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But the zero function is not a weak derivative of c, as can be seen by comparing against an appropriate test function . More theoretically, c does not have a weak derivative because its distributional derivative, namely the Cantor distribution, is a singular measure and therefore cannot be represented by a function.
Weak artificial intelligence (weak AI) is artificial intelligence that implements a limited part of the mind, or, as Artificial Narrow Intelligence, [1] [2] [3] is focused on one narrow task. Weak AI is contrasted with strong AI , which can be interpreted in various ways:
The weak interaction has a very short effective range (around 10 −17 to 10 −16 m (0.01 to 0.1 fm)). [b] [14] [13] At distances around 10 −18 meters (0.001 fm), the weak interaction has an intensity of a similar magnitude to the electromagnetic force, but this starts to decrease exponentially with increasing distance.
In mathematics, a weak solution (also called a generalized solution) to an ordinary or partial differential equation is a function for which the derivatives may not all exist but which is nonetheless deemed to satisfy the equation in some precisely defined sense. There are many different definitions of weak solution, appropriate for different ...
Both the weak topology and the weak* topology are special cases of a more general construction for pairings, which we now describe.The benefit of this more general construction is that any definition or result proved for it applies to both the weak topology and the weak* topology, thereby making redundant the need for many definitions, theorem statements, and proofs.
The nm command identifies weak symbols in object files, libraries, and executables. On Linux a weak function symbol is marked with "W" if a weak default definition is available, and with "w" if it is not. Weakly defined variable symbols are marked with "V" and "v". On Solaris "nm" prints "WEAK" instead of "GLOB" for a weak symbol.
A weak base is a base that, upon dissolution in water, does not dissociate completely, so that the resulting aqueous solution contains only a small proportion of hydroxide ions and the concerned basic radical, and a large proportion of undissociated molecules of the base.
In mathematics, especially order theory, a weak ordering is a mathematical formalization of the intuitive notion of a ranking of a set, some of whose members may be tied with each other. Weak orders are a generalization of totally ordered sets (rankings without ties) and are in turn generalized by (strictly) partially ordered sets and preorders ...