The study of long-span structures developed from a design problem for an aircraft hangar. The problem of the aircraft hangar was concerned... Show moreThe study of long-span structures developed from a design problem for an aircraft hangar. The problem of the aircraft hangar was concerned with the development of a reasonable structurtal type into an architectural solution. Several types were considered; the truss, the arch, a rigid frame system in prestressed concrete. These were discarded in favor of a rigid frame system of steel that seemed to give the best visual solution. Show less
Automatic cubatures approximate multidimensional integrals to user-specified... Show moreAutomatic cubatures approximate multidimensional integrals to user-specified
error tolerances. In many real-world integration problems, the analytical solution is
either unavailable or difficult to compute. To overcome this, one can use numerical
algorithms that approximately estimate the value of the integral.
For high dimensional integrals, quasi-Monte Carlo (QMC) methods are very
popular. QMC methods are equal-weight quadrature rules where the quadrature
points are chosen deterministically, unlike Monte Carlo (MC) methods where the
points are chosen randomly. The families of integration lattice nodes and digital nets
are the most popular quadrature points used. These methods consider the integrand
to be a deterministic function. An alternate approach, called Bayesian cubature,
postulates the integrand to be an instance of a Gaussian stochastic process. Show less
