What's the point of hyperbolic trigonometric functions?
Real world uses of hyperbolic trigonometric functions
One thing that seems to be missing in the Top&nbsp;Bar is a link to the Stack&nbsp;Exchange portal. It only displays under the "Current&nbsp;Community" section when you are in the community, but it disappears as soon as you go to another one.  Would it be possible to add a link that would always be there no matter which community you are currently on? If $11z^{10}+10iz^9+10iz-11 = 0$. Then possible value of $\mid z \mid,$ is Frequently when EM waves are taught, it is said that the change in electric field causes a change in the magnetic field, which then causes a change in the electric field, and so on and so forth.   But from my understanding of basic electromagnetics, it is not necessarily a changing electric field that creates a change in magnetic field, but instead an accelerating charge. and it is this charge that creates both the electric and magnetic field. Again, from my understanding, a changing magnetic field is not generated by a changing electric field, but instead just happens to always be present perpendicular to a changing electric field due to the laws of electromagnetism.   Am I wrong? Or is the "mutual generation" concept between the electric and magnetic components of an EM wave an actual thing? says:     squinch (skwɪntʃ)      (US)      transitive verb         to squint (the eyes); squinched up her eyes in disgust.               2.         a. to pucker or screw up (the face, nose, brow, etc.); Jonathan squinched his face into a grimace.       b. to squeeze or compress; She squinched the paper up in an angry twist and stood to throw it into the stove ; Robert squinched the ketchup bottle, trying to get the last bit out.      intransitive verb         to squint, pucker, or contort   to crouch down or draw oneself together so as to seem smaller; ;  (Source: .)   to flinch         Word Origin: probably blend of squint and pinch      First Known Use: 1835      Example Sentences Including "squinch:"      Cooper saw her squinch up her eyes, trying to make out who was standing outside her kitchen window.      An unhappy smile is still a smile, insofar as the corners of the mouth are drawn back or upturned. However, the eyebrows may be furrowed, and the eyes may be squinched or teary. Also, the lips tend to be pressed together, rather than relaxed as in a happy smile.    My question is, how do native speakers of AmEng use the verb squinch in the senses supported above by CAED?  In addition, what's the difference between using either "squinch" or "squint/flinch" as in the following examples:     She squinched (up) her eyes, trying to make out who was standing outside.      She squinted her eyes, trying to make out who was standing outside.   -and-     The driver squinched as the sun hit his windshield.         -and-              -and-     He squinched as the cold water struck him.         -and- dpkg exit with error parsing file `/var/lib/dpkg/status`, what to do? Does an Evocation shield have a reactive utility to it? Dynamic loading of python modules Let G be a finitely generated abelian group and M a compact manifold,  I want to prove that $H_r(M,G)$ is finitely generated for $r\ge 0 $.  First I was thinking if  I could do induction over $r$ because for $r=0$, $H_0(M,G) \cong \bigoplus_{i=1}^nG$ where $n$ denotes the number of connected components of M.But for $r&gt;0$ I can't see a way to relate $H_r(M,G$) and $H_{r+1}(M,G)$.  Then I tried to use the fact that for every compact surface there exists a finite cover $\{A_i\}_{i=1}^m$ such that the finite intersections of $A_i$'s are contractile.Let $\{A_i\}_{i=1}^m$ such cover for $M$.Then,using induction on $m$, we have :  -For $m=0$, $M$ is contractile and $G$ finitely generated then $H_r(M,G) $is finitely generated.  -For $m=r$ it's true by induction hypothesis.  -For $m=r+1$ now putting $A_{r+1}=B$ and $\cup_{i=1}^r A_i=A$, and using Mayer Vietoris we get:  $$ ...\rightarrow H_{r+1}(A\cap B,G)\rightarrow  H_{r+1}(A,G) \oplus H_{r+1}(B,G) \rightarrow H_{r+1}(M,G)\rightarrow H_{r}(A\cap B,G) \rightarrow...