I conclude the other post from stack-exchange, and Wikipedia, I come up with the following explanation of white noise process. My question is simply want to know whether my understanding is correct or not My explanation:  if a_t is said to be a white noise process white noise process , can be viewed as combination of 2 part, &quot;white noise&quot;&amp;&quot;process&quot; the first part use the physical properties of white noise to describe the statistical properties of the process. The latter part is to point out this sequence of no. is a process. Therefore the white noise process should have the following properties: 1.E(a_t)=0 2.var(a_t)=S^2 3.ACF of a_t =0
What is the best way of defining white noise process so it is intuitive and easy to understand?
Are DSLRs a dying breed, making now the time to switch to a mirrorless camera system? I'm trying to find the infinite sum that is defined by:  $$ 3 \cdot \frac{9}{11} + 4 \cdot \left(\frac{9}{11}\right)^2 + 5 \cdot \left(\frac{9}{11}\right)^3 + \cdots $$  However, I do not know of any known formula to do this. Am I missing something really simple? Thanks! Allow the user to hide its own reputation value and/or badges similarly as visible on wiki pages. If the visitor wants to know your reputation, he/she has to view it on your user page.  Scenarios why to do it:   You have so much rep/badge, that your name gets recognized wherever you post You want to be just helpful and you show this by not advertising how 'good repped' you are, but rather focus on a good answer Implicit 'reputation' by name within the community - same as in the real world   Scenarios why not to do it:   Could impose transparency problems regarding to the site's basic concepts Hard to implement on a per user basis Concerns about showing/hiding it in the question part or in answers.   Discussion welcome.  Follow-up to  of mine. I was considering playing a Summoner in my next Pathfinder campaign, and I decided that I wanted my Eidolon to be a a four-armed giant (the character being a Gnome with a height complex).  Well, I thought to myself: If it has four arms, then shouldn't it be able to wield two two-handed weapons?  As far as I can tell, it should work. That said, how would that work, exactly? I would assume that it would work like usual two-weapon wielding as far as feats and the like, and it would gain all the bonuses from two-weapon wielding as well. However, as this isn't exactly something that happens often, and thus there are no rules for it (that I can find) I can't be sure of any of this. Does anyone know of anything that could help me with this? Split string every nth character? Pure significance of line integrals of vector fields I can understand how the line integral of a scalar function has pure-mathematical significance, representing an area beneath a curve. But is there a pure significance to the line integral of a vector field? The only understanding I have of this is the physical example of work done on a moving particle. Thanks for any insight. Redshifting of Light and the expansion of the universe So I have learned in class that light can get red-shifted as it travels through space. As I understand it, space itself expands and stretches out the wavelength of the light. This results in the light having a lower frequency which equates to lowering its energy.  My question is, where does the energy of the light go? Energy must go somewhere!   Does the energy the light had before go into the mechanism that's expanding the space? I'm imagining that light is being stretched out when its being red-shifted. So would this mean that the energy is still there and that it is just spread out over more space? Why can't I buy the Windhelm house (Hjerim)? I have two user profile fields "Last Name" and "First Name". I also have a user list views. I want to expose "Name" as filter which can search for both Last Name and First Name. How can I do single filter of combination of those two fields? Can I create it from views UI?  One possible way is to create another profile field "Name" which will be hidden in the form. On user save, I would combine the two field values into the "Name" field and then expose it as filter in the views. But this solution is hard coding and it needs to write hooks. has been, have been , had been Please anyone tell me when we have to use "has been, have been , had been" and something  started in past and still continuing is it possible to use has been ? Embedding $S_n$ into $A_{n+2}$ I am trying to prove that for all $n$, $S_n$ is isomorphic to a subgroup of $A_{n+2}$.  Say $S_n$ acts on $\{\alpha_1,...,\alpha_n\}$ and $A_{n+2}$ acts on $\{\alpha_1,...,\alpha_n,\alpha_{n+1},\alpha_{n+2}\}$.  Let $\sigma \in S_n$ and let $\phi: S_n \to A_{n+2}$ be given by $\phi(\sigma)=\sigma$ if $\sigma$ is an even permutation, and $\phi(\sigma)=\sigma(\alpha_{n+1}\alpha_{n+2})$ if $\sigma$ is an odd permutation.  This way $\phi(\sigma) \in A_{n+2}$.  Now, let $\sigma, \rho \in S_n$.  Then $\phi(\sigma \rho)=\sigma \rho (\alpha_{n+1}\alpha_{n+2})$.  Also, $\phi(\sigma)\phi(\rho)=\sigma(\alpha_{n+1}\alpha_{n+2})\rho(\alpha_{n+1}\alpha_{n+2})=\sigma\rho$.  So, $\phi(\sigma \rho)$ does not seem to equal $\phi(\sigma)\phi(\rho)$.  But the idea is that we want $\phi(S_n) \cong S_n$, and $(\alpha_{n+1}\alpha_{n+2})$ does not permute any members of $\{\alpha_1,...,\alpha_n\}$, so $\phi(\sigma \rho)$ and $\phi(\sigma)\phi(\rho)$ are equal as permutations on this (sub)set.  This feels a little subtle to me and I'm not sure if my idea is valid or not.  If it is not, can this proof still be saved?  I appreciate any thoughts on this.  Thanks. Why does a free-falling body experience no force despite accelerating? In C#/VB.NET/.NET, which loop runs faster, for or foreach?  Ever since I read that a for loop works faster than a foreach loop a  I assumed it stood true for all collections, generic collections, all arrays, etc.  