Why are oscillations so ubiquitous in nature? I'm aware that you can always approximate a potential by a quadratic term. But is this the most 'fundamental' reason for the pervasiveness for oscillations?
Why is the harmonic oscillator so important? I've been wondering what makes the  such an important model. What I came up with:   It is a (relatively) simple system, making it a perfect example for physics students to learn principles of classical and quantum mechanics. The harmonic oscillator potential can be used as a model to approximate many physical phenomena quite well.   The first point is sort of meaningless though, I think the real reason is my second point. I'm looking for some materials to read about the different applications of the HO in different areas of physics.
What does size of a directory mean in output of 'ls -l' command? What does size of a directory mean in output of ls -l command? How can I disable the "Welcome, Name!" banner notification for Game Center? Exporting Data From Salesforce - REST or SOAP? We have a requirement where we need to export records from salesforce tables into our application programmatically. I am reading on the various API's for data integration from salesforce mainly SOAP vs REST API's.  From what I understand, REST should be used when the web service requests are from mobile devices or browser based clients (since they understand JSON). Is that true? If that's the case how do Bulk REST API's fit the bill (since they are meant for bulk data transfers)?  I would like to get your thoughts on what are pros and cons in using SOAP or REST API's to export data records. Note that the requests are being made a java ee server application programmatically. After retrieving the records (probably in batches) from salesforce records we process (validate, filter etc) them and load them in our internal tables.  Thanks. Starting yesterday, I have a very odd problem on my Windows 10 desktop-- my CPU is constantly running at 100% (according to Task Manager), and it isn't throttling down. Because of this, it's constantly running at 3.3 GHz and the temperatures are rising to the point where the fans kick in at full force. If I go into the Windows power settings screen and manually change the processor power maximum to 50%, then it's capped at 50% frequency (~1.5 GHz), but it never goes below the maximum possible frequency.  The weird thing is, when I look at the process list, there isn't really anything obvious that's triggering it. None of the processes are abnormal, and though the process CPU percentages do add up to 100%, it doesn't make sense to me that each individual process is taking up as much CPU as Task Manager says it is. Everything seems to be "using" a significantly higher amount of CPU resources than it normally does.  As an attempt to diagnose the problem, I've also tried using Process Explorer. The really weird thing is that Process Explorer shows only 1-2% usage when idle, with the System Idle Process taking up the remaining ~98% as I would expect. Again, nothing looks out of the ordinary in the process list, but the processes are showing the levels of activity I would expect in Process Explorer.  I've already run both Windows Defender and Malware Bytes (a virus was my first guess), but nothing has turned up yet.  This same issue also occurs in Safe Mode, so I'm guessing that it's more along the lines of something to do with Windows itself...  