\mathrlap type instruction but only 'locally'
Too many blanks between summation symbol and its associated expression
An  can be identified by its  together with isolating intervals with rational bounds for its real and imaginary parts. The degree of an algebraic number is the  of its minimal polynomial. There are known algorithms that allow to easily compute sum and product of algebraic numbers in this representation, raise them to a rational power, extract real and imaginary parts, compare them, or evaluate them numerically to an arbitrary precision.  Is there an efficient algorithm that given an algebraic number $\alpha$ in this representation can decide if $\alpha$ can be represented as a sum or product of algebraic numbers of smaller degree? How can I define a mathematical function as a LaTeX macro? Is it true that $\mathbb{R}$ and $\mathbb{R}^2$ are isomorphic as abelian groups? ssh master - execute su remotely I have a server S that I need to connect to.  I'm connecting to S as user asdf with control master and after that I perform some stuff:  ssh -N -f -M -o ControlPath=$SSHSOCKET ${USER}@${IP} -p ${PORT} -i id_rsa ssh -to ControlPath=$SSHSOCKET ${USER}@${IP} -p ${PORT} "su -c whoami &amp;&amp; hostname &amp;&amp; exit"   It works as expected, but second line asks me  for password.  I am trying such fix:  echo 'qwerty' | ssh -t -to ControlPath=$SSHSOCKET ${K3_USER}@${IP} -p ${PORT} "su -c whoami &amp;&amp; hostname &amp;&amp; exit"   but it gets even worse:  muxserver_accept_control: tcgetattr: Inappropriate ioctl for device tcgetattr: Inappropriate ioctl for device Password:   For me, it's mandatory to ssh as asdf first. I also can't make any other ssh control master connections. I also can't modify any config on the target machine.  I just need to switch to root via ssh somehow. Any ideas ? Can a single player build a clan dojo? Is it possible for an one-or-two-person clan to build a dojo? If so, what are the resources involved?   I'd like to experience the whole Dojo building experience so I don't plan to join an existing Clan with a dojo already. I'd like to create a Windows bootable USB stick, but I don't have a Windows machine with me at the moment to do so. How could I achieve the same using Ubuntu? Is there a tool to encrypt a file or directory? What's the most popular way to encrypt individual files or folders? Implicit Differentiation Help I have to use implicit differentiation to find $\frac{dy}{dx}$ given:  $$x^2 \cos(y) + \sin(2y) = xy$$  I don't even know where to begin, I missed the class where we went over implicit differentiation, and because of that, I am completely stuck.   Thank you everyone.  Edit: I don't know how to make the equation look all nice and whatnot, so sorry about that How to rank a million images with a crowdsourced sort I'd like to rank a collection of landscape images by making a game whereby site visitors can rate them, in order to find out which images people find the  most appealing.  What would be a good method of doing that?   Hot-or-Not style? I.e. show a single image, ask the user to rank it from 1-10. As I see it, this allows me to average the scores, and I would just need to ensure that I get an even distribution of votes across all the images. Fairly simple to implement. Pick A-or-B? I.e. show two images, ask user to pick the better one. This is appealing as there is no numerical ranking, it's just a comparison. But how would I implement it? My first thought was to do it as a quicksort, with the comparison operations being provided by humans, and once completed, simply repeat the sort ad-infinitum.   How would you do it?  If you need numbers, I'm talking about one million images, on a site with 20,000 daily visits. I'd imagine a small proportion might play the game, for the sake of argument, lets say I can generate 2,000 human sort operations a day! It's a non-profit website, and the terminally curious will find it through my profile :) How to Deserialize XML document Pressure and weight? (hydrostatic paradox) Consider two different shaped containers having same area: one is cylinder, the other is like an inverted pyramid (roughly). Both have the same level of water, the weight of the inverted pyramidal container will therefore be greater than that of the cylinder. But I know from Pascal's law that the pressure should be same in both containers. If the base areas are the same then the force (weight as measured by a scale) should also be the same. Why are the weights different? What's the difference between Normalization and Standardization? At work we were discussing this as my boss has never heard of normalization. In Linear Algebra, Normalization seems to refer to the dividing of a vector by its length. And in statistics, Standardization seems to refer to the subtraction of a mean then dividing by its SD. But they seem interchangeable with other possibilities as well.   When creating some kind of universal score, that makes up $2$ different metrics, which have different means and different SD's, would you Normalize, Standardize, or something else? One person told me it's just a matter of taking each metric and dividing them by their SD, individually. Then summing the two. And that will result in a universal score that can be used to judge both metrics.  For instance, say you had the number of people who take the subway to work (in NYC) and the number of people who drove to work (in NYC).   $$\text{Train} \longrightarrow x$$ $$\text{Car} \longrightarrow y$$  If you wanted to create a universal score to quickly report traffic fluctuations, you can't just add $\text{mean}(x)$ and $\text{mean}(y)$ because there will be a LOT more people who ride the train. There's 8 million people living in NYC, plus tourists. That's millions of people taking the train everyday verse hundreds of thousands of people in cars. So they need to be transformed to a similar scale in order to be compared.  If $\text{mean}(x) = 8,000,000$  and $\text{mean}(y) = 800,000$  Would you normalize $x$ &amp; $y$ then sum? Would you standardize $x$ &amp; $y$ then sum? Or would you divide each by their respective SD then sum?  In order to get to a number that when fluctuates, represents total traffic fluctuations.  Any article or chapters of books for reference would be much appreciated. THANKS!  Also here's another example of what I'm trying to do.   Imagine you're a college dean, and you're discussing admission requirements. You may want students with at least a certain GPA and a certain test score. It'd be nice if they were both on the same scale because then you could just add the two together and say, "anyone with at least a 7.0 can get admitted." That way, if a prospective student has a 4.0 GPA, they could get as low as a 3.0 test score and still get admitted.  Inversely, if someone had a 3.0 GPA, they could still get admitted with a 4.0 test score.  But it's not like that. The ACT is on a 36 point scale and most GPA's are on 4.0 (some are 4.3, yes annoying). Since I can't just add an ACT and GPA to get some kind of universal score, how can I transform them so they can be added, thus creating a universal admission score.  And then as a Dean, I could just automatically accept anyone with a score above a certain threshold.  Or even automatically accept everyone whose score is within the top 95%.... those sorts of things.  Would that be normalization? standardization? or just dividing each by their SD then summing? Internal "get/set" function of property? Here is my test code and picture:  import bpy   # Simple property reading/writing from ID properties. # This is what the RNA would do internally. def get_float(self):     return self["testprop"]   def set_float(self, value):     self["testprop"] = value  #bpy.types.Scene.test_float = bpy.props.FloatProperty(get=get_float,set=set_float) bpy.types.Scene.test_float = bpy.props.FloatProperty()   bpy.context.scene.test_float = 12.34     When I don't explicitly set the "get/set" function for my property, after assigning the value, I can get the property value by 'scene["test_float"]', but if I explicitly set the "get/set" function, then if I try to type in the same commands, I will receive a error "KeyError: 'bpy_struct[key]: key "test_float" not found'" . So what should I do to get the same results by using explicitly  "get/set" function? Calculate $\lim\limits_{x\to4} \frac {\sqrt {1+2x}-3} {\sqrt x -2}$ After I just learned there are ways to cancel out $0$s in the divisor of fractions onto limits I looked back at a task where I gave up when I got the result $\lim\limits_{x\to4} \frac {\sqrt {1+2x}-3} {\sqrt x -2}$ so I tried to find a way to get the $0$ out here, as well. Am I just not seeing the solution or is there no way to do it? I'm looking for a story that was probably written somewhere from the 1940s to the 1960s. I think I read it in an anthology, possibly in the 1970s.  A group of human explorers landed on a planet with primitive aliens, living in hunter-gatherer villages. They hoped to make a profit from trading our goods for—well, I'm not clear on what they wanted from the aliens.  The native people learned the human language before the explorers could learn theirs. Then the natives suddenly started producing technological innovations far beyond what they originally used. I remember that wooden sailing ships suddenly replaced their canoes. All the natives had to do was hear a story once from the explorers before copying the technology in the story.  Finally, the explorers realized that the natives were much, much smarter than us and that Earth faced a serious problem.  I'm fairly certain that it wasn't a Heinlein story, but I remember that it had some qualities similar to his work. Can I attack a specific player? I was in a clan and someone kicked me from it.   I think I'm stronger than him. Is there any way I can attack him? The only method I see to attack is random players. Can I attack a specific player? Understanding DNA match of 1,723 cM I have a DNA match of 1,723 cM with a male 6 years younger than me. His father is one of a twin, could my match be not my half-sibling but my 1st cousin. A Banach space is reflexive if and only if its dual is reflexive How to show that a Banach space $X$ is reflexive if and only if its dual $X'$ is reflexive? Let mods see the names of the flaggers for chat offensive flags There have been    (not to pick on the Bridge, just that these are the ones I found) occurrences where users abuse chat flags to cause drama. Random stuff gets flagged, and users from other rooms are needlessly summoned into the room. The issue is, while mods can tell the room to stop flagging random things, there's no way to enforce this. Spam/offensive flags in chat are anonymous, and can be abused with impunity without the mods finding out. I don't think there's anything stopping a user from letting out an endless stream of flags, annoying everyone. Can mods have the ability to see who flagged a message in chat? Can the system leave a deletion reason when it deletes a question?