Suppose, $K_n$ is a complete simple graph with each edge label $k$. Then its adjacency matrix $A(K_n)$ has all the entries zero along the diagonal, and each non-diagonal entries are $k$.  What  are the eigenvalues or, the spectrum of $K_n$? Is there any known formula for this?
I have the following $n\times n$ matrix:  $$A=\begin{bmatrix} a &amp; b &amp; \ldots &amp; b\\ b &amp; a &amp; \ldots &amp; b\\ \vdots &amp; \vdots &amp; \ddots &amp; \vdots\\ b &amp; b &amp; \ldots &amp; a\end{bmatrix}$$  where $0 &lt; b &lt; a$.  I am interested in the expression for the determinant $\det[A]$ in terms of $a$, $b$ and $n$.  This seems like a trivial problem, as the matrix $A$ has such a nice structure, but my linear algebra skills are pretty rusty and I can't figure it out.  Any help would be appreciated.
In the 70's I had a stack of old Amateur Radio magazines (50s-60s), and for a long time I saved an article about using the  to combine a number of resistors to achieve a specific value. Does anyone recall and have a copy of this article, or know how the Euclidean algorithm is applied to solve this problem? Suppose that $X_1,X_2,...,X_n$ is a random sample from a normal distribution, $X_i\sim N(\mu,9)$.  Find the UMVUE (uniformly minimum variance unbiased estimator) of $P(X\le c)$ where $c$ is a known constant.  Do this by finding the conditional distribution of $X_1$ given $\bar{X}={\bar{x}}$ and apply the Rao-Blackwell theorem with $T=u(X_1)$, where $u(x_1)=1$ if $x\le c$ and zero otherwise.  So clearly the parameter that we're trying to estimate given the problem description can be written as $\Phi\left( \frac{c-\mu}{3} \right)$ where $\Phi$ represents the CDF of the standard normal distribution.  However, I get stuck when I need to try and find the conditional distribution.  Without knowing the joint distribution or the other conditional distribution, how can I possibly find the conditional distribution of $X_1$ given $\bar{X}={\bar{x}}$? I have a computer with Windows XP installed.  My user does not have a password.  When Windows starts, it goes to the login screen. Because my user has no password, is there any way to bypass this screen, and log in automatically? Round function in Excel, worksheet function vs VBA I had an application for returning closest matches to certain values in a large  cluster of values( as in my earlier )   and I chose a VBA solution. While in the course of using the said application, I observed that the results for the value of 0.5 were not correct. I had been using the VBA Round function which I found to be returning 0 for 0.5 rounded to integer whereas the worksheet round function returns 1. Strangely, the VBA round function returns 2 for 1.5. I had to substitute the worksheet function in place of the VBA one.  Am I missing something? Fancy Chapter Headings Style I would like make a fancy chapter like the figure.    However, i made this code  \documentclass[12pt,a4paper]{book}   \usepackage{lmodern} \usepackage{titlesec} \usepackage{microtype} \usepackage{tikz}    \titleformat{\chapter}[display]   {\normalfont\bfseries\color{black}}   {%\filleft%     \begin{tikzpicture}     \node[       outer sep=-10pt,       text width=2.5cm,       minimum height=3cm,       fill=black,       font=\color{white}\fontsize{80}{90}\selectfont,       align=center       ] (num) {\thechapter};     \node[       rotate=0,       anchor=south,       font=\color{black}\Large\normalfont       ] at ([yshift=43pt,xshift=30]num.west)  {\textls[180]{\textsc{\chaptertitlename}}};       \end{tikzpicture}%  }    {-90pt}   {\titlerule[2.5pt]\vskip3pt\titlerule\vskip4pt\LARGE\sffamily \raggedright }    \begin{document} \chapter{The Singular Sturm-Liouville Problems in Spectral Parameter}    \end{document}      that produces this one    How can I produce the chapter like the First Figure? How can I execute command on startup (rc.local alternative) on Ubuntu 16.10 I am setting up quota on my Linode server running Ubuntu 16.10, and I get the following error      Cannot stat() mounted device /dev/root: No such file or directory   So to fix this, I reached  for the fix which is done by adding   ln -s /dev/xvda /dev/root /etc/init.d/quota restart   to the /etc/rc.local. But Ubuntu 16.10 doesn't uses rc.local anymore instead uses . What is the alternative for rc.local, How can I run the above commands on startup?  Also I enabled the service using systemctl enable rc-local.service but it didn't work for me. Any lead would be appreciated. I just enabled the Blenderkit addon but cannot seem to figure out how to edit the objects. I looked in this reddit thread and amazingly none of the solutions worked for me.  Making it a single user object, data, and materials did not work. I do not see any option to append when adding a model form the Blenderkit asset bar (I even tried saving it and appending the object in another instance of Blender and it still would not let me edit it). And when I right click I do not see an option to make local on outliner collection. I am using Blender 2.83 if that makes a difference but can use 2.9 if need be. Any other solutions? Why is the QGIS map composer grid showing unreasonable lat/lon? I need to print a map with coordinates in the format of Degree, Minute and second. CRS is set to WGS 84 (EPSG 3857) for both layers and on the project properties it is set to enable transformation on the fly. But then, when in map composer I get the following coordinates, which make no sense to me. Shannon confusion and diffusion concept I read the document(not the whole document) from Shannon where he speaks about the concepts of confusion and diffusion. I read in many places(not in the document but around the internet) that confusion is enforced using substitution. Diffusion is enforced using permutation/transposition. Ciphers must use both of them because either confusion or diffusion alone are not enough. I read that a substitution cipher can apply by itself confusion(only). Permutation/Transposition applies by itself diffusion(only). It's precisely the last case that bothers me: Can a permutation/transposition cipher by itself apply diffusion?  