I have recently bought a property and am re-doing the kitchen. Whilst stripping the old kitchen the builder has come accross some pipes which I ideally want removed. Have attached images of the pipes. These pipes seem to end up below the staircase and are capped over there. So they dont seem to be going anywhere further. Can someone let me know if these are water or gas pipes and if it safe to tamper with them i.e. cut and cap them at the floor level itself.!  enter image description here
I recently moved into an in-law unit of a large old house.  In the kitchen, there are two pipes coming out of the wall (one protruding out a little more than the other).  I had assumed they were gas lines to connect my stove.  But since the stove only connects to one pipe, I'm now wondering if they're actually water lines. Can anyone explain how I can tell the difference? On the other side of the wall is a large closet with the air conditioning system, water heater, and what I think is the gas shutoff valve.
Let $A$ be a $3\times 4$ and $b$ be a $3\times 1$ matrix with integer entries.Suppose that the system $Ax=b$ has a complex solution. Then which of the following are true? (CSIR December 2014)         $Ax=b$ has an integer solution.    $Ax=b$ has a rational solution.   The set of real solutions to $Ax=0$ has a basis consisting of rational solutions.   If $b$ is not equal to zero then $A$ has positive rank.      Is it possible to say that 1 and 2 are true as $Ax=b$ has a complex solution? If not  what we have to understand from the statement "the system $Ax=b$ has a complex solution " ? What about 3 and 4  ? Let $D = B(0,1) \subset \mathbb{C} $ a disc, $f$ holomorphic on $D$. I want to demonstrate that if $$ 2|f^{'}(0)| = \sup_{z, w \in D} |f(z)-f(w)|$$  then $f$ is linear.   I know this is a well-known result. Where can I find the proof ? What makes a field not groupable I'm trying to use an aggregate query, but one of the fields I want to group by is not groupable (saw it in the soql error and then verified groupable=false in the metadata).  It's just a number field that holds an integer (number 2,0 in salesforce field spec-speak).  Is there a trick to make it groupable?  Any way around this problem? I don't want to write hundreds of lines of code just to average a list by this field. If $G/Z(G)$ is cyclic, then $G$ is abelian Continuing my work through Dummit &amp; Foote's "Abstract Algebra", 3.1.36 asks the following (which is exactly the same as exercise 5 in ):     Prove that if $G/Z(G)$ is cyclic, then $G$ is abelian. [If $G/Z(G)$ is cyclic with generator $xZ(G)$, show that every element of $G$ can be written in the form $x^az$ for some $a \in \mathbb{Z}$ and some element $z \in Z(G)$]      The hint is actually the hardest part for me, as the quotient groups are somewhat abstract. But once I have the hint, I can write:  $g, h \in G$ implies that $g = x^{a_1}z_1$ and $h = x^{a_2}z_2$, so \begin{align*}gh &amp;= (x^{a_1}z_1)(x^{a_2}z_2)\\\  &amp;= x^{a_1}x^{a_2}z_1z_2\\\ &amp; = x^{a_1 + a_2}z_2z_1\\\ &amp;= \ldots = (x^{a_2}z_2)(x^{a_1}z_1) = hg. \end{align*} Therefore, $G$ is abelian.  1) Is this right so far?  2) How can I prove the "hint"? What is the principle of underdetermination? While studying I read about the principle of underdetermination of scientific theories. I made some researches online but I am more confused than before. I read about the Quine-Duhem holistic thesis, but I do not know if is the same as underdetermination. How do I integrate the Poisson equation to determine the electric potential along a particular direction (e.g., $z$)? This question is a sequel of sorts to my  about .  In the paper, the authors performed molecular dynamics (MD) simulations of parallel-plate supercapacitors, in which liquid resides between the parallel-plate electrodes.  The system has a "slab" geometry, so the authors are only interested in variations of the liquid structure along the $z$ direction.  In my previous question, I asked about how particle number density is computed.  In this question, I would like to ask about how the electric potential is computed, given the charge density distribution.  Recall that in CGS (Gaussian) units, the Poisson equation is   $$\nabla^2 \Phi = -4\pi \rho$$  where $\Phi$ is the electric potential and $\rho$ is the charge density.  So the charge density $\rho$ is proportional to the Laplacian of the potential.  Now suppose I want to find the potential $\Phi(z)$ along $z$, by integrating the Poisson equation.  How can I do this?  In the paper, on page 254, the authors write down the average charge density $\bar{\rho}_{\alpha}(z)$ at $z$:  $$\bar{\rho}_{\alpha}(z) = A_0^{-1} \int_{-x_0}^{x_0} \int_{-y_0}^{y_0} dx^{\prime} \; dy^{\prime} \; \rho_{\alpha}(x^{\prime}, y^{\prime}, z)$$  where $\rho_{\alpha}(x, y, z)$ is the local charge density arising from the atomic charge distribution of ionic species $\alpha$, $\bar{\rho}_{\alpha}(z)$ is the average charge density at $z$ obtained by averaging $\rho_{\alpha}(x, y, z)$ over $x$ and $y$, and $\sum_{\alpha}$ denotes sum over ionic species.  The authors then integrate the Poisson equation to obtain $\Phi(z)$:  $$\Phi(z) = -4\pi \sum_{\alpha} \int_{-z_0}^z (z - z^{\prime}) \bar{\rho}_{\alpha}(z^{\prime}) \; dz^{\prime} \; \; \; \; \textbf{(eq. 2)}$$  My question is, how do I "integrate the Poisson equation" to obtain equation (2)?  How do I go from  $\nabla^2 \Phi = -4\pi \rho$ to equation (2)?  In paricular, where does the $(z - z^{\prime})$ factor come from?   Thanks for your time. Prove that : $$\sum_{k=0}^{\infty} \frac{(-1)^{k}}{(2k+1)^3}=\frac{\pi^3}{32}.$$    I think this is known (see ), I appreciate any hint or link for the solution (or the full solution). In the double-slit experiment of electrons (observed by photons), is it correct to say the collapse is caused by the momentum of the photons? I'm working off the article, . I think it's well-written, but I'm not convinced about this part:     So what is causing the change in the particle’s behaviour?      