What is the main physical mechanism behind the generation of negative ions in air by a high negative voltage electrode ?
Can a negative charge ionize air? Adding to this question, I have studied that positive charge ionizes air but never studied that negative charge ionize air. If possible, please explain how does it ionize air?
How to fix the incompatility between BiBer and BiBLaTeX versions in TeXmaker? Cannot Buy Land in Falkreath Distribution of $-\log X$ if $X$ is uniform. For $X$ and $Y$ random variables; $X$ follows the uniform distribution.  (1): if $Y=-\log X$  (2): then it can be shown that $-\log X$ is distributed as $\exp(1)$ {i.e. exponential with mean 1}.  Why is this so? Intuitively statement (2) make sense to me. But i'd like a mathematical proof.  -Probably wrong working:  (1) seems to imply $\exp(-Y) = X$ (which is like saying $X$ is exponentially distributed, which is a contradiction, since its actually uniform!); or is it incorrect for me to do this since $X$ and $Y$ are random variables?  Ultimately how do I prove (2)?  Thanks List comprehension rebinds names even after scope of comprehension. Is this right? Finding Maximum value of consecutive positive integers with constraints Let, $x,y,z$ be consecutive positive integers such that $\frac{1}{x} + \frac{1}{y} + \frac{1}{z} &gt; \frac{1}{10}$ I need to find the maximum value of $x+y+z$ ?  My attempt:  I tried guessing first, To maximise $x+y+z$ it is necessary to have high value for $x$, But not too high which will contradict the constrain of the problem. As we can roughly split the $0.1$ into three parts so I started with numbers closer to $30$ with trial an error I got that for $x=29$ we get the optimum and final result would be 90 (=max. value of $x+y+z$).   Is there any way to arrive at this conclusion with using inequalities? Any hints will be appreciated... I am trying to burn a shapefile to a raster using GDAL's RasterizeLayer. I pre-create an area of interest raster from a different shapefile, given a specific pixel size. This AOI then serves as a base for all following rasterizations (same number of collumns and rows, same projection and geotransform).  The issue occurs, however, when I go to burn the shapes to their own raster, based on the same pixel size and projections. The link below (don't have enough rep to post the image), shows the original shapefile in tan, and the dark pink where RasterizeLayer has burned data. The light pink is nodata values for the dark pink raster data. The grey is the AOI based on which the shapefile burn was completed.  Given the extents of the shapefile polygons, I would expect to see burn values in the bottom two corners, as well as the two pixels underneath the data that does show. Obviously, however, this is not the case.    As follows is the code that I used to generate these. All of the shapes were created using QGIS, and were all created in the same projection.  (It should be noted that the gridding in the picture shown was just to give an idea of the pixel size I was using.)  from osgeo import ogr from osgeo import gdal  aoi_uri = 'AOI_Raster.tif' aoi_raster = gdal.Open(aoi_uri)  def new_raster_from_base(base, outputURI, format, nodata, datatype):      cols = base.RasterXSize     rows = base.RasterYSize     projection = base.GetProjection()     geotransform = base.GetGeoTransform()     bands = base.RasterCount      driver = gdal.GetDriverByName(format)      new_raster = driver.Create(str(outputURI), cols, rows, bands, datatype)     new_raster.SetProjection(projection)     new_raster.SetGeoTransform(geotransform)      for i in range(bands):         new_raster.GetRasterBand(i + 1).SetNoDataValue(nodata)         new_raster.GetRasterBand(i + 1).Fill(nodata)      return new_raster  shape_uri = 'activity_3.shp' shape_datasource = ogr.Open(shape_uri) shape_layer = shape_datasource.GetLayer()  raster_out = 'new_raster.tif'  raster_dataset = new_raster_from_base(aoi_raster, raster_out, 'GTiff',                                 -1, gdal.GDT_Int32) band = raster_dataset.GetRasterBand(1) nodata = band.GetNoDataValue()  band.Fill(nodata)  gdal.RasterizeLayer(raster_dataset, [1], shape_layer, burn_values=[1])   Is this a bug in GDAL, or is RasterizeLayer burning data based on something other than just the presence or lack of a polygon within a specified pixel area?  