photoshop – Erase tool partial opacity on Layer Mask?

Don’t use Erase on layer masks, just use the brush.
Pick a colour – well, two colours, white to paint in, black to paint out, grey if you need finer control [though I personally use the opacity & flow controls instead of greys].

Use X to flip between the two quickly. enter image description here

Erase erases to the current background colour, which not only is a variable, just like the brush, but will also erase bits you didn’t mean to, as it indiscriminately erases both black & white [and any grey in between] back to itself.

backup – How to import partial Firefox browsing history?

Strangely my Firefox browsing history that’s older than a few months is missing. I don’t know why as I have set “Firefox will Remember history” in the options and expected it to have it remember all browsing history (and I can’t increase places.history.expiration.max_pages). But that would be a separate question.

Now I’d like to restore my browsing history from a backup of the places.sqlite file. It has browsing history older than the few months currently stored in the browser (I checked it with “DB Browser for SQLite”).

How can I restore the browsing history stored in that file without losing the latest history? Simply replacing the places.sqlite file wouldn’t work. Basically I just need to merge entries of the older places.sqlite into the newer file (probably via the url column). Furthermore, I’d like to try to restore various places.sqlite files from backups so that it only imports entries if it detected that the file has entries that are missing from the current browsing history.

I’m using Debian/KDE and while restoring partial history backups doesn’t seem to be possible with WhatsApp I’m sure it’s possible with Firefox.

Partial correctness for array multiplication [closed]

Can someone help me to prove partial correctness and termination for array multiplication.

google sheets – Conditional Formatting w/multiple conditions and partial text match

cells that do not match the conditions are getting highlighted and cells with the conditions are being omitted

That sound like you need a NOT to negate the result.

column C’s matching row begins with “EM”

The regular expression now matches all content which contains EM, so you probably need to replace the argument with "^EM"; the caret indicates the beginning of the content. (That’s a standard regex operator; as indicated here, Google Sheets uses the RE2 version.)

You could try this:


and see whether it works for you.

Partial sums of $sum_0^infty z^n$

Let $z$ be a complex number with $|z|<1$. For every subset $Asubsetmathbb N$, the series $sum_{min A}z^m$ is convergent. Denote $S(A)$ is sum and $Sigma$ the set of all numbers $S(A)$. Remark that the cardinal of $Sigma$ is (likely) that of ${cal P}({mathbb N})$, the continuum.

Is it possible that $Sigma$ be a neighbourhood of the origin ?

partial differential equations – Difference between Fourier series on $(0,l)$ and Fourier series on $[0,l]$

I’m currently using Strauss’s partial differential equations book and there is something that confuses me. The Fourier series of $f(x)=x$ on $(0,l)$ is not the same on $(0,l)$.

For $(0,l)$ the Fourier series is
$$x=frac{2l}{pi} sum_{n=1}^{infty} frac{(-1)^{n+1}}{n}text{sin}left(frac{npi x}{l}right)$$
For $(0,l)$ the Fourier series is
$$x=frac{l}{2}-frac{4l}{pi^{2}}sum_{n=1,3,5,…}text{cos}left(frac{mpi x}{l}right)$$

Why $(0,l)$ has sine series but $(0,l)$ has cosine series?

Calculate Aliexpress partial refund sum when using coupons

Consider following order:

Total:              440.86  -  Price of 2 pieces
Seller coupons:      77.62  -  Seller coupon 77.62 of 350
Coins:                6.99  -  Mobile coins discount
Total Amount:       356.26

AliExpress coupons: 200.00  -  Aliexpress coupon 200 of 350
Payed:              156.26  -  The sum I've payed to aliexpress

Now I’m opening dispute.

I want to receive 156.26 / 2 = 78.16 as money.
Aliexpress specifies limits up to 356.26.

I’m not sure what discounts will be subtracted from the sum I will specify for refund. As I understand Aliexpress coupon will be, so I have to specify at least 278.16. But I remember that in previous disputes Seller coupons was subtracted too.

How should I calculate the correct sum to specify in dispute?

Laplace equation with mixed partial

I would like to numerically solve a modified Laplace PDE (with source terms) and that has a mixed second order partial derivative,

enter the image description here

and is limited to the following region

enter the image description here

and periodic boundary conditions.

The code used is

eq = m Sin((Theta)) + 
   A2 Sin((Theta)) Cos((Theta)) D(
     F((Theta), (Phi)), {(Theta), 1}) + 
   A2 Sin((Theta))^2 D(F((Theta), (Phi)), {(Theta), 2}) + 
   A3 D(F((Theta), (Phi)), {(Phi), 2}) + 
   D(F((Theta), (Phi)), {(Theta), 1}, {(Phi), 1});

sol = NDSolveValue({eq == 0, F(0, (Phi)) == F(2 (Pi), (Phi)), 
    F((Theta), 0) == F((Theta), (Pi)) == 0}, 
   F, {(Theta), 0, 2 (Pi)}, {(Phi), 0, (Pi)});

However, the following note appears.

NDSolveValue :: ivone: Limit values ​​can only be specified for one
independent variable. Initial values ​​can only be specified in one
value of the other independent variable. >>

Can anybody help me?

Performance: Combine array elements based on partial array key names

I have a multidimensional array given as:

$givenArray = (
    'one__111__' => ( 'more' => '000'),
    'one__111__xyz' => ( 'more' => '000'),
    'hey__121__' => ( 'more' => '000'),
    'hey__121__abc' => ( 'more' => '000'),
    'zzz__212__' => ( 'more' => '000'),
    'zzz__212__b' => ( 'more' => '000'),
    'abc__3__' => ( 'more' => '000'),

I need to assign the pairs if they start with the same key name. so one__111__ and one__111__xyz it's a pair because both code names start with one__111__

The result looks like this:

    ('one__111__') => (
        (0) => ('one__111__' => ('more' => '00')),
        (1) => ('one__111__xyz' => ('more' => '000'))
    ('hey__121__') =>
        (0) => ('hey__121__' => ('more' => '00')),
        (1) => ('hey__121__abc' => ('more' => '00'))
    ('zzz__212__') =>
        (0) => ('zzz__212__' => ('more' => '00')),
        (1) => ('zzz__212__b' => ('more' => '00'))
    ('abc__3__') =>
        (0) => ('abc__3__' => ('more' => '00'))

It is solved with O (n2), which I hope can be done better.

$result = ();

foreach($givenArray as $key => $value) {
    foreach($result as $resultItemKey => $resultItemValue) {
        if(substr($key, 0, strlen($resultItemKey)) === $resultItemKey)  {
            $result($resultItemKey)() = ($key => $value);
            continue 2;
    $result($key)() = ($key => $value);

Can anyone show me how? Sandbox code to play

Partial Differential Equations – Solution Test for Nonlinear PDE

How can you prove that a nonlinear PDE, let's say heat equation
begin {cases}
u_ {tt} = u_ {xx} + u ^ 2 -3, quad x in (0,1), t> 0 \
u (0, t) = u (1, t) = 0 \
u (x, 0) = g (x)
end {cases}

has at most one solution in $ C ^ 2 ((0,1) times (0, infty)) $?

The book I am using already assumes this is true and does not go into detail as to why this is so. I have tried searching the Internet for answers but with no luck.