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I have a model as follows:
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Disclaimer

All serial numbers are tested by our staff, but we can not guaranty the validity in all cases.Q:

Arrange array items by first letter of each array item

I have an array in php, and I want to sort it like this:
a -> A
b -> B
c -> C
d -> D
e -> E
f -> F

etc.
How can I do that? Is there a built-in function?

A:

array_map :
array_map ( callback $callback, array $array [, array $map_override = [] ] )

This is exactly what you need.

A:

You can use array_map:
$arr = array_map(function($i){
return strtoupper($i);
}, $inputArray);

Q:

Applying the Möbius transformation $\frac{(az+b)+(\bar{b}z+\bar{a})}{1-z\bar{a}}$ to a complex function $f(z)$ such that $f(z)$ is analytic over the whole complex plane.

Let $f(z)$ be an entire complex function. Let $M(z)=\dfrac{(az+b)+(\bar{b}z+\bar{a})}{1-z\bar{a}}$ be a Möbius transformation with $a,b\in \mathbb{C}$ not both zero and $\bar{a}$ not equal to $0$. Prove that $f(z)$ can be modified to an analytic function.
My attempt
$M(z)$ is a Möbius transformation with $\bar{a}$ not equal to $0$ if and only if
\begin{align}
\frac{(az+b)+(\bar{b}z+\bar{a})}{1-z\bar{a}}&=\frac{(a-z)(z+b)+(b-z)(\bar{z}+\bar{a})}{1-(z+b)\bar{z}}
\end{align}
Let $g(z)=\dfrac{(a-z)(z+b)+(b-z)(\