So I am struggling to understand the purpose of the Automatic properties in classes.   See examples below:   This code lets me set the name of the test class, and read it. All works fine, I can set it to "tom" and read "tom" from it.   namespace ConsoleApplication1 {     class test     {         public string name;     }     class Program     {         static void Main(string[] args)         {             test tom = new test();             tom.name = "tom";             Console.Write(tom.name);         }     } }   now this code, using the automatic property does exactly the same thing:   namespace ConsoleApplication1 {     class test     {         public string name { get; set; }     }     class Program     {         static void Main(string[] args)         {             test tom = new test();             tom.name = "tom";             Console.Write(tom.name);         }     } }   So, what is the benefit of using one over the other? Since both seem to work the same way, as far as I can see.   Thanks in advance for any help people can give me!
In C#, what makes a field different from a property, and when should a field be used instead of a property?
Prove that $4\sin\frac{2\pi}{7}- \tan\frac{\pi}{7}= \sqrt{7}$ . Prove that $$4\sin\frac{2\pi}{7}- \tan\frac{\pi}{7}= \sqrt{7}$$   I think midway calculations are not easy formulas, I can't find what kind of formula transformation to solve! I think the best solution here is using right triangle . . . I have one solution too, but not pretty . ! What happens to the Windows 7 key when upgrading to Windows 8? Microsoft is offering "Microsoft Windows 8 Professional Upgrade" at a discounted price compared to the OEM version. However it states:     If you currently have a personal computer running Windows 7, Windows XP or Windows Vista then you can upgrade to Windows 8 Pro (Professional).   My question is what happens to the Windows 7 key that I use to upgrade? Will it become the Windows 8 key or will it generate a new Windows 8 key?  Basically if I upgrade using my Windows 7 key from my laptop for my desktop will I be able to continue using the laptop on Windows 7 while concurrently using Windows 8 upgrade on my Desktop? Distributional Laplacian of logarithm and the Dirac delta distribution Consider $S(\mathbb{R}^2)$ .  Consider $F(x) = \displaystyle\frac{1}{2 \pi} \ln|x| , x \in \mathbb{R}^2 - \{ 0 \}$.  I want to prove this  : $\Delta F = \delta $ in $S^{'}(\mathbb{R}^2).$  My try: For every $\varphi \in S({\mathbb{R}}^2)$ we have  $$\langle \Delta F, \varphi\rangle  = \langle F , \Delta \varphi\rangle  = \displaystyle\int_{\mathbb{R}^2} F(x) \Delta\varphi(x) \ dx = \displaystyle\lim_{r \rightarrow + \infty} \displaystyle\lim_{\epsilon \rightarrow 0^{+} } \displaystyle\int_{\epsilon \leq |x| \leq R} F(x) \Delta \varphi(x) \ dx $$  I don't know how to prove this :$\displaystyle\lim_{r \rightarrow + \infty} \displaystyle\lim_{\epsilon \rightarrow 0^{+} } \displaystyle\int_{\epsilon \leq |x| \leq R} F(x) \Delta\varphi(x) \ dx = \varphi (0) = \delta(\varphi)$  I don't know what to do from here. How can I improve viewport performance when using Dyntopo? I'm doing a Blendercookie course on how to sculpt a Scifi weapon with dyntopo. The fact is that when some piece reach a certain level of compleiity (about 1.1 million tris) the systems starts to lags too much and is so frustrating.  I've tried the several options:   Disable double sided lighting Enable VBO    I've so also reduced the topology of hidden faces. But that´s how far I've reached.  I'm using a late Imac Intel I5 Nvidia GPU GTX 680mx  any tips out there? New tab in chromium is empty What if the answers of a historical locked question become obsolete? My understanding is that a question is historically locked because the information in it is too valuable for the question to be deleted.   But if the "valuable information" becomes obsolete, what happens then?  