So, to recap:   Windows 10 Desktop Intel 970, 3.3 GHz, 6 cores Task manager and resource monitor graphs shows 100% usage total No individual process is taking up significant resources in the resource monitor list CPU is not throttling down automatically based on the dynamic load, causing high temperatures and the fan to kick in Process Explorer is only showing 1-2% CPU usage   Before I go uninstalling everything, how would I figure out what's causing the issue if nothing weird is showing up in Task Manager or Process Explorer? In wikipedia FKT algorithm is given for planar graphs. Not anything for complete graphs. I need to find the number of perfect matchings in complete graph of six vertices. Prove that the normalisation of $A=k[X,Y]/(Y^2-X^2-X^3)$ is $k[t]$ where $t=Y/X$ (Reid, Exercise 4.5) This is a problem about finding the normalisation of a quotient polynomial ring. So I have to find the integral closure of the ring in its field of fractions. The problem statement is as follows:     Let $A=k[X,Y]/(Y^2-X^2-X^3)$. Prove that the normalisation of $A$ is $k[t]$ where $t=Y/X$.   Can I do this by showing that the field of fractions $\text{Frac} A$ of $A$ is equal to $k[t]$, and subsequently showing that the field of fractions is normal? (This could be done by showing that $k[t]$ is a UFD?)  I am lost at calculating/determining $\text{Frac}A$, or similarly proving that $k[t]=\text{Frac}A$. Also, how do I show that it is normal?  I hope you can help! Keeping chunks loaded in minecraft I have built an iron farm somewhere far away from my actual spawn chunks in my single player world. In hindsight, this was a dumb idea, but I can't exactly change it anymore. I'd like to keep the thing running all the time, so I'm looking for a way to keep the chunks loaded.  I'm running minecraft 1.12.1, is it possible at the moment? I have looked at some chunk loader mods, but chicken chunk loader hasn't been updated yet, and the others simply didn't work.  I have tried moving the spawn chunks, but that hasn't done anything either.  Edit: I have worked this out with IronAnvil, and it ended up being a render setting in optifine which didn't load them correctly somehow. It has been working fine after I reset my optifine settings to default. I am giving a LaTeX course and have the idea to let the students find and solve problems within a few documents. Basically they shall learn how to create minimal examples and read error messages.  However, currently I have no document with 'typical' errors around.  If someone has such examples from him- or herself or within this forum I would like to have the code or link. It does not matter if its short or long. It should just be enough to let the students play with it for some minutes. How can one link / merge / combine / associate two accounts / users? (Anonymous / unregistered / cookie, or Google / Facebook / registered) I am trying to make a custom food recipe. I'm using spawn eggs with /replaceitem because spawn eggs are not obtainable in survival. This works fine when the player crafts only one spawn egg, but when I scroll over multiple spawn eggs, I receive only 1 of the custom food. BTW this food uses custommodeldata, so I can't simply add it into the crafting recipe. I cannot seem to find a way around this. If I make the item non-stackable, such as a piece of armor, mass crafting would be impossible. If I make an item.dropped scoreboard, the player could keep the item and use it to spawn mobs (griefing or for own profit.)  My command:    execute as @a[nbt={SelectedItem:{id:"minecraft:villager_spawn_egg"}}] run replaceitem entity @s weapon  minecraft:melon_slice{CustomModelData:10000101,display:{ Name:"{\"text\":\"Blue Melon Slice\",\"italic\":\"false\"}"}}     My problem is that the command does not see item count, as it is often used for weapons and armor only.    One way I thought to fix this issue is by storing the amount of custom food crafted in a scoreboard item and then giving the player that same count of the custom food, but I do not know how to do this; consequently, I don't know if this works.    Is there a way to do this method, or is there another, simpler method possible? Mounting Flashdrive - mounted to home directory I wanted to mount my flashdrive, and made the mistake of setting the mount path as /home/my_name. Now all of my documents, downloads, pictures, etc. are unavailable since my flashdrive has replaced my previous home folder.  