## Clear variables on window close

I’m using

DynamicModule[{ var1, var2 },  CreateDialog[ (*some code here*) ]] 

In order to be able to deal with memory isolation for multiple copies of a program running at once. Is there an option to use in CreateDialog to run a command upon the closing of that Dialog? When that window gets closed I would like to clear all the variables to free up the memory.

## Use global variables with Elementor page builder

I have created a short code with php and widget for sidebar to control the results of the short code I made and I need to use some global variables to send from the short code to the sidebar widget, everything working fine, But when I am using Elementor page builder global variables disappears!! However when using another page builder everything working well!! any help about that as I wish to use Elementor in my site! Cheers Mo

## Compile function with only some variables

I made the simple example below for explaining the problem. How can I compile only some variables?
For example, in the example only a and b are Integer, c can be any type.

In[218]:= cf = Compile[{{a, _Integer}, {b, _Integer}, c}, a*b + c]; cf[2, 3, d] CompiledFunction::cfsa: Argument d at position 3 should be a machine-size real number. Out[219]= 6 + d 

How can I solve this warning and make this work for any c?
I want "c" to be anything.

## Specifying statistical models / Equations between Random Variables

I’m new to Mathematica and confused about how random variables work.

Say I have a standard normal random variable $$X\sim \mathcal N(0,1)$$ and set $$Y := 2X$$. Then $$\operatorname{Cov}(X,Y) = 2$$. Now if I generate $$N$$-iid. draws for $$X$$, the sample covariance of $$X_1,\dots, X_N$$ and $$Y_1,\dots, Y_N$$ with $$Y_n := 2X_n$$ should be close to $$2$$.

My question is: how can I compute statistics (e.g. sample covariance) in Mathematica? Naively, I tried

x:=RandomVariate[NormalDistribution[], 5000] y:=2*x Covariance[x,y] 

but the result is clearly incorrect (usually not close to $$2$$), because in actuality (I presume) under this model $$Y$$ is independent of $$X$$.

What is the most convenient way of achieving the correct result?

## Solving trigonometric equations with two variables in fixed range?

I am trying to use ‘Solve’ function to solve two trigonometric equations with two variables a1 and a2 (with range 0,2Pi). I wrote the code in the following:

  Vets={Cos[2a1](I+Cos[2a2])+Sin[2a1]Sin[2a2], (I-Cos[2a2])Sin[2a1]+Cos[2a1]Sin[2a2]};   Solve[Vets[[1]] == 1 && Vets[[2]] == 0 && 0<=a1<=2Pi && 0<=a2<=2Pi, {a1,a2}]  

but it gives errors:

Solve::nsmet: This system cannot be solved with the methods available to Solve.

I looked up the documents for Solve function and it should be no problem with the above code. But it doesn’t do anything and give errors, I don’t understand why?

It will be super cool if anyone could answer this question, thank you very much in advance!

## How to safely change Innodb variables

I’m using Maria DB, version 10.2.22, where one database column uses FULLTEXT for a broad document searching. However, I’ve ran into a "Table handler out of memory" on some searches. The table itself is only 4.4 GB. I’ve read on stackoverflow, that changing some of the InnoDB variables such as:

• innodb_buffer_pool_size

• innodb_ft_result_cache_limit

from their default value to say 4 GB could potential solve to the memory issue. My question is three parts, I suppose.

1. Are there any other variables I should consider changing.

• innodb_buffer_pool_instances
• innodb_ft_cache_size
• innodb_ft_total_cache_size

1. Because this DB is fairly critical to run, after running the command lines to change the variables would I need to stop and start the MariaDB service to fetch these changes?

2. If, restarting MariaDB services is needed, can anyone point me to a guide as far as how to safely change these variables?

## How to use a List of indexed variables inside a Module?

This is a trivial function, just to show that Module does not recognize the List generated by Table.

f1[x_] := Module[Table[out[i], {i, 1, Length[x]}], 42]    f1[{1, 2, 3}] 

## Maximize an expression with respect to a variable and minimize it with respect to other variables

I started to use Mathematica a few time ago. I want to minimize the following expression (function of $$l,p,q,r,c$$) with respect to variables $$l, p, q, r$$ and then maximize the result obtained with respect to variable $$c$$. However, when I try to obtain an expression function of $$c$$ to maximize later using Minimize, I do not get any result because it takes too long. How can I solve this issue?

Minimize[{(((l^2/2)*(1-(1/4-c))+(l*p)*(1-1/4)+(l*q)*(1-(1/4+c))+(l*r)*(1-1/2)+(p^2/2)*(1-c)+(p*q)*(1-2*c)+(p*r)*(1-(1/4+c))+(q^2/2)*(1-c)+(q*r)*(1-1/4)+(r^2/2)*(1-(1/4-c)))/((l^2/2)*(1-(1/4-c))+(l*p)*(1-1/4)+(l*q)*(1-(1/4-c))+(l*r)*(1-0)+(p^2/2)*(1-c)+(p*q)*(1-(1/4-c))+(p*r)*(1-0)+(q^2/2)*(1-(1/4-c))+(q*r)*(1-1/4)+(r^2/2)*(1-0))), l >= 1, p >= 0, q >= 0, r >= 0, l + p + q + r == 1000000, 1/7<c<1/5}, {l, p, q, r}] 

## UPDATE with variables to renumber column gives syntax error

Searching for a way to renumber a column within mysql, I’ve found multiple articles showing the same approach:

• Renumbering an Ordering Field in MySQL
• How to update a MySql column with ascending numbers

among others.

But trying it on my table I get a syntax error.

mysql> SET @rankStart = 10; mysql> SET @rankInc = 10; mysql> UPDATE fileFileTbl SET rank = (@rankStart := @rankStart + @rankInc) ORDER BY rank ASC; ERROR 1064 (42000): You have an error in your SQL syntax; check the manual that corresponds to your MySQL server version for the right syntax to use near 'rank = (@rankStart := @rankStart + @rankInc) ORDER BY rank ASC' at line 1 

The command looks identical to the articles posted. What am I missing?

Here’s the table (with some columns omitted):

CREATE TABLE fileFileTbl (   id int(11) unsigned NOT NULL AUTO_INCREMENT,   fileEngineId int(11) DEFAULT NULL,   rank int(11) DEFAULT '0',   fileName varchar(30) CHARACTER SET utf8 COLLATE utf8_general_ci DEFAULT 'newfile',   PRIMARY KEY (id),   UNIQUE KEY fileEngineId (fileEngineId,rank) ) ENGINE=InnoDB AUTO_INCREMENT=16 DEFAULT CHARSET=utf8; 

System is Centos 8, with mysql as:

# mysql --version mysql  Ver 8.0.17 for Linux on x86_64 (Source distribution) 

## SAT satisfaction with 10 variables

I am trying to prove that the next problem is NPC:

$$A=$${$$<\phi>|\phi \,\,\,is\,\,\,a\,\,\,CNF\,\,\,and\,\,\,has\,\,\,satisfying\,\,\,assignment\,\,\,where\,\,\,exactly\,\,\,10\,\,\,variables\,\,\,are\,\,\,TRUE$$}

I am trying to find polynomial mapping reduction from SAT but I can’t find a way to force exactly 10 variables to get TRUE assignment. My idea was to create new formula, with 10 clauses, each clause is the intersection of a new variable $$x_i$$ with the old formula, but I don’t see how my idea helpful.

I would appreciate help.