We cannot modify the question content, or the answers for a historically locked question, right? Syntax error due to using a reserved word as a table or column name in MySQL \includegraphics PDF, color problem I'm using pdflatex, and use \includegraphics to include content of figures from PDF. PDF are exported from InkScape.  \begin{figure} [!h]     \centering     \includegraphics[height=3cm]{fig/SUSAN.pdf} \end{figure}   Included PDF or source SVG has same colors. Green has always RGB value (0, 255, 0). Problem occurs when I include this files from LaTeX. In output PDF on some pages colorspace is darker. Even same image on other page has different colourity.  My PDF  . As you can see on page 7 (11 in PDF) USAN areas are bright green, but then on page 5 (9 in PDF) are green points on corners more darker. I have a bash script which must call another bash script which varies per-user in order to get some configuration information, like so:  somescript:  #!/bin/bash ${HOME}/.ssconfig echo "Hello, ${VARIABLE}!"   ~/.ssconfig  #!/bin/bash VARIABLE=world   Which, instead of giving me Hello, world! as expected, gives me Hello, ! How can I pass variables up from a script to the one that called it? Bump right-aligned text to next line iff no room Let $\theta \in R^{n}$. The Fisher Information Matrix is defined as:  $$I(\theta)_{i,j} = -E\left[\frac{\partial^{2} \log(f(X|\theta))}{\partial \theta_{i} \partial \theta_{j}}\bigg|\theta\right]$$  How can I prove the Fisher Information Matrix is positive semidefinite? Quotes insert problem while working with webservice quotes are not inserting may i know what i have to do. my code is     for(integer l=0;l&lt;reqquotes;l++){          qu = new Quote();          qu.Name = qName;          //opp.CloseDate =system.today();           qList.add(qu);             insert oppList;          insert qList;     } This question has an inverse:     What would be the most efficient way to translate a combination of $k$-tuple into its positions within the $\left(\!\!\binom{n}{k}\!\!\right)$ combinations? I need this to be fast for combinations of $\left(\!\!\binom{70}{7}\!\!\right)$ order of magnitude - very large, but not exceeding 2 billion (fits into int32 maximum value).  Below is an example of $\left(\!\!\binom{6}{3}\!\!\right)$, where the aim is to quickly translate (a, d, f) tuple to value 9, while in the real problem $k$ ranges between 5 and 8.  $$\begin{array} {cccccc|c} a&amp;b&amp;c&amp;d&amp;e&amp;f&amp;^{combination}/_{sort\_order}&amp; \\\hline x&amp;x&amp;x&amp; &amp; &amp; &amp;1\\ x&amp;x&amp; &amp;x&amp; &amp; &amp;2\\ x&amp;x&amp; &amp; &amp;x&amp; &amp;3\\ x&amp;x&amp; &amp; &amp; &amp;x&amp;4\\ x&amp; &amp;x&amp;x&amp; &amp; &amp;5\\ x&amp; &amp;x&amp; &amp;x&amp; &amp;6\\ x&amp; &amp;x&amp; &amp; &amp;x&amp;7\\ x&amp; &amp; &amp;x&amp;x&amp; &amp;8\\ x&amp; &amp; &amp;x&amp; &amp;x&amp;9\\ x&amp; &amp; &amp; &amp;x&amp;x&amp;10\\ .&amp;.&amp;.&amp;.&amp;.&amp;.&amp;.\\  &amp; &amp; &amp;x&amp;x&amp;x&amp;20\\ \end{array}$$  I know that I could pre-calculate all the combinations and reverse the lookup dictionary. However, such dictionary would not be efficient in terms of memory usage. Therefore I am looking for either calculation-based approach, or a more efficient data structure to perform this mapping. A map is continuous if and only if for every set, the image of closure is contained in the closure of image Why can't this be done with Master Theorem Apparently recurrences like this cannot be solved with the Master Theorem:  $T(n) = 2T\left(\frac{n}{2}\right) + \frac{n}{\log(n)}$  Because $n^{\log_b(a)} = n^1$ is not a polynomial multiple of $f(n) = \frac{n}{\log(n)}$ since $\frac{n}{\frac{n}{\log(n)}} = \log(n)$, which is less than $n^\epsilon$ for any positive $\epsilon$.  But when is this really even an issue?   For example why wouldn't the time complexity be $n \log n$ using case 2 of the Master Theorem? Unrolling the recursion:  $$T(n) = n\sum_{k=1}^{\log_2(n)} \frac{1}{\log_2(2^k)}$$  $$T(n) = n\sum_{k=1}^{\log_2(n)} \frac{1}{k}$$  Doesn't this suggest $\Theta(n \log n)$ even though it supposedly cannot be done with Master Theorem? Was the singularity at Big Bang perfectly uniform and if so, why did the universe lose its uniformity? The internal storage on my phone is almost full. The storage screen tells me    2.77GB / 2.91 GB taken Apps 0.89GB Other 1.89 GB Available 138MB   What is this "other" and how can I clean it up? I already followed the steps of "make more space", it barely makes a difference.   