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Finally, the adjective strong or the adverb strongly may be added to a mathematical notion to indicate a related stronger notion; for example, a strong antichain is an antichain satisfying certain additional conditions, and likewise a strongly regular graph is a regular graph meeting stronger conditions. When used in this way, the stronger ...
To describe Y in geometric terms: a curve C in X maps to a point in Y if and only if L has degree zero on C. As a result, there is a one-to-one correspondence between the contractions of X and some of the faces of the nef cone of X. [15] (This correspondence can also be formulated dually, in terms of faces of the cone of curves.)
Inflection of the Scottish Gaelic lexeme for 'dog', which is cù for singular, chù for dual with the number dà ('two'), and coin for plural. In linguistic morphology, inflection (less commonly, inflexion) is a process of word formation [1] in which a word is modified to express different grammatical categories such as tense, case, voice, aspect, person, number, gender, mood, animacy, and ...
Common geometric terms of location are: Radial (solid and colored lines) and circumferential roads (dashed and gray lines) in Metro Manila's road network. Axial – along the center of a round body, or the axis of rotation of a body; Radial – along a direction pointing along a radius from the center of an object, or perpendicular to a curved ...
The reason the definition of closed subschemes relies on such a construction is that, unlike open subsets, a closed subset of a scheme does not have a unique structure as a subscheme. Cohen–Macaulay A scheme is called Cohen-Macaulay if all local rings are Cohen-Macaulay.
Some other normalization conditions must be imposed, usually depending on the type of geometry under consideration. In Riemannian geometry, the Levi-Civita connection requires compatibility of the Christoffel symbols with the metric (as well as a certain symmetry condition). With these normalizations, the connection is uniquely defined.
Compatibility conditions are mathematical conditions that determine whether a particular deformation will leave a body in a compatible state. [ 2 ] In the context of infinitesimal strain theory , these conditions are equivalent to stating that the displacements in a body can be obtained by integrating the strains .
This is a glossary of properties and concepts in symplectic geometry in mathematics. The terms listed here cover the occurrences of symplectic geometry both in topology as well as in algebraic geometry (over the complex numbers for definiteness). The glossary also includes notions from Hamiltonian geometry, Poisson geometry and geometric ...