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In mathematics, an expansion of a product of sums expresses it as a sum of products by using the fact that multiplication distributes over addition. Expansion of a polynomial expression can be obtained by repeatedly replacing subexpressions that multiply two other subexpressions, at least one of which is an addition, by the equivalent sum of products, continuing until the expression becomes a ...
This inline template is placed after any acronym, abbreviation or initialism that needs to be expanded. Template parameters [Edit template data] This template prefers inline formatting of parameters. Parameter Description Type Status Tag and hover text type 1 Change text. in = initialism | ab = abbreviation | (null or invalid value) = acronym Auto value String optional Month and year date The ...
A Laurent series is a generalization of the Taylor series, allowing terms with negative exponents; it takes the form = and converges in an annulus. [6] In particular, a Laurent series can be used to examine the behavior of a complex function near a singularity by considering the series expansion on an annulus centered at the singularity.
Heinz Hunsdiecker described the synthesis of 2,5-undecanedione from 5-methylfurfural in 1942. 5-Methylfurfural 1 is first reacted with methyl propyl ketone 2 in an aldol condensation reaction to form an α,β-unsaturated carbonyl compound 3. The double bond of the side chain condensation product is reduced with sodium amalgam.
A stericated 5-simplex can be constructed by an expansion operation applied to the regular 5-simplex, and thus is also sometimes called an expanded 5-simplex.It has 30 vertices, 120 edges, 210 faces (120 triangles and 90 squares), 180 cells (60 tetrahedra and 120 triangular prisms) and 62 4-faces (12 5-cells, 30 tetrahedral prisms and 20 3-3 duoprisms).
Print/export Download as PDF; Printable version; In other projects Wikidata item; Appearance. move to sidebar hide. 2/5 or 2 ⁄ 5 may refer to: February 5 ...
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The open sets of X ∪ P are of the form Q, where Q is a subset of P, or A ∪ P, where A is an open set of X. Note that P is open in X ∪ P and X is closed in X ∪ P . If Y is a topological space and R is a subset of Y , one might ask whether the closed extension topology of Y – R plus R is the same as the original topology of Y , and the ...
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