.6 1.4 - 1.6east one positive solution withasemmat1.1 and least 1.2.

With few exceptions, our list is simply a recounting of studies that combine data from genetic markers with ethnobotanical history to establish that problem plants evolved from domesticates.

In "Credit contingent interest rate swap" section, we establish that the pricing problem of CCIRS is equivalent to a CVA problem for interest rate swap.