iPhone - Edited photos reverting to original state
Edited photos have reverted to originals on iphone
An inequality for a sum of sine functions I want to show for $x\in\mathbb{R}$, the following inequality holds. $$ \left|\sin x\right|+\left|\sin (x+1)\right|+\left|\sin (x+2)\right|&gt;8/5. $$ This trigonometric inequality has been verified by Mathematica using the Plot commend. However, using the sum formula for the sine function seems doesn't work, and I cannot give a rigorous proof of it. Any suggestion, idea, or comment is welcome, thanks! This is an example from Munkres's Topology (Example 4 in Section 22 titled &quot;The Quotient Topology&quot;, 2nd edition).  Example 4: Let $X$ be the closed unit ball $$\{ x \times y \mid x^2 + y^2 \le 1\}$$ in $\mathbb{R}^2$, and let $X^{\ast}$ be the partition of $X$ consisting of all the one-point sets $\{ x \times y \}$ for which $x^2 + y^2 &lt; 1$, along with the set $S^1= \{ x \times y \mid x^2 + y^2 = 1 \}$. Typical saturated open sets in $X$ are pictured by the shaded regions in the figure below. One can show that $X^{\ast}$ is homeomorphic with the subspace of $\mathbb{R}^3$ called the unit 2-sphere, defined by $$S^2 = \{ x \times y \times z \mid x^2 + y^2 + z^2 =1 \}.$$  I am confused about two points in the example.  Problem 1: About the saturated open sets in $X$. In the example, the typical ones are pictured by the shaded regions ($U, V$) in the figure. However, I am not sure whether the boundaries (visually, by picture) of $U$ and $V$ are included. Particularly, there are two boundaries for $U$. Are they both contained in $U$? And why? Problem 2: How to show that $X^{\ast}$ is homeomorphic with $S^2$? What is the mapping between them?  The following is my understanding:  Solution to problem 1: For $V$, the boundary is not included. For $U$, the outer boundary is included, while the inner one not. Is this solution right? Execute command in remote active terminal Does 'but for' mean:  'If we had X (but we didn't), Y would have been the consequence'?  Or can it also mean; because we had X, as a result Y happened?   Some different examples of but for:  (Case 1)     But for a cup coffee, it was to be a productive day of writing.   Unfortunately, I'd run out, and spent the day craving.    (Case 2)     But for the glass of wine I had dinner, the house work didn't get   done.   (Case 3)     But for the glass of wine I had for dinner, I would have got the   house work done   What is the correct usage of "but for"? Finding the inverse of the arc length function I currently have a Yongnuo YN560-TX trigger and a Yongnuo YN-560 Mark III. I would like to get a iTTL flash that also works with remote triggering.  How compatible are are different flash brands (Neewer, Yongnuo, etc.) when it comes to things like setting zoom, etc. ? I'm trying to understand an algorithm that tries to map points from a lie group to its lie algebra using the exponential map. The background is the representation of 3d coordinate transformations as a lie group.  I can imagine, how one can map points on a manifold (eg a sphere) to the tangent space (tangent plane) at some point x on the sphere. I can imagine to create the tangent space by computing derivatives at that point x. But I cannot imagine how the exponential of some matrix is giving me that tangent space?  How can I envision the exponential of a matrix? Is there some picture or analogy I can use as intuition? Zsh says "no matches found" when trying to download video with youtube-dl I downloaded youtube-dl using pip on CrunchBang (a Debian Wheezy distro). When I run   youtube-dl {video URL}   I get  zsh: no matches found: {video URL}   I guess it has something to do with zsh, because I found some users on Arch forums complaining about it. When I switched to bash it worked. How to stop "Monkey Test" and "Time Service" apps When I long-press the "home" button to close all apps, there is an app named "time service" with android symbol and another named "monkey test" that are always open.   How to stop this? Split polygons into equal areas within each region I've a set of regions within a city. I'd like to split each region into five subregions and then get the centroid of each one of them.  I know how to make a vector grid, but the problem I have is that the generated points are not taking into account the regions, they're only related to the general map.  