How did the Jedi learn of the Rule of Two in canon?
When & how did Yoda come to know about the Rule of Two?
74190 counter problem So, I got my 74190 counter shows number like this  9-8-7-6-5-4-3-2-1-0-5-4-3-2-1-0-5-4-3-2-1-0-5-4-3-2-1-0 and so on.  My questions:   What can I do to change the output count down into 5-4-3-2-1-0-5-4-3-2-1-0 and so on? When it changes 0 into 5 it moves so fast. How could I fix this one? MacBook Pro Trackpad Suddenly Stopped Working Completely The trackpad on my Macbook Pro of 2 years has suddenly stopped working out of blue.  The trackpad doesn't move, respond to any gestures nor do any clicks work. This is really frustrating as I used gestures a lot to navigate around my laptop, and even though I use a bluetooth mouse it makes using my laptop unnecessarily laborious.  Does anyone know what may be causing the problem, and any solutions? Is it safe to fully cook a stuffed turkey the night before thanksgiving? Temporal Table that doesn't use system time We want to implement temporal tables in SQL Server 2016. We are creating a Datawarehouse and developing Type 2 Slowly changing Dimension Tables.  For the BeginDate, we want it to be dependent on transaction date and not the current getdate time. We are reprocessing a history of transactions. Example below, customer has gym or bank status, and goes from inactive, to active, or pending, dependent on transaction date.  We currently have this.  CREATE TABLE dbo.Department (     CustomerId int primary key,     MembershipStatus int,     TransactionDate datetime  );   We we would like to create a table like this.  CREATE TABLE dbo.DepartmentHistory (     CustomerId int primary key,     MembershipStatus int,     TransactionDate datetime,     BeginDatetime datetime,     EndDatettime datetime  );   Example usage would be:   first Customer Transaction on 3/5/2018 as Pending P        +------------+--------+-----------+---------+     | CustomerId | Status | BeginDate | EndDate |     +------------+--------+-----------+---------+     | 1          | P      | 3/5/2018  | NULL    |     +------------+--------+-----------+---------+    second transaction is 4/21/2018 is Active A        +------------+--------+-----------+-----------+     | CustomerId | Status | BeginDate | EndDate   |     +------------+--------+-----------+-----------+     | 1          | P      | 3/5/2018  | 4/21/2018 |     | 1          | A      | 4/21/2018 | NULL      |     +------------+--------+-----------+-----------+ Did Sam's memories transfer to the displacee when he leaped? In the TV show Quantum Leap Sam Beckett would travel history and "right" wrongs, temporarily displacing someone native to that timeline in the process. Would the memories of what Sam did transfer to the person he displaced upon his leaping out, or would they wind up with amnesia for the time Sam was there? Conjunction Puzzle: Is this clause dependent or independent? Third grade teacher here. I plan to teach students to distinguish between simple, compound and complex sentences — but only if I can demonstrate a clear and meaningful difference between the latter two!  Complex or Compound? Each sentence in the following pairs is similar to its partner.   All dogs are mammals, so huskies are mammals. All dogs are mammals, therefore huskies are mammals. I come bearing soup, for Kate is sick. I come bearing soup, because Kate is sick.   Are the sentences above complex or compound?   First, we need to decide whether each italicized clause is independent or dependent. To me, they all look dependent. If that is the case, there's not much need to teach about compound sentences. Is there a meaningful difference between the sentences in each pair that I am missing? (Are the FANBOYS as special as they'd like to think?) Proof that the coefficients in an OLS model follow a t-distribution with (n-k) degrees of freedom Background  Suppose we have an Ordinary Least Squares model where we have $k$ coefficients in our regression model, $$\mathbf{y}=\mathbf{X}\mathbf{\beta} + \mathbf{\epsilon}$$  where $\mathbf{\beta}$ is an $(k\times1)$ vector of coefficients, $\mathbf{X}$ is the design matrix defined by  $$\mathbf{X} = \begin{pmatrix} 1 &amp; x_{11} &amp; x_{12} &amp; \dots &amp; x_{1\;(k-1)} \\ 1 &amp; x_{21} &amp; \dots  &amp;       &amp;   \vdots \\ \vdots &amp;   &amp; \ddots &amp;       &amp;   \vdots \\ 1 &amp; x_{n1} &amp; \dots  &amp; \dots &amp;   x_{n\;(k-1)}     \end{pmatrix}$$ and the errors are IID normal,  $$\mathbf{\epsilon} \sim \mathcal{N}\left(\mathbf{0},\sigma^2 \mathbf{I}\right) \;.