Drawing a variable width line in openGL (No glLineWidth)
OpenGL Line Width
Is it possible to create a list of all the figures at the end of a document (this I can do) and make it appear in the table of contents?  So in the the table of content there will be a line saying List of figures ... 19 for example? What is the relation between normal extension and separable extension? What is the relation between normal extension and separable extension? Let F be the algebraic extension of K, if F is a separable extension of K,if and only if F is a normal extension of K? is this correct? My husband wanted me to set up a Facebook account for him and I accidentally used our shared email address, which is set against my own account.  Since then, neither of us has been able to log in, so I can't alter any settings.  Can anyone advise how to resolve this please? File Upload using Selenium WebDriver and Java Robot Class Find all natural numbers $n$ and $m$ for which $n^m=(n-1)!+1$ Can older cards that refer to a player/opponent ever be used on planeswalkers? Many older cards refer to players or opponents, e.g. "deal 3 damage to target player". Can any of these be used on planeswalkers, beyond the fact that you can simply attack them with creatures?  For example:   Would my opponent discard a card if  damaged a planeswalker they control? Would my opponent, the planeswalker, neither, or both amass poison counters from an unblocked ? Can  target a planeswalker? Does  affect planeswalkers? Can  prevent damage to a Planeswalker? Would  be obligated to take damage being dealt to a planeswalker? Can a planeswalker gain loyalty from ? Can  prevent damage to a planeswalker? I am trying to prove $(a)$ is a maximal ideal in $\mathbb{Z}$,  if and only if $a$ is prime number.  Now I wrote: assume $a \in\mathbb{Z}$, while it's not prime number we can write as $a=xy$, for some integers $x$ and $y$. then $(a)\subset (x)$ and $(a)\subset (y)$  while if $(a)$ is maximal ideal, it's not exist $(k)$ such that $(a)\subset (k)\subset\mathbb{Z}$. so $(a)$ cannot be maximal ideal. we can say by contradictory if $a$ is prime, $(a)$ is maximal ideal.  is this correct?  and how to prove the other way. Why has this configuration chosen for feedback? Reputation and inbox notification shows up again after refresh This was asked before too. .  Currently I am facing the issue of appearance of reputation notification in above toolbar.  I can see the reputation notification, for every page refresh even after clicking and viewing the notification.  current browser: Chrome Version 36.0.1985.143 m We all know that in an idealised world all objects accelerate at the same rate when dropped regardless of their mass.  We also know that in reality (or more accurately, in air) a lead feather falls much faster than a duck's feather with exactly the same dimensions/structure etc.  A loose explanation is that the increased mass of the lead feather somehow defeats the air resistance more effectively than the duck's feather.  Is there a more formal mathematical explanation for why one falls faster than the other? Clip for each feature I want to clip a polyline feature class by a polygon feature class (buffers created from points). Several polygons overlap, so I want to get each polygon feature clipped with each polyline feature.  Using the Clip_analysis tool, I get the orange lines:   whereas I want the following red lines:    In a python script, I tried the following code to clip every polyline with each polygon:          temp = arcpy.ValidateTableName("clip_temp")     bufferCursor = arcpy.SearchCursor(buffer)     n = 0     for pRow in bufferCursor:         arcpy.AddMessage(n)         feat = pRow.Shape         arcpy.Clip_analysis(inputPolylineLayer, feat, temp, "#")         if n == 0:             arcpy.Copy_management(temp, clip)         else:             arcpy.Append_management(temp, clip)         n=n+1   But the execution is very very slow and it crashes before finishing.  I also tried the Intersect_analysis tool but I didn't get the right geometries:   Do you have any idea of a better methods to do it? Examples of PCA where PCs with low variance are "useful" LWC Get Pick-list Field Values In LWC, is it possible to get a pick-list field's possible values?  I'm writing a component that is embded into a lightning record page. I need my component to be able to load the record from the page, get data from the fields and use that data to pre-populate my search form with default values.  