I have this:    And I want to split each region in five equal size areas. Something like this:    I'd like to build a visualization similar to this one: . In order to accomplish that, I need to split each region, because the original ones are pretty big. GPS PPS signal corresponds to data time? I currently have an Adafruit Ultimate GPS connected to an Arduino that outputing GPS data (nmea sentences) once per second.  There is also a pin on the GPS outputting 1 PPS signal.    My question is whether the pulse of the PPS suppose to match the time that the GPS data is coming in i.e are they are coming in at the same time?    Also does PPS pulse come in at the beginning of a UTC second or is it random and simply once a second? Exporting Data From Salesforce - REST or SOAP? We have a requirement where we need to export records from salesforce tables into our application programmatically. I am reading on the various API's for data integration from salesforce mainly SOAP vs REST API's.  From what I understand, REST should be used when the web service requests are from mobile devices or browser based clients (since they understand JSON). Is that true? If that's the case how do Bulk REST API's fit the bill (since they are meant for bulk data transfers)?  I would like to get your thoughts on what are pros and cons in using SOAP or REST API's to export data records. Note that the requests are being made a java ee server application programmatically. After retrieving the records (probably in batches) from salesforce records we process (validate, filter etc) them and load them in our internal tables.  Thanks. I'm trying to write a simple bash function that takes, as its arguments, a number of files and/or directories. It should:   Fully qualify the filenames. Sort them. Remove duplicates. Print all that actually exist. Return the number of non-existent files.   I have a script that almost does what I want, but falls down on the sorting. The return value of the script as it stands is correct, but the output is not (unsorted and duplicates). If I uncomment the | sort -u statement as indicated, the output is correct but the return value is always 0.  N.B. Simpler solutions to solve the problem are welcome but the question is really about why is this occurring in the code I have. That is, why does adding the pipe seemingly stop the script incrementing the variable r?  Here's the script:  function uniqfile {     local r=0       for arg in "$@"     do           readlink -e "$arg" || (( ++r ))      done #| sort -u    ## remove that comment      return $r } Both apt-get update and upgrade hang:  sudo apt-get update [sudo] password for xxx:  0% [Connecting to archive.ubuntu.com (2001:67c:1360:8001::17)]   I'm able to ping archive.ubuntu.com:  ping archive.ubuntu.com PING archive.ubuntu.com (91.189.88.162) 56(84) bytes of data. 64 bytes from yukinko.canonical.com (91.189.88.162): icmp_seq=1 ttl=50 time=42.2 ms 64 bytes from yukinko.canonical.com (91.189.88.162): icmp_seq=2 ttl=50 time=42.1 ms 64 bytes from yukinko.canonical.com (91.189.88.162): icmp_seq=3 ttl=50 time=42.1 ms ^C --- archive.ubuntu.com ping statistics --- 3 packets transmitted, 3 received, 0% packet loss, time 2002ms rtt min/avg/max/mdev = 42.169/42.206/42.265/0.240 ms   I checked , and I don't think its the same issue.  Any tips for investigating this further? Do I need an airport transit visa through Switzerland (Schengen) if I have no Schengen visa? Do I need an airport transit visa through Switzerland if I have no Schengen visa? Am traveling from Cairo to Moscow via Swiss Air Why Cooper or Dr. Brand can't send message? Why does cancellation of dots $\frac{\partial \dot{\mathbf{r}}_i}{\partial \dot{q}_j} = \frac{\partial \mathbf{r}_i}{\partial q_j}$ work? How do I identify which Linux distro is running? We have some new hardware in our office which runs its own customized Linux OS.   How do I go about figuring which distro it's based on? Complete local ring which is not complete valuation ring Complete valuation ring is obviously complete local, because valuation ring is always local ring. I would like to know the example of  Complete local ring which is not complete valuation ring  Any examples? I could find example of local ring which is not valuation ring, but the example ring is not complete. Thank you for your help. SubView slide in animation, iphone