Chemical kineticsChemical kinetics, also known as reaction kinetics, is the branch of physical chemistry that is concerned with understanding the rates of chemical reactions. It is different from chemical thermodynamics, which deals with the direction in which a reaction occurs but in itself tells nothing about its rate. Chemical kinetics includes investigations of how experimental conditions influence the speed of a chemical reaction and yield information about the reaction's mechanism and transition states, as well as the construction of mathematical models that also can describe the characteristics of a chemical reaction.
Essential singularityIn complex analysis, an essential singularity of a function is a "severe" singularity near which the function exhibits odd behavior. The category essential singularity is a "left-over" or default group of isolated singularities that are especially unmanageable: by definition they fit into neither of the other two categories of singularity that may be dealt with in some manner – removable singularities and poles. In practice some include non-isolated singularities too; those do not have a residue.
Removable singularityIn complex analysis, a removable singularity of a holomorphic function is a point at which the function is undefined, but it is possible to redefine the function at that point in such a way that the resulting function is regular in a neighbourhood of that point. For instance, the (unnormalized) sinc function, as defined by has a singularity at z = 0. This singularity can be removed by defining which is the limit of sinc as z tends to 0. The resulting function is holomorphic.
Tagged unionIn computer science, a tagged union, also called a variant, variant record, choice type, discriminated union, disjoint union, sum type or coproduct, is a data structure used to hold a value that could take on several different, but fixed, types. Only one of the types can be in use at any one time, and a tag field explicitly indicates which one is in use. It can be thought of as a type that has several "cases", each of which should be handled correctly when that type is manipulated.
ResultantIn mathematics, the resultant of two polynomials is a polynomial expression of their coefficients that is equal to zero if and only if the polynomials have a common root (possibly in a field extension), or, equivalently, a common factor (over their field of coefficients). In some older texts, the resultant is also called the eliminant. The resultant is widely used in number theory, either directly or through the discriminant, which is essentially the resultant of a polynomial and its derivative.
Cusp (singularity)In mathematics, a cusp, sometimes called spinode in old texts, is a point on a curve where a moving point must reverse direction. A typical example is given in the figure. A cusp is thus a type of singular point of a curve. For a plane curve defined by an analytic, parametric equation a cusp is a point where both derivatives of f and g are zero, and the directional derivative, in the direction of the tangent, changes sign (the direction of the tangent is the direction of the slope ).
Ring singularityA ring singularity or ringularity is the gravitational singularity of a rotating black hole, or a Kerr black hole, that is shaped like a ring. When a spherical non-rotating body of a critical radius collapses under its own gravitation under general relativity, theory suggests it will collapse to a 0-dimensional single point. This is not the case with a rotating black hole (a Kerr black hole). With a fluid rotating body, its distribution of mass is not spherical (it shows an equatorial bulge), and it has angular momentum.
Bézout's theoremBézout's theorem is a statement in algebraic geometry concerning the number of common zeros of n polynomials in n indeterminates. In its original form the theorem states that in general the number of common zeros equals the product of the degrees of the polynomials. It is named after Étienne Bézout. In some elementary texts, Bézout's theorem refers only to the case of two variables, and asserts that, if two plane algebraic curves of degrees and have no component in common, they have intersection points, counted with their multiplicity, and including points at infinity and points with complex coordinates.
Elimination theoryIn commutative algebra and algebraic geometry, elimination theory is the classical name for algorithmic approaches to eliminating some variables between polynomials of several variables, in order to solve systems of polynomial equations. Classical elimination theory culminated with the work of Francis Macaulay on multivariate resultants, as described in the chapter on Elimination theory in the first editions (1930) of Bartel van der Waerden's Moderne Algebra.
Birational geometryIn mathematics, birational geometry is a field of algebraic geometry in which the goal is to determine when two algebraic varieties are isomorphic outside lower-dimensional subsets. This amounts to studying mappings that are given by rational functions rather than polynomials; the map may fail to be defined where the rational functions have poles. A rational map from one variety (understood to be irreducible) to another variety , written as a dashed arrow X Y, is defined as a morphism from a nonempty open subset to .
