Now I know this question has been posted a lot but I cant find a satisfying answer anywhere on the internet.  So 2x4GB vs 1X8GB.  What are all the pros and cons in terms of speed, performance, temperatures and power consumption?  PS: I dont want to hear anything related to cost or saving slots for future upgrades.
I'm building a Core  system which supports dual-channel memory (up to 16&nbsp;GB in four DIMMs), my target is 8&nbsp;GB. From the performance perspective, is it better to have two times 4&nbsp;GB or four times 2&nbsp;GB?
Why do we care about eigenvalues of graphs?  Of course, any novel question in mathematics is interesting, but there is an entire discipline of mathematics devoted to studying these eigenvalues, so they must be important.  I always assumed that spectral graph theory extends graph theory by providing tools to prove things we couldn't otherwise, somewhat like how representation theory extends finite group theory.  But most results I see in spectral graph theory seem to concern eigenvalues  not as means to an end, but as objects of interest in their own right.  I also considered practical value as motivation, e.g. using a given set of eigenvalues to put bounds on essential properties of graphs, such as maximum vertex degree.  But I can't imagine a situation in which I would have access to a graph's eigenvalues before I would know much more elementary information like maximum vertex degree.  (EDIT: for example, dtldarek points out that $\lambda_2$ is related to diameter, but then why would we need $\lambda_2$ when we already have diameter?  Is this somehow conceptually beneficial?)     So, what is the meaning of graph spectra intuitively?  And for what practical purposes are they used?  Why is finding the eigenvalues of a graph's adjacency/Laplacian matrices more than just a novel problem? How Can i make save and load for bge I probably need the help of a Python script to make this work.  What I want is: The player will be able to save and turn off the game, but continue from where they saved when they next log in. Items such as gold, weapons, etc. must be stored.  It feels like something hard to do and I am not managing to figure it out alone. Although I love problems and solving them, in this case I need help.  I know that BSE People should not  ask more questions.  But.  Is this stupid or must I have several Scenes in my game. Say that my player goes into a house. Should the house then be in another Scene, or should I move camera and player to inside the house from the same Scene?  Any advice would be very helpful. I have no one near me whom I can ask.  //  Robin W How to Convert 0 to 10V analog signal to 0 to 2.5V for ADC input? I have an analog signal which ranges between 0V and 10V.  I want to linearly scale it down to 0 to 2.5V for my ADC.     I'm concerned that using a resistive voltage divider will affect signal quality.  Is this true?  If it's not true, what value resistor should I use for voltage divider? Why can't I define a static method in a Java interface? How to format a USB flash drive? In Windows there is a straightforward "Format" option in a flash drive's right-click pop-up menu. Where's that in Ubuntu? I'm trying to install Lubuntu on my laptop (sorta old 2005). [Laptop stats: Intel® Celeron® CPU 410 @ 1.46 GHz 1.47GHz, 448 MB of RAM]  I press Install and this message appears:   This kernel requires an x86-64 CPU, but only detected an i686 CPU.  Unable to boot - please use a kernel appropriate for your CPU.   What can I do to install Lubuntu on my computer? Comparison of backup tools Why is it that we have to use the gerund form for the first example? I have been told that it is not grammatical to use the infinitive form.  For some verbs, it's okay:     I wanted to study English.   I had to study English.   I needed to study English.   I tried to study English.   I traveled to study English.   But, for some verbs, it's incorrect:     I ended up to study English.     Why is that the case? What kind of power management circuit do I need to embedded a rechargeable battery in my electronics project? I am doing a project where my electronics runs on 5V which I wanted to power from a 7.2v lipo regulated down to that voltage. I'd really like to include the opportunity to charge the lipo without removing it from the project. What kind of circuit/components do I need to do it properly?  Say, would putting a battery charging ic at the battery's terminals in parallel to my system be enough to achieve what I need? $ d = \gcd(a,b)\Rightarrow\ \gcd(a/d,b/d) = 1$ Could someone please help me with this proof?     Suppose that $a, b \in N$, and $d = \gcd(a, b)$. Since $d$ divides $a$, we have $a = de$ for some integer $e,$ and similarly $b = df$ for some integer $f$. Prove that $\gcd(e, f) = 1$.   I understand why it works. Since d is all the common factors of $a$ and $b, e$ and $f$ had no common factors, therefore the $\gcd(e,f) = 1$. But how do I prove this?  Thanks in advance. I just upgraded my texlive distribution and can no longer insert space in table rows using \\[x pt] syntax when colortbl is loaded.  It seems that recent changes to array.sty might be the problem as this is the only package to change recently.  Can anyone suggest a workaround?  MWE  \listfiles \documentclass{article} \usepackage{colortbl} \begin{document} \begin{tabular}{l}   \hline   No space below with \texttt{colortbl.sty} loaded. \\[10mm]   \hline \end{tabular} \end{document}   File versions in use:   article.cls    2014/09/29 v1.4h Standard LaTeX document class   size10.clo    2014/09/29 v1.4h Standard LaTeX file (size option) colortbl.sty    2012/02/13 v1.0a Color table columns (DPC)    array.sty    2018/04/07 v2.4g Tabular extension package (FMi)    color.sty    2016/07/10 v1.1e Standard LaTeX Color (DPC)    color.cfg    2016/01/02 v1.6 sample color configuration   pdftex.def    2018/01/08 v1.0l Graphics/color driver for pdftex I have what seems to me a very simple proof that $A_{n}$ is the only subgroup of $S_{n}$ of index 2.  