differential equations – Solve PDE with contraints and unknown boundary conditions

I have a 2D PDE

mu = -0.1;
lambda = -1;
x10 = 0;
x20 = 0;
eq = {mu*x1 + D(h1(x1, x2), x1)*mu*x1 + 
     D(h1(x1, x2), x2)*lambda*(x2 - x1^2) == mu*(x1 + h1(x1, x2)), 
   lambda*(x2 - x1^2) + D(h2(x1, x2), x1)*mu*x1 + 
     D(h2(x1, x2), x2)*lambda*(x2 - x1^2) == 
    lambda*(x2 + h2(x1, x2))};

The problem is that I don’t know the boundary condition of the PDE, but I do have a constraint that the gradient of h1 and h2 at point (x10, x20) is zero.

D(h1(x1, x2), x1)/.{x1 -> x10, x2 -> x20} == 0
D(h1(x1, x2), x2)/.{x1 -> x10, x2 -> x20} == 0
D(h2(x1, x2), x1)/.{x1 -> x10, x2 -> x20} == 0
D(h2(x1, x2), x2)/.{x1 -> x10, x2 -> x20} == 0

How can I approximate h1(x1, x2) and h2(x1, x2) numerically in Mathematica?

fitting – finding FWHM of a dataset with unknown mathematical equation


dataset = {{0., 0.0518175}, {1., 0.0306299}, {1.9, 0.610295}, {2., 
    1.32653}, {2.2, 4.01183}, {2.5, 6.37931}, {3., 6.50091}, {5., 
    6.54052}, {6., 6.57276}, {8.2, 6.59119}, {15., 6.56125}, {20., 
    6.5267}, {30., 6.4484}, {45., 6.2987}, {60., 6.11953}, {75., 
    5.84962}, {90., 5.43738}, {100., 4.96757}, {105., 4.54382}, {120., 
    3.42917}, {135., 2.23092}, {150., 1.55222}, {165., 0.679385}, {180., 

f = Interpolation(dataset, InterpolationOrder -> 1);

The peak of the function is

max = MaxValue({f(x), 0 < x < 180}, x)

(* 6.59119 *)

The full width at half maximum (FWHM) is

FWHM = Subtract @@ 
  Reverse(HM = (x /. FindRoot(f(x) == max/2, {x, #}) & /@ {2.1, 125}))

(* 119.525 *)

pts = {Log(#), max/2} & /@ HM;

dataplot = ListLogLinearPlot(dataset,
  PlotStyle -> {Dashing({.0071, 0.005, 0.005}), Blue},
  PlotMarkers -> {●, 15},
  Joined -> True, Frame -> True,
  FrameStyle -> Directive(Black, Thickness(0.002)),
  FrameLabel -> {Style("x", Black, FontFamily -> "Times New Roman", 
     FontSize -> 26), 
    Style("y", Black, FontFamily -> "Times", FontSize -> 26)},
  PlotRange -> {{1, 190}, {1, 7.2}},
  FrameTicks -> Automatic,
  ImageSize -> 360,
  BaseStyle -> {FontFamily -> "Times", FontSize -> 10},
  Epilog -> {Text(StringForm("FWHM = ``", FWHM), {Log(15), max/2}, {0, -2}),
    Red, Line(pts)})

enter image description here

hardware – What does voice network type unknown mean in my settings

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seo – URL is unknown to Google – Will this still be indexed?

I am cloaking my website over a site I have developed in replit, but found a way to cloak over a pre-existing domain through managing DNS records and choosing a “cloak” method. This is a simple way to benefit easily from the domain without paying any extra cost, other than buying the domain name itself, which is what I have used.

I know a substantial amount of SEO and ranking, but never have used it. I am trying to get my page indexed by google, this displays this page after testing for a URL inspection.

Could this be a potential block due to “cloaking” as it could be used maliciously or is there any other way to do this in a similar way? Or use of CNAME to display over a domain?

The page is also very simple, mobile friendly design and does not have any other pages that may need to be crawled which is why something must be going on as it would have already been indexed for a page like this within 24 hours or less even.
enter image description here

However, on the status page of my website, it includes:
URL is unknown to Google and doesn’t provide much else information on about it.
enter image description here

Does this information seem normal to be “Not Applicable” as it just wasn’t indexed? then why would it say “indexing allowed? N/A” when it also displays it can be reached by google and “could” be indexed and selected as canonical.
enter image description here

I have done research about this issue, but most of them are old and outdated which doesn’t help or provide extended detail about the issue.
I just find it gets confusing as it says “URL is available to google” and it could be selected and scanned as canonical, on the other hand, some research shows that it won’t be indexed but never provides any other information about the issue.

