recursion – Finding a threshold such that one function is always larger than the other

Given the recursively defined function $ c $, which I believe is a variant of the Fart-Ackermann function:
$$ c (m, n) = begin {cases} 0 & text {for} m = 0 \
n ^ 2 + n + 1 & text {for} m = 1 text {and} n ge 0 \
c (m-1, 1) & text {for} m> 1 text {and} n = 0 \
c (m-1, c (m, n-1)) & text {for} m> 1 text {and} n> 0 \
end {cases} $$

and function $ d $ who is building a "tower" of powers of $ 2 $ of size $ n + $ 2:

$$ underbrace {2 ^ {2 ^ {. ^ {. ^ {. ^ {. ^ {2}}}}}}} _ { text {$ n + 2 $}} $$

The entrees $ m $ and $ n $ are both natural numbers. I am asked to find a $ x $, so that for all numbers $ y ge x $, $ c (y, y)> d (y) $.

I rewrote the two functions using Python to calculate certain values:

 c(m, n):
    if m == 0:
        return 0
    else if m == 1 and n >= 0:
        return n**2+n+1              # return n^2+n+1
    else if m > 1 and n == 0:
        return c(m-1, 1)
    else if m > 1 and n > 0:
        return c(m-1, c(m, n-1))

    exp_num = n-1
    result = 2
    while exp_num != -1:
        result = result**2           # result = result^2
        exp_num = exp_num - 1
    final_result = 2**result         # final_result = 2^result
    return final_result

Some inputs and outputs:

c(1, 1) = 3

c(2, 2) = 183

d(1) = 16

d(2) = 65536

d(3) = 115792089237316195423570985008687907853269984665640564039457584007913129639936

I believe the threshold is $ 3 $, as c(3, 3) does not seem to be realistically computable since there are more than 19 K digits in A (4, 2) (where A is the Fart-Ackermann function). Unfortunately, I don't know how to prove it. Any help would be greatly appreciated.

SharePoint Online index to avoid the list view threshold

In SharePoint, the threshold problem has been an impending problem for more than a decade. To solve this problem, we need to first understand what indexing is in the database and how the index works in SharePoint, then see how to create a column. indexing, then learn how to create a dynamic filter column with the function of today … …. so please browse these articles where you will explain the concept of indexing and how to solve this problem threshold.

What is database indexing in SharePoint?

A database index is a data structure that improves the speed of data retrieval operations from a database table and it works on the basis of the key value pair technique – algorithms Basic binary search and linear search are built on the indexing technique.

In other words, we can say – an index is a copy of selected columns of data from an original table that can be searched very efficiently, which links directly to the full row of data from where it was copied. Again, there are different types of indexing in the database like cluster and noncluster etc. I did not go in this direction since the aim of this article is different. In a short note – indexing is a technique to get the fastest query result from the database table. Indexing costs us additional writes and storage space in the file system.

In SharePoint, there is only one table, that is to say "AllUserData"In all content databases that store all of the items in the SharePoint list, I mean that this is a common table for all lists in the site collection. there are a lot of internal columns in the table than what the number of columns we create in the SharePoint list – so what we see in the list are just a few columns. For example: 64 nvarchar, 16 units, 12 floats and so on.

If we look at the Microsoft documentation on the "AllUserData”Structure of the table, we will be surprised how complex it is. Please click here to learn more about "AllUserData”Table structure.

How does the indexing column work in SharePoint?

The items in the list are stored in the "AllUserData”In SQL. For each defined indexed column, SharePoint stores the index value for each list item in a separate table, that is, "NameValuePair »Table that we saw above. Suppose we have 20,000 items in the list, which means we have 20,000 rows in "AllUserData" and an additional 20,000 rows in "NameValuePair”Table (used for indexing).

So requests to view SharePoint list items are processed based on the key value in the "NameValuePair"Table and choose the appropriate mapping items from the main menu"AllUserData"Table which is the actual data source. This is how the SharePoint index column accelerates query performance.

Database indexing example:

enter description of image here

Learn more about exactly what SharePoint column indexing is:

SharePoint – O365 – How does the database column indexing work in SharePoint?

