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 Under u&.v  mv mv mv

 The verb u &.v is equivalent to the composition u & v except that the verb obverse to v is applied to the result for each cell. That is (subject to the monadic rank of v),     u&.v y ↔ vi u v y   x u&.v y ↔ vi (v x) u (v y) where vi is the obverse of v . The obverse is normally the inverse, as discussed more fully under the power conjunction ^: .

```   3 +&.^. 4                   Inverse of natural log is the exponential
12

(^.^:_1) (^.3)+(^.4)
12

(<b), <|. b=: 1 2 3 ; 2 3 5 7 ; 'abcde'
+---------------------+---------------------+
|+-----+-------+-----+|+-----+-------+-----+|
||1 2 3|2 3 5 7|abcde|||abcde|2 3 5 7|1 2 3||
|+-----+-------+-----+|+-----+-------+-----+|
+---------------------+---------------------+

(<|. &. > b),(<|. each b)   Reversal under open
+---------------------+---------------------+
|+-----+-------+-----+|+-----+-------+-----+|
||3 2 1|7 5 3 2|edcba|||3 2 1|7 5 3 2|edcba||
|+-----+-------+-----+|+-----+-------+-----+|
+---------------------+---------------------+
```
In mathematics, certain cases of under are called dual or, dual with respect to:
```   f=: +. &. -.                Dual with respect to boolean negation
f/~ d=: 0 1
0 0
0 1

D=: &. -.                   The adverb dual with respect to negation
(+.D/~d);(*./~d);(=D/~d);(~:/~d)
+---+---+---+---+
|0 0|0 0|0 1|0 1|
|0 1|0 1|1 0|1 0|
+---+---+---+---+

DWL=: &.^.                  Dual with respect to natural logarithm
DAN=: &. -                  Dual with respect to arithmetic negation
(3 + DWL 4),(3*4),(3 <. DAN 4) , (3 >. 4)
12 12 4 4
```

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