text
stringlengths 3
1.74M
| label
class label 2
classes | source
stringclasses 3
values |
|---|---|---|
How to configure Windows 7 in live mode (readonly C:) like Linux. <p>I usually create headless box with a raw Debian and AUFS file system to set the CF card in read-only mode. All is load in RAM and not change append on CF card.
So i can safely shutdown the box by unplug the power supply and run on battery, etc...</p>
<p>Now i want to do the same headless box with a Windows 7 but i don't know if it's possible. I want the box with Windows 7 can be shutdown safely by unplug the power supply without destroying the file system or got a long checkdisk at the next reboot.</p>
<p>Can someone help me ?</p>
| 0non-cybersec
| Stackexchange |
view video bitrate of a flv file in linux,how?. <p>Is there any command to check the video bitrate of a flv file in debian/ubuntu ? I have some flv files and I want to find out their video bitrate. </p>
<p>I check 'file' command It only says 'Macromedia Flash Video' but no more information.</p>
<p>Thank you.</p>
| 0non-cybersec
| Stackexchange |
Bard is love, Bard is Life. | 0non-cybersec
| Reddit |
[MY SURVEY] Do you like solo games?. | 0non-cybersec
| Reddit |
HP Spectre X-360 Sound Problem. <p>I am facing a sound problem for a long time. Let me tell you my device info first-</p>
<blockquote>
<p>Device name : HP Spectre X-360 Processor :
Intel(R) Core(TM) i7-8550U CPU @ 1.80GHz 1.99 GHz RAM : 16.0 GB (15.8
GB usable) System type : 64-bit operating system, x64-based processor</p>
</blockquote>
<p>I installed ubuntu about 50 times in my machine but every time I had to leave for sound problem. The problem is-</p>
<blockquote>
<ul>
<li>Sound goes up and down automatically delayed 10-15 seconds</li>
<li>Switch left and right speaker automatically</li>
<li>Hardly seen to use both speaker together which is actual sound</li>
<li>With headphone sound works fine</li>
</ul>
</blockquote>
<p>I must tell you that the same problem happens whenever I install windows also. But a driver called <strong>Realtek High Definition(HD) Audio Driver</strong> which is recommended by HP solves the problem perfectly. But I could not find any solution with Linux</p>
<p>I will be very grateful if you guys can solve my problem and allow me to use Ubuntu. Thanks in advance!!</p>
| 0non-cybersec
| Stackexchange |
Is there any way to implement Initializer lists (kind of) in older version of c++ (Before c++11)?. <p>i have tried to implement (kind of :) Initializer lists in older version of c++. like below..</p>
<pre><code>#include <vector>
#include <cstdarg>
#include <iostream>
using namespace std;
template <class T>
vector <T> VEC_VA(size_t argCount,T arg1, ... )
{
va_list arguments;
vector <T> sList;
va_start ( arguments, argCount);
for ( int x = 0; x < (int)argCount; x++ )
sList.push_back(va_arg ( arguments, T));
va_end ( arguments );
return sList;
}
struct Test
{
Test(int _x,std::string _s):x(_x),s(_s){}
int x;
std::string s;
};
void methodWithArgs(vector<Test> testObjs)
{
cout<<"Size:"<<testObjs.size()<<endl;
for (std::vector<Test>::const_iterator it = testObjs.begin();it != testObjs.end();++it)
std::cout << it->x <<":"<< it->s.c_str()<< std::endl;
}
int main()
{
methodWithArgs(VEC_VA(2,Test(1,"one"),Test(2,"two")));
return 0;
}
</code></pre>
<p>But this kind of implementation works in Visual studio 2012 (v11.0). But not in Linux g++ compiler. And ended with an Error: "cannot pass objects of non-trivially-copyable type ‘struct Test’ through ‘...’"</p>
<p>So is there any better idea?</p>
| 0non-cybersec
| Stackexchange |
US tech giants knew of NSA data collection - NSA general counsel contradicts months of angry denials. | 0non-cybersec
| Reddit |
Iptables - Allowing only a single dhcp (relay) client. <p>I am trying to create a firewall rule on an Ubuntu 10.04 server running isc-dhcpd. I only want dhcp to be accessible by a single relay host (172.1.1.1). I have iptables set up like so:</p>
<pre><code># iptables -vnL
Chain INPUT (policy ACCEPT 5325 packets, 523K bytes)
pkts bytes target prot opt in out source destination
0 0 ACCEPT udp -- * * 172.1.1.1 0.0.0.0/0 udp dpt:67
1497 533K DROP udp -- * * 0.0.0.0/0 0.0.0.0/0 udp dpt:67
</code></pre>
<p>This is my attempt to drop all UDP traffic destined to port 67 unless it's coming from 172.1.1.1.</p>
<p>However, with this rule in place, when I start the dhcpd I immediately see DHCP requests start to come in via broadcast (the log says via eth0).</p>
<p>Do I need another firewall rule to catch the broadcast traffic? I've tried adding a rule like </p>
<p><code>iptables -A INPUT -p udp -d 255.255.255.255 -j DROP</code></p>
<p>which should drop all UDP broadcast traffic. But again when I start dhcpd I see tons of requests via broadcast.</p>
<p>EDIT:
According to <a href="http://www.shorewall.net/dhcp.htm" rel="nofollow noreferrer">this page</a>:</p>
<blockquote>
<p>For most operations, DHCP software interfaces to the Linux IP stack at a level below Netfilter. Hence, Netfilter (and therefore Shorewall) cannot be used effectively to police DHCP.</p>
</blockquote>
<p>So is there any way to accomplish what I want here?</p>
| 0non-cybersec
| Stackexchange |
During World War II, it was common for soldiers to keep family photos under clear grips on their 1911 pistols. They were called “Sweetheart Grips.”. | 0non-cybersec
| Reddit |
19.04 Bluetooth Audio (LDAC, aptxhd) - Choppy, Stutter. <p>I have a pair of Sony <a href="https://www.sony.com/electronics/headband-headphones/wh-h900n" rel="nofollow noreferrer">WH-H900N</a> headphones. They work perfectly on android (LDAC), Mac (aptx-hd (no LDAC available)), and Windows (Aptx-hd). LDAC is astounding quality for wireless, which is why I'm pursuing it on Linux.</p>
<p>On Ubuntu, they were working only on some kind of "headset" codec that sounded terrible (scratchy, telephone quality). I followed the instructions here: <a href="https://github.com/EHfive/pulseaudio-modules-bt" rel="nofollow noreferrer">https://github.com/EHfive/pulseaudio-modules-bt</a>. This enabled LDAC and similar: </p>
<p><a href="https://i.stack.imgur.com/WDlUs.png" rel="nofollow noreferrer">LDAC enabled.</a></p>
<p>The sound is much improved. However, the sound is choppy to the point of uselessness. Distance is not an issue (I'm right at the source). </p>
<p>My motherboard is <a href="https://www.msi.com/Motherboard/B450-GAMING-PRO-CARBON-AC/Specification" rel="nofollow noreferrer">a MSI Gaming Pro Carbon AC</a>, which shows an Intel chip (Intel® Dual Band Wireless-AC 9260). </p>
<p>Adjusting the selection in the menu as shown doesn't actually change it, when I click back, it goes back to LDAC.</p>
<p>I would have thought if the board was not compatible with LDAC, it simply would not have worked. Is that incorrect? </p>
<p>Is there anything I can do to get BT audio to work on Ubuntu? </p>
| 0non-cybersec
| Stackexchange |
PrimeFaces 3.0 - <p:dataTable> headers do not line up with using scrollable="true". <p>I have a JSF 2 webapp that is using PrimeFaces 3.0 components. On one page, I'm using the <code><p:dataTable></code> component inside a composite component to display a table of objects. I've had success with this component until I tried to use the <code>scrollable="true"</code> option. Now the table column headers do not line up with the column content. I have tried using IE 7 (which is the target browser for my client environment) and Firefox 4.0.1 for comparison. Both exhibit the problem, but it is more pronounced in IE 7.</p>
<p><strong><em>IE 7 screenshot</em></strong>:</p>
<p><img src="https://i.stack.imgur.com/LLWim.jpg" alt="IE 7 screenshot"></p>
<p><strong><em>Firefox 4.0.1 screenshot</em></strong>:</p>
<p><img src="https://i.stack.imgur.com/Sq3mJ.jpg" alt="Firefox 4.0.1 screenshot"></p>
<p>Here is some of my Facelet page code:</p>
<pre><code><p:dataTable
id="vesselsDataTable"
value="#{cc.attrs.vesselAdapterList}"
var="currentRow"
selection="#{editVesselBean.selectedRow}"
selectionMode="single"
scrollable="true"
height="500">
<p:column
id="imoColumn"
style="width:45px"
sortBy="#{currentRow.imo}">
<f:facet name="header">
<h:outputText value="IMO" />
</f:facet>
<div class="#{currentRow.imoStyleClass}">
<h:outputText value="#{currentRow.imo}"
</div>
</p:column>
<p:column
id="notesIndicatorColumn"
style="width:35px"
sortBy="#{currentRow.hasNotes}">
<f:facet name="header">
<h:outputText value="#{bundle.labelNotes}" />
</f:facet>
<h:outputText
styleClass="noteIndicator"
id="vesselNotesIndicator"
value="#{bundle.stringNoteIndicatorText}"
title="#{currentRow.notesAsTooltipText}"
rendered="#{currentRow.hasNotes}"
</p:column>
<ui:remove>other column definitions omitted for brevity...</ui:remove>
<p:dataTable>
</code></pre>
<p>Each of my columns has a style with a fixed width in pixels defined, and the dataTable itself has the <code>height</code> attribute set. This seems to be the same as what is shown in the Showcase demo and in the 2.2 manual PDF.</p>
<p>To quote the manual:</p>
<blockquote>
<p><em>Scrolling is a way to display data with fixed headers, in order to enable simple scrolling set scrollable options to true, define a fixed height in pixels and set a fixed width to each column.</em></p>
</blockquote>
<p><strong>Can anyone tell me what I'm doing wrong?</strong></p>
<p>I'm using the current PrimeFaces 3.0-M2-SNAPSHOT with the current Mojarra 2.1 JSF RI.</p>
<p><strong>UPDATE</strong></p>
<p>I have moved to the PrimeFaces 3.0-M2 (not snapshot) release and the problem still exists. Following the suggestions by Maple and BalusC, I have (temporarily) removed the column sorting and tried different doc types. I finally settled on the XHTML 1.0 Strict doc type. It does not show any improvement in IE 7, but does show some improvement in Firefox 4.</p>
<p><strong>IE 7 with XHTML 1.0 Strict</strong></p>
<p><img src="https://i.stack.imgur.com/rTj2j.jpg" alt="IE 7 with XHTML 1.0 Strict"></p>
<p><strong>Firefox 4 with XHTML 1.0 Strict</strong></p>
<p><img src="https://i.stack.imgur.com/ZKvDP.jpg" alt="Firefox 4 with XHTML 1.0 Strict"></p>
<p>The <code><p:dataTable></code> is inside a <code><p:panel></code> which is inside a <code><p:layout></code>. Could this be related?</p>
| 0non-cybersec
| Stackexchange |
European countries by percentage of population living in the capital metropolitan area. | 0non-cybersec
| Reddit |
What are Fail2ban duration accepted notations?. <p>I've been searching around for the accepted duration formats for Fail2ban Jail configuration file (maybe it is not exclusive to F2B).</p>
<p>I want to make sure which suffixes are valid when expressing an amount of time.</p>
<p>F2B configuation is not explicit regarding this: <a href="https://www.fail2ban.org/wiki/index.php/MANUAL_0_8#Jails" rel="nofollow noreferrer">https://www.fail2ban.org/wiki/index.php/MANUAL_0_8#Jails</a></p>
<p>So far, it seems that following notations are accepted : m, h, d </p>
<p>Can anyone point me the a complete list of such suffixes ?</p>
| 0non-cybersec
| Stackexchange |
How to use spot instance with amazon elastic beanstalk?. <p>I have one infra that use amazon elastic beanstalk to deploy my application.
I need to scale my app adding some spot instances that EB do not support.</p>
<p>So I create a second autoscaling from a launch configuration with spot instances.
The autoscaling use the same load balancer created by beanstalk.</p>
<p>To up instances with the last version of my app, I copy the user data from the original launch configuration (created with beanstalk) to the launch configuration with spot instances (created by me).</p>
<p>This work fine, but:</p>
<ol>
<li><p>how to update spot instances that have come up from the second autoscaling when the beanstalk update instances managed by him with a new version of the app?</p>
</li>
<li><p>is there another way so easy as, and elegant, to use spot instances and enjoy the benefits of beanstalk?</p>
</li>
</ol>
<p><strong>UPDATE</strong></p>
<p>Elastic Beanstalk add support to spot instance since 2019... see:
<a href="https://docs.aws.amazon.com/elasticbeanstalk/latest/relnotes/release-2019-11-25-spot.html" rel="nofollow noreferrer">https://docs.aws.amazon.com/elasticbeanstalk/latest/relnotes/release-2019-11-25-spot.html</a></p>
| 0non-cybersec
| Stackexchange |
Veggie Needs Help Cooking Lovely Meat Dish For Gf!!. Hey all!
I'm looking for inspiration here. I've decided that the next time my gf comes to visit I want to cook a delicious dinner for her. She puts up with me being a veggie (yeah yeah, I don't like bacon, fuck me right?!) and I'd really like to treat her to something she'll enjoy.
The catch? I've never, ever cooked meat before. I really don't enjoy the taste or texture of meat and have been a natural veggie my entire life! I can and do cook, but veggies and sauces are (I suspect) quite different to a good lump of, i dunno - lamb, beef, pork???
So yeah, recipes and advice on how the meat should look/behave would be brilliant!
Cheers :) | 0non-cybersec
| Reddit |
ios7 can't get login in gamecenter gain after cancel 3 times. <p>The problem is strange. My system version is IOS7. Everything goes fine on ios7 simulator. However, when I try authenticate on my iphone, the error in the callback block is always <strong><code>"GkErrorCanceled: the requested operation has been canceled or disabled by the user".</code></strong> <br>
Even if I've already logged in game center, the error still pops.
I tried google the problem, and find someone on stackoverflow had conquered the issue:<br> <a href="https://stackoverflow.com/questions/14095993/iphone-simulator-6-0-not-able-to-connect-to-gamecenter-in-sandbox-mode">iPhone Simulator 6.0 not able to connect to gamecenter in sandbox mode</a>. <br>
I tried following the way, however, it didn't work for me. I don't know if I did anything wrong.
Could some one give me a more detailed solution on this issue?
Thanks a lot!</p>
| 0non-cybersec
| Stackexchange |
Harry Potter's Forgotten Predecessor - Twenty-five years ago, Neil Gaiman introduced another bespectacled teen boy with a magical destiny.. | 0non-cybersec
| Reddit |
How to use spot instance with amazon elastic beanstalk?. <p>I have one infra that use amazon elastic beanstalk to deploy my application.
