Split (1)

train · 6.32M rows

url stringlengths 14 2.42k	text stringlengths 100 1.02M	date stringlengths 19 19	metadata stringlengths 1.06k 1.1k
http://winassist.org/thread/730794/installed-4x-port-usb-to-Window-7-pc-USB-wont-read-win7-quot-FATAL-ERROR-quot-message.php	Windows Support Forum # installed 4x port usb to Window 7 pc - USB wont read + win7 "FATAL ERROR" message Q: installed 4x port usb to Window 7 pc - USB wont read + win7 "FATAL ERROR" message Hi I have a win7 64bit Processor Intel (R) Core(TM) i5-2500K CPU @ 3.30Ghz 3.60Ghz 8GB Ram Manufacture : Gigabyte Rating: 5.0 Window experience Index I have brought a 4 USB 3.0 2.0 PCI-E PCIE USB Port Express Expansion card I fitted it to my pc, loaded the drivers and it was working great until I went to close down the pc, it came up with fatal error it shutdown my pc and i had to go into safe mode to remove the drivers for pci-e card. i have tried every pci slot x3 still not working. Does anyone know what might be wrong? Thanks Relevancy 100% Preferred Solution: installed 4x port usb to Window 7 pc - USB wont read + win7 "FATAL ERROR" message I recommend downloading and running Reimage. It's a computer repair tool that has been proven to identify and fix many Windows problems with a high level of success. I've used it in the past to identify and fix everything from blue screens (BSOD's), ActiveX errors, corrupt files and processes, dll/exe/sys errors, recover lost memory, Windows update problems, defragging, malware removal etc. A: installed 4x port usb to Window 7 pc - USB wont read + win7 "FATAL ERROR" message Quote: Originally Posted by soash Hi I have a win7 64bit Processor Intel (R) Core(TM) i5-2500K CPU @ 3.30Ghz 3.60Ghz 8GB Ram Manufacture : Gigabyte Rating: 5.0 Window experience Index I have brought a 4 USB 3.0 2.0 PCI-E PCIE USB Port Express Expansion card I fitted it to my pc, loaded the drivers and it was working great until I went to close down the pc, it came up with fatal error it shutdown my pc and i had to go into safe mode to remove the drivers for pci-e card. i have tried every pci slot x3 still not working. Does anyone know what might be wrong? Thanks Check your BIOS for settings on that port you seated that pci card in. Relevancy 23.65% Please refer to the message below for information on how to remove your Dell laptop BIOS password. The information also applies to other manufacturers and summarizes a wealth of data collected from previous threads and thousand of posts related to this problem. We no longer support any further discussion on this topic as we believe all the free help that could be given is already out there (the post below sums it up pretty well). You can always go back to your system manufacturer for support, as well as google for the dozens of third party paid support providers that are available online. http://www.techspot.com/vb/topic109612.html If all options have been tried and you still require help removing your password, search Google for 3rd party alternatives TechSpot forums and all support is provided freely at all times, it is against our guidelines to link to external paid services You are advised to try any or all options, with your first point of contact being the laptop manufacture, being the best option TechSpot forums are FREE and manufacture support only Click >Dell Support and System Information for a particular Service Tag > Click > HP Live Chat, Drivers, Warranty and Support Information thread > Click > Toshiba BIOS Setup / BIOS settings -- access instructions Reset password on Satellite A205: http://www.techspot.com/vb/post613153-2.html Reset password on Satellite A100 / A105: http://www.techspot.com/vb/post572530-1.html Power On Password (pop). this password can be reset by unplugging the cmos battery for a while, and plugging it back in. Supervisor/bios Password (svp). this requires reading the eeprom chip (8 leg or 14 leg) with an electronic device by using another pc's serial port or by paperclip method if model type available. Hard Drive Password (hdp). this is usually tied to svp, but not all the time. it requires special software and a library of known manufacturer's password. but can be cracked either recovering the data or wiping the data. Transfer of Product Ownership US: http://support.dell.com/support/top...tag_transfer?c=us&cs=19&l=en&s=dhs&redirect=1 International: http://support.dell.com/support/top...ansfer_form1?c=us&cs=19&l=en&s=dhs&redirect=1 International warranty contact phone numbers http://support.dell.com/support/top...dellcare/international_travel?c=us&l=en&s=gen Old closed threads, with lots of info: Dell BIOS password removal (Jun 07 - Sep 07) http://www.techspot.com/vb/topic79263.html (543 replies) http://www.techspot.com/vb/topic97423.html (533 replies) HP / Dell / etc. Laptop password help (April - July 2008) http://www.techspot.com/vb/topic59293.html (937 replies) HP / Dell / etc. laptop password help thread (Aug 08 - Apr 2009) http://www.techspot.com/vb/topic109612.html (2200+ replies) Dell Manuals : http://support.dell.com/support/systemsinfo/documentation.aspx?c=us&l=en&s=gen&~cat=12#12 DSTCD.iso : (Release date: 22-November-2005) http://www.savefile.com/files/2063585 "Paperclip Procedure" HTML Document: http://web.archive.org/web/20031103020606/http://qasimtoep.tripod.com/dell/dell6.html PDF Document: http://www.savefile.com/files/2059217 laptops unlocked: http://www.techspot.com/vb/post645683-913.html Chip 24C02 24C04: http://www.techspot.com/vb/post698486-1134.html Dell IC Numbers: http://www.techspot.com/vb/post645922-916.html SvcTag.exe : ftp://ftp.us.dell.com/utility/svctag.exe Asset.com : ftp://ftp.us.dell.com/utility/asset.com Command line Uses => asset /? (eg Asset /o for owner tag) CmosPwd : http://www.cgsecurity.org/wiki/CmosPwd Attachments HP OldPass .zip includes: HP Oldpass2 .zip: As above, made as a copy, using another Zip program Dell Latitude .zip: Dell MasterPW .zip: How to use Relevancy 22.36% SO close Help me get this ball across the goal line I have a old quot Microtek ScanMaker E quot scsi flatbed scanner that originally came with an ISA scsi interface to give you some idea of how old it is I connected it to my PC using a equally ancient Tekram F pci SCSI card c 64bit my got scanner Almost w/Win7 old working that I ve been using with bit WinXP Pro for years The scanner has an - quot x quot scanning bed dpi and bit color reproduction It works great and I see no reason to spend a few hundred dollars to replace it just for Win compatibility so I m trying to get it to work with the bit Almost got my old scanner working w/Win7 64bit version of Windows To complicate things the company that made my SCSI card Tekram went out of business years ago so the bit XP driver was the last they made But after MUCH Googling I found a bit Win compatible driver for another card using the same chipset and low amp behold Windows recognized it It then quot detected quot my scanner for the first time but didn t have a driver Again after much searching I found a Vista bit version of Microtek s quot ScanWizard quot scanner software with bit driver and now bit Windows detects my scanner Yeah But when I try to access the scanner I get an error telling me I quot must install Color Matching System first quot for the scanner to work I don t remember any such software being needed to use the scanner with XP and there is no such program in the ScanWizard software I just installed searching online suggests I will also need to run an quot ICC Color Profiler quot Anyone have any ideas So close yet so far I love doing things I was told were quot impossible quot Help nbsp A:Almost got my old scanner working w/Win7 64bit That Microtek ScanMaker E3 scsi flatbed scanner ... didn't even work well with Windows XP... and the cost in time and components to attempt to make it work are much higher than a decent Canon or Epson scanner which can be had fof $40... Less if used... On what system are you runny SCSI ? http://www.techspot.com/community/topics/almost-got-my-old-scanner-working-w-win7-64bit.157055/ Relevancy 51.6% I just solved my own problem and thought others might benefit since I could not find the solution using internet search My Realtek HD Audio manager seemed to be creating an echo on my quot Line In quot HD Audio Realtek "line from effect) (if in" echo it Removing output sound not a is audio signal I had already set the environment and equalizer sound effects options to lt None gt but the echo persisted I found the problem seems that I was essentially duplicating the Removing "line in" echo from Realtek HD Audio output (if it is not a sound effect) Line In audio stream The first quot source quot I found was the HD Audio manager You can open the manager and view the Line In tab - mine had a non-zero playback volume the slider was NOT all the way to Removing "line in" echo from Realtek HD Audio output (if it is not a sound effect) the left for zero playback If you want Removing "line in" echo from Realtek HD Audio output (if it is not a sound effect) output from the HD Manager that makes sense I also found out a second Line In quot source quot It was in the Line In properties settings where I had checked off the option to quot Listen to this device quot When I disabled that the echo disappeared To view this Line In properties tab right-click on the speaker icon in the notification area then select Recording Devices yes quot Recording quot Then the tab will display in a window with the title Sound You should see the Line In device in the list Right-click on this item and select Properties The Line In properties window pops up Then select the Listen tab UNselect Listen to this device The echo should disappear if you re experiencing my problem I hope this helps someone I m just trying to help the community from which I ve received so much help grinthumb nbsp A:Removing "line in" echo from Realtek HD Audio output (if it is not a sound effect) Two same signals You're doing the right thing... getting rid of the other input signal. http://www.techspot.com/community/topics/removing-line-in-echo-from-realtek-hd-audio-output-if-it-is-not-a-sound-effect.178881/ Relevancy 24.08% I have an SSD Intel Series GB SATA Generic Single Pack which on my PC has a maximum speed rate at MB sec but on other PC has MB sec My PC features OS Name Microsoft Windows Enterprise Version Service Pack Build OS Manufacturer Microsoft Corporation INTEL SSDSC BW A GB SATA quot SSD System Manufacturer Dell Inc System Model OptiPlex System Type x -based PC Processor Intel R Core TM i - CPU GHz Mhz Core s Logical Processor s BIOS Version Date Dell Inc A SMBIOS Version Windows Directory read SSD 264mb/sec slow rate C Windows System Directory C Windows system Boot Device Device HarddiskVolume Locale United States Hardware Abstraction Layer Version quot quot Installed Physical Memory RAM SSD slow read rate 264mb/sec GB Total Physical Memory GB Available Physical Memory GB Total SSD slow read rate 264mb/sec Virtual Memory GB Available Virtual Memory GB Page File Space GB Page File C pagefile sys SiSoftware Sandra Benchmark Results Drive Score MB s Results Interpretation Higher Scores mean Better Performance Binary Numeral System base GB s MB s MB s kB s kB s bytes s etc Benchmark Status Result ID INTEL SSDSC BW A GB SATA quot SSD Computer Dell OptiPlex Dell GY Y Platform Compliance x System Timer MHz Use Overlapped I O Yes I O Queue Depth request s Block Size MB nbsp A:SSD slow read rate 264mb/sec There's a known issue with SSD storage: SSDs degrade in performance overtime - - DON'T run benchmarks and you don't need defrag either. http://www.techspot.com/community/topics/ssd-slow-read-rate-264mb-sec.216431/ Relevancy 44.29% I have a choice to make on a new monitor. It needs to be VESA mountable and will be for strategy gaming and work purposes. Games like Wargame, Supreme Commander and World of Tanks. I work as a sysadmin so think lots of windows open! Do I get a 24" monitor like this Benq (recommendations on a different one are welcome) Or do I get a 27" monitor. If you think 27" what res would you recommend baring in mind I am sporting a 760gtx. Thanks, A:24" monitor or 27" I think 1080P is the best bet for your GTX 760. 2560x1600 or 2560x1440 (27 inch panels) might be a bit too much. It is really personal preference whether you weant a 24 inch or a 27 inch. There are 1080P monitors in both sizes. I recommend Dell, BenQ, ASUS, Samsung, and ACER monitors. There are some other good ones, but I cant think of them off the top of my head. http://www.techspot.com/community/topics/24-monitor-or-27.201808/ Relevancy 20.64% My Asus Q550LF crapped out on me. I was browsing when a whole bunch of black rectangles appeared on my screen, about an inch long. I restarted my computer thinking it just froze or something. I could occasionally get to the desktop page if I unplugged the charger but now it doesn't even turn on. It'll make one beep when I push the power button but that's it. What might the issue be and is it gonna be expensive? Because this computer has been one of the worst I have ever owned and I would just scrap it or something if it might end up being costly. A:Laptop wont turn on anymore How old is it? It sounds like it could be a multiple of hardware failures including the motherboard. The black rectangles sounds like what we call video card artifacting which means the video card is dying. But the fact that it is not even booting up could point to a failed hard drive. Again, it could be anything. Asus is known for poor customer service but you could try giving them a call. Do you know anyone who can do some diagnostics on it? I certainly would be checking out the hard drive. http://www.techspot.com/community/topics/laptop-wont-turn-on-anymore.214221/ Relevancy 50.74% Hey there all. This problem just happened recently. Every time I put a blank CD in my CD drive, a message appears saying "E:\ is not accessible. Incorrect Function. I can watch DVDs but it won't recognize any blank CDs I put. Any ideas? Thanks in Advance. A:Drive is not accessible - "incorrect function" First try this from the Windows Explorer after you have inserted a disc. Right-Click on E: drive Select Properties from the pop up menu Select the Recording Tab then check the "Enable CD Recording On This Drive" box. . http://www.techspot.com/community/topics/drive-is-not-accessible-incorrect-function.166087/ Relevancy 54.61% I have a three month old Dell Dimension GHZ P Gig Ram and a gig SATA Hard Drive When I got the computer I used the files and transfer PC Relocator utility And had in Error system drives did hard Message: disk find Setup not your installed any a bunch of unwanted extras that came with it I m having a Satellite Internet system installed and they wanted a clean install of windows XP So I opened the owner s manual and got out the reinstallation disk and the problems began By the way Dell tech support s only response has been to say gee that s not right and would send a tech sometime after Christmas Anyway heres step by step what I did I boot to the Dell reinstallation disk Error Message: Setup did not find any hard disk drives installed in your system The windows setup screen appears and loads files The next screen says welcome to setup and offers three options -to setup XP press enters To repair XP press R to exit without installing XP press F I press enter and the following message comes up Setup did not find any hard disk installed in your computer Make sure any hard disk drives are powered on and properly connected And any disk related configuration is correct ect Press F to quit It dose this if I try repair also Dell had me check the connections to the HD and Motherboard They re good And debug the hard drive No luck Everything worked fine until I put in the reinstallation disk Any help would be welcome nbsp A:Error Message: Setup did not find any hard disk drives installed in your system During Setup, it will ask you if you need any extra drivers such as SCSI (or SATA in your case). If so, press F6. Now you are in trouble, because SATA drivers come on a floppy and new(er) Dells don't have a floppy anymore. Borrow a floppy-drive from another PC and install that in your Dell. Setting up with the Dell disks, I'm not sure if they are RESTORE-disks or full XP-disks. That may cause another problem. http://www.techspot.com/community/topics/error-message-setup-did-not-find-any-hard-disk-drives-installed-in-your-system.18329/ Relevancy 13.33% Hello everyone, One fine evening while watching a movie, my laptop stopped responding and in frustration I switched off the laptop by holding the power button long enough to turn off. Next Morning it showed a blue screen and a message to recover my windows, which I failed to do and by the afternoon this message showed up. Detection Error on HDD0 (main HDD) and hence forth I've been unable to install windows from a USB drive since ( and I suppose) it is not able to read my HDD. I do not care about my data at all, I just want my laptop up and running. If I can have the data back it will be perfect otherwise I don't mind not getting my data back. I know for a fact that my Hard disk is fine because I went into command prompt, diskpart , and list disk, and saw the status of HDD as healthy, this is after the error (detection error on HDD). SO my question is: Why this error? IS there a problem in the motherboard? Why the error shows once and then doesn't show the next time and then comes up again. A:2100: Detection Error on HDD0 (Main HDD); Lenovo Thinkpad Yoga The error might be bad sectors, but I'm not sure. if my guessing is correct, you might have to get a new drive to replace. also you need to reinstall OS http://www.techspot.com/community/topics/2100-detection-error-on-hdd0-main-hdd-lenovo-thinkpad-yoga.212391/ Relevancy 51.17% I have scoured the from computer, sounds" can speakers "computing my hear my through I internet for a solution to this and have found nothing First my dxdiag is attached I have had this issue for over a year now and I am getting fed up If I put my ear to my pc I can hear computer noises coming from it I can not compare it to another sound as there is nothing else to compare it too it just sounds like my CPU or Hard Drive thinking That doesnt bother me though I expect my computer to make some noise HOWEVER I dont expect to hear it in my speakers too I have a lot of speakers and a lot of headphones no they are not I can hear "computing sounds" from my computer, through my speakers the problem Right now I am using a knappenberger tube hooked up to a GK MB just cuz I can When I plug in any speakers I can hear the CPU sound through them regardless of the volume level I can turn the speaker all the way down and yet the sound will come through This leads me to believe I can hear "computing sounds" from my computer, through my speakers it is a grounding issue or electrical to some degree I would like to try physically grounding my case to see if it would eliminate this God awful feedback However I can not find a guide as to I can hear "computing sounds" from my computer, through my speakers the best way to do this or any other suggestions So here I am Help me and earn my eternal gratitude Some notes If I unplug all of my cables except power and the speaker cable I still hear it if I plug in my speaker cable to my monitor instead of my PC I still hear it Front port still hear it I have yet to try a different sound card as I dont have one Once I find one I will update nbsp A:I can hear "computing sounds" from my computer, through my speakers Checked some settings in the Bios, noticed the sound isnt there while navigating it. Static started once windows loaded. Maybe it is some sort of issue with the hard drive http://www.techspot.com/community/topics/i-can-hear-computing-sounds-from-my-computer-through-my-speakers.202182/ Relevancy 49.88% I have a desktop computer that is running on Windows Xp, up until this morning, everything was fine, I could connect to the internet with no problem. I turned on my computer, and it is telling me that the network cable is unplugged, as well as my network is not showing when i go to "my network connections" But yet..... I AM connected to my router, and there is no problem with the cord (I tried it on different computers as well as my Xbox 360 on the same port....so I know its not the router)....when I go into device manager, everything seems to be working correctly, and my network adapter and ethernet card both are marked as working properly. Any ideas how I can fix this issue ? A:"Network cable is unplugged" but its really not.. sadgyrl514 said: I have a desktop computer that is running on Windows Xp, up until this morning, everything was fine, I could connect to the internet with no problem. I turned on my computer, and it is telling me that the network cable is unplugged, as well as my network is not showing when i go to "my network connections" But yet..... I AM connected to my router, and there is no problem with the cord (I tried it on different computers as well as my Xbox 360 on the same port....so I know its not the router)....when I go into device manager, everything seems to be working correctly, and my network adapter and ethernet card both are marked as working properly. Any ideas how I can fix this issue ?Click to expand... Try rebooting, http://www.techspot.com/community/topics/network-cable-is-unplugged-but-its-really-not.166539/ Relevancy 24.08% Apple's decision to include just a single port on its new 12-inch MacBook provoked the ire of many, and perhaps rightfully so. Adapters are the obvious answer for devices lacking a USB Type-C interface but what if you have multiple... Read more A:Single USB-C port? No problem. InfiniteUSB-C is a viable solution to the MacBook's limitation I'll bet Apple is kicking themselves right now for now making this little device themselves. I feel bad for Apple users though... having to spend extra money to get what should be basic functionality. http://www.techspot.com/community/topics/single-usb-c-port-no-problem-infiniteusb-c-is-a-viable-solution-to-the-macbooks-limitation.212016/ Relevancy 21.07% Hi I have an HP zbook white a K610m GPU. I want to play GTA V and I read on forums it helps to disable your gpu. howerver when I disabled my GPU the screes flashes black for like 1 sec and then my gpu isnt disabled. can you help me to resolve this? http://www.techspot.com/community/topics/gpu-wont-stay-disabled.212026/ Relevancy 21.93% Neither my keyboard or mouse are working on any of the 7 USB ports on my computer. My mouse was initially working, but I read somewhere if you delete the keyboard drivers you can reinstall them and it will work again. BUT when I was doing that I stupidly uninstalled my mouse driver so now NOTHING works. I can't try if it works in safe mode because my keyboard doesn't respond when I hit f12 during boot up. When I plug in the mouse or keyboard, I get a window that pops up asking if I want to install the hardware, but it's impossible for me to do anything because my mouse and keyboard don't work! If anyone has any ideas I would greatly appreciate the help. Thanks! A:My Dell Demension e510's (Window's XP) keyboard and mouse don't work First I would try to find a different working keyboard because you should at less be able to boot into safe mode because the drivers don't even load until windows start loading. http://www.techspot.com/community/topics/my-dell-demension-e510s-windows-xp-keyboard-and-mouse-dont-work.211116/ Relevancy 49.88% I'm trying to record some karaoke but every time I play back the recorded track, the music is "doubled" with a slight delay, as if the laptop's built-in microphone was picking up the music along with my voice. Here is an example: http://www.singsnap.com/karaoke/watchandlisten/play/c58ef46c3 Notice how those staccato notes are doubled with that slight delay. I'm using Windows 7 on a Dell laptop with Realtek. Under Playback I have two devices: Loudspeaker (enabled) and Realtek Digital Output (disabled) Under Recording I have: Microphone (enabled) and Stereomix (disabled) I'm recording using headphones and the laptop's built-in microphone. This is what the Realtek Audio Manager looks like: It's in German but most options are self-explanatory. If you could help I'd be very grateful. Thanks for reading. http://www.techspot.com/community/topics/bleeding-when-trying-to-record-on-laptop.211024/ Relevancy 51.17% I have been having this issue for about 2 weeks now. Ive literally tried everything including uninstalling/reinstalling network card, restore points (there are none), a windows update download, and reformatting the hard drive (wont let me). Any help is appreciated. I cant afford a new pc or any new hardware at this time. A:"Failed to query TCP/IP settings of the connection. Cannot proceed." failed to query tcp/ip settings of the connectionClick to expand... what did you do when this occurred? Describe network equipment {modem, router} ISP, and your system. Connect it all