## A geometry problem solved by Manjul Bhargava

Manjul Bhargava found at age 8 that a pyramid can contain maximum $$frac{1}{6}n(n+1)(n+2)$$ number of orange how does he get it?

## abstract algebra – Proof in the context of Galois theory that quintics and above can’t be solved by the trigonometric and exponential function

I have been studying Galois theory as of late and recently I came across this proof in the context of Complex Analysis which not only prove the unsolvability of the general quintic and higher degree polynomials using radicals but also using trigonometric and exponential functions.

Is there a proof in the context of Abstract Algebra/ Galois theory that is equivalent? Preferably this proof should follow the same line of reasoning as the Abel-Ruffini theorem (the version that I found on Wikipedia specifically).

## Equation with logarithms, why it can’t be solved?

I’m trying to find the -3 dB frequency of a filter in Mathematica. Yet, my code doesn’t seem to work as it produces imaginary values for the frequency.

``````Tfilter=(9.36*^6 + 44226.*s + 9.477*s^2)/(2.35521*^9 + 495801.*s + 9.477*s^2)
Eqn1 = 20*Log(10, Abs(Tfilter /. s -> I*2*Pi*f)) == -3
Solve(Eqn1, f)
``````

What am I doing wrong? Is there any additional command I shall give to Mathematica?

## reference request – Recommendation for books on boundary-value problems that include perturbed boundaries and many solved problems

I am looking for a book or resource that contains applied math analytical methods and a lot of solved problems in Boundary-Value Problems for second-order PDEs, and if it could be related to wave-equation problems in 2D or 3D domains/structures, such as electromagnetics, it would be even better. I have found texts that have extensive treatment of perturbations (e.g. Bender and Orzag), but they mainly focused on initial value problems, not perturbations of the boundary geometry itself. I also like the book by Dudley, but it doesn’t have much solved problems with perturbations. The classic tomes by Morse and Feshbach are also great, but have very few solved problems that help one to practice more.

Ideally, something in the spirit of Schaum’s outline series for solved problems would be perfect, but I couldn’t find such a source yet for advanced boundary-value problems and/or perturbed boundaries. The aim is to practice more in this topic and develop my techniques in approximate analytical solutions for different boundary shapes and perturbations.

## oracle – Execute privilege granted successfully, but I can’t execute the procedure [SOLVED]

I am using the database as me.

The procedure exists as an object that belongs to me.

Grant sucessful.

But when I attempt to `EXECUTE insert_into_purified;` i get

``````Error starting at line : 469 in command -
BEGIN insert_into_purified; END;
Error report -
ORA-01031: insufficient privileges
ORA-06512: at "C##ELLIE.INSERT_INTO_PURIFIED", line 5
ORA-06512: at line 1
01031. 00000 -  "insufficient privileges"
*Cause:    An attempt was made to perform a database operation without
the necessary privileges.
administrator to grant you the necessary privileges
``````

SOLUTION: i didn’t have the privilege to do what the procedure did.

## windows – Old assemblers can’t jump too far in byte indexes (Re-asking a solved question to circumvent an incompetent moderator’s deletion)

The original question was deleted by a moderator who failed to read it carefully, claiming that “it was an error caused by typos.” As there’s no appeal system, I’m just putting it back up here with the solution to help other assembly learners who encounter this same (fairly common) problem

Original question:

``````0ADF:100  jmp 115 ; Execute starting at byte index 115
0ADF:102  db 'Type y or n\$', 0D, 0A ; Storing the string "Type y or n"
0ADF:115  mov ah, 09 ; Executing beginning here here, we're printing a string now
0ADF:117  mov dx, 102 ; move the value at index 102 (the stored string) to what we're printing
0ADF:120  int 21 ; do it
0ADF:122  mov ah, 01 ; Action is getting input
0ADF:124  int 21 ; do it
0ADF:126  cmp al, 79 ; comparing the input to hex value 79, a lowercase y
0ADF:128  je 150 ; This is where it says the syntax error is -- jump if equal to index 150, which hasn't been written yet
----------------^Error
``````

“Error,” is of course, what the command prompt prints when I type that. I have no clue what I’m doing wrong, could anybody help me out, maybe?

## combinatorics – Can the cyclic permutation of a specific situation always be solved in reference to its linear variant? Why?

