When I run the command sudo apt-get update , I found an error on ubuntu 16.04 LTS
How can I fix apt error "W: Target Packages ... is configured multiple times"?
Find the general solution of $y'= a^{x + y}$ where y is the function Well, the original task was to figure out what the following expression evaluates to for any $n$.  $$\begin{pmatrix} 1 &amp; 1 \\ 0 &amp; 1\end{pmatrix}^{\large n}$$  By trying out different values of $n$, I found the pattern: $$\begin{pmatrix} 1 &amp; 1 \\ 0 &amp; 1\end{pmatrix}^{\large n} = \begin{pmatrix} 1 &amp; n \\ 0 &amp; 1\end{pmatrix}$$  But I have yet to figure out how to prove it algebraically.   Suggestions? does not appear to actually define what a rigid shape is. Rather it defines 'same shape' and 'rigid transformations' without giving any definitions of what is necessary and sufficient for a shape to be considered rigid.  For instance, I've seen the following image:    I understand intuitively why the triangle is rigid and quadrilateral is non-rigid. It is also my understanding that inserting a single diagonal connection into the quadrilateral would make the shape rigid? However, given the following image (labeling the shapes $S_1$, $S_2$ and $S_3$ in sequence left to right):    If $S_1$ had a single diagonal connection AB, it would be possible to flip ADB over axis q to obtain a shape similar to $S_2$ with the addition of connection AB (my explanation may not be the greatest). This shape is clearly not the same as $S_1$, so how can we say $S_1$ with a single diagonal connection CD is rigid? I feel I am unclear on what the definition of rigidity actually is. Construct a field of 25 elements. We need to construct a field of 25 elements.  By using a result : For a prime p and a monic irreducible polynomial $p(x)$ in $\Bbb F_p [x]$ of degree $n$ , then the ring $(\Bbb F_p [x] / &lt;p(x)&gt;)$ is a field of order $p^{n}$.  So , for the question problem above , we need a irreducible polynomial of degree $2$ in $\Bbb Z_5 [x]$.  Solution says , $x^{2} + x +1$ does our job , since it's irreducible in $\Bbb Z_5 [x]$.  My question : Can't we take $ x^{2} + 2$ , it has no zeroes in $\Bbb Z_5$ , and is irreducible. In every solution I've gone through , the polynomial $x^{2} + x+1$ is taken. Can't we consider $ x^{2} + 2$ ? Calculate total sum of all numbers in c:forEach loop I have a Java bean like this:  class Person {   int age;   String name; }   I'd like to iterate over a collection of these beans in a JSP, showing each person in a HTML table row, and in the last row of the table I'd like to show the total of all the ages.  The code to generate the table rows will look something like this:  &lt;c:forEach var="person" items="${personList}"&gt;   &lt;tr&gt;&lt;td&gt;${person.name}&lt;td&gt;&lt;td&gt;${person.age}&lt;/td&gt;&lt;/tr&gt; &lt;/c:forEach&gt;   However, I'm struggling to find a way to calculate the age total that will be shown in the final row without resorting to scriptlet code, any suggestions? Today, after returning from vacations, I started my QGIS 1.7 and got this terrible message:    Help, anyone? Can mobs go through doors? I was wondering if mobs can go through doors or not. It's the difference between me just putting up a door to my house, or putting up dirt instead. Hybrids are fairly common in Star Trek:  is half Vulcan,  is half Betazoid,  is half Klingon and, just for good measure,  is ¼ Romulan.  However, in all of these cases that I can think of, the other half is always human.  Are there any non-human hybrid characters? Especially ones that are recurring or at least the focus of an episode?  If not, is there an out-of-universe explanation for their absence/rarity/scarcity? From a fandom point of view, I can’t imagine a half-Klingon half-Vulcan might not make for an interesting story, for example. How to find application's path from command line? For example, I have git installed on my system. But I don't remember where I installed it, so which command is fit to find this out? I'm stuck with the proof of the following:  Suppose that $(s_n)$ converges to $s$, $(t_n)$ converges to $t$, and $s_n \leq t_n \: \forall \: n$. Prove that $s \leq t$.   I've tried starting with $s_n \leq t_n \: \forall : n$ and the definitions of each limit (i.e. $|s_n - s| \leq \epsilon \: \forall \: n &gt; N_1$), but I'm not really getting very far. Any help is appreciated! Difference between differentiation and derivatives What is the difference between differentiation  and derivatives of a function ? How can I get Google to stop thinking I'm a Bot? So, I'm getting the occasional CAPTCHA message, which is irritating but fine, but occasionally Google just blocks my network wholesale. I've submitted automated requests to unblock it, but I have no idea who I can email directly to clarify the issue.  I've run all manner of anti-virus, parsed my router's logs, combed through Fiddler to see if any errant packets were slipping by. Nothing. The only Google searches that happen are made by me through the web-browser.  