## Finding lower and upper limits of a function of four variables

Is it possible to tell Mathematica to find the lower and upper limits of the following function

`````` fun(x1_, x2_, y1_, y2_) =
1/2 (2 x1 (1 - y1) + 2 x2 (1 - y2) + x1 x2 (-2 + y1 + y2));
``````

where $$0le x_1 le 1$$, $$0le x_2 le 1$$, $$0le y_1 le 1$$, and $$0le y_2 le 1$$.

## Add Ui Dynamic forms to Custom Variables module

I want to add UI dynamic rows for Custom Variables module.
https://devdocs.magento.com/guides/v2.4/ui_comp_guide/components/ui-dynamicrows.html

But it doesn’t have xml layouts.

Maybe someone could help me. How can I add dynamic rows for that module?

Example

## random variables – Does the entropy H(X+Y|Y) = H(X)?

Suppose I have random variables $$X, Y$$ that are independent and identically distributed. If we denote the entropy by $$H$$, then does the following equality hold?

$$H(X+Y|Y) = H(X)$$

My intuition says yes since the only randomness in $$X+Y$$ that remains when $$Y$$ is observed is $$X$$. However, I struggle to prove this formally.

## cv.complex variables – Sokhotski–Plemelj theorem (With Sqrt Term)

I am reading up on the Sokhotski-Plemelj theorem, and so far I’ve seen it being applied on equation with the general form (ref: http://scipp.ucsc.edu/~haber/ph214/Plemelj.pdf):

$$lim_{epsilonto0}frac{1}{x-x_0pm iepsilon} = Pfrac{1}{x-x_0} mp ipidelta(x-x_0)$$

Can the same theorem be applied to the following equation with an additional sqrt term?
$$lim_{epsilonto0}frac{1}{sqrt{x-x_0pm iepsilon}}$$

I can only think of bringing out the sqrt term and applying the formula to get the same result but with the additional sqrt term:

$$sqrt{lim_{epsilonto0}frac{1}{x-x_0pm iepsilon}} = sqrt{Pfrac{1}{x-x_0} mp ipidelta(x-x_0)}$$

Is there any way to simplify that? Or is there another way of applying the theorem? Thank you.

## android – ¿Cómo puedo programar notificaciones locales con Kotlin desde variables?

buenas tardes.
Feliz domingo a todos.

Me estoy iniciando en la programación de apps para Android con kotlin y me gustaría poder programar notificaciones locales pero en vez de usar un DatePickerDialog y TimePickerDialog quisiera programarlas desde dos variables en las que tengo guardadas la fecha y la hora, estas variables están en String.

Encontré este tutorial pero lo hacen desde los pickers para la fecha y el horario

Código: https://github.com/sriharsha1507/set_repetitive_exact_alarm

¿Conocen algún tutorial o material en el que expliquen como se pueden programar las notificaciones desde variables y no desde los pickers?

Ojalá puedan ayudarme.
Saludos

## postgresql – View Expansion and Removing “dead variables”

I have a large set of interwoven views in Postgres that sometimes are make inefficient use of other views.

For example,

``````CREATE VIEW C AS
SELECT A.a, B.b
FROM A
LEFT JOIN B on A.id = B.id
``````

Then,

``````SELECT C.a, COUNT(*)
FROM C
GROUP BY C.a
``````

It’s more complicated, but the idea is that the second query doesn’t make use of the JOIN from the VIEW. In the EXPLAIN, this is not optimized away by Postgres.

I’m looking for an automated way to “expand” the second query to something like,

``````SELECT C.a, COUNT(*)
FROM (
SELECT A.a, B.b
FROM A
LEFT JOIN B on A.id = B.id
) C
GROUP BY C.a
``````

So I could then easily see the optimization and make the change my hand.

## probability – Showing that the limit of random variables is neither continuous nor discrete (base 3 representations)

Let $$X_1,X_2,…$$ be i.i.d such that $$X_iin{0,1}$$ with probability $$1/2$$ each. Let $$R_n=sum_1^n2X_i3^{-i}$$.

It is easy to show that $$R_n$$ converges almost surely, and that the limit takes the values in $$(0,1)$$ that can be written in ternary (base-$$3$$) using only $$0s$$ & $$1s$$.

I have shown that the limit cannot be a discrete random variable, since the set of possible values is uncountable, and I am also quite sure it is not continuous either, but I cannot think of a straightforward way to show this! How can I show this?

I have only studied basic analysis and fundamentals of Riemann integration so it would be great if any help could not go too complex! Thank you

## 7 – How to pass theme variables in #theme in a form element?

I need to pass product variable defined in hook_theme() and invoked in #theme
but not sure how to pass product variables in #theme

``````    function storeinv_theme() {
return array(
'storeinv_pickup' => array(
'variables' => array('product' => NULL),
),
);
}

function storeinv_uc_product_description(\$product)      {
\$description = array(
'pickup' => array(
'#product' => array(
'#type' => 'value',
'#value' => \$product,
),
'#theme'  =>'storeinv_pickup',
'#weight' => 1,
),
);

return \$description;
}

function theme_storeinv_pickup(\$product){

\$data = \$product('#value')->data;

if (isset(\$data('pickup')('store_id')))
{
\$store_id = \$data('pickup')('store_id');
\$day = \$data('pickup')('day');
\$date = date( 'l m/d/Y g:ia', strtotime( \$day ) );
\$result = views_get_view_result('field_altstoreid_value','default');
foreach(\$result as \$k => \$v){
if (\$store_id == \$v->field_altstoreid){
\$name = \$v->title;
return "<p>Pickup " .\$date."at " . \$name." </p>";
}
}
}
else {
return '';
}
}
``````

## cv.complex variables – Is there a decision procedure for analytic continuation?

Let an analytic element be a power series associated with an open disc of the complex plane over which the series is convergent. W.l.o.g. assume the series is a Taylor expansion about the center of the disc. It is easy to show that analytic continuation is an equivalence relationship between analytic elements. Is there a decision procedure to determine if an analytic element is in a particular equivalence class? Put equivalently, given two analytic elements, is there a way to determine if they are analytic continuations of each other?

## functions – Why do people (authors) use clear variables of angle for length.

I see how a function can be described in two variables but solution isn’t fully described with out the addition of a new basis??

This makes me wonder. 3 things

Is the complex iy a basis ??

Am i missing something simple about polynomais ?? And there mappings

Am i missing something about about the wonder of triangles … No im not they be shizzit??

How can a 2d function map on to C but only when the problem has states of a complex nature ?×=