Homological algebraHomological algebra is the branch of mathematics that studies homology in a general algebraic setting. It is a relatively young discipline, whose origins can be traced to investigations in combinatorial topology (a precursor to algebraic topology) and abstract algebra (theory of modules and syzygies) at the end of the 19th century, chiefly by Henri Poincaré and David Hilbert. Homological algebra is the study of homological functors and the intricate algebraic structures that they entail; its development was closely intertwined with the emergence of .
Magnetic anisotropyIn condensed matter physics, magnetic anisotropy describes how an object's magnetic properties can be different depending on direction. In the simplest case, there is no preferential direction for an object's magnetic moment. It will respond to an applied magnetic field in the same way, regardless of which direction the field is applied. This is known as magnetic isotropy. In contrast, magnetically anisotropic materials will be easier or harder to magnetize depending on which way the object is rotated.
Magnetic pressureIn physics, magnetic pressure is an energy density associated with a magnetic field. In SI units, the energy density of a magnetic field with strength can be expressed as where is the vacuum permeability. Any magnetic field has an associated magnetic pressure contained by the boundary conditions on the field. It is identical to any other physical pressure except that it is carried by the magnetic field rather than (in the case of a gas) by the kinetic energy of gas molecules.
Standard ModelThe Standard Model of particle physics is the theory describing three of the four known fundamental forces (electromagnetic, weak and strong interactions – excluding gravity) in the universe and classifying all known elementary particles. It was developed in stages throughout the latter half of the 20th century, through the work of many scientists worldwide, with the current formulation being finalized in the mid-1970s upon experimental confirmation of the existence of quarks.
Molecular machineMolecular machines are a class of molecules typically described as an assembly of a discrete number of molecular components intended to produce mechanical movements in response to specific stimuli, mimicking macromolecular devices such as switches and motors. Naturally occurring or biological molecular machines are responsible for vital living processes such as DNA replication and ATP synthesis. Kinesins and ribosomes are examples of molecular machines, and they often take the form of multi-protein complexes.
Nuclear magnetic resonance spectroscopy of proteinsNuclear magnetic resonance spectroscopy of proteins (usually abbreviated protein NMR) is a field of structural biology in which NMR spectroscopy is used to obtain information about the structure and dynamics of proteins, and also nucleic acids, and their complexes. The field was pioneered by Richard R. Ernst and Kurt Wüthrich at the ETH, and by Ad Bax, Marius Clore, Angela Gronenborn at the NIH, and Gerhard Wagner at Harvard University, among others.
Earth's inner coreEarth's inner core is the innermost geologic layer of planet Earth. It is primarily a solid ball with a radius of about , which is about 20% of Earth's radius or 70% of the Moon's radius. There are no samples of Earth's core accessible for direct measurement, as there are for Earth's mantle. Information about Earth's core mostly comes from analysis of seismic waves and Earth's magnetic field. The inner core is believed to be composed of an iron–nickel alloy with some other elements.
Nine lemmaIn mathematics, the nine lemma (or 3×3 lemma) is a statement about commutative diagrams and exact sequences valid in the category of groups and any . It states: if the diagram to the right is a commutative diagram and all columns as well as the two bottom rows are exact, then the top row is exact as well. Likewise, if all columns as well as the two top rows are exact, then the bottom row is exact as well. Similarly, because the diagram is symmetric about its diagonal, rows and columns may be interchanged in the above as well.
AntiferromagnetismIn materials that exhibit antiferromagnetism, the magnetic moments of atoms or molecules, usually related to the spins of electrons, align in a regular pattern with neighboring spins (on different sublattices) pointing in opposite directions. This is, like ferromagnetism and ferrimagnetism, a manifestation of ordered magnetism. The phenomenon of antiferromagnetism was first introduced by Lev Landau in 1933.
NanoroboticsNanoid robotics, or for short, nanorobotics or nanobotics, is an emerging technology field creating machines or robots whose components are at or near the scale of a nanometer (10−9 meters). More specifically, nanorobotics (as opposed to microrobotics) refers to the nanotechnology engineering discipline of designing and building nanorobots with devices ranging in size from 0.1 to 10 micrometres and constructed of nanoscale or molecular components.
