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Qué (quién) es lower semicontinuous decomposition - definición

PROPERTY OF FUNCTIONS WEAKER THAN CONTINUITY

Semicontinuous; Semicontinuity; Semi-continuous; Lower semi-continuous; Upper semi-continuous; Lower semicontinuous; Upper semicontinuous; Semi-continuous function; Semi-continuous mapping; Semicontinuous function; Upper-semicontinuous; Upper semicontinuity; Lower semicontinuity; Upper semi-continuity; Lower semi-continuity

$A lower semicontinuous function that is not upper semicontinuous. The solid blue dot indicates <math>f\left(x_0\right).</math>$
$An upper semicontinuous function that is not lower semicontinuous. The solid blue dot indicates <math>f\left(x_0\right).</math>$

Lossless join decomposition

DECOMPOSITION OF A DATABASE RELATION SUCH THAT A NATURAL JOIN OF THE RESULTING RELATIONS YIELDS BACK THE ORIGINAL RELATION

Lossless-join decomposition; Lossless-Join Decomposition

In database design, a lossless join decomposition is a decomposition of a relation R into relations R_1, R_2 such that a natural join of the two smaller relations yields back the original relation. This is central in removing redundancy safely from databases while preserving the original data.

https://en.wikipedia.org/wiki/Lossless_join_decomposition

Semi-continuity

In mathematical analysis, semicontinuity (or semi-continuity) is a property of extended real-valued functions that is weaker than continuity. An extended real-valued function f is upper (respectively, lower) semicontinuous at a point x_0 if, roughly speaking, the function values for arguments near x_0 are not much higher (respectively, lower) than f\left(x_0\right).

https://en.wikipedia.org/wiki/Semi-continuity

Chemical decomposition

BREAKDOWN OF A SINGLE ENTITY (NORMAL MOLECULE, REACTION INTERMEDIATE, ETC.) INTO TWO OR MORE FRAGMENTS; OPPOSITE OR REVERSE PROCESS OF A SYNTHESIS REACTION

Decomposition reaction; Decompose (chemistry); Chemical degradation; Chemical breakdown; Decomposition product; Decomposition (chemistry)

Chemical decomposition, or chemical breakdown, is the process or effect of simplifying a single chemical entity (normal molecule, reaction intermediate, etc.) into two or more fragments.

https://en.wikipedia.org/wiki/Chemical_decomposition

Wikipedia

Semi-continuity

In mathematical analysis, semicontinuity (or semi-continuity) is a property of extended real-valued functions that is weaker than continuity. An extended real-valued function $f$ is upper (respectively, lower) semicontinuous at a point $x_{0}$ if, roughly speaking, the function values for arguments near $x_{0}$ are not much higher (respectively, lower) than $f\left(x_{0}\right).$

A function is continuous if and only if it is both upper and lower semicontinuous. If we take a continuous function and increase its value at a certain point $x_{0}$ to $f\left(x_{0}\right)+c$ for some $c>0$ , then the result is upper semicontinuous; if we decrease its value to $f\left(x_{0}\right)-c$ then the result is lower semicontinuous.

The notion of upper and lower semicontinuous function was first introduced and studied by René Baire in his thesis in 1899.

https://en.wikipedia.org/wiki/Semi-continuity