$$  We minimize the sum-of-squared-errors by setting our estimates for $\mathbf{\beta}$ to be $$\mathbf{\hat{\beta}}= (\mathbf{X^T X})^{-1}\mathbf{X}^T \mathbf{y}\;. $$   An unbiased estimator of $\sigma^2$ is  $$s^2 = \frac{\left\Vert \mathbf{y}-\mathbf{\hat{y}}\right\Vert ^2}{n-p}$$ where $\mathbf{\hat{y}} \equiv \mathbf{X} \mathbf{\hat{\beta}}$ ().   The covariance of $\mathbf{\hat{\beta}}$ is given by $$\operatorname{Cov}\left(\mathbf{\hat{\beta}}\right) = \sigma^2 \mathbf{C}$$ where $\mathbf{C}\equiv(\mathbf{X}^T\mathbf{X})^{-1}$ () .  Question  How can I prove that for $\hat\beta_i$, $$\frac{\hat{\beta}_i - \beta_i} {s_{\hat{\beta}_i}} \sim t_{n-k}$$ where $t_{n-k}$ is a t-distribution with $(n-k)$ degrees of freedom, and the standard error of $\hat{\beta}_i$ is estimated by $s_{\hat{\beta}_i} = s\sqrt{c_{ii}}$.    My attempts  I know that for $n$ random variables sampled from $x\sim\mathcal{N}\left(\mu, \sigma^2\right)$, you can show that  $$\frac{\bar{x}-\mu}{s/\sqrt{n}} \sim t_{n-1} $$ by rewriting the LHS as $$\frac{ \left(\frac{\bar x - \mu}{\sigma/\sqrt{n}}\right)  }   {\sqrt{s^2/\sigma^2}}$$ and realizing that the numertor is a standard normal distribution, and the denominator is square root of a Chi-square distribution with df=(n-1) and divided by (n-1) ().  And therefore it follows a t-distribution with df=(n-1) ().  I was unable to extend this proof to my question...  Any ideas?  I'm aware of , but they don't explicitly prove it, they just give a rule of thumb, saying "each predictor costs you a degree of freedom". Proving that the set of limit points of a set is closed What's the starting wealth for higher levels? The PHB only gives starting wealth for Level 1 PCs. Based on my experience in other games, specifically Pathfinder, I would expect to get more at higher levels. Where can I find an appropriate table or calculation? How to turn off Wireless power management permanently How do you get assembler output from C/C++ source in gcc? How does one do this?  If I want to analyze how something is getting compiled, how would I get the emitted assembly code? Unicode char {U+200B} When I try to cite more than two authors, I got this: ! Package inputenc Error: Unicode char ​ (U+200B) (inputenc)                not set up for use with LaTeX.   \documentclass[a4paper,oneside,BCOR=10mm,12pt,titlepage]{scrreprt}  \usepackage[polutonikogreek,ngerman,english]{babel} \usepackage[maxlevel=4,autostyle,german=guillemets]{csquotes} \usepackage[T1]{fontenc} \usepackage[utf8]{inputenc} \usepackage[style=mla]{biblatex} \DeclareMultiCiteCommand{\parencites}[\mkbibparens]{\parencite}{\multicitedelim‌​}  \begin{document}  \parencites[cf.][]{key1}{key2}{key3}  \end{document} Geodesics equations via variational principle I would like to recover the (timelike) geodesics equations via the variational principle of the following action:  $$ \mathcal{S}[x] = -m \int d\tau = -m \int \sqrt{-g_{\mu\nu}\,dx^{\mu}\,dx^{\nu}} $$  Using an arbitrary auxiliary parameter $\lambda$, then one is able to rewrite the action and obtains: $$ d\tau = \sqrt{-g_{\mu\nu}\, \tfrac{dx^{\mu}}{d\lambda}\tfrac{dx^{\mu}}{d\lambda}} d\lambda $$ $$ -m \int d\tau = -m \int (d\tau / d\lambda) d\lambda =  -m\int\sqrt{-g_{\mu\nu}\, \tfrac{dx^{\mu}}{d\lambda}\tfrac{dx^{\mu}}{d\lambda}} d\lambda $$  Now we can vary the paths $x^{\mu}(\tau) \rightarrow x^{\mu}(\tau) + \delta x^{\mu}(\tau)$.  I need the following equation to be true, so i get the geodesics equations, but I don't know how one can say the following: $$ \int d\tau \,\delta g_{\mu\nu}\frac{dx^{\mu}}{d\tau} \frac{dx^{\nu}}{d\tau} = \int d\tau\, g_{\mu\nu, \rho} \frac{dx^{\mu}}{d\tau} \frac{dx^{\nu}}{d\tau} \delta x^{\rho} $$ I know there is a simpler action, which leads to the same equation of motion, but there one has to do the same manipulation, which I sadly don't understand.  Thanks for helping me! Using oscilloscope safely with AC mains I know there is quite few discussions already on this topic, but since English isn't my first language, I though it better to get some more information about this.  I have used oscilloscopes to troubleshoot electronics problems and measure AC engine current spikes at startup, but I have no experience using them to measure high voltage levels and my experience is with old analog scopes.  So now I have this new DSO and the input rating is 400V peak to peak AC, so it can handle about 140V AC RMS? Not that I'm going to input that much there.  Since I live in Europe the mains here are 230 V @ 50 Hz I can't measure them directly.  If I set the attenuation from the scope and probe to 10X, the voltage is 23 RMS and it is safe to measure? And yes the probes are rated for 1kV.  