networking – Using 2nd router as extension of my main router, LAN works but WLAN doesn’t and after “x” time it just refuses to work at all

I recently followed a guide how to use an old router to extend my network at home. Everything was smooth, made sure the range I have set the DHCP Server won’t conflict with anything (Main Router, from my ISP.) I’ve used –

Moving on to the old router. I’ve disabled it’s DHCP so it wouldn’t conflict with the server, set the old router’s IP Address as I’ve setup the wireless options as well, made sure it has a different SSID, even changed the channel selection so it wouldn’t collide with anything. The LAN interface works, at the moment I’m connected to it as I’m typing this question. The only problem I’ve had is whenever an I try to connect to it wirelessly via an Android or iPhone it has limited connectivity. I am connected to the network, but I do not have an internet, the LAN ports work however. The 2nd/old router acts like a switch it seems. Any advice how to set this up properly?

nt.number theory – When did the Main Conjecture in Vinogradov’s Mean Value Theorem first appear in literature?

Recently I was asked about the history of Vinogradov’s Mean Value Theorem that I was hoping someone here could clarify. Let me first start with some terminology. Let $J_{s, k}(X)$ be the number of $2s$-tuples $(x_1, ldots, x_s, y_1, ldots, y_s)$ such that
x_1 + cdots + x_{s} &= y_{1} + cdots + y_{s}\
x_{1}^{2} + cdots + x_{s}^{2} &= y_{1}^{2} + cdots + y_{s}^{2}\
x_{1}^{k} + cdots + x_{s}^{k} &= y_{1}^{k} + cdots + y_{s}^{k}

for $1 leq x_{i}, y_{i} leq X$. It is not hard to see that $$J_{s, k}(X) gtrsim_{s, k} X^{s} + X^{2s – frac{1}{2}k(k + 1)}.$$

The now proven Main Conjecture in Vinogradov’s Mean Value Theorem is that this lower bound is essentially an upper bound. More precisely, the conjecture was:

Conjecture: For every $epsilon > 0$, $$J_{s, k}(X) lesssim_{epsilon, s, k} X^{epsilon}(X^{s} + X^{2s – frac{1}{2}k(k + 1)}).$$

This conjecture follows from classical methods for $k = 2$, first proven by Wooley for $k = 3$ using efficient congruencing in 2014 and then proven by Bourgain, Demeter, and Guth for $k geq 4$ using decoupling methods in 2015.

My question is: when did this conjecture as stated above first appear in the literature?

Looking through Vinogradov’s 1935 paper “New estimates for Weyl sums”, it seems that this conjecture is not stated. The term “Vinogradov’s Mean Value Theorem” referring to any bound of the form $J_{s, k}(X)lesssim X^{2s – frac{1}{2}k(k + 1) + Delta_{s, k}}$ for some $Delta_{s, k}$ positive and $s gtrsim k^{2}log k$ seems to appear in print as early as 1947 or 1948 in these two works by Hua:

  1. Page 49 of the Russian version of his Additive Theory of Prime Numbers (
  2. In Hua’s paper “An Improvement of Vinogradov’s Mean-Value Theorem and Several Applications” (

Though in both, it seems to imply that this term was in use as early as 1940. However neither also state the conjecture as mentioned above.

analytic number theory – How to determine the coefficient of the main term of $S_{k}(x)$?

Let $kgeqslant 2$, suppose that $p_1,p_2,dotsc,p_k$ are primes not exceeding $x$. Write
$$ S_{k}(x) = sum_{p_1 leqslant x} dotsb sum_{p_k leqslant x} frac{1}{p_1+dotsb +p_k}. $$
By AM-GM inequality, $p_{1}+dotsb + p_{k} geqslant k sqrt(k){p_{1}dotsm p_{k}}$, we have
$$ S_{k}(x) leqslant frac{1}{k} sum_{p_{1}leqslant x}dotsb sum_{p_{k} leqslant x}
frac{1}{sqrt(k){p_{1}dotsm p_{k}}} = frac{1}{k} left( sum_{p leqslant x} p^{-frac{1}{k}} right)^{k}. $$

