functions – Computing the sign of an expression

As $sigma>0$ we can divide the expression by $sigma$ without changing its sign. Then, defining $x=(p-v_0)/sigma$, the expression becomes

Sign(Sqrt(2) + E^(x^2/2)*Sqrt(π)*x*Erfc(-x/Sqrt(2)))

This expression seems to be positive for any $xinmathbb{R}$, so I’d say that the answer to your question is that your Sign(...) is always 1:

LogPlot(Sqrt(2) + E^(x^2/2)*Sqrt(π)*x*Erfc(-x/Sqrt(2)), {x, -1000, 10},
  WorkingPrecision -> 100, PlotRange -> All)

enter image description here

The asymptotes of your expression are

  • $sqrt{2}/x^2$ for $xto-infty$, which is positive,
  • $2xsqrt{pi} e^{frac{x^2}{2}}$ for $xto+infty$, which is positive.

When I sign a git commit, what is my signature actually based on?

I took a look at the function “commit_tree_extended” in the git source code for the file “commit.c” (e.g., in this blob).

Based on reviewing this function, when you sign a commit it seems to be signing a string that contains identifiers for the tree object_id, parent object_id, author, committer, encoding (if not utf-8), commit_extra_header, and the commit message.

calculus and analysis – Evaluating the sign of a derivative

Can you kindly help me with the following issue. I am new to Mathematica.
I would like to know the sign of the derivative of a function (for instance whether it is always positive or not). Also, how can I specify that the parameter with respect to which I differentiate can only take positive values?

Here is the function:

D(expr(p, v0, (Sigma)), p)

and below the expressions for the other functions or variables used.

ER(p_, v0_, (Sigma)_) := v0 - (Sigma) (Psi)((p - v0)/(Sigma))/(CapitalPhi)((p - v0)/(Sigma));

del(p_, v0_, (Sigma)_) := - (Psi)((p - v0)/(Sigma))/(CapitalPhi)((p - v0)/(Sigma)) *(- (Psi)((p - v0)/(Sigma))/(CapitalPhi)((p -v0)/(Sigma)) - (p - v0)/(Sigma));

VAR(p_, v0_, (Sigma)_) := (Sigma)^2 (1 - del(p, v0, (Sigma)));

expr(p_, v0_, (Sigma)_) := (p -ER(p, v0, (Sigma)))^2 (CapitalPhi)((p - v0)/(Sigma)) (1 - (CapitalPhi)((p - v0)/(Sigma))) + VAR(p, v0, (Sigma)) (CapitalPhi)((p - v0)/(Sigma));

(CapitalPhi)(x_) := CDF(NormalDistribution(), x);

(Psi)(x_) := PDF(NormalDistribution(), x);

I have tried the following code but it returns an error (probably because it cannot take as an input a function)

Assuming(p > 0 && v0 > 0 && (Sigma) > 0, Simplify(Sign((D(expr(p, v0, (Sigma)), p)))))

Would the compile function be useful in this case?
Thank you so much for your help, highly appreciated.

best practices – Do subdomains inherit DKIM keys? Can a DKIM SDID for one domain be used to validly sign mail that appears to be sent from another domain?

Suppose no DKIM keys are defined for, but a key with selector mykey is defined for; that is, a DKIM record exists at in the DNS. Can <> send mail that is signed using the key described in that DNS record? That is, does inherit the keys defined for its parent,, if it has no keys defined for itself? I can’t seem to find any info about this, neither online in general nor in the RFCs.

A separate, but related concern: For now, I am using the parent domain as the SDID; that is, email sent from <> has a DKIM-Signature header with Receiving mail servers state that it passes the DKIM test, as well as the DMARC test when has a DMARC policy of p=reject;sp=reject. Despite this passing the tests, is this good practice? Would it be better from the perspective of receiving mail servers if had its own DKIM record as well, and then mail from that domain had in the DKIM-Signature header?

I ask this because email for which has seems to be flagged as spam, and it occurred to me that, for example, email from <> or whatever domain could be signed by a key for and pass the DMARC test as long as the DKIM-Signature header has Is this correct, and if so, is this a common/valid spam tactic? If so, are there any measures I can take to prevent spammers from abusing this vulnerability in order to appear as if they are sending mail from domains (or subdomains thereof) that I administer?

It looks like I would have to explicitly define SPF/DKIM/DMARC policies for all domains/subdomains that I intend to send mail from in order to achieve utmost authenticity, but this is undesirable because it is time consuming to maintain. Even then, the DKIM vulnerability described above could still be taken advantage of.

can’t sign up for instagram


I am trying to sign up with instagram for a new account. Whenever I choose a username it shows “Sorry, that username is taken.” then I click on the round arrow for automatic username generator and I click sign up and i get an error “Sorry, something went wrong creating your account. Please try again soon.” and if I click again I get the same as first message “
Sorry, that username is taken.”

so what’s wrong? why can’t I sign up?