together, get a command prompt, enter ipconfig /all >myTcp.txt and come back here and paste the contents of myTcp.txt as your reply http://www.techspot.com/community/topics/failed-to-query-tcp-ip-settings-of-the-connection-cannot-proceed.177223/ Relevancy 23.22% I have one problem with my PC sound on board, My pc is windows 7 ultimate 32bit, Intel Desktop Board E210882, The driver is already install but the icon of sound still red cross like image attach file, I already plug in the headset, any one please help me? thank, seahong heng A:No audio output device is installed Well, one way or another, your computer isn't using the device, so have you checked to see if it's disabled in any way? right click the speaker and go to playback devices, it'll come up with a list of your sound devices, make sure the one you're trying to use isn't disabled (right click to change that) if you're unsure which is yours, just enable them all lemme know if that helps at all http://www.techspot.com/community/topics/no-audio-output-device-is-installed.188878/ Relevancy 50.74% Hi my daughter tried to adjust the resolution and now the screen is Black and stuck on Out Of Range. I cannot even get it safe mode or anything. Just a black screen with the writting. It's a windows xp 32. My son is so sad if anyone knows what to do please help. Thank you. A:PC monitor screen is black & says "Out Of Range" Repeatedly press F8 while the system is booting.. The very first stuff you see on screen will either be your motherboard splash screen or some text. When you get to the menu where you can make a selection, choose VGA mode NOT Safe Mode. That will boot your computer at 640x480, but it will boot with full driver support, just as if things were normal. Change the resolution to what you want after that. Remember if you change it to something that goes 'out of range' DO NOT touch anything for 15 seconds. It will revert back to what it was after that time and you can try again. Unrelated.. Go to school at UMR? or different Miner? http://www.techspot.com/community/topics/pc-monitor-screen-is-black-says-out-of-range.210867/ Relevancy 24.51% I'm in deep doggy-doo. When my 2TB Sata-III drive wasn't being recognized (ported to a new build), I pulled the data cable off to check the connection and off came the little plastic tab that guides the plug onto the pins! Without it, there is nothing to press contact between the cable & pins, let alone hold the cable firmly in place. Worse, I can't even plug it in to rescue the data off it! I suspect I must have damaged the connection somehow when I plugged it in. The pins appear fine (within reason considering what happened.) Gluing the tab back in place is no help if the connection still doesn't work and I need to unplug it again. Am I screwed or is there a way around this mess (short of paying hundreds to some recovery service)? A:Plastic tab on SATA drive port broke off Oh boy do I know the feeling, I once pulled off the same thing from a month old mobo, but I was able to find a replacement in a shop and soldered it back, maybe you can do the same ? Try finding a female SATA and soldering the other end of it to the HDD ? http://www.techspot.com/community/topics/plastic-tab-on-sata-drive-port-broke-off.209316/ Relevancy 50.74% For the past month, Nvidia has faced its fair share of bad PR thanks to the GeForce GTX 970's memory allocation issue. As has been uncovered by users and explained by Nvidia, the GTX 970's last 512 MB of VRAM... Read more A:Nvidia CEO says GTX 970 memory controversy "won't happen again" Again: the performance didn't change overnight; it's today the same performance than the advertised on launch date. Even that technicality can kill the case. Specifications were the "misleading" part. http://www.techspot.com/community/topics/nvidia-ceo-says-gtx-970-memory-controversy-wont-happen-again.209149/ Relevancy 13.76% Hello, I bought a R9 270X by XFX. My current specs are: CPU: AMD A10 7800k (Standard Clock Speeds, Graphics Disabled) RAM: 4GB (2 sticks, both working) Motherboard: FM2, Gigabyte PSU: 500 watt 80+ Cert Silver HDD: 500GB WD Blue So the issue is that the R9 card consistenly crashes out of all games no matter if I uninstall the drivers or reinstall them. I have tried removing the drivers through catalyst control center and through application based tools (DisplayDriverUninstaller). Once I uninstall and reinstall, it works, until the computer is restarted and then rinse and repeat. Is this the card saying it is dying? If so it is a weird way of graphics card dying. http://www.techspot.com/community/topics/r9-270x-doa-or-user-error.209138/ Relevancy 23.22% Hi Guys I'm not so clued up about how to use forums but I tried looking for similar problem here for a solution but nothing. every time I plug on a new USB flash/external HDD or mobile phone it gives me a message "device was unsuccessfully installed" now I cant access any removable device. yet all my old devices still work. Please help!!! A:Unsucessfully installed usb devices win 7 64 bit Hello there, Have you tried to update your USB Host controller drivers? If updating doesn't work reinstall them. Hope that helps. http://www.techspot.com/community/topics/unsucessfully-installed-usb-devices-win-7-64-bit.208840/ Relevancy 51.6% As you've probably heard by now, Nvidia is having a few issues with their GeForce GTX 970 graphics card. In response, AMD has lowered the price of the card's main competitor, the Radeon R9 290X, in an attempt to get... Read more A:AMD cuts Radeon R9 290X price amid GTX 970 "issues" Meaning AMD could have been selling the card cheaper this whole time. AMD needs to stand more firmly in their business decisions. Changing prices on a whim every time the wind blows, shows lack of confidence in their product to sell itself. http://www.techspot.com/community/topics/amd-cuts-radeon-r9-290x-price-amid-gtx-970-issues.208450/ Relevancy 20.64% Hopefully someone can answer this as im baffle, my computer will turn on and of with no problem as ling my printer is plug in but if printer cable unplug it won't turn on but if printer cable in plug in it will turn on but while the comptuer turn on and I unplug the printer cable it will shut down nothin making since but as long the printer is unplug it will not start or boot blank screen but printer plug in I can get to the boot or cmos screen please help Thanks PS it a Dell PP17L Latitude http://www.techspot.com/community/topics/pc-wont-turn-on-if-printer-not-plug-in.208502/ Relevancy 13.76% Hi, I am having a problem with my external hard drive not working. My laptop cannot read the drive, it does not display properly in my computer and when I try to click on it it freezes and the message appears "Drive is not accessible, parameters are incorrect". I used it about three weeks ago and it was fine so I don't know what happened. I always make sure to safely remove it and am careful not to damage it. The light still still turns on when plugged in and I can hear it trying to work. I really want to keep the files as they are from my previous laptop which died and do not have them stored anywhere else. My fault I know, but I had thought external hard drives were more reliable and I do not like the idea of cloud storage. Because of this I am hesitant to try CHKDSK. Is there anything else I can do to recover the files or fix the drive? If I take it to a computer technician would they be able to do it? http://www.techspot.com/community/topics/external-hdd-error-not-accessible-parameters-incorrect.208079/ Relevancy 21.07% Hi, I have a MSI g31m3 v2 s-7529 motherboard and wont turn on. I change the power supply I put on some themical paste in the cpu I put away all hard drivers but didnt work, only the fan turn on then its turn off I think the motherboard dosent work. A:Motherboard wont turn on Please provide list of make and model for everything you have for this setup (CPU, RAM, GPU, Hard Drives, Optical Drives, Power Supply, Aftermarket coolers, etc.). We need to make sure that you have all compatible parts. Also, have you tried to disconnect all things except the power supply connection to the motherboard, CPU & RAM and see if the motherboard starts? http://www.techspot.com/community/topics/motherboard-wont-turn-on.208015/ Relevancy 25.37% Hey all, This is my first time trying to port forward anything and I'm having trouble finding a guide for my router the bell homehub 2000 (sagemcom fast 5250). If anyone has experience with this router, some help would be greatly appreciated. I'm trying to port forward for my xbox one. A:Port forwarding UPDATE: ok so I went ahead and did some more reading using a guide for a linksys router and attempting to translate it to mine. From my understanding I have to set a static ip address on my xbox one and then open the specific ports through my router settings, can anybody confirm this? http://www.techspot.com/community/topics/port-forwarding.207844/ Relevancy 25.8% Hi, Can someone tell me what is this port do? Its not hdmi cuz I try to fit one with my new monitor and did not work. Thank A:What is this port on this VGA It is DisplayPort. http://en.wikipedia.org/wiki/DisplayPort http://www.techspot.com/community/topics/what-is-this-port-on-this-vga.207754/ Relevancy 14.19% Ok, I have the question of `em all: at every game I try to unzip it gives me the crc error. I tried reinstalleing my windows, tested my RAMs(noo error found)reinstalled the drivers, nothing. I have the next output: amd a8 6600k 4gb ram r7 260X video card and gigabyte f2a55m-s1 motherboard. what should I do? also tried 7zip and latest version of winrar, and I get the memory managemet error A:CRC error Seems a bit odd you are unzipping games.. Do they unzip on other computers fine? If so, run a hard drive diagnostics utility like SeaTools. If you can't test on other computers, what are you trying to unzip specifically, games shouldn't be zipped... http://www.techspot.com/community/topics/crc-error.207554/ Relevancy 51.6% I have a mystery on my hands. I received a Bluetooth speaker as a gift. The BT-4.0 adapter plugged into my computer (USB-2.0 port) detects it (as a "Bluetooth headset"), but when I try to select it as my output device (from the "Sound" Control Panel), Windows reports it as "Disconnected". If I open "Devices and Printers" and right-click the "Bluetooth headset" icon, I get an alert that the device "Failed to initialize". I've tried rebooting, tried a different BT adapter, updated my BT drivers off the makers' website, Device Manager shows everything is connected & working (including "Bluetooth Audio"). 64bit Win7 Home. Inateck BT-4.0 usb adapter. Speaker is a "MicroBoom" BT v2.1: Any ideas? PS: Eliminated the obvious. Speaker is fully charged and works just fine with my phone. http://www.techspot.com/community/topics/bluetooth-headphones-paired-but-disconnected-failed-to-initialize.207624/ Relevancy 14.19% I've never seen this before. It just popped up a bit ago on my W7 pc. What does it mean? I hope its nothing bad. A:RAID error? I found this in a google search http://h30434.www3.hp.com/t5/Desktop-Hardware/AMD-RAIDXpert-Warning-Errors/td-p/342708 I've known this pc has RAID on it because everytime it reboots/boots up it shows it. I've had this pc for two years this month & just hoping nothing bad is happening. http://www.techspot.com/community/topics/raid-error.207317/ Relevancy 25.37% I recently bought several Dell Optiplex GX computers online for repair I usually do a thorough review of what I am getting but this was a a with VGA Help DVI-D on port computer monitor using a cheap deal on a big lot and a few things slipped by me For one it takes a special power cord that I can t find for less than and there were none Help using a VGA monitor with a DVI-D port on computer with the lot I ordered one to test them with for now but that is not my main problem but if anyone knows where I can get those DA- adapter power cords any cheaper please let me know where My main problem is that these are the small form factor cases so they have no card slots I am dependent upon the motherboard options only So here is my problem the only connector for a monitor on the back of the computer is for a DVI-D which would be great if I had monitors with those connections The only connections I have on my monitors are the VGA I bought some adapters from e-bay that were supposed to convert the DVI port to the VGA which the connector did but I have no screen using this adapter and I am thinking that I was cheated Can this even be done this way I have always just changed the video card but this computer has no way I can see to do that it is all in the motherboard Does anyone know what I can do here I put a fresh install of io xp pro on several of then since that is what they came with They only have pentium s with hyperthreading and single core processors and I didn t think windows would help any If anyone knows what I can do to use these VGA monitors please tell me because without being able to put a video card in it I am lost sincerely cableman nbsp A:Help using a VGA monitor with a DVI-D port on computer Your best bet for Global spares is www.pchub.com. As to the DVI to D-Sub you did the right thing in buying an adapter. It should work period. Did you get the joblot from eBay? Was it sold as untested? Are the PCs even powering on? Maybe there are issues with memory/cpu/motherboard.... http://support.dell.com/support/edocs/systems/opgx620/en/ug/A02/solve00.htm#wp1286323 Yes you have to be very careful when upgrading the CPUs for this unit as they follow a narrower roadmap. Top line CPU would appear to be a Pentium D3.4Ghz which worked in a GX620 usff with bios revision A11. Good luck! http://www.techspot.com/community/topics/help-using-a-vga-monitor-with-a-dvi-d-port-on-computer.172534/ Relevancy 25.37% I have a D945GCR MoBo.... does it have a Graphics card port? A:Does my mobo have a graphics port? Nick OZ said: I have a D945GCR MoBo.... does it have a Graphics card port?Click to expand... Yes it has, the motherboard in question has a "PCI-x16" which means that all and any new graphics card (GPU) should fit. However, you may want to check what power supply (PSU) you have since new GPU might require more power. http://www.techspot.com/community/topics/does-my-mobo-have-a-graphics-port.207195/ Relevancy 13.76% My toshiba will not get on the Internet Google will come up and search but everytime it says Internet error A:Laptop Internet error Need specific; try looking in the cmd-> enter eventvwr.msc http://www.techspot.com/community/topics/laptop-internet-error.207423/ Relevancy 13.33% We just bought a monitor U2713H direct from Dell. When we click on Factory Reset, the monitor doesn?t go back to Factory default setting. -In particular, Contrast/Brightness: 0. In terms of Color Setting, Input color Format: None. Preset Modes: Movie -Then we click on Reset Color Settings, Input Color Format: RGB, Preset Modes: Standard. -When click on Factory Reset again, Contrast/Brightness and Color Setting come back to the same condition as above (Contrast/Brightness are 0, Input color Format: None. Preset Modes: Movie). -After we try to set up Contrast/Brightness to 50/50, we shut down desktop or turn off the power button on the monitor. Then we turn on computer or turn on power button on the monitor, Contrast/Brightness are 0, Input Color Format: None, Preset Modes: Movie. -In summary, all menu settings can?t be saved by the monitor and Factory Reset doesn?t work. Any idea would be highly appreciated. Thank you a lot in advance A:Dell monitor U2713H error: settings can't be saved What I would suggest is ask Dell if they would warenty it new it should have one and Dell should honor it. I would say they will but I have not done business with them in years, although the monitor I am using right now is one of theirs and is many years old. http://www.techspot.com/community/topics/dell-monitor-u2713h-error-settings-cant-be-saved.207032/ Relevancy 24.51% Hi I had this problem a DVD-R 7 Won't Windows Vaio read - couple months ago fixed it and am now facing the same problem again I have a Vaio Windows My CD DVD player isn t reading any of my DVD-R cds Whenever I put in a DVD-R cd autoplay comes up and it asks to format the cd I checked these DVDs and they work on other computers They re all burned DVD with files on them Before when this happened I tried many different things I Deleted upper lower filters -- Actually I didn t have upper or lower filters to delete System restored Deleted and updated drivers Finally found a post talking about creating a new key in the regedit NoCDburning After doing this it started working Fast forward three months later my cd dvd player won t read any Vaio Windows 7 - Won't read DVD-R of my DVD-R cds again I did the same things all over again System restored Deleted and updated re-installed drivers Ran Fixit Looked for upper lower filters -- not there Tried looking at the NoCDburning thing again -- deleted and repeated the steps and nothing is happening I don t want to reboot my computer because I already did a month ago and it just takes way too much time for me to reboot everything all over again I cleaned my CD player as well like most of you guys said before I know my drive is still working as it worked before after I fixed it I checked and the last time this happened was in June Since then the only new things I installed updated were CC Cleaner Itunes and some other programs I have Spybot as well Can someone please please please help me I ve been looking for an answer everywhere and I m running into the same answers Thank you nbsp A:Vaio Windows 7 - Won't read DVD-R Have you tried a a system file check to see if Windows can sort this issue out? sfc /scannow (in admin mode.) Also if you just explore the DVD do you see the list of files on it? Or is the DVD-R not 'seen' by Windows at all? Or is the error only with the autoplay part? (Windows trying to help you choose a media player from whatever you have installed?) http://www.techspot.com/community/topics/vaio-windows-7-wont-read-dvd-r.206920/ Relevancy 51.6% Hello It may seem like a simple problem but I know nothing of the subject and I ve had the problem for ages Whenever I copy large files Movie size think MB the copy progresses very remaining" drives "5 sec Copying to/from stuck before for flash on 30 finishing seconds fast MB s until it reaches about where it gets stuck for about seconds to a minute and it says quot Time remaining seconds quot during all that time I have this problem with any flash drive in any USB port amp It also happens when copying to network drives and external harddrives which leads me to think it s a software windows issue Some vital information Copying to/from flash drives stuck on "5 seconds remaining" for 30 sec before finishing The flash drive I mainly use is USB quite new and easily capable of MB s writing speeds It reaches about - MB s during the copy until the final point where it still says MB s but does nothing for seconds USB port is also and I ve also tried every single other port in my computer None are broken and none ever show any signs of being slow The flash drive is NTFS formatted but it used to be FAT I ran checkdisk to see if there was anything wrong but there wasn t It s NTFS since I occasionally need files gt GB I tried using TeraCopy to bypass the issue but this way doesn t reach speeds of over MB s which takes even longer in the end It does fix the hanging at issue I tried converting the drive back to FAT which removes the issue of it hanging at but again the speed doesn t go above MB s which means it takes longer in the end making it not worth it What bothers me is that the files transfer at the maximum speed right until the very end where it just magically gets stuck for seconds or more before finishing like nothing happened Please advise P S I shamefully have to admit I never safely remove my hardware nbsp A:Copying to/from flash drives stuck on "5 seconds remaining" for 30 sec before finishing Marty9231 said: Hello! It may seem like a simple problem, but I know nothing of the subject and I've had the problem for ages. Whenever I copy large files (Movie size, think 700MB+), the copy progresses very fast (~100MB/s) until it reaches about 99% where it gets stuck for about 30 seconds to a minute, and it says "Time remaining: 5 seconds" during all that time. I have this problem with any flash drive, in any USB port (2 & 3). It also happens when copying to network drives and external harddrives, which leads me to think it's a software/windows issue. Some vital information: The flash drive I mainly use is USB 3.0, quite new and easily capable of ~150MB/s writing speeds. It reaches about 120-130 MB/s during the copy until the final point where it still says 130 MB/s but does nothing for 30 seconds. USB port is also 3.0, and I've also tried every single other port in my computer. None are broken, and none ever show any signs of being slow. The flash drive is NTFS formatted, but it used to be FAT32. I ran checkdisk to see if there was anything wrong, but there wasn't. It's NTFS since I occasionally need files >4GB. I tried using TeraCopy to bypass the issue, but this way doesn't reach speeds of over 20MB/s which takes even longer in the end. It does fix the 'hanging at 99% issue'. I tried converting the drive back to FAT32, which removes the issue of it hanging at 99%, but again the speed doesn't go above 20MB/s which means it takes longer in the end, making it not worth it. What bothers me is that the files transfer at the maximum speed right until the very end, where it just magically gets stuck for 30 seconds or more, before finishing like nothing happened. Please advise!! P.S.: I shamefully have to admit I never safely remove my hardware. Click to expand... Although I've had the same happen on my downloads, this "P.S.: I shamefully have to admit I never safely remove my hardware." could be part of the problem, good luck. http://www.techspot.com/community/topics/copying-to-from-flash-drives-stuck-on-5-seconds-remaining-for-30-sec-before-finishing.207001/ Relevancy 22.36% Hi all Apologies in advance for such a long post I headaches + installation = hardware New Win7 don t know if I just have a corrupt New hardware + Win7 installation = headaches Windows Ultimate installation or what but this all started three weeks ago or so after installing new hardware specifically New hardware + Win7 installation = headaches motherboard Asus A M-A New hardware + Win7 installation = headaches processor AMD A K and RAM Kingston HyperX GB DDR Since I had the extra RAM slot I also put in one of the Aeneon XTune GB DDR I have from before the upgrade The sticker on it says it s but it shows up in BIOS POST as Since then I ve had the following problems Internet Unable to establish any connection at all when using the ethernet cable plugged into my Cisco Linksys EA Router I can connect wirelessly but that connection is lousy and I m not sure why especially since the router is only about feet from the computer To be fair the lousy wireless connection is something I was dealing with since before the hardware upgrade Windows reinstall which is why I finally gave up and bought a ethernet cable the computer used to be in a different room though on the same floor of the house The problem with being unable to get any type of connection when plugged in started after reinstalling Windows and then doing something like updates and then moving the PC to the new spot I made a point of moving the tower myself just so that I could be sure nothing happened to it so I know there was no physical damage done because of dropping or otherwise banging it around at all I ve checked the ethernet cable that runs from the modem to the router as well as the one and neither of them appear to be damaged at all I ve also tried plugging the one into all of the ports on the back of the router in the event that one of them just bit the dust somehow but nothing changed Any thoughts on how I can either get my wired connection working again or what might be making the wireless connection so horrible For clarification on quot horrible quot I m not talking dial-up speeds but some sites either load slowly or not at all sites that load up just fine on every other device in the house - specifically cell phones and iPod an Xbox a Wii and a laptop My connection to Battle net for playing WoW Starcraft II Diablo III is also pretty lag-tastic My NIC is an onboard Realtek GR PCIe Gigabit LAN controller according to the motherboard manual In terms of anything that may be interfering with the wireless signal there s a metal support post and a metal I-beam a few feet from where the router currently sits though it was previously or so feet from both Other than being in close proximity to those the room is wide open I was told that water can interfere with a wireless signal and we do have a lot of ground water under around the house can anyone verify whether ground water can degrade the signal