Faltung

Faltung, /. folding, plaiting, plication, wrin kling. 

Die weitere dreidimensionale Faltung von einzelnen Molcktilab-schnitten mit jeweils individueller Sekundarstruktur nennt man Ter-tiarstruktur. Diese schliefit bei Proteinen auch die Konformation der Seitenketten ein. 

A convolution is an integral that expresses the amount of overlap of one function g as it is shifted over another function /. It therefore blends one function with another. The convolution is sometimes also known by its German name, Faltung (folding). Abstractly, a convolution is defined as a product of functions / and g that are objects in the algebra of Schwartz functions in M". Convolution of two functions f(z) and g z) over a finite range [0, f] is given by... 

Abb. 15. Sekundarkeim. a) bei herausragenden. Kettenenden, b) bei Faltung der Ketten [nach Lauritzen... 

Convolution Theorem. The convolution (German Faltung, i.e. folding) of a function/(x) times a function with a different origin g(x) is the very useful... 

Convolution — The convolution (or faltung) of two functions, /(f) and g(t), of time is the mathematical operation f] f(t)g(t - r)dr or equivalently /0 f(f - r)g(r) dr. Sometimes a lower limit other than zero, such as -oo, is appropriate. When functions are folded together in this way they are said to have been convolved (not convoluted ), and the symbol /(f) g( t) may be used to indicate this. 

In contrast to the Fourier transformation, convolution effects a transformation of the function only, and not of the variable and the function together. Convolution denotes a folding operation (Faltung) of two signals ki(t) and jc(t) ... 

There is a useful theorem for the Fourier transform of a product of two functions, called the convolution theorem or the Faltung theorem iFaltung is German for folding ). The convolution of two functions fix) and g(x) is defined as the integral... 

An integral of the type figuring in Eq. (9.78) is called faltung or convolution integral. Its treatment using Laplace transforms facilitates the extension of Eq. (9.79) to the general case of N components. For this purpose... 

Problem 1.2.2 Show that in the non-aging case, operator multiplication as defined by (1.2.10) is commutative. In fact, this is probably perceived more easily by using the alternative form, akin to matrix multiplication, derived from (1.2.32). The easiest way to show it is to take into account a result of Sect. 1.5, namely that in the frequency representation, operator multiplication becomes simple multiplication, by virtue of the Faltung theorem (Sect. A3.1). 

We seek here to generalize the observation contained in (1.5.1) to the three-dimensional context. Consider (1.8.9- 11). On taking Fourier transforms (FTs), these become, with the aid of the Faltung theorem [(A3.1.14- 17)] ... 

The Faltung or Convolution Theorem is a result of central importance for the Theory of Linear Viscoelasticity. It states that if... 

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