If I have Optimize iPhone Storage enabled on my iPhone and my phone storage is completely full, I understand that iOS will only store a low-res thumbnail of many of my photos on the device. (The full high-res version of the image will only exist in iCloud and on devices with Download and Keep Originals enabled.)  But when only thumbnails exist on the device, how does that work in relation to other photo apps on iOS? For example, do third-party cloud-based photo apps (like Google Photos, Dropbox's Carousel, or Amazon Prime Photos) have access to the full high-res images from the iCloud Photo Library? Or will they only see the low-res thumbnails in some cases?
I am considering to use iCloud Photo Library to store a growing number of family photo albums, shared to web or set of AppleIDs.  I dont need to keep original photos on iDevices for 99.9% of photos.  How much space will be used on the photo-originating set of devices (iOS, OS X, Windows)? I.e. what (roughly) is the function from the original size and number of photos, device storage space available, any other variables?
How do I install a .deb file via the command line? How do I install a .deb file via the command line? Can I define keyboard shortcuts using the Super key? What are the options for traveling to the airports in Paris? Paris has 3 airports (Orly, Roissy, Beauvais), what are the options to go to or to come from there?  (There is also Vatry (XCR) but there is very few flights and i see the shuttle system is currently off.) User logout on browser / tab close How to modify Drupal user's cookie so the cookie is not available anymore after a predefined time or when the user close his web browser or close all of the websites pages open in tabs ?  After some online searches i found that by setting the cookie lifetime to 0 should create temporary cookies that would be deleted once the browser is closed:  I first tried by modifing some ini_set() values in the settings.php :  ini_set('session.cookie_lifetime',  0); ini_set('session.gc_maxlifetime',   0);   I created a php.ini file located at the drupal site root, containing:  session.cookie_lifetime = 0;   But it does not work on my test site. Any ideas? Idempotents in a ring without unity (rng) and no zero divisors. Question: Given a ring without unity and with no zero-divisors, is it possible that there are idempotents other than zero?   Def: $a$ is idempotent if $a^2 = a$.   Originally the problem was to show that $1$ and $0$ are the only idempotents in a ring with unity and no zero-divisors, but I wonder what happens if we remove the unity condition.   I am trying to find a ring with idempotents not equal to $0$ or $1$. So far my biggest struggle has been coming up with examples of rings with the given properties.   Does anyone have any hints? How should I attack this problem? Just watched the 'How Big is the Universe?' TV program and it indicated that the universe is believed to be infinite in size. They used an approach involving measuring the internal angles of triangles. Or something like that anyway.  But hang on, the Universe has a known starting time and size followed by a finite time expanding at a finite speed. So surely, by definition, it cannot be infinite? I can accept it is honking big but by definition it cannot be infinite. Are they misleading me? What Is Energy? Where did it come from? Generate multiple renders of same scene, each at a different resolution? I would like to generate several renders of a static scene, each render being a different size (eg 1024x1024, 512x512 etc). Other than the size, each render will be identical.  Is there a way of doing this using, say, the command line, or a script? I am currently doing this by manually changing the dimensions within the render panel every time, but I was wondering if there's a quicker way.  I am using Blender Internal in this specific instance.  Many thanks Find $x,y$ given $\gcd(x,y)$ and ${\rm lcm}(x,y)$ These two exercises I encountered recently seem to develop some type of connection between GCD and LCM I can't quite figure out. Exercise 1:  Find all the numbers $x$ and $y$ such that: $a) \ GCD(x,y)=15, \ LCM(x,y)=150$ $b) \ GCD(x,y)=120 \ LCM(x,y)=1320$ $c) \ GCD(x,y)=100 \ LCM(x,y)=990$  Exercise 2:   Find all the numbers $m,n$ such that $GCD(m,n)=pq , \ LCM(m,n)=p^2qs$  where $p,q,s$ are prime  The first thing that is known to me is that $GCD(x,y) \cdot LCM(x,y)= x \cdot y$ Also $LCM(x,y)$ is at most $x \cdot y$ while $GCD(x,y)$ is at most $\max \{x,y\}$. Last thing is that $GCD(x,y)|LCM(x,y)$. Using all this I tried to solve the first exercise: $a)$ First two obvious pairs are $x=15, y=150$ and $y=15, x=150$. Now neither of the numbers can be bigger than $150$ or smaller than $15$. So we are looking for numbers in the range $15-150$ that satisfy $x \cdot y = 15 \cdot 150$ Another such pair is $(x,y)=(30,75), \ (x,y)=(75,30)$. Similarly for $b)$ we find that the only possible values are