so much over such a relatively small space Hard drive partition issues Until the upgrade when the computer just wouldn t boot presumably because Windows couldn t handle dealing with such big hardware changes all at once I had Windows installed on a partition on a TB Western Digital drive Since I had to reinstall anyway I installed Windows to a partition on a smaller but faster TB Seagate drive Up until this afternoon when I installed Seagate Discwizard one of the partitions on the big drive was inaccessible showing up in disk management and a couple of rd-party hard drive utility partitioning programs as simply quot unallocated space quot Since this afternoon though that partition is now showing up as a completely separate hard drive in disk management AND as quot unallocated space quot on the drive it s actually a part of I m a little leery of just leaving things as they are and using that partition since it s showing up different ways Discwizard only shows that partition as a separate drive there is no quot unallocated space quot showing on the TB drive Is this something I sh... Read more A:New hardware + Win7 installation = headaches Update: Wired connection issue is fixed. I have to (sheepishly) admit that I completely forgot to install the router via the CD that came with it. The lousy wireless performance is still a problem, though, as well as the hard drive/partition issues. http://www.techspot.com/community/topics/new-hardware-win7-installation-headaches.206345/ Relevancy 13.33% Printer Problems in Windows XP sp3 Dell Personal Printer all in one A940 After trying to speed up an older computer running Windows XP I may have cut off the Print Spooler (or it was already off ?) I went back to Services dialog box & selected Print Spooler I clicked the "Start" link at left of service list & got a message tgat said "could not start print spooler service on local computer error 1068 The dependency service or group failed to start." Printer is still not working can anyone help? A:Could not start print spooler service on local computer error 1068 On Win/7 the dependencies are HTTP Remote Procedure Call (RPC) DCOM Server Process Launcher RPC Endpoint Mapper Manually start each on and set to AUTOSTART as you go. If one fails, then that is the root problem. http://www.techspot.com/community/topics/could-not-start-print-spooler-service-on-local-computer-error-1068.206839/ Relevancy 22.36% Hi, if anyone can help ill be really thankful. pc 1, 2 runnging win7 ultimate x64 1 adsl modem, 1 tp-link router, 2 computers (pc1, pc2). ADSL(modem) - LAN1 - PC1 , LAN2 - Tp-link Tp-link - LAN1 - PC2, WAN - ADSL(modem) Everything is working, but computers cant see each other in HomeGroup. Tried various methods but nothing work. So my question is how to set HomeGroup for those 2 computers. Any suggestions? Thank you A:Win7 Homegroup problem @Moirax . I can't answer your question, but your mention of Homegroup makes me ask what is it for? To avoid hijacking this thread,I'll PM you. http://www.techspot.com/community/topics/win7-homegroup-problem.206524/ Relevancy 51.6% Please help.. Can't connect to the wifi but using ethernet is working fine.. My phone could connect to the same wifi though tried to backread some of the threads but didn't work on my laptop A:Cannot "fully" connect to wifi but works fine on ethernet Additional info. I am using Atheros AR5006EXS Wireless Network Adapter and I did deleted the driver and it installed again automatically, but sadly it still doesn't work http://www.techspot.com/community/topics/cannot-fully-connect-to-wifi-but-works-fine-on-ethernet.206650/ Relevancy 50.74% I've been having an issue which started this morning. The previous night, I forgot to plug in my Dell Inspiron N5050 after using it. I woke up to find that my battery had died (obviously). I plugged in the laptop, running Windows 7 HE 64 bit, and turned it on. It booted normally and I was able to do all of my tasks as needed. Then I noticed my problem. The battery icon down on the taskbar showed that the device was plugged in, but was not charging. It has stayed at a constant 2% charge for more than 24 hours now. The Battery Meter stated that my battery is performing normally, so I ruled the battery out as the cause. The adapter I am using is the default one that came with the laptop when I bought it, and it appears to be functioning normally as well. What could be the cause of this incident, and what can I do to fix it? A:Battery Stated as "Plugged in, Not Charging" Most likely you have a bad battery. Dell has had whole series of batteries that they shipped out in a not fully functional state. I have an HP laptop (about 8 years old now) that the battery took a "steamy one" and it will no longer charge properly. You can try this trick (it may not work, but worth a try because did work for me a couple times): power down laptop and take the battery out for 30 minutes; replace battery and plug in charger but do not power on; wait 4 hours of charge and power on. I had it work a couple times that it gave a full 100% charge. Again, if it doesn't work then sorry, but at least you tried. http://www.techspot.com/community/topics/battery-stated-as-plugged-in-not-charging.203683/ Relevancy 20.21% Hi, So I have noticed my pc would shut off randomly and its because the 24 volt connector wasn't in all the way so when the pc would move slightly the connector would disconnect itself. When I go to push the 24 volt in all the way it wont clip onto the clip on the motherboard. It will stay in but it wont fully go in and I can easily just pull it out or it will just fall out from movement. Any ideas how to fix this? Motherboard- http://www.newegg.com/Product/Product.aspx?Item=N82E16813130741 PSU- http://www.newegg.com/Product/Product.aspx?Item=N82E16817139026 A:24 Volt connector wont fully connect to Motherboard I think it is not 24 volts. it is a 24-pin(also labelled as 20+4pin) , 12volts main power connector. the slots are designed so that the power connector will slide into the slot to form like a 'lock and key'. to remove it. see to it that the power connector is inserted in the right direction as shown in the pics (towards the side): edit, any moderator: please delete this post. (my second post to this thread is more 'presentable') http://www.techspot.com/community/topics/24-volt-connector-wont-fully-connect-to-motherboard.206189/ Relevancy 21.07% My new build wont power on all I hear is a few high pitch sounds coming from what I think is the psu. My specs: SSD 128GB SAMSUNG 850 Pro 1TB HDD (from previous build it was working fine 2 days ago) 2TB HDD(from previous build it was working fine 2 days ago) GPU = GTX 680 2GB (from previous build it was working fine 2 days ago) MSI GTX 970 GAMING 4G GeForce GTX 970 4GB 256-Bit on it's way in the mail. Case is pretty old and doesnt have a lid but it was working fine with my pervious buid) PSU = CORSAIR Enthusiast Series TX750 V2 750W ATX12V v2.31/ EPS12V v2.92 80 PLUS BRONZE Certified Active PFC High Performance Power Supply (from previous build it was working fine 2 days ago) Heatsink = Scythe Ashura Universal Processor Cooler CPU = Intel Core i7-4790K Haswell Refresh Quad-Core 4.0GHz Motherboard = MSI Z97-Gaming 7 Intel Z97 Motherboard Memory = CORSAIR Vengeance 16GB (2 x 8GB) 240-Pin DDR3 SDRAM DDR3 1600 (PC3 12800) Desktop Memory Please help me A:New build wont power on Disconnect everything except the monitor, cpu, ram. In fact, go down to 1 stick of ram. Will it POST now? http://www.techspot.com/community/topics/new-build-wont-power-on.206021/ Relevancy 49.88% I used RV042 10/100 4-Port VPN Router. I've configured the dual WAN, and enable Load Balancing for faster internet. But if I accessedhttp://ipchicken.com/ my IP Address is always chaging? How can I setup the router sticking to just one IP address? A:How to "Load Balance" without changing the IP? Let me preface by saying....taking two circuits and using them at the same time, even with protocol management from the LB is most likely not worth the effort. But for the sake of the argument, the first hurdle you have is that both circuits need to have static IPs. What type of connections are they? http://www.techspot.com/community/topics/how-to-load-balance-without-changing-the-ip.205897/ Relevancy 21.07% Hi guys im new in the forum don t ON PC wont stay know PC wont stay ON if I can start threading right away but here goes My setup k stock ASROCK Z pro x gb of gskill ripjaw HX WD Black gb PC wont stay ON SG gb Shappire My problem started quite a while ago with another motherboard one day I started my PC and it just wouldn t boot it ran for about - sec and then it would shut off infinite loop So PC wont stay ON at the time I just swapped my HX psu for a temporary w one and it was all ok apart from having to take the gpu out since this psu wouldn t handle it Then that motherboard burned and I swapped it for a brand new one z pro At the same time as I got the new board I went to a electronic repair shop with my HX psu since I was sure it was broke And a week later they call me to go get it back and the guy tells me shes in perfect condition which was very awkward since ive been messing around with computers for years and I usually dont make this sorta stupid mistake I thought well maybe it was the previous board Even if she did work with the w PSU it didnt really make any sense but I thought wtv lets give it a try anyway Got home got it running and voila works perfectly For TWO days After those two days with a new board and the rest of the same components the PC went back to the same simptoms it would power on and off for seconds and loop and loop Again I switched to the old w psu and it works perfectly Went back to the store they tested it and swap some internal components just to keep it safe and deliver it to me saying it ran for days without a hiccup with HDDs and a bunch of different OS s If that even mattered So I got back home tested it and hurray its finally over its running perfectly and im playing a bunch of games without any problems But its been two days Wont boot LOOP LOOP Same old story HX wont work and im back to the w psu Any ideas Im out of options this makes sense Thanks in advance nbsp A:PC wont stay ON I would rather think the PSU is bad. Your best bet would be to invest in a new one. This more or less would save time and the problems you are having. Plus the expense of repair a PSU that keeps failing. http://www.techspot.com/community/topics/pc-wont-stay-on.205436/ Relevancy 20.64% Laptop wont load bios or OS Interesting wont load Laptop bios OS or issue here When I press the power button the HD activity led light comes on for just a second I feel the HD spinning up and running the fan kicks in and runs then nothing No Laptop wont load bios or OS leds flahing just power led no beeps no screen and no bios I v discharged static build up battery out power button held down quot and tried both mains amp battery to no effect There were no precursors to this issue So I can deduce the laptop is unable to complete POST in pre bios despite the lack of beeps yet can supply power to fan amp HD Now the GPU is Laptop wont load bios or OS GForce m GS aware of the issues with the xxx series I v kept the air flow clean and use a laptop cooler Possible suspect though it never ran hot and all worked fine till I turned on a couple of Laptop wont load bios or OS days ago Now I understood that a failure of the xxx series usually presented a degraded screen lines etc rather than failing post I m backed up and use my second laptop so nothing urgent just a oportunity to learn I am interested in hearing from hardware geeks and their thoughts nbsp A:Laptop wont load bios or OS Seem to have been redirected here for some unknown reason !! http://www.techspot.com/community/topics/laptop-wont-load-bios-or-os.205327/ Relevancy 25.37% Not sure if you cover this, but I have a Motorola Surfboard SBG6580, but am not sure how to open up the ports. I have searched all over the web for advice on this, but no one seems to have a screenshot that looks like mine. My problem is, that my brother and I play the game together, so when I go in to open the ports do I start with hims IP address, since the ending number is lower than mine, and then how far out should I go.I'm including a screenshot, so you will see what I mean. Also, it asks for an external ip address. I have mine, haven't gotten his, but if they're different, how do I adjust for his. Or do I have to open the same ports for both machines? My Cisco router was not this complicated, but the surfboard is our router and modem and takes up less space.If anyone understands what I'm trying to do, please answer back. When we're online on the game together, we lag terribly. We can play separate games online without a hitch. A:Port Forwarding The typical problem is the PUBLIC ip-addresses for you/bro can change overnite. what you see with IPCONFIG is your local lan address, not the PUBLIC address given to your router by the ISP http://www.techspot.com/community/topics/port-forwarding.205317/ Relevancy 20.64% My internet wont work, ive tried using both crome and IE but both browsers say that I am not connected to the internet despite the fact my computer says that I am connected to the internet. I know its not a network problem because my other devices are connecting fine. Also I tried connecting to the wifi at home and at school and it still does not work. My laptop is a HP ProBook 6390b and I am using windows 7. This problem started occurring after about 4 months disuse of my laptop which I think might be a factor as to why its not working. I have run windows updater and run a scan with my antivirus but still nothing helps. Thank you for any assistance in advance. A:Internet wont work on laptop Have you kept up and installed all the Windows 7 updates and are there any yellow (!) in the device manager? http://www.techspot.com/community/topics/internet-wont-work-on-laptop.204944/ Relevancy 20.21% Hi can any one help I cant hear any sound on my laptop its all turned up but when I conect it to my tv the volumes fine but soon as I disconnet from the tv the sound ont go. A:Audio wont work on asus x53u laptop Did you fix this? http://www.techspot.com/community/topics/audio-wont-work-on-asus-x53u-laptop.204577/ Relevancy 24.51% Hey, I don't know what read means. I transferred some file to and from a USB 3 thumb drive. Files transferred much faster from the thumb drive to a hard disk. Looking at the image it seems that read means transfer to the hard drive but that doesn't make sense to me because in my thought process the thumb drive isn't reading it's writing to hard drive. Could someone explain to me what I am failing to understand? Thanks A:Diskmark read/write The data (on the thumb drive) has to be read by the OS. The OS is writing what it read from the thumb drive to the hard drive. http://www.techspot.com/community/topics/diskmark-read-write.205029/ Relevancy 13.76% Hi, I am having a problem with my DVD hardware. Every time I put a disc in and open it in Explorer I get I a popup asking me to burn a disc (image file attached). I've tried going through all kinds of settings but nothing works. I am running Windows 8.1. Any help would be appreciated. Thanks, Verity A:Burn Disc Error That's autoplay setting for blank disk media. http://www.techspot.com/community/topics/burn-disc-error.205054/ Relevancy 34.83% Dell is releasing a new 5K monitor in Q4 this year. That's your ideal 2560 x 1440 quadrupled for retina effect, while keeping the perfect proportions, with the software that supports it that is, for the total of 5120 x 2880 madness. A:Dell 27" 5K Monitor VitalyT said: Dell is releasing a new 5K monitor in Q4 this year. That's your ideal 2560 x 1440 quadrupled for retina effect, while keeping the perfect proportions, with the software that supports it that is, for the total of 5120 x 2880 madness.Click to expand... And I thought 4K was crazy high resolution already xD. http://www.techspot.com/community/topics/dell-27-5k-monitor.205015/ Relevancy 13.76% I decided to upgrade my old hard drive to a new hard drive. When I tried to install Windows Xp on the hard drive it wouldn't let me. I have a Dell Xps 400 bought back in 2006. The new HD is a WE 1tb. The error codes comes when I try to install windows xp on the hd. It says I got a blue screen error after clicking enter at the screen where there is no partition found: Check to be sure you have adequate diskspace. If a driver is identified in the stop message, disable the driver or check with manufacturer for driver updates. Try changing video adaptors. Check with your hardware vendor for any bios updates. Disable bios memory options such as caching or shadowing. If you need to use safe mode to remove or disable components. Restart your computer, press f8 to select advanced startup options, and select safe mode. Technical information: Stop:0x0000008E (0X0000005, 0XF7419CAD, 0XF6FF17E4, 0X00000000) Setupdd.sys ? address f7419cad base at F73ED000, datastamp 48025277 http://www.techspot.com/community/topics/error-on-trying-to-install-new-sata-hd.204857/ Relevancy 13.76% Hello all, Windows 7 doesn't recognize my SSD drive. When I go to disk management, it shows a message to initialize it (image no.1) but when I press OK to do that, one another message appears and says: Data error cyclic redundancy check (image no.2). My computer windows doesn't show that drive and also when I went to cmd->diskpart, again it didn't show that disk to use of chkdsk /f command. How to solve the problem please? A:Data error cyclic redundancy check ssd I could to revive that disk in diskpart using PartedMagic in boot. I've uploaded a new image from that. The remained problem here is that I can't delete it there. http://www.techspot.com/community/topics/data-error-cyclic-redundancy-check-ssd.204783/ Relevancy 48.16% Hi, when I typed " dxdiag " it said n/a, last time I checked there was something written in it.. A:When I typed " dxdiag " it said n/a Check your graphics drivers and install the latest one. http://www.techspot.com/community/topics/when-i-typed-dxdiag-it-said-n-a.204746/ Relevancy 13.76% I am running Windows 8.1. After restarts, the laptop screen would be blank, yet the computer would load. If I hooked up a 2nd monitor, it would show the desktop on that screen but laptop screen blank. Now when I try to type on that computer (I'm currently on a different computer) the typing of the keys is all off (none of the letters actually type what they are supposed to and some open up random windows and command prompts) I am wondering if this is a virus. Currently running Malwarebytes. I did a system restore earlier and the problem wasn't solved. A:Blank Screen error and typing issues Could be a virus, but could also mean the motherboard is faulty. If still in warranty, RTM. Does the laptop have a bootable CD reader? If so, then download and make a bootdisk of a small linux (e.g. puppy linux). Booting off that will virtually prove if the motherboard is faulty or not. http://www.techspot.com/community/topics/blank-screen-error-and-typing-issues.204596/ Relevancy 20.64% As the title states I cant seem to get my monitor to turn on when I put ram in slots 3-4.. I currently have 2x2gb ram installed and im trying to install 2x1gb more(in slots 3-4) both sets are matching pairs Any suggestions? CPU: amd phenom ii x4 GPU: Radeon hd 7700 MOBO: Gigabyte M720-US3 64 bit* A:Monitor wont turn on with ram in slots 3-4 What's the timings, frequency, and voltage on the RAM sets? Also confirming, that you are putting them into matching ram slots? 3-4 tells me nothing and can be misunderstood anyway. http://www.techspot.com/community/topics/monitor-wont-turn-on-with-ram-in-slots-3-4.204476/ Relevancy 20.64% So my laptop will not connect to the internet only by the ethernet cable. Ive made sure my wifi is on but for some reason everytime I click troubleshooting it will only tell me to try to connect to the ethernet cable. I tried to find different interney connection or try to disconnect to my router but that option does not even show up. Ive gone through device manager n unstall things like the newtwork adapter of course after I restrted the computer itll reinstall it. Ive tried the options of restarting the router try to turn off the wifi restarting a an d reconnecting. Please help!! Lol A:My laptop wont connect to the internet I have a laptop and use wired connection when at home. Laptops typically have an enable/disable key or switch for the wifi - - on my Dell, <fn>F2 toggles wifi on/off. I normally run with it off and the device manager looks like this EVEN when F2 has it disabled! Notice, no red/yellow flags because it's just fine. The system tray (for a wired connection) looks like and IF I enable wifi, it changes to *** SO BE SURE your wifi is 'enabled' (that is not the same as the device mgr enbled) http://www.techspot.com/community/topics/my-laptop-wont-connect-to-the-internet.204212/ Relevancy 24.51% Hello to all I m going to install Win XP properly port The ps/2 of doesn't work the motherboard on my computer I had win but had some problem with installing the HP printer on it and so I decide to install XP because that printer seems to be installed properly The ps/2 port of the motherboard doesn't work properly on XP Now When I put the XP CD on the CD driver it says press a ker to boot from CD and I press the Enter key now the keyboard works after that within installation time when that I should press Enter to install XP this time the keyboard doesn t work My guess is that the ps port of the case has problem it s old and somewhat has been broad Now what is the solution in your point of The ps/2 port of the motherboard doesn't work properly view please My system manufacturer is quot ECS quot and the system model is quot pl-A quot PS there are two black amp white screens which mobo shows First screen shows the amount of RAM the model of CPU the IDEs and info like these which is common for first screen But the here when I want to enter to BIOS by pressing Del key it seems that keyboard doesn t work so it doesn t go to bios The second black amp white screen shows fewer info and it says quot Press shift-F to configure and when I press these two I can to enter to an environment that seems to not be the BIOS the keyboard here WORKS It has very few options And apparently doesn t have options of manipulating the keyboard settings nbsp A:The ps/2 port of the motherboard doesn't work properly No idea!!? http://www.techspot.com/community/topics/the-ps-2-port-of-the-motherboard-doesnt-work-properly.204104/ Relevancy 34.83% My sister's 13" MBP (2011) died a few hours ago. According to what she told me, she was using it, and then, poof, black screen and no power. She doesn't have the cash at the moment to have it properly checked by a tech, so I did a basic troubleshoot in an attempt to narrow things down. While the internals are a bit dirty, I didn't see any obvious signs of physical damage (it was relevant to check for this). Furthermore, the machine doesn't seem to respond to any power sources. I tried a couple different power cables and, while the little amber light on the magsafe (sp?) tab will come on briefly, the computer with neither power on nor display a charge on the built-in charge indicator. I will also note that the machine failed while disconnected from an outlet source with a full battery indicated. My initial conclusions are a) the computer fried itself or b) the battery is toast. Any suggestions? A:2011 MBP 13" Won't Power Up If no one here can offer any insight, I would post this to the Apple discussion forum. There are usually people there that can diagnose this from just a description so that is your best bet. http://www.techspot.com/community/topics/2011-mbp-13-wont-power-up.204013/ Relevancy 25.37% A recent power outage has caused some of my hardware to function oddly... My tv's hdmi ports seem to still work for say a ps3, but when hooking up to my gtx 760 I get "No Signal"? I only have one hdmi port but several other dvi ports. My smaller monitor(plugged into dvi port 1) is functioning normally. It also seems the gpu is still functioning because I booted Dota 2 just fine with 60fps(vsync). Could this outage have fried the hdmi port? Should I be worried, should I return it or just buckle down with 2 dvi connectors? I was gonna test out hdmi to dvi cables to test my theory but am unsure what to do otherwise. MSI TF/OC 760 TV:NS-39L240A13 A:Faulty HDMI port? Did the pc->tv work before the outage and did the pc suffer immediate power off too? http://www.techspot.com/community/topics/faulty-hdmi-port.203802/ Relevancy 34.4% I'm wondering whether I can overclock my ASUS R500VD notebook it has an INTEL sandy bridge core I5 3210M 2.50 GHz processor 4GB (max 8) of ram running puppy linux and windows xp home edition SP2 32 bit I have benchmarked it and ill email the results to anyone who replys and gives me their email and if you're wondering