wireless – Ubuntu (dual boot) can see mobile hotspot but not main network

I can only see other networks including my phone’s hotspot but not my main wifi network.

Everything worked fine up until randomly the connection would be lost at boot and only after restarting the router a couple times (sometimes once, sometimes more) would the network appear and I could connect to it.

my network driver is BCM4352 802.11ac from the bcmwl-kernel-source package.

I tried a lot of the advice online but nothing worked.

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?

mysql – Can I use the main Multisite as a backend only?

I need to implement an admin solution to manage a multitude of existing sites that each lives on an individual subdirectory on the same domain, with their own respective databases, users, themes, etc.

I would like to know if it is possible to have a multisite setup that would use the main site as the backend only, i.e. this main site would not have a public-facing website, and if it is possible, if it would require any special settings? With settings, I am referring to SEO, security, databases, etc.

I am aware that this would require a single database with separate tables instead of separate databases as it currently is used, but could this not be achieved using MySQL imports and exports?

networking – How to configure a optical fiber router modem to allow port forwarding with other connected router/or from main router itself?

I recently got a new fibre connection, the ISP provided me with a wifi modem, although I have a router. Anyway back to the point, I was able to port forward with my old non-wifi modem and router set up
but now I can’t port forward. I have searched the internet fully and I found almost the same situation like this one – How to configure cable modem router to allow port forwarding to other connected router?
But this also did not help me, I hope anyone would help me in this topic relatively soon

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 (http://mi.mathnet.ru/eng/tm1019)
  2. In Hua’s paper “An Improvement of Vinogradov’s Mean-Value Theorem and Several Applications” (https://doi.org/10.1093/qmath/os-20.1.48)

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 $S_{k}(x)$? Thanks!

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.

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.