I have this working with city/state and checkbox fields. Right now the city/state fields are built pull data from an aggregate query of contacts to find all possible state/city combinations (I know this is doomed to fail when the records reach over 50k contacts but Its good enough for now).  I have a pick-list field on my object called skill level, I need to be able to build a combo box that has all the possible values for skill level and set the default value to the value on the associated record.  I'd like to avoid hard-coding the available options if possible.  In LWC, is it possible to get a pick-list field's possible values? When should \cdot be used to indicate multiplication? Is this purely personal style, or are the generally accepted guidelines? Clearly, when dealing with numbers either $2 \cdot 2$ or $2 \times 2$ is needed, but within formulae where an absence of an operator implies multiplication, when should a \cdot be used? I tend to use it only sparingly if it aids in grouping. (Of course, barring the cases where it's required, e.g. a dot product.) I have a lot of Excel sheets for all sorts of things - but none has ever acted up like this one here:    This used to be a totally normal Excel 2007 sheet which I was able to resize, maximize etc. - but not anymore. The MDI child window is fixed, both in position and size. I cannot move it around, more can I maximize it to use the full size of the screen anymore. I cannot double-click on it's title bar to maximize it either :-(  What happened? What can I do to "undo" whatever I did to it.  Any ideas? I tried to share / undo sharing, I tried to protect / unprotect the sheet - nothing seems to work... I have created an FME workspace which inputs a pipeline as well as other linear features which cross it (waterways, roads, railways, fences, other pipelines, etc).  The output is a point file which contains the crossing type.  What I would like to do is calculate the distance along the pipe from the start of the pipeline for each intersection.  So, as you travel along the pipeline, the distance attribute will increase.   I'm thinking that I'll need to use some of the linear referencing tools like MeasureGenerator, MeasureExtractor, or something like that, but I'm not sure how to do so.  Does anyone have an idea of how to do this? Main tag of a question As far as I know, if I have some tags in a question, system will choose the tag which has more questions as main tag (shows in title of page)  But, sometimes this is not correct. For example, I have a question about PhoneGap which applies to both android and iOS. So my question is about PhoneGap, not Android. but system chooses Android as main tag...  Is there any way to manually choose the main tag of a question? if not, Isn't it better to have a feature like this? Deployment error regarding translations when generating package version How can I prevent inline math formulas from overflowing into the margin? When I compile my document in LaTeX, some formulas in the document in math mode, between $ $, go into the right margin area beyond all the text.  Is there a way to fix this aesthetic problem? I have to prove that if $E$ is a connected space, then so is $\overline{E}$ (the closure of $E$) a connected space. I tried to prove the contrapositive. So suppose that $\overline{E}$ is not connected in a metric space $X$. This implies there are $A\subset X$ and $B\subset X$ such that $A\cap B=\emptyset$, $A\cap \overline{E}\neq \emptyset$, $B\cap \overline{E}\neq \emptyset$ and $\overline{E}\subset A\cup B$. I will try to prove that this $A$ and $B$ will also work for $E$. Suppose that $A\cap E=\emptyset$ and $B\cap E=\emptyset$, this implies that $A\cup B$ is a subset of the limit points of $E$, because $A\cap \overline{E}\neq \emptyset$ and $B\cap \overline{E}\neq \emptyset$. This contradicts the fact that $\overline{E}\subset A\cup B$, so we have to conclude that $A\cap E\neq \emptyset\neq B\cap E$. Since $E\subset\overline{E}\subset A\cup B$, we have that $E$ is also not connected.  My question is whether my proof is correct, because I have a little bit doubt. If it's not correct, what is the best I can do? Thanks in advance!   Edit1: The definition we use for a connected space $E$ in a metric space $X$ is that if $E$ is connected, then there are no open $A,B\subset X$ such that $A\cap B=\emptyset$, $A\cap E\neq \emptyset\neq B\cap E$ and $E\subset A\cup B$.  Edit2: $A$ and $B$ must be open.