why I'm running windows xp read my article in the Alternative OS section of the forums called "If all else is too hard try puppy linux" bye A:Can I overclock my asus notebook 17" Nope sorry, the I5 3210M isn't OC enabled. http://www.techspot.com/community/topics/can-i-overclock-my-asus-notebook-17.202019/ Relevancy 34.83% Hi all, I have an Acer Aspire Z5610 AIO computer.When I first bought it a few years back the @ and " were transposed.Hit the @ and " would come up and vice versa.At the time I contacted someone (can't remember who) and with their advice I was able to correct the problem.Due to age the PC was running v.slowly,painfully so.I decide to revert back to Factory default settings,unwisely it turns out,but the old problem of @ and " transposition is back.Has anyone out there got a solution to this problem.It is fixable as I have done it before,but how !!! Thanks in advance, Frank. A:Keyboard @ and" are transposed It's not really a problem particularly as you know which keys to press to get @ or ". This is one of the few differences between UK and US keyboard layouts. You can change the English language version from one of the options in Control Panel. http://www.techspot.com/community/topics/keyboard-and-are-transposed.203000/ Relevancy 24.51% I have tried to fix a mates sony vaio's hdd issue. Re installed windows, and it boots fine from my pc. When I put it back into the laptop it doesn't boot. gives a blue screen with some writing on for a split second, then nothing - black screen.... Any ideas? A:HDD will read in desktop but not laptop Are both the same version of Windows? Win/7 & 8 don't like XP or Vista boot environments http://www.techspot.com/community/topics/hdd-will-read-in-desktop-but-not-laptop.203466/ Relevancy 22.79% I finally bit the bullet and upgraded yesterday Before installing the new OS I installed g of ram gb sticks Got thru all the installation BS my goodness Microsoft eats up a from Upgraded XP to Win7 lot to memory with all those updates Any way I was checking out the specs on my systems on the My Computer page and it only shows that I have g of Ram The other problem is I have a gb but it s only showing that I have gb total I know you want my system info so I ll do Upgraded from XP to Win7 the best I can AMD Athlon tm X Dual Core Processor Ghz bit I m going to check out my memory sticks Maybe one of them isn t seated properly I have them side by side as it was shown in my MB book but was wondering if I should skip a slot Also is there something I need to do about my drivers I m really worried about my HD space I know before the guy who built my system had a partition put in That got wiped out when I tried to to a repair on my Windows XP and had to do a clean install When I got the system back up and running it showed all my HD space now I m barely showing a third of the space that should be there I m really at a lost nbsp A:Upgraded from XP to Win7 Well since no one is answering, I'll get you up to date. I found my lost HD memory and got it all back, so I'm at full capacity there. As for my sticks of RAM, I just don't know. I removed one, but the system wouldn't boot. Then I put the other one in and the system still wouldn't boot. So I put them both back in and the system booted right up. I'm getting the feeling that I bought 2 2gb or ram and ended up with 2 1gb sticks. Also, I thought the system was suppose to recognize when you put new ram in. Mine didn't. http://www.techspot.com/community/topics/upgraded-from-xp-to-win7.203160/ Relevancy 24.51% I have downloaded movies from online, then burned them onto a dvd or cd. I can play them back from the disc on my computer but when I load them into my CD/DVD Player to watch them on the TV...it says "Can Not Read Disc" or it just says "Disc Empty". What am I doing wrong? A:DVD Player can not read DVD or CD The disk will likely need to be in DVD format before your DVD Player will play it. Are you using a media builder application to burn the disk? You can't simply burn MP4/AVI to disk and have them play. Only players that have been optimized for them will play them. And speaking from experience, even when burning the correct format, the burns may give issues reading in the player. One player may recognize the disk while another will not. http://www.techspot.com/community/topics/dvd-player-can-not-read-dvd-or-cd.203348/ Relevancy 20.21% So I have windows 7 installed on my pc ..... I cant hear any sound from my headphones or speakers whether plugged into the front or rear panel. and also windows shows that there are headphones plugged into the front panel. maybe that's the reason I cant hear any sound....but I tried all possible ways....also disconnected the front panel from the motherboard but still it says its connected. A:Front audio jack panel wont disconnect in any way Have you checked out the Sound section in Control Panel. Also check Device Manager. http://www.techspot.com/community/topics/front-audio-jack-panel-wont-disconnect-in-any-way.202869/ Relevancy 20.64% I built a gaming PC and it wont connect to the monitor. Also the keyboard and mouse won't turn on. My graphics card is a NVIDIA Geforce GTX 700 A:Built own computer, but it wont connect to monitor Could you please provide the specs for your build? Need to list the exact parts you used, including make and model. It makes things easier to help with diagnosing your issue or issues. http://www.techspot.com/community/topics/built-own-computer-but-it-wont-connect-to-monitor.203102/ Relevancy 20.21% when i start my computer, it goes to the gateway start page, and after a while (it's quite slow) it goes to the black page, and this is what it says: Intel Boot Agent FE v4.1.10 Copyright (C) 1997-2003 Intel Corporation Intel Boot AGent PXE Base Code (BA 1210BC-GW1) Copyright (C) 1997-2003 Intel Corporation PXE-E61 media test failure check cable PXE-M0F exiting Intel Boot Agent Reboot and select proper boot device or insert boot media in selected boot device. it just stays on that screen until i do a CTRL ALT DEL, then it goes back to the Gareway screen and after about 30 seconds finally boots up and i get the Windows XP start up page, and it opens up my desktop and i can continue . Can anyone tell me why this started happening and how to correct it? A:Computer start up is bringing up boot agent message How old is the computer, or the hard drive. It appears you have a failed or failing hard drive. http://www.techspot.com/community/topics/computer-start-up-is-bringing-up-boot-agent-message.150663/ Relevancy 36.98% My laptop had headphones plugged in because I was watching a film but while I was in another room my laptop was knocked onto the floor around - ft drop change mic to a HD audio headphones Realtek port? port a manager, landing on the headphones jack the wire is fine but the ports completely broken I can see cracks and its loose and everything The laptop has Realtek HD audio manager and in my experience of this program on other desktops I ve had I was able to change Realtek HD audio manager, change a mic port to a headphones port? what port does what My laptop only has a headphones port and Realtek HD audio manager, change a mic port to a headphones port? a mic port and I would like to see if I can switch the mic port to be the headphones port because I never use an external mic however in Realteks audio manager I can t find out how to do this In pictures I ve seen on the internet there is a quot Device Advanced Settings quot button as seen in this picture http www vistax com attachments ealtek-hd-audio-driver-version-hd manager jpg but my program doesn t have this Do I need to download a newer version of the software or is it just not possible to change my mic port to be my headphone port I dont mind if I have to use third party software I just want it to tide me over till I can get it sent away Thanks for suggestions greatly appretiated nbsp A:Realtek HD audio manager, change a mic port to a headphones port? I doubt very much if this will be possible. The mic and headphone ports are wired directly to the Audio section of the motherboard, there connections cannot be altered. Your best bet is to get the damaged port repaired. http://www.techspot.com/community/topics/realtek-hd-audio-manager-change-a-mic-port-to-a-headphones-port.166497/ Relevancy 23.22% Hello all!!!! My name is John. I am trying to find some help with an issue that arose after I installed a new hard drive in my computer. I started getting a message that stated: C:\Users\Owner\App Data\Local\Conduit\API Support\API Support.dll Anyone know how I can repair this? I saved an image of my system before installing the new hard drive and then just downloaded the image to the new hard drive. HELP!!! please!! A:Installed new hard drive You might just need to run some registry cleaners to fix and remove those corrupt registry keys. http://www.techspot.com/community/topics/installed-new-hard-drive.201991/ Relevancy 63.64% Hi I have an older PC which I gave to my mum It originally ran Vista but I bought and installed Windows Ultimate around weeks ago after it had been inactive for months It was running great but a couple of weeks ago it just started hanging for no real reason Also at startup it would say that the computer had not been shut down properly even if it had This was only when it was switched off at the wall not after checksum defaults loaded" replaced error battery after - "cmos a restart or when the PC was left plugged in and switched on She only "cmos checksum error - defaults loaded" after battery replaced uses the PC to look at You Tube and some webcams from her grandkids and that s it she s not very computer literate Initially I left Windows repair to run overnight but when I looked at it the following morning it was still in the repair screen so I assume it had hung I spoke to a local repair shop and they suggested I test the RAM test the hard drive and replace the CMOS battery The RAM and hard drive checks went without any errors and after I replaced the battery the hanging stopped I played with the computer all evening and shut it down as normal and switched it off at the wall Next day I thought I would start it up just to check it and I was faced with a quot cmos checksum error - defaults loaded quot message I thought that was strange but maybe the battery was dead so I swapped it over with one from my perfectly working desktop to try it out and my desktop worked fine but after shutting down my mum s one it had the same problem when power was pulled So battery was ruled out Incidentally I will say that I reset the BIOS date and time every time I was faced with the error following up with a save and exit It worked fine until I unplugged the computer I then moved on to the BIOS and set it back to default and the same again After this opened the case and used the jumpers to reset the BIOS to default again but no difference My mum will not leave it switched on at the wall constantly in case it self-combusts same with her washing machine TV lamps etc otherwise I would just do that and ignore it Is there anything else someone can suggest that I try System Shop bought by Mesh Motherboard is an ASUS PSN-E SLI gb Ram - samsung gb hard drive - ASUS Thanks for any help nbsp A:"cmos checksum error - defaults loaded" after battery replaced I must add that the PC is the same as when I bought it new from the shop, except for adding a Creative Labs sound card (approx 2012) and installing Windows 7 (around 6 weeks ago). All Windows updates are downloaded and installed. http://www.techspot.com/community/topics/cmos-checksum-error-defaults-loaded-after-battery-replaced.201304/ Relevancy 20.64% My laptop does not identify my home wifi... while my phone, Ipad and work laptop all identify and connect. it identifies very rarely and this started about a few weeks ago.. this same laptop identifies other wifis but not my home WIFI... even while I am next to it.. it connects very easily when I connect a ethernet cable... what could be wrong.. please help Shantanu A:Why wont my laptop connect to my WIFI Specs on your laptop would be a big help. Other than that, is there a switch you need to turn/switch on? How old is this laptop? Give more info so we don't have to play 20 questions. http://www.techspot.com/community/topics/why-wont-my-laptop-connect-to-my-wifi.202025/ Relevancy 24.51% Hi there, I purchased an edifier mh 1370 multimedia speaker a while back it has been working fine. I took it to a mates place for a birthday party and when I brought it back to mine and connected it up, it seems that the right speaker out port does not work.. I've plugged the right speaker into the left port and vice versa and both speakers work so it's definitely not the speakers. I've checked my audio software and properties nothing has changed. I've checked the 3.5mm audio connecting cable. I mean all I did was bring it to a party let it run for about 9hours I think and came back used it and the right speaker port doesn't work Would it be an internal problem? if so how would I fix it? I don't know anything about electronics and I really don't wanna buy a new one trying to be handy here haha.... A:Edifier 2.1 speakers mh 1370 speaker out port problem Plug some headphones or earbuds into the jack to make sure both channels are working. If it sounds okay, your most likely problem is the wires in your speaker system - usually the 3.5 plug or the nearby wire has separated inside the insulation. I would cut the original plug off and solder in a new one from Radio Shack, if you're okay with soldering, or have a repair shop do it if you're not able to. http://www.techspot.com/community/topics/edifier-2-1-speakers-mh-1370-speaker-out-port-problem.202022/ Relevancy 50.74% My dell 1905fp finally crashed after a lot of years. I'm not a gamer, but I was very happy with that monitor. Of course they no longer make it, and I understand refurbished monitors of this type are not necessarily a good option. I can't seem to find reviews or comparisons which point the way to other similar monitors. I'm retired and just can't afford the$600 and way up price of what I've seen so far. I just need a basic monitor with VGA and DVI, but would like the screen performance to be decent, incl for watching movies etc. Any recommendations, and where to get a reasonable price? Again, don't want a wide screen. Thanks much! A:Reasonably priced 19" or 20" monitor, not wide-screen? Nothing wrong with buying refurbs. They may have a few blemishes in the frame but nothing serious to keep them from functioning. I've bought a few myself and have had no issues with them. Although the monitors I bought were 20" widescreens that averaged $120 or less. For what you need/want, I wouldn't spend more than$150. I know you said no widescreen, but movies do view better on widescreen. http://www.amazon.com/Dell-UltraSharp-1905FP-Rotating-Landscape/dp/B00091R6KC - less than \$100 http://www.techspot.com/community/topics/reasonably-priced-19-or-20-monitor-not-wide-screen.201641/ Relevancy 14.19% I recently receive a pop out error message everytime I start up my laptop. Can anyone please advise? Thank you! The error message is below. There was a problem starting C:\Users\XXX\AppData\Roaming\newnext.me\nengine.dll The specified module could not be found http://www.techspot.com/community/topics/rundll-error.201803/ Relevancy 33.11% A:"Logon failure: unknown user name or bad password” even with correct credentials I experienced a similar problem when I was trying to network my 8.1 machine the host network. As you say the host PC can see and connect to all of the machines, but not the other way around. Not sure if it is the same in your situation but I found that Microsoft's idea of network sharing on the Windows 8 class of OS differs greatly from previous OS's in that you can connect to it from an external host, but when trying to do the other way around it doesn't "see" the PC in question due to differing network sharing protocols included in the OS. Anyone feel free to correct me if I am wrong, I am speaking only from what happened with my network. Relevancy 33.97% So newegg is offering the Acer 29" B6 B296CLbmlidprz IPS monitor for about 350. Seems like a pretty good deal but I can't find many reviews on it. I was wondering if anybody had any experience with this monitor and/or if you guys have better options for someone who is looking for an IPS monitor below 400 bucks. I want to game with it as well as do some 3d modeling and photoshop work. So I need reasonable response time for gaming. I was also looking at the HP ZR2440w and was gonna get that until I saw this deal on newegg for a larger monitor. 24" models are fine but if there are good deals on some 27" inch ones then I would be interested in those as well. Any suggestions? Thanks. A:Question on Acer 29" monitor and other monitors Heres the link for that monitor. http://www.newegg.com/Product/Product.aspx?Item=9SIA24G1GC2421 http://www.techspot.com/community/topics/question-on-acer-29-monitor-and-other-monitors.201698/ Relevancy 24.94% I have downloaded a program called Anomos, it tells me please forward your ports so the program can work, 5061. Ok so I go into my century link modem and it wants a ip address to forward the ports what ip address do I enter? A:How do I port forward the Anomos program? The LAN address of the system you want the data to go to. It must always be the same address, so you need to make it so using Address Reservation on the router OR a static address on the target machine (not recommended for laptops). http://www.techspot.com/community/topics/how-do-i-port-forward-the-anomos-program.201628/ Relevancy 14.19% Hello, When I play BF4 I get a direct X error after awhile claiming that it cannot allocate any more memory and that I should use a GPU with at least 512 MB RAM. I have tried to search around but cannot find a solve really. Some people advise to disable the Intel integrated Graphics in the device manager but no one can confirm if it works or not so I am hesitant to try it... I have updated drivers for Dx and the GPU without resolve, also tried reinstalling them. It has not happened for any other games so far but the only game that really demands any memory I play is BF4 ... I will try with Crysis 3 or something similar demanding to see if the error happens there too. A:DirectX error for AMD R9 290 Tri x 4GB Obzoleet said: Hello, When I play BF4 I get a direct X error after awhile claiming that it cannot allocate any more memory and that I should use a GPU with at least 512 MB RAM. I have tried to search around but cannot find a solve really. Some people advise to disable the Intel integrated Graphics in the device manager but no one can confirm if it works or not so I am hesitant to try it... I have updated drivers for Dx and the GPU without resolve, also tried reinstalling them. It has not happened for any other games so far but the only game that really demands any memory I play is BF4 ... I will try with Crysis 3 or something similar demanding to see if the error happens there too. Anyone have any advices?Click to expand... Well in all technicality the game should not be defaulting to the integrated unless you have your monitor hooked up to the on board connectors so I would not worry about that. If its reading as a memory problem in BF4 then it maybe a problem with BF4 drivers. I have not played in a few days on my 290X setup but an update was just downloaded I noticed a day or two ago. Have you tried changing over from directX to Mantle and seeing if that helps or vice versa? Also try the latest Beta 14.2 because it makes things alot more stable than 14.1 was in terms of Mantle at least. See what happens after trying this, the Intel Integrated should not be interfering so I would not worry about that. http://www.techspot.com/community/topics/directx-error-for-amd-r9-290-tri-x-4gb.200757/ Relevancy 13.76% A:NICs not working Windows 7 Error 31, this one is weird "so the problem is related to windows and follows the drive"... Re-install Windows on this drive. Error 31 relates to a bad driver that may be reflected in the device manager http://www.techspot.com/community/topics/nics-not-working-windows-7-error-31-this-one-is-weird.200795/ Relevancy 14.19% The web server in my IIS has the Default web site stopped. When I hit start, I get an error message there was an error while performing this operation. Details: the process cannot accdess the file because it is being used by another process. (Exception from HRESULT: 0X80070020) The site bindings are: ::57772 (http),:443 (https), 808:(net.tcp), (net.pipe), locathost (net.msmq), localhost (msmqformatname) Can anyone point out what is wrong? A:IIS error That error is saying 1) one program (process) as a file open 2) another attempted to modify or delete it A most common case is when a process is running and the current directory is \temp\foo\bar and some process is attempting to delete foo http://www.techspot.com/community/topics/iis-error.200665/ Relevancy 22.36% I bought a Samsung 840 SSD (120GB) for my gigabyte GA-770T-USB3 motherboard. I am unable to install win 7 64bit on it. It is a SATA SSD. I have tried ACHD mode in the BIOS, I have tried IDE mode. The drive works as I have tested it as an external drive on other computers. I bought the drive specifically to be used as a primary drive. My regular hard drives work fine on the motherboard. A:Unable to install SSD on Win7 x64 system Well, first of all, your motherboard only supports 3GB/s and the 840 is a 6GB/s drive. Just by that you won't really get your moneys worth. And how so are you unable to install? Also can you please list your system specs? http://www.techspot.com/community/topics/unable-to-install-ssd-on-win7-x64-system.190141/ Relevancy 25.37% A:Port forwarding not working :( This is EXACLTY what is happening to me and it makes me SO mad. I also need help with this problem. http://www.techspot.com/community/topics/port-forwarding-not-working.182343/ Relevancy 13.76% When I am accessing wifi network I get dns failed error message. what is the problem? pls help A:DNS failed error in WiFi network Can you connect using a wired connection? Get a command prompt and enter ipconfig /all >myTCP.txtthen open that file, copy the contents and paste into your follow-up http://www.techspot.com/community/topics/dns-failed-error-in-wifi-network.200577/ Relevancy 22.36% Hi All Right problem As stated above my laptop does not recognize my external The drive spins up inside the enclosure the power led lights up but it does not show I have been a Field Support Engineer Tier III for many years and following that a Technical Analyst all within the IT field and this one on not hdd recognize Win7 does external Compaq6710b has me totally STUMPED Steps followed Checked Win7 on Compaq6710b does not recognize external hdd Compmgmt - gt DrvMgmt drive does not show same as DevMgmt msc - gt Drvmgmt Went into CMD prompt - gt Diskpart - gt list disk only picks up my primary internal I e disk I have moved the hdd from one USB port to another - still no difference I have tried disconnecting and reconnecting it multiple times - no avail Tried rebooting - no avail Tried rebooting both with without the external connected - no change Connected the external to multiple other machines - it picks up on every single one of them Run RSOP machine is on a domain but there are as confirmed by domain admins no restriction policies in place seeing that my other smaller in capacity flash drives all pick up and show Ran a full malware scan - clean with the following in turn not at the same time also not installed simultaneously MBAM MSSE AVAST ESET - All came back clean Ran CCleaner getting desperate now and after all cleaning and clearing etc sorted rebooted machine - still no change Checked if the drive shows in BIOS upon restart - it does Just to slam dunk point above - checked if the drive shows as a possible boot media upon reboot - it does Only thing left to do is to try any Linux Unix based boot GUIs to see if it shows in thee as wel apps in the line of Knoppix to name but one Oh yeah also accessed the Advanced Properties af all the available USB Root Hubs and ensured that the computer is not allowed to turn off these devices in order to save power I have also downloaded EVERY POSSIBLE LATEST DRIVER from HP s site so everything THERE is up to date all drivers and firmwares up to date Flashed the CMOS Updated the BIOS as well If I connect any of my flash drives or any other mobile device tablet phone usb modem with micro sd card installed configured as storage to the laptop they all get recognized and are accessible but NOT my external even though every single other machine I have connected it to picks it up As per all my points above please do not suggest the following A Use of various or random drive checking tools - they won t work as the O S does not recognize the drive B Right click quot My Computer quot anything starting with that will be a waste as I have already gone through all those steps by means of accessing all relevant interfaces via cmd line interface - I cannot see the drive so I can also NOT change it s drive letter just read another post on another forum where the OP requests assistance as he cannot access his drive at all kind of similar to my scenario and the suggestions on there drove me out the walls - people missing obvious things and making suggestions which would be declared useless by using some common sense I am going to try and upload prt shots of both diskpart cmd result and compmgmt msc results okay failure with bmp jpg and png HA loaded successfully Any assistance would be appreciated Oh yeah it is a USB powered quot external hdd not the quot type which requires external power nbsp A:Win7 on Compaq6710b does not recognize external hdd Have you tried your Ext Hard drive to be connected to any other PC or Laptop. If the drive is still not recognized consult an expert for this. http://www.techspot.com/community/topics/win7-on-compaq6710b-does-not-recognize-external-hdd.200463/ Relevancy 51.17% I just got new SSD - Transcend 128GB. Installed Windows. When I cold boot my PC -- from a shut off state -- I get this message before Windows loads: "Reboot and select proper boot device or insert boot media in selected boot device and press a key." However, if I press Ctrl+Alt+Delete and reboot I come into Windows. If I enter BIOS from cold boot, it does not detect my SSD. After rebooting it detects my SSD. Seems like the SSD is slow at firing up? I have run chkdsk and memory test without any errors. My motherboard is the MSI Z87-G55. A:"Reboot and select proper boot device" Just installed newest BIOS, it didn't help. When I go into Board Explorer in BIOS it says SATA port 1 is empty. After reboot it says the same port is occupied by my SSD. Update: Plugged in another hard drive (non-SSD). Same rules apply to it. On cold boot, none of the drives are detected. After reboot, both drives are detected. I used a non-SSD as system drive before this, worked perfectly. http://www.techspot.com/community/topics/reboot-and-select-proper-boot-device.200351/ Relevancy 25.37% What do you mean the hdmi port from my graphics card? Did you find out that hdmi port was bad? If so how can I replace it. Moderator note: Moved from this thread - http://www.techspot.com/community/topics/tv-is-not-detecting-my-pc-via-hdmi.197533/#post-1382473 You can't. Return the card to retailer/manufacturer for a repair if it's within warranty.	2018-10-20 17:35:21	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.18956886231899261, "perplexity": 3977.0526238555935}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583513009.81/warc/CC-MAIN-20181020163619-20181020185119-00023.warc.gz"}