Shannon explains diffusion as a property that spreads statistic properties of text all over the text preventing statistic analysis. It's frequently translated to: an alteration to a plaintext symbol affects many cipher text symbols. Assuming permutation of bits or characters, how can diffusion be achieved by simple permutation? I mean, if you permute bits, there will be no other bits affected. But if you consider a symbol a character and you permute bits, a change in a character will affect many other characters. It's a question of what is a symbol.  I also read versions of this diffusion concept where the point was just changing bits order just to avoid pattern analysis of the text. But, where is the avalanche effect in simple permutation?  So, what is the correct definition and the implications of diffusion?  I hope you understand what is troubling me.  Thank you once more My problem is that I have only one reference. So I would like the head of this part to appear "Reference" instead of commonly "References". More generally, could we change the title "References" to an arbitrary name?  Thank you very much for your help! Code coverage for wrapper class is 0% I am building a drupal site using Views, search API module and user-points module.  I created the "database server", and indexed many fields of nodes.  I created a search page using views and the search API, that present content (image, title etc.) In addition, I want to add to every content in this search view the name of the author that wrote it, his author picture.  I add the Indexed Content: Author relationship. Unfortunately, I can't find a way to add the author picture and the current total point to my view.  Can somebody advice how to do that? Short story that takes place off planet, involving sun and rain I read this short story about 20 years ago, and I'd love to find the title and author. This is what I can recall about the story:   It takes place in a classroom full of kids (around 10 years old?) The planet always gets rain The kids lock the main character (a girl, I think) in the closet during the very rare occurrence of sunlight and she misses the entire event.    I know it's not much to go on, but I hope it rings a bell for someone! If you know the Index, Value or Text. also if you don't have an ID for a direct reference.  ,  and  are all helpful answers.  Example markup  &lt;div class="selDiv"&gt;   &lt;select class="opts"&gt;     &lt;option selected value="DEFAULT"&gt;Default&lt;/option&gt;     &lt;option value="SEL1"&gt;Selection 1&lt;/option&gt;     &lt;option value="SEL2"&gt;Selection 2&lt;/option&gt;   &lt;/select&gt; &lt;/div&gt; How to restrict some websites in Ubuntu 14.04 I would like to restrict some websites to be surfed. I mean I want to prevent access to some websites. Please guide me on how to do the same in Ubuntu 14.04 LTS. Debug JavaScript within IE6 U.K visitor visa with very old criminal conviction - do I disclose it? I have been travelling to the U.K for 25 years at least 8-10 times a year,  receiving 5 year visas, never breaking the stay period, with no problem. I've gone through immigration with no problem till my last time in London. I was stopped for eight hours and questioned about a run with the law while I was in college. This was in the US, I was around 20, it was for a credit card use. I received a conditional discharge / probation conviction which was discharged one year later. It was stupid, I was young and in college, more than 28 years ago.  After being questioned about the issue in the US, I was allowed in. They were very polite and professional.  I was also asked if I ever changed my name: I did not change it, but one letter was added in the middle of my first and last names around 20 years ago as our names are translated from Arabic to English and before the digital biometric passports, hand written passports some times varied. It was a common thing at the time.  Now I am applying for my new 5 year visas and I intend to answer truthfully  about previous conviction (previously I answered no because my conviction was spent and I expunged my record.) I want to answer yes and explain it. Is that the right thing to do?  Should I answer yes to the question about having a different name even though it was something as simple as spelling Bryan instead of Brian or Teresa and Theresa -- not really changing it and never thought of it as a change.  I have an impeccable credit rating in the Uk and the last 28 years have never received a moving violation or ever had a run in with the law.  I made one mistake when I was very young but I am  very worried about how to go ahead. I believe honesty is the best approach, is it? What would be the material or shaders node set up for a smooth gem in blender cycles engine?  I want a result similar to this image: Is it possible to search every field of every table for a particular value in Oracle?  There are hundreds of tables with thousands of rows in some tables so I know this could take a very long time to query. But the only thing I know is that a value for the field I would like to query against is 1/22/2008P09RR8. &lt;  I've tried using this statement below to find an appropriate column based on what I think it should be named but it returned no results.  SELECT * from dba_objects  WHERE object_name like '%DTN%'   There is absolutely no documentation on this database and I have no idea where this field is being pulled from.  Any thoughts? Is it possible to only allow specific packages updates from a PPA