$mail = new PHPMailer(true);             try {                 //Server settings                 $mail-&gt;AddReplyTo('from@from.com','Post');                 $mail-&gt;SMTPDebug = 1;                                                  $mail-&gt;isSMTP();                                                       $mail-&gt;Host = 'smtp.example.com';                   $mail-&gt;SMTPAuth = true;                                                $mail-&gt;SMTPSecure = 'ssl';                 $mail-&gt;Username = 'from@from.com';                                  $mail-&gt;Password = 'loginPassword';                                            $mail-&gt;Port = 465;                 $mail-&gt;isHTML(true);                  $mail-&gt;setFrom('from@from.com,'Name');                 $mail-&gt;addAddress('to@to.com', 'Name');                  //Content                 $mail-&gt;isHTML(true);                                                   $mail-&gt;Subject = $mailSub;                 $mail-&gt;Body    = $mailMsg;                 $mail-&gt;AltBody = $mailMsgAlt;                  $mail-&gt;send();                 echo "Mail sent!;             }catch (Exception $e){                 echo "Mail not sent! Try again.";             }   This is how my code looks like, ofc the $mailSub, $mailMsg, $mailMsgAlt variables are defined! Can you help me please, I can't find why the mails always go to the spam folder.
This is a tricky one and I've always relied on techniques, such as permission-based emails (i.e. only sending to people you have permission to send to) and not using blatantly spamish terminology.  Of late, some of the emails I send out programmatically have started being shuffled into people's spam folder automatically and I'm wondering what I can do about it.  This is despite the fact that these particular emails are not ones that humans would mark as spam, specifically, they are emails that contain license keys that people have paid good money for, so I don't think they're going to consider them spam  I figure this is a big topic in which I am essentially an ignorant simpleton.
Folland, "Real Analysis", Chapter 5.3, Exercise 36:     Let $\mathcal{X}$ be a separable Banach space and let $\mu$ be   counting measure on $\mathbf{N}$.  Suppose that   $\left\{x_n\right\}_1^\infty$ is a countable dense subset of the unit   ball of $\mathcal{X}$, and define $T \colon L^1(\mu) \to \mathcal{X}$   by $Tf = \sum_1^\infty f(n) x_n$.  (a)  $T$ is bounded.  (b)  $T$ is   surjective.   I have proved (a).  I would like help on (b).  Here are my ideas so far.    Say we want to show $y \in \mathcal{X}$ is in the image of $T$.  Reduce to the case $||y|| = 1$ and let $x_{n_m} \to y$.  My thought is to produce for each $N$ a function $f_N \in L^1(\mu)$ such that $||y - \sum_n^\infty f(n)x_n|| &lt; 1/N$ and also such that the $f_N$ converge in $L^1(\mu)$ to some $f \in L^1(\mu)$.  Then use the continuity of $T$ to conclude $T(f) = y$.    The way I have been setting up my inequalities is as follows. Pick $M_N$ such that for all $m &gt; M_N$, $||y - x_{n_m}|| &lt; 1/N$.  Then I want to define $f_N$ so that $$\sum_n^\infty f_N(n) = \sum_{m &gt; M_N}^\infty f_N(m) = 1, $$ hence $$||y - T(f_N)|| = ||\sum_{m &gt; M_N}^\infty f_N(m) y + \sum_n^\infty f_N(n)x_n|| \leq \sum_{m &gt; M_N}^\infty f_N(m) || y - x_{n_m} || &lt; \frac{1}{N}. $$  Presumably, if the $f_N$ are appropriately chosen, then I can find a dominating function and apply the Dominated Convergence Theorem to finish up.    However, getting all these hypotheses to hold simultaneously has been difficult.  In essence, the difficulty seems to be in requiring that the $f_N$ be "normalized" as well as possess a dominating function.  If this method is feasible, at least it seems to require a bit of analysis to show the desired series all converge.  Perhaps I am missing something cleaner.  If so, a simpler solution would be much appreciated.    -Thanks. Show $f$ can't be irreducible over a finite field if $f^\prime$ is the zero polynomial. Proving that $\arctan(x)+\arctan(1/x)=\pm \pi/2$, could this line of reasoning possibly be correct? Spurious space above align environment at top of page/minipage It seems that the align environment adds additional vertical space if it starts at the top of a page or minipage.  Below are two pages, and two minipages (on Page 1), where the first page/minipage has text followed by an align* environment, and the second page/minipage starts with an align* environment, and note that the equations are still aligned.  Attempted Solution: The closest related question I found was:    I attempted to use the  at the above by adding \setlength\abovedisplayskip{0pt} (after the preamble as per ).  