http://www.askmehelpdesk.com/high-school/verifying-trig-identity-71427.html	# Verifying trig identity! I can't solve this for the life of me and I am sure I will feel like an idiot after seeing the solution. Any help would be greatly appreciated before I pull my hair out over this little problem! Argh! Verify the identity: Sin4x = 8cos"cubed"xsinx - 4cosxsinx If any help, I tried factoring out 4cosxsinx leaving 2cos"squared"x - 1, however I didn't get too far into this before getting stuck.. asterisk_man Posts: 476, Reputation: 175 Full Member #2 Mar 13, 2007, 12:05 PM This one was pretty easy. We're just deriving the "quad angle formula for sin", similar to the double angle formula. I just looked at a table of trig identities: Table of Trigonometric Identities There are 2 important ones there: $\sin\left(2u\right)=2\sin\left(u\right)\cos\left(u \right) \\ \cos\left(2u\right)=2\cos^2\left(u\right)-1 $ So we just use these two to expand the sin(4x) First let u=2x and expand with the double angle sin formula, then substitute the 2x for the you and use both double angle formulas to expand $ U=2x \\ \sin(4x) \\ \text{substitute you for 2x} \\ \sin(2u) \\ \text{apply double angle \sin formula} \\ 2\sin(u)\cos(u) \\ \text{substitute 2x for u} 2\sin(2x)\cos(2x) \\ \text{apply double angle \sin and \cos formulas} \\ 2(2\sin(x)\cos(x))(2\cos^2(x)-1) \\ \text{multiply out the terms} \\ 8\sin(x)\cos^3(x)-4\sin(x)\cos(x) $ This is the same as what you wrote in your question. If you looked at your table of trig identities you should have seen that cos^2(x)-1 was cos(2x) and maybe that would have given you an idea. Ask questions if you have any left. Thanks! minnieirl55 Posts: 1, Reputation: 1 New Member #3 Dec 10, 2008, 07:46 PM How to solve 1+ sin 2x = (sin x + cos x)^2 snowflake317 Posts: 3, Reputation: 5 New Member #4 May 20, 2010, 07:54 AM If we take the Right Side of this equation (sinx + cosx)^2 then we can expand it according to the identity (a+b)^2= a^2 + b^2 +2ab => sin^2x + cos^2x +2sinxcosx According to the basic trigonometry identities , sin^2x + cos^2x=1 and 2sinxcosx=sin2x => 1+sin2x which is equal to the left side of your equation. If you want to solve it using the left side, you just have to go from bottom to top of the solution written above. Unknown008 Posts: 8,147, Reputation: 3745 Uber Member #5 May 20, 2010, 08:21 AM Yes, except that you need to check the date... For the last question, it was 11 Dec 2008... Two years ago Next time, check the date snowflake317 Posts: 3, Reputation: 5 New Member #6 May 20, 2010, 08:41 AM Thanks. . I'll keep that in mind next time :P ## Check out some similar questions! Have a take home quiz that I need to do well on. Having trouble with these: Simplify. + Factor and then simplify. (sec^2x-1)/(1+secx) Factor then simplify. Cos^4x-2cos^2+1 Verify. (cotx tanx)/sinx=cscx Verifying US Citizenship [ 2 Answers ] Is there a legal way to verify one's US citizenship, for example, comparing name & social security number to an official database?	2013-05-20 07:31:01	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 2, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6795178055763245, "perplexity": 1860.0919020525032}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368698554957/warc/CC-MAIN-20130516100234-00037-ip-10-60-113-184.ec2.internal.warc.gz"}
https://stats.stackexchange.com/questions/124705/forming-confidence-interval-using-a-sampling-distribution	# Forming confidence interval using a sampling distribution I know the relation between the distribution of sample means (for a given sample size) and the population parameters, from which samples are taken. My question is, how exactly do we use this relation to do interval estimation? More specifically, when we have a sample and attempt to make an inference about population from which sample is taken, we form the distribution of sample means as if the population mean is equal to mean of our sample, and then use this distribution as the probability density function of the population mean. It seems right, intuitively, but I couldn't see a formal proof. Edit: This question is because of a big confusion. I was taught that, X % confidence intervals are intervals, where parameter to be inferred lies with X % probability. As that statement is wrong, this question is also meaningless. • You could try working the problem backwards: if the population mean is m with variance v, what are the possible values of the observed mean with what probabilities. – user1566 Nov 19, 2014 at 19:19 Step 1: Form a pivotal quantity for the parameter in question. That is, form a statistic, a function of the parameter ($\theta$, say) and the data $\mathbf{x}$, $Q=g(\mathbf{x},\theta)$ whose distribution doesn't depend on $\theta$. We can specify an interval that would contain the desired fraction of random $Q_i$'s (has the desired coverage probability). So we could for example, write an inequality representing the interval along the lines of $l\leq Q \leq u$, which across many such random $Q$ values would contain the given proportion of them. Step 2: Back out an interval in terms of $\theta$ (i.e. rearrange the inequality to put $\theta$ by itself in between the $\leq$ values). Everything else in the inequality is determined once the sample is observed. This will have the desired coverage for $\theta$. e.g. for i.i.d. data from a $N(\mu,\sigma^2)$, a pivotal quantity for $\mu$ is $Q = \frac{\bar{x}-\mu}{s/\sqrt{n}}$, since $Q$ has a standard t-distribution with $n-1$ d.f.	2022-05-26 05:49:01	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.945611834526062, "perplexity": 267.9144690633511}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662601401.72/warc/CC-MAIN-20220526035036-20220526065036-00717.warc.gz"}
http://math.stackexchange.com/questions/130248/clarification-about-what-the-symbol-means	# Clarification about what the symbol - > means? What does this symbol: -> , mean? - Isn't there a computing site where this question would not be off-topic? – Gerry Myerson Apr 11 '12 at 0:22 See e.g. this Wikipedia section – joriki Apr 11 '12 at 0:24 I was tempted to post an answer, but I voted to close as off-topic. This question belongs to Computer Science. Stackexchange. – user2468 Apr 11 '12 at 0:29 Great. For your benefit, the types of the said language are either t = int, t = bool or functions t -> t. So things like (bool -> (int -> bool)) -> (bool -> int) are legitimate types here. – user2468 Apr 11 '12 at 0:34 Voting to reopen. @JD: We were explicitly promised when the CS.SE ghetto opened that it would not affect what is on topic at MSE. Do you have any information that this has changed? – Henning Makholm Apr 12 '12 at 11:38 It is a function type, e.g. $\mathbb{R} \to \mathbb{R}$ would denote the type (you can think of this as kind of set) of all functions from reals to reals. In mathematics (especially set theory) this is usually denoted as $\mathbb{R}^\mathbb{R}$, but again this would denote a set of all functions and the type is just a formal notion (that of course can have some intuitive interpretations). - Thank You Very Much, so it's a special type in a way. Awesome thanks a lot. – Adel Apr 11 '12 at 0:30 Please give a reference in the MinML documentation which states that this is what is the meaning. – Aryabhata Apr 13 '12 at 21:42 @Aryabhata I didn't checked anywhere, it is just a widespread convention and traditional notation in simply typed lambda calculus, majority of statically typed functional languages (especially Standard ML, OCaml and probably any other derivatives of ML), and almost all modern (i.e. post Hindley-Milner type-system) papers in type theory. However, if you still want a reference, here it is. – dtldarek Apr 13 '12 at 22:24 @dtldarek: Just giving a link to the whole document? :-) The point I wanted to make was, you cannot be reasonably sure of this answer, without a reference to some MinML programming language documentation. – Aryabhata Apr 13 '12 at 22:30 @dtldarek: Of course you don't have to formalize every word you type. That will be pointless. All I was saying is that this is more of a programming language question, than a type theory question! Notice that when asked for references, you can only refer to MinML documentation, rather than a book on type theory. I refer you to this meta thread: meta.math.stackexchange.com/questions/3954/…. – Aryabhata Apr 14 '12 at 15:56 On the slide here, which only defines the syntax of types and not their semantics, -> is just some symbol. It has no particular meaning, except that certain nodes in the abstract syntax tree are labeled with it. (And other nodes are labeled int and bool). Later in the slide set, one hopes, there will be some typing rules that tell you what you can do with types built using the -> symbol. These rules will implicitly define what it "means". But it has no meaning beyond what follows deductively from the typing rules.	2014-03-11 08:13:53	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7408617734909058, "perplexity": 1044.4766748208433}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-10/segments/1394011155657/warc/CC-MAIN-20140305091915-00022-ip-10-183-142-35.ec2.internal.warc.gz"}
https://tex.stackexchange.com/questions/12419/use-tikz-decoration-in-a-scope	# Use TikZ decoration in a scope Rather than define a single decorator for all lines at the tikzpicture level, I'd like to use scopes to selectively apply certain decorations to certain parts of my drawing. As a minimal example: \documentclass{minimal} \usepackage{tikz} \usetikzlibrary{decorations} \begin{document} \begin{tikzpicture} %%% Draw the axis. \begin{scope}[decoration={ticks}] \draw [->] (0,0) -- (8,0); \draw [decorate] (0,0) -- (8,0); \end{scope} \end{tikzpicture} \end{document} This should produce an axis eight units long with tick marks, and the decoration should not "bleed" into other areas of the figure. Instead, I get an axis, but no tickmarks! EDIT: It turns out, calling \usetikzlibrary{decorations} in the preamble doesn't work. Instead, use \usetikzlibrary{decorations.pathreplacing}. Can anyone tell me why loading the whole decorations library doesn't work? • Please post a complete and compilable, but minimal example. This means with all required packages and TikZ libraries but with no unrelated thing like scale (there is a ] missing anyway). Thanks. – Martin Scharrer Mar 1 '11 at 17:22 • You mean using a full preamble with minimal document class? – jrhorn424 Mar 1 '11 at 17:25 • Yes a full preamble. If now with article or minimal class doesn't matter. The minimal refers to no unrelated code, not to the minimal class. Also you should put an @Martin in your comment so that I get notified about your comment. This isn't required for the original author of the question or answer, which is the reason I skipped the @jrhorn424 in my comments. – Martin Scharrer Mar 1 '11 at 17:27 • The minimal example doesn't compile for me (even with decorations.pathmorphing), it complains about not knowing the axis key. Is this a style you defined yourself somewhere else? Also, if you manage to find a solution to your problem, you can post that as an answer and accept it, to close the issue. – Jake Mar 1 '11 at 17:48 • In answer to your question about why doesn't \usetikzlibrary{decorations} result in the decorations.pathmorphing library also be loaded, it's better to think of decorations as a base library and decorations.pathmorphing as an extension, rather than decorations.pathmorphing as a sub-library of decorations. The dot doesn't have any special LaTeX meaning here; it's just the file that contains the code is called tikzlibrarydecorations.pathmorphing.code.tex. – Matthew Leingang Mar 1 '11 at 18:18 It requires the library decorations.pathreplacing. The axis style for a path doesn't exist by default. Perhaps you can clarify that. The code below works. But perhaps not as expected. \documentclass{minimal} \usepackage{tikz} \usetikzlibrary{decorations.pathreplacing} \begin{document} \begin{tikzpicture} \begin{scope}[decoration={ticks}] \draw[->] (0,0) -- (8,0); \draw[decorate] (0,0) -- (8,0); \end{scope} \end{tikzpicture} \end{document}	2021-08-01 23:05:56	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8480809330940247, "perplexity": 1705.722006483053}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046154277.15/warc/CC-MAIN-20210801221329-20210802011329-00536.warc.gz"}
http://stackoverflow.com/questions/333043/use-of-threads-in-c/333049	# Use of threads in C++ Can you tell me how can I use threads in C++ programs, and how can I compile it as it will be multithreaded? Can you tell me some good site where I can start from root? Thanks - I made the edit to my answer after talking to my prof about sharing his library here. – caglarozdag Dec 2 '08 at 18:20 I haven't used it myself, but I'm told that the Boost thread libraries make it incredibly easy. - They make it VERY easy. :) – Rob Dec 2 '08 at 7:52 Threads are never easy, regardless of the library/API – Nemanja Trifunovic Dec 2 '08 at 18:13 For Unix/Linux/BSD, there's pthread library: tutorial. I guess there are equivalent in Win32 API. - - I also use tbb, good stuff – Robert Gould Dec 2 '08 at 9:52 There are many threads libraries wich are compatible with c++. So at first you must select one. I prefer OpenMP or POSIX threads (also known as pthreads). How to compile it depends on library you have choose. - I use a library my university prof wrote. It is very simple to implement and works really well (used it for quite some time now). I will ask his permission to share it with you. Sorry for the wait ahead, but gotta check :) ++++++EDIT+++++++ Ok, so I talked to my prof and he doesn't mind if I share it here. Below are the .h and .cpp files for the 'RT Library' written by Paul Davies http://www.filefactory.com/file/7efbeb/n/rt_h http://www.filefactory.com/file/40d9a6/n/rt_cpp 0) This tutorial will explain thread creation and use on a windows platform. 1) Threads in c++ are usually coded as part of the same source (unlike processes where each process has its own source file and function main() ) 2) When a process is up and running, it can create other threads by making appropriate Kernel calls. 3) Multiple threads run faster than multiple processes since they are a part of the same process which results in less of an overhead for the OS, and reduced memory requirements. 4) What you will be using in your case is the CThread class in the rt library. 5) (Make sure rt.h and rt.cpp are a part of your 'solution' and make sure to include rt.h in your main.cpp) 6) Below is a part of code from your future main thread (in main.cpp, of course) where you will create the thread using the CThread class. void main() { . . . } The arguments of t1 in order are: Name of the function acting as our thread, the thread status (it can be either ACTIVE or SUSPENDED - depending on what you want), and last, a pointer to an optional data you may want to pass to the thread at creation. After you execute some code, you'll want to call the WaitForThread() function. 7) Below is a part of code from your future main thread (in main.cpp, of course) where you will describe what the child thread does. UINT _ _stdcall ChildThread1(void *args) { . . . } The odd looking thing there is Microsoft's thread signature. I'm sure with a bit of research you can figure out how to do this in other OSs. The argument is the optional data that could be passed to the child at creation. 8) You can find the detailed descriptions of the member functions in the rt.cpp file. Here are the summaries: Suspend() - Suspends a child thread effectively pausing it. Resume() - Wakes up a suspended child thread SetPriority(int value) - Changes the priority of a child thread to the value specified Post(int message) - Posts a message to a child thread 9) Below is an example of a sample complete program. A clever thing you can do is create multiple instantiations of a single thread. #include “..\wherever\it\is\rt.h” //notice the windows notation { for ( int i = 0; i < 100; i ++) return 0 ; } int main() { // Create 8 instances of the above thread code and let each thread know which number it is. for ( int i = 0; i < 8; i ++) { printf ("Parent Thread: Creating Child Thread %d in Active State\n", i) ; } // wait for threads to terminate, then delete thread objects we created above for( i = 0; i < 8; i ++) { delete Threads[i] ; // delete the object created by ‘new’ } return 0 ; } 10) That's it! The rt library includes a bunch of classes that enables you to work with processes and threads and other concurrent programming techniques. Discover the rest ;) - You may want to read my earlier posting on SO. (In hindsight, that posting is a little one-sided towards pthreads. But I'm a Unix/Linux kind of guy. And that approach seemed best with respect to the original topic.) - Check the threading tutorial at msdn (for c#) http://msdn.microsoft.com/en-us/library/aa645740(VS.71).aspx -	2014-12-18 14:42:42	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2219032198190689, "perplexity": 2167.908206475062}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-52/segments/1418802767198.25/warc/CC-MAIN-20141217075247-00144-ip-10-231-17-201.ec2.internal.warc.gz"}
https://www.groundai.com/project/high-order-variational-integrators-in-the-optimal-control-of-mechanical-systems/	HOVI in optimal control # High order variational integrators in the optimal control of mechanical systems Cédric M. Campos IMUVA, Universidad de Valladolid, 47011 Valladolid, Spain; Instituto de Ciencias Matemáticas, 28049 Madrid, Spain Sina Ober-Blöbaum Department of Mathematics, University of Paderborn, 33098 Paderborn, Germany and Emmanuel Trélat Sorbonne Universités, UPMC Univ. Paris 06, CNRS UMR 7598, Laboratoire; Jacques-Louis Lions, Institut Universitaire de France, F-75005, Paris, France ###### Abstract. In recent years, much effort in designing numerical methods for the simulation and optimization of mechanical systems has been put into schemes which are structure preserving. One particular class are variational integrators which are momentum preserving and symplectic. In this article, we develop two high order variational integrators which distinguish themselves in the dimension of the underling space of approximation and we investigate their application to finite-dimensional optimal control problems posed with mechanical systems. The convergence of state and control variables of the approximated problem is shown. Furthermore, by analyzing the adjoint systems of the optimal control problem and its discretized counterpart, we prove that, for these particular integrators, dualization and discretization commute. ###### Key words and phrases: optimal control, mechanical systems, geometric integration, variational integrator, high order, Runge-Kutta, direct methods, commutation property ###### 1991 Mathematics Subject Classification: Primary 65P10, Secondary 65L06, 65K10, 49Mxx ## 1. Introduction In practice, solving an optimal control problem requires the a priori choice of a numerical method. Many approaches do exist, that are either based on a direct discretization of the optimal control problem, resulting into a nonlinear programming problem, or based on the application of the Pontryagin Maximum Principle, reducing into a boundary value problem. The first class of approaches are called direct, and the second ones, based on the preliminary use of the Pontryagin maximum principle, are called indirect. It can be noted that indirect methods, although very precise, suffer from an important drawback: Unless one already has a good knowledge of the optimal solution, they are very difficult to initialize since they are extremely sensitive to the initial guess. Although many solutions exist in order to carefully initialize a shooting method (see [50, 51]), in most of engineering applications direct approaches are preferred due to their simplicity and robustness. Roughly speaking, direct methods consist of 1. discretizing first the cost and the differential system, in order to reduce the optimal control problem to a usual nonlinear minimization problem with constraints, also called nonlinear programming problem (NLP), with dimension inversely proportional to the smoothness of the discretization; 2. and then dualizing, by applying for instance a Lagrange-Newton method to the NLP, deriving the Karush-Kuhn-Tucker equations (KKT), also called discrete adjoint system, and applying a Newton method to solve the resulting optimality system. Many variants exist, e.g. [3]). In contrast, indirect methods consist of 1. first dualizing the optimal control problem to derive the adjoint system, by applying the Pontryagin Maximum Principle (PMP) (or, equivalently, the Lagrange multipliers necessary condition for optimality in infinite dimension), 2. and then discretizing, by applying a shooting method (that is, a Newton method composed with a numerical integration method). In shorter words, direct methods consist of 1) discretize, 2) dualize, and indirect methods consist of the converse: 1) dualize, 2) discretize. It is natural to wonder whether this diagram is commutative or not, under usual approximation assumptions. Since the pioneering works of [17, 42], it is well known by now that, in spite of usual assumptions ensuring consistency and stability, direct methods may diverge. In other words discretization and dualization do not commute in general. This is due to a complex interplay with the mesh, to the appearance of spurious highfrequencies ultimately causing the divergence (see [17] for very simple finite-dimensional linear quadratic problems and [53] for infinite-dimensional wave equations). Several remedies and solutions exist, from which [4, 16, 17, 43] are a representative sample. For instance, the results of [17] assert the convergence of optimal control problems under specific smoothness and coercivity assumptions provided that the underlying discretization method be based on a Runge-Kutta method. However, the convergence order of the optimal control solution, which depends on the convergence order of the state and the resulting adjoint scheme, is reduced compared to the order of the Runge-Kutta method applied to the state system. Indeed, the discrete state and adjoint