$$   Here I don't know what to do, maybe I'm missing some algebraic argument It's easy to see that $H_{r+1}(A\cap B,G)$ and $H_{r+1}(A,G) \oplus H_{r+1}(B,G)$ are finitely generated.But how can I argue that $H_{r+1}(M,G)$ is finitely generated? Any idea would be aprecciated. Invalid SSL certificate when pushing to Git server How to disable grub menu at boot time in Ubuntu 20.04? Is `if (condition = value)` the correct syntax for comparison? Positive series problem: $\sum\limits_{n\geq1}a_n=+\infty$ implies $\sum_{n\geq1}\frac{a_n}{1+a_n}=+\infty$ Prove $x \equiv a \pmod{p}$ and $x \equiv a \pmod{q}$ then $x \equiv a\pmod{pq}$ I am trying to prove the following by Mathematical Induction:  $$\sum_{i=1}^n i\cdot i! = (n+1)!-1\quad\text{for all integers $n\ge 1$}$$   My proof by Induction follows: First prove $P(1)$ is true,  $$\sum_{i=1}^1 i\cdot i! = (1+1)! - 1$$  Then, for all integers $k &gt;= 1$, if $P(k)$ is true then $P(k+1)$ is also true,  $$ \sum_{i=1}^k i\cdot i! = (k+1)! - 1$$ Then, we must show that $P(k+1)$ is true   $$ \sum_{i=1}^{k+1} i\cdot i! = ((k+1)+1)! - 1\\ \sum_{i=1}^{k+1} i\cdot i! = (k+2)! - 1$$  I am currently struggling with the next step to show that $P(k)$ is equal to $P(k+1)$. How would I finish this prove by induction? Are there any tools for Windows 7 that will allow me to enable/disable monitors from the command-line?  For example, my GTX 480 has three outputs (2x DVI and 1x HDMI) but only two displays can be active at any given time.  I'd like for a command-line to allow me to disable one of the DVI monitors and enable the HDMI monitor, etc.  (I've found NirCmd which is an amazing utility but it doesn't seem to support this...)  EDIT: UltraMon seems capable of doing this but I really hoping for a more light-weight command-line solution... Adverb sentence query "Nikki's and Alice's X" vs. "Nikki and Alice's X" Which option is grammatical?        There will be readings from Nikki Giovanni’s and Alice Walker’s writings.   There will be readings from Nikki Giovanni and Alice Walker's writings.      Saying it out loud the latter sounds right, but looking at it the former looks better. Java reading a file into an ArrayList? Finding the search terms behind 'not provided' We use Google Analytics to track the vistors to our websites, were currently putting together a big audit of our SEO and one of the things we want to see is what search terms are working for us.  About 90% of our organic search traffic comes under 'not provided' which as i understand means a user is signed into a Google account when coming to our site, thus Google doesn't track their search terms.   This makes it really hard to conduct a meaningful study, (i suppose we could get the data of the 10% that we do have search terms for and multiply them it but i dont think thats a particularly good or meaningful approach).  Is there a workaround to see behind the 'not provided' data and see the search terms actually used ?    UPDATE  I read  last night from Hacker news, which states :     [using https will allow you] more complete referrer information in Google Analytics for people   visiting from sites already using HTTPS   and contained a link to this , it seems to say that because Google's users are using https that an https site cannot pass data to an http site, as the http site is not secure, none of the sites i manage have https / sll setup, could some one confirm if Google will pass you more referrer data if your site has https implemented ? How can a network with only ReLU nodes output negative values? I'm trying to use an api with a feedforward neural network for time series forecasting.  For dense aggregate data it works fine, but for sparse data it sometimes forecasts negative values, even though my historical data has only positive values.   The source code is very dense, and I might be missing a line or two, but as far as I can tell, the input layers and the hidden layers are all ReLU nodes.   Assuming I am correct, how can a network with only ReLU layers lead to negative values, especially if none of the training data has negative values?