Examples of using Continuous function in English and their translations into Danish
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Colloquial
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Official
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Medicine
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Financial
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Ecclesiastic
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Official/political
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Computer
Where G(x, y)is a continuous function.
Affect the continuous functioning of the financial undertaking, or.
Rd control circuit with continuous function.
Affect the continuous functioning of the credit institution, or.
In the following year Netto showed that such a mapping cannot be a continuous function.
To do this, start with a continuous function f discretized as shown in the figure.
Around this time he discovered conditions under which a function is a limit of a sequence of continuous functions.
Du Bois-Reymond published an example of a continuous function which is nowhere differentiable in 1875.
It constructs, with prescribed degree of exactness,a polynomial of the best Chebyshev approximation for a given continuous function.
Theorem 3: Let F(x, y, u, v) and G(x, y, u, v)be continuous function with continuous partial derivatives.
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He proved strong results on continuous functions containing Sierpinski 's curve and wrote several papers on functional spaces.
A similar algorithm was later developed which allowed rational approximation of continuous functions defined on an interval.
For example, let a continuous function f(x) be represented by means of a polynomial of degree n, and let Pn(x) be such a polynomial.
In 1873 du Bois-Reymond was the first person to give an example of a continuous function whose Fourier series diverges at a point.
Every continuous function that transforms a compact linear set into a plane set with interior points takes the same value in at least three points.
Under her supervision Arins wrote a thesis on partially continuous functions on products of topological spaces which he defended in 1954.
The lectures gave an excellent introduction to a central problem of algebraic topology and its applications,namely the problem of extending continuous functions.
Theorem 1: Let F(x, y, z)be a continuous function with continuous partial derivatives defined on an open set S containing the point P=x0,y0,z0.
He is remembered particularly for'Urysohn's lemma' which proves the existence of a certain continuous function taking values 0 and 1 on particular closed subsets.
Gauss had shown that if a continuous function f on Rn has at each point x a value equal to its mean value on every sphere of centre x, then f is harmonic.
Up to the end of the 19th century,mathematical analysis was limited to continuous functions, based largely on the Riemann method of integration.
Some of his early work is described in or:In 1897 he published a deep investigation into the subject of uniform convergence of sequences of real continuous functions.
His doctoral thesis Trigonometric interpolation of absolutely continuous functions was an extended form of the work which he had submitted for his Master's degree.
One particularly important result proved by Stone during this period was a substantial generalisation of Weierstrass 's theorem on uniform approximation of continuous functions by polynomials.
Osgood's main work was on the convergence of sequences of continuous functions, solutions of differential equations, the calculus of variations and space filling curves.
Given a continuous function f on R 2 a new function F(x) can be defined where F(x) is the maximum, relative to the radius, of the averages of the values of f on circles centred at x.
This example contradicted most mathematicians' intuition,for it was generally believed that a continuous function was differentiable everywhere except in special points.
They independently proved that:… every continuous function that transforms a compact linear set into a plane set with interior points takes the same value in at least three points.
It begins with the implicit use of the theorem in various proofs of the theorem stating that a continuous function on a closed, bounded interval is uniformly continuous. .