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

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

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...

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

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...

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

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...

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...

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

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...

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

"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...

requirements Hilbert envisioned is unclear: there is no generally accepted definition of exactly what is meant by a finitistic proof, and Hilbert himself never...

integral involving the Riemann zeta function Hilbert–Pólya conjecture: the nontrivial zeros of the Riemann zeta function correspond to eigenvalues of a self-adjoint...

finite-dimensional Hilbert spaces to calculate or approximate the answers to mathematical questions involving continuous functions. A major motivation...

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...

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

\|)} 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...

real-valued random variable. The general form of its probability density function is f ( x ) = 1 2 π σ 2 e − ( x − μ ) 2 2 σ 2 . {\displaystyle f(x)={\frac...

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

one-parameter automorphisms of the algebra of all bounded operators on the Hilbert space of observables (which are self-adjoint operators). These dynamics...

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

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

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

Chow (algebraic geometry) Roger Godement, Sommes continues d'espaces de Hilbert, I (functional analysis, direct integrals) Charles Pisot, Démonstration...

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

image of the other. Euclid's terminology continued in the work of David Hilbert in his Grundlagen der Geometrie, who further refined Euclid's ideas by...

theory, orthonormal bases for a Hilbert space represent measurements that can be performed upon a system having that Hilbert space. Each vector in a basis...