Numerical methods for ordinary differential equationsNumerical methods for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs). Their use is also known as "numerical integration", although this term can also refer to the computation of integrals. Many differential equations cannot be solved exactly. For practical purposes, however – such as in engineering – a numeric approximation to the solution is often sufficient. The algorithms studied here can be used to compute such an approximation.
Image registrationImage registration is the process of transforming different sets of data into one coordinate system. Data may be multiple photographs, data from different sensors, times, depths, or viewpoints. It is used in computer vision, medical imaging, military automatic target recognition, and compiling and analyzing images and data from satellites. Registration is necessary in order to be able to compare or integrate the data obtained from these different measurements.
Computed tomography angiographyComputed tomography angiography (also called CT angiography or CTA) is a computed tomography technique used for angiography—the visualization of arteries and veins—throughout the human body. Using contrast injected into the blood vessels, images are created to look for blockages, aneurysms (dilations of walls), dissections (tearing of walls), and stenosis (narrowing of vessel). CTA can be used to visualize the vessels of the heart, the aorta and other large blood vessels, the lungs, the kidneys, the head and neck, and the arms and legs.
Heat kernelIn the mathematical study of heat conduction and diffusion, a heat kernel is the fundamental solution to the heat equation on a specified domain with appropriate boundary conditions. It is also one of the main tools in the study of the spectrum of the Laplace operator, and is thus of some auxiliary importance throughout mathematical physics. The heat kernel represents the evolution of temperature in a region whose boundary is held fixed at a particular temperature (typically zero), such that an initial unit of heat energy is placed at a point at time t = 0.
BrassBrass is an alloy of copper (Cu) and zinc (Zn), in proportions which can be varied to achieve different colours and mechanical, electrical, and chemical properties, but copper typically has the larger proportion. In use since prehistoric times, it is a substitutional alloy: atoms of the two constituents may replace each other within the same crystal structure. Brass is similar to bronze, another copper alloy that uses tin instead of zinc.
CrucibleA crucible is a ceramic or metal container in which metals or other substances may be melted or subjected to very high temperatures. Although crucibles have historically tended to be made out of clay, they can be made from any material that withstands temperatures high enough to melt or otherwise alter its contents. The form of the crucible has varied through time, with designs reflecting the process for which they are used, as well as regional variation. The earliest crucible forms derive from the sixth/fifth millennium B.