The files that I was using can be found . How long does the Truffle take to move in after building the mushroom biome? I currently find myself in a pickle because even after I've built the mushroom biome and met all other requirements, the Truffle NPC won't move in.   I've defeated not only the Wall of Flesh but Ocram already. Created a surface mushroom biome. Built a house made out of mushrooms with mushroom furniture.   I have no idea how long it takes for the NPC to move in or if I'm wrong in any of the steps. If $f$ is continuous with $f(x) = f(2x),f(1) = 3$, then what is $ \int_{-1}^{1}f(f(x))\,dx$? If $f(x)$ is a continuous function such that $f(x) = f(2x)$ and $f(1) = 3\;,$ Then $\displaystyle \int_{-1}^{1}f(f(x))\,dx$   $\bf{My\; Try::}$ Here $-\infty &lt;x&lt;\infty$ and Given $f(x) = f(2x)$  So Using Recursively $$\displaystyle f(x) = f(2^1x)=f(2^2x)=..........=\lim_{n\rightarrow \infty}f\left(2^{n-1}x\right)$$   OR we can write it as $$f(x) = f\left(\frac{x}{2}\right)=f\left(\frac{x}{2^2}\right)=........=\lim_{n\rightarrow \infty}f\left(\frac{x}{2^{n-1}}\right)$$  Now How can i prove that $f(x)$ is a constant function.  Help me  Thanks Removing columns in a SpatialPolygonsDataFrame in R? My spatial polygon data frame (SPDF) contains too many columns (variables) and I want to remove most of the columns entirely.   I know how to do this with a regular data frame in R, but I am unsure how to do this when dealing with object of class SpatialPolygonsDataFrame? Does Windows still rely on MS-DOS? I am just about to start an OS course and as an Apple user I am not very familiar with the underlying details of Windows OS. I was wondering, is MS DOS still used with Windows running on top or is ONLY Windows used now as the OS? I was a little confused because I read somewhere that MS-DOS is used for booting but Windows has all other OS capabilities built into it and thus is used for all other OS operations... Is it possible to have a monoid with a proper class as the collection of elements? My question if it possible for us to have, for example, a monoid(any algebraic structure really) with a class as the collection of the elements, instead of a set.  An example would be the class of sets and set union as addition. Clearly, it is closed under the operation, is associative and it has an identity element, so it is a monoid. Is it possible to say so? Suppose I have a python object x and a string s, how do I set the attribute s on x? So:  &gt;&gt;&gt; x = SomeObject() &gt;&gt;&gt; attr = 'myAttr' &gt;&gt;&gt; # magic goes here &gt;&gt;&gt; x.myAttr 'magic'   What's the magic? The goal of this, incidentally, is to cache calls to x.__getattr__(). At the very end of Deathly Hallows, after Harry repaired his own wand with the Elder Wand, he tells Dumbledore's Portrait in the office:     “I’m putting the Elder Wand,” he told Dumbledore, who was watching him with    enormous affection and admiration, “back where it came from. It can stay there. If I die a    natural death like Ignotus, its power will be broken, won’t it? The previous master will    never have been defeated. That’ll be the end of it.   Now, this seems incredibly foolish to me.  "The previous master will never have been defeated" would only have been assuredely true if Harry had died right after depositing the Elder Wand back into Dumbledore's Tomb.   If not, Harry (the Wand owner) would still be alive, and at the risk of being Disarmed (as was shown with Harry and Draco Malfoy, it doesn't matter if the Elder Wand's owner is defeated by death or simple disarming, AND it's not even required that the Disarming would involve the Elder Wand!).  So, if Harry merely put the Elder Wand back into the Tomb, and some years later, someone would disarm him (or, even worse, kill him) - then that someone would become the Elder Wand owner, either by accident or by design:    By accident - Harry is likely to get into plenty of magical duels in the future. Even discounting friendly one (teaching people the Expelliramus), he plans on becoming an Auror!  By design - plenty of people have been in the Great Hall hearing Harry explaining to Voldemort that he, Harry, was now the owner of the Elder Wand, so the fact of his ownership would most assuredly NOT remain a secret, inviting countless people tempted by owning the Deathstick to hunt Harry down. Oh, and the location is now also known!   So "its power will be broken" is quite unlikely to come true!  