How to fix 5000 list view threshold problem:

We can increase the limit of list items from 5000 to 50,000 (fifty thousand) in on-premise SharePoint, in fact, we can turn off the list view threshold limit which is not recommended, but in SharePoint online, we have no control over it, we need to move to the defined limitation, i.e. 5000.

Here, based on my experience, I will list a few tips and tricks to avoid this problem that will work for both online and on-premises SharePoint.

  • Planning – before creating the list or library, analyze the data and
    plan accordingly. Try to divide the data into multiple lists or libraries.

  • Create multiple views and add "AND"Condition in the list filter
    criteria, never add "OR"Condition"OR"Condition will try
    to get all the data.

  • Create an index column – we can only have 20 columns indexed in a data
    listing. so we need to plan this thoughtfully!

  • We cannot create an indexed column if the list is already hitting
    the list view limit.

  • Maintain list of archives – here we need to review the items in the list
    periodically and should check whether certain items can be deleted or
    archived in another list – here we can write an automation job
    which will periodically move items to another archive list

  • In the list filtering criteria, we have to filter the list items such as
    so that at any given time, the list view returns less than
    5000 items using a filter on the column column technique created (please see
    the explanation below).

Create a filter (today) – "number of days technique:

One of the techniques here is to create a filter on the "Created" column and use the (Today & # 39; hui) – "number of days"With a condition less than or equal to, something like below:
enter description of image here


The logic behind the filter on the created column is – this will try to get the items that will return less than 5000 items. If this condition also returns more than 5000 articles, we need to divide this column condition created by multiple "AND"Condition with combination of another column to ensure that the filter returns less than 5000 elements as an example below – although the implementation of this technique takes a long time.
enter description of image here

Reference URL: How to fix listview 5000 threshold error

List view threshold error(5000 items issue) in SharePoint On-Premise/SharePoint Online

Reference URL – How to create an indexed column in SharePoint?

How to create indexed column in SharePoint on-premise and online – O365?

performances – Impossible to exceed the threshold of 4000 RPS on the HTTP server Golang localhost

I have been trying to measure the bandwidth of the default HTTP Go server implementation on my local machine. The server simply accepts any HTTP request, increments the counter using sync.atomic and send 200 OK reply. In addition, the server collects the number of requests every second, prints it and resets the counter to zero:

type hand struct {
    cnt int32

func (h *hand) ServeHTTP(rsp http.ResponseWriter, req *http.Request) {
    atomic.AddInt32(&h.cnt, 1)
    if req.Body != nil {

func main() {
    h := new(hand)
    s := &http.Server{
        Addr:    ":8080",
        Handler: h,
    ticker := time.NewTicker(1 * time.Second)
    go func() {
        for tick := range ticker.C {
            val := atomic.SwapInt32(&h.cnt, 0)
            fmt.Printf("(%v) %d RPSn", tick, val)

Target client is trying to send 100,000 GET simultaneously requests:

const total = 100000

func main() {
    var r int32
    var rsp int32
    r = total
    rsp = r
    for r > 0 {
        go func() {
            p, err := http.Get("http://localhost:8080")
            atomic.AddInt32(&rsp, -1)
            if err != nil {
                fmt.Printf("error: %sn", err)
            if p.StatusCode != 200 {
                fmt.Printf("status %dn", p.StatusCode)

    for {
        x := atomic.LoadInt32(&rsp)
        fmt.Printf("sent : %dn", total-x)
        if x == 0 {
        time.Sleep(1 * time.Second)

I am using a Linux machine with 5.3.2-gentoo core. i changed ulimits (both soft and hard) of nofile at 100000. When I run these tests, all other user applications have been stopped.

I don't expect to get accurate results, but I just need to know the level of this threshold, something like X000 or X0000 or X00000.

But the server cannot process more than 4000 requests per second, it seems too low:

# removed timestamps
3953 RPS
3302 RPS
387 RPS
37 RPS
1712 RPS

How can I increase the bandwidth of the HTTP server? Or maybe there is a problem with my test method or my local configuration?

