Search results
Results From The WOW.Com Content Network
The function in example 1, a removable discontinuity. Consider the piecewise function = {< = >. The point = is a removable discontinuity.For this kind of discontinuity: The one-sided limit from the negative direction: = and the one-sided limit from the positive direction: + = + at both exist, are finite, and are equal to = = +.
6.1 Example 1. 6.2 Example 2. ... Similarly, the Chebyshev polynomials of the second kind ... At a discontinuity, the series will converge to the average of the right ...
The self-similar solution of the second kind also appears in different contexts such as in boundary-layer problems subjected to small perturbations, [8] as was identified by Keith Stewartson, [9] Paul A. Libby and Herbert Fox. [10] Moffatt eddies are also a self-similar solution of the second kind.
The following table gives an overview of Green's functions of frequently appearing differential operators, where = + +, = +, is the Heaviside step function, () is a Bessel function, () is a modified Bessel function of the first kind, and () is a modified Bessel function of the second kind. [2]
Let be a real-valued monotone function defined on an interval. Then the set of discontinuities of the first kind is at most countable.. One can prove [5] [3] that all points of discontinuity of a monotone real-valued function defined on an interval are jump discontinuities and hence, by our definition, of the first kind.
Again, f(z) = 1 is more than 1 ⁄ 2 away from f(y) = 0. Its restrictions to the set of rational numbers and to the set of irrational numbers are constants and therefore continuous. The Dirichlet function is an archetypal example of the Blumberg theorem .
Landau theory (also known as Ginzburg–Landau theory, despite the confusing name [1]) in physics is a theory that Lev Landau introduced in an attempt to formulate a general theory of continuous (i.e., second-order) phase transitions. [2]
and the problem is, given the continuous kernel function and the function , to find the function .. An important case of these types of equation is the case when the kernel is a function only of the difference of its arguments, namely (,) = (), and the limits of integration are ±∞, then the right hand side of the equation can be rewritten as a convolution of the functions and and therefore ...