When I go to terminal and type sudo umount /home/my_name I get the error message:   umount: /home/my_name: device is busy.         (In some cases useful info about processes that use          the device is found by lsof(8) or fuser(1))   Is there a way to fix this, where I can restore my old /home/my_name folder and then mount the flashdrive to a proper location? What are the difference between:    the action $\int_{t_{1}}^{t_{2}}(L+H) dt$ that we use in the principle of least action, and  the action integral $\int_{t_{1}}^{t_{2}}L dt$ that we use in Hamilton's variational principle?   References:   H. Goldstein, Classical Mechanics, Section 8.6. H. Goldstein, Classical Mechanics, Chapter 2. Firefox running with rare arguments I got this output from ps aux|grep firefox command:  $ ps aux|grep firefox auraham   5443 17.3 11.0 2600628 426484 ?      Sl   18:10   0:54 /usr/lib/firefox/firefox auraham   5496 24.0 17.9 2558108 691700 ?      Sl   18:10   1:15 /usr/lib/firefox/firefox -contentproc -childID 1 -isForBrowser -intPrefs 5:50|6:-1|18:0|28:1000|33:20|34:10|43:128|44:10000|49:0|51:400|52:1|53:0|54:0|59:0|60:120|61:120|91:2|92:1|106:5000|117:0|119:0|130:10000|155:24|156:32768|158:0|159:0|167:5|171:1048576|172:100|173:5000|175:600|176:4|177:1|186:2|200:60000| -boolPrefs 1:0|2:0|4:0|26:1|27:1|30:0|35:1|36:0|37:0|38:0|41:1|42:1|45:0|46:0|47:0|48:0|50:0|55:1|56:1|57:0|58:1|62:1|63:1|64:0|65:1|66:1|67:0|68:1|71:0|72:0|75:1|76:1|80:1|81:1|82:1|83:0|85:0|86:0|87:1|88:0|93:1|94:0|100:0|105:0|108:1|109:0|111:1|112:1|114:1|118:0|120:0|122:0|124:1|125:1|131:0|132:0|133:1|135:0|146:0|153:0|154:0|157:1|160:0|162:1|164:1|165:0|170:0|174:1|179:0|180:0|181:0|182:1|183:0|184:0|185:1|188:1|192:0|193:0|194:1|195:1|196:0|197:1|198:1|199:1|201:0|202:0|204:0|212:1|213:1|214:0|215:0|216:0| -stringPrefs 3:7;release|134:3;1.0|151:332;  ¼½¾ǃː??։֊׃״؉؊٪۔܁܂܃܄ᅟᅠ᜵           ???‐’․‧??????? ‹›⁁⁄⁒ ⅓⅔⅕⅖⅗⅘⅙⅚?⅜⅝⅞⅟∕∶⎮╱⧶⧸⫻⫽⿰⿱⿲⿳⿴⿵⿶⿷⿸⿹⿺⿻　。〔〕〳゠ㅤ㈝㈞㎮㎯㏆㏟꞉︔︕︿﹝﹞?．／｡ﾠ???￼�|152:8;moderate| -greomni /usr/lib/firefox/omni.ja -appomni /usr/lib/firefox/browser/omni.ja -appdir /usr/lib/firefox/browser 5443 true tab auraham   5694  0.0  0.0  15444  1092 pts/2    S+   18:15   0:00 grep --color=auto firefox   According to , this error occurs after firefox crashes. However, every time I run Firefox again, that large line of arguments appears too.  I already try these things:   Run Firefox with addons disabled Reinstall Firefox (sudo apt-get purge firefox; sudo apt-get install firefox)   However, it did not work.  Is it possible to remove such a line of arguments? Minimum of the Gamma Function $\Gamma (x)$ for $x>0$. How to find $x_{\min}$? Inverse metric in linearised gravity From what I've read, in the framework of linearised gravity, one perturbs the metric around a Minkowski background, $\eta_{\mu\nu}$, such that  $$g_{\mu\nu}(x)=\eta_{\mu\nu}+h_{\mu\nu}(x)\tag{1}$$  where $h_{\mu\nu}(x)$ is a small perturbation, i.e. $$\big\lvert h_{\mu\nu}\big\rvert&lt;&lt;1.\tag{2}$$  The inverse metric is then found by assuming the following ansatz:  $$g^{\mu\nu}(x)=\eta^{\mu\nu}+\tilde{h}^{\mu\nu}\tag{3}$$  where $\tilde{h}^{\mu\nu}$ is also small (i.e. $\big\lvert \tilde{h}_{\mu\nu}\big\rvert&lt;&lt;1$).   Using this, it is easy to find that  $$g^{\mu\nu}(x)=\eta^{\mu\nu}-h^{\mu\nu} \tag{4}$$  to first order.   My question is, what is the justification for this ansatz? Is it simply that one expects the inverse metric to have a similar form to the metric in order to satisfy $$g^{\mu\alpha}g_{\alpha\nu}=\delta^{\mu}_{\;\nu}~?\tag{5}$$ My connection was fine until now, but my wired connection is not working in Ubuntu 12.04.  I have installed Ubuntu 12.04 along side Windows 7 partition and the connection works on Windows but not on Ubuntu 12.04. I have no problem with wireless connection as well.  