Sentences with FUNCTIONALS
Check out our example sentences below to help you understand the context.Sentences
1
"In mathematics, functionals are used to map functions to real numbers."
2
"Optimization problems often involve functionals."
3
"Variational calculus relies heavily on functionals."
4
"The study of functionals is an important area of research in mathematics."
5
"Linear functionals are linear maps from a vector space to its scalar field."
6
"Continuous functionals are continuous linear maps between topological vector spaces."
7
"In physics, functionals are used to model physical systems."
8
"Euler-Lagrange equations are used to find critical points of functionals."
9
"Dirichlet functionals are used in the study of partial differential equations."
10
"Variational functionals are employed in the calculus of variations."
11
"Some functionals are convex, while others are not."
12
"Evaluating functionals requires applying them to specific functions."
13
"Hilbert spaces provide a natural framework for studying functionals."
14
"The dual space of a function space consists of all functionals on that space."
15
"The Riesz representation theorem establishes a correspondence between functionals and elements of a Hilbert space."
1
"The set of all bounded linear functionals on a normed vector space is a Banach space."
2
"In quantum mechanics, functionals are used to represent observables."
3
"In optimization, functionals are used to define the objective function."
4
"The Euler-Lagrange equation is used to find critical points of functionals."
5
"The space of functionals can have a topology induced by various convergence criteria."
6
"Variational problems can be formulated as optimization problems over functionals."
7
"In physics, functionals are used to describe variational principles."
