This thesis presents two significant results in the field of precision measurements in low-energy nuclear physics. Firstly, it presents a precise half-life determination of 11C, leading to the most precise ft-value for a beta decay transition between mirror nuclides, an important advance in the testing of the electroweak sector of the Standard Model. Secondly, it describes a high-precision mass measurement of 56Cu, a critical nucleus for determining the path of the astrophysical rapid-proton capture process, performed by the author using the LEBIT Penning trap at the National Superconducting Cyclotron Laboratory. This new measurement resolves discrepancies in previously-reported calculated mass excesses. In addition, the thesis also presents the construction and testing of a radio-frequency quadrupole cooler and buncher that will be part of the future N = 126 factory at Argonne National Laboratory aimed at producing nuclei of interest for the astrophysical rapid-neutron capture process for the first time.

Applied mathematics connects the mathematical theory to the reality by solving real world problems and shows the power of the science of mathematics, greatly improving our lives. Therefore it plays a very active and central role in the scientific world.This volume contains 14 high quality survey articles — incorporating original results and describing the main research activities of contemporary applied mathematics — written by top people in the field. The articles have been written in review style, so that the researcher can have a quick and thorough view of what is happening in the main subfields of applied mathematics.