Sentence examples for functions that are continuous from inspiring English sources

In the following, the computations will be made in the space X = ( C ♯ ( [ 0, T ] × [ 0, 2 π ] ), ∥ ⋅ ∥ ∞ ), where C ♯ stands for the functions that are continuous in time and continuous and periodic in phase.

Since harmonic functions that are continuous to the boundary satisfy the maximum principle [17], we obtain the uniqueness by the standard argument for linear differential equations satisfying the maximum principle.

We compute the Bass stable rank of the algebra A(K sym of real-symmetric functions that are continuous on symmetric compact planar sets K and holomorphic in the interior K∘ of K.

For convenience, we give some notation, BC denotes the set of (mathbb{R}^{n} -valued functions that is continuous and bounded on ((-infty,s_{0}]_{Pi_{varepsilon}}, s_{0}inPi_{varepsilon}); for each (phiin BC) we define (Vert phi Vert _{varepsilon}=sup_{sin(-infty,s_{0}]_{Pi _{varepsilon}}} vert phi(s)vert ).

In 1872, German mathematician Karl Weierstrass devised a function, that is continuous everywhere but differentiable nowhere.

An Orlicz function M is a function that is continuous, nondecreasing, and convex with (M 0) = 0), (M x)>0) for (x>0) and (M x) longrightarrowinfty) as (x longrightarrowinfty).

Csiszár introduced the concept of -divergence for a convex function, that is continuous at 0 as follows (cf. [8], see also [9]).

Weierstrass's 1872 paper, describing a real-valued function that is continuous everywhere but differentiable nowhere,[4] was well known and provided an example of an ungraphable functions that places limits on intuition.

Let (x t)) be an (mathbb{R}^{n} -valued function that is continuous and bounded on (mathbb{R}^{n} -valued function (thatathbb{T}cap(cupmathbb{T}^{Pis{varepsilon}})), (x_{t}(s)=x(t+s)) for (-sinPi_{varepsilon}).

However, in 1872 Weierstrass found the first example of a function that is continuous everywhere but differentiable nowhere.

According to this model, digestion has a smoothing effect by translating the discontinuous feeding process into an input function that is continuous over time.