My answer to this is no. But I am after the explanation on why this is so. Also, when is it suppose to be equivalent to each other.

Let us say there are 6 people that have to sit in 6 chairs.

Values

• Number of ways they can sit without restriction: 6! = 720
• Number of ways two specific people can sit together: 2! * 5! = 240
• Number of ways two specific people cannot sit together: 6! – 2! * 5! = 480

• Number of ways they can sit without restriction: (6-1)! = 120
• Number of ways two specific people can sit together: 2! (5-1)! = 48
• Number of ways two specific people cannot sit together: (6-1)! – 2! (5-1)! = 72

Let me try to do that by using the concept that the cyclic permutation of a specific arrangement is equal to its linear variant divided by the number of slots. But I would like for someone knowledgeable to explain to me why is it that it works in some cases and it doesn’t for others without just resorting to plain intuition. I want to make a generalization.

Computing the cyclic versions based on linear values

• Number of ways they can sit without restriction: 720 / 6 = 120
• Number of ways two specific people can sit together: 240 / 5 = 48
With two people that have to be together, the slots have become 6 – 1 or 5.
• Number of ways two specific people cannot sit together: Yeah this won’t work out. You can’t divide 480 by any integer to make it 72.

Why is it so? Yes, I know that linear and cyclical events are not really stated in any textbook to have this general relationship. I just made it because it worked in some cases.

I do believe linear and cyclic events have that relationship if their values are not obtained by simply subtracting the sample space from their complement, based from what I have shown. I just need confirmation if this is true.

Intuitively, you can say that the linear and cyclic permutations do not correspond because you can place the two people at both ends of the six chairs and when you put them in a circle they are gonna be beside each other.

My intention for this question is to be able to make a generalization that for “this situation” the linear and cyclic permutations can correspond to each other. So if something complicated pops up, I could solve for the linear permutation method first and then simply divide it by the number of slots which do already depend on the problem as you have seen by 6 changing to 5.

As you know, problems like these come with really weird situations like two people having to be together or not, groups of people, alternating genders and the like.

## Is there any rich problems that can be solved using several algorithm techniques?

I am wondering if there are some particularly rich problems that have a large intersection with algorithms and data structures. An example could be the travelling salesman problem. Any other suggestions ?

## Combinatorics challenge solved it Python

The easiest way to explain this problem is to show these two test cases:

``````assert solution('ABC') == ('A', 'B', 'C', 'AB', 'AC', 'BC', 'ABC')
assert solution('ABCD') ==  ('A', 'B', 'C', 'D', 'AB', 'AC', 'AD', 'BC', 'BD', 'CD', 'ABC', 'ABD', 'ACD', 'BCD', 'ABCD')
``````

my solution is below:

``````def subsolution(lst, length):
return (lst + (x) for x in·
range(lst(-1)+1, length))

def solution(symbols):
length = len(symbols)
result = (((x) for x in range(length)))
while True:
subres = ()
for x in result(-1):
subres.extend(subsolution(x, length))
if not subres:
break
result.append(subres)
result = ( item for sublist in result
for item in sublist
)
result = (
''.join(symbols(s) for s in el)
for el in result
)
return result
``````

we have a serious problem with the cart-view in our shop: https://www.murergrej.dk/checkout/cart/

• Problem 1: Not all buttons are clickable anymore.
• Problem 2: The message “Free shipping” is shown all the time.
• Problem 3: The right sidebar is missing its content, which is the overview of the different prices, the calculation of the shipping price and the possibility to add a discount code.

Situation:
We had the website on a development server and moved it to the live server. The problem wasn’t on the dev-server present.
All JS files seem to be loaded and we can’t identify any relevant error messages, what makes debugging really uncomfortable.

What I tried so far:

• Deactivating modules installed after we moved
• Disable custom JS
• Switch from production back to development mode
• Deploy, deploy, deploy (of course with setup:upgrade, di:compile, cache:clean/flush)
• Reindex (what shouldn’t do any difference)

Any new perspective/idea on how to approach the debugging would be a great help.

Thank you very much!

Robert

EDIT

A module from a third party was altered by them, which caused the error. I will contact them, so that they fix the bug.

It is/was caused by cached jquery-data.