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This page will attempt to list examples in mathematics. To qualify for inclusion, an article should be about a mathematical object with a fair amount of concreteness. Usually a definition of an abstract concept, a theorem, or a proof would not be an "example" as the term should be understood here (an elegant proof of an isolated but particularly striking fact, as opposed to a proof of a ...
No matter what dual topology is placed on ′ (), [note 13] a sequence of distributions converges in this topology if and only if it converges pointwise (although this need not be true of a net). No matter which topology is chosen, D ′ ( U ) {\displaystyle {\mathcal {D}}^{\prime }(U)} will be a non- metrizable , locally convex topological ...
A material property is an intensive property of a material, i.e., a physical property or chemical property that does not depend on the amount of the material. These quantitative properties may be used as a metric by which the benefits of one material versus another can be compared, thereby aiding in materials selection.
Rigor is a cornerstone quality of mathematics, and can play an important role in preventing mathematics from degenerating into fallacies. well-behaved An object is well-behaved (in contrast with being Pathological ) if it satisfies certain prevailing regularity properties, or if it conforms to mathematical intuition (even though intuition can ...
Any irreducible tempered representation is a basic representation, and conversely any basic representation is the sum of a finite number of irreducible tempered representations. More precisely, it is a direct sum of 2 r irreducible tempered representations indexed by the characters of an elementary abelian group R of order 2 r (called the R ...
These identities also hold much more broadly in the sense of tempered distributions if one of f or g is a rapidly decreasing tempered distribution, a compactly supported tempered distribution or a Schwartz function and the other is a tempered distribution. On the other hand, two positive integrable and infinitely differentiable functions may ...
The beauty of mathematics is experienced when the physical reality of objects are represented by mathematical models. Group theory, developed in the early 1800s for the sole purpose of solving polynomial equations, became a fruitful way of categorizing elementary particles—the building blocks of matter.
In meantone temperament, this effect is even more pronounced (the fifth over the break in the circle is known as the Wolf interval, as its intense beating was likened to a "howling"). 53 equal temperament provides an extension of Pythagorean tuning, and 31 equal temperament is used nowadays to extend quarter-comma meantone.