Sentence examples for mathematical proof based from inspiring English sources

Only a mathematical proof, based on logic, can handle questions of the infinite.

Validation can be obtained based on mathematical proof of correctness by comparing the results of the model with other models [38, 39].

Provision of the mathematical proof of this statistic, which we based on the GLMM, is beyond the scope of this paper.

In this paper, a new data-driven bottleneck detection method is proposed based on rigorous mathematical proof for general serial production systems, which uses the routinely available industrial data on the plant floor to identify the throughput bottleneck location within production systems in both the short-term (transient) and long-term (steady-state) periods.

Therefore, our use of exponential functions in the case of migration events is justified by a heuristic argument and is not based on a mathematical proof that the associated approximations converge to the exact solution (for evidence using simulated data that both approaches converge to the same solution see Comparison of different diffusion theory-based approaches in Results).

This is based on a sound mathematical proof rather than a belief, and it is this essential feature of pi that attracted these artists to use it in the first place.

We gave mathematical proofs for these properties, based on which we can design a set of orthogonal moment invariants particularly for symmetric images.

Proof Our proof is based on mathematical induction.

The mathematical proof and simulation results are found in Qu et al [ 3].

A measurement matrix based on Kronecker product is devised, and it has been proved in mathematical proof.

A mathematical proof that the infinite expansion converges to the well known solution, given by the implicit formulation and based on radiosities balance, is provided.