The page is a portfolio site, which I am first practicing SEO on with all the the knowledge I have read from the guides that google has fully provided. But I need it to be indexed as a goal that I can use for further websites or highly informational websites I use or create in the future. Hope anyone here has knowledge about Search engine optimization, as the google support is always slow and I have tried to search for other communities but none were available.

Hopefully someone can give some reason or a detailed explanation of what is going on. Thanks!

magento2.3 – PHP: How to move an array element with an unknown key to end?

<?php $array = array(array
        "value" => 4,
        "label" => "red",
        "value" => 5,
        "label" => "pink",
        "value" => 6,
        "label" => "blue",
        "value" => 7,
        "label" => "yellow",
        "value" => 8,
        "label" => "white",
        "value" => 9,
        "label" => "black",

foreach ($array as $key => $val) {
    if ($val("label") == 'blue') {
        $item = $array($key);
        array_push($array, $item);


$val(“label”) change it on your need


8 – Unknown column when trying to use JSON_EXTRACT in where clause

This query is working directly in Mysql:

SELECT entity_id FROM node__field_json WHERE
JSON_EXTRACT(field_json_value, “$.mpk”) = ‘014005’

I cannot make it working in Drupal:

$query = 'SELECT entity_id FROM node__field_json WHERE JSON_EXTRACT(field_json_value, "$.mpk") = :symbol';
$result = $this->database->query($query, (':symbol' => '014005'))->execute();

An error:

SQLSTATE(42S22): Column not found: 1054 Unknown column ‘$.mpk’ in
‘where clause’: SELECT entity_id FROM node__field_json WHERE
JSON_EXTRACT(field _json_value, “$.mpk”) = :symbol; Array

  (:symbol) => 014005                                                                                                                               > )

ubuntu – unknown site pages under domain/sub-domain

few months ago i’ve created two subdomains pointing to wordpress sites, like i did for my main domain, the only difference is that i found that both of them have strage results in google search.

enter image description here

Right now google sent me an email sayng that something was wrong with my subdomains and i’m wondering what happend and what can i do.

I’m using didgitalocean as server provider and ubuntu 20 as os.
I did an hardening on the server using this script that make the setup of tools like
ufw, fail2ban, aide, clamAv, maldet, rkhunter, logwatch, auditd, psad, lynis, and relative mail alerts, but i recived nothing strange from mails.

Any thoughts?

I’ don’t know what kind of informations can be usefull so if needed ask them, thanks!

Unknown Address Format Parsing Bitcoin Addresses from Blockchair Data

Having investigated this following @MCCCS answer, the following is information about the addresses provided by Blockhair support:

In fact, there are no addresses on the Bitcoin blockchain. There are
only scripts, some of them are standard and can be converted to a
Bitcoin address, some of them can’t β€” like nulldata (OP_RETURN)
outputs, nonstandard, and bare multisig. We use the d- prefix for
nulldata, m- for bare multisig, and s- for everything else.

This is briefly mentioned in this API documentation section:

Therefore, these addresses (for want of a better word) are valid transactions on the Bitcoin blockchain.

The prefixes used are:

  • d- nulldata
  • m- bare multisig
  • s- everything else

In conclusion, the data is valid but the outputs are not addresses in the normal sense of the word.

A link to the issue I raised on the Blockchair GitHub is here.

PHP Regex preg_match: Unknown modifier

I’m trying to make a function that allows a string only certain characters, but it’s not working. Here is my code:

$passRegex = '/(^A-Za-z0-9!";#$%&'()*+,-./:;<=>?@()^_`{|})/';

if(preg_match($passRegex, $str)) // invalid 

But it throws

Warning:  preg_match(): Unknown modifier ''

This is the char list I want to allow:


cpu – What is wrong with my Mac? Unknown df process

I am using a 13-inch MBP 2019 running macOS 11.1.

My Mac has been running extremely slowly starting today. It seems as though a process called “df” is the problem, but I can’t figure out what it is:
Activity monitor showing df process

What is it and why is it using all of my CPU? I was barely able to open the Activity Monitor because the computer was running so slowly and hot (spotlight didn’t work, so I had to find it in Finder). The only thing that helps is restarting the computer, but it keeps happening.