The problem is specific to the wired connection on Ubuntu 12.04. I have included a few details below.  ifconfig  eth0      Link encap:Ethernet  HWaddr 00:1e:ec:8d:f0:03             inet6 addr: fe80::21e:ecff:fe8d:f003/64 Scope:Link           UP BROADCAST RUNNING MULTICAST  MTU:1500  Metric:1           RX packets:1 errors:0 dropped:0 overruns:0 frame:0           TX packets:376 errors:0 dropped:0 overruns:0 carrier:0           collisions:0 txqueuelen:1000            RX bytes:316 (316.0 B)  TX bytes:33769 (33.7 KB)           Interrupt:19   eth2      Link encap:Ethernet  HWaddr 00:21:00:4e:ac:58             inet6 addr: fe80::221:ff:fe4e:ac58/64 Scope:Link           UP BROADCAST MULTICAST  MTU:1500  Metric:1           RX packets:1660 errors:0 dropped:0 overruns:0 frame:28           TX packets:1846 errors:61 dropped:0 overruns:0 carrier:0           collisions:0 txqueuelen:1000            RX bytes:1372676 (1.3 MB)  TX bytes:254576 (254.5 KB)           Interrupt:18   lo        Link encap:Local Loopback             inet addr:127.0.0.1  Mask:255.0.0.0           inet6 addr: ::1/128 Scope:Host           UP LOOPBACK RUNNING  MTU:16436  Metric:1           RX packets:1862 errors:0 dropped:0 overruns:0 frame:0           TX packets:1862 errors:0 dropped:0 overruns:0 carrier:0           collisions:0 txqueuelen:0            RX bytes:155767 (155.7 KB)  TX bytes:155767 (155.7 KB)     sudo lshw -C network    *-network                       description: Wireless interface        product: BCM4312 802.11b/g LP-PHY        vendor: Broadcom Corporation        physical id: 0        bus info: pci@0000:03:00.0        logical name: eth2        version: 01        serial: 00:21:00:4e:ac:58        width: 64 bits        clock: 33MHz        capabilities: pm msi pciexpress bus_master cap_list ethernet physical wireless        configuration: broadcast=yes driver=wl0 driverversion=5.100.82.38 ip=10.0.0.3 latency=0 multicast=yes wireless=IEEE 802.11bg        resources: irq:18 memory:99700000-99703fff    *-network        description: Ethernet interface        product: RTL8101E/RTL8102E PCI Express Fast Ethernet controller        vendor: Realtek Semiconductor Co., Ltd.        physical id: 0        bus info: pci@0000:04:00.0        logical name: eth0        version: 02        serial: 00:1e:ec:8d:f0:03        size: 100Mbit/s        capacity: 100Mbit/s        width: 64 bits        clock: 33MHz        capabilities: pm msi pciexpress msix vpd bus_master cap_list rom ethernet physical tp mii 10bt 10bt-fd 100bt 100bt-fd autonegotiation        configuration: autonegotiation=on broadcast=yes driver=r8169 driverversion=2.3LK-NAPI duplex=full firmware=N/A latency=0 link=yes multicast=yes port=MII speed=100Mbit/s        resources: irq:19 ioport:3000(size=256) memory:93410000-93410fff memory:93400000-9340ffff memory:93420000-9343ffff Is Dishonored an open-world game? I was considering whether or not to buy Dishonored, and watching gameplay of it on Youtube, when a thought popped into my head: is Dishonored free-roam? Can you go anywhere you want, similarly to Fallout or The Elder Scrolls? The editor should be able to convert multi-line blocks to lists Given two points (defined, for instance using nodes), I want to compute the distance between them.   Is there some build in functionality in tikz to do this? If not, how can it be done using the mathematical engine?   The application I have in mind is to draw an circular arc centered at (a) and passing through some second point (b), where only (a) and (b) are known. Standard value of PATH variable Windows 10 After having poorly handled the PATH system variable (resulting in deletion), I'm now looking to reinstate the variable with the original value. I found answers like  about Windows 8 and below, but not for Windows 10. I guess values are virtually identical, but I'd like to know the exact string so I'm not missing anything. EDIT: Also, Regedit tree have changed and I'm not able to locate the variable