what's the meaning of putting :: before a namespace name?
scope resolution operator without a scope
Bathroom vanity light with no junction box The external Flash is not showing up in the configuration Menu when using Pixel TF-321 hot shoe. Is this the wrong adapter for that camera, as there is no X connection? I want to trigger a studio flash via sync connection. Can you recommend me a working hot shoe? Thanks! Is there a simple reason why the expected number of coin flips till getting $m$ more heads than tails or $n$ more tails than heads should be $mn$? I flip a coin until I get $m$ more heads than tails, or $n$ more tails than heads. Let the expected number of flips of the coin before stopping be $f(m,n)$.  I obtained $f(m,n)=mn$ from the recursion $f(m,n)=1+\frac{f(m-1,n+1)+f(m+1,n-1)}2$ with $f(k,0)=f(0,k)=0$ for all $k$.   Other than going through this recursion (and either solving by inspection or by writing as linear recurrence in single variable and solving brute force), is there an intuitive reason you should expect this process to take $mn$ flips? I was thinking about the more general problem with probability $p$ of getting heads and was struck by how simple the formula became when handling, what turned out to be a special case (general formula broke down) of $p=\frac12$. Coefficient growth in the power series $\sum u_n z^n = e^{1/(1-z)}$? Regression: Transforming Variables Should the mean be used when data are skewed? Often introductory applied statistics texts distinguish the mean from the median (often in the the context of descriptive statistics and motivating the summarization of central tendency using the mean, median and mode) by explaining that the mean is sensitive to outliers in sample data and/or to skewed population distributions, and this is used as a justification for an assertion that the median is to be preferred when the data are not symmetrical.  For example:     The best measure of central tendency for a given set of data often depends on the way in which the values are distributed.... When data are not symmetric, the median is often the best measure of central tendency. Because the mean is sensitive to extreme observations, it is pulled in the direction of the outlying data values, and as a result might end up excessively inflated or excessively deflated."   —Pagano and Gauvreau, (2000) Principles of Biostatistics, 2nd ed. (P&amp;G were at hand, BTW, not singling them out per se.)   The authors define "central tendency" thus: "The most commonly investigated characteristic of a set of data is its center, or the point about which observations tend to cluster."  This strikes me as a less-than forthright way of saying only use the median, period, because only using the mean when the data/distributions are symmetrical is the same thing as saying only use the mean when it equals the median. Edit: whuber rightly points out that I am conflating robust measures of central tendency with the median. So it is important to keep in mind that I am discussing the specific framing of the arithmetic mean versus the median in introductory applied statistics (where, mode aside, other measures of central tendency are not motivated).  Rather than judging the utility of the mean by how much it departs from the behavior of the median, ought we not simply understand these as two different measures of centrality? In other words being sensitive to skewness is a feature of the mean. One could just as validly argue "well the median is no good because it is largely insensitive to skewness, so only use it when it equals the mean."  (The mode is quite sensibly not getting involved with this question.) $K\subseteq \mathbb{R}^n$ is a compact space iff every continuous function in $K$ is bounded. I need to prove that $K\subseteq \mathbb{R}^n$ is a compact space iff every continuous function  in $K$ is bounded.  One direction is obvious because of Weierstrass theorem. How can i prove the other direction? I tried to assume the opposite but it didn't work for me.  Thanks a lot. How can I securely erase a hard drive? I'm planning on selling a USB external hard drive that currently contains an old Ubuntu installation with stored passwords and banking information.  How can I securely erase the drive before selling it? Why is FIFA against adding instant replay to the game? Is there any evidence or reason why FIFA is so against adding instant replay to soccer? I find myself seeing many unlucky or just plain wrong decisions made by refs that could be corrected with instant replay. What are the 'types' of parametric down conversion? What happens if my order exceeds the bid or ask sizes? What will happen if my order exceeds the bid or ask size? For example, if the bid or ask is 100 shares, but I want to buy 100,000 shares, is it possible to do so? To be honest, I have no idea how to even start this problem. I'm sorry I don't have any work to show, but I'm just at a blank. Help?  