I need to scale my app adding some spot instances that EB do not support.</p>
<p>So I create a second autoscaling from a launch configuration with spot instances.
The autoscaling use the same load balancer created by beanstalk.</p>
<p>To up instances with the last version of my app, I copy the user data from the original launch configuration (created with beanstalk) to the launch configuration with spot instances (created by me).</p>
<p>This work fine, but:</p>
<ol>
<li><p>how to update spot instances that have come up from the second autoscaling when the beanstalk update instances managed by him with a new version of the app?</p>
</li>
<li><p>is there another way so easy as, and elegant, to use spot instances and enjoy the benefits of beanstalk?</p>
</li>
</ol>
<p><strong>UPDATE</strong></p>
<p>Elastic Beanstalk add support to spot instance since 2019... see:
<a href="https://docs.aws.amazon.com/elasticbeanstalk/latest/relnotes/release-2019-11-25-spot.html" rel="nofollow noreferrer">https://docs.aws.amazon.com/elasticbeanstalk/latest/relnotes/release-2019-11-25-spot.html</a></p>
| 0non-cybersec
| Stackexchange |
Free Money. | 0non-cybersec
| Reddit |
Dog train!. | 0non-cybersec
| Reddit |
Problems after deleting Bootcamp/little partition left. <p>I use 2014 model iMac and last year I decided to bootcamp it. After a year I start having hard drive usage issues therefore I uninstalled my bootcamp. But the program couldn't uninstall it properly therefore it left empty space. The disk was deleted somehow. I tried to recover the space with using Disk Utility but now when I use <em>diskutil list</em> I get </p>
<pre><code>/dev/disk0 (internal, physical):
#: TYPE NAME SIZE IDENTIFIER
0: GUID_partition_scheme *1.0 TB disk0
1: Apple_HFS Macintosh HD 999.9 GB disk0s1
</code></pre>
<p>I would like to bootcamp my iMac again but the bootcamp program gives the error: </p>
<blockquote>
<p>The startup disk cannot be partitioned or restored to a single partition. </p>
</blockquote>
<p>How can I set my Macintosh disk to use the full capacity (1TB)?</p>
<p>I tried using internet recovery but I ended up getting -2002F errors. ( even though I changed my DNS).</p>
<p>Also when I press alt while starting the iMac I still can see the Windows Disk even though i deleted it.</p>
<p>Thank you for your attention.</p>
<p>(here is an image of disk utility)
<a href="https://i.stack.imgur.com/tKO1J.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/tKO1J.png" alt="disk utility page"></a></p>
| 0non-cybersec
| Stackexchange |
How to use spot instance with amazon elastic beanstalk?. <p>I have one infra that use amazon elastic beanstalk to deploy my application.
I need to scale my app adding some spot instances that EB do not support.</p>
<p>So I create a second autoscaling from a launch configuration with spot instances.
The autoscaling use the same load balancer created by beanstalk.</p>
<p>To up instances with the last version of my app, I copy the user data from the original launch configuration (created with beanstalk) to the launch configuration with spot instances (created by me).</p>
<p>This work fine, but:</p>
<ol>
<li><p>how to update spot instances that have come up from the second autoscaling when the beanstalk update instances managed by him with a new version of the app?</p>
</li>
<li><p>is there another way so easy as, and elegant, to use spot instances and enjoy the benefits of beanstalk?</p>
</li>
</ol>
<p><strong>UPDATE</strong></p>
<p>Elastic Beanstalk add support to spot instance since 2019... see:
<a href="https://docs.aws.amazon.com/elasticbeanstalk/latest/relnotes/release-2019-11-25-spot.html" rel="nofollow noreferrer">https://docs.aws.amazon.com/elasticbeanstalk/latest/relnotes/release-2019-11-25-spot.html</a></p>
| 0non-cybersec
| Stackexchange |
How Vermont could save the nation from patent trolls. | 0non-cybersec
| Reddit |
Valle del Pisueña, Cantabria, Spain [500x671]. | 0non-cybersec
| Reddit |
Overwatch Hoodie. So, I ordered an Overwatch Hoodie from Blizzard and here are some pictures of the hoodie (and the box) for those interested in such things.
http://imgur.com/a/wbw1y | 0non-cybersec
| Reddit |
On Windows: is it safe to do a robocopy in order to clone the system?. <p>Let me start by giving a bit of a background. On Linux systems, I frequently rely on the fact that as long as I can get all files over from one hard drive to another, and as long as I fix up the boot loader, I'll be left with an identical, bootable, fully functional system. Same thing works for backups and restores (no special system state backup required, just the files) ... even MySQL is recoverable <em>sometimes</em> even when it wasn't frozen at the time of the backup</p>
<p>On Windows, I've never had luck with cloning the system by doing it at a file level. I always need a tool such as VMWare Converter, Ghost, diXML etc .. they are based on taking the image of the drive as a whole. At first I assumed that this was mainly because of the special/magical way windows does it's registry and I didn't question it (it worked). Until today. I realized that this kind of thinking was dumb, and that in reality Windows is also just a collection of files. So as a test I took an offline Windows 2003 server drive, I copied the files over to a blank hard drive, made the drive active and .. it worked perfectly! </p>
<p>Or did it? Why do I have this irrational fear that it will fail just because it's not a verbatim clone like I would have expected with Ghost? Should I be scared? Why was it so easy? Are AD servers any different? Are there cases where this method will fail?</p>
<p>If file-by-file copy is the way to go, why is it that when I tried to do the same thing with VSS (exposing shadow copied C: drive as an S: drive) the same approach failed. More specifically I got a booting system all the way to the login screen. It even accepted my password, but then immediately logged off my user with no error in the GUI. I even tried shutting off all but un-stoppable services before copying ... same result.</p>
<p>By the way I'm using <code>robocopy /E /SEC</code> for all these copy operations</p>
<p>Am I just looking for trouble by using these methods? I know that Ghost etc are proven .. so why reinvent the wheel? ... I get all that ... but as a professional I want to know why the things work the way they do. That's why it's important for me to figure this out. (not to mention a rare possibility of having to do a bare metal restore on a system where I never had system state backup)</p>
| 0non-cybersec
| Stackexchange |
Been thinking about trying to get into the W40K books for a little while now and I just found this Partwork, seem like a good jumping on point?. | 0non-cybersec
| Reddit |
What’s the best movie for a good cry?. | 0non-cybersec
| Reddit |
Why is IntelliJ IDEA hanging on "Indexing"?. <p>I'm running on Arch Linux, on an i7-5930k 6 core CPU and 64GB of DDR4 RAM, and I'm using IntelliJ IDEA 14.</p>
<p>IDEA was working just fine for me several days ago, but one day, suddenly, it began hanging after opening a project, during the "Indexing" stage. I did not update IDEA and nothing changed about my projects. The IDE's UI hangs after it opens the project, with just a tiny little sliver of the progress bar for "Indexing" complete. Every 5-10 minutes or so it unfreezes and the progress bar crawls forward a little bit, before the IDE freezes again for another few minutes. This happens repeatedly for anywhere between 15 minutes and an hour, until it is finally finished indexing, at which point it hangs for another 5-10 minutes doing nothing, before it finally unlocks and allows me to develop.</p>
<p>While this is happening, my system is fairly unresponsive - Firefox tabs take a long time to switch, and scrolling in them is laggy. Opening a new terminal window takes a long time. Switching windows in general takes awhile. In <code>htop</code>, one of my CPU cores is loaded at 100% while the rest have a normal load, and about 6GB of RAM is used (fairly normal load when this system is idle.)</p>
<p>Things I have tried that have not helped:</p>
<ul>
<li>Delete caches folder</li>
<li>Delete entire ~/.IntelliJIDEA14 folder</li>
<li>Reinstall IntelliJ package</li>
<li>Download IntelliJ manually from JetBrains' site and run it from my Downloads folder (to see if there was something wrong with the Arch AUR package)</li>
<li>Configure IntelliJ to use my system JVM and Maven for importing instead of its embedded tools</li>
<li>Opening multiple different projects (not just the one I initially experienced the issue on.)</li>
</ul>
<p>This issue is really hurting my workflow, if anybody has any solution to this I would be very greatful.</p>
| 0non-cybersec
| Stackexchange |
How to prove that there exist $a$ and $b$ in [0,1] such that $\left| f\left( a \right) +g\left( b \right) -ab \right| \ge \frac { 1 }{ 4 } $?. <p>Let $f$ and $g$ be any real-valued functions defined on [0,1],Prove that there exist $a$ and $b$ in [0,1] </p>
<p>such that </p>
<p>$$\left| f\left( a \right) +g\left( b \right) -ab \right| \ge \frac { 1 }{ 4 } $$</p>
<ul>
<li>I don't know how can I start with this question. So , I need some hints which can help me to approach this problem .</li>
</ul>
| 0non-cybersec
| Stackexchange |
Random errors thrown by Bash shell: cannot open named pipe. <p>I have found that keeping a detailed log of every command I run, from which path I ran it from and which user I sudo'd from, is extremely valuable as the years go by and I'm trying to remember what I did. Some time ago, after browsing various articles on this site as well as others I came up with a solution that works really well. Here is what I have in my .bashrc:</p>
<pre><code>SUDOUSER=`who am i | awk '{print $1}'`
SUDOIP=`who am i | awk '{print $6}'`
DT=`date +"%Y%m%d%H%M%S"`
export HISTCONTROL=ignoredups
export HISTFILE=~/.history
DETAILHISTORY=~/.historydetail
echo $DT $SUDOUSER:$SUDOIP[$$] \|\|\| $(finger $SUDOUSER | head -1) logged in on $(date) \|\|\| >> $DETAILHISTORY
export PROMPT_COMMAND='trap "" 1 2 15; DT=`date +"%Y%m%d%H%M%S"`; history -a >(tee -a ~/.bash_history | while read line; do cwd=$(echo "$cwd" | sed "s|$HOME|~|g"); if [[ $line =~ ^#[0-9]*$ ]] ; then continue; fi; echo "$DT $SUDOUSER:$SUDOIP[$$] {$cwd} $line" >> $DETAILHISTORY; done); if [[ $(history 1) == "cd" ]]; then cwd=$OLDPWD; else cwd=$PWD; fi; trap 1 2 15;'
</code></pre>
<p>I get output like this:</p>
<pre><code>20180919150704 MyUsername:(192.168.24.207)[14090280] ||| Login name: MyUsername In real life: MyName logged in on Wed Sep 19 15:07:04 EDT 2018 |||
20180919150704 MyUsername:(192.168.24.207)[14090280] {~} clear
20180919150708 MyUsername:(192.168.24.207)[14090280] {~} cd user_scripts/
20180919150708 MyUsername:(192.168.24.207)[14090280] {~/user_scripts} ll
20180919150714 MyUsername:(192.168.24.207)[14090280] {~/user_scripts} cat file.sh
20180919151013 MyUsername:(192.168.24.207)[14090280] {~/user_scripts} cd
20180919151015 MyUsername:(192.168.24.207)[14090280] {~} cat .bashrc
</code></pre>
<p>Fantastic! It's saved my sanity so many times.</p>
<p>There is a down side however; every so often, out of the blue I'll get this message:</p>
<pre><code>bash: cannot open named pipe /tmp//sh-np.5ARMam for reading: A system call received an interrupt.
</code></pre>
<p>and sometimes I'll get a whole bunch at once:</p>
<pre><code>bash: cannot open named pipe /tmp//sh-np.4QRMal for reading: A system call received an interrupt.
bash: cannot open named pipe /tmp//sh-np.zqRMaj for reading: A system call received an interrupt.
bash: cannot open named pipe /tmp//sh-np.y7RMai for reading: A system call received an interrupt.
bash: cannot open named pipe /tmp//sh-np.6ARMan for reading: A system call received an interrupt.
</code></pre>
<p>I don't see any rhyme or reason for it; sometimes it happens when I adjust the size of the putty/terminal window, which I don't understand. This started happening when I added the detailed history logging (and stops when I disabled it).</p>
<p>Can anyone offer any guesses as to what portion of the history logging in PROMPT_COMMAND may be contributing to this issue, and even better how it might be prevented?</p>
| 0non-cybersec
| Stackexchange |
Sometimes the Lord of the Memes really helps. | 0non-cybersec
| Reddit |
Handoff on mid 2010, El Capitan iMac?. <p>Since I recently upgraded my iPhone, I wanted to try the Continuity features that the Apple ecosystem has to offer. However, since I have a mid 2010 iMac, Handoff is not supported. I've been looking for unofficial resources, and have reached no conclusions.</p>
<p>Has anyone achieved this, or know how to? Thanks a lot!</p>
<p>P.S: Here are some articles I've found, just in case they can be useful for you:</p>
<p><a href="http://www.macworld.co.uk/how-to/mac-software/get-continuity-handoff-airdrop-on-old-mac-3582632/" rel="nofollow">http://www.macworld.co.uk/how-to/mac-software/get-continuity-handoff-airdrop-on-old-mac-3582632/</a>
<a href="http://www.macrumors.com/2014/10/23/continuity-activation-tool/" rel="nofollow">http://www.macrumors.com/2014/10/23/continuity-activation-tool/</a></p>
| 0non-cybersec
| Stackexchange |
What didn't you notice about yourself until someone told you?. | 0non-cybersec
| Reddit |
Person actually changes their opinion when faced with alternate perspective!. | 0non-cybersec
| Reddit |
[Help] Serious aggression issues.. Some background first.
My dogs a male 86 lb Bull Mastiff cross. He was my mothers for the first 4-5 months but got too aggressive so she left him with me. I wasn't willing to take him as I had little experience with dogs (much less aggressive ones) but it was either that or have him put down.
He's now turning 4 in a few months and my knowledge of dogs has grown immensely since as has my fondness of him. He's still very aggressive when up close but he no longer barks at everything within a 15m radius (and this is definitely an aggressive bark, not a "back off or I'll hurt you" kind.) I found I cannot trust him at all around strangers or animals as several instances have already happened. Unfortunately I'm now recently finding out I cannot trust him with family anymore. He's now tried to attack two members in the family. I've tried so many things over the years which many seemed to help but I feel I can longer keep him. The closest trainer is $1,800 and uses shock collars whereas the next is several hours away.
I write this because today was the second attack on my brother (he's fine, I managed to get the dog before anything happened. Unfortunately I've become accustom to this so my reaction time is fairly quick) , who afterwards threatened to kill him if he tries again. He not the violent type and I'm positive he wouldn't do anything but it has opened my eyes a little more to the situation. My family nor friends feel safe around him. He lives a life of isolation due to his issues (he goes for walks and runs with me as well as plays everyday either at the house or the lake but it's always just me and him, far from anyone else. I really wish he had others to play with.)
I love him so much but I'm really out of ideas here. I want a better life for him. I really don't know if I should call it quits and find someone more capable. | 0non-cybersec
| Reddit |
Does changing web hosting affect search engine rankings?. <p>I have been hosting in a server from last 2 years. I am planning to change the hosting server. Before I change the hosting server I would like to know whether it affects my site's rankings or not?</p>
| 0non-cybersec
| Stackexchange |
i love you baby. | 0non-cybersec
| Reddit |
Windows 8/10 file backup to QNAP NAS with file history & enrypted remote backup. <p>I have a QNAP TS-251+ NAS (connected via VPN + SMB if it matters) and would like to backup files from two machines to it (running Windows 8.1 and Windows 10), mostly user profile data (My Documents, etc.).