Who or what do I have to do to get Google to stop falsely flagging my network as a spam-bot? PHP script not executing on Apache server How many people have undergone carbon freezing in Star Wars? We all know the story of Han Solo being a guinea pig for the planned freezing of Luke Skywalker, but how often are people "stored" in this way? Comparing mixed-effects and fixed-effects models (testing significance of random effects) Given three variables, y and x, which are positive continuous, and z, which is categorical, I have two candidate models given by:  fit.me &lt;- lmer( y ~ 1 + x + ( 1 + x | factor(z) ) )   and  fit.fe &lt;- lm( y ~ 1 + x )   I hope to compare these models to determine which model is more appropriate. It seems to me that in some sense fit.fe is nested within fit.me. Typically, when this general scenario holds, a chi-squared test can be performed. In R, we can perform this test with the following command,  anova(fit.fe,fit.me)   When both models contain random-effects (generated by lmer from the lme4 package), the anova() command works fine. Owing to boundary parameters, it is normally advisable to test the resulting Chi-Square statistic via simulation, nonetheless, we can still use the statistic in the simulation procedure.  When both models contain only fixed-effects, this approach---and, the associated anova() command---work fine.  However, when one model contains random effects and the reduced model contains only fixed-effects, as in the above scenario, the anova() command doesn't work.  More specifically, I get the following error:   &gt; anova(fit.fe, fit.me)  Error: $ operator not defined for this S4 class   Is there anything wrong with using the Chi-Square approach from above (with simulation)? Or is this simply a problem of anova() not knowing how to deal with linear models generated by different functions?  In other words, would it be appropriate to manually generate the Chi-Square statistic derived from the models? If so, what are the appropriate degrees of freedom for comparing these models? By my reckoning:  $$ F = \frac{\left((SSE_{reduced}-SSE_{full})/(p-k)\right)}{\left((SSE_{full})/(n-p-1)\right)} \sim F_{p-k,n-p-1} $$  We are estimating two parameters in the fixed effects model (slope and intercept) and two more parameters (variance parameters for the random slope and random intercept) in the mixed-effects model. Typically, the intercept parameter isn't counted in the degrees of freedom computation, so that implies that $k=1$ and $p=k+2=3$; having said that I'm not sure if the variance parameters for the random-effects parameters should be included in the degrees of freedom computation; the variance estimates for fixed-effect parameters are not considered, but I believe that to be because the parameter estimates for fixed effects are assumed to be unknown constants whilst they are considered to be unknowable random variables for mixed effects. I would appreciate some assistance on this issue.  Finally, does anybody have a more appropriate (R-based) solution to comparing these models? Shrink exFAT partition Is there any way to shrink an exFAT partition?   The windows disk manager has the "Shrink" option greyed out. Who knows about the summation of this series: $$\sum\limits_{i=1}^{n}i^m $$  where $m$ is constant and $m\in \mathbb{N}$?  thanks Knots in Smoothing Splines In , there's this line under the section describing Smoothing Spline's tuning parameter $\lambda$:       In fitting a smoothing spline, we do not need to select the number or   location of knots - there will be a knot at each training observation,   $x_1,...,x_n$.   But, in my opinion wouldn't that be overfitting?     Reason for such a claim: If there are more points which act as knots in the Spline fit, then the range for each slot for fitting is very small. Thus each change in the data, is recognized and imititated in the fit. Thus fitting the changes, which are random, and do not mean anything. Thus overfitting.    Possibilities: We know that cubic splines and Smoothing splines are different. The basic differences are:     Smoothing splines try to minimize the function $$\sum_{i=1}^n(y_i-g(x_i))^2+\lambda\int g''(t)^2dt$$ Smoothing splines shrink the parameters.   Moreover, Smoothing Splines are basically natural cubic splines, and thus they're smooth too.  So, how can these differences( and properties) save the Smoothing Spline from overfitting? Is there anything else that I'm missing here? When choosing cards for a deck, one of the most important things to consider is the number of land you put in. The biggest issue is mana curve, of course. What shortcuts are best for determining the proper amount of land with a given mana curve? Redshifting of Light and the expansion of the universe So I have learned in class that light can get red-shifted as it travels through space. As I understand it, space itself expands and stretches out the wavelength of the light. This results in the light having a lower frequency which equates to lowering its energy.  My question is, where does the energy of the light go? Energy must go somewhere!   Does the energy the light had before go into the mechanism that's expanding the space? I'm imagining that light is being stretched out when its being red-shifted. So would this mean that the energy is still there and that it is just spread out over more space?