Since I've seen other people prove it with what feel like really complicated methods (), I'm wondering if I've overlooked something.  Proof: Let $H$ be any subgroup of index 2 in $S_{n}$.  Then $H\cap A_{n}$ is a normal subgroup of $A_{n}$ and since $A_{n}$ is simple, $H$ is either the trivial or the improper subgroup of $A_{n}$.  If it's the trivial subgroup it doesn't have index 2 in $S_{n}$, and otherwise the theorem is proved. Apparent Violation of Newton's $3^{\text{rd}}$ Law and the Conservation of Momentum (and Angular Momentum) For a Pair of Charged Particles Consider a system of the two identical positive point charges situated in free space (isolated from the influence of any other external fields) as shown in the attached diagram. Particle $1$ is at $(a,a,0)$ and particle $2$ is at $(0,a,0)$. Their velocities, at the considered instant of time, are as shown in the diagram ($\mathbf{v}_1$ along the $+x$ axis, $\mathbf{v}_2$ along the $+z$ axis).    Now, by applying the Biot-Savart law, we find that the magnetic field due to particle $2$ at the position of particle $1$ is along $+y$ axis, which means that the force acting on particle $1$ is along $+z$ axis according to Fleming’s left-hand rule. A similar analysis shows that there is no magnetic force on particle $2$ as the magnetic field of particle $1$ should vanish at positions (relative to particle $1$) located along its velocity vector.  Now, if we observe the net torque on the system of two particles about the $y$ axis then it is non-zero and is directed along the $-y$ axis. Here, there are no external forces or torques acting on the isolated two-particle system, and yet the net torque, as well as the net force on the particles, are nonzero. Why? Also, Newton's third law of motion seems to be broken in this scenario. Why?    Edit $1$  I have come to know from the responses that the electromagnetic field itself takes away some momentum and angular momentum about the considered axis. However, I think that if I consider only two charged particles as my system then the Abraham-Lorentz force can be assumed to be acting upon the system, and that is sufficient to make sure that we have considered the momentum being carried away by the electromagnetic field itself.   Even after considering the action of the Abraham-Lorentz force for the two-particle system, the scenario breaks both Newton's third law and the conservation of linear and angular momentum. This is because the Abraham Lorentz forces do not exactly counterbalance the force and the torques, on the two-particle system under consideration, due to the magnetic field.    Edit $2$  The previous edit was a result of confusion and misunderstanding on my part. The force associated with the momentum carried away by the electromagnetic field as a result of the electromagnetic interaction described in the question is the Lorentz force itself which simply doesn't obey the third law of motion. The Abraham-Lorentz force is a different story. It is associated with the momentum carried away by the radiation emitted by the accelerated charged particles. This is an additional force apart from the Lorentz force and corresponds to an additional carriage of momentum by the electromagnetic field. The momentum carried away by the electromagnetic field in correspondence with the Lorentz force doesn't correspond to radiation. How to compute PCA scores from eigendecomposition of the covariance matrix? Given a data matrix $\mathbf X$ of $12 \times 7$ size with samples in rows and variables in columns, I have calculated centered data $\mathbf X_c$ by subtracting column means, and then computed covariance matrix as $\frac{1}{N-1} \mathbf X_c^\top \mathbf X_c$.  The dimensions of this covariance matrix are $7 \times 7$. After that I have calculated the eigenvalue decomposition, obtaining eigenvector matrix $\mathbf V$ with eigenvectors in columns.  Now I want to know about projections (i.e. principal component scores in PCA): is it $\mathbf{V}^\top \mathbf{X}_c$ or $\mathbf{X}_c \mathbf{V}$?  mean_matrix = X - repmat(mean(X),size(X,1),1); covariance = (transpose(mean_matrix) * mean_matrix)/(12-1);  [V,D] = eig(covariance); [e,i] = sort(diag(D), 'descend'); V_sorted = V(:,i); In the 3d-view workspace, we can use a random color to give our separated object a distinct look.  What if I don't like the result and I want to randomize the color again?   Swapping the setting doesn't change the random seed in color.    (Blender 2.80.64.) Is "chutzpah" used by non-Jewish English speakers? What is vector division? My question is:  We have addition, subtraction and muliplication of vectors. Why cannot we define vector division? What is division of vectors? I've just had to write a string reverse function in C# 2.0 (i.e. LINQ not available) and came up with this:  public string Reverse(string text) {     char[] cArray = text.ToCharArray();     string reverse = String.Empty;     for (int i = cArray.Length - 1; i &gt; -1; i--)     {         reverse += cArray[i];     }     return reverse; }   Personally I'm not crazy about the function and am convinced that there's a better way to do it. Is there? How to show or hide Keyboard Viewer with a keyboard shortcut? I would like to display and hide the Keyboard Viewer using a shortcut.   Is there a way to display the Keyboard Viewer via a keyboard shortcut? Is there a way to automatically display the Keyboard Viewer once I switch to a specific language? Laptop using 14.04 won't get past login GUI