real analysis – sum limit of small functions oh

I wonder if what I show below is allowed and why.

Suppose you have an interval $ (0, T) $. For each $ n $ you divide the
interval in $ 2 ^ n $ n parts. In each interval, you have a function
$ o ( Delta t) $. We have the summation

$ sum limits_ {i = 1} ^ {2 ^ n} o ( Delta t) = 2 ^ no ( Delta t) = T frac {o ( Delta
t)} { frac {T} {2 ^ n}} = T frac {o ( Delta t)} { Delta t} $

So, it goes to zero as n goes to infinity.

I saw this argumentation in a book. Is it permissible or do we need more constraints on the $ o ( Delta t) $ functions? The problems I have are:

  • Let n, the $ o ( Delta t) $ the functions may be different, so can we just say that they are $ 2 ^ n $ once a $ o ( Delta t) $ a function?

  • When $ n $ increases, we get new $ o ( Delta t) $-functions. Does this affect the outcome? For the limit to reach zero as $ n $ increases we need to be the same $ o ( Delta t) $-a function?

So, is the result valid or are there counterexamples where they are not? Do we need more conditions on the functions for this to work?

probability – Maximize a limit, logarithmic utility

We have a game with $ m $ different results, labeled 1.2 … m $. Who every occurrence with probability $ p_1, p_2, … p_m $. If result $ i $ Sometimes you get m-times what you bet on that result in return. Every other bet loses. (So, basically, a simple price wheel)

Say you play with a fortune of K and bet $ K cdot q_i $ on the result $ i $ with $ q_1, q_2 … q_m> 0 $ and $ sum_ {i = 1} ^ m q_i = 1 $. So, every turn, you bet all your money distributed among the different results, but you must always bet at least something on each result.

I've calculated the fortune after n rounds as follows:

$$ K_n = K_0 cdot m ^ n cdot prod_ {j = 1} ^ n q_ {X_j} $$

with independent random variables $ X_j $.

Now I needed (what I suspect to be the logarithmic utility):

$$ lim_ { rightarrow infty} frac { log (K_n)} {n} $$

that I found to be:

$$ log (m) + sum_ {i = 1} ^ n log (q_i) cdot p_i $$

But the last part is to find values ​​for everyone $ q_i $ to maximize the limit above?

So basically:

$$ max: sum_ {i = 1} ^ n log (q_i) cdot p_i $$
so that:
$$ forall i in {1 … m }: q_i> 0 $$
$$ sum_ {i = 1} ^ m q_i = 1 $$
with fixed values ​​for $ p_i $

Thanks in advance 🙂

How to limit the connection on the web server

Centos + Apache + Nginx (as a proxy)
this configuration is what we have right now and try to test our security with aconetix,
aconetix will send numerous requests to the web server to check the status of the website, the web site and … … (with a unique IP address)
at the beginning of the scan, the 2000 request is sent and the loading time goes from 0.0 to 9 and more.

I'm trying to limit the ip connection with CT_LIMIT in the CSF to 150, what happens if this limit is reached? the users will be wrong? free time ????

Is there a solution that allows Apache and Nginx to limit connections without CSF? prevent amortization of this load increase?

PS: Limits the number of connections with LCR dosing and resolves the charging time.

Is it possible to exceed the character limit in forms on websites?

I'm trying to enter my address on a website with a character limit for the address and I can not type the entire text. Is it possible to extend this with an extension or something?

analysis – Proof of average value property using a specific limit

I'm trying to prove the following:

assume $ u in C ^ 2 ( Omega) $. For some people $ x in Omega $ we have that

begin {align} Delta u (x) = lim_ {r to 0} frac {2n} {r ^ 2} left (
frac {1} {w_n} int _ { B_ {1}} partial u (x + ry) mathrm {d} S_y – u (x)
right). end {align}

Yes $ u $ is harmonic, so $ u $ has the property of average value.

I think we basically need to see that limit intelligently, but I still could not do it. Can any one give me a hint about this? But you have to use the limit above.

Thank you in advance.

Functional Analysis – Upper Limit of Lp Distance of Functions Before and After Change of Variables


I'm trying to superimpose the difference between two functions: one before changing variables and the other after.