What does the blue square and a yellow equal sign mean?

Ive seen this symbol a few time on peoples cars and since it looks like my favicon Im curious what it actually stands for. Its just a blue square with a gold equal sign in the middle, do you know what it is?

A mysterious case of some Yahoo accounts that can’t be used to log in, nor to sign up, what’s the matter?

Yahoo mail deactivates mailboxes that are inactive for at least 12 months, but does not delete the Yahoo account itself.

So if we try to login using the Yahoo login page, and we type an email address, there are 2 possible messages that we would get:

1.] to provide a password for the Yahoo account we entered

2.] or, a message saying that the account does not exist [this message can either appear because either the account really does not exist, or because it once existed, but the owner deleted it, so the username is gone forever and cannot be reused.]

HOWEVER, check out this case yourself: Go to the Yahoo login page. Enter the email, and then see what appears. The following message:


This account has been deactivated due to inactivity, but we would love to welcome you back! Click Sign up below to create your new account.

What could this message mean? I am not sure, so I tried to sign up for that email address, and got the following message on the account registration page:

This email address is not available for sign up, try something else

I am confused. What could be the story behind There are many other addresses with the same story. Did Yahoo delete such accounts due to inactivity? Because they can’t even be used to log in, nor to sign up. What’s the matter?

matrix – ReplaceAll doesn’t replace all, factor out negative sign first

I have this matrix:$$left(
{{0},{0,0,0}} & {{1},{0,0,0}} & {{0},{0,0,0}} & {{0},{0,0,0}} & {{0},{0,0,0}} \
{{-1},{0,0,0}} & {{0},{0,0,0}} & {{0},{0,0,0}} & {{0},{0,0,0}} & {{0},{0,0,0}} \
{{0},{0,0,0}} & {{0},{0,0,0}} & {{0},{0,0,0}} & {{0},{0,z,-y}} & {{0},{-z,0,x}} \
{{0},{0,0,0}} & {{0},{0,0,0}} & {{0},{0,-z,y}} & {{0},{0,0,0}} & {{0},{y,-x,0}} \
{{0},{0,0,0}} & {{0},{0,0,0}} & {{0},{z,0,-x}} & {{0},{-y,x,0}} & {{0},{0,0,0}} \

When I run ReplaceAll (/.) on it using this$$left{{{1},{0,0,0}}to X_1,left{{t},left{frac{2 x}{3},frac{2 y}{3},frac{2 z}{3}right}right}to X_2,{{0},{y,-x,0}}to X_3,{{0},{z,0,-x}}to X_4,{{0},{0,z,-y}}to X_5,{{0},{0,0,0}}to 0right}$$

it doesn’t replace everything:

0 & X_1 & 0 & 0 & 0 \
{{-1},{0,0,0}} & 0 & 0 & 0 & 0 \
0 & 0 & 0 & X_5 & {{0},{-z,0,x}} \
0 & 0 & {{0},{0,-z,y}} & 0 & X_3 \
0 & 0 & X_4 & {{0},{-y,x,0}} & 0 \

I expect:$$left(
0 & X_1 & 0 & 0 & 0 \
-X_1 & 0 & 0 & 0 & 0 \
0 & 0 & 0 & X_5 & -X_4 \
0 & 0 & -X_5 & 0 & X_3 \
0 & 0 & X_4 & -X_3 & 0 \

Is there an automated way of doing these replacements?

How to digitally sign some pdfs inside a SharePoint, but without Adobe Sign

So, my main question is: How do I digitally sign a pdf in SharePoint using(after it’s implemented/ created in Visual Studio) a personal Add-In, without using that Adobe Sign stuff. I tried the links from Microsoft, but didn’t do anything and had lots of errors.

I think the main problem is that I have to upload the files in SharePoint (from a developer site to a Communication Site, I think, or just in the dev site) and after that how should that sign be happening?

redirect – What page should be shown to the user after s/he sign out?

Logging out is a particular task users will do, and should be treated like any other. It needs its own page, which should accomplish the following:

  1. Let the user know they have successfully logged out. (If the user is taking the time to log out, privacy is important to them. You want to assure them logout is complete.)
  2. Leave a good final impression, for instance by thanking your user.
  3. Provide the user with the options they may want, for example, to log back in (but don’t make this obnoxiously prevalent)

Logging out is a “Happy Ending” User Story

A user logging out means they had logged in before — that means you are dealing with your most engaged users. Don’t be “clingy” when they say bye.

Consider user stories for someone logging out. (And check your website analytics to fact-check your notions.)


  1. They may be finished with what they came to do.

  2. They may want to log into a different account.

  3. Maybe they just want to see what your site looks like when they are
    not logged into their own account (for example, they might want to
    see what their online profile/resume looks like to the public).

Let the Marketing Department worry about what they want the user to see (or consider that when you are wearing your “marketing hat.”) As a UX professional, focus on what your users want to do.