Is Harry hopelessly wrong? Or am I missing something in the above logic? Was this addressed in canon/JKR info? These badges were only recently added to StackExchange. I would like to know if there is any way I can find out how many more questions I should ask to get these badges.   For e.g. like the counters for the review-related badges: This is a follow-up to .  Suppose you want to denote vectors by upright bold letters; then \mathbf{u} works fine, except that if it's a Greek letter you have to use \boldsymbol{\omega} instead.  Question: Is it possible to define a generic vector command in LaTeX which automatically chooses between \mathbf and \boldsymbol, so that one can write just \vect{u} and \vect{\omega} without having to treat the Greek symbols specially by hand?  (Just to be clear: \newcommand{\vect}[1]{\boldsymbol{#1}} is no good in this situation, since \boldsymbol{u} gives bold italic instead of roman.) I'm not asking the diagonal values, but the length and breadth ones of the Nexus 7. And only of the LCD screen, not the entire hardware. How to change specific values in a List One of the topics that seems to come up regularly on mailing lists and online discussions is the merits (or lack thereof) of doing a Computer Science Degree. An argument that seems to come up time and again for the negative party is that they have been coding for some number of years and they have never used recursion.  So the question is:   What is recursion? When would I use recursion? Why don't people use recursion? How was this character killed without Avada Kedavra? Questions like  dealing with Ancalagon in particular, and Middle-earth's dragons in general, clearly show that Ancalagon was ridiculously, absurdly, unimaginably enormous.      The non-canonical image above shows one person's impression of how the different dragons of Middle-earth stacked up, with Smaug looking absolutely tiny at the far left, and Ancalagon on the right, too big to even fit in the picture.    Below, a presumably canonical picture, painted by Tolkien himself, shows Smaug in relation to Bilbo.  The rough measurements I took from this image suggest that Smaug is about 11 times longer than Bilbo is tall.  Depending on how tall Bilbo is - almost certainly somewhere between 3'6" and 4' tall - Smaug is approximately 38-44 feet long.      If the first picture is even vaguely accurate, Ancalagon would appear to be a minimum of something like 720 feet long from the tip of his nose to the end of his tail:  the visible portions of his head and body are at least 6 times longer than Smaug is from end to end, and we have to assume that the portion of his body that is out of frame is at least 3 times longer still, perhaps even 4 times or more (so the upper range of his length might exceed 1,000 feet).  Does Tolkien give us any way to estimate how big Ancalagon was?  It isn't his normal practice to describe things in great detail, I realize, but he often gives a few hints that allow for some rough approximation to be made.  Does anything he says suggest that the first image is anything like what he had in mind?  Note:  I haven't read anything about Ancalagon from Tolkien's own pen, except a few quotes on this site;  the most important bit of information I've gleaned is that he smashed 3 volcanoes to pieces when he died (or something like that).  How accurate is this, and what else did Tolkien say?    This question is not a duplicate of "", because none of the answers to that question address Ancalagon's size in any detail - except my own, which is based on what little information I was able to glean from the two pictures I included in this question.  All the other answers address how Ancalagon was killed, not how big he was.  I have no interest in how he died, only how big he was, or rather, what hints we can find that might give some indication of how big he was.  I wouldn't ask this question, linking that question in my own, if it contained the information I am interested in.    Note 2:  Regarding the relative sizes and impressiveness of Smaug and Ancalagon:  Imagine a meeting between Smaug and Ancalagon in Dragon Heaven: Smaug: "How'd you die?" Ancalagon: "A flying boat full of fire made by the Angels and driven by a Magic Elf smashed into me, so I fell onto a mountain and broke it, and I died. The Magic Elf lives in outer space now, and the boat turned into a star. How'd you die?" Smaug: "Um... Some dude shot me with an arrow."