I'm currently not using the snapshot function of the NAS, it's running a standard RAID setup.</p>
<p>I think it would be nice to copy the data on a file level to be sure they are accessible later. I have slight trust issues with proprietary backup formats and it would also give me access to the files from my phone.
It would be a one-way sync, so that I can delete stuff from my PC, but it would still be available on the NAS until I delete it manually from there.
I guess robocopy would be the standard choice here?</p>
<p>But I'd also like to keep file history. For instance in case files get corrupted locally and I don't notice before the server has been updated with the changes.
I guess this would be difficult/impossible to do on a file level if one wants to keep the directory structure etc.
So maybe a combination with a "file history" tool on the NAS?</p>
<p>Finally, I would also like to backup the whole NAS to some cloud storage in an encrypted way. Any good candidates for that?</p>
<p>Thanks.</p>
| 0non-cybersec
| Stackexchange |
AOKP founder Roman Birg doesn’t want to Kang anymore, joins Cyanogen Inc. | 0non-cybersec
| Reddit |
Difference between Stream Analytics and Time Series Insights. <p>In the context of Azure IoT hub, when would one use Stream Analytics over Time Series Insights?</p>
<p>The product pages and documentation for both indicates they are heavily geared for IoT/data applications. However, I'm not clear on the differences.</p>
<p>The use case I have is both real time monitoring as well as ETL analysis. Could (or even should?) the two be used together?</p>
<p>One immediate difference I can see is that Time Series Insights stores the data whereas Stream Analytics (I think) would need the developer to integrate storage.</p>
| 0non-cybersec
| Stackexchange |
Pear and arugula salad. Refreshing spring salad of pear and arugula. Light and energetic meal.
Ingredients
4 larger sweet pears
400 g arugula
walnuts (two full hands)
two tablespoons of freshly grated Parmesan cheese
1 lemon juice
salt and ground black pepper
extra virgin olive oil
Directions
1. Peel the pears, and cut each pear into 4 parts. Wash the arugula and dry it.
2. Onto 4 plates place 4 slices of each pear. And on top of it washed arugula.
3. Pour it with quality olive oil and lemon juice. Add salt and ground black pepper.
4. On top of everything, add grated Parmesan cheese, and walnuts.
For more details with photo visit [Pear and arugula salad](http://www.cooktroop.com/recipes/pear-and-arugula-salad/) | 0non-cybersec
| Reddit |
Bad Rabbit ransomware technical dive. | 1cybersec
| Reddit |
ssh: connecting through localhost port 22. <p>Hey so whenever I try connecting ssh through port 22 I get this error,</p>
<p>ssh: connect to host localhost port 22: Connection refused</p>
<p>The linux computers have a static IP of 192.168.2.128/129 </p>
<p>I reinstalled ssh fresh and still get this error, I've been able to get
access to my device but without privileges<br>
Can someone help or guide me in sucessfully connecting both linux terminals,
any help is appreciated. Thx</p>
<p>When i ssh -v pwnie@localhost 192.168.2.128 from my laptop I get a permissions token error</p>
<pre><code>OpenSSH_7.4p1 Debian-6, OpenSSL 1.0.2h 3 May 2016
debug1: Reading configuration data /etc/ssh/ssh_config
debug1: /etc/ssh/ssh_config line 19: Applying options for *
debug1: Connecting to localhost [::1] port 22.
debug1: connect to address ::1 port 22: Connection refused
debug1: Connecting to localhost [127.0.0.1] port 22.
debug1: connect to address 127.0.0.1 port 22: Connection refused
ssh: connect to host localhost port 22: Connection refused
</code></pre>
| 0non-cybersec
| Stackexchange |
Need help installing FinchTv from a package. <p>I need to install FinchTv for a school. I've downloaded the <code>tar.gz</code> and extracted it. There doesn't seem to be an install readme. I've attempted to run <code>/.configure</code>, <code>make</code>, and <code>install</code>, on a executable in the file called `finchtv, but nothing happens. </p>
<p>In the notes it reads, "Note: </p>
<pre><code>FinchTV on Solaris requires libCstd.so.1.
All Solaris 8 installs include this library except for the minimum installation cluster.
The 108434 and 108435 patches will install libCstd.so.1 if SUNWlibC is
installed."
</code></pre>
<p>On the requirments it states it has been tested on, <strong>RedHat: v. 9, Enterprise WS release 3 / SuSE Linux: v. 8.2</strong></p>
<p>So what's the deal? Do I need to download some library or something before I can install it? I'm new to Ubuntu so any help would be great. Thanks. </p>
| 0non-cybersec
| Stackexchange |
Almost done with my pre-roll when I noticed that it came with instructions. | 0non-cybersec
| Reddit |
Could intelligent life have appeared very early in the Universe?. We're talking years, or thousands or even hundreds of thousands of years after the big bang has happened | 0non-cybersec
| Reddit |
This is what scum of the earth looks like. | 0non-cybersec
| Reddit |
Request: Help to hookup raspberry pi to Smith Thompson home security system. I currently have a Smith Thompson Home Security System along with a key fob that can be used to set the alarm to away, stay,panic or unlock.
Smith Thompson is asking for an additional monthly fee in order to provide me the ability to perform the same functions via wifi/internet.
I figured there must be a way for me to either hookup a raspberry pi to the key fob or home module directly to achieve this same functionality.
I already have the ability to VPN back to my home network via DD-WRT.
It would seem that Smith Thompson has partnered with the following company to provide this functionality:
https://www.uplink.com/our-products/remote-interactive-services/
Appreciate any help or ideas in order to achieve this. | 0non-cybersec
| Reddit |
Cat not letting maintenance do their job. | 0non-cybersec
| Reddit |
LookAndFeel-independent reference of color keys. <p>I am currently working on a set of custom controls for a product of the company I'm working in. For this, I am extending a lot of Swing controls and also overriding a lot of <code>paint</code> methods.</p>
<p>In order to maintain a consistent color scheme, I receive the colors for my <code>paint</code>, <code>setBackground</code> etc. methods using <code>UIManager.getColor</code>.</p>
<p>This was perfectly fine until we noticed that the <em>Nimbus</em> LookAndFeel, which is shipped with current JRE versions, uses totally different color keys, thus many things looks totally out of place.</p>
<p>For instance, while all other stock LookAndFeels (Metal, Windows Classic, Windows, CDE/Motif, GTK) have defined the key <em>"text"</em> as a bright background for texts and <em>"textText"</em> as the corresponding foreground color, <em>"text"</em> in Nimbus is actually a black foreground color, and a standard text background color does not seem to exist.</p>
<p><em>"TextField.background"</em> would work, but that, for instance, doesn't exist for the Windows LookAndFeels.</p>
<p>I suppose you get the problem by now. I don't want to have to maintain a set of color keys for each LAF, who knows what LAFs will be added in the future and which my company may decide to use.</p>
<p>A simple solution would be getting rid of Nimbus, of course, but understandably my boss doesn't like this idea at all, besides Nimbus is part of the JRE these days and should be supported.</p>
<p>So I wonder whether there is <em>any</em> standardized way to get LAF-dependent colors like, say, "text background / foreground", "selected text bg/ fg", etc.?</p>
| 0non-cybersec
| Stackexchange |
Network connectivity lost when using NordVPN Kill Switch. <p>I'm using NordVPN with the Kill Switch feature enabled.</p>
<p>If my computer does not shut down gracefully, the file <code>/etc/resolv.conf</code> is set immutable, and any future attempts to resolve names fail.</p>
<p>Sometimes, even without an unclean shutdown, when running <code>ping</code> as <code>root</code>, I see:</p>
<blockquote>
<p>ping: sendmsg: Operation not permitted</p>
</blockquote>
<p>How do I use the kill switch and have uninterrupted connectivity?</p>
| 0non-cybersec
| Stackexchange |
Fascinating.. | 0non-cybersec
| Reddit |
Does mounting a large disk image require a certain amount of free space on the internal drive?. <p>I've got a bunch of Mac disk images (.dmg files) that are 100 GB or larger. I'm currently on an iMac with a few hundred gigabytes of free space, but I'm going to be moving to a Mac laptop with 128 GB storage.</p>
<p>So, I'm wondering, would that be a problem when I have less than 100 GB of free space on my computer, but I'm opening a disk image larger than 100 GB? My guess would be <em>no</em>, but is ANY space on the internal drive used at all when mounting an image? </p>
<p>How exactly does mounting an image work, does it just change the way the operating system sees the files as one file (the disk image) rather than the actual files within the disk image, until it is mounted? Therefore, no internal space is necessary for the mount operation?</p>
<p><strong>Follow-up question:</strong> Is it any slower to read from a DMG on an external drive than it is to read from any other files on the same external drive? Basically, is there any performance hit from having files in a DMG?</p>
| 0non-cybersec
| Stackexchange |
Proof Verification: If $y\neq 0$ and $|y-y_0|<\min(\frac{|y_0|}{2},\frac{ε|y_0|^2}{2})$ then $y_0\neq 0$ and $|\frac {1}{y}-\frac{1}{y_0}|<ε$. <p>This is problem 22 from Spivak's Calculus 4th ed., Chapter 1:</p>
<blockquote>
<p>If <span class="math-container">$y\neq 0$</span> and <span class="math-container">$|y-y_0|<\min\left(\frac{|y_0|}{2},\frac{\varepsilon|y_0|^2}{2}\right)$</span> then <span class="math-container">$y_0\neq 0$</span> and <span class="math-container">$\left|\frac {1}{y}-\frac{1}{y_0}\right|<\varepsilon$</span>.</p>
</blockquote>
<p>This is my proof:</p>
<p><span class="math-container">$$|y_0|-|y|\leq|y-y_0|<\frac{|y_0|}{2} \Rightarrow \frac{|y_0|}{2}<|y|\Rightarrow\frac{\varepsilon|y_0|^2}{2}<\varepsilon|y_0||y|$$</span></p>
<p>Therefore, <span class="math-container">$$|y-y_0|<\varepsilon|y_0||y|=\varepsilon|y_0\cdot y|$$</span></p>
<p><span class="math-container">$$|y-y_0| \cdot\left|\frac{1}{y_0 \cdot y}\right| < \varepsilon \Rightarrow \left|\frac{1}{y_0}-\frac{1}{y}\right|=\left|\frac{1}{y}-\frac{1}{y_0}\right|<\varepsilon\,,$$</span> which completes the proof. </p>
<p>My proof is slightly different to the one Spivak offers, so I'm posting it to get it verified. Is it correct?</p>
| 0non-cybersec
| Stackexchange |
arXiv:gr-qc/9304028v1 20 Apr 1993
ar
X
iv
:g
r-
qc
/9
30
40
28
v1
2
0
A
pr
1
99
3
Static solutions of the spherically symmetric
Vlasov-Einstein system
G. Rein
Mathematisches Institut der Universität München
Theresienstr. 39, W8000 München 2, Germany
Abstract
We consider the Vlasov-Einstein system in a spherically symmetric
setting and prove the existence of static solutions which are asymptot-
ically flat and have finite total mass and finite extension of the matter.
Among these there are smooth, singularity-free solutions, which have
a regular center and may have isotropic or anisotropic pressure, and
also solutions, which have a Schwarzschild-singularity at the center.
The paper is an extension of previous work, where only smooth, glob-
ally defined solutions with regular center and isotropic pressure were
considered, cf. [8]
1 Introduction
It is well known that the only static, spherically symmetric vacuum solutions
of Einstein’s field equations are the Schwarzschild solutions which possess
a spacetime singularity (or are identically flat). In the present note we
couple Einstein’s equations with the Vlasov or Liouville equation for a static,
spherically symmetric distribution function f on phase space, describing an
ensemble of identical particles such as stars in a galaxy, galaxies in a galaxy
cluster etc.. This results in the following system of equations:
v√
1+v2
·∂xf−
√
1+v2µ′
x
r
·∂vf =0, x,v∈ IR3, r := |x|,
e−2λ(2rλ′−1)+1 = 8πr2ρ,
e−2λ(2rµ′+1)−1 = 8πr2p,
1
http://arxiv.org/abs/gr-qc/9304028v1
where
ρ(x)=ρ(r) :=
∫
IR3
√
1+v2f(x,v)dv,
p(x)=p(r) :=
∫
IR3
(
x ·v
r
)2
f(x,v)
dv√
1+v2
.
Here the prime denotes derivative with respect to r, and spherical symmetry
of f means that f(Ax,Av)= f(x,v) for every orthogonal matrix A and x,v∈
IR3. If we let x= r(sinθcosφ,sinθsinφ,cosθ) then the spacetime metric is
given by
ds2=−e2µdt2+e2λdr2+r2(dθ2+sin2θdφ2).
Asymptotic flatness is guaranteed by the boundary condition
lim
r→∞
λ(r)= lim
r→∞
µ(r)=0,
a regular center at r=0 is guaranteed by the boundary condition
λ(0)=0.
We refer to [6] on the particular choice of coordinates on phase space leading
to the above formulation of the system. It should be pointed out that
the above equation for f is only equivalent to the Vlasov equation if f is
spherically symmetric.
A brief overview of the literature related to the present investigation
seems in order. In [6] the initial value problem for the corresponding time
dependent system is investigated and the existence of singularity-free solu-
tions is established for small initial data. In [7] it is shown that the classical
Vlasov-Poisson system is the Newtonian limit of the Vlasov-Einstein system.
The existence of globally defined, smooth, static solutions with a regular cen-
ter, finite radius, and finite total mass is investigated in [8]; that investigation
is restricted to solutions with isotropic pressure. For the Vlasov-Poisson sys-
tem the existence of spherically symmetric steady states is established in [3],
and we briefly recall the general approach followed there: Taking the distri-
bution function f as a function of the local energy and the modulus of the
angular momentum, which are conserved along characteristics, the problem
is reduced to solving a nonlinear Poisson problem. For certain cases corre-
sponding to the so-called polytropes it can then be shown that this leads to
solutions with finite radius and finite total mass, cf. also [4]. Cylindrically
symmetric, static solutions of the Vlasov-Poisson system are investigated in
2
[2]. A system in some sense intermediate between the Newtonian and the
general-relativistic setting is the relativistic Vlasov-Poisson system, where
similar results as for the nonrelativistic version hold, cf. [1]. In [11] it is
shown that coupling Einstein’s equations with a Yang-Mills field can lead
to static, singularity-free solutions with finite total mass. Static solutions of
general-relativistic elasticity have been studied in [5]. For further references,
especially on the astrophysical literature, we refer to [10].
