pr.probability – Ljapunow condition on scheme of random variables for generalization of central limit theorem

on numerical tests I see that the scaled and centered sum of dependent variates
begin{equation}
{X_1, X_2, …, X_m}hspace{1cm} text{ with } hspace{1cm} X_i sim Bin(n,theta_i), hspace{1 cm }theta_i sim Beta(alpha_i, beta_i)
end{equation}

is normal distributed. For the Ljapunow or Lindeberg version of the CLT it is not a problem that the random variables are not identical distributed. And I guess that the variates meet the requirements. (will check that)

I assume that the dependence can be described as a mixing process. The dependence might vary as it is derived via a minimum spanning tree. I guess the next step would be to find a scheme of random variables and check again if the Ljapunow or the Lindeberg requirement apply.

Could one of you smart guys approve this approach? Or are you experienced with dependencies of the variates with respect to the CLT? Is there a good paper suggestion? Do you have tipps about how create a scheme of random variables? Do you have suggestions which of the both requirements is more easily accessible?

Thanks a lot

dnd 5e – In D&D 5e, what are all the ways to inflict the Paralyzed Condition on a creature?

In D&D 5e, what are all the ways to inflict the Paralyzed Condition on a creature?

I am talking about all the ways, not just spells.

The reason I am wondering is that I play a Barbarian and what to find ways to use my half-orc’s Savage Attack racial feature more often.

differential equations – NDSolve How do I insert another boundry condition

So I’m new to programming and I am trying to solve a very simple differential equation (i can do this by hand but the thing is i can’t program it), the equation is a'(t) == - 0.0118, with the boundary conditions a(0)==3 and I want to know a(180)=?, how do I insert this (a(180)=?) into the code, this is my short code.

Sol = NDSolve({a'(t) == -0.0118 , a(0) == 3 }, a, {t, 0, 180})
Plot(Sol, {t, 0, 180}) 

It doesn’t show anything in the plot

Thanks a lot, any type of help will be appreciated

8 – How do I set a condition to only show a block to members of a group?

Programmatically you can use Group::getMember() to determine if an account is a member of a group.

if ($group->getMember(Drupal::currentUser())) {
  // the current user is a member of the group.
}

Note that Group::getMember() returns a GroupMembership entity.

You would then create a condition plugin, using the above methodology to determine if the current user is a member of the group.

Note that I’ve created a tutorial on how to use the Conditions API to create conditions plugins, using this example of a condition where a member is a member of the group: https://www.jaypan.com/blog/custom-block-visibility-plugins-and-condition-plugin-api

If condition in differential equation

I need to plot the Integrate the Fire model of neuron. The differential equation is $frac{dV}{dt} + frac{V}{tau} = frac{I}{C}$. The initial condition is $V(0) = 0$. And there is this condition if whenever $V(t) = theta$ then $V(t+h) = 0$ where h->0. If you leave the condition then I know how to solve the equation using NDSolve but I don’t know how to use that condition and sove the equation.
Sample Values $I = 60 × 10^{-9}, R = 10^9,C = 10^{-11}, theta=5$.

Edit1 – Code for NDSolve using WhenEvent() NDSolve({V'(t)+ V(t)/0.01 == 6000,V(0)==0,WhenEvent(V(t)==50,V(t)->0)},V(t),{t,0,10}).

Code for DSolve using WhenEvent-> DSolve({V'(t)+ V(t)/0.01 == 6000,V(0)==0,WhenEvent(V(t)==50,V(t)->0)},V(t),{t,0,0.1}). Here you need to specify the range also.

Thanks everyone who helped.

infopath formatting condition not working

I have these 2 button:

enter image description here

When amount is more than 1,000,000, I want to hide button approved and show button approved & forward to gceo.

When amount is less than or equal 1,000,000, I want to show button approved and hide button approved & forward to gceo.

enter image description here

I have set condition as per above for approved button.

enter image description here

and above for approved & forward to gceo, but when the amount for budgeted is 1,000,001 both button disappear.

I have tried multiple ways but still not correct! Please help.

Infinite number of positive integers that satisfies a condition

Prove that there is an ifinite number of positive integers n $geq 2$ such that the greatest prime divisor of $2^n-1$ is smaller than $2^{n/2021}-1$

I tried to prove this,by taking n,as a product of many prime numbers such that I can identify a lot of its divisors and then prove that the remaining,unknown divisors are smaller than $2^{n/2021}-1$

I also taught about cosidering n as something related to primitive roots, so I can find its prime divisors but that didn’t really help either

Do you have any idea?

mysql if else with a statement as its condition?

I am trying to calculate something from the DB level and would like to know if its possible to an if/else or ifnull or other to evaluate this? IF not what is a good approach?

Is it possible to do something this way?

I’ve tried several ways, but here is my latest example.

IF (SELECT markups.markup FROM markups LIMIT 1) 
THEN
    SELECT ((SELECT AVG(products.price) FROM products WHERE products.code = "8G435G232AB") * (SELECT markups.markup FROM markups LIMIT 1)) + (SELECT AVG(products.price) FROM products WHERE products.code = "8G435G232AB") AS code_8G435G232AB FROM products ORDER BY products.code LIMIT 1
ELSE
    SELECT AVG(products.price) FROM products WHERE products.code = "8G435G232AB"