Search results

In [[algebraic geometry]], a '''universal homeomorphism''' is a [[morphism of schemes]] <math>f: X ...l homeomorphism if and only if it is [[integral element#Integral morphisms|integral]], [[radicial morphism|radicial]] and surjective.<ref>EGA IV₄, 1 ...

...[[nilradical of a ring|nilradical]]) is an [[integral domain]], and the [[integral closure]] ''B'' of ''A''_red is also a local ring.{{fact|date=Aug ...and geometrically unibranch points are used in some theorems in algebraic geometry. For example, there is the following result: ...

*[[Victor Guillemin]] and [[Shlomo Sternberg]], ''Some problems in integral geometry and some related problems in microlocal analysis'', [[American Journal of M *[[Fourier integral operator]] ...

{{Short description|Integral transform type in mathematics}} ...s the [[spherical mean]] operator to [[homogeneous space]]s. Instead of [[integral|integrating]] over [[sphere]]s, one integrates over generalized spheres: fo ...

In [[differential geometry]], the '''tangent indicatrix''' of a closed [[space curve]] is a [[curve]] The [[total curvature]] of <math>\gamma</math> (the integral of curvature with respect to arc length along the curve) is equal to the [[ ...

{{Short description|Class of integral and differential operator}} ...d of [[harmonic analysis]], an '''oscillatory integral operator''' is an [[integral operator]] of the form ...

{{Short description|Integral transform}} ..., the X-ray transform of a function is defined by integrating over [[line (geometry)|line]]s rather than over [[hyperplane]]s as in the Radon transform. The X- ...

...the axis, a [[roulette curve]].<ref name="oprea">John Oprea, Differential Geometry and its Applications, MAA 2007. pp. 147–148</ref> ...the elliptic modulus and <math>E(u,k)</math> is the [[incomplete elliptic integral of the second kind]] and sn, cn and dn are [[Jacobi's elliptic functions]]. ...

...ied to find solutions to [[Plateau's problem]]. In 2001 the notion of an integral current was extended to arbitrary metric spaces by [[Luigi Ambrosio|Ambrosi ==Integral currents== ...

...{section link|Ideal sheaf|Algebraic geometry}}.<ref>Eisenbud-Harris, ''The geometry of schemes''. Springer-Verlag, 197, 2000</ref> ...math>\dim R[It, t^{-1}]=\dim R+1</math>.<ref name=":0">{{Cite book|title = Integral Closure of Ideals, Rings, and Modules|last = Swanson|first = Irena|author1- ...

{{about|an extension of the theory of the [[Lebesgue integral]] to [[manifold]]s|numerical method|geometric integrator}} ...]] to [[manifold]]s. Rather than functions or [[differential form]]s, the integral is defined over [[current (mathematics)|currents]] on a manifold. ...

...th>\overline{I}</math>, is the set of all elements ''r'' in ''R'' that are integral over ''I'': there exist <math>a_i \in I^i</math> such that ...follows that <math>\overline{I}</math> is an ideal of ''R'' (in fact, the integral closure of an ideal is always an ideal; see below.) ''I'' is said to be ''' ...

...The notion is important both in [[scheme theory]] and [[complex algebraic geometry]]. For the theory of reflexive sheaves, one works over an [[Integral domain|integral]] [[Noetherian scheme|noetherian]] [[Scheme (mathematics)|scheme]]. ...

...ed by |''F''|, is a [[topological space]] which as a set is the set of all integral substacks of ''F'' and which then is given a "[[Zariski topology]]": an ope {{algebraic-geometry-stub}} ...

...element of a compact [[Lie group]] acting in given setting in terms of the integral over the [[fixed point (mathematics)|fixed points]] of the element. If the [[Category:Differential geometry]] ...

{{short description|Relates the integral of Gaussian curvature of surfaces to the Euler characteristic}} ...ntegral of [[Gaussian curvature]] of a non-compact [[surface (differential geometry)|surface]] to the [[Euler characteristic]]. It is akin to the [[Gauss–Bonn ...

...language=en}}</ref> [[Half-space (geometry)|Half-space]]s and [[Half-line (geometry)|half-lines]] are sometimes described as semi-infinite regions. A semi-infinite [[integral]] is an [[improper integral]] over a semi-infinite interval. More generally, objects indexed or parame ...

...ions. [[Kernel function]]s can be useful in approximating and solving this integral equation. ...ry of the enclosure and its surface properties. Kernel function depends on geometry of the body. ...

...me the geometric fibers are integral schemes; Mumford's example shows the "integral" cannot be omitted.</ref> as a quotient ''Q'' (of the scheme ''Z'' parametr ...re, N. ''Construction of Hilbert and Quot schemes.'' Fundamental algebraic geometry: Grothendieck’s FGA explained, Mathematical Surveys and Monographs 123, Ame ...

{{Short description|Change of time of the value of an integral}} ...of a [[volume integral|volume]] or [[surface integral]] whose domain of [[integral|integration]], as well as the [[integrand]], are [[Function (mathematics)|f ...