Although, this did move the equations up vertically, they were still vertically aligned:  And since the problem occurs at top of a page as well, I don't think this is related to  Question:  How can I adjust the align environment to automagically not have additional space at the top of a page or minipage? Is there a reason for this behavior, and perhaps should not be changed?  Code: \documentclass{article} \usepackage[showframe,paperwidth=3.5in,paperheight=2.2in,margin=0.5in]{geometry} \usepackage{amsmath}  \begin{document}%\setlength\abovedisplayskip{0pt} Top of Page 1 \begin{align*}% Text above at top of page  e &amp;= m c^2 \end{align*}  \hrule \begin{minipage}[t]{0.45\linewidth}     Top of minipage 1     \begin{align*}% Text above this minipage      e &amp;= m c^2     \end{align*} \end{minipage} \begin{minipage}[t]{0.45\linewidth}     \begin{align*}% No text above in this minipage      e &amp;= m c^2     \end{align*} \end{minipage}  \newpage \begin{align*}% No text above at top of page  e &amp;= m c^2 \end{align*} \end{document} Definitions of "linearity" across branches of mathematics or levels of math education Linearity is a ubiquitous concept in mathematics; however, each branch of mathematics appears to have its own definition of what a linear map (function, functional, functor, transformation, form, operator, or whatsoever) is. These different definitions can lead to confusion, especially when people apply conflicting definitions of linearity to the same mathematical object (just  to figure out what I mean).  One of my favorite examples with potential for conflict is the natural logarithm $\ln : \mathbb{R}_{&gt;0} \to \mathbb{R}$, which the majority of people, as I could learn during hot disputations not only  but also with colleagues in my field, regard as clearly non-linear, even though it fully complies with the definition of a linear map from the vector space $\mathbb{R}_{&gt;0}$ to the vector space $\mathbb{R}$ (cf. Definition 4 below). A similar conflict arises analogously for the exponential function $\exp :\mathbb{R} \to \mathbb{R}_{&gt;0}$.  I do not want to initiate yet another discussion here, about what the right and what the wrong definition of linearity is! Rather, ...  ... I would like to compile a list of existing definitions, to get a better overview of the different uses of the term "linearity" across the different branches of mathematics and levels of education.    Let be begin with the following four, which are certainly far from constituting a complete list. What about bilinear or multilinear forms, linear morphisms and linear functors in category theory, linear metrics, or other concepts of linearity? I am looking forward to see your answers.  At school I was taught that     Definition 1:   A function $f$ is linear if it is of the form $f(x) = ax + b$.   Later I learned that $f(x) = ax + b$ is affine, rather than linear, because     Definition 2:   A function $f$ is linear if it is of the form $f(x) = ax$.   From real analysis and systems theory, I know the following     Definition 3:   A map $f$ is linear if         $f(x + y) = f(x) + f(y)$   $f(a \cdot x) = a \cdot f(x)$.      This definition also applies to the expected value in statistics, as        $\mathrm{E}(X + Y) = \mathrm{E}(X) + \mathrm{E}(Y)$   $\mathrm{E}(a \cdot X) = a \cdot \mathrm{E}(X)$.      In a linear algebra course, I learned for the first time that we must not forget to take into account that the vector-space operations of the domain and the codomain of a map $f$ may be dissimilar. In fact, if $(V, \oplus, \odot)$ and $(W, \boxplus, \boxdot)$ are two $\mathbb{K}$-vector spaces, then     Definition 4:   A map $f : V \to W$ is linear if         $f(x \oplus y) = f(x) \boxplus f(y)$   $f(a \odot x) = a \boxdot f(x)$.         Notice that I deliberately used distinct symbols for the operations in both vector spaces, to emphasize how this definition differs from Definition 3.   Correct me if I am wrong, but this definition should also apply to maps between two modules.    Updates: I accidentally killed the orphanage lady before I started the quest. She just pissed me off, sadly it will not acknowledge that I have finished the quest and I haven't been contacted. Is there another way to join the Dark Brotherhood? Why were the villagers and the axe-wielding hitman brothers crawling towards a shrine? At the start of Season 3 Breaking Bad, we see a bunch of villagers and Tuco's cousins crawling on their bellies towards some shrine where they put a drawing of Walter White as some kind of "offering".  Why were the villagers and the cousins crawling towards this shrine? I'm running macOS 10.15 Catalina Beta.  When I try to install Spotify I see the following error:    Is this a Spotify issue or a Catalina issue?  