The present investigation proceeds as follows: In the next section we
give two conserved quantities, which correspond to the local energy and
angular momentum in the Newtonian limit, and reduce the existence prob-
lem for static solutions of the Vlasov-Einstein system to solving a nonlinear
system of ordinary differential equations for λ and µ. The fact that the
distribution function f indeed has to be a function of the local energy and
angular momentum—usually referred to as Jeans’ Theorem—is rigorously
established for the Vlasov-Poisson system in [3] but not known in the present
situation. In other words, it is not clear whether our ansatz for f covers all
possible spherically symmetric, static solutions. The existence of solutions to
the remaining system for λ and µ is investigated in the third section. There
we dispose of the restriction that f depends on the local energy only, which
was used in [8] and lead to solutions with necessarily isotropic pressure.
Nevertheless, the arguments used in the present, more general situation are
considerably simpler than the ones used in [8]; a key element in the proof
that the solutions exist globally in r is the Tolman-Oppenheimer-Volkov
equation. In the fourth section we show that—for an appropriate ansatz
for f , corresponding to the polytropes in the classical case—the solutions
obtained by our approach have regular center, finite mass, and finite radius.
This is done by treating the Vlasov-Einstein system as a perturbation of
the Vlasov-Poisson system and using the criteria for a finite radius from the
classical Lane-Emden-Fowler equation. In the last section we prove the exis-
tence of solutions with a Schwarzschild-singularity at the center, surrounded
by Vlasov-matter with finite radius and finite total mass. Surprisingly, the
latter features of these solutions can be obtained easily and without the
perturbation argument used in the nonsingular case mentioned above.
3
2 Conserved quantities and reduction of the prob-
lem
As explained in the introduction, a key point in our investigation is to reduce
the full system to a nonlinear system of ordinary differential equations for λ
and µ. This is achieved by the ansatz that the distribution function depends
only on certain integrals of the characteristic system. In the coordinates used
above, the characteristic system corresponding to the above equation for f
reads
ẋ =
v√
1+v2
,
v̇ = −
√
1+v2µ′(r)
x
r
;
note that these equations are not the geodesic equations. One immediately
checks that the quantities
E := eµ(r)
√
1+v2, F :=x2v2−(x ·v)2= |x×v|2
are conserved along characteristics; in Sect. 4 the relation of E to the classical
local energy will become apparent, F can be interpreted as the modulus of
the angular momentum. If we take f to be of the form
f(x,v)=Φ(E,F )
for some function Φ, the Vlasov equation is automatically satisfied. Inserting
this into the definitions of ρ and p we obtain the following nonlinear system
for λ and µ:
e−2λ(2rλ′−1)+1 = 8πr2GΦ(r,µ), (2.1)
e−2λ(2rµ′+1)−1 = 8πr2HΦ(r,µ). (2.2)
Here
GΦ(r,u) =
2π
r2
∫ ∞
1
∫ r2(ǫ2−1)
0
Φ(eµ(r)ǫ,F )
ǫ2
√
ǫ2−1−F/r2
dF dǫ,
HΦ(r,u) =
2π
r2
∫ ∞
1
∫ r2(ǫ2−1)
0
Φ(eµ(r)ǫ,F )
√
ǫ2−1−F/r2dF dǫ
for r,u>0 which follows by a simple transformation of variables in the in-
tegrals defining ρ and p. These latter quantities are then given by
ρ(r)=GΦ(r,µ(r)), p(r)=HΦ(r,µ(r)),
4
once a solution of the system (2.1), (2.2) is known to exist.
Of course one has to make some assumptions on Φ in order to obtain
existence results for the above system and to investigate the properties of its
solutions. The assumption used below is certainly not the weakest possible,
but on the one hand it is sufficiently general to encompass a large class of
examples, leading to quite different classes of solutions, and on the other
hand the main ideas of the proofs are not buried under technicalities. We
require Φ to satisfy the following
Assumption on Φ:
Φ(E,F )=φ(E)(F −F0)l+, E >0, F >0,
where F0≥0, l>−1/2, and φ∈L∞(]0,∞[) is nonnegative with φ(E)=
0, E >E0, for some E0>0.
Under this assumption the functions GΦ and HΦ are easily seen to take
the form
GΦ(r,u) = clr
2le−(2l+4)ugφ
(
eu
√
1+F0/r2
)
, (2.3)
HΦ(r,u) =
cl
2l+3
r2le−(2l+4)uhφ
(
eu
√
1+F0/r2
)
, (2.4)
where
gφ(t) :=
∫ ∞
t
φ(E)E2(E2− t2)l+
1
2dE, (2.5)
hφ(t) :=
∫ ∞
t
φ(E)(E2− t2)l+
3
2dE (2.6)
for t>0, and
cl :=2π
∫ 1
0
sl√
1−s
ds.
3 Existence of solutions
As a first step we show that the functions gφ and hφ defined by (2.5) and
(2.6) are well behaved for functions φ as considered in the assumption above.
More precisely:
5
Lemma 3.1 Eqns. (2.5) and (2.6) define decreasing functions gφ,hφ∈
C1(IR+) and
h′φ(t)=−(2l+3)t
∫ ∞
t
φ(E)(E2− t2)l+1/2dE, t>0.
Proof: Obviously, the integrals defining gφ and hφ exist. Lebesgue’s
dominated convergence theorem implies that the functions gφ and hφ are
continuous. For t>0 and ∆t>0 such that t−∆t>0 we have
1
∆t
(hφ(t−∆t)−hφ(t))=
1
∆t
∫ t
t−∆t
φ(E)
(
E2−(t−∆t)2
)l+3/2
dE
+
∫ ∞
t
φ(E)
1
∆t
(
(E2−(t−∆t)2)l+3/2−(E2− t2)l+3/2
)
dE
=: I1+I2.
Obviously, I1→0 as ∆t→0. The term I2 has a limit as ∆t→0 by Lebesgue’s
theorem. Thus, the function hφ is left-differentiable with
d
dt
−
hφ(t)=−(2l+3)t
∫ ∞
t
φ(E)(E2− t2)l+1/2dE.
Again by Lebesgue’s theorem this function is continuous, and a continuous
and continuously left-differentiable function is continuously differentiable.
Similarly, we see that
d
dt
−
gφ(t)=−(2l+1)t
∫ ∞
t
φ(E)E2(E2− t2)l−1/2dE,
which is again continuous. The derivatives are negative, and thus gφ and hφ
decrease. ✷
The regularity of the functions gφ and hφ being established, we can now
prove local existence and uniqueness of λ and µ. Note that in the last section
we will need to pose initial data at some r0>0 which is why we include this
case in the following results.
Theorem 3.2 Let Φ satisfy the general assumption and let GΦ and HΦ
be defined by Eqns. (2.3), (2.4), (2.5), (2.6). Then for every r0≥0 and
λ0,µ0∈ IR with λ0=0 if r0=0 there exists a unique maximal solution λ,µ∈
C1([r0,R[), R>r0, of the Eqns. (2.1) and (2.2) with
λ(r0)=λ0, µ(r0)=µ0.
6
Proof: Due to the regularity of the right hand sides in (2.1), (2.2)—cf.
Lemma 3.1—the result is of course trivial in the case r0>0. In the case
r0=0 one has to deal with the singularity of the Eqns. (2.1) and (2.2) at
r=0. Using the boundary condition at r=0, Eqn. (2.1) can be integrated
to give
e−2λ(r)=1− 8π
r
∫ r
0
s2GΦ(s,µ(s))ds. (3.1)
If we insert this into Eqn. (2.2) we obtain an equation for µ alone:
µ′(r)=
4π
1− 8π
r
∫ r
0 s
2GΦ(s,µ(s))ds
(
rHΦ(r,µ(r))+
1
r2
∫ r
0
s2GΦ(s,µ(s))ds
)
.
(3.2)
Integrating Eqn. (3.2) subject to the initial condition µ(0)=µ0 we obtain
the following fixed point problem for µ:
µ(r)= (Tµ)(r), r≥0
where
(Tµ)(r) :=µ0 +
∫ r
0
4π
1− 8π
s
∫ s
0 σ
2GΦ(σ,µ(σ))dσ
(
sHΦ(s,µ(s))+
1
s2
∫ s
0
σ2GΦ(σ,µ(σ))dσ
)
ds.
A lengthy but straight forward argument shows that T maps the set
M :=
{
µ : [0,δ]→ IR | µ(0)=µ0, µ0≤µ(r)≤µ0+1,
8π
r
∫ r
0
s2GΦ(s,µ(s))ds≤
1
2
, r∈ [0,δ]
}
into itself and acts as a contraction with respect to the norm ‖·‖∞, pro-
vided δ>0 is chosen small enough. This gives the existence of a solution of
Eqn. (3.2) on the interval [0,δ]. On this interval we define λ by Eqn. (3.1)
and obtain a local solution λ,µ∈C1([0,δ]) of (2.1), (2.2). Obviously, the
boundary conditions at r=0 are satisfied, and the solution is unique. ✷
In order to show that the above solutions actually extend to r=∞ we
need a relation which is known as the Tolman-Oppenheimer-Volkov equation
in the context of the general relativistic description of spherically symmetric
fluid balls, cf. [12, Eqn. 6.2.19].
7
Lemma 3.3 Define
pT (r) :=
1
2
∫
IR3
∣
∣
∣
∣
x×v
r
∣
∣
∣
∣
2
f(x,v)
dv√
1+v2
,
and let λ,µ be a solution of the system (2.1), (2.2) on the interval [r0,R[.
Then pT has the form
pT (r)= (l+1)p(r)+
cl
2
F0r
2l−2e−(2l+2)µ(r)kφ
(
eµ(r)
√
1+F0/r
2
)
,
where
kφ(t) :=
∫ ∞
t
φ(E)(E2− t2)l+1/2dE, t>0,
defines a decreasing C1-function, and
p′(r)=−µ′(r)(p(r)+ρ(r))−
2
r
(p(r)−pT (r)) , r∈]r0,R[.
Proof: The formula for pT is obtained by a transformation of variables,
and the regularity and monotonicity of kφ follow as in Lemma 3.1. Using
(2.4), (2.6), and Lemma 3.1 one obtains the relation
p′(r) =
2l
r
p(r)−(2l+4)µ′(r)p(r)
−cl
(
1+F0/r
2
)
r2le−(2l+2)µ(r)kφ
(
eµ(r)
√
1+F0/r2
)
µ′(r)
+clr
2l−3F0e
−(2l+2)µ(r) kφ
(
eµ(r)
√
1+F0/r2
)
which, after some further calculations, leads to the Tolman-Oppenheimer-
Volkov equation. ✷
Remark: The quantity pT is the tangential pressure generated by the phase
space density f , as opposed to the radial pressure p. Note that if F0=0 then
p and pT differ only by a multiplicative constant, and if F0= l=0, i. e. the
phase space distribution is independent of the angular momentum, then
p=pT , i. e. the solution has isotropic pressure.
Theorem 3.4 Let Φ satisfy the general assumption and let GΦ and HΦ be
defined by Eqns. (2.3), (2.4), (2.5), (2.6). Then for every r0≥0 and λ0≥0,
µ0∈ IR with λ0=0 if r0=0 there exists a unique solution λ,µ∈C1([r0,∞[)
of the Eqns. (2.1) and (2.2) with
λ(r0)=λ0, µ(r0)=µ0.
8
Proof: Let λ,µ∈C1([r0,R[) be the maximal solution to (2.1), (2.2) which
exists by Thm. 3.2. We have the following equations on [r0,R[:
e−2λ(2rλ′−1)+1=8πr2ρ(r), (3.3)
e−2λ(2rµ′+1)−1=8πr2p(r), (3.4)
p′(r)=−µ′(r)(p(r)+ρ(r))− 2
r
(p(r)−pT (r)) . (3.5)
Note that—as opposed to the case considered in [8]—the functions ρ and
p are not necessarily strictly decreasing on their support so that we cannot
write ρ as a function of p, and we cannot use the analysis in [9] directly.
Nevertheless, the proof given here is somewhat simpler than the one given
in [8]. If we integrate Eqn. (3.3) we obtain
e−2λ(r)=1− 8π
r
∫ r
r0
s2ρ(s)ds− 1
r
r0(1−e−2λ0). (3.6)
Inserting this into Eqn. (3.4) yields
µ′(r)=4πe2λ(r) (p(r)+w(r)) (3.7)
where
w(r) :=
1
r3
(
∫ r
r0
s2ρ(s)ds+
r0(1−e−2λ0)
8π
)
. (3.8)
Finally, by adding Eqns. (3.3) and (3.4) we have
(λ′+µ′)(r)=4πre2λ(r) (p(r)+ρ(r)) . (3.9)
We now wish to establish a differential inequality for the quantity eλ+µ(p+
w), which will allow us to bound λ and µ and conclude that R=∞. Using
Eqns. (3.9), (3.5), (3.7), and (3.8) we see that
(
eλ+µ(p+w)
)′
(r) = eλ+µ
(
−
2p
r
+
2pT
r
−
3w
r
+
ρ
r
)
≤ eλ+µ
(
2pT
r
+
ρ
r
)
;
note that the terms which were dropped are indeed negative by the as-
sumption λ0≥0. Now assume that R<∞. Without loss of generality, we
may assume that there exists r1∈]r0R[ and C>0 such that w(r)≥C for
9
r∈ [r1,R[, since otherwise the solution is trivial. The fact that µ is increas-
ing and the functions gφ and kφ are decreasing implies that ρ and pT and
thus also ρ/r and pT /r are bounded on the interval [r1,R[. Thus, we can
continue the above estimate to obtain
(
eλ+µ(p+w)
)′
(r)≤Ceλ+µ≤Ceλ+µ(p(r)+w(r)) .
This implies that
eλ(r)+µ(r)≤ C
p(r)+w(r)
≤C, r∈ [r1,R[.
Since λ(r)≥0 by (3.6) and µ(r)≥µ0 by monotonicity, this implies that λ
and µ are bounded on [r0,R[ which is a contradiction to the maximality of
R. Thus R=∞, and the proof is complete. ✷
Remarks:
1. If r0>0 then λ,µ∈C2([r0,∞[) and ρ,p∈C1([r0,∞[).
2. If r0=F0=0 then λ,µ∈C1([0,∞[)∩C2(]0,∞[) with λ′(0)=µ′(0)=
0 and ρ,p∈C1(]0,∞[). If in addition l=0 or l>1/2 then λ,µ∈
C2([0,∞[)∩C2(IR3) and ρ,p∈C1([0,∞[)∩C1(IR3) with ρ′(0)=p′(0)=
0 where functions in r are identified with the corresponding radially
symmetric functions on IR3. Thus we see that in the case r0=0 the
solutions are as regular at the center as anywhere else if various pa-
rameters are chosen appropriately.
3. The phase space density f :=Φ(E,F ) is a solution of the Vlasov equa-
tion in the sense that it is constant along characteristics. If Φ is con-
tinuous or continuously differentiable then in addition f has the same
regularity, and in the latter case satisfies Vlasov’s equation classically.
4 Singularity-free solutions with finite mass and
finite radius
In this section we are interested in smooth, singularity-free solutions with
with a regular center. Thus, we consider the boundary condition λ(0)=0.
