Shape of the universeThe shape of the universe, in physical cosmology, is the local and global geometry of the universe. The local features of the geometry of the universe are primarily described by its curvature, whereas the topology of the universe describes general global properties of its shape as a continuous object. The spatial curvature is described by general relativity, which describes how spacetime is curved due to the effect of gravity.
Principal curvatureIn differential geometry, the two principal curvatures at a given point of a surface are the maximum and minimum values of the curvature as expressed by the eigenvalues of the shape operator at that point. They measure how the surface bends by different amounts in different directions at that point. At each point p of a differentiable surface in 3-dimensional Euclidean space one may choose a unit normal vector. A normal plane at p is one that contains the normal vector, and will therefore also contain a unique direction tangent to the surface and cut the surface in a plane curve, called normal section.
Sea levelMean sea level (MSL, often shortened to sea level) is an average surface level of one or more among Earth's coastal bodies of water from which heights such as elevation may be measured. The global MSL is a type of vertical datum a standardised geodetic datum that is used, for example, as a chart datum in cartography and marine navigation, or, in aviation, as the standard sea level at which atmospheric pressure is measured to calibrate altitude and, consequently, aircraft flight levels.
Error functionIn mathematics, the error function (also called the Gauss error function), often denoted by erf, is a complex function of a complex variable defined as: Some authors define without the factor of . This nonelementary integral is a sigmoid function that occurs often in probability, statistics, and partial differential equations. In many of these applications, the function argument is a real number. If the function argument is real, then the function value is also real.
Trivially perfect graphIn graph theory, a trivially perfect graph is a graph with the property that in each of its induced subgraphs the size of the maximum independent set equals the number of maximal cliques. Trivially perfect graphs were first studied by but were named by ; Golumbic writes that "the name was chosen since it is trivial to show that such a graph is perfect." Trivially perfect graphs are also known as comparability graphs of trees, arborescent comparability graphs, and quasi-threshold graphs.
Sea level riseBetween 1901 and 2018, the average global sea level rose by , or an average of 1–2 mm per year. This rate accelerated to 4.62 mm/yr for the decade 2013–2022. Climate change due to human activities is the main cause. Between 1993 and 2018, thermal expansion of water accounted for 42% of sea level rise. Melting temperate glaciers accounted for 21%, with Greenland accounting for 15% and Antarctica 8%. Sea level rise lags changes in the Earth's temperature.
Gamma functionIn mathematics, the gamma function (represented by Γ, the capital letter gamma from the Greek alphabet) is one commonly used extension of the factorial function to complex numbers. The gamma function is defined for all complex numbers except the non-positive integers. For every positive integer n, Derived by Daniel Bernoulli, for complex numbers with a positive real part, the gamma function is defined via a convergent improper integral: The gamma function then is defined as the analytic continuation of this integral function to a meromorphic function that is holomorphic in the whole complex plane except zero and the negative integers, where the function has simple poles.
Chiral anomalyIn theoretical physics, a chiral anomaly is the anomalous nonconservation of a chiral current. In everyday terms, it is equivalent to a sealed box that contained equal numbers of left and right-handed bolts, but when opened was found to have more left than right, or vice versa. Such events are expected to be prohibited according to classical conservation laws, but it is known there must be ways they can be broken, because we have evidence of charge–parity non-conservation ("CP violation").
Track gaugeIn rail transport, track gauge (in American English, alternatively track gage) is the distance between the two rails of a railway track. All vehicles on a rail network must have wheelsets that are compatible with the track gauge. Since many different track gauges exist worldwide, gauge differences often present a barrier to wider operation on railway networks. The term derives from the metal bar, or gauge, that is used to ensure the distance between the rails is correct.
Shona languageShona (ˈʃoʊnə; chiShona) is a Bantu language of the Shona people of Zimbabwe. The term is variously used to collectively describe all the Central Shonic varieties (comprising Zezuru, Manyika, Korekore and Karanga) or specifically Standard Shona, a variety codified in the mid-20th century. Using the broader term, the language is spoken by over 14,000,000 people. The larger group of historically related languages—called Shona or Shonic languages by linguists—also includes Ndau (Eastern Shona) and Kalanga (Western Shona).
Distance-hereditary graphIn graph theory, a branch of discrete mathematics, a distance-hereditary graph (also called a completely separable graph) is a graph in which the distances in any connected induced subgraph are the same as they are in the original graph. Thus, any induced subgraph inherits the distances of the larger graph. Distance-hereditary graphs were named and first studied by , although an equivalent class of graphs was already shown to be perfect in 1970 by Olaru and Sachs.
Induced pathIn the mathematical area of graph theory, an induced path in an undirected graph G is a path that is an induced subgraph of G. That is, it is a sequence of vertices in G such that each two adjacent vertices in the sequence are connected by an edge in G, and each two nonadjacent vertices in the sequence are not connected by any edge in G. An induced path is sometimes called a snake, and the problem of finding long induced paths in hypercube graphs is known as the snake-in-the-box problem.