Thanks. Threshold Secret sharing - How to create a shared secret from pre existing secret parts? In usual $(t, n)$ secret sharing schemes, a secret $S$ is split into $n$ parts so that any $t$ out of $n$ parts reconstruct the original secret. So, suppose that there is a group of $n$ participants each one has a secret $x_i$ ($x_i$ may be its private key). My question is, is it possible to create a secret $S$ using the prexisting secrets $x_i$ ($i=1...n$) so that with any $t$ out of $n$ from these secrets ($x_i$) we can find the secret $S$? Schwarz's Lemma, fixed points question Why do metals only glow red, yellow and white and not through the full range of the spectrum? When do mobs despawn in Minecraft? I understand monsters only spawn in a 9 x 9 grid of chunks centered on the player, and I assume they stay around while they remain within that distance of you. But do they despawn as soon as you move away from them? Or do they remain? If so what (if anything) causes them to despawn? Are the rules any different for passive mobs?  Will running far away from an area and then coming right back clear it of monsters? How many squares actually ARE in this picture? Is this a trick question with no right answer? This is one of those popular pictures on sites like Facebook. I always see a huge variation of answers such as $8, 9, 16, 17, 24, 28, 30, 40, 41, 52,$ etc., yet I've never seen a definitive answer on any website.    I counted $16$ whole squares ($4$ going down on left side, $4$ going down on right side, $8$ small squares in the centre). With this method the answer could also be $17$ if you want to count the entire shape as one big square.  I can also see the answer being $24$ if you count the smaller squares separately, as if they were floating above the main grid instead of intersecting with it.  Is there a right answer, or is it possible that there is no 'right' answer and it just depends on your counting method? Today I was told a tale by a Unix trainer where the root password got leaked to the students, and one of the fellas removed the execute permission from /usr/bin/chmod itself. How do you recover chmod in this case and make it executable again? Let's say getting it from an external source or recompiling it is not a preferable option, is there some smart hack that can recover this chmod itself?   Note that this happened a long time ago and I'm not looking for a solution for some current problem, just curious about what ways Unix provides us around such an issue. Log color bar/meta data in PGFPLOT Play a Sound with Python What are routed events and how it's different from normal events Run 32bit applications on Windows 10 64 Bit I've got a Windows 10 Computer (home edition), which has 4GB of Ram and an i5 processor. I need to run an old 32 bit accounting programme. The vendor said it won't release a 64 bit version (although a 64bit version exists, it's missing key features from the older version).  The programme installs fine, but when I click on the programme icon, it says the programme won't work on a 64 bit system.   What options do I have?    I've done a fair bit of research, but it seems to run up dead ends.   1) WoW64     Apparently, this is supposed to let you run 32 bits on 64 bit Windows. However, I am not sure how to install it. I think it's for web servers only. However,  says it can work on Windows 7, but doesn't explain how to set it up (or if it will work on Windows 10).  2) XP mode     A 32bit Windows XP emulator. However, it seems to be for Windows 7 only. Also according to this , you need Windows Professional.   3) Virtual Box Machine    Let's you emulate Windows. Seems overkill for my purposes. Plus I would need to buy a 32 bit Windows license. I think it would run slowly with 4GB of Ram.  4) Partition drive into 32bit and 64 bit versions Apparently, you can use the free tool  to split the drive into two and then install separate 32bit and 64 bit versions.   Again, seems overkill and it looks like I would need buy a 32 bit Windows 10 license.   Are these my only options?     Images  Installation    First run (From the error message I guess it's a 16-bit program)   Clicking on programme What are good starting settings to store for exposure bracketing shots? I started experimenting with the Custom Functions (C1,C2,C3) on my Canon 7D and I decided a useful one to have may be setting it up for exposure bracketing. So it's a quick switch if I ever need it, as opposed to going through the menu to set it up.  I realize the settings would vastly depend on the situation, but do you have any suggestions for some good all round settings to program in as a starting point?    Examples: 1 stop vs 1 1/3 vs 2 stop brackets / ISO choices / Metering mode / shooting mode and so on. How to navigate to C drive in bash on WSL-Ubuntu?