Changing NAD27 to NAD83 in R, Error in proj4string
Assigning CRS to Lat/Lon in R giving error: "Geographical CRS given to non-conformant data"
Calculating the longest distance within polygon in QGIS I want to calculate the "diameter" of polygons in QGIS.  The "diameter" defined as the distance between the two most distant points of the polygon.  I couldn't find a fitting solution in the field calculator. Maybe you have some ideas? Question  The following is from Bartle:  Give an example of a function $f$ on $X$ to $\mathbb{R}$  which is not $X-$measurable but is such that $|f|,$ and $f^2$ are measurable.  Relavant Information  A family $\textbf{X}$ of subsets of $X$ is a $\sigma$ algebra in case:   $\phi, \mathbb{R} \in \textbf{X}$ $X \setminus A \in \textbf{X}$ if $A \in \textbf{X}$ If $(A_n) \in \textbf{X}$, then the union $\bigcup_{n=1}^{\infty} A_n \in \textbf{X}$  Any set in $\textbf{X}$ is called $X-$ measurable.   A function is $X-$ measurable if for every real $\alpha$, the set $\{x \in X : f(x)&gt;\alpha\}$ belongs to $\textbf{X}$  Attempt  Consider the following function: $$f=\begin{cases} 1 &amp;\mbox{ if} \ x \not\in\mathbb{Q} \\                   -1 &amp;\mbox{ if} \ x \in \mathbb{Q}  \end{cases}$$ defined from $\mathbb{R}$ to $\mathbb{R}$ with $\textbf{X}$ being the Borel algebra (the $\sigma$ algebra generated by all open intervals $(a,b)$) Then if $\alpha \in [-1,1)$, the set $\{x: f(x)&gt;\alpha\}$ consists of the irrational numbers. If I can show that the irrationals are not in the Borel Algebra, then I would be done since $|f|=f^2$ is a constant and easily shown to be measurable. Unfortunately I do not know how to show that the irrationals are not in the Borel Algebra.  Edit it has been brought to my attention that the irrationals are in the Borel algebra. I think this is because the rationals, being countable, can be shown to be in the Borel algebra by constructing appropriate small neighborhoods around each rational and then taking the intersections. I now seek to construct a set that is not in the Borel algebra  Alternatively I have tried to define a set other than the irrationals that is not in the Borel Algebra and define a similar function but to no avail. I am currently self studying this book so it would be of great help to me if the answer could contain heuristics on how to tell when a set if borel measurable (although I do not require this in the answer). I am a new user for Ubuntu. I downloaded 13.10 yesterday and made a bootable USB with universal USB installer on my Lenovo IdeaPad Z580 laptop which is now using UEFI; everything appeared OK.  When I booted from the LiveUSB I got the choices of trying or installing Ubuntu but both of them keep giving me these error:  [ 1.929082] kernel panic-not syncing vfs unable to mount root fs on unknown-block (0.0)   Please tell me what is going wrong? Embed .mov file via 'Add Media' not working What graphics packages are there for creating graphics in LaTeX documents? Adding coordinate system to layout in QGIS composer? I would like to know if there is a way to add a dynamic coordinate system field into a QGIS composer layout.  I can use an expression to add many items such as document name, file path, etc but I can;t seem to figure out how to add the coordinate system? I would like to clarify the differences between by value and by reference.  I drew a picture     So, for passing by value,  a copy of an identical object is created with a different reference, and the local variable is assigned the new reference, so to point to the new copy  How to understand the words: " If the function modifies that value, the modifications appear also within the scope of the calling function for both passing by value and by reference "  Thanks! With regard to the theory that each time a wave function collapses the universe  so that each possible outcome really exists - where does all the energy required to create all the new universes come from? How can I show that $\frac{1}{1+|z|^2}$ isn't analytic at $z=1$? I know that it does consider ' ' as NULL, but that doesn't do much to tell me why this is the case.  As I understand the SQL specifications, ' ' is not the same as NULL -- one is a valid datum, and the other is indicating the absence of that same information.  Feel free to speculate, but please indicate if that's the case.  If there's anyone from Oracle who can comment on it, that'd be fantastic! It is an usual practice that any quantum field theory starts with a suitable Lagrangian density. It has been proved enormously successful. I understand, it automatically ensures valuable symmetries of physics to be preserved. But nevertheless the question about the generality of this approach keeps coming to my mind. My question is how one can be sure that this approach has to be always right and fruitful. Isn't it possible, at least from the mathematical point of view that a future theory of physics does not subscribe to this approach? Prove that $\displaystyle \sum_{x=1}^{n} \frac{1}{x (x+1)(x+2)} = \frac{1}{4} - \frac{1}{2 (n+1) (n+2)}$.   I tried using the partial fraction decomposition $a_j = \frac{1}{2j} - \frac{1}{j+1} + \frac{1}{2(j+2)}$, but I don't see how that helps. How do I add a non-deformed end cap to a tube? I want to create some parts that I can reuse for models. I was trying to make a steam punkish exhaust pipe. I want to be able to make the pipe of any length, and as curvy as I like but I want to keep the end cap always undeformed. I approximated my results by hand placing the "crown" at the end of this bezier curve.  I tried to make an array modifier that included the crown as the end cap, but that results in the end cap deforming. ubuntu terminal is not working properly in vi editor HDMI/Displayport audio control for OS X There are many tutorials that use a pull-up or pull-down resistor in conjunction with a switch to avoid a floating ground, e.g.        Many of these projects use a 10K resistor, merely remarking that it is a good value.  Given a a particular circuit, how do I determine the appropriate value for a pull-down resistor?  Can it be calculated, or is it best determined by experimentation? WordPress twenty eleven sidebar on Pages I am using 2011 theme, any how I managed to get sidebar on single.php pages by installing child theme,  But now I want sidebar on pages,  How do I get it? Equation's symbols or parameters description are shown below, however, the = and the details of parameter are not aligned.     I want to make a parameters list for a equation like this, in which symbols, = and detail information are aligned in terms of vertical position.  where    ...    P   =   notional permeability factor    N   =   number of waves    Sd  =   damage level    ...   A tabular environment will produce more spacing before and after text. So how to make the = vertical aligned?   The codes is provided:  \begin{equation} \frac{H_s}{\Delta D_{n50} } = 1.0~ P^{0.13}~ \left(\frac{S_d}{N} \right)^{0.2} \xi_m^P~ \sqrt{\cot \alpha} \end{equation} where:   $H_s$ = significant wave height, equal to the average of the highest 1/3 of the waves  $\Delta$  = relative buoyant density, equal to $\rho_r / \rho_w - 1$, where     $\rho_w$ is the water density  $D_{n50}$ = nominal  diameter defined in Equation (2)  $P$ = notional permeability factor  $S_d$ = damage level   $N$ = number of waves  $\xi_m$ = breaker parameter based on mean wave period $T_m$  $\alpha$ = slope angle According to this question:  entire ruSO site shouldn't become hot. But I just saw the following while searching MSE:        Direct link to the question on ruSO:   Perhaps the HNQ filter works on question title (in the current case there are no non-Latin symbols) instead of site origin. Hence, according to the post mentioned before this behaviour should be interpreted as a bug.   However, I suggest to fix such "bug" by taking another feature request in mind: unicode-math broken