By Prime Number Theorem and (Riemann–Stieltjes) integration by parts we see that
$$ sum_{p leqslant x} p^{-frac{1}{k}} = mathrm{Li}big( x^{1-frac{1}{k}} big) + O left( x^{1-frac{1}{k}}mathrm{e}^{-csqrt{log x}} right), $$
Here $mathrm{Li}(x)$ is the logarithmic integral, and $mathrm{Li}(x)sim x/log x$. Hence
$$ S_{k}(x) leqslant left( frac{k^{k-1}}{(k-1)^{k}} +o(1) right) frac{x^{k-1}}{log^{k} x}. $$
On the other hand, $p_{1}+dotsb +p_{k} leqslant kx$, we have
$$ S_{k}(x) geqslant frac{1}{kx} sum_{p_{1} leqslant x} dotsb sum_{p_{k} leqslant x} 1 = frac{1}{kx} left( sum_{p leqslant x} 1 right)^{k} = frac{pi^{k}(x)}{kx} = frac{(1+o(1))}{k} frac{x^{k-1}}{ log^{k} x}. $$
My question is how to determine the coefficient of the main term of $S_{k}(x)$?

Can Forex Be A Main Job? – General Forex Questions & Help

Fundamental analysis is a way of looking at the forex market by analyzing economic, social, and political forces that may affect the supply and demand of an asset. If you think about it, this makes a whole lot of sense. Just like in your Economics 101 class, it is supply and demand that determines price, or in our case, the currency exchange rate. A suitable broker can help you to understand fundamental analysis in forex market. I use TP Global FX as my broker. They are very reliable and easy of use.

What are the main limitation of Blockchain technology and what could be an ideal solution?

If Blockchain allows to store data in an outsourced environment without having to trust the peer hosting the ledger and is not a perfect solution to protecting data from unwanted usage.

So then what are the main limitation of this technology and what could be an ideal solution?

unity – Should I do interactions between a new class and the main engine via a redirector class, or directly refer to only the classes the new class needs?

I’m making an open-source voxel engine, and there’s an architectural problem that I would like an answer to. I have come up with 2 different solutions, and would like your opinions on:

When I’m creating a new class for a feature that uses the voxel engine, should the new class only refer to a big re-director class called VoxelWorld that redirects the calls to whatever component is responsible for it (solution 1), OR should the new class directly refer to only the classes it actually needs. Simply put, should the new class refer to the entire voxel engine, or just the parts it needs to?

This may be similar to a monolithic vs microservice problem?

Solution 1: All interactions go through a single entry point (I shall call it the VoxelWorld class). It’s a single class, which would redirect all calls to whichever component is responsible for it. Examples of those calls would be for example VoxelWorld.GetVoxelData(position) or VoxelWorld.UnloadChunk(position). These calls would be coming from wherever, maybe a custom class made by the user such as a TerrainDeformer.

The TerrainDeformer would only have a reference to VoxelWorld, and nothing else (except for all the parameters it needs to deform the terrain, such as the deformation range). The TerrainDeformer would simply call VoxelWorld.EditTerrain(listOfModifications), and that’s it. The VoxelWorld would be responsible for redirecting the EditTerrain call to whichever class is responsible for editing the terrain, for example, a VoxelWorldEditor.

The VoxelWorld.UnloadChunk call would be redirected to ChunkManager, which is responsible for managing chunks. Here’s a picture to better explain it:

Visualization of solution 1

The public VoxelWorld would be the only public class in assembly A. Everything else is internal, meaning they are only visible for other classes inside assembly A. The assembly A is also like a black box, it is mostly (except for the VoxelWorld) hidden from the outside project. It just works, that’s not a good ideology, but sometimes a necessary one. Everything in assembly B is easily extensible and public to the user. It contains the code the user would be messing with.

VoxelWorld would essentially by only a redirector of calls. It would have absolutely no logic, only redirections. A function in VoxelWorld.cs could look like this:

public void LoadChunk(int x, int y, int z){
    ChunkManager.LoadChunk(x, y, z);

Solution 2: Everything that the user wants to add refers to only the classes it really needs. Now, forget all that public/internal/redirecting stuff from solution 1, but keep in mind the different classes. This is kind of like the interface segregation principle, but just without the interface part.

The interface-segregation principle (ISP) states that no client (e.g.
should be forced to depend on methods it does not use
(e.g. LoadChunk)

In solution 1, everything depends on everything. That’s the blessing and the curse of solution 1. In solution 2, that’s not a problem because a class only depends on what it actually needs.

Visualization of solution 1

Solution 2 is more traditional and maybe cleaner -> easier to maintain. I feel like I like solution 2 more than solution 1, but both seem good. Here’s the main benefits and disadvantages:

Solution 1:

+Easy to use API (VoxelWorld.DoWhatever())

-It contains a black box, so it’s harder for the user to extend the very core features. (Of course, it wouldn’t be an actual black box, this is open source, it’s just something that the user shouldn’t mess with)

Solution 2:

+Easier to maintain and extend

-More difficult API, everything is scattered so the user has to explicitly know if some feature already exists (in solution 2, the user can just scroll through the suggested functions for VoxelWorld.___())

So, which solution do you recommend, and why? Or is there some third solution that I haven’t thought about?

