I’ve been having this strange problem on my Redmi Note 7 running MIUI 12.0.2.0 Global.
I’ve been using Shuttle and Musicolet players interchangeably because of their varying features and I have a lot of MP3 files stored in my SD card. The problem is that track numbers for tracks #8 and #9 on random folders keep getting erased.
I use Musicolet’s tag editor and correct the track numbers but after a few days, new tracks appear with the same problem.
Any ideas???
Given the following sheet in numbers: 
I would like to highlight the maximum value for each column in green, and the minimum value of each column in red. I thought this can be done with conditional formatting. However, it seems not possible to use formulas, so I intruduced a new row at the top, which holds the max value of each column.
Now I can add conditional formatting, like so:
However, the problem is, that this only sets the correct conditional formattign for cell F3. For the remaining cells of the column, the conditional formatting auto-advances the referenced cell in the condition, e.g. :
This means I would need to adjust the formula in every cell, thus beeing the same effort as just coloring the cells myself, without conditional formatting.
So the question is: how can I easily hightlight the min/max values of a column as described above, without the need to do this manually for every cell?
Maybe as side note, I will enter new entries row by row, but once entered, those values will never change.
I have an array of numbers for ex. (20000, 30000, 40000)
I want to add a $ sign in front of those numbers and add a comma to form it into (“$30,000, $40,000, $50,000)
I know to utilize the .map() function to address the array but within the function what should I do to transform the numbers within?
A little bit more than a year ago I was able to prove that the sum of the prime numbers less than the square root of some number was asymptotically equivalent to the number of primes up that number (see http://vixra.org/abs/1911.0316).
In this same pre-print, I studied the numbers for which the number of prime numbers up to some number was exactly equal to the sum of the prime numbers less than the square root of that number. As a result, I derived the set of prime numbers that you can see here (http://oeis.org/A329403) and conjectured that there existed infinitely many of such prime numbers. This would imply that the value of the prime counting function of a given number would be infinitely often equal to the sum of prime numbers up to the square root of that number, and in other cases the sum described would be a very good estimator of the prime counting function.
A little bit more than a year after, I am unable to prove or disprove this conjecture. Unfortunately, as an amateur mathematician I feel uncapable of bringing this interesting research further, but it would be great if someone were able to prove or disprove the conjecture.
I find the relationship exposed between sums of prime numbers and the prime counting function really appealling and misterious, and I feel that there might be some hidden and profound mathematics there that I am not able to grasp.
I would like to hear your thoughts and ideas (if any) of how to bring the research to a happy ending. Thanks in advance for your time and effort!
Try this:
=IF(LEN((YourColumn))=9,IF(MID((YourColumn),6,1)=".",IF(ISNUMBER(VALUE((MID((YourColumn),1,5)))),ISNUMBER(VALUE((MID((YourColumn),7,3)))),FALSE),FALSE),FALSE)
First it validates if it’s a 9 character string or not, then checks if the 6th character is a dot (.), then it validates the first 5 and last 3 characters.
Of course, it might be possible to write in an easier way.
Let me know if this helps.
Your question is not the right one.
An AVL tree is a binary tree that has additional properties. First it is a search tree, which means we can easily find each number in the tree. Second it is balanced, meaning that there are no leafs very far form the root. (Formal definitions on request.)
Assume you have a set of $n$ numbers in advance, and an arbitrary “empty” binary tree with $n$ nodes, you can make the tree into a search tree putting the nodes at a well defined position. So, If you can find an empty tree with AVL structure it is no problem to fill it with the values. And indeed, a completely balanced binary tree, adding nodes level by level, satisfies the requirement of AVL trees.
The proper question is: “can we keep a binary tree in AVL form when the values are added and deleted one by one“. When we can do this we have build a quite efficient data structure for sets of values.
In Coq, the nat, the type of natural numbers, has type Set. By the Curry-Howard Isomorphism, all propositions of type Prop are types of corresponding proof terms. How do nats or other instances of Set figure into this isomorphism?
In other words, is there a correspondent for Sets in the Curry-Howard isomorphism, as there is for Props and proof terms, or are they outside the things that have correspondents in the Curry-Howard Isomorphism?
Sorry for the imprecise wording, I’m struggling to express my question clearly, probably because of a poor understanding of the Curry-Howard Isomorphism, happy to be corrected on any misunderstandings I have expressed above.
This question is a generalization of this other question. To recap, I was looking for a function that mapped the set of natural numbers to the set of natural numbers excluding multiples of 2 or 3 or both. So a function $f: x mapsto y$ where $x = {0, 1, 2, 3,…,m}$ and $y={1,5,7,11,13,17,…,n}$ for some arbitrary limit $m$. @A.J. gave a great solution
$y=qquad 6left lceil dfrac{x}{2} right rceil + (-1)^x$
Now I’m wondering about a generalization that allows for the set $y$ to start at an arbitrary point (that is not a multiple of 2 nor 3). For example instead of $x=0$ mapping to $y=1$ it would instead map to $y=5$ and the formula would then be $y=6left lceil dfrac{x+3}{2} right rceil + (-1)^{x+3}$ in other words translated 3 units. Or if we wanted $x=0$ to may to $y=41$ then it would be $y=6left lceil dfrac{x+13}{2} right rceil + (-1)^{x+13}$. But I only know this because I precomputed the set starting at 1 and translated the number per the number of skipped members. If the number is bigger this would be non-trivial. For example, $101$ is not a multiple of 2 nor 3 so what function would start with $x=0$ mapping to $y=101$ and then continue by skipping multiples of 2 and 3 e.g. $103, 107, 109$.
Is there a generalization for a function that given the “starting point” $a$ that is not a multiple of 2 nor 3, and the parameter $x$, it maps $x={0,1,2,3,…,m}$ to $y$ where each member of $y$ is $ge$ $a$ and each subsequent term is the next non-multiple of 2 nor 3?
How do sequence numbers and timeouts provide a reliable channel for application-layer data?
For the purpose of this question, let us define the Radon-Hurwitz number $rho(n)$ to be the maximal dimension of a subspace $W$ of the the real vector space $mathbb{R}^{ntimes n}$ of $ntimes n$ matrices, such that $Wsubsetmathrm{GL}_n(mathbb{R})cup {0}$.
Question:
Is there an elementary proof of the inequality $rho(16n) le rho(n) + 8$?
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