Also, we set F0=0 in this section, the case F0>0 will play its role in the
next section.
10
In order to decide whether a solution obtained in the previous section
has finite total mass or whether ρ(r) vanishes for r large, one has to have
rather detailed information on the behaviour of the function µ. Due to
the complexity of Eqn. (3.2) we have not been able to decide these ques-
tions directly, even for simple examples of Φ and without dependence on F .
However, it is possible to show that the solutions obtained above converge
to solutions of the corresponding Newtonian problem as the speed of light
tends to infinity. It is then possible to use the results on finite mass and
finite radius which are known in the Newtonian case for the so-called poly-
tropes to obtain solutions with the same properties for the Vlasov-Einstein
system.
To carry out this program we introduce the parameter γ := 1
c2
where
c denotes the speed of light, define ν := 1
γ
µ, and recall from [7] that the
Vlasov-Einstein system with γ inserted in the appropriate places reads
v
√
1+γv2
·∂xf−
√
1+γv2ν ′
x
r
·∂vf =0,
e−2λ(2rλ′−1)+1 = 8πγr2ρ,
e−2λ(2rν ′+1/γ)−1/γ = 8πγr2p,
where
ρ(x) :=
∫
IR3
√
1+γv2f(x,v)dv,
p(x) :=
∫
IR3
(
x ·v
r
)2
f(x,v)
dv
√
1+γv2
.
The conserved quantity E now becomes
√
1+γv2eγν(x),
and F remains unchanged. In order to obtain the correct limit as γ→0,
we have to rewrite our ansatz for the distribution function in the following
form:
f(x,v)=φ
(
1
γ
√
1+γv2eγν(r)−
1
γ
)
F l. (4.1)
As above the Vlasov-Einstein system can then be reduced to a single equa-
tion for ν alone, namely
ν ′(r)= (4.2)
4π
1− 8π
r
γ
∫ r
0 s
2l+2gφ,γ(ν(s))ds
(
γr2l+1hφ,γ(ν(r))+
1
r2
∫ r
0
s2l+2gφ,γ(ν(s))ds
)
,
11
where
gφ,γ(u) := cle
−2(l+2)γu
∫ ∞
e
γu
−1
γ
φ(E)(1+γE)2
(
1
γ
(1+γE)2− 1
γ
e2γu
)l+1/2
dE,
(4.3)
hφ,γ(u) :=
cl
2l+3
e−2(l+2)γu
∫ ∞
e
γu
−1
γ
φ(E)
(
1
γ
(1+γE)2−
1
γ
e2γu
)l+3/2
dE,
(4.4)
so that
ρ(r)= r2lgφ,γ(ν(r)), p(r)= r
2lhφ,γ(ν(r)). (4.5)
For the Newtonian case the corresponding ansatz
f(x,v)=φ
(
v2
2
+U(r)
)
F l
reduces the Vlasov-Poisson system to the equation
U ′(r)=
4π
r2
∫ r
0
s2l+2g0(U(s))ds, (4.6)
where
g0(u) := cl
∫ ∞
u
φ(E)(2(E−u))l+1/2dE.
Assume that φ∈L∞(IR) and E0=0, and fix ν0<0. Clearly, the results of
the previous section apply so that for every γ >0 Eqn. (4.2) has a unique,
nontrivial, global solution with ν(0)=ν0. Let U ∈C1([0,∞[) be the global
solution of (4.6) with U(0)=ν0. We shall prove that ν converges to U as
γ→0, more precisely:
Lemma 4.1 For every R>0 there exist constants C>0 and γ0>0 such
that for every γ∈]0,γ0] the solution ν of (4.2) with ν(0)=ν0 satisfies the
estimate
|ν(r)−U(r)|≤Cγmin{l+1/2,1}, r∈ [0,R],
where U is the solution of (4.6) with U(0)=ν0.
Proof: We have the estimate
|ν ′(r)−U ′(r)|≤ I1+I2+I3+I4,
12
where
I1 :=
4π
1− 8π
r
γ
∫ r
0 s
2l+2gφ,γ(ν(s))ds
γr2l+1hφ,γ(ν(r)),
I2 :=
∣
∣
∣
∣
∣
1
1− 8π
r
γ
∫ r
0 s
2l+2gφ,γ(ν(s))ds
−1
∣
∣
∣
∣
∣
4π
r2
∫ r
0
s2s+2gφ,γ(ν(s))ds,
I3 :=
4π
r2
∫ r
0
s2l+2 |gφ,γ(ν(s))−g0(ν(s))| ds,
I4 :=
4π
r2
∫ r
0
s2l+2 |g0(ν(s))−g0(U(s))| ds.
Since for r≥0 we have ν(r)≥ν0 and since φ is bounded with φ(E)=0 for
E>0, it is easily seen that
gφ,γ(ν(r))≤C, hφ,γ(ν(r))≤C, r≥0, γ∈]0,1],
where the constant C depends only on φ and ν0. Thus, for R>0 fixed and
r∈ [0,R] we obtain the estimate
I1≤
1
1−CR2l+2γ0
CR2+1γ≤Cγ
where γ∈]0,γ0], and γ0∈]0,1] is chosen such that 1−CR2l+2γ0>0. Simi-
larly,
I2≤Cγ
for γ∈]0,γ0]. Next we estimate the difference |gγ,φ(ν(r))−g0(ν(r))|. We can
restrict ourselves to the case ν(r)<0 since otherwise this difference is zero.
Thus,
eγν(r)−1
γ
≥ν(r),
which implies that we can split the difference in the following way:
|gγ,φ(ν(r))−g0(ν(r))|≤C(J1+J2+J3),
where
J1 :=
∣
∣
∣e−2(l+2)γν −1
∣
∣
∣
∫ ∞
e
γν
−1
γ
φ(E)(1+γE)2
(
1
γ
(1+γE)2−
1
γ
e2γν
)l+1/2
dE,
J2 :=
∫ e
γν
−1
γ
ν
φ(E)(2(E−ν))l+1/2dE,
13
J3 :=
∫ ∞
e
γν
−1
γ
φ(E)
∣
∣
∣
∣
∣
(1+γE)2
(
1
γ
(1+γE)2− 1
γ
e2γν
)l+1/2
−(2(E−ν))l+1/2
∣
∣
∣
∣
∣
dE.
Now
J1 ≤ Cγ
e−2(l+2)γν(r)−1
γ
≤Cγ,
J2 ≤ C
(
eγν(r)−1
γ
−ν(r)
)
≤Cγ,
and
∣
∣
∣
∣
∣
(1+γE)2
(
1
γ
(1+γE)2− 1
γ
e2γν
)l+1/2
−(2(E−ν))l+1/2
∣
∣
∣
∣
∣
≤C
∣
∣
∣(1+γE)2−1
∣
∣
∣+
∣
∣
∣
∣
∣
(
1
γ
(1+γE)2− 1
γ
e2γν
)l+1/2
−(2(E−ν))l+1/2
∣
∣
∣
∣
∣
≤C
∣
∣
∣(1+γE)2−1
∣
∣
∣+C
∣
∣
∣
∣
(
1
γ
(1+γE)2− 1
γ
e2γν
)
−(2(E−ν))
∣
∣
∣
∣
l+1/2
≤Cγ+C
∣
∣
∣
∣
∣
1+2γν(r)−e2γν(r)
γ
+γE2
∣
∣
∣
∣
∣
min{l+1/2,1}
≤Cγ+Cγmin{l+1/2,1}.
Finally, using the method of Lemma 3.1 it is easily seen that g0∈C1(IR)
and |g′0(u)|≤C for u≥ν0. Thus
I4≤
C
r2
∫ r
0
s2l+2|ν(s)−U(s)|ds.
If we combine all the above estimates we see that
|ν ′(r)−U ′(r)|≤Cγmin{l+1/2,1}+
C
r2
∫ r
0
s2l+2|ν(s)−U(s)|ds
for r∈ [0,R] and γ∈]0,γ0]. The assertion of the lemma now follows by the
usual Gronwall argument. ✷
In order to exploit the above result, we have to restrict our investigation
to such cases where finiteness of the radius and total mass is known in the
Newtonian situation. Thus we consider
Φ(E,F ) := (−E)k+F l,E∈ IR, F >0, (4.7)
14
where k≥0 and l>−1/2 are such that k<3l+7/2. Then we know from
[3, 5.4] that the Newtonian potential U has a zero, which is also the radius
where the density vanishes. Since by the assumption ν0<0 the solution
is nontrivial, U has to strictly increase so that there exists R>0 such that
U(R)>0. The above lemma then tells us that for all γ>0 sufficiently small,
ν(R)>0 which by the definition of Φ and Eqn. (4.5) implies that ρ(r)=
p(r)=0 for r≥R. Thus we have proved the following theorem:
Theorem 4.2 Let Φ be defined by Eqn. (4.7) and take ν0<0. Then for all
γ >0 sufficiently small the corresponding solution ν has a zero, the density ρ
and radial pressure p as defined by Eqns. (4.5), (4.3), and (4.4) have finite
support, and
0<4π
∫ ∞
0
s2ρ(s)ds<∞
i.e. the solution is nontrivial with finite total mass.
Remarks:
1. In this section we have obtained static solutions of the spherically
symmetric Vlasov-Einstein system with finite radius and finite mass,
provided γ >0 is sufficiently small. However, if f,λ,ν is such a solution
then γ−3/2f(γ−1/2·,γ−1/2·),λ(γ−1/2·),γν(γ−1/2·) is a solution of the
system with γ=1, which again has finite radius and finite total mass.
2. If Φ is defined by Eqn. (4.7) then at least f ∈C1(suppf), and f ∈
C(IR6) or f ∈C1(IR6) if k>0,l≥0 or k>1,l≥1 respectively. The
Vlasov equation then holds classically on suppf or on IR6 respectively.
3. The finiteness of the total mass implies that λ(r)→0 as r→0 and ν
and µ have a finite limit as r→∞. This means that the spacetime
is asymptotically flat; the fact that the limit of µ is not zero only
corresponds to a rescaling of the time coordinate t.
4. Our solutions are not only global in the coordinates which we used,
but are singularity-free in the sense that the corresponding spacetime
is timelike and null geodesically complete.
15
5 Solutions with a Schwarzschild singularity at the
center
In this last section we take Φ as in Sect. 1, with F0>0, E0=1, and φ(E)>0
for E<1. This implies that
GΦ(r,u)=HΦ(r,u)=0 if e
u
√
1+F0/r
2≥1,
GΦ(r,u),HΦ(r,u)>0 if e
u
√
1+F0/r
2<1.
Consider the field equations (2.1), (2.2). It is well kwown that in the vacuum
case, i. e. if the right hand sides are identically zero, the asymptotically flat
solutions are given by
e2µ(r)=1− 2M0
r
, e2λ(r)=
(
1− 2M0
r
)−1
, r>2M0,
the so-called Schwarzschild metric; M0≥0. This metric is investigated in
probably every textbook on general relativity, it represents a spacetime sin-
gularity which is hidden inside of an event horizon, a black hole. In passing
we mention that the apparent singularity at r=2M0 is only a coordinate
singularity, i. e. in other coordinates the spacetime can be extended beyond
this radius, which is also called Schwarzschild radius, cf. [12, Ch. 6]. In the
present section we wish to construct static solutions of the spherically sym-
metric Vlasov-Einstein system which have such a black hole at the center.
Let us first see if or where the Schwarzschild metric solves our system
(2.1), (2.2). This is obviously the case if
√
1− 2M0
r
√
1+
F0
r2
≥1,
i. e. for r∈ [r−,r+], where
r± :=
F0±
√
F 20 −16M20F0
4F0
.
If we take F0>16M
2
0 >0 we obtain 2M0<r−<r+, and we may set
e2µ(r)=1− 2M0
r
, e2λ(r)=
(
1− 2M0
r
)−1
16
and
ρ(r)=p(r)= f(x,v)=0
for 2M0<r≤ r+. At r0 := r+ we now pose initial conditions
µ(r0)=µ0 :=
√
1− 2M0
r0
,λ(r0)=λ0 :=
√
1− 2M0
r0
−1
,
and solve (2.1), (2.2) to the right of r0 according to Thm. 3.4; note that
λ0>0. In this way we obviously obtain a static solution of the spherically
symmetric Vlasov-Einstein system, which coincides with the Schwarzschild
solution for r≤ r0. The phase space density f is no longer given by one
function of E and F because the vacuum solution is not consistent with
our ansatz f =Φ(E,F ) in the region ]2M0,r−[, but f still solves the Vlasov
equation everywhere in the region ]2M0,∞[ since no characteristics which
carry mass can cross the region ]r−,r0[.
What remains to be seen is that our solution is not vacuum everywhere
for r>2M0, i. e. we really get Vlasov matter for r>r0, and that this matter
outside r0 again has finite radius and finite total mass. First note that
eµ(r)
√
1+
F0
r2
′
|r=r0
<0
which implies that ρ(r)>0 and p(r)>0 in a right neighborhood of r0. To
show that for large enough values of r the density vanishes again, it is
obviously sufficient to show that limr→∞µ(r)>0. To see the latter we first
recall that by integrating Eqn. (2.1) we obtain
e−2λ(r)=1− 2m(r)
r
− 1
r
r0(1−e−2λ0)=1−
2M(r)
r
, r>2M0,
where
M(r) :=M0+m(r) :=M0+4π
∫ r
r0
s2ρ(s)ds.
Inserting this into Eqn. (2.2) we obtain
µ′(r) =
1
1− 2M(r)
r
(
M(r)
r2
+4πrp(r)
)
≥ M0
r(r−2M0)
+
m(r)
r2
,
17
and integrating this yields
µ(r) ≥ µ0+M0
∫ r
r0
ds
s(s−2M0)
+
∫ r
r0
m(s)
s2
ds
= µ0+ln
√
1−
2M0
r
− ln
√
1−
2M0
r0
++
∫ r
r0
m(s)
s2
ds
= ln
√
1− 2M0
r
+
∫ r
r0
m(s)
s2
ds.
Therefore
lim
r→∞
µ(r)≥
∫ ∞
r0
m(s)
s2
ds>0,
which proves that the density vanishes for r large enough. Note also that
the inner boundary of the Vlasov matter satisfies the estimate
r0>
F0
4M0
>4M0.
We collect these results in the following theorem:
Theorem 5.1 Let Φ satisfy the general assumption in Sect. 1 with E0=1
and φ(E)>0 for E>1, and let F0>16M
2
0 >0. Then there exists a static
solution (f,λ,µ) of the spherically symmetric Vlasov-Einstein system such
that
e2µ(r)=1− 2M0
r
, e2λ(r)=
(
1− 2M0
r
)−1
, 2M0<r<r0,
ρ(r)=p(r)= f(x,v)=0, 2M0<r<r0 or r>R,
and
0<4π
∫ R
r0
ρ(r)dr<∞,
where
r0 :=
F0+
√
F 20 −16M20F0
4F0
>4M0
and R>r0. Furthermore, λ,µ∈C2(]2M0,∞[), ρ,p∈C1(]2M0,∞[), and the
spacetime in asymptotically flat.