system constitutes a symplectic partitioned Runge-Kutta method for which order conditions on the Runge-Kutta coefficients are derived to preserve the convergence rates. Whereas in [17] the symplectic partitioned Runge-Kutta scheme for state and adjoint is explicitly derived, in a recent overview article [44] a proof is given based on a relation between quadratic invariants (that are also naturally preserved by symplectic partitioned Runge-Kutta integrators) and the fulfillment of the KKT equations. The preservation of convergence rates is referred to as the Covector Mapping Principle (CMP) (see e.g. [16]). More precisely, the CMP is satisfied if there exists an order-preserving map between the adjoint variables corresponding to the dualized discrete problem (KKT) and the discretized dual problem (discretized PMP). For the class of Legendre pseudospectral methods the CMP is proven if additional closure conditions are satisfied (see [16, 43]), whereas for Runge-Kutta methods the CMP holds if the order conditions on the Runge-Kutta coefficients derived in [17] are satisfied. For a detailed discussion on the commutation properties we refer to [42]. While for general dynamical systems, many studies of discretizations of optimal control problems are based on Runge-Kutta methods (see e.g. [12, 13, 18, 21, 52]), particularly for mechanical systems, much effort in designing numerical methods for the simulation and optimization of such systems has been put into schemes which are structure preserving in the sense that important qualitative features of the original dynamics are preserved in its discretization (for an overview on structure preserving integration methods see e.g. [19]). One special class of structure preserving integrators is the class of variational integrators, introduced in [36, 47], which are symplectic and momentum-preserving and have an excellent long-time energy behavior. Variational integrators are based on a discrete variational formulation of the underlying system, e.g. based on a discrete version of Hamilton’s principle or of the Lagrange-d’Alembert principle for conservative [29, 30] or dissipative [24] mechanical systems, respectively. They have been further extended to different kind of systems and applications, e.g. towards constrained [11, 25, 31], non smooth [14], multirate and multiscale [32, 46, 48], Lagrangian PDE systems [28, 35] and electric circuits [41]. In the cited works, typically quadrature rules of first or second order are used in order to approximate the action functional of the system. To design high order variational integrators, higher order quadrature rules based on polynomial collocation can be employed. Such so called Galerkin variational integrators have been introduced in [36] and further studied in [6, 20, 27, 38, 40]. For numerically solving optimal control problems by means of a direct method, the use of variational integrators for the discretization of the problem has been proposed in [8, 33, 39]. This approach, denoted by DMOC (Discrete Mechanics and Optimal Control), yields a finite-difference type discretization of the dynamical constraints of the problem which by construction preserves important structural properties of the system, like the evolution of momentum maps associated to symmetries of the Lagrangian or the energy behavior. For one class of Galerkin variational integrators, that is equivalent to the class of symplectic partitioned Runge-Kutta methods, the adjoint system and its convergence rates are analyzed in [39]. It is shown that, in contrast to a discretization based on standard Runge-Kutta methods in [17], the convergence order of the discrete adjoint system is the same as for the state system due to the symplecticity of the discretization scheme. In particular, we obtain the same symplectic-momentum scheme for both state and adjoint system, that means that discretization and dualization commute for this class of symplectic schemes and the CMP is satisfied. For general classes of variational integrators, the commutation property is still an open question. The contribution of this work is twofold: 1. We derive two different kinds of high order variational integrators based on different dimensions of the underling polynomial approximation (Section 3). While the first well-known integrator is equivalent to a symplectic partitioned Runge-Kutta method, the second integrator, denoted as symplectic Galerkin integrator, yields a “new” method which in general, cannot be written as a standard symplectic Runge-Kutta scheme. 2. For the application of high order variational integrators to finite-dimensional optimal control problems posed with mechanical systems, we show the convergence of state and control variables and prove the commutation of discretization and dualization (Sections 4 and 5). The paper is structured as follows: In Section 2 the optimal control problem for a mechanical system is introduced. Its discrete version is formulated in Section 3 based on the derivation of two different kinds of high order variational integrators. The first main result is stated in Section 4: Under specific assumptions on the problem setting we prove the convergence of the primal variables for an appropriate choice of the discrete controls (Theorem 4.1). Along the lines of [18], we demonstrate the influence of the control discretization on the convergence behavior by means of several examples. In Section 5 the discrete adjoint system for the symplectic Galerkin method is derived. It turns out that the reformulation of the variational scheme in Section 3 simplifies the analysis. Whereas commutation of discretization and dualization for symplectic partitioned Runge-Kutta methods has already been shown in [39], we prove the same commutation property for the symplectic Galerkin discretization (Theorem 5.2), which is the second main result of this work. In contrast to the discretization with Legendre pseudospectral methods or classical Runge-Kutta methods, no additional closure conditions (see [16]) or conditions on the Runge-Kutta coefficients (see [17]) are required to satisfy the CMP, respectively. Furthermore, using the high order variational integrators presented here, not only the order but also the discretization scheme itself is preserved, i.e. one yields the same schemes for the state and the adjoint system. We conclude with a summary of the results and an outlook for future work in Section 6. ## 2. Optimal control for mechanical systems ### 2.1. Lagrangian dynamics One of the main subjects of Geometric Mechanics is the study of dynamical systems governed by a Lagrangian. Typically, one considers a mechanical system with configuration manifold together with a Lagrangian function , where the associated state space describes the position and velocity of a particle moving in the system. Usually, the Lagrangian takes the form of kinetic minus potential energy, , for some (positive definite) mass matrix . A consequence of the principle of least action, also known as Hamilton’s principle, establishes that the natural motions of the system are characterized by stationary solutions of the action, thus, motions satisfying (1) δ∫T0L(q(t),˙q(t))dt=0 for zero initial and final variations . The resulting equations of motion are the Euler-Lagrange equations (refer to [1]), (2) ddt∂L∂˙q−∂L∂q=0. When the Lagrangian is regular, that is when the velocity Hessian matrix is non-degenerate, the Lagrangian induces a well defined map, the Lagrangian flow, by , where is the unique solution of the Euler-Lagrange equation (2) with initial condition . By means of the Legendre transform , where is the phase space of positions and momenta , one may transform the Lagrangian flow into the Hamiltonian flow defined by . Moreover, different preservation laws are present in these systems. For instance the Hamiltonian flow preserves the natural symplectic structure of and the total energy of the system, typically (here still denotes the kinetic energy, but depending on rather than on ). Also, if the Lagrangian possess Lie group symmetries, then Noether’s theorem asserts that the associated momentum maps are conserved, like for instance the linear momentum and/or the angular momentum. If external (non conservative) forces are present in the system, Hamilton’s principle (1) is replaced by the Lagrange-d’Alembert principle seeking for curves that satisfy the relation (3) δ∫T0L(q,˙q)dt+∫T0F(q,˙q)⋅δqdt=0 for zero boundary variations , where the second term is denoted as virtual work. This principle leads to the forced Euler-Lagrange equations (4) ddt∂L∂˙q−∂L∂q=F(q,˙q). The forced version of Noether’s theorem (see e.g. [36]) states that if the force acts orthogonal to the symmetry action, then momentum maps are still preserved by the flow. Otherwise, the change in momentum maps and energy is determined by the amount of forcing in the system. ### 2.2. Optimal control problem Since we are interested in optimally controlling Lagrangian systems, we assume that the mechanical system may be driven by means of some time dependent control parameter with being the control set. Typically, the control appears as an extra variable in the external force such that in the following we consider forces of the form and we replace the right-hand side of (4) by the control dependent force term . An optimal control problem for a mechanical system reads (also denoted as Lagranigan optimal control problem in [39]) ###### Problem 2.1 (Lagrangian optimal control problem (LOCP)). (5a) minq,˙q,uJ(q,˙q,u)=∫T0C(q(t),˙q(t),u(t))dt+Φ(q(T),˙q(T)) subject to (5b) δ∫T0L(q(t),˙q(t))dt+∫T0F(q(t),˙q(t),u(t))⋅δq(t)dt = 0, (5c) (q(0),˙q(0)) = (q0,˙q0), with minimization over , and . The interval length may either be fixed, or appear as degree of freedom in the optimization problem. Since any optimal control problem with free final time can easily be transformed into a problem with fixed final time (see e.g. [15]), we assume the time to be fixed from now on. The control set is assumed to be closed and convex, and the density cost function and the final cost function are continuously differentiable, being moreover bounded from below. Henceforth we should assume that the Lagrangian is regular, i.e. there is a (local) one-to-one correspondence between the velocity and the momentum via the Legendre transform and its inverse p=∂L∂˙q(q,˙q)and˙q=(∂L∂˙q)−1(q,p). Thus, the forced Euler-Lagrange equations (4) can be transformed into the partitioned system (6) ˙q(t)=f(q(t),p(t)),˙p(t)=g(q(t),p(t),u(t)) with (7) f(q,p)=(∂L∂˙q)−1(q,p)and% g(q,p,u)=∂L∂q(q,f(q,p))+F(q,f(q,p),u). With some abuse of notation we denote the force and the cost functions defined on and , respectively, by , and such that Problem 2.1 can be formulated as an optimal control problem for the partitioned system (6). ###### Problem 2.2 (Optimal control problem (OCP)). (8a) minq,p,uJ(q,p,u)=∫T0C(q(t),p(t),u(t))dt+Φ(q(T),p(T)) subject to (8b) ˙q(t) =f(q(t),p(t)),q(0)=q0, (8c) ˙p(t) =g(q(t),p(t),u(t)),p(0)=p0, with minimization over , and and the functions , are assumed to be Lipschitz continuous. The first order necessary optimality conditions can be derived by means of the Hamiltonian for the optimal control problem given by (9) H(q,p,u,λ,ψ,ρ0)=ρ0C(q,p,u)+λ⋅f(q,p)+ψ⋅g(q,p,u) with and and are covectors in . ###### Theorem 2.3 (Minimum Principle, e.g.[15]). Let be an optimal solution to Problem 2.2. Then there exist functions and and a constant satisfying for all such that (10a) H(q∗(t),p∗(t),u∗(t),λ(t),ψ(t),ρ0)=minu∈UH(q(t),p(t),u,λ(t),ψ(t),ρ0), for t∈[0,T], and (ρ0,λ,ψ) solves the following initial value problem: (10b) ˙λ =−∇qH(q∗,p∗,u∗,λ,ψ,ρ0), λ(T)=ρ0∇qΦ(q∗(T),p∗(T)), (10c) ˙ψ =−∇pH(q∗,p∗,u∗,λ,ψ,ρ0), ψ(T)=ρ0∇pΦ(q∗(T),p∗(T)). The vectors and are the costate or the adjoint variables of the Hamiltonian equations of optimal control. The scalar is called the abnormal multiplier. In the abnormal case, it holds , and otherwise the multiplier can be normalized to . Since no final constraint on the state is present in the optimal control problem, the above principle holds true with (as proved for instance in [50]). ###### Remark 2.4. If is affine w.r.t. , then the topologies can be taken as for the controls, on and on , and the PMP would still be valid for these classes. Besides, optimal control problems where the optimal control is in but not in are very seldom. For instance, if one is able to express in function of , as for the assumptions of Theorem 5.2, then is clearly in . ## 3. Discretization Since we are interested in solving optimal control problems by some kind of direct method, a discrete approximation of Problem 2.2 is required. To this end, we first introduce two different variational integrators that we employ for the approximation of the control system given in (8b)-(8c). Based on these discrete schemes, we derive the discrete approximations of the optimal control problem that can be solved by standard numerical optimization methods. The controls play no role in the derivations of the variational integrators, therefore we will omit temporarily the dependence of the external force on , which will lighten the notation. The discrete schemes including the approximation of the controls are given in Section 3.3. ### 3.1. Discrete Mechanics and Variational Integrators Discrete Mechanics is, roughly speaking, a discretization of Geometric Mechanics theory. As a result, one obtains a set of discrete equations corresponding to the Euler-Lagrange equation (4) above but, instead of a direct discretization of the ODE, the latter are derived from a discretization of the base objects of the theory, the state space , the Lagrangian , etc. In fact, one seeks for a sequence that approximates the actual trajectory of the system (), for a constant time-step . A variational integrator is an iterative rule that outputs this sequence and it is derived in an analogous manner to the continuous framework. Given a discrete Lagrangian and discrete forces , which are in principle thought to approximate the continuous Lagrangian action and the virtual work, respectively, over a short time (11a) Ld(qk,qk+1) ≈∫tk+1tkL(q(t),˙q(t))dt, (11b) F−d(qk,qk+1)⋅δqk+F+d(qk,qk+1)⋅δqk+1 ≈∫tk+1tkF(q(t),˙q(t))⋅δq(t)dt, one applies a variational principle to derive the well-known forced discrete Euler-Lagrange (DEL) equation, (12) D1Ld(qk,qk+1)+D2Ld(qk−1,qk)+F−d(qk,qk+1)+F+d(qk−1,qk)=0, for , where stands for the partial derivative with respect to the -th component. The equation defines an integration rule of the type , however if we define the pre- and post-momenta (also denoted as discrete Legendre transforms) (13a) p−k :=−D1Ld(qk,qk+1)−F−d(qk,qk+1),k=0,…,N−1,and (13b) p+k :=D2Ld(qk−1,qk)+F+d(qk−1,qk),k=1,…,N, the discrete Euler-Lagrange equation (12) is read as the momentum matching and defines an integration rule of the type . The nice part of the story is that the integrators derived in this way naturally preserve (or nearly preserve) the quantities that are preserved in the continuous framework, the symplectic form, the total energy (for conservative systems) and, in presence of symmetries, the linear and/or angular momentum (for more details, see [36]). Furthermore, other aspects of the continuous theory can be “easily” adapted, symmetry reduction [7, 10, 22], constraints [23, 25], control forces [8, 39], etc. ### 3.2. High Order Variational Integrators High order variational integrators for time dependent or independent systems (HOVI[t]) are a class of integrators that, by using a multi-stage approach, aim at a high order accuracy on the computation of the natural trajectories of a mechanical system while preserving some intrinsic properties of such systems. In particular, symplectic-partitioned Runge-Kutta methods (spRK) and, what we call here, symplectic Galerkin methods (sG) are -stage variational integrators of order up to . The derivation of these methods follows the general scheme that comes next, the specifics of each particular case are detailed in the following subsections. For a fixed time step , one considers a series of points , refereed as macro-nodes. Between each couple of macro-nodes , one also considers a set of micro-data, the stages: For the particular cases of sG and spRK methods, we consider micro-nodes and micro-velocities , respectively. Both macro-nodes and micro-data (micro-nodes or micro-velocities) are required to satisfy a variational principle, giving rise to a set of equations, which properly combined, define the final integrator. Here and after, we will use the following notation: Let denote a set of collocation points and consider the associated Lagrange polynomials and nodal weights, that is, lj(t):=∏i≠jt−cicj−ciandbj:=∫10lj(t)dt, respectively. Note that the pair of ’s define a quadrature rule and that, for appropriate ’s, this rule may be a Gaussian-like quadrature, for instance, Gauss-Legendre, Gauss-Lobatto, Radau or Chebyshev. Now, for the sake of simplicity and independently of the method, we will use the same notation for the nodal coefficients. We define for spRK and sG, respectively, (14) aij:=∫ci0lj(t)dtandaij:=dljdt∣∣ci. Moreover, for spRK, we will also use the nodal weights and coefficients given by Equation (22) and, for sG, the source and target coefficients αj:=lj(0)andβj:=lj(1). Finally, if denotes a Lagrangian from to coupled with an external force , then we define Pi:=∂L∂˙q∣∣i=∂L∂˙q∣∣(Qi,˙Qi)and˙Pi:=∂L∂q∣∣i+Fi=∂L∂q∣∣(Qi,˙Qi)+F(Qi,˙Qi), where are couples of micro-nodes and micro-velocities given by each method. Besides, will stand for the partial derivative with respect to the -th component. #### 3.2.1. Symplectic-Partitioned Runge-Kutta Methods Although the variational derivation of spRK methods in the framework of Geometric Mechanics is an already known fact (see [36] for an “intrinsic” derivation, as the current, or [19] for a “constrained” one), both based on the original works of [47, 45], we present it here again in order to ease the understanding of and the comparison with sG methods below. Given a point and vectors , we define the polynomial curves ˙Q(t):=s∑j=1lj(t/h)˙QjandQ(t):=q0+hs∑j=1∫t/h0lj(τ)dτ˙Qj. We have (15) ˙Qi=˙Q(h⋅ci)andQi:=Q(h⋅ci)=q0+hs∑j=1aij˙Qj. Note that the polynomial curve is uniquely determined by and . In fact, it is the unique polynomial curve of degree such that and . However, if we define the configuration point (16) q1:=Q(h⋅1)=q0+hs∑j=1bj˙Qj and consider it fixed, then is uniquely determined by , and the ’s but one. Namely, take any such that and fix it, then ˙Qi0=⎛⎝q1−q0h−∑j≠i0bj˙Qj⎞⎠/bi0. We now define the multi-vector discrete Lagrangian (17) Ld(˙Q1,…,˙Qs):=hs∑i=1biL(Qi,˙Qi) and the multi-vector discrete force Fd(˙Q1,…,˙Qs)⋅(δQ1,…,δQs):=hs∑i=1biF(Qi,˙Qi)⋅δQi. Although not explicitly stated, they both depend also on . If we write the micro-node variations in terms of the micro-velocity variations (by definition (15)), we have that the multi-vector discrete force is Fd(˙Q1,…,˙Qs)⋅(δQ1,…,δQs)=h2s∑j=1s∑i=1biaijF(Qi,˙Qi)⋅δ˙Qj. The two-point discrete Lagrangian is then (18) Ld(q0,q1):=extPs([0,h],Rn,q0,q1)Ld(˙Q1,…,˙Qs) where is the space of polynomials of order from to such that and and the vectors ’s determine such polynomials as discussed above. The so called “extremal” is realized by a polynomial such that (19) δLd(˙Q1,…,˙Qs)⋅(δ˙Q1,…,δ˙Qs)+Fd(˙Q1,…,˙Qs)⋅(δQ1,…,δQs)=0 for any variations , taking into account that and that . For convenience, the previous equation (19) is developed afterwards. The two-point discrete forward and backward forces are then (20) F±d(q0,q1)⋅δ(q0,q1):=hs∑i=1biF(Qi,˙Qi)⋅∂Qi∂q±δq±, where and . Using the previous relations, we may write F−d=hs∑i=1bi(1−aii0/bi0)FiandF+d=hs∑i=1biaii0/bi0Fi. By the momenta-matching rule (13), we have that −p0 = −Di0Ld(˙Q1,…,˙Qs)/(hbi0)+Dq0Ld(˙Q1,…,˙Qs)+F−d, p1 = Di0Ld(˙Q1,…,˙Qs)/(hbi0)+F+d. where stands for the partial derivative with respect to . Combining both equations, we obtain that Di0Ld+h2s∑i=1biaii0Fi=hbi0p1andp1=p0+Dq0Ld+hs∑i=1biFi. Coming back to Equation (19), we have that 0 =δLd(˙Q1,…,˙Qs)⋅(δ˙Q1,…,δ˙Qs)+Fd(˙Q1,…,˙Qs)⋅(δQ1,…,δQs) =∑j≠i0⎛⎝DjLd+h2s∑i=1biaijFi+∂˙Qi0∂˙Qj(Di0Ld+h2s∑i=1biaii0Fi)⎞⎠δ˙Qj. Therefore, for , we have that DjLd+h2s∑i=1biaijFi=bj/bi0⋅(Di0Ld+h2s∑i=1biaii0Fi). Thus, the integrator is defined by (21a) DjLd(˙Q1,…,˙Qs)+h2s∑i=1biaijFi=hbjp1, (21b) q1=q0+hs∑j=1bj˙Qj, (21c) p1=p0+Dq0Ld(˙Q1,…,˙Qs)+hs∑i=1biFi. Besides, using the definition of the discrete Lagrangian, we have DjLd(˙Q1,…,˙Qs)+h2s∑i=1biaijFi = h2s∑i=1biaij˙Pi+hbjPj, Dq0Ld(˙Q1,…,˙Qs)+hs∑i=1biFi = hs∑i=1bi˙Pi. Therefore, we may write Pj=p0+hs∑i=1bi(1−aij/bj)˙Pi=p0+hs∑i=1¯aji˙Pi, p1=p0+hs∑i=1bi˙Pi=p0+hs∑i=1¯bi˙Pi, were and are given by (22) bi¯aij+¯bjaji=bi¯bj,bi=¯bi. In summary, the equations that define the spRK integrator (with forces), are together with (22) (23a) q1= q0+hs∑j=1bj˙Qj, p1= p0+hs∑j=1¯bj˙Pj, (23b) Qi= q0+hs∑j=1aij˙Qj, Pi= p0+hs∑j=1¯aij˙Pj, (23c) Pi= ∂L∂˙q(Qi,˙Qi), ˙Pi= ∂L∂q(Qi,˙Qi)+F(Qi,˙Qi). #### 3.2.2. Symplectic Galerkin Methods Galerkin methods are a class of methods to transform a problem given by a continuous operator (such as a differential operator) to a discrete problem. As such, spRK methods fall into the scope of this technique and could be also classified as “symplectic Galerkin” methods. However, we want to stress on the difference between what is called spRK in the literature and what we refer here as sG. The wording should not be confused by the one used in [36]. Given points , we define the polynomial curves Q(t):=s∑j=1lj(t/h)Qjand˙Q(t):=1hs∑j=1˙lj(t/h)Qj. We have Qi=Q(h⋅ci)and˙Qi:=˙Q(h⋅ci)=1hs∑j=1aijQj. Note that the polynomial curve is uniquely determined by the points . In fact, it is the unique polynomial curve of degree such that . However, if we define the configuration points (24) q0:=Q(h⋅0)=s∑j=1αjQjandq1:=Q(h⋅1)=s∑j=1βjQj and consider them fixed, then is uniquely determined by , and the ’s but a couple. For instance, we may consider and as functions of the others, since the relations (24) define a system of linear equations where the coefficient matrix has determinant (if and only if ). More precisely, (Q1Qs)=1γ(βs−αs−β1α1)⎛⎝q0−∑s−1j=2αjQjq1−∑s−1j=2βjQj⎞⎠. We now define the multi-point discrete Lagrangian (25) Ld(Q1,…,Qs):=hs∑i=1biL(Qi,˙Qi) and the multi-vector discrete force Fd(Q1,…,Qs)⋅(δQ1,…,δQs):=hs∑i=1biF(Qi,˙Qi)⋅δQi. The two-point discrete Lagrangian is then (26) Ld(q0,q1):=extPs([0,h],Rn,q0,q1)Ld(Q1,…,Qs) where is the space of polynomials of order from to such that the points ’s determine such polynomials as discussed above. The so called “extremal” is realized by a polynomial such that (27) δLd(Q1,…,Qs)⋅(δQ1,…,δQs)+Fd(Q1,…,Qs)⋅(δQ1,…,δQs)=0 for any variations , taking into account that and that , . For convenience, the previous equation (27) is developed afterwards. The two-point discrete forward and backward forces are then formally defined by Equation (20). Using the previous relations, we may write F−d=h(βsb1F1−β1bsFs)/γandF+d=h(α1bsFs−αsb1F1)/γ. By the momenta-matching rule (13), we have that −p0 =−βs/γ⋅(D1Ld+hb1F1)−β1/γ⋅(DsLd+hbsFs) and p1 =−αs/γ⋅(D1Ld+hb1F1)+α1/γ⋅(D	2019-12-15 19:05:28	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9211930632591248, "perplexity": 526.0236126937267}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575541309137.92/warc/CC-MAIN-20191215173718-20191215201718-00052.warc.gz"}