Phone Storage then tells me 43.00MB / 1.09GB is taken.  And on the SD card I have 1.86GB / 14.72GB taken.  I have plenty of storage in various places yet when I try to install apps I'm unable to do so cause of "insufficient storage". How can I fix this? I'm getting the following error when trying to update a taxonomy field value via REST api:  {   "error": {     "code": "-1, Microsoft.SharePoint.Client.ClientServiceException",     "message": {       "lang": "en-US",       "value": "Cannot deserialize data for type Microsoft.SharePoint.Taxonomy.TaxonomyFieldValueCollection."     }   } }   The request:  https://server/_api/web/GetFileByServerRelativeUrl('/Shared Documents/file.txt')/ListItemAllFields  {   "__metadata": {     "type": "SP.Data.Shared_x0020_DocumentsItem"   },   "Title": "some title",   "Project": {     "results": [       {         "Label": "Term1",         "TermGuid": "897bdf7f-08d6-44b9-a71a-ddc4cf131664",         "WssId": 5       }     ]   } } Separate Biblatex bibliographies with newest entry and highest reference number at the top I would like to have a similar biblatex behaviour as described , i.e. separate bibliographies for different publication types, each bibliography should 1) be prefixed with a corresponding label (C for conference publications, J for journals etc), 2) sorted so that the newest entry is at the top (defined by the publication year) and 3) with reference numbers sorted in descending order per bibliography, i.e. the newest entry should have the highest number.  Journal articles ---------------- [J3]    reference from 2017 [J2]    reference from 2016 [J1]    reference from 2015  Conference publications ----------------------- [C4]    reference from 2017 [C3]    reference from 2017 [C2]    reference from 2016 [C1]    reference from 2015   I currently have the following:  \usepackage[backend=biber,         isbn=true,         giveninits=true,         style=numeric,         maxnames=99,         sorting=ydnt,         defernumbers=true,         autocite=superscript]{biblatex}  \subsection*{Journal articles} \begin{refcontext}[labelprefix=J] \printbibliography[type=article] \end{refcontext}  \subsection*{Conference publications} \begin{refcontext}[labelprefix=C] \printbibliography[type=inproceedings]   Separate bibliographies works fine, labelprefix also works as desired, sorting by year in descending order as well. However, if I try the solution mentioned in the above question I get very high reference numbers (in the 500s).  Is the above behaviour possible at all and, if yes, what is the most elegant solution using current biblatex etc.?  Thanks a lot in advance! I want to create a table like this using Latex        ---------------------------------       |               sets            |       ---------------------------------       | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | --------------------------------------- | I1  | * |   | * | * |   | * |   | * | ---------------------------------------   Here is what I wrote  \begin{table} \caption{Multiprogram sets} \label{multiprogram}  \begin{tabular}{| c | c | c | c | c | c | c | c | c |}   \cline{3-9}   \multicolumn{8}{}{}    &amp;   Sets  \\   \hline   \multicolumn{1}{}{}   &amp; 1 &amp; 2 &amp;  3 &amp; 4 &amp; 5 &amp;  6 &amp; 7  &amp; 8 \\   \hline    astar         &amp;  &amp; * &amp;  &amp; * &amp;  &amp;  &amp; * &amp;   \\   \hline  \end{tabular} \end{table}   But it doesn't work! The output look like            -----------------------------                                  sets | ---------------------------------------         1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | --------------------------------------- | I1  | * |   | * | * |   | * |   | * | ---------------------------------------   Any way to fix that?