permutations of the set {$120,1320$} and in $c)$ since $100$ does not divide $990$ no such numbers exist. Now exercise 2 is what made me think there is actually another connection I'm not quite aware of since now it's about arbitrary prime numbers and the previous method doesn't work anymore. My intuition is that it has something to do with $GCD$ or $LCM$ of the $GCD(x,y), \ LCM(x,y)$ Get all non-unique values (i.e.: duplicate/more than one occurrence) in an array XeLaTeX update [20201004] and item ball in Beamer Is there a detailed user's documentation for KDE Plasma 5? Algebraic Proof that $\sum\limits_{i=0}^n \binom{n}{i}=2^n$ I have an uploaded video and I want to cut sections of audio (strong language) or add beeps on top without reuploading the video. What is a reasonable depth and diameter for postholes dug in clay soil to support an 8' fence? What is a reasonable depth and diameter for postholes dug in clay soil where the frost line is no more than 12” and that will support an 8 foot tall solid wood fence that uses PostMaster metal posts?  I hope to have someone else install an 8 foot high PT wood fence.  There will be no light or air passing through or under the fence and it will be heavier than average, given the additional height and board weight.  One side will run for 135’.  The attached diagram provides more detail.  The PostMaster Installation Instructions describe a 30” deep, sloped, 10” diameter hole, filled with 6” of gravel plus 24” of concrete for a 6 foot high fence.  They caveat that the “exact diameter and depth will be determined by local weather and soil conditions.”  Got it.  Huntsville, AL; very clay soil.  Maximum wind gusts of 65 mph.  (This is not in the normal tornado path and is not intended to withstand a tornado.)  In reviewing the StackExchange posts on fencing and post holes I came across the concept that the diameter of the pier may be increased to compensate for a shallower post hole.  I would like to know the recommended depth and diameter without relying on the 2 buttress posts, which are my small overbuild idea.  We will be able to walk under them.  26 APR 18 update: I just found a Master Halco youtube video specifying 6-8" diameter holes dug 36" deep for an 8' board-on-board fence, such as I would like to have.   - I also spoke to a fence builder experienced using PostMaster posts who opined that the 10" diameter and 30 deep holes were more than adequate, but that the gravel was of no value in our climate.  So, 30" x 10" dia inches of concrete vs. 36" x 8" dia of concrete. How prove there is no continuous functions $f:[0,1]\to \mathbb R$, such that $f(x)+f(x^2)=x$. Prove that there is no continuous functions $f:[0,1]\to R$, such that   $$ f(x)+f(x^2)=x. $$   My try. Assume that there is a continuous function with this property. Thus, for any $n\ge 1$ and all $x\in [0,1]$, \begin{align*} f(x)&amp;=x-f(x^2)=x-\big(x^2-f(x^4)\big)=x-x^2+\big(x^4-f(x^8)\big)=\cdots\\ &amp;=x-x^2+x^4-\cdots+(-1)^n\left(x^{2^n}-f\big(x^{2^{n+1}}\big)\right) \end{align*}  since $f(0)=0$ and $\displaystyle\lim_{n\to \infty}x^{2^{n+1}}=0$ for any $x\in(0,1)$,it follows by the continuity of $f$ that $\displaystyle\lim_{n\to \infty}f\big(x^{2^{n+1}}\big)=0$, hence $$f(x)=x-x^2+x^4-x^8+\cdots+(-1)^nx^{2^n}+\cdots$$ for any $x\in (0,1)$  Why do I have prove that there is exists such a continuous functions $f$? Maybe  my example is wrong? Why?  if my   method is wrong,then How prove this problem ? Thank you. During the 'Hard Answers' Thieves Guild quest, Karliah asked me to meet her at the Ragged Flagon.  However, it seems that she doesn't show up at the rendezvous point.  Where do I find her? Flames with no gravity? I was watching  today, and noticed this: in some moment the space station changed orbit and the people inside experienced zero-gravity. At that moment, a candlestick passed floating in the air, with the candles burning ().   But in our environment the flames go upward because the hot air is less dense, and that effect should disappear when no gravity is present, am I right? How would a candle flame look then? Is mass converted into energy in exothermic chemical/nuclear reactions?  My (A Level) knowledge of chemistry suggests that this isn't the case. In a simple burning reaction, e.g.   $$\mathrm{C + O_2 \to CO_2}$$  energy is released by the $\mathrm{C-O}$ bonds forming; the atoms lose potential energy when they pull themselves towards each other, in the same way that a falling object converts GPE to KE. There are the same number of protons, electrons etc. in both the reactants and products. I would have assumed that this reasoning extends to nuclear fission/fusion as well, but one physics textbook repeatedly references very small amounts of mass being converted into energy in nuclear reactions.  So I just wanted to know if I was wrong about either of these types of reactions, and if so, what mass is lost exactly? Solving of a seperable differential equation