This was quite a long question, but I hope it can help others who might have the same problem. I tried googling but didn’t find anything related to this kind of problem, but I didn’t really even know what to search for.

hard drive – How to merge empty partitions to main partition without data loss in main in macOS?

I tried to install Windows in my MacBook Pro (13-inch, Mid 2012) having macOS Mojave. Tried without the bootcamp assistant as directed in the link –

But after re creating the partition as mentioned in the link above, and after the starting of the installation, an error popped up saying – “We couldn’t create a new partition or locate an existing one.”
Upon trying to find out a possible solution, I came across –

‘We couldn’t create a new partition or locate an existing one’ from bootcamp

As I was stuck, the last link having lots of successful results made me understand that I need to have all the partitions combined back to one. Reset the PRAM, and then do the same steps.

To get all the partitions to one, I deleted the ones that showed during the Windows Installation, and formatted them, as the unformatted ones, did not show up in the macOS.

But even after the formatting, the partitions did not show as active in the “Disk Utility”, and showed error either upon mounting, restoring or Erasing.

I am tired of trying to install Windows, as there is some or the other error. I have somehow preserved my MacOS thankfully.

I just want to know how can I get back all the partitioned drives into the main drive as free space.

The combined screenshot of the partitions is below :
enter image description here

And About This Mac shows the storage as below :
enter image description here

I still have the Windows 10 bootable USB.Do I need to delete(and format) partitions from there first?
Any help is greatly appreciated.

postgresql – Update main and second table with a before update trigger for message logging

I currently have the following testing schema:

CREATE TABLE userMessage (
    creator_id BIGINT NOT NULL REFERENCES "User" (id),
    created_at BIGINT NOT NULL,
    modified_at BIGINT NOT NULL,
    content TEXT NOT NULL

CREATE TABLE userMessageLog (
    message_id BIGINT PRIMARY KEY,
    modified_by BIGINT NOT NULL REFERENCES "User"(id),
    modified_at BIGINT NOT NULL,
    content TEXT NOT NULL,

    foreign key (message_id) references userMessage (message_id)

Where who created the message, when and it’s actual content. Then another table where I keep track of who modified (can be another user) the message, when and the previous content.

I also created the following trigger for when the message is first created:

        INSERT INTO userMessageLog(message_id, modified_by, modified_at, content) VALUES (NEW.message_id, NEW.creator_id, NEW.created_at, NEW.content);
        RETURN NEW;
    LANGUAGE plpgsql;


Which works as expected. As soon as something is inserted on userMessage a new log entry will appear on userMessageLog.

My question is, when the user or another user edits that message, how can I create a trigger and modify the content, modified_at columns from userMessage table and add a new entry to the userMessageLog? Is there a more better approach to this schema/trigger design?

My only approach resulted in a failed attempt of creating a trigger on BEFORE UPDATE for userMessage which would make the entry on userMessageLogand then UPDATE the userMessage table, but that would result in recursive calls because of the trigger and I also have no way of letting it know who modified it for modified_by and when it was modified for modified_at column.

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> won’t change after Ajax loaded just the main content

i’m using Ajax to load only the main content of my website, as i have a music player and i don’t want it to stop playing while browsing website.

Everything is working well, except that, as the body is not loading when i change pages, the body classes are not changing either.

How can i force the classes from <body <?php body_class(); ?>> to load even if the body is not loading himself?

Is there a way of adding classes to body after the ajax page is loaded?

I try to get something down inspired by that old post, but i’m SO lost.

  url: "yourloop.php",
  context: document.body
}).done(function() { 

1/ Should i put this code into functions.php or in the javascript file who call the ajax ,at the end?
I tried into functions.php but i get a fatal error, i tried in the .js and nothing happened.

2/ “yourloop.php” should be something like “page.php” or “single.php” (the wp templates)

3/ So if i want to add differents class for a Page or a Post, i should write something like this?

  url: "page.php",
  context: document.body
}).done(function() { 

  url: "single.php",
  context: document.body
}).done(function() { 

4/ What is i want the body class to be dynamic as the <body <?php body_class(); ?> > do it ?

I would appreciate if you can give me more detailed code. 🙂
Thank you for you help!