https://math.libretexts.org/Bookshelves/Calculus/Book%3A_Calculus_(Apex)/4%3A_Applications_of_the_Derivative/4.4%3A_Differentials	# 4.4: Differentials $$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$ $$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$ In Section 2.2 we explored the meaning and use of the derivative. This section starts by revisiting some of those ideas. Recall that the derivative of a function $$f$$ can be used to find the slopes of lines tangent to the graph of $$f$$. At $$x=c$$, the tangent line to the graph of $$f$$ has equation $$y = f'(c)(x-c)+f(c).$$ The tangent line can be used to find good approximations of $$f(x)$$ for values of $$x$$ near $$c$$. For instance, we can approximate $$\sin 1.1$$ using the tangent line to the graph of $$f(x)=\sin x$$ at $$x=\pi/3 \approx 1.05.$$ Recall that $$\sin (\pi/3) = \sqrt{3}/2 \approx 0.866$$, and $$\cos (\pi/3) = 1/2$$. Thus the tangent line to $$f(x) = \sin x$$ at $$x=\pi/3$$ is: $$\ell(x) = \frac12(x-\pi/3)+0.866.$$ Figure $$\PageIndex{1}$$: Graphing $$f(x) = \sin x$$ and its tangent line at $$x=\pi/3$$ in order to estimate $$\sin 1.1$$. In Figure $$\PageIndex{1a}$$, we see a graph of $$f(x) = \sin x$$ graphed along with its tangent line at $$x=\pi/3$$. The small rectangle shows the region that is displayed in Figure $$\PageIndex{1b}$$. In this figure, we see how we are approximating $$\sin 1.1$$ with the tangent line, evaluated at $$1.1$$. Together, the two figures show how close these values are. Using this line to approximate $$\sin 1.1$$, we have: \begin{align} \ell(1.1) &= \frac12(1.1-\pi/3)+0.866 \\ &= \frac12(0.053)+0.866 = 0.8925. \end{align} (We leave it to the reader to see how good of an approximation this is.) We now generalize this concept. Given $$f(x)$$ and an $$x$$--value $$c$$, the tangent line is $$\ell(x) = f'(c)(x-c)+f(c)$$. Clearly, $$f(c) = \ell(c)$$. Let $$\Delta x$$ be a small number, representing a small change in $$x$$ value. We assert that: $$f(c+\Delta x) \approx \ell(c+\Delta x),$$ since the tangent line to a function approximates well the values of that function near $$x=c$$. As the $$x$$ value changes from $$c$$ to $$c+\Delta x$$, the $$y$$ value of $$f$$ changes from $$f(c)$$ to $$f(c+\Delta x)$$. We call this change of $$y$$ value $$\Delta y$$. That is: $$\Delta y = f(c+\Delta x)-f(c).$$ Replacing $$f(c+\Delta x)$$ with its tangent line approximation, we have \begin{align} \Delta y &\approx \ell(c+\Delta x) - f(c) \notag\\ &= f'(c)\big((c+\Delta x)-c\big)+f(c) - f(c)\notag \\ &=f'(c)\Delta x \end{align} This final equation is important; we'll come back to it in Key Idea 7. We introduce two new variables, $$dx$$ and $$dy$$ in the context of a formal definition. Definition: Differentials of $$x$$ and $$y$$. Let $$y=f(x)$$ be differentiable. The differential of $$x$$, denoted $$dx$$, is any nonzero real number (usually taken to be a small number). The differential of $$y$$, denoted $$dy$$, is $$dy = f'(x)dx.$$ We can solve for $$f'(x)$$ in the above equation: $$f'(x) = dy/dx$$. This states that the derivative of $$f$$ with respect to $$x$$ is the differential of $$y$$ divided by the differential of $$x$$; this is not the alternate notation for the derivative, $$\frac{dy}{dx}$$. This latter notation was chosen because of the fraction--like qualities of the derivative, but again, it is one symbol and not a fraction. It is helpful to organize our new concepts and notations in one place. Key Idea 7: Differential Notation Let $$y = f(x)$$ be a differentiable function. 1. $$\Delta x$$ represents a small, nonzero change in $$x$$ value. 2. $$dx$$ represents a small, nonzero change in $$x$$ value (i.e., $$\Delta x = dx$$). 3. $$\Delta y$$ is the change in $$y$$ value as $$x$$ changes by $$\Delta x$$; hence $$\Delta y = f(x+\Delta x)-f(x).$$ 4. $$dy = f'(x)dx$$ which, by Equation $$\PageIndex{7}$$, is an approximation of the change in $$y$$ value as $$x$$ changes by $$\Delta x$$; $$dy \approx \Delta y$$. What is the value of differentials? Like many mathematical concepts, differentials provide both practical and theoretical benefits. We explore both here. Example $$\PageIndex{1}$$: Finding and using differentials Consider $$f(x) = x^2$$. Knowing $$f(3) = 9$$, approximate $$f(3.1)$$. Solution The $$x$$ value is changing from $$x=3$$ to $$x=3.1$$; therefore, we see that $$dx=0.1$$. If we know how much the $$y$$ value changes from $$f(3)$$ to $$f(3.1)$$ (i.e., if we know $$\Delta y$$), we will know exactly what $$f(3.1)$$ is (since we already know $$f(3)$$). We can approximate \Delta y\ with $$dy$$. \begin{align} \Delta y &\approx dy \\ &= f'(3)dx \\ &= 2\cdot 3\cdot 0.1 = 0.6. \end{align} We expect the $$y$$ value to change by about $$0.6$$, so we approximate $$f(3.1) \approx 9.6.$$ We leave it to the reader to verify this, but the preceding discussion links the differential to the tangent line of $$f(x)$$ at $$x=3$$. One can verify that the tangent line, evaluated at $$x=3.1$$, also gives $$y=9.6$$. Of course, it is easy to compute the actual answer (by hand or with a calculator): $$3.1^2 = 9.61.$$ (Before we get too cynical and say "Then why bother?", note our approximation is really good!) So why bother? In "most" real life situations, we do not know the function that describes a particular behavior. Instead, we can only take measurements of how things change -- measurements of the derivative. Imagine water flowing down a winding channel. It is easy to measure the speed and direction (i.e., the velocity) of water at any location. It is very hard to create a function that describes the overall flow, hence it is hard to predict where a floating object placed at the beginning of the channel will end up. However, we can approximate the path of an object using differentials. Over small intervals, the path taken by a floating object is essentially linear. Differentials allow us to approximate the true path by piecing together lots of short, linear paths. This technique is called Euler's Method, studied in introductory Differential Equations courses. We use differentials once more to approximate the value of a function. Even though calculators are very accessible, it is neat to see how these techniques can sometimes be used to easily compute something that looks rather hard. Example $$\PageIndex{2}$$: Using differentials to approximate a function value Approximate $$\sqrt{4.5}$$. Solution We expect $$\sqrt{4.5} \approx 2$$, yet we can do better. Let $$f(x) = \sqrt{x}$$, and let $$c=4$$. Thus $$f(4) = 2$$. We can compute $$f'(x) = 1/(2\sqrt{x})$$, so $$f'(4) = 1/4$$. We approximate the difference between $$f(4.5)$$ and $$f(4)$$ using differentials, with $$dx = 0.5$$: $$f(4.5)-f(4) = \Delta y \approx dy = f'(4)\cdot dx = 1/4 \cdot 1/2 = 1/8 = 0.125.$$ The approximate change in $$f$$ from $$x=4$$ to $$x=4.5$$ is $$0.125$$, so we approximate $$\sqrt{4.5} \approx 2.125.$$ Differentials are important when we discuss integration. When we study that topic, we will use notation such as $$\int f(x)\ dx$$ quite often. While we don't discuss here what all of that notation means, note the existence of the differential $$dx$$. Proper handling of integrals comes with proper handling of differentials. In light of that, we practice finding differentials in general. Example $$\PageIndex{3}$$: Finding differentials In each of the following, find the differential $$dy$$. $y = \sin x \qquad\quad 2. y = e^x(x^2+2) \quad\qquad 3. y = \sqrt{x^2+3x-1}$ Solution 1. $$y = \sin x$$: As $$f(x) = \sin x$$, $$f'(x) = \cos x$$. Thus $$dy = \cos (x)dx.$$ 2. $$y = e^x(x^2+2)$$: Let $$f(x) = e^x(x^2+2)$$. We need $$f'(x)$$, requiring the Product Rule. We have $$f'(x) = e^x(x^2+2) + 2xe^x$$, so $$dy = \big(e^x(x^2+2) + 2xe^x\big)dx.$$ 3. $$y = \sqrt{x^2+3x-1}$$: Let $$f(x) = \sqrt{x^2+3x-1}$$; we need $$f'(x)$$, requiring the Chain Rule. We have $$\Delta s f'(x) = \frac{1}{2}(x^2+3x-1)^{-\frac12}(2x+3) = \frac{2x+3}{2\sqrt{x^2+3x-1}}.$$ Thus $$dy = \frac{(2x+3)dx}{2\sqrt{x^2+3x-1}}.$$ Finding the differential $$dy$$ of $$y=f(x)$$ is really no harder than finding the derivative of $$f$$; we just multiply $$f'(x)$$ by $$dx$$. It is important to remember that we are not simply adding the symbol "$$dx$$" at the end. We have seen a practical use of differentials as they offer a good method of making certain approximations. Another use is error propagation. Suppose a length is measured to be $$x$$, although the actual value is $$x+\Delta x$$ (where we hope \Delta x\ is small). This measurement of $$x$$ may be used to compute some other value; we can think of this as $$f(x)$$ for some function $$f$$. As the true length is $$x+\Delta x$$, one really should have computed $$f(x+\Delta x)$$. The difference between $$f(x)$$ and $$f(x+\Delta x)$$ is the propagated error. How close are $$f(x)$$ and $$f(x+\Delta x)$$? This is a difference in "y" values; $$f(x+\Delta x)-f(x) = \Delta y \approx dy.$$ We can approximate the propagated error using differentials. Example $$\PageIndex{4}$$: Using differentials to approximate propagated error A steel ball bearing is to be manufactured with a diameter of 2cm. The manufacturing process has a tolerance of $$\pm 0.1$$mm in the diameter. Given that the density of steel is about 7.85g/cm$$^3$$, estimate the propagated error in the mass of the ball bearing. Solution The mass of a ball bearing is found using the equation "mass = volume $$\times$$ density." In this situation the mass function is a product of the radius of the ball bearing, hence it is $$m = 7.85\frac43\pi r^3$$. The differential of the mass is $$dm = 31.4\pi r^2 dr.$$ The radius is to be 1cm; the manufacturing tolerance in the radius is $$\pm 0.05$$mm, or $$\pm 0.005$$cm. The propagated error is approximately: \begin{align} \Delta m & \approx dm \\ &= 31.4\pi (1)^2 (\pm 0.005) \\ &= \pm 0.493\text{g} \end{align} Is this error significant? It certainly depends on the application, but we can get an idea by computing the relative error. The ratio between amount of error to the total mass is \begin{align} \frac{dm}{m} &= \pm \frac{0.493}{7.85\frac43\pi} \\ &=\pm \frac{0.493}{32.88}\\ &=\pm 0.015,\end{align} or $$\pm 1.5$$. We leave it to the reader to confirm this, but if the diameter of the ball was supposed to be 10cm, the same manufacturing tolerance would give a propagated error in mass of $$\pm12.33$$g, which corresponds to a \textit{percent error} of $$\pm0.188$$\%. While the amount of error is much greater ($12.33 > 0.493$), the percent error is much lower. We first learned of the derivative in the context of instantaneous rates of change and slopes of tangent lines. We furthered our understanding of the power of the derivative by studying how it relates to the graph of a function (leading to ideas of increasing/decreasing and concavity). This chapter has put the derivative to yet more uses: • Equation solving (Newton's Method) • Related Rates (furthering our use of the derivative to find instantaneous rates of change) • Optimization (applied extreme values), and • Differentials (useful for various approximations and for something called integration). In the next chapters, we will consider the "reverse" problem to computing the derivative: given a function $$f$$, can we find a function whose derivative is $$f$$? Be able to do so opens up an incredible world of mathematics and applications. ## Contributors • Gregory Hartman (Virginia Military Institute). Contributions were made by Troy Siemers and Dimplekumar Chalishajar of VMI and Brian Heinold of Mount Saint Mary's University. This content is copyrighted by a Creative Commons Attribution - Noncommercial (BY-NC) License. http://www.apexcalculus.com/ • Integrated by Justin Marshall.	2019-10-19 02:47:26	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 5, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9923954010009766, "perplexity": 320.85953344473296}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986688674.52/warc/CC-MAIN-20191019013909-20191019041409-00448.warc.gz"}
https://cstheory.stackexchange.com/tags/randomness/new	# Tag Info (Posting this as an answer because I am unable to comment.) There may be some confusion between models here. Width 5 read many branching programs capture $NC_1$, and width poly$(n)$ ordered branching programs (a subset of read-once branching programs where the input variables are read in a known fixed order) capture the behavior of a logspace machine over ...	2021-10-23 02:48:04	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7001118063926697, "perplexity": 764.0234165015305}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585537.28/warc/CC-MAIN-20211023002852-20211023032852-00407.warc.gz"}
https://www.physicsforums.com/threads/each-action-there-is-a-responsive-reaction.70272/	# Each action there is a responsive reaction 1. Apr 6, 2005 ### Werg22 We all know that to each action there is a responsive reaction. Let's take the case of a falling ball. Ignoring factors such as friction, elasticity and thermal energy, the ball is dropped from a certain distance perpendicularly above the ground with an inexistent initial velocity. At the instant the ball hits the ground with a certain a certain force, the ground applies an equal force on the ball. The ball is then reflected in the opposite direction. But to get from a direction to one that is opposite, the ball has to, at a certain point drop to a velocity of zero. My thoughts were, naturally, that the reaction force reaccelerates the ball until a certain velocity is reached (witch is equivalent to the final velocity of the falling motion). And here is my problem; if really this is the case, then the force needs a certain time to reaccelerate the ball. Since the force is equivalent to the one of gm, so the time needed would be the same as the time the ball was in the air… this is obviously wrong, but by what logic? 2. Apr 6, 2005 ### Staff: Mentor What makes you think the force equals the weight? It's much greater than that (at least for ball hitting a hard surface). 3. Apr 6, 2005 ### Werg22 Okay, so the acceleration would be relative to the mass of the floor... thank you for teaching me! 4. Apr 6, 2005 ### Davorak That is not what Doc Al ment. Hardness $\neq$ Mass. Typical harder the surface the less energy lost from the ball and its return bounce. 5. Apr 6, 2005 ### Werg22 This i know, but I am talking about the force, and ignoring such factors... Wouldnt the time the ball stays on the ground (then again ignoring all other factors) would be: T= 2vm/F? Correct me if I am still wrong... 6. Apr 6, 2005 ### Davorak The time the ball spends on the ground depends on how the ground and ball deform. In the ideal case where the ball and the ground do not deform then the ball spends zero time on the ground. Your equation only works if the force provided by deformation is a constant this will not typically be true. $$\int_{t_o}^{t_f}\vec{F}dt = 2\vec{v} m$$ 7. Apr 6, 2005 ### Werg22 Hummm I would be lying if I said I completly understand... thanks for helping, Ill investigate this.	2018-06-23 01:05:18	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6929765939712524, "perplexity": 794.8734440784692}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-26/segments/1529267864848.47/warc/CC-MAIN-20180623000334-20180623020334-00466.warc.gz"}
https://mathlearnit.com/circle-circumference.html	Page Content ## Circumference The entire edge of a circle is known as the circle "circumference", it is the distance around the circle. Every point on the circumference of a circle is the same distance from the circle center. The "diameter" is any straight line that passes through the center of the circle, where both end points of the line lie on the circle circumference. The "radius" is any line drawn from the center of the circle to it’s edge, it is half the length of the diameter. This information about the radius and diameter gives us two helpful formula for sums that deal with circles. a) DIAMETER = 2 × RADIUS Examples (1.1) What is the diameter of a circle with radius 8cm? Solution Diameter = 2 × 8cm = 16cm (1.2) What is the radius of a circle with diameter 50m? Solution m ## Circle Circumference Formula The Circumference, like the radius, also has a relationship with the diameter. A relationship that involves the number pi, π. [ CIRCUMFERENCE = π × DIAMETER ] Examples Use the circle circumference formula to calculate the circumference of the following circles. (2.1) Circle with diameter 8cm. Solution Circumference = π × 8cm = 25.1cm to 1 decimal place. (2.2) Circle with diameter 16.5cm. Solution Circumference = π × 16.5cm = 51.8cm to 1 decimal place. (2.3) Circle with diameter 10cm. Solution Diameter = 2 × Radius => 2 × 10cm = 20cm Circumference = π × 10cm = 62.8cm to 1 decimal place. ## Circle Circumference, Radius and DiameterFurther Examples (3.1) A swing in a playground swings back and forth at an angle of 90° when being used. Calculate the distance traveled by the swing from when it leaves point A , to when it also travels back to point A from point B. Solution Pictures can help show what’s going on when answering this question. The swing doesn’t swing full circle, but at 90°, &nbspits journey is part of a full circle. Its journey is in fact \bf{\frac{1}{4}} of a full circle. So what we need to do first, is to work out the circumference, and then divide it by 4. We know the Radius is 3m, thus the diameter is: 2 × 3m = 6m Now we can work out the circumference: Circumference = π × 6m = 18.8m The journey from &nbspA to &nbspB is: 18.8m &div 4 = 4.7m Just remember though that the question asked for the distance traveled from &nbspA to &nbspB, and then back to &nbspA again, so it will be 4.7m traveled twice. Thus the final answer is: 2 × 4.7m = 9.4m The swing travels 9.4m when it goes from &nbspA to &nbspB , and then back to &nbspA again. (3.2) What is the Radius of a circle with Circumference 90cm. Solution We know the Circumference formula which is: CIRCUMFERENCE = π × DIAMETER. Here 90cm = π × DIAMETER. If we divide both sides by π, we can work out the diameter. \bf{\frac{90}{\pi}} = \bf{\frac{\pi \space \times \space DIAMETER}{\pi}} \bf{\frac{90}{\pi}} = DIAMETER = 28.6cm Now that we know the &nbspDIAMETER of the circle, we can work out the radius. Radius = \bf{\frac{28.6}{2}} cm = 14.3cm The radius of the circle is 14.3cm. 1. Home 2. › 3. The Circle 4. › Circle Circumference	2021-12-06 09:14:26	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9036954045295715, "perplexity": 9709.918591105974}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964363290.59/warc/CC-MAIN-20211206072825-20211206102825-00546.warc.gz"}
https://dealii.org/developer/doxygen/deal.II/classFEValuesViews_1_1Scalar.html	Reference documentation for deal.II version GIT d1e6af55b6 2023-02-07 07:50:02+00:00 FEValuesViews::Scalar< dim, spacedim > Class Template Reference #include <deal.II/fe/fe_values.h> Inheritance diagram for FEValuesViews::Scalar< dim, spacedim >: [legend] Classes struct OutputType struct ShapeFunctionData Public Types using value_type = double using gradient_type = ::Tensor< 1, spacedim > using hessian_type = ::Tensor< 2, spacedim > using third_derivative_type = ::Tensor< 3, spacedim > template<typename Number > using solution_value_type = typename ProductType< Number, value_type >::type template<typename Number > template<typename Number > using solution_laplacian_type = typename ProductType< Number, value_type >::type template<typename Number > using solution_hessian_type = typename ProductType< Number, hessian_type >::type template<typename Number > using solution_third_derivative_type = typename ProductType< Number, third_derivative_type >::type Public Member Functions Scalar () Scalar (const FEValuesBase< dim, spacedim > &fe_values_base, const unsigned int component) Scalar (const Scalar< dim, spacedim > &)=delete Scalar (Scalar< dim, spacedim > &&)=default ~Scalar ()=default Scalaroperator= (const Scalar< dim, spacedim > &)=delete Scalaroperator= (Scalar< dim, spacedim > &&) noexcept=default value_type value (const unsigned int shape_function, const unsigned int q_point) const hessian_type hessian (const unsigned int shape_function, const unsigned int q_point) const third_derivative_type third_derivative (const unsigned int shape_function, const unsigned int q_point) const template<class InputVector > void get_function_values (const InputVector &fe_function, std::vector< solution_value_type< typename InputVector::value_type >> &values) const template<class InputVector > void get_function_values_from_local_dof_values (const InputVector &dof_values, std::vector< solution_value_type< typename InputVector::value_type >> &values) const template<class InputVector > template<class InputVector > template<class InputVector > void get_function_hessians (const InputVector &fe_function, std::vector< solution_hessian_type< typename InputVector::value_type >> &hessians) const template<class InputVector > void get_function_hessians_from_local_dof_values (const InputVector &dof_values, std::vector< solution_hessian_type< typename InputVector::value_type >> &hessians) const template<class InputVector > void get_function_laplacians (const InputVector &fe_function, std::vector< solution_laplacian_type< typename InputVector::value_type >> &laplacians) const template<class InputVector > void get_function_laplacians_from_local_dof_values (const InputVector &dof_values, std::vector< solution_laplacian_type< typename InputVector::value_type >> &laplacians) const template<class InputVector > void get_function_third_derivatives (const InputVector &fe_function, std::vector< solution_third_derivative_type< typename InputVector::value_type >> &third_derivatives) const template<class InputVector > void get_function_third_derivatives_from_local_dof_values (const InputVector &dof_values, std::vector< solution_third_derivative_type< typename InputVector::value_type >> &third_derivatives) const Private Attributes const SmartPointer< const FEValuesBase< dim, spacedim > > fe_values const unsigned int component std::vector< ShapeFunctionDatashape_function_data Detailed Description template<int dim, int spacedim = dim> class FEValuesViews::Scalar< dim, spacedim > A class representing a view to a single scalar component of a possibly vector-valued finite element. Views are discussed in the Handling vector valued problems module. You get an object of this type if you apply a FEValuesExtractors::Scalar to an FEValues, FEFaceValues or FESubfaceValues object. Definition at line 147 of file fe_values.h. ◆ value_type template<int dim, int spacedim = dim> using FEValuesViews::Scalar< dim, spacedim >::value_type = double An alias for the data type of values of the view this class represents. Since we deal with a single components, the value type is a scalar double. Definition at line 155 of file fe_values.h. template<int dim, int spacedim = dim> using FEValuesViews::Scalar< dim, spacedim >::gradient_type = ::Tensor<1, spacedim> An alias for the type of gradients of the view this class represents. Here, for a scalar component of the finite element, the gradient is a Tensor<1,dim>. Definition at line 162 of file fe_values.h. ◆ hessian_type template<int dim, int spacedim = dim> using FEValuesViews::Scalar< dim, spacedim >::hessian_type = ::Tensor<2, spacedim> An alias for the type of second derivatives of the view this class represents. Here, for a scalar component of the finite element, the Hessian is a Tensor<2,dim>. Definition at line 169 of file fe_values.h. ◆ third_derivative_type template<int dim, int spacedim = dim> using FEValuesViews::Scalar< dim, spacedim >::third_derivative_type = ::Tensor<3, spacedim> An alias for the type of third derivatives of the view this class represents. Here, for a scalar component of the finite element, the Third derivative is a Tensor<3,dim>. Definition at line 176 of file fe_values.h. ◆ solution_value_type template<int dim, int spacedim = dim> template<typename Number > using FEValuesViews::Scalar< dim, spacedim >::solution_value_type = typename ProductType::type An alias for the data type of the product of a Number and the values of the view this class provides. This is the data type of scalar components of a finite element field whose degrees of freedom are described by a vector with elements of type Number. Definition at line 185 of file fe_values.h. template<int dim, int spacedim = dim> template<typename Number > using FEValuesViews::Scalar< dim, spacedim >::solution_gradient_type = typename ProductType::type An alias for the data type of the product of a Number and the gradients of the view this class provides. This is the data type of scalar components of a finite element field whose degrees of freedom are described by a vector with elements of type Number. Definition at line 194 of file fe_values.h. ◆ solution_laplacian_type template<int dim, int spacedim = dim> template<typename Number > using FEValuesViews::Scalar< dim, spacedim >::solution_laplacian_type = typename ProductType::type An alias for the data type of the product of a Number and the laplacians of the view this class provides. This is the data type of scalar components of a finite element field whose degrees of freedom are described by a vector with elements of type Number. Definition at line 204 of file fe_values.h. ◆ solution_hessian_type template<int dim, int spacedim = dim> template<typename Number > using FEValuesViews::Scalar< dim, spacedim >::solution_hessian_type = typename ProductType::type An alias for the data type of the product of a Number and the hessians of the view this class provides. This is the data type of scalar components of a finite element field whose degrees of freedom are described by a vector with elements of type Number. Definition at line 214 of file fe_values.h. ◆ solution_third_derivative_type template<int dim, int spacedim = dim> template<typename Number > using FEValuesViews::Scalar< dim, spacedim >::solution_third_derivative_type = typename ProductType::type An alias for the data type of the product of a Number and the third derivatives of the view this class provides. This is the data type of scalar components of a finite element field whose degrees of freedom are described by a vector with elements of type Number. Definition at line 224 of file fe_values.h. ◆ Scalar() [1/4] template<int dim, int spacedim> FEValuesViews::Scalar< dim, spacedim >::Scalar Default constructor. Creates an invalid object. Definition at line 182 of file fe_values.cc. ◆ Scalar() [2/4] template<int dim, int spacedim> FEValuesViews::Scalar< dim, spacedim >::Scalar ( const FEValuesBase< dim, spacedim > & fe_values_base, const unsigned int component ) Constructor for an object that represents a single scalar component of a FEValuesBase object (or of