J-couplingIn nuclear chemistry and nuclear physics, J-couplings (also called spin-spin coupling or indirect dipole–dipole coupling) are mediated through chemical bonds connecting two spins. It is an indirect interaction between two nuclear spins that arises from hyperfine interactions between the nuclei and local electrons. In NMR spectroscopy, J-coupling contains information about relative bond distances and angles. Most importantly, J-coupling provides information on the connectivity of chemical bonds.
Pappus's hexagon theoremIn mathematics, Pappus's hexagon theorem (attributed to Pappus of Alexandria) states that given one set of collinear points and another set of collinear points then the intersection points of line pairs and and and are collinear, lying on the Pappus line. These three points are the points of intersection of the "opposite" sides of the hexagon . It holds in a projective plane over any field, but fails for projective planes over any noncommutative division ring. Projective planes in which the "theorem" is valid are called pappian planes.
CollineationIn projective geometry, a collineation is a one-to-one and onto map (a bijection) from one projective space to another, or from a projective space to itself, such that the of collinear points are themselves collinear. A collineation is thus an isomorphism between projective spaces, or an automorphism from a projective space to itself. Some authors restrict the definition of collineation to the case where it is an automorphism. The set of all collineations of a space to itself form a group, called the collineation group.
Lunar phaseConcerning the lunar month of approximately 29.53 days as viewed from Earth, the lunar phase or Moon phase is the shape of the Moon's directly sunlit portion, which can be expressed quantitatively using areas or angles, or described qualitatively using the terminology of the four major phases (new moon, first quarter, full moon, last quarter) and four minor phases (waxing crescent, waxing gibbous, waning gibbous, and waning crescent). The lunar phases gradually change over a synodic month (29.
Nuclear spectroscopyNuclear spectroscopy is a superordinate concept of methods that uses properties of a nucleus to probe material properties. By emission or absorption of radiation from the nucleus information of the local structure is obtained, as an interaction of an atom with its closest neighbours. Or a radiation spectrum of the nucleus is detected. Most methods base on hyperfine interactions, which are the interaction of the nucleus with its interaction of its atom's electrons and their interaction with the nearest neighbor atoms as well as external fields.
Fano planeIn finite geometry, the Fano plane (after Gino Fano) is a finite projective plane with the smallest possible number of points and lines: 7 points and 7 lines, with 3 points on every line and 3 lines through every point. These points and lines cannot exist with this pattern of incidences in Euclidean geometry, but they can be given coordinates using the finite field with two elements. The standard notation for this plane, as a member of a family of projective spaces, is PG(2, 2).
