How to create spaced text fields with a description of the text field at the top of each text field
how to show textview and edittextview on same line?
Solving functional differential equation $f'(x)=2f(2x)-f(x)$ Scenario  I created a journey with a Contact Data entry event that is triggered via the API. A subscriber should be able to be injected multiple times and the values in the data extension are updated while the subscriber is in the journey. The updated values should determine the path the subscriber follows.  Setup  As changed data needs to be evaluated and the contactkey cannot be used as primary key, I added a random id as primary key and created an attribute group for the data extension in Data Designer. The data extension is linked to the contact's contactkey using a one-to-many relationship as a contact should be able to enter the journey multiple times.  In the journey I'm using a decision split that is configured to use contact data from the created attribute group and has two branches (as it checks a boolean value).  Problem  For multiple entries the decision split doesn't evaluate correctly and always leads to same branch (value equals false). I suppose the problem is that journey builder doesn't use the primary key to identify the correct row in the data extension. Is there any way to make sure the row is matched using this id and not the contactkey as this leads to some strange behaviour as described here: if $x_i$ are IID  continuous random variables, with $E[x_i]=μ$, is the following correct?   $E\left[\prod_{i=1}^n(1+⍺\space x_i)^i\right] = \prod_{i=1}^nE\left[(1+⍺\space x_i)^i\right] =  \prod_{i=1}^n(1+⍺\space E\left[x_i\right])^i = (1+⍺\space μ)^n$  thanks! Is it acceptable to use "whose" when referring to an object? Whose is used for people (e.g. "Whose that girl?"), but is it acceptable to use whose for objects too? Is there another word I should use for objects?  To make the question clearer, when I ask "Whose that car?" I am expecting an answer similar to "It's X's car." where X refers to a person. I could say "a man whose opinion I respect." and whose opinion would refer to the opinion of a person. Could I say "the desk whose drawer was broken by my brother"? Should I replace whose with another word? Hadamard Product of $e^z-1$ Assuming the formulas $$\sin(z)=\frac{e^{iz}-e^{-iz}}{2i}\quad\text{and}\quad\frac{\sin(\pi z)}{\pi z}=\prod_{n=1}^\infty\left(1-\frac{z^2}{n^2}\right),$$ I want to find the Hadamard product of $e^z-1$. I think I've done the work correctly, but I end up having an extra factor of $2\pi i$ at the end (this is from Stein and Shakarchi's book and they list the answer for this particular problem). So, my work is \begin{align} e^z-1&amp;=e^{z/2}\left(e^{z/2}-e^{-z/2}\right)\\ \\ &amp;=e^{z/2}\left(e^{i(-iz/2)}-e^{-i(-iz/2)}\right)\\ \\ &amp;=2ie^{z/2}\left(\frac{e^{i(-iz/2)}-e^{-i(-iz/2)}}{2i}\right)\\ \\ &amp;=2ie^{z/2}\sin(-iz/2)\\ \\ &amp;=2\pi i ze^{z/2}\frac{\sin(-iz/2)}{\pi z}\\ \\ &amp;=2\pi i ze^{z/2}\frac{\sin\left(\pi(\frac{-iz}{2\pi})\right)}{\pi z}\tag{*}\\ \\ &amp;=2\pi i ze^{z/2}\prod_{n=1}^\infty\left(1-\frac{\left(\frac{-iz}{2\pi}\right)^2}{n^2}\right)\\ \\ &amp;=2\pi i ze^{z/2}\prod_{n=1}^\infty\left(1+\frac{z^2}{4n^2\pi^2}\right). \end{align}  The answer according to the book is $$e^z-1=e^{z/2}z\prod_{n=1}^\infty\left(1+\frac{z^2}{4n^2\pi^2}\right).$$Have I made a simple mistake in calculation, or are the two somehow compatible with each other?  Update: Thomas Andrews has pointed out a mistake in my infinite product formula. I've corrected that mistake.  $(*)$ The error occurs from this line to the next. Instead of multiplying and dividing by $z$, I should have multiplied and divided by $\frac{-iz}{2\pi}$. That would cause the appropriate cancellation. How to change the name of a thread How did Harry breach the Statute of Secrecy? Something always bothered me with Fudge's accusations:     “Disciplinary hearing of the twelfth of August,” said Fudge in a   ringing voice, and Percy began taking notes at once, “into offences   committed under the Decree for the Reasonable Restriction of Underage   Sorcery and the International Statute of Secrecy by Harry James   Potter, resident at number four, Privet Drive, Little Whinging,   Surrey." - OotP Ch. 8 "The Hearing"   Harry cast the Patronus Charm, so he violated the Decree for Reasonable Restriction of Underage Sorcery alright - extinuating circumstances aside - but how did he breach the Statute of Secrecy?  The only witnesses were Dudley and Mrs. Figg, both of whom already knew that Harry is a wizard. Earlier, even Hermione gets it wrong (don't tell her!):     They haven’t even reported that you broke the International Statute of   Secrecy. We thought they would,... - OotP Ch. 4 "#12"   Yes, Harry does use magic in front of a Muggle, Dudley, but even Dudley is not so thick that the fact that Harry's a wizard would come as a revelation to him. Harry cannot breach the Statute of Secrecy to someone already in the know.  Shouldn't Dumbledore point out that glaring error in the indictment sooner rather than later? Or at least mention it, at all?  