Remarks:
18
1. As pointed out above, the phase space density f is not given as a
function of E and F globally for r>2M0.
2. If we start at the center with a smooth static solution as obtained
in Sect. 4 instead of the Schwarzschild singularity we can use the
method of the present section to obtain static solutions of the fol-
lowing kind: For 0≤ r≤ r0 the nontrivial matter distribution is given
by f(x,v)=Φ0(E), for r0<r<r1 we have vacuum, for r1≤ r≤ r2 the
matter distribution is again nonzero and given by f(x,v)=Φ1(E,F ),
and this procedure can be continued. The resulting solution is smooth,
geodesically complete, asymptotically flat, with finite mass and finite
radius, and consists of rings of Vlasov matter separated by vacuum.
Contrary to our expectation it is not clear that such a solution violates
Jeans’ Theorem, which in spite of 1) might still be valid for smooth
solutions. Note however that as the radius increases, the pressure can
change from isotropic to unisotropic.
3. In the Newtonian case one can construct analogous solutions, where
the role of the Schwarzschild singularity is played by a point mass
M0 situated at the center r=0. It then turns out that the resulting
solution does not violate Jeans’ Theorem—in the above notation, r−=
0 in the Newtonian case. Thus one can at least say that the range
of validity of Jeans’ Theorem is larger in the classical case than in
the general relativistic. One can also construct solutions of the type
described in 2) for the Newtonian case.
References
[1] Batt, J.: Steady state solutions of the relativistic Vlasov-Poisson sys-
tem. In Ruffini, R. (ed.): Proceedings of the Fifth Marcel Grossmann
Meeting on General Relativity. 1988
[2] Batt, J., Berestycki, H., Degond, P., Perthame, B.: Some families of
solutions of the Vlasov-Poisson system. Arch. Rational Mech. Anal.
104, 79–103 (1988)
[3] Batt, J., Faltenbacher, W., Horst, E.: Stationary spherically symmetric
models in stellar dynamics. Arch. Rational Mech. Anal. 93, 159–183
(1986)
19
[4] Batt, J., Pfaffelmoser, K.: On the radius continuity of the models of
polytropic gas spheres which correspond to the positive solutions of the
generalized Emden-Fowler equation. Math. Meth. in the Appl. Sci. 10,
499–516 (1988)
[5] Kijowski, J., Magli, G.: A generalization of the relativistic equilibrium
equation for a nonrotating star. General Relativity and Gravitation 24,
139–158 (1992)
[6] Rein, G., Rendall, A.: Global existence of solutions of the spherically
symmetric Vlasov-Einstein system with small initial data. Commun.
Math. Phys. 150, 561–583 (1992)
[7] Rein, G., Rendall, A.: The Newtonian limit of the spherically sym-
metric Vlasov-Einstein system. Commun. Math. Phys. 150, 585–591
(1992)
[8] Rein, G., Rendall, A.: Smooth static solutions of the spherically sym-
metric Vlasov-Einstein system. To appear in Ann. de l’Inst. H. Poincaré,
Physique Théorique
[9] Rendall, A., Schmidt, B.: Existence and properties of spherically sym-
metric static fluid bodies with a given equation of state. Class. Quantum
Grav. 8, 985–1000 (1991)
[10] Shapiro, S. L., Teukolsky, S. A.: Relativistic stellar dynamics on the
computer, I. Motivation and numerical method. Astrophysical Journal
298, 34–57 (1985)
[11] Smoller, J., Wasserman, A., Yau, S.-T., McLeod, J.: Smooth static
solutions of the Einstein/Yang-Mills equations. Commun. Math. Phys.
143, 115–147 (1991)
[12] Wald, R. M.: General Relativity. The University of Chicago Press, 1984
20
| 0non-cybersec
| arXiv |
Losing weight seems a lot harder when you‘re already at a healthy BMI. I‘m a tiny woman and have always been thin. Until last year. It‘s been a rough year and my emotional eating got blown out of proportion. On bad days I would drink 1,5 litres of chocolate milk - the store bought where half a liter has 500kcal. And would eat cookies and chocolate on top of that. My diet basically was sugar only.
So now I have gained 10kg.
But at a height of 160cm (5“1‘ I think?), my weight still falls under a healthy BMI. But I hate not fitting into my old clothes anymore (I gained the weight mostly around the belly) and want to lose ~8kg.
I‘m doing CICO and ride my bike everywhere (i live in a big city) and feel like I‘ll be getting there quite easily - but sometimes it is soo easy to look in the mirror thinking „You are far from being fat or overweight, why go through all the trouble you‘re fine!!“ - but then again, I wanna fit into my old jeans again desperately.
Anyone in a similar situation know what I‘m talking about?
Guess I need some encouragement to keep this going. | 0non-cybersec
| Reddit |
Limit of sum of $\sqrt{\frac{\delta^2}4+N\left(N+\delta\right)\sin^2\left(\frac{\pi n}N\right)}$. <p>How can we prove that this limit exists? It would be even better if it could be computed ( even in terms of an infinite series would be good). (<span class="math-container">$N$</span> is obviously an integer)</p>
<p><span class="math-container">$f\left(\delta\right)=\lim\limits_{N\rightarrow\infty}\left(N-2\sum\limits_{n=1}^{\left\lfloor\frac N2\right\rfloor}\left(\sqrt{\frac{\delta^2}4+N\left(N+\delta\right)\sin^2\left(\frac{\pi n}N\right)}-\sqrt{\frac{\delta^2}4+N\left(N+\delta\right)\sin^2\left(\frac{\pi n}N-\frac\pi{2N}\right)}\right)\right)$</span></p>
<p>I found the limit at <span class="math-container">$\delta=0$</span> to be <span class="math-container">$\frac\pi4$</span> as then the square roots disappear and the sum of <span class="math-container">$\sin$</span> terms can be evaluated directly. or the other cases I tried proving that the sequence was Cauchy, but I couldn't do that.</p>
| 0non-cybersec
| Stackexchange |
Effective bounds on root discriminant assuming GRH?. <p>It is known conditionally on GRH that, for all $\alpha<44.7632 \dots$, there are are only finitely many number fields $K$ satisfying $\Delta_K ^{ 1/[K:\mathbb Q]}< \alpha$.</p>
<p>For which $\alpha$ can we make this effective by giving an upper bound on $[K:\mathbb Q]$ for all fields satisfying $\Delta_K ^{ 1/[K:\mathbb Q]}< \alpha$, assuming GRH and maybe some other conjecture?</p>
| 0non-cybersec
| Stackexchange |
How to use spot instance with amazon elastic beanstalk?. <p>I have one infra that use amazon elastic beanstalk to deploy my application.
I need to scale my app adding some spot instances that EB do not support.</p>
<p>So I create a second autoscaling from a launch configuration with spot instances.
The autoscaling use the same load balancer created by beanstalk.</p>
<p>To up instances with the last version of my app, I copy the user data from the original launch configuration (created with beanstalk) to the launch configuration with spot instances (created by me).</p>
<p>This work fine, but:</p>
<ol>
<li><p>how to update spot instances that have come up from the second autoscaling when the beanstalk update instances managed by him with a new version of the app?</p>
</li>
<li><p>is there another way so easy as, and elegant, to use spot instances and enjoy the benefits of beanstalk?</p>
</li>
</ol>
<p><strong>UPDATE</strong></p>
<p>Elastic Beanstalk add support to spot instance since 2019... see:
<a href="https://docs.aws.amazon.com/elasticbeanstalk/latest/relnotes/release-2019-11-25-spot.html" rel="nofollow noreferrer">https://docs.aws.amazon.com/elasticbeanstalk/latest/relnotes/release-2019-11-25-spot.html</a></p>
| 0non-cybersec
| Stackexchange |
Solution for this inequality $a^2 - 4b + 8 > 0$. <p>I dont know where I messed up, this is what I have done:</p>
<p>This is the isolated x of a function
$$x = \frac{1}{2}\biggl(\pm\sqrt{a^2 - 4 b + 8} - a - 4\biggr)$$</p>
<p>The root above must be positive and greater than $0$ so a function could have inflection points.</p>
<p>So: $a^2 - 4 b + 8 > 0$ </p>
<p>$b$ isolated:</p>
<p>$b<\frac{1}{4}\ (a^2 + 8)$</p>
<p>And $a$ isolated:</p>
<p>$a> \sqrt{4b-8}$</p>
<p>$b$ must be $\geq 2$ so that the root above could be real</p>
<p>With this in mind</p>
<p>if $a=1$ </p>
<p>then $b<\frac{9}{4}\ $</p>
<p>And here is where I dont know what's wrong because It works even if I use $b$ values greater than $\frac{9}{4}\ $</p>
| 0non-cybersec
| Stackexchange |
PuTTY continuous scrolling. <p>I am trying to capture (via session logging) a very long config output from a device. Is there a way I can stop PuTTY from pausing on each line? My finger is getting very tired from holding the enter key down.</p>
| 0non-cybersec
| Stackexchange |
What is wrong with the attempts at defining a Recursive Function. <p>What is wrong with these attempts at defining a recursive function?</p>
<p>(i) $f(0) = 0, f(1) = 1, f(2) = 1, f(3) = 3, f(n) = f(n - 1) + f(n - 2)$ $\quad$$for \ n \ge 2$ <br></p>
<p>(ii) $f(0) = 0, f(n) = f(n - 1) + f(n - 2)$ $\quad$$for \ n \ge 2$ <br></p>
| 0non-cybersec
| Stackexchange |
Wifi issue after running sudo dkms add ./rtlwifi_new-master. <p>I've already solved my initial wifi problem here: <a href="https://askubuntu.com/questions/939758/wifi-drops-after-5-minutes-with-rtl8821ae">Wifi drops after ~ 5 minutes with RTL8821AE | Ask Ubuntu</a> but I've tried to optimize it (because anytime there was a kernel update I have to execute all the commands of the solution again) and I've messed up something.</p>
<p>To solve the kernel update problem I tried </p>
<pre><code>sudo dkms add ./rtlwifi_new-master
</code></pre>
<p>just before an update. I ran the command in the Desktop folder but I got this output: </p>
<pre><code>Error! Could not find module source directory.
Directory: /usr/src/.-rtlwifi_new-master does not exist.
</code></pre>
<p>So I thought that I should have run the given command while in <code>/usr/src/</code> folder, so I did so, but after doing that my wifi problem got worse and now every time I reboot the PC I need to execute the whole solution again, whereas before this process was necessary only after a kernel update.</p>
<p>Also, on the main screen I see something like </p>
<pre><code>there is an error! rtlwifi_new-master is an external package. Please remove it
</code></pre>
<p>In summary:</p>
<ol>
<li><p>I got a notification of a system update</p></li>
<li><p>I executed <code>sudo dkms add ./rtlwifi_new-master</code> in src folder</p></li>
<li><p>I didn't reboot</p></li>
<li><p>I executed the update</p></li>
<li><p>I rebooted</p></li>
<li><p>Worse problem than before</p></li>
</ol>
<p>I thought of running</p>
<pre><code>rm -R rtlwifi-new-0.10
</code></pre>
<p>in the /src folder but I don't have the permission and I've already messed up with that one time. You can see it here:</p>
<p><a href="https://askubuntu.com/questions/939477/ubuntu-16-04-lts-lost-administrator-rights-bash-etc-profile-permission-denied">Ubuntu 16.04 lts lost administrator rights bash: /etc/profile: Permission denied | Ask Ubuntu</a></p>
<p>Suggestions??</p>
| 0non-cybersec
| Stackexchange |
Android EditText Gmail like to field. <p>I'm working at an app, and I'm trying to make a gmail like "To" field, which has blocks inside which cannot be edited once added, but just removed entirely (like in the attached image). If it can have an image too, that would be perfect.
<img src="https://i.stack.imgur.com/fpJZJ.png" alt="gmail "To" field"></p>
| 0non-cybersec
| Stackexchange |
Suported hardware (i.e. trackpad) and streaming? ASUS Zenbook UX305CA. <p>I'm on the verge to swap windows for ubuntu. However, I'm very, very green when it comes to basically all-things-computers. I won't be using the OS for anything but surfing, music and all them simple things. Never, ever got along with windows anyway.</p>
<p>I have, basically two questions;
1. Might seem like a small thing (but to me very important, since I have bad eyesight), I need to be able to make full use of the trackpad (ASUS smart gesture multitouche, no idea WHAT trackpad it is), most important is the zoom function, but also the two-finger-scroll. How can I see if it'd work?</p>
<ol start="2">
<li>I'm streaming Spotify > AVR via LAN (wi-fi). This is built into Spotify, so I can pick whatever device to stream to in the Spotify GUI. Would this work on ubuntu?</li>
</ol>
<p>(Some) Laptop specs:
Intel M3 6Y30
8GB memory
Currently running Win- 10 on a 256gb SSD</p>
<p>Peace</p>
| 0non-cybersec
| Stackexchange |
Student Banned from Areas of Campus for Resembling Classmate’s Rapist. | 0non-cybersec
| Reddit |
kernel panic - get log. <p>My system keeps hanging every several hours.
I think the problem is somehow connected with network, because plugging ethernet cable eliminates the problem (even if ethernet is used locally only). If I try to use WiFi without ethernet plugged - system hangs in couple of hours.</p>
<ul>
<li>I see no common pattern in kernel logs after it. If I am getting the idea right - it means that system can't write to HDD at that moment? </li>
<li>I can't use netconsole, because my wifi doesn't support spooling and with ethernet plugged problem doesn't show itself. </li>
<li><p>If I leave terminal opened - it fades to black after error so gives
no information.</p>
<p>How can I diagnose and eleminate the problem in such situation?</p></li>
</ul>
| 0non-cybersec
| Stackexchange |
Xamarin.Forms + .resx string resources - System.IO.FileNotFoundException: Invalid Image. <p>I am creating a Xamarin.Forms app based on a C# shared code project and another two projects for the actual Android + iOS app. </p>
<p>I now want to implement string localization like it is documented <a href="https://docs.microsoft.com/en-us/xamarin/xamarin-forms/app-fundamentals/localization/text?tabs=windows" rel="noreferrer">here</a>. So I created a .net standard 2.0 library project in my solution for the .resx file and referenced this project in my two main projects, and I did all the other steps described in the linked article, of course.</p>
<p>When I now want to access any of my string resources from one of my app projects, <code>ResourceManager.GetString</code> throws this Exception: <code>System.IO.FileNotFoundException: Invalid Image</code></p>
<p>Example code would be that line, but it can be also any other string resource.</p>
<pre><code>public static string global_copyright {
get {
return ResourceManager.GetString("global_copyright", resourceCulture);
}
}
</code></pre>
<p>I can confirm that the assembly of this library project is found and loaded correctly, since I can create instances of other classes defined in that project.</p>
<p>Now I put this code directly at the beginning of the App() constructor like it is described in that article to debug for such issues:</p>
<pre><code>var assembly = typeof(AppResources).GetTypeInfo().Assembly;
foreach (var res in assembly.GetManifestResourceNames())
{
System.Diagnostics.Debug.WriteLine("found resource: " + res);
}
var test = AppResources.global_copyright;
</code></pre>
<p>The first lines are executed fine and it shows me that one resource file is found in that assembly. Its name is also correct. But on the last line it crashes with that exception.