Sharepoint list display threshold – even with folders

I have a problem where my SharePoint document folder has a problem with the list display thresholds
193757 items (the list display threshold is 5000).
However, what I do not understand is that these documents are all stored in folders and that the current list should never contain more than 100 items at a time. Is there a missing parameter? I use online sharepoint.

sharepoint enterprise – Wondering if a custom list filter helps solve the view threshold problem 5000

Is the 5000 View Threshold a server-side or client-side problem? In other words, would I waste my time creating a custom client-side "view filter" from the Allitems list, who will still process the 5000 filter, then? I'm trying to filter through FY and the OOB view filter does not allow me to do it. So I think to create a custom.

How does damage resistance, damage reduction, damage threshold and half damage caused by a successful backup work together?

It's mostly a theoretical question.
Imagine that a creature has a variety of items that reduce the damage built into its stats block.
Let's pretend that it's a giant gemstone of melt, because it seems at least plausible for these bonuses:

  • The fire damage suffered by the golem is reduced by 9. (according to the wording as the tour de force of Heavy Armor Master)
  • The golem has a reduced damage of 12. (usually only objects have DR, but humor me!)
  • The golem has resistance to fire damage.

Now, imagine that the golem has made a dexterity saving throw against a fireball.
Before any reduction, imagine that the fireball causes 40 fire damage on the golem.

The question:

How much damage would the golem suffer and what steps should be taken to reduce the damage to that amount?

sharepoint online – How to handle a list threshold error?

I write the script below for SharePoint Online and I have encountered an error regarding list thresholds.
I'm trying to find the amount of files in a certain document library and I would eventually like to write code that allows me to remove specific permissions from different sites.
Is it something that I can correct in this code?

$fullSite = ""
$list = "name"

Connect-PnPOnline -Url $fullSite -UseWebLogin 

$listItems = Get-PnPListItem -List $list 

    $count = 0
    foreach($listItem in $listItems){
        $count = $count + 1
    Write-Output $count

How can I set a threshold for the points I want to select in an image?

I would like to ask you how I can correct a number of points to show in an image.
In the previous article (Is it possible to get the coordinates only for points highlighted from an image?), JimB suggested a good solution for determining the outline of the image. Image and get the coordinates of these points. It would be interesting to know if there is a way to select a certain number of points that can "draw" the image (for example, 10).
I've tried using MaxFeatures -> 10 in ImageCorners, but he selects the points randomly.

enter the description of the image here

Thank you for all the help you will bring.

php – Excludes products whose stock is below the low stock threshold of the store loop

On our Shop page, we have various badges (things like "Series 1") that, when clicked, are linked to their respective product tag pages. However, we also want a "weak stock" badge. The problem is that we have to dynamically determine if a stock is weak. We can not just mark it.

I make the weak stock insignia link to his own page with Woocommerce (products) shortcode, but now I only have to show those with stocks in this range. So far, all the solutions I've found mention the deletion of products by performing a taxonomy query, but I can not do it because I can not manually assign them to a label / category to low stock.

For reference, here is the taxonomy query that I used as a basis:

function custom_pre_get_posts_query( $q ) {
    if( is_shop() ) {
        $tag_query = (array) $q->get( 'tax_query' );

        $tag_query() = array(
               'taxonomy' => 'product_tag',
               'field' => 'slug',
               'terms' => array( 'retired' ), // Don't display products with the tag "retired"
               'operator' => 'NOT IN'

        $q->set( 'tax_query', $tag_query );
add_action( 'woocommerce_product_query', 'custom_pre_get_posts_query' );

dnd 5th – Does Arcane Abandonment permanently ban creatures below the threshold?

Arcana domain clerics get a Channel Divinity option called Arcane abjuration. Here is the relevant part of the description:

Once you have reached the 5th level, when a creature fails its save roll against your Arcane Abuse trait, the creature is banned for 1 minute (as in the banish spell, no concentration required) if it is not on his original plan nor in his challenge. the score is equal to or less than a certain threshold, as shown in the Arcane Banishing Chart.

The description of the spell for banishment says:

If the target is native to an existence plan different from the one you are on, the target is banned with a slight popping sound and returns to its original aircraft. If the spell ends after one minute, the target reappears in the space it left or in the nearest unoccupied space, if that space is occupied. Otherwise, the target does not return.

It looks like a creature below the CR threshold for Arcane Banishment is permanently returned to its original plane. However, the word "banished for a minute" could be interpreted as saying that after a minute they come back.

Are creatures banished by Arcane Abjuration returned to their original aircraft permanently, or only for one minute?