Is there maybe a source that mentions the Statute of Secrecy containing a clause, that even the mere possibility of magic being witnessed by an uninitiated muggle is sufficient for its breach?? Cause if so, wouldn't even adult wizards have a really tough time doing anything, ever.  Possibly related: How to disable Ctrl+Shift+U? Ctrl+Shift+U is a combined shortcut in Eclipse. But when I press it, it shows up a u, just like input with an underline. I guess this shortcut has been declared by Ubuntu, so I can't use it. I used to solve this problem by typing Caps Lock first. Is there any better method? I am a Chinese citizen married to a US citizen last year. I am going to apply for a UK tourist visa. The name shows on my passport is my maiden name, while any other documents the UK visa needed, such as bank statement, is with my married name. I can provide my marriage license to prove the link between my maiden name and married mane.   Can I apply for this UK visa with my situation? This is a basic question on Box-Jenkins MA models. As I understand, an MA model is basically a linear regression of time-series values $Y$ against previous error terms $e_t,..., e_{t-n}$. That is, the observation $Y$ is first regressed against its previous values $Y_{t-1}, ..., Y_{t-n}$ and then one or more $Y - \hat{Y}$ values are used as the error terms for the MA model.  But how are the error terms calculated in an ARIMA(0, 0, 2) model? If the MA model is used without an autoregressive part and thus no estimated value, how can I possibly have an error term? Why do prisms work (why is refraction frequency dependent)? It is well known that a  can "split light" by separating different frequencies of light:    Many sources state that the reason this happens is that the  is different for different frequencies.  This is known as .  My question is about why dispersion exists.  Is frequency dependence for refraction a property fundamental to all waves?  Is the effect the result of some sort of non-linearity in response by the refracting material to electromagnetic fields?  Are there (theoretically) any materials that have an essentially constant, non-unity index of refraction (at least for the visible spectrum)? Why does the Prime Directive not apply to Rubicun III? In a first season episode of Star Trek: The Next Generation the Enterprise visits a planet named Rubicun III where () the Edo live.  It is often mentioned in Star Trek that the Prime Directive requires that pre-Warp civilisations be ignored until they discover Warp mechanics. But this planet and civilisation appears to be exempt from that status. Why? Get the size of the screen, current web page and browser window Is it okay to ask a professor from another university for class lecture notes of a course that he offered on that university? I find two very interesting courses that were offered in the Spring 2019 semester at ETH Zürich. Unfortunately, their class lecture notes are not shared publically. I wonder if it is appropriate to email the professors and ask them for class notes. Why 'mkpasswd -m sha-512' produce different result every time it is called? I am using this function to create a password in the shadow file  $ mkpasswd -m sha-512 password $6$o50n4EfNOBzfs$K5l5AcOI5e0I9n2df0LmR11OLSPKSVM6AGBOnWVfDDfMubb46MrAj0zehdLNEoYzD2fj5q4XUdDwexj/dWLHy/ $ mkpasswd -m sha-512 password $6$ADmDOhDpW$gsYQuiKPpV1ewaUpRq2VGAvrcocffLQ8XGF94e6LNLZfKIjy6Ku.cZoR/5exeCi1ESjPB9TRM6HxCiY5BCNCV0 $ mkpasswd -m sha-512 password $6$Efj1agaI$HGkny3q1OTYT4KREh18gueHJae/3Bvil0iOEhfXj8bD.qy9Lg2UIQJMuBcq0XtG3xzueK.7cp0GfKr7tEo5YI/ $ mkpasswd -m sha-512 password $6$zdVPlCPai4Y$x3CBvlP99xZXZcr4PTiE..YLpZx39h5OHDxqazd9wFLImPuwsXF0M6KmqLzlCCrnQhI2lmEPdCzfmHA/fDiOz.   It makes me wonder how does the output value work as a password Why does the field of an electric dipole drop off as $1/r^3$? Electric field of a point charge drops off inverse squarely but that of a dipole varies as $1/r^3$. Why the field drops off more quickly for a dipole? Can I travel domestically within the United States with my USA expired passport? I need to fly domestically within the United States. The only ID I have is an expired USA passport.  Can I use that to pass T.S.A.?  Can I use it as ID? Where do I put item tags on items inside a chest or your inventory? I am making a Minecraft Mini Game adventure map, and one of the levels has a /setblock command, I am using the command in a way to spawn an item in a chest (Wooden Button) I need the wooden button to have CanPlaceOn tag so it can be placed on a log. I have tried this command: setblock 294 5 -1251 minecraft:chest 0 replace {Items:[{Count:1,Slot:0,id:minecraft:wooden_button,CanPlaceOn:[log]}]}` Two homologous but not homotopic loops on a closed surface of genus greater than one Suppose $S$ is a closed surface with genus greater than $1$. Give an example of two loops on $S$ which are not homotopic, but are homologous to each other.   I need help solving this question. I have read the Wikipedia page on it and I realize that it does not contain the necessary knowledge to visualize this problem.  And I was also wondering the relation between the fundamental group $\pi_1(S)$ and the first homology group $H_1(S)$? Some restrictions is that $S$ is a closed surface and the genus is greater than $1$. How do I create Fortify Alchemy enchantments up to 29%?