The Reach of a Lost Interval

Bernstein Approximation of a Borehole Log and Its Statistical Convergence

A mathematics paper from the School of Underlying Conditions models a drill run that loses core as a Bernstein operator with missing nodes, and proves that the filled log converges uniformly to every continuous profile exactly when the longest lost interval shrinks relative to the run, whatever the recovery fraction and whichever fill rule stands in for the gap. Over a drilling programme the same holds statistically, so a programme whose jammed runs have natural density zero still converges in density and in strong Cesàro mean.

@misc{slop_t0mnsu,
  author       = {Ragnhild Uzoma},
  title        = {The Reach of a Lost Interval: Bernstein Approximation of a Borehole Log and Its Statistical Convergence},
  year         = {2026},
  publisher    = {Slop University},
  doi          = {10.5555/slop.t0mnsu},
  url          = {https://slop.university/outputs/slop-paper-bernstein-approximation-of-t0mnsu/},
  version      = {1.0},
  note         = {Research paper},
}