What did I wrong? Why is ResourceManager not able to load string resources from that assembly?</p>
<p>Visual Studio 2017 (15.9.6) with Xamarin.Forms v3.4</p>
| 0non-cybersec
| Stackexchange |
Side Table with Wood Top and Steel Legs (first album!). | 0non-cybersec
| Reddit |
Maximal domain of the the function $f(x)=\sqrt{4e^{x}-e^{2x}-1-a}$. <p>This question about finding the widest range of values the constant $a$ can take.</p>
<p>After completing the square for the expression inside the square root, and then solving the inequality
that must satisfy (I did assume $2 < a\le 3$ in this step), I obtained
$$\log_{e}(2-\sqrt{3-a})\le x\le \log_{e}(2+\sqrt{3-a}).$$</p>
<p>My question is, is there a bigger interval for $a$ for which the inequality holds true?</p>
<p>Wolfram gave $-1 < a\le 3$ if I remember correctly but I cannot justify why.</p>
<p>Thank you.</p>
| 0non-cybersec
| Stackexchange |
How to use spot instance with amazon elastic beanstalk?. <p>I have one infra that use amazon elastic beanstalk to deploy my application.
I need to scale my app adding some spot instances that EB do not support.</p>
<p>So I create a second autoscaling from a launch configuration with spot instances.
The autoscaling use the same load balancer created by beanstalk.</p>
<p>To up instances with the last version of my app, I copy the user data from the original launch configuration (created with beanstalk) to the launch configuration with spot instances (created by me).</p>
<p>This work fine, but:</p>
<ol>
<li><p>how to update spot instances that have come up from the second autoscaling when the beanstalk update instances managed by him with a new version of the app?</p>
</li>
<li><p>is there another way so easy as, and elegant, to use spot instances and enjoy the benefits of beanstalk?</p>
</li>
</ol>
<p><strong>UPDATE</strong></p>
<p>Elastic Beanstalk add support to spot instance since 2019... see:
<a href="https://docs.aws.amazon.com/elasticbeanstalk/latest/relnotes/release-2019-11-25-spot.html" rel="nofollow noreferrer">https://docs.aws.amazon.com/elasticbeanstalk/latest/relnotes/release-2019-11-25-spot.html</a></p>
| 0non-cybersec
| Stackexchange |
Micrisoft Excel. So I need to have Excel at my exam but the Excel program that my teacher uses looks nothing like the one I have.
Mine is called "Microsoft Excel" and I have a MacBook Air.
Is this an issue? | 0non-cybersec
| Reddit |
the worst kind of person.. | 0non-cybersec
| Reddit |
Countable path-connected Hausdorff space. <p>Is there a topology $\tau$ on $\omega$ such that $(\omega,\tau)$ is Hausdorff and path-connected?</p>
| 0non-cybersec
| Stackexchange |
Is the derivative of a function the secant line?. <p>I am just learning derivatives and I found the derivative of $4x-x^2$ to be $4-2x$. At point $(1,3)$ the tangent line is $2x+1$. Now when I graph this, the derivative $4-2x$ cuts through the function $4x-x^2$. Does that mean the derivative is the secant line?</p>
| 0non-cybersec
| Stackexchange |
Blue Origin Blasts Vehicle Into Space and Nails Landing. | 0non-cybersec
| Reddit |
setting the first responder view of the table but we don't know its type (cell/header/footer). <p>I have <strong>UITableViewController</strong>. In this controller I add a subview UIView with UITextField in it. When the UITextField get first responder got </p>
<blockquote>
<p>setting the first responder view of the table but we don't know its
type (cell/header/footer)</p>
</blockquote>
<p>Code as below:</p>
<pre><code>@interface UserAlbumListViewController (){
NSString *newAlbumName;
UITextField *albumNameField;
}
@end
-(void)addAlbumButtonPressed:(id)sender{
self.tableView.scrollEnabled = NO;
CGRect frame = self.view.frame;
UIView *opaqueView = [[UIView alloc] initWithFrame:frame];
opaqueView.tag = 1001;
opaqueView.backgroundColor = [UIColor colorWithWhite:0 alpha:0.5];
UIView *controllerView = [[UIView alloc] init];
controllerView.tag = 1002;
controllerView.backgroundColor = [UIColor whiteColor];
controllerView.frame = CGRectMake(10.0f, 60.0f, frame.size.width - 20.0f, 90.0f);
[opaqueView addSubview:controllerView];
albumNameField = [[UITextField alloc] init];
albumNameField.borderStyle = UITextBorderStyleRoundedRect;
albumNameField.placeholder = NSLocalizedString(@"Album Name",nil);
albumNameField.keyboardType = UIKeyboardTypeDefault;
albumNameField.returnKeyType = UIReturnKeyDefault;
albumNameField.autocorrectionType = UITextAutocorrectionTypeNo;
albumNameField.autocapitalizationType = UITextAutocapitalizationTypeNone;
albumNameField.clearButtonMode = UITextFieldViewModeWhileEditing;
albumNameField.clearsOnBeginEditing = NO;
albumNameField.text = @"";
albumNameField.frame = CGRectMake(10.0f , 10.0f, controllerView.frame.size.width - 20.0f, 30.0f);
[albumNameField becomeFirstResponder];
[controllerView addSubview:albumNameField];
UIButton *_cancelButton = [UIButton buttonWithType:UIButtonTypeRoundedRect];
_cancelButton.backgroundColor = [UIColor clearColor];
[_cancelButton setTitle:NSLocalizedString(@"Cancel",nil) forState:UIControlStateNormal];
_cancelButton.frame = CGRectMake( controllerView.frame.size.width - 90.0f, albumNameField.frame.origin.y + albumNameField.frame.size.height + 10.0f, 80.0f, 30.0f);
[_cancelButton addTarget:self action:@selector(opaqueViewCancelButtonClicked:) forControlEvents:UIControlEventTouchDown];
[controllerView addSubview:_cancelButton];
UIButton *_OKButton = [UIButton buttonWithType:UIButtonTypeRoundedRect];
_OKButton.backgroundColor = [UIColor clearColor];
[_OKButton setTitle:NSLocalizedString(@"OK",nil) forState:UIControlStateNormal];
_OKButton.frame = CGRectMake( _cancelButton.frame.origin.x - 90.f, _cancelButton.frame.origin.y, 80.0f, 30.0f);
[_OKButton addTarget:self action:@selector(opaqueViewOKButtonClicked:) forControlEvents:UIControlEventTouchDown];
[controllerView addSubview:_OKButton];
[self.view addSubview:opaqueView];
[controllerView release];
[opaqueView release];
}
</code></pre>
<p>How to avoid this warning?</p>
| 0non-cybersec
| Stackexchange |
Why does it feel so cringy to see someone you know in a movie/youtube video, or hear them do voice acting, but it's totally normal to see/hear strangers do the same exact thing?. Or is it just me?
Current conclusion:
it's mainly because you see them act differently, or their voice sound differently, when they aren't acting different at all, they will probably do something that they aren't supposed to do, which will look cringy, so it's either changing how they usually act, which will look cringy, or act too normal which is also cringy most of the time. | 0non-cybersec
| Reddit |
When are geometric and harmonic means used?. <p>From what little statistics I know, the only 'mean' commonly used is the arithmetic mean, and the rest are irrelevant. Any reading I've done has pretty much said something along the lines of "acceleration or something".</p>
<p><strong>So, under what situations are geometric, harmonic, and the other types of means are genuinely useful, and why are they used for those situations?</strong></p>
| 0non-cybersec
| Stackexchange |
Garbage collection of unneeded event listeners in javascript. <p>I am building a single page webapp. This means over a period of time I get new DOM elements, remove unneeded ones. For example when I fetch a new form I just replace the contents of a specific div with that form HTML and also set up listeners unique to this form's elements. After some period I replace the contents of this form with a new instance of form (having different ID's).</p>
<p>I set up the event listeners again for this new form. Now the previous form is no longer part of the DOM so I the DOM elements should be automatically garbage collected. I am also expecting the listener functions pointing to the elements removed from the DOM to disappear.</p>
<p>However the following profile gathered from Chrome suggests that my listener count is increasing over time. Can you tell me why this is so? I tried clicking on the "Collect Garbage" button. But this is the profile I get. Is there something wrong with the way I am building my application? Is there a problem and if so how should I fix it?</p>
<p><img src="https://i.stack.imgur.com/yJVu7.png" alt="Chrome snapshot of my webapp for a few minutes"></p>
<p>In case it matters I am using JSP templating language with jquery, jquery-ui and some other plugins.
This is how the dynamic fragments that I add/remove on my page look like.</p>
<pre><code><script>
$(document).ready(function() {
$("#unique_id").find(".myFormButton").button().click(
function() {
$.ajax({url: "myurl.html",
success: function(response) {
console.log(response);
}
});
});
});
</script>
<div id="unique_id">
<form>
<input name="myvar" />
<button class="myFormButton">Submit</button>
</form>
</div>
</code></pre>
<p><strong>Update</strong></p>
<p>If you want to have a look at the actual code here is the relevant portion.
<a href="https://github.com/C4G/V2V/blob/503f07f676e75f1af48689347627a4188de69e2c/war/WEB-INF/jsp/findDonorForm.jsp#L49" rel="nofollow noreferrer">This</a> link shows that when clear button is pressed the function clearFindForm is called which effectively refetches content (HTML fragment) using an ajax request and replaces the entire div in this jsp with the content fetched.
The refetchContent function works as below: <a href="https://github.com/C4G/V2V/blob/503f07f676e75f1af48689347627a4188de69e2c/war/js/common.js#L448" rel="nofollow noreferrer">Here</a> is the link to the code in case that helps in giving a better answer.</p>
<pre><code>function refetchContent(url, replaceTarget) {
$.ajax({
url: url,
data: {},
type: "GET",
success: function (response) {
replaceTarget.replaceWith(response);
},
error: function (response) {
showErrorMessage("Something went wrong. Please try again.");
}
});
}
</code></pre>
| 0non-cybersec
| Stackexchange |
[ART] Jacket off. | 0non-cybersec
| Reddit |
How to use spot instance with amazon elastic beanstalk?. <p>I have one infra that use amazon elastic beanstalk to deploy my application.
I need to scale my app adding some spot instances that EB do not support.</p>
<p>So I create a second autoscaling from a launch configuration with spot instances.
The autoscaling use the same load balancer created by beanstalk.</p>
<p>To up instances with the last version of my app, I copy the user data from the original launch configuration (created with beanstalk) to the launch configuration with spot instances (created by me).</p>
<p>This work fine, but:</p>
<ol>
<li><p>how to update spot instances that have come up from the second autoscaling when the beanstalk update instances managed by him with a new version of the app?</p>
</li>
<li><p>is there another way so easy as, and elegant, to use spot instances and enjoy the benefits of beanstalk?</p>
</li>
</ol>
<p><strong>UPDATE</strong></p>
<p>Elastic Beanstalk add support to spot instance since 2019... see:
<a href="https://docs.aws.amazon.com/elasticbeanstalk/latest/relnotes/release-2019-11-25-spot.html" rel="nofollow noreferrer">https://docs.aws.amazon.com/elasticbeanstalk/latest/relnotes/release-2019-11-25-spot.html</a></p>
| 0non-cybersec
| Stackexchange |
Compile/Link error building BerkeleyDB on Windows 7 (64bit) with Perl64. <p>I want to use the perl BerkleyDB module on Windows, but I do not manage to do it.</p>
<p>I know there are a lot problems with this and I read many of the questions here on
SO and also on other sources. But I found no solution for it.</p>
<p>For example there is: <a href="https://stackoverflow.com/questions/10030151/use-cpan-berkeleydb-module-on-windows-7-64-bit">Use CPAN BerkeleyDB module on Windows 7 (64 bit)</a>
But there is no answer. There is a hint to a 64-bit patch, but the link is broken.</p>
<h3>Environment</h3>
<ul>
<li><p>Windows 7 Professional</p></li>
<li><p>Perl 5.16</p>
<pre><code>C:\> perl -v
This is perl 5, version 16, subversion 3 (v5.16.3) built for MSWin32-x64-multi-thread
(with 1 registered patch, see perl -V for more detail)
Copyright 1987-2012, Larry Wall
Binary build 1603 [296746] provided by ActiveState http://www.ActiveState.com
Built Mar 13 2013 13:31:10
Perl may be copied only under the terms of either the Artistic License or the
GNU General Public License, which may be found in the Perl 5 source kit.
Complete documentation for Perl, including FAQ lists, should be found on
this system using "man perl" or "perldoc perl". If you have access to the
Internet, point your browser at http://www.perl.org/, the Perl Home Page.
</code></pre></li>
<li><p>MinGW</p>
<p>With my first attempt to install the BerkelyDB from CPAN MinGW64 (4.5.4) and dmake (4.12.20090907) was automatically installed. </p>
<pre><code>C:\>cpan
Set up gcc environment - gcc.exe (rubenvb-4.5.4) 4.5.4
</code></pre></li>
<li><p>BerkeleyDB 0.54 (Perl-Binding) </p>
<p>Downloaded using cpan.</p></li>
<li><p>BerkeleyDB (Lib from Oracle) </p>
<p>First I installed BerkeleyDB 6.1.19 from <a href="http://www.oracle.com/technetwork/database/database-technologies/berkeleydb/downloads/index-082944.html" rel="nofollow noreferrer">Oracle</a> (using .msi). Thought that
the newest version would be the best. After some problems I read the description
of <a href="https://metacpan.org/pod/distribution/BerkeleyDB/BerkeleyDB.pod" rel="nofollow noreferrer">cpan BerkeleyDB</a> again:</p>
<pre><code>BerkeleyDB - Perl extension for Berkeley DB version 2, 3, 4 or 5
</code></pre>
<p>So I deinstalled it and took BerkeleyDB 5.3.28 (using .msi). But this did not work either.
