In commutative algebra the Hilbert–Samuel function, named after David Hilbert and Pierre Samuel, of a nonzero finitely generated module M {\displaystyle...

Hilbert number Hilbert plane Hilbert polynomial Hilbert series Hilbert ring Hilbert–Samuel function Hilbert projection theorem Hilbert R-tree Hilbert...

to d. A key ingredient in the strong resolution is the use of the Hilbert–Samuel function of the local rings of the points in the variety. This is one of...

x^{7}+ax^{3}+bx^{2}+cx+1=0} . Regarding this equation, Hilbert asked whether its solution, x, considered as a function of the three variables a, b and c, can be expressed...

In commutative algebra, the Hilbert function, the Hilbert polynomial, and the Hilbert series of a graded commutative algebra finitely generated over a...

a Hilbert system, sometimes called Hilbert calculus, Hilbert-style system, Hilbert-style proof system, Hilbert-style deductive system or Hilbert–Ackermann...

Pierre Samuel (12 September 1921 – 23 August 2009) was a French mathematician, known for his work in commutative algebra and its applications to algebraic...

The Hilbert spectrum (sometimes referred to as the Hilbert amplitude spectrum), named after David Hilbert, is a statistical tool that can help in distinguishing...

{p}}_{1})} . (This essentially follows from the Artin–Rees lemma; see Hilbert–Samuel function for the statement and the proof.) In R / p 1 {\displaystyle R/{\mathfrak...

observables, which are self-adjoint operators acting on the Hilbert space. A wave function can be an eigenvector of an observable, in which case it is...

changing its form, the wave function keep moving from one Hilbert space to another Hilbert space. Since the wave function contains all the relevant information...

In mathematics, Hilbert's Nullstellensatz (German for "theorem of zeros", or more literally, "zero-locus-theorem") is a theorem that establishes a fundamental...

"Fréchet space". Banach spaces originally grew out of the study of function spaces by Hilbert, Fréchet, and Riesz earlier in the century. Banach spaces play...

morphism Semistable elliptic curve Grothendieck's relative point of view Hilbert scheme Grothendieck topology Topos Derived category Descent (category theory)...

{I}}).} Dimension theory (algebra) j-multiplicity Hilbert–Samuel multiplicity Hilbert–Kunz function Normally flat ring Vasconcelos, Wolmer (2006-03-30)...

processes. These can be viewed as elements of some infinite-dimensional Hilbert space H, and thus are the analogues of multivariate normal vectors for...

kernel Hilbert space with positive definite kernel R {\displaystyle R} . Driscoll's zero-one law is a result characterizing the sample functions generated...

kernel Hilbert space via the kernel embedding of distributions. This framework may be viewed as a generalization of the characteristic function under specific...

define the slope of the subscheme Z {\displaystyle Z} , consider the Hilbert-Samuel polynomial of the subscheme Z {\displaystyle Z} , χ ( L r ⊗ I Z x r...

polynomials that are zero on an affine algebraic set (this is a consequence of Hilbert's Nullstellensatz). If A is a square matrix, then the product of A with...

At the International Congress of Mathematicians in Paris in 1900, David Hilbert presented a list of mathematical problems, where his sixth problem asked...

H. (1989). "5 Dimension theory §S3 Graded rings, the Hilbert function and the Samuel function". Commutative Ring Theory. Cambridge Studies in Advanced...

Kernels and Screw Functions". p. 2. arXiv:1302.4343 [math.FA]. Alpay, Daniel; Levanony, David (2008). "On the Reproducing Kernel Hilbert Spaces Associated...

results of Julia Robinson) Matiyasevich's theorem, which implies that Hilbert's tenth problem has no effective solution; this problem asked whether there...

and | y ⟩ {\displaystyle |y\rangle } range over the basis vectors of the Hilbert space describing a one-particle system, then the tensor product produces...

rings spanned the 1870s to the 1920s, with key contributions by Dedekind, Hilbert, Fraenkel, and Noether. Rings were first formalized as a generalization...

\|)} is, what is the maximal dimension k {\displaystyle k} such that the Hilbert space ℓ 2 k {\displaystyle \ell _{2}^{k}} can be linearly embedded into...

}} . Hardy–Littlewood zeta function conjectures Hilbert–Pólya conjecture: the nontrivial zeros of the Riemann zeta function correspond to eigenvalues of...

and so on. The dimension of the Hilbert space may be infinite, as it is for the space of square-integrable functions on a line, which is used to define...

transform functions, used in mathematics and computer science. Curry was born on (1900-09-12)September 12, 1900 in Millis, Massachusetts, to Samuel Silas...