A Silurian armoured jawed vertebrate with large marginal jaw bones previously associated with bony vertebrates.

An Early Devonian Mongolian jawed vertebrate whose braincase contains a trabecular internal tissue interpreted as endochondral bone. Implications for ancestral bone depend on both tissue identity and phylogenetic placement.

An Early Devonian Siberian jawed vertebrate whose braincase–shoulder relationship supplies evidence for a posterior pharyngeal component of the pectoral girdle.

Mechanical strain induced by an applied electric field. It complements the direct conversion of mechanical stress into electrical polarization.

Slow displacement relaxation following a change in piezoelectric scanner drive, even after the commanded voltage is held fixed. Settling and position-sensor closed-loop control reduce its effect on image coordinates.

Dependence of piezoelectric displacement on the history and direction of the applied voltage. It differs from the continuing time-dependent relaxation called piezoelectric scanner creep.

Linear electrical-displacement response to mechanical stress in a suitable piezoelectric material. It is distinct from the converse effect, in which an applied electric field causes strain. The measured voltage also depends on electrical loading and mechanical constraints.

A transducer using stress-induced electrical charge. A uniformly loaded slab of thickness $t$ has ideal open-circuit voltage sensitivity $dt/({ϵ}_0\kappa )$; leakage and input capacitance change its measured response.

The Chudnovsky algorithm computes Pi to high precision by evaluating the Chudnovsky series with controlled truncation and rounding errors. A direct implementation updates the ratio of successive terms rather than recomputing every factorial. Large computations use binary splitting to combine rational partial sums through a balanced recursion tree, reducing expensive high-precision divisions. Roughly one term is needed per fourteen requested decimal digits, with additional guard precision and a bound on the remaining tail. Fast convergence of the series does not alone certify printed digits: finite-precision arithmetic errors must also be bounded.

The released 2015 paper uses this historical course title. Generic physical and mathematical parts are covered; biological questions remain deferred.

2016 paper: Public original PDF, physical page 768. Student-answer availability for this paper remains unverified.