I scoured Google and found a few articles, but most of them are inconclusive (read comments on the articles) and open ended.  What would be ideal is to have each scenario listed and the best solution for the same.  For example (just an example of how it should be):   for iterating an array of 1000+ strings - for is better than foreach for iterating over IList (non generic) strings - foreach is better than for   A few references found on the web for the same:               [Edit]  Apart from the readability aspect of it, I am really interested in facts and figures. There are applications where the last mile of performance optimization squeezed do matter. I've tried everything I can think of. Resetting the router, changing the channel number and band.   The internet connection is fine, and then just hangs for a minute or 2, then returns to normal.   The wifi icon remains connected, and I have the latest 10.10.4 update installed. At first I thought it was a DNS bug with Yosemite, and have played with the settings such as changing DNS provider, changing the IPV6 to IPV4 only etc.  Driving me nuts. Has anyone had a similar problem? I've checked the surroundings with wifi scanners and have chosen the best channel available.     One thing I have noticed, it seems a lot more reliable on 5GHz as opposed to 2.4Ghz It seems to affect my Macbook Pro Retina 13in Early 2015 a lot more than the other devices on the network. I'm using a Virginmedia  1. Blocking comment spam without using captcha Once a world enters hardmode, corruption and hallows being spreading at an alarming rate, including the underground. Grass, which grows on dirt, succumbs easily to both. Jungles and glowing mushrooms grow on mud and provide unique and valuable items. Will corruption/hallows destroy these if left unchecked? If they do destroy mud-based life, how can I preserve these fragile ecosystems? How to pull data from internal memory on an unrooted phone? Yesterday, I suddenly discovered that I had lost all the user files on the internal memory of my android phone. All my photos, my music, my PDFs, audio recordings, everything. I will explain the events leading up to this in a separate paragraph below.  I have a Lava Z90 phone and I do not use an external SD card, so I must work with my phone to recover all data. I've been googling and following stuff I get from the internet(including Stack Overflow). Here's what I have done so far.   Tried using photo recovery apps available on Play Store. None of them worked. Decided to go more technical. Enabled USB Debugging and OEM Unlocking from Developer options in my phone. Then I used ADB pull command, pull /dev/block/mmcblk0 /home/data.img to try create an image of the entire internal storage so I can analyse it using PhotoRec. It says pull: not found I assumed this is because my phone isn't rooted?  I tried to root it with the KingoRoot apk but that didn't work. I have Ubuntu on my PC and there is not KingoRoot for Ubuntu. My next step would be to use Wine to run KingoRoot on my machine and try to root my phone that way.   I have the following questions:   How can I create an image, a data dump of my entire internal storage that i can later analyse for my data? Can I do it with an unrooted phone? If not, how can I root my phone with ADB? Am I going about this right? Is there a better, easier way to recover data that I should use instead?   Thank you very much.  How I lost my data  I recently uninstalled the TikTok app from my phone. Yesterday I connected my phone to my PC over mtp and found that there were certain leftover folders on the internal memory. One was a folder with Chinese name, one was a folder called ByteDance and one folder called Thumbnails. I assumed that the first two were leftovers from the TikTok app and the third was mere thumbnails. So I deleted them to save space. Nothing happened that day, except that I couldn't access any of my WhatsApp images through WhatsApp(they were still accessible through the gallery). However, when I woke up the next morning, all my data on the internal memory was gone. I still have contacts my messages and my settings, just that everything that was accessible through the file explorer has disappeared. I read news on the BBC (on its website) this morning. When I was reading the news I noticed the definite article the was missing in a sentence. As per my opinion, the reporter missed the article the. But I also thought that the reporter also had some point as he did not use the article there. So I just wanted to confirm so landed here to get some help on it.     On the website:      It also proclaimed the group's leader, XYZ  (name), as caliph and   "leader for Muslims everywhere".      As per my opinion it should have been:      It also proclaimed the group's leader, XYZ  (name), as the caliph and   "leader for Muslims everywhere".   Source link: What is the function of the RNA primer in DNA replication? During DNA replication, RNA primase puts an RNA primer in the lagging strand. What is the function of this RNA primer? Why can't the enzymes put DNA fragments directly? This is from  .      Let $\mathcal{A}$ be a locally small category, and let $A,A' \in \mathcal{A}$ with $\operatorname{Hom}(-,A) \cong \operatorname{Hom}(-,A')$. Prove directly that $A \cong A'$.     My thoughts:      Let $\eta$ denote the natural isomoprhism between the two functors.    We have    $$H(A,A) \xrightarrow{ \eta_A} H(A,A')$$   So $\eta_A(id_A): A \rightarrow A'$ is a candidate. Now I want to construct inverse.    $$ H(A',A') \xrightarrow{\eta_{A'}} H(A',A)$$   Then the map $\eta^{-1}_{A'} (id_{A'}):A' \rightarrow A$.    So I'd like to show that the composition is identity. By the naturality condition of $\eta$, from $H_A(A) \rightarrow H_{A'}(A')$ (and similarly on other direction)    $$ \eta_A(id_A) \circ \eta^{-1}_{A'}(id_{A'}) = \eta_{A'}(\eta_{A'}^{-1}(id_{A'}))= id_{A'} $$   We deduce these two maps are inverses. Hence $A' \cong A$.    Is this correct? Or is there a neat way to see this?