Chapter 2: Problem 27:  University B, once boasted $17$ tenured professors of mathematics. Tradition prescribed that at their weekly luncheon meeting, faithfully attended by all $17$, any members who had discovered an error in their published work should make an announcement of this fact, and promptly resign. Such an announcement had never actually been made, because no professor was aware of any errors in her or his work. This is not to say that no errors existed, however. In fact, over the years, in the work of every member of the department at least one error had been found, by some other member of the department. This error had been mentioned to all other members of the department, but the actual author of the error had been kept ignorant of the fact, to forestall any resignations. One fateful year, the department was augmented by a visitor from another university, one Prof. X, who had come with hopes of being offered a permanent position at the end of the academic year. Naturally, he was apprised, by various members of the department, of the published errors which had been discovered. When the hoped-for appointment failed to materialize, Prof. X obtained his revenge at the last luncheon of the year. &quot;I have enjoyed my visit here very much&quot;, he said, &quot;but I feel that there is one thing that I have to tell you. At least one of you has published an incorrect result, which has been discovered by others in the department.&quot; What happened the next year?&quot;   Chapter 2: Problem 28:  After figuring out, or looking up, the answer to Problem 27, consider the following: Each member of the department already knew that Prof.X asserted, so how could his saying it change anything? I have a text box that will have a currency string in it that I then need to convert that string to a double to perform some operations on it.   "$1,100.00" → 1100.00  This needs to occur all client side. I have no choice but to leave the currency string as a currency string as input but need to cast/convert it to a double to allow some mathematical operations. A method to count occurrences in a list Eevee - Light inside a bulb lamp not passing through glass Using Eevee, I'm trying to simulate a light bulb. I have a sphere with glass material and inside it, I have a Point light. But the light is not passing through the glass:  However, if I disable the sphere object, the light is working:   How to make the light inside a bulb lamp pass through glass (using Eevee)? Here my test project: is a light side power that many Jedi, including  are capable of. In Episode I, Qui-Gon uses it twice (once to outrun droids and once on Jar Jar's tongue), Obi-Wan uses it once and Anakin uses high speed reflexes for the entire duration of the pod race with no formal training.  According to  the power has a high drain and requires a longer recovery period than other powers. And then of course there are hilarious drawbacks such as .  But why wasn't this power used in the following scenarios (and many, many others):   The Redshirt Jedi who accompanied Windu to arrest Palpatine, before they were summarily dispatched to the Nether. Qui-Gonn, to avoid a lightsaber through his gut. Yoda, to avoid flying senate seats. By Windu, who is supposedly a notable practitioner. Example of non-isomorphic structures which are elementarily equivalent Could someone give an example of a ‘very’ discontinuous derivative? I myself can only come up with examples where the derivative is discontinuous at only one point. I am assuming the function is real-valued and defined on a bounded interval. Let $\mathbb F$ be a field and $\mathbb  K $ be an extension field of $\mathbb F$  such that $\mathbb K$ is algebraically closed.   Let $\mathbb L$ be the field of all elements of $\mathbb K$ which are algebraic over $\mathbb F$. Then $\mathbb L_{|\mathbb F}$ is an algebraic extension.   My question is : Is $\mathbb L$ algebraically closed ?  I am trying to prove the existence of algebraic closure, so please don't assume that every field has an algebraic closure. I recently re-watched Contact for the first time since my childhood, and while I thoroughly enjoyed it, I realized that there was something I'd never understood: why couldn't they corroborate Ellie's account of her journey?  As far as I could tell, the pod fell harmlessly through the machine.  That is, it didn't break anything, and the machine wasn't destroyed.  I don't recall any dialogue about circuits being fried or the system shutting down, so presumably it wouldn't be hard to simply hoist the pod up and go again.  I imagine the energy draw was substantial on the local Japanese power grid, but given the amount of effort and money already invested in the machine, surely "Round 2" wasn't out of the question?  I mean, they almost certainly expected that this machine would get more than one good use out of it, anyway!  So given Ellie's vehement insistence that the machine had worked, the public nature of the controversy surrounding her testimony, and the government's (secret) findings that her device had recorded 18 hours of static, why wasn't it the obvious choice to have someone else suiting up the next day, ready to drop through the machine and corroborate her story?