If that is true, it's also safe to measure voltage between two main lines (400V RMS), since the peak-to-peak would be about 112 volts?  SAFETY: When I am measuring AC, I will be using the scope from its internal battery or with a isolating transformer (1:1) so that it is floating, meaning that there is no connection to earth ground. Are there any other safety issues I have not realized? Presentation of SL$(n,\mathbb{Z}_p)$ I know a presentation of the special linear group SL$(2,3)$(). My question is that-     Can we give a presentation for SL$(n,\mathbb{Z}_p)$ in general or in more general can we  give a presentation for SL$(n,\mathbb{F})$,where $\mathbb{F}$ is field.   As J.P. Serre had given presentation for SL$(2,\mathbb{Z})$   $$\mathrm{SL}_2(\mathbb{Z}) = \langle \,S, T \mid S^4 = 1, (ST)^3 = S^2 \,\rangle$$ where, \begin{align}     S &amp;=     \begin{pmatrix}     \phantom{-}0&amp; 1 \\ -1 &amp; 0     \end{pmatrix},     &amp;     T &amp;=      \begin{pmatrix}     1 &amp; 0 \\ 1 &amp; 1     \end{pmatrix}. \end{align} I wants it to be more general. A generalized version of the second Borel-Cantelli lemma says     Theorem 5.3.2. Second Borel-Cantelli lemma, II. Let $\mathcal F_n, n \ge 0$ be a filtration   with $F_0 = \{\emptyset, \Omega\}$ and $A_n , n \ge 1$ a sequence of events with $A_n ∈ \mathcal F_n$ . Then   $$ \{A_n \,i.o.\} = \left\{\sum_{n \ge 1} P (A_n |\mathcal F_{n−1}) =\infty \right\}. $$   An exercise of this lemma is     Exercise 5.3.6. Show    $\sum_{n \ge 2} \mathbb P (A_n | \cap_{m=1}^{n−1} A_m^c ) = \infty$ implies $P (∩_{m \ge 1} A_m^c ) = 0$.   I think we can actually prove that $\cap_{m \ge 1} A_m^c = \emptyset$. My proof is like this: Let $B_n = \cup_{m = 1}^n A_n$. Let $\mathcal F_n = \sigma(A_1,\dots,A_n)$, which forms a filtration. It is easy to verify that $$ \mathbb P (A_n | B_{n-1}^c ) = \mathbb P (A_n | \mathcal F_{n-1})(\omega) $$ when $\omega \in B_{n-1}^c$.  Assume there exist $\omega \in \cap_{m \ge 1} A_m^c$. It follows from the previous lemma that $$ \omega \in \left\{\sum_{n \ge 1} P (A_n |\mathcal F_{n−1}) =\infty \right\} = \{A_n \,i.o.\}. $$ In other words, $\omega \in \cap_{m \ge 1} \cup_{n \ge m} A_n$, which contradicts $\omega \in \cap_{m \ge 1} A_m^c$.  Is this the right proof? Is there anyway to get tuple operations in Python to work like this:  &gt;&gt;&gt; a = (1,2,3) &gt;&gt;&gt; b = (3,2,1) &gt;&gt;&gt; a + b (4,4,4)   instead of:  &gt;&gt;&gt; a = (1,2,3) &gt;&gt;&gt; b = (3,2,1) &gt;&gt;&gt; a + b (1,2,3,3,2,1)   I know it works like that because the __add__ and __mul__ methods are defined to work like that. So the only way would be to redefine them? Separators for author group (IF conditon) I am new to LaTeX, just a beginner, basically a Perl developer.  I have created a LaTeX file  \begin{document}  \cont{\iname{\isurname{Name1}\ifname{K. C. G.}}\iname{\isurname{Name11}\ifname{Y. Q.}}\iname{\isurname{Name111}\ifname{C.-Z.}}\ititles{Some title Text}\ipage{995}}  \end{document}   Now my need is to define LaTeX commands so that the output should appear as below     Name1 K. C. G., Name11 Y. Q. and Name111 C.-Z. Some title Text - 995.   \iname - Person Name will repeat several times \isurname - Surname of a person \ifname - First Name of a person    \iname will repeat any number of times, say 1 to ...  If only one \iname found inside \cont, display should be like the below     Name1 K. C. G. Some title Text - 995.   If only two \iname found inside \cont, display should be like the below     Name1 K. C. G. and Name11 Y. Q. Some title Text - 995.   If more than two \iname found inside \cont, display should be like the below (and should come after last \iname)     Name1 K. C. G., Name11 Y. Q. and Name111 C.-Z. Some title Text - 995.   I can define input for \iname separated by commas, but I don't know how to write a macro to define \iname with different outputs based on the if condition.  I hope to have clearly explained my doubt. Equivalent Rotation using Baker-Campbell-Hausdorff relation Is there a way in which one can use the BCH relation to find the equivalent angle and the axis for two rotations? I am aware that one can do it in a precise way using Euler Angles but I was wondering whether we can use just the algebra of the rotation group to perform the same computation? Given the following HTML:   &lt;div id="container"&gt;   &lt;!-- Other elements here --&gt;   &lt;div id="copyright"&gt;     Copyright Foo web designs   &lt;/div&gt; &lt;/div&gt;    I would like #copyright to stick to the bottom of #container. Can I achieve this without using absolute positioning?