For example, leave $ r in mathbb {N} cup { infty }, 1 leq p < infty $ and
g in L ^ p ( mathbb {R} ^ D): C ^ r text {-function} \
T: mathbb {R} ^ D to mathbb {R} ^ D: C ^ r text {-function} \
f_T (x): = g (T (x)) left | t fr { mathrm {d} T} { mathrm {d} x} (x) right |.


I would like to link the disturbance due to $ T $, in terms of $ L ^ p $ standard.

F (T): = | f_T – g | _ {L ^ p}: = left ( int | f_T (x) – g (x) | ^ p dx right) ^ {1 / p}.

For two $ C ^ r ( mathbb {R} ^ D, mathbb {R} ^ D) $-functions, $ T, T $, I would like to have an upper limit on the difference of $ F $, that is to say.,
F (T) – F (T) leq ( text {An upper bound of} (T – T)).

The result does not have to be for everyone $ p $ and $ r $but I'm interested in any result of this type for a specific set of $ p $ or $ r $. The space in which these functions reside is also variable for me, and any suggestion of appropriate change is highly appreciated.


  1. Are there known results of such an upper limit under certain mild conditions?
  2. Is the above example an appropriate configuration? Are there any suggestions such as the function space to use or the properties to assume on the functions?
  3. If not, does anyone have an idea of ​​how I should get an upper limit?

P.S. I do not know very well the functional analysis. Therefore, if there are ambiguities or imprecise terminology, I will correct it if you could report them.

What should you prefer to limit the flow? AWS WAF or nginx as a proxy server or both?

We have our server on the Jetty server and the interface on the Apache server.
These two elements are on the AWS EC2 instance. We now want to implement API throttling for our application. So what would be the right approach to follow? AWS WAF or nginx as a proxy server between the front-end server and the main server, or both?

Command File – How to Limit WSUS Setup Hotfixes for Windows Update

In fact, we have several WSUS servers, but for the sake of example, we will only focus on a WSUS server.
So here is the situation:

  • I have received several WU patches to download and install on nearly 1,000 machines,
  • the problem is that on some machines we have more than 250 Windows Update patches that have not been downloaded or installed (yeah yeah 250 !!! ^^)
  • if we push them (download and install) one after another (on a single machine), we sometimes encounter problems and all the fixes are uninstalled,

So we need to download all patches again and reinstall them 30 by 30 to make sure they are installed correctly.

So what I wanted was to create a .bat or .vbs script (yeah, I need to run it on XP ^ ^ machines too) to stop the installation process when Windows Update is up to 30 patches.

In fact, I do it manually: D and I can not find what I was looking for ^^

If any of you can help me on this specific topic, I would be happy: D

Manual shutdown of the installation image


magento2.3.2 – How to limit "related products" in Magento 2.3.2

I am used to being able to define "product related" limits in /app/design/frontend/theme/theme/Magento_Catalog/product/list/items.phtml


case 'related':
    /** @var MagentoCatalogBlockProductProductListRelated $block */
    if ($exist = $block->getItems()->getSize()) {
        $type = 'related';
        $class = $type;

        $image = 'related_products_list';
        $title = __('Related Products');
        $items = $block->getItems();
        $limit = 4;
        $shuffle = 0;
        $canItemsAddToCart = $block->canItemsAddToCart();

        $showAddTo = false;
        $showCart = false;
        $templateType = null;
        $description = false;

Notice the $limit = 4;

However, in Magento 2.3.2, this method does not seem to be an option anymore. On the desktop, I will get at least 6 images per line, with what appears in the form no no limit on the total number of items listed.

In the EE version, it seems easy to set up, but in the CE version, I do not know where to limit the number of elements, nor how to display. For example, if there are 4 related products, they stay on the surface, or it seems to be the case. Centered would be ideal, but so much has changed that I am unable to understand how 1) limit the "related products" 2) affect their display on a page (position.size / etc.) Or 3) where to even start.

If anyone has an idea, suggestions are appreciated. Apparently, 2.2 versus 2.3 are very different products.

Magento2: How to Resolve a Memory Limit Error When Using the Composer Update Command

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I came out of a memory error by running the "compose update" command,
I already check memory_limit and that is 2048 M that I also get the error above
does anyone know how can I solve this problem?