In the example given above, when electrons are fired at a fluorescent screen, when we bombard the electrons with photons the interaction changes the state of the system catastrophically as, despite lacking mass, photons do carry momentum.   Here the author strongly implicates the momentum of photons as being responsible for the collapse. But is that correct to say?  I have read that the  verified that obscuring which-way information restores wave-like behavior. So it feels to me it's more about some "outer" state (perhaps well-characterized as "information") that we don't yet understand that collapses the system, not per se the photon-electron interaction.  Or am I wrong, and in fact for example, the process of obscuring in the quantum eraser experiments somehow "undoes" the photon-electron interaction or restores the quantum state through another interaction? How could a statement be true without proof? When did our universe and the Star Trek universe diverge? Note that my question assumes as a given that Star Trek is in an alternate universe which diverged from ours at some point in history.  That seems really, really obvious and undeniable to me.  So the question then becomes: at what point in time did the two universes diverge and have different histories? How to prove floor identities? Let $f$ be a complex function with the property that $f^{(n)} = 0$.  Does this imply that $f$ is a polynomial?  If so, why?  Upon thinking about this problem myself, I can easily observe that every $n$ degree polynomial satisfies $f^{(n+1)} = 0$.  Still, this doesn't show that some non-polynomial function couldn't also have this property. I have just upgraded to Ubuntu 17.10 and found out there is no option to have 2 by 2 workspaces. I was able to configure 4 "static" workspaces using , but I would like to have them in 2 rows by 2. Any ideas? Zsh says "no matches found" when trying to download video with youtube-dl I downloaded youtube-dl using pip on CrunchBang (a Debian Wheezy distro). When I run   youtube-dl {video URL}   I get  zsh: no matches found: {video URL}   I guess it has something to do with zsh, because I found some users on Arch forums complaining about it. When I switched to bash it worked. Suppose Player 1 has a Dragon on the table and  in hand, while Player 2 has two Spiders on the table.  Player 1 chooses to attack with the Dragon and Player 2 chooses to block with one of the Spiders.  Before combat damage is to be dealt, Player 1 uses Unsummon on the blocking Spider.    Does Player 2 take any life damage from the attacking Dragon? On approving an edit, I just get this pop up since morning. At first I thought there might be some internet connection issue, but this is now the 3rd to 4th time I got the same error; also, the review is accepted because on refresh I can see my name with approved text beside, but it still throws this error.    I am on a Windows 7 machine, running Firefox 24 (Icognito/Private Mode)    Also, this happens only when edit(1) is written on an question/answer, I don't go to review queue and approve, these reviews were directly loaded from the notification beneath the question/answer.  Martijn Pieters reproduced the problem from the review queue three times; each time the improve option was picked, accepting the suggested edit but editing the post some more. The network console shows that posting to https://stackoverflow.com/review/task-reviewed fails, the server responds with a 404 error:  Request headers: POST /review/task-reviewed HTTP/1.1 Host: stackoverflow.com Connection: keep-alive Content-Length: 137 Accept: application/json, text/javascript, */*; q=0.01 Origin: http://stackoverflow.com X-Requested-With: XMLHttpRequest User-Agent: Mozilla/5.0 (Macintosh; Intel Mac OS X 10_7_5) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/31.0.1650.63 Safari/537.36 Content-Type: application/x-www-form-urlencoded DNT: 1 Referer: https://stackoverflow.com/review/suggested-edits/3575396 Accept-Encoding: gzip,deflate,sdch Accept-Language: en,en-US;q=0.8,nl;q=0.6,nb;q=0.4,no;q=0.2,de;q=0.2,fr;q=0.2 Cookie: &lt;redacted&gt;  POST data: taskTypeId=1&amp;reviewTaskId=3575396&amp;taskResultTypeId=5&amp;fkey=f8791a329b445b658876f4d3afe7961e&amp;postCommentId=null&amp;taskResultSubtypeFlags=null  Response headers: HTTP/1.1 404 Not Found Cache-Control: private Pragma: no-cache Content-Type: application/json X-Frame-Options: SAMEORIGIN Date: Fri, 13 Dec 2013 12:04:53 GMT Content-Length: 0   On the  itself, no record is made of the accept; instead the suggested edit is recorded as approved by 3 people not including Martijn Pieters. In this case the improve review arrived too late.  In , improve again resulted in the error, but the Community account is shown rejecting the edit. Was Daenerys actually trying to hatch the eggs? I was reading @Aegon' s response   and I realized that I've never been clear on whether Dani was intentional in her pyre building to do blood magic and wake the dragons, or if she was just grieving Drogo and killing Mirri and her statement about "only death can pay for life" was a slap in the Maegi's face, since in the end she sacrificed her unborn child for the husk of Drogo.    I know she had tried baking the eggs previously and had felt like they could hatch then, but was clearly disappointed and chastised herself for foolishness when they did not. I don't recall inner monologue or statements after that where she said, "ya know what I should have done..."   I guess what I'm asking is whether there is evidence outside her statement to the Maegi that she was intentional in her blood magic rite or if the miracle was a happy accident? How does one account for the momentum of an absorbed photon? In Mootools, I'd just run if ($('target')) { ... }.  Does if ($('#target')) { ... } in jQuery work the same way? Scanner issue when using nextLine after nextXXX