Then I found an article where the writer said that he successfully compiled BerkeleyDB
4.7.25 on Windows. So I took this one. </p></li>
</ul>
<h3>Changes and Problems</h3>
<p>As described above I'm on BerkeleyDB library version 4.7.25, but the follwing problems also occured with the other versions.</p>
<p>After downloading BerkeleyDB-0.54 from CPAN I did</p>
<pre><code>perl Makefile.PL
dmake
</code></pre>
<p>I got an error:</p>
<pre><code>BerkeleyDB.xs:76:16: fatal error: db.h: No such file or directory
</code></pre>
<p>Reason: The perl module needs to know where the lib is. So I edited the <code>config.in</code>
to</p>
<pre><code>INCLUDE = C:\App\BerkeleyDB4.7.25\include
LIB = C:\App\BerkeleyDB4.7.25\lib
DBNAME = -ldb47
</code></pre>
<p>The filename in <code>C:\App\BerkeleyDB4.7.25\lib</code> is <code>libdb47.lib</code>. But I'm not sure what <code>DBNAME</code> expects. So I tried different values:</p>
<pre><code>DBNAME = -llibdb47
</code></pre>
<p>Now running </p>
<pre><code>dmake
</code></pre>
<p>I get </p>
<pre><code>C:\Perl64\cpan\build\BerkeleyDB-0.54-rjSkdy>dmake
Skip blib\lib\BerkeleyDB.pm (unchanged)
Skip blib\lib\BerkeleyDB\Hash.pm (unchanged)
Skip blib\lib\scan.pl (unchanged)
Skip blib\lib\BerkeleyDB.pod (unchanged)
Skip blib\lib\mkconsts.pl (unchanged)
Skip blib\lib\BerkeleyDB\Btree.pm (unchanged)
C:\Perl64\site\bin\gcc.exe -c -IC:\App\BerkeleyDB4.7.25\include -DNDEBUG -DWIN32 -D_CONSOLE -DNO_STRICT -DWIN64 -DCONSERVATIVE -DPERL_TEXTMODE_SCRIPTS -DUSE_SITECUSTOMIZE -DPERL_IMPLICIT_CONTEXT -DPERL_IMPLICIT_SYS -DUSE_PERLIO -DHASATTRIBUTE -fno-strict-aliasing -mms-bitfields -O2 -DVERSION=\"0.54\" -DXS_VERSION=\"0.54\" "-IC:\Perl64\lib\CORE" BerkeleyDB.c
</code></pre>
<p>No errors while compiling, but then </p>
<pre><code>Running Mkbootstrap for BerkeleyDB ()
C:\Perl64\bin\perl.exe -MExtUtils::Command -e chmod -- 644 BerkeleyDB.bs
C:\Perl64\site\bin\dlltool.exe --def BerkeleyDB.def --output-exp dll.exp
C:\Perl64\site\bin\g++.exe -o blib\arch\auto\BerkeleyDB\BerkeleyDB.dll -Wl,--base-file -Wl,dll.base -mdll -L"C:\Perl64\lib\CORE" BerkeleyDB.o C:\Perl64\lib\CORE\perl516.lib C:\App\BerkeleyDB4.7.25\lib\libdb47.lib dll.exp
BerkeleyDB.o:BerkeleyDB.c:(.text+0x536): undefined reference to `db_strerror'
...
BerkeleyDB.o:BerkeleyDB.c:(.text+0xd5d): undefined reference to `db_strerror'
BerkeleyDB.o:BerkeleyDB.c:(.text+0xf6d): more undefined references to `db_strerror' follow
BerkeleyDB.o:BerkeleyDB.c:(.text+0x1a73): undefined reference to `db_version'
BerkeleyDB.o:BerkeleyDB.c:(.text+0x1eb8): undefined reference to `db_strerror'
...
BerkeleyDB.o:BerkeleyDB.c:(.text+0x3793): undefined reference to `db_strerror'
BerkeleyDB.o:BerkeleyDB.c:(.text+0x39a6): more undefined references to `db_strerror' follow
BerkeleyDB.o:BerkeleyDB.c:(.text+0xa877): undefined reference to `db_sequence_create'
BerkeleyDB.o:BerkeleyDB.c:(.text+0xabb9): undefined reference to `db_strerror'
...
BerkeleyDB.o:BerkeleyDB.c:(.text+0xe10a): undefined reference to `db_strerror'
BerkeleyDB.o:BerkeleyDB.c:(.text+0xeb30): more undefined references to `db_strerror' follow
BerkeleyDB.o:BerkeleyDB.c:(.text+0x18224): undefined reference to `db_create'
BerkeleyDB.o:BerkeleyDB.c:(.text+0x1825e): undefined reference to `db_strerror'
BerkeleyDB.o:BerkeleyDB.c:(.text+0x184f4): undefined reference to `db_create'
BerkeleyDB.o:BerkeleyDB.c:(.text+0x1852e): undefined reference to `db_strerror'
BerkeleyDB.o:BerkeleyDB.c:(.text+0x189b9): undefined reference to `db_env_create'
BerkeleyDB.o:BerkeleyDB.c:(.text+0x18ccc): undefined reference to `db_create'
BerkeleyDB.o:BerkeleyDB.c:(.text+0x18dd8): undefined reference to `db_strerror'
BerkeleyDB.o:BerkeleyDB.c:(.text+0x19799): undefined reference to `db_strerror'
BerkeleyDB.o:BerkeleyDB.c:(.text+0x20e53): undefined reference to `db_env_create'
BerkeleyDB.o:BerkeleyDB.c:(.text+0x20fcb): undefined reference to `db_strerror'
BerkeleyDB.o:BerkeleyDB.c:(.text+0x219ad): undefined reference to `db_create'
BerkeleyDB.o:BerkeleyDB.c:(.text+0x26a9a): undefined reference to `db_version'
c:/perl64/site/lib/auto/mingw/bin/../lib/gcc/x86_64-w64-mingw32/4.5.4/../../../../x86_64-w64-mingw32/bin/ld.exe: BerkeleyDB.o: bad reloc address 0x20 in section `.data'
c:/perl64/site/lib/auto/mingw/bin/../lib/gcc/x86_64-w64-mingw32/4.5.4/../../../../x86_64-w64-mingw32/bin/ld.exe: final link failed: Invalid operation
collect2: ld returned 1 exit status
dmake.exe: Error code 129, while making 'blib\arch\auto\BerkeleyDB\BerkeleyDB.dll'
</code></pre>
<p>I would very much appreciate your assistance.</p>
<p><em>Comments like 'change to Strawberry, change to Linux, ...' are welcome, but I hope we can fix this problem in the current environment.</em></p>
| 0non-cybersec
| Stackexchange |
Opening a .mdb created by 64-bit ACE with 32-bit client. <p>I'm creating Access .mdb files out of a 64-bit application via <a href="https://www.microsoft.com/en-au/download/details.aspx?id=13255" rel="nofollow noreferrer">ACE</a>. This process works fine. However, the only MS Access client available in the organisation is 32-bit. </p>
<p>I've done some basic testing, and there doesn't appear to be any issues opening these files in the 32-bit client, however I am curious if there are any risks or problems I haven't yet encountered that could arise down the line or produce inconsistent results?</p>
| 0non-cybersec
| Stackexchange |
Ah yes, the world renowned Chinese Singer, Drake.. | 0non-cybersec
| Reddit |
Changing background color in a two columns page. <p>I want to have this result: The first column in grey and the second color is white:</p>
<p><a href="https://i.stack.imgur.com/BiSQU.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/BiSQU.png" alt="Two columns page with two colors"></a></p>
<p>I am using <code>\usepackage{multicol}</code>.</p>
| 0non-cybersec
| Stackexchange |
'BATMAN - The Telltale Series' Unveiled in First Look Ahead of Summer 2016 Premiere. | 0non-cybersec
| Reddit |
Expanding $\frac{\Gamma(n)}{\Gamma(n-k)}$ as a polynomial. <p>I want to expand $\frac{\Gamma(n)}{\Gamma(n-k)}$ as a polynomial, where $\Gamma$ is the gamma function.</p>
<p>For $k\in\mathbb{N}$, it can be "simplified" as</p>
<p>$$\frac{\Gamma(n)}{\Gamma(n-k)}=(n-1)(n-2)(n-3)\dots(n-k)$$</p>
<p>I was wondering if it were possible to expand that into $\sum_{i=0}^ka_in^{k-i}$ form.</p>
<p>Then, there is the harder case of $k\in\mathbb R$.</p>
<p>I imagined that it would be of the form $\Pi_{i=0}^\infty(n-r_i)$ where $r_n$ is the $n$th root.</p>
<p>If this were the case, we see that</p>
<p>$$\Gamma(n)\ne0\implies\frac1{\Gamma(n-k)}=0$$</p>
<p>This occurs at the poles</p>
<p>$$\implies r_i-k=-i$$</p>
<p>$$r_i=i+k$$</p>
<p>And put into product form</p>
<p>$$\frac{\Gamma(n)}{\Gamma(n-k)}=\Pi_{i=0}^\infty(n-r_i)=\Pi_{i=0}^\infty(n-k-i)$$</p>
<p>Sadly, I don't think it is possible to multiple the product out because it diverges.</p>
<ul>
<li><p><strong>Q1</strong> Is there a polynomial/expanded form for $k\in\mathbb N$ using summations if needed?</p></li>
<li><p><strong>Q2</strong> What about $k\in\mathbb R$?</p></li>
</ul>
<p><strong>EDIT</strong></p>
<p>From below, you can see I have worked the case for $k\in\mathbb N$, but I still need $k\in\mathbb R$.</p>
<p>$$\frac{\Gamma(u)}{\Gamma(u-n)}=\sum_{k=0}^n(-1)^{n-k}s(n,k)(u-n)^k$$</p>
<p>My assumption for $n\in\mathbb R$ is that the formula becomes</p>
<p>$$\frac{\Gamma(u)}{\Gamma(u-n)}=\sum_{k=0}^\infty(-1)^{n-k}s(n,k)(u-n)^k$$</p>
<p>For similar reasons for why Euler extended binomial expansion the way he did. I note that my proposed formula holds true if $n\in\mathbb N$, but doesn't make much sense for $n\in\mathbb R$.</p>
| 0non-cybersec
| Stackexchange |
The way the smoke curls off when the incense sticks touch. | 0non-cybersec
| Reddit |
How to get rid of annoying and quickly disappearing firewall popups on Mac. <blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="https://superuser.com/questions/100013/why-does-the-mac-os-x-firewall-dialog-recurringly-pop-up-and-disappear-by-itself">Why does the Mac OS X firewall dialog recurringly pop-up and disappear by itself (without letting me respond) under Snow Leopard?</a> </p>
</blockquote>
<p>Hi,</p>
<p>Often when I have smb file shares connected to my mac (10.6.4, but if I remember correctly i've had this problem at least on some 10.5.x versions too on the same machine) Apple's firewall popup asks if I want to allow Finder or what ever application I happen to be using (even something like System Preferences sometimes) to accept or deny connections. This popup disappears so quickly that it's impossible to click on it. Sometimes appearing multiple times when for example in Save as dialog, even if saving to a local disk.</p>
<p>In my firewall settings I've allowed File Sharing (SMB), Remote Login (SSH), Screen Sharing and Web Sharing. It doesn't make any difference if the application is not mentioned in the Firewall settings or set to Allow or Block incoming connections.</p>
<p>Just tested this for TextEdit, typed something random into it, chose Save As, waited for two seconds and the popup appeared. Nothing in any logs about TextEdit at all.</p>
<p>Automatically allow signed software to receive incoming connections is disabled, as is Enable stealth mode.</p>
| 0non-cybersec
| Stackexchange |
I dry humped a married man at the bar last night(f32). Last night I went out for the first time since I've been single. I wasn't there long before I noticed a very attractive guy across the bar. Once we made eye contact he knew I was interested and made his way over to me. We spent most of the night together dancing, me grinding on him and touching. I held his dick all night playing with it through his jeans. He couldn't keep his hands off my body and it felt so good to feel like a woman again. He would pull my hair which is a huge turn on for me. At one point I turned to him and made out for awhile which was amazing. I figured by these actions my intentions were very clear I was looking for a one night stand. At the end of the night we exchanged numbers and begain texting for a few hours sending provocative photos and he said he would rather sleep with me when we hadn't been drinking. Good guy I guess. This morning I was awaken by some nice messages from him and plans to meet up next weekend. At this point I was kinda excited to know that there are good guys out there who aren't gonna take advantage of a situation. I little later I get a call from a friend saying to look at his fb profile btw she was with me last night watched the whole thing happen. So I did only to see that he's married with children. There was no ring last night I know I checked. Now I feel horrible about everything I did. It just goes to confirm maybe there are no good guys left. I just needed to get this off my chest. | 0non-cybersec
| Reddit |
Let $f($z$)= \sum _{n=0}^{\infty } a_nz^n$ be the power series expansion of f about $0$. Prove that $|a_n| \le (n+1)(1+1/n)^{n} < e(n+1)$. <p>Suppose that $f$ is analytic in the unit disc D = {$z \in \mathbb{C}$ : |$z$| < 1} and $|$f($z$)$| \le 1/(1-|$z$|)$ for all $z\in D$.</p>
<p>Let $f($z$)= \sum _{n=0}^{\infty } a_nz^n$ be the power series expansion of f about $0$.</p>
<p>Prove that $$|a_n| \le (n+1)(1+1/n)^{n} < e(n+1)$$</p>
| 0non-cybersec
| Stackexchange |
Best Little OFC in China.. | 0non-cybersec
| Reddit |
I can't login to vps ubuntu after change ssh port. <p>After changing the port from 22 to 2200 from <code>/etc/ssh/sshd_config</code>
then I run :
<code>sudo service ssh restart</code></p>
<p>I disabled the UFW and by check <code>sudo service ssh status</code>
it's working and listing to port 2200 but when I try to connect by this line : </p>
<pre><code>sudo ssh -vvv -i LightsailDefaultPrivateKey-us-east-1.pem [email protected] -p 2200
</code></pre>
<p>it gives me <code>time out</code>, if I change the port again to 22, it'll work, but I want to use another port inside of 22, 2222 gives me the same issue </p>
<p><strong>my ubuntu VPS from amazon lightsail</strong> </p>
| 0non-cybersec
| Stackexchange |
[Serious] What are your reasons for not smoking/ingesting weed?. | 0non-cybersec
| Reddit |
What's next in lifting?. Maybe this is a question for /r/AskHistorians, but I don't want all the replies to be deleted because of broscience so here goes.
So back in the day in like 1910ish, buddy Hermann Goerner was probably the first guy to deadlift in the modern sense of the exercise. Then you have a hundred years of beasts following suit.
The bench press as we know it (or close to it) came up around the late 1800s with Hackenshmidt floor pressing the universe.
Similarly the squat was introduced in the early 1900s by Henry Steinborn. I'm not sure about the half- and quarter-squat, but I'm assuming about two reps later.
The military press or OHP is mentioned around the same time in 1903 by some dude named Calvert who ran a barbell store.
Most of the record keeping and standardization started in the 1928 Olympics in Amsterdam, and all the standard Olympic lifts listed above were included.
From my exhaustive research that has no methodological holes, it looks like we've been doing the same lifts for a hundred years and more. As people who lift, what do you think the next big lift is going to be? Is there a lift that we started doing recently that will be spoken about in the same breath as the squat or deadlift in a century? Aren't we 'due' for a new lift?
Apologies to runners, yoga practitioners, and believers in other physically strenuous forms of exercise. I selfishly only concentrated on lifting because that's what I do.
| 0non-cybersec
| Reddit |
Petition to re-hire James Gunn nears 250,000 signatures. | 0non-cybersec
| Reddit |
Is it just me or do you call the menu button and view button on the controller ‘start’ and ‘select’?. | 0non-cybersec
| Reddit |
The most watched sport finals in the world [x-post /r/dataisbeautiful]. | 0non-cybersec
| Reddit |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.