For other statistics and other populations the formulas are more complicated, and often they don't exist in bootstrap methods, or asymptotic distribution theory.
12.
Also, on the base of his approximation theory results, Arakelian has disproved an old conjecture of Rolf Nevanlinna from the value distribution theory.
13.
His main approaches revolved around the labor theory of value, an analysis of capital and distribution theory ( based on a concept of marginal productivity ).
14.
For those who subscribe to the geographical-distribution theory, it's notable that the prize has never gone to a writer from the world's most populous country _ China.
15.
As a mathematical tool, Colombeau algebras can be said to combine a treatment of singularities, differentiation and nonlinear operations in one framework, lifting the limitations of distribution theory.
16.
Though this is a full formal solution of this possibility, it requires infinitely many derivatives of Dirac delta functions, far beyond the reach of any ordinary tempered distribution theory.
17.
This condition is set up so as to be self-dual under Fourier transform, so that the corresponding distribution theory of " tempered distributions " will have the same good property.
18.
The classical definition of a locally integrable function involves only distribution theory on Euclidean spaces, all the definitions in this and the following sections deal explicitly only with this important case.
19.
Mollifiers are an important special case of bump functions as they can be used in distribution theory to create sequences of smooth functions approximating nonsmooth ( generalized ) functions, via convolution.
20.
A rigorous mathematical approach to renormalization theory is the so-called causal perturbation theory, where ultraviolet divergences are avoided from the start in calculations by performing well-defined mathematical operations only within the framework of distribution theory.
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