one of the classes derived from FEValuesBase). Definition at line 145 of file fe_values.cc. ◆ Scalar() [3/4] template<int dim, int spacedim = dim> FEValuesViews::Scalar< dim, spacedim >::Scalar ( const Scalar< dim, spacedim > & ) delete Copy constructor. This is not a lightweight object so we don't allow copying and generate a compile-time error if this function is called. ◆ Scalar() [4/4] template<int dim, int spacedim = dim> FEValuesViews::Scalar< dim, spacedim >::Scalar ( Scalar< dim, spacedim > && ) default Move constructor. ◆ ~Scalar() template<int dim, int spacedim = dim> FEValuesViews::Scalar< dim, spacedim >::~Scalar ( ) default Destructor. ◆ operator=() [1/2] template<int dim, int spacedim = dim> Scalar& FEValuesViews::Scalar< dim, spacedim >::operator= ( const Scalar< dim, spacedim > & ) delete Copy operator. This is not a lightweight object so we don't allow copying and generate a compile-time error if this function is called. ◆ operator=() [2/2] template<int dim, int spacedim = dim> Scalar& FEValuesViews::Scalar< dim, spacedim >::operator= ( Scalar< dim, spacedim > && ) defaultnoexcept Move assignment operator. ◆ value() template<int dim, int spacedim = dim> value_type FEValuesViews::Scalar< dim, spacedim >::value ( const unsigned int shape_function, const unsigned int q_point ) const Return the value of the vector component selected by this view, for the shape function and quadrature point selected by the arguments. Parameters shape_function Number of the shape function to be evaluated. Note that this number runs from zero to dofs_per_cell, even in the case of an FEFaceValues or FESubfaceValues object. q_point Number of the quadrature point at which function is to be evaluated. Note For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_values flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information. template<int dim, int spacedim = dim> gradient_type FEValuesViews::Scalar< dim, spacedim >::gradient ( const unsigned int shape_function, const unsigned int q_point ) const Return the gradient (a tensor of rank 1) of the vector component selected by this view, for the shape function and quadrature point selected by the arguments. Note The meaning of the arguments is as documented for the value() function. For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_gradients flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information. ◆ hessian() template<int dim, int spacedim = dim> hessian_type FEValuesViews::Scalar< dim, spacedim >::hessian ( const unsigned int shape_function, const unsigned int q_point ) const Return the Hessian (the tensor of rank 2 of all second derivatives) of the vector component selected by this view, for the shape function and quadrature point selected by the arguments. Note The meaning of the arguments is as documented for the value() function. For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_hessians flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information. ◆ third_derivative() template<int dim, int spacedim = dim> third_derivative_type FEValuesViews::Scalar< dim, spacedim >::third_derivative ( const unsigned int shape_function, const unsigned int q_point ) const Return the tensor of rank 3 of all third derivatives of the vector component selected by this view, for the shape function and quadrature point selected by the arguments. Note The meaning of the arguments is as documented for the value() function. For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_third_derivatives flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information. ◆ get_function_values() template<int dim, int spacedim> template<class InputVector > void FEValuesViews::Scalar< dim, spacedim >::get_function_values ( const InputVector & fe_function, std::vector< solution_value_type< typename InputVector::value_type >> & values ) const Return the values of the selected scalar component of the finite element function characterized by fe_function at the quadrature points of the cell, face or subface selected the last time the reinit function of the FEValues object was called. This function is the equivalent of the FEValuesBase::get_function_values function but it only works on the selected scalar component. The data type stored by the output vector must be what you get when you multiply the values of shape functions (i.e., value_type) times the type used to store the values of the unknowns $$U_j$$ of your finite element vector $$U$$ (represented by the fe_function argument). Note For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_values flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information. Definition at line 1547 of file fe_values.cc. ◆ get_function_values_from_local_dof_values() template<int dim, int spacedim> template<class InputVector > void FEValuesViews::Scalar< dim, spacedim >::get_function_values_from_local_dof_values ( const InputVector & dof_values, std::vector< solution_value_type< typename InputVector::value_type >> & values ) const Same as above, but using a vector of local degree-of-freedom values. In other words, instead of extracting the nodal values of the degrees of freedom located on the current cell from a global vector associated with a DoFHandler object (as the function above does), this function instead takes these local nodal values through its first argument. A typical way to obtain such a vector is by calling code such as cell->get_dof_values (dof_values, local_dof_values); (See DoFCellAccessor::get_dof_values() for more information on this function.) The point of the current function is then that one could modify these local values first, for example by applying a limiter or by ensuring that all nodal values are positive, before evaluating the finite element field that corresponds to these local values on the current cell. Another application is where one wants to postprocess the solution on a cell into a different finite element space on every cell, without actually creating a corresponding DoFHandler – in that case, all one would compute is a local representation of that postprocessed function, characterized by its nodal values; this function then allows the evaluation of that representation at quadrature points. Parameters [in] dof_values A vector of local nodal values. This vector must have a length equal to number of DoFs on the current cell, and must be ordered in the same order as degrees of freedom are numbered on the reference cell. [out] values A vector of values of the given finite element field, at the quadrature points on the current object. Template Parameters InputVector The InputVector type must allow creation of an ArrayView object from it; this is satisfied by the std::vector class, among others. Definition at line 1578 of file fe_values.cc. template<int dim, int spacedim> template<class InputVector > void FEValuesViews::Scalar< dim, spacedim >::get_function_gradients ( const InputVector & fe_function, std::vector< solution_gradient_type< typename InputVector::value_type >> & gradients ) const Return the gradients of the selected scalar component of the finite element function characterized by fe_function at the quadrature points of the cell, face or subface selected the last time the reinit function of the FEValues object was called. This function is the equivalent of the FEValuesBase::get_function_gradients function but it only works on the selected scalar component. The data type stored by the output vector must be what you get when you multiply the gradients of shape functions (i.e., gradient_type) times the type used to store the values of the unknowns $$U_j$$ of your finite element vector $$U$$ (represented by the fe_function argument). Note For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_gradients flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information. Definition at line 1602 of file fe_values.cc. template<int dim, int spacedim> template<class InputVector > void FEValuesViews::Scalar< dim, spacedim >::get_function_gradients_from_local_dof_values ( const InputVector & dof_values, std::vector< solution_gradient_type< typename InputVector::value_type >> & gradients ) const This function relates to get_function_gradients() in the same way as get_function_values_from_local_dof_values() relates to get_function_values(). See the documentation of get_function_values_from_local_dof_values() for more information. Definition at line 1632 of file fe_values.cc. ◆ get_function_hessians() template<int dim, int spacedim> template<class InputVector > void FEValuesViews::Scalar< dim, spacedim >::get_function_hessians ( const InputVector & fe_function, std::vector< solution_hessian_type< typename InputVector::value_type >> & hessians ) const Return the Hessians of the selected scalar component of the finite element function characterized by fe_function at the quadrature points of the cell, face or subface selected the last time the reinit function of the FEValues object was called. This function is the equivalent of the FEValuesBase::get_function_hessians function but it only works on the selected scalar component. The data type stored by the output vector must be what you get when you multiply the Hessians of shape functions (i.e., hessian_type) times the type used to store the values of the unknowns $$U_j$$ of your finite element vector $$U$$ (represented by the fe_function argument). Note For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_hessians flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information. Definition at line 1656 of file fe_values.cc. ◆ get_function_hessians_from_local_dof_values() template<int dim, int spacedim> template<class InputVector > void FEValuesViews::Scalar< dim, spacedim >::get_function_hessians_from_local_dof_values ( const InputVector & dof_values, std::vector< solution_hessian_type< typename InputVector::value_type >> & hessians ) const This function relates to get_function_hessians() in the same way as get_function_values_from_local_dof_values() relates to get_function_values(). See the documentation of get_function_values_from_local_dof_values() for more information. Definition at line 1686 of file fe_values.cc. ◆ get_function_laplacians() template<int dim, int spacedim> template<class InputVector > void FEValuesViews::Scalar< dim, spacedim >::get_function_laplacians ( const InputVector & fe_function, std::vector< solution_laplacian_type< typename InputVector::value_type >> & laplacians ) const Return the Laplacians of the selected scalar component of the finite element function characterized by fe_function at the quadrature points of the cell, face or subface selected the last time the reinit function of the FEValues object was called. The Laplacians are the trace of the Hessians. This function is the equivalent of the FEValuesBase::get_function_laplacians function but it only works on the selected scalar component. The data type stored by the output vector must be what you get when you multiply the Laplacians of shape functions (i.e., value_type) times the type used to store the values of the unknowns $$U_j$$ of your finite element vector $$U$$ (represented by the fe_function argument). Note For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_hessians flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information. Definition at line 1710 of file fe_values.cc. ◆ get_function_laplacians_from_local_dof_values() template<int dim, int spacedim> template<class InputVector > void FEValuesViews::Scalar< dim, spacedim >::get_function_laplacians_from_local_dof_values ( const InputVector & dof_values, std::vector< solution_laplacian_type< typename InputVector::value_type >> & laplacians ) const This function relates to get_function_laplacians() in the same way as get_function_values_from_local_dof_values() relates to get_function_values(). See the documentation of get_function_values_from_local_dof_values() for more information. Definition at line 1740 of file fe_values.cc. ◆ get_function_third_derivatives() template<int dim, int spacedim> template<class InputVector > void FEValuesViews::Scalar< dim, spacedim >::get_function_third_derivatives ( const InputVector & fe_function, std::vector< solution_third_derivative_type< typename InputVector::value_type >> & third_derivatives ) const Return the third derivatives of the selected scalar component of the finite element function characterized by fe_function at the quadrature points of the cell, face or subface selected the last time the reinit function of the FEValues object was called. This function is the equivalent of the FEValuesBase::get_function_third_derivatives function but it only works on the selected scalar component. The data type stored by the output vector must be what you get when you multiply the third derivatives of shape functions (i.e., third_derivative_type) times the type used to store the values of the unknowns $$U_j$$ of your finite element vector $$U$$ (represented by the fe_function argument). Note For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_third_derivatives flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information. Definition at line 1764 of file fe_values.cc. ◆ get_function_third_derivatives_from_local_dof_values() template<int dim, int spacedim> template<class InputVector > void FEValuesViews::Scalar< dim, spacedim >::get_function_third_derivatives_from_local_dof_values ( const InputVector & dof_values, std::vector< solution_third_derivative_type< typename InputVector::value_type >> & third_derivatives ) const This function relates to get_function_third_derivatives() in the same way as get_function_values_from_local_dof_values() relates to get_function_values(). See the documentation of get_function_values_from_local_dof_values() for more information. Definition at line 1795 of file fe_values.cc. ◆ fe_values template<int dim, int spacedim = dim> const SmartPointer > FEValuesViews::Scalar< dim, spacedim >::fe_values private A pointer to the FEValuesBase object we operate on. Definition at line 629 of file fe_values.h. ◆ component template<int dim, int spacedim = dim> const unsigned int FEValuesViews::Scalar< dim, spacedim >::component private The single scalar component this view represents of the FEValuesBase object. Definition at line 635 of file fe_values.h. ◆ shape_function_data template<int dim, int spacedim = dim> std::vector FEValuesViews::Scalar< dim, spacedim >::shape_function_data private Store the data about shape functions. Definition at line 640 of file fe_values.h. The documentation for this class was generated from the following files:	2023-02-07 11:07:33	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4178014397621155, "perplexity": 6108.817386663418}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500456.61/warc/CC-MAIN-20230207102930-20230207132930-00410.warc.gz"}
https://socratic.org/questions/how-do-you-solve-3x-3-3-and-8x-6-0	# How do you solve 3x+3<3 and -8x+6>=0? Jul 9, 2015 $x < 0$ #### Explanation: Simplify the inequalities: $3 x + 3 < 3$ => $x < 0$ and $- 8 x + 6 \ge 0$ => $x \le \frac{6}{8}$ Take a union of the in equalities we see the first equality is only true if the second is true (the second is therefore redundant).	2020-01-22 14:12:49	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 5, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9799770712852478, "perplexity": 1933.877926334388}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579250607118.51/warc/CC-MAIN-20200122131612-20200122160612-00448.warc.gz"}
http://www.exampleproblems.com/wiki/index.php/104_number	104 number 104 is the natural number following 103 and preceding 105. Template:Numbers 100s Cardinal one hundred [and] four Ordinal 104th (one hundred [and] fourth) Factorization ${\displaystyle 2^{3}\cdot 13}$ Roman numeral CIV Binary 1101000 Hexadecimal 68 In mathematics One hundred four is a primitive semiperfect number and a composite number, with its divisors being 2, 4, 8, 13, 26 and 52. In regular geometry, 104 is the smallest number of unit line segments that can exist in a plane with four of them touching at every vertex. In science In astronomy, Messier object M104, a magnitude 9.5 spiral galaxy in the constellation Virgo, also known as the Sombrero Galaxy The New General Catalogue object NGC104, a magnitude 4 globular cluster in the constellation Tucana Asteroid 104 Klymene The Saros number of the solar eclipse series which began on 470 April 17 and ended on 1714 May 13. The duration of Saros series 104 was 1244.0 years, and it contained 70 solar eclipses. The Saros number of the lunar eclipse series which began on 465 July 24 and ended on 1781 October 20. The duration of Saros series 104 was 1316.2 years, and it contained 74 lunar eclipses. 104 is also:	2021-02-25 22:12:29	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 1, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.39731070399284363, "perplexity": 5147.8974644370755}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178355937.26/warc/CC-MAIN-20210225211435-20210226001435-00287.warc.gz"}
https://brilliant.org/problems/the-root-of-all-roots/	The Root Of All Roots Algebra Level 4 If the roots of the equation $\sqrt {x^2 + {\sqrt { x^2+11}}} + \sqrt {x^2 - {\sqrt {x^2+11}}} = 4$ are of the form $$a \pm \sqrt{b}$$, where $$a$$ and $$b$$ are integers, find the value of $$a^2 + 3ab +b^2$$. × Problem Loading... Note Loading... Set Loading...	2017-07-25 22:43:18	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7915676236152649, "perplexity": 776.2978463986611}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-30/segments/1500549425407.14/warc/CC-MAIN-20170725222357-20170726002357-00090.warc.gz"}
http://mathoverflow.net/questions/130886/new-differintegral-formula-how-is-it-related-to-other-differintegral-formulas	# New differintegral formula: how is it related to other differintegral formulas? Lets define new differintegral formula as $$\mathbb{D}^s_xf(x)= \sum_{m=0}^{\infty} \binom {s}m \sum_{k=0}^m\binom mk(-1)^{m-k}f^{(k)}(x)$$ or, equivalently, $$\mathbb{D}^s_xf(x)= \lim_{t\to s} \lim_{n\to\infty}\frac{\sum_{k=0}^{n} \frac{(-1)^k f^{(k)}(x)}{(t-k)k!(n-k)!}}{\sum_{k=0}^{n} \frac{(-1)^k }{(t-k) k!(n-k)!}}$$ with the conditions that the above expression converges, and $(\mathbb{D}^{-s}_xf(x))^{(s)}=f(x)$ for each x and natural s. Will this formula where the conditions are met give the same results as Riemann–Liouville differintegral, Grunwald–Letnikov differintegral and Weyl differintegral? Update I have started a bounty. - @Gerald Edgar do you have something to say here? – Anixx May 17 '13 at 11:24 Why in the second formula there is the limit $t\to x$? What will change if to take in the rhs $f^{(k)}(x)$ instead of $f^{(k)}(t)$? – Andrew May 25 '13 at 6:56 @Andrew indeed it is typo. I have corrected. – Anixx May 25 '13 at 16:05 One of the ways to do fractional derivatives and integrals is to do them as multiplications in Laplace transform space. A drawback might be the difficulty of computing the inverse Laplace transform to get back. If you are using all the derivatives of the function, as here, then maybe you can do the inverse Laplace transform using Post's inversion formula en.wikipedia.org/wiki/Post%27s_inversion_formula – Gerald Edgar May 31 '13 at 13:28 Your formula is based on the identity for $s\in\mathbb N$, $$\partial^s=(1+(-1)+\partial)^s=\sum_{m\ge 0}C_s^m((-1)+\partial)^m=\sum_{m\ge 0\atop 0\le k\le m}C_s^mC_m^k(-1)^{m-k}\partial^k. \tag{\flat}$$ It is interesting to compare it to the Fourier multiplier method $$\partial =(2iπ\xi)^s=(2π)^s\exp{(s\text{Log}(i\xi))}$$ with the principal determination of the logarithm ($i\xi\in i\mathbb R$). We have $$\widehat{\partial^s u}=(2iπ\xi)^s\hat u(\xi),\quad (\partial^s u)(x)=\int e^{2iπ x\xi}(2iπ\xi)^s\hat u(\xi)d\xi. \tag{\sharp}$$ Of course, using here the notation $D=\frac{\partial}{2iπ\partial x}$, we can also write as you did $$\partial^s=(1+(-1)+2iπ D)^s$$ but the radius of convergence of $(1+z)^s$ is 1 and you will be forced to drastic assumptions on the decay of the derivatives to have something convergent. Note however that the coefficients in the expansion are the same as in $(\flat)$. A very natural requirement is that $\partial^s$ sends the homogeneous Sobolev space $\dot H^m$ into $\dot H^{m-s}$: we can define in $n$ dimensions for $m>-n/2$ $$\dot H^m=\{u\in\mathscr S'(\mathbb R^n),\hat u\in L^2_{loc}, \vert\xi\vert ^m \hat u\in L^2(\mathbb R^n)\}.$$ In one dimension, for $s\in\mathbb R$, $m>s+\frac12$, Definition $(\sharp)$ provides the continuity of $\partial^s$ from $\dot H^m$ into $\dot H^{m-s}$. I believe that with Formula $(\flat)$, since the homogeneity is not obvious, it should not be so easy to prove that continuity property. On the other hand, for $s\in \mathbb R$, the property $$\partial ^s\partial^{-s} u=u$$ is obvious with $(\sharp),$ provided we assume that $u$ belongs to $\dot H^{m}$ with $m>\frac12+\vert s\vert$, which is a mild requirement compared to the decay estimates on derivatives that you will need to have $(\flat)$ convergent.	2014-11-23 12:28:09	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9663890600204468, "perplexity": 159.716354596029}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-49/segments/1416400379466.35/warc/CC-MAIN-20141119123259-00128-ip-10-235-23-156.ec2.internal.warc.gz"}
http://pipingdesigner.co/index.php/mathematics/algebra/474-mean	Mean Written by Jerry Ratzlaff on . Posted in Algebra Mean, abbreviated as m, is the average value for a group of data or the sum of all the values divided by the number of values. Mean formula $$\large{ m = \frac{ high \;-\; low }{ 2 } }$$	2020-07-10 22:24:20	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9510442614555359, "perplexity": 949.1141448789926}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655912255.54/warc/CC-MAIN-20200710210528-20200711000528-00480.warc.gz"}
https://www.riverpublishers.com/journal_read_html_article.php?j=JWE/18/6/4	## Journal of Web Engineering Vol: 18 Issue: Combined Issue 4, 5 & 6 Published In: June 2019 ### Model-Driven Skills Assessment in Knowledge Management Systems Article No: 4 Page: 353-380 doi: https://doi.org/10.13052/jwe1540-9589.18464 Model-Driven Skills Assessment in Knowledge Management Systems Antonio Balderas1, Juan Antonio Caballero-Hernández2, Juan Manuel Dodero1, Manuel Palomo-Duarte1 and Iván Ruiz-Rube1 1 Department of Computer Science, University of Cadiz, Av. de la Universidad de Cá diz 10, 11519, Puerto Real, Spain 2EVAL for Research Group, University of Cadiz, Av. República Árabe Saharaui s/n, 11519, Puerto Real, Spain E-mail: antonio.balderas@uca.es; juanantonio.caballero@uca.es; juanma.dodero@uca.es; manuel.palomo@uca.es; ivan.ruiz@uca.es Accepted 03 June 2019 ## Abstract Organizations need employees who perform satisfactorily in generic skills, such as teamwork, leadership, problem solving or interpersonal abilities, among others. In organizational environments, employees perform work that is not always visible for supervisors and, thus, they can hardly assess their performance in generic skills. By using a knowledge management system, the users are able to leave a trace of their activity in the system’s records. This research aims to address a computer supported assessment of the user’s generic skills from the perspective of Model-Driven engineering. First, a systematic mapping study is carried out to understand the state of the art. Second, a proposal based on Model-Driven engineering is presented and is then validated through an organizational learning process model. Our results are promising and we are able to conduct a scalable assessment based on objective indicators of the employee’s planning, time management and problem solving skills. Keywords: knowledge management system, generic skills assessment, organizational learning, Model-Driven engineering. ## 1 Introduction Model Driven Engineering (MDE) supports the creation of central artifacts in software engineering through the development or automatic execution of software systems based on models [15]. The growing complexity of organizational processes requires tools to automate or partially automate their operations [2]. MDE provides an appropriate paradigm to implement these tools by developing environments that are based on domain models using the specific field terminology. Learning is a continuous process that takes place within the workplace, both for individuals operating in the learning society and for organizations competing in international markets [46]. To be competitive, an MDE-based solution must support organizations to automate learning in the workplace. Organizational learning can be defined as the advance in the knowledge of organizations that takes place due to experience, which aims to enhance the organization’s proficiency in the relationship between knowledge transfer and dynamic competence [4, 23]. Therefore, organizational learning is crucial for organizations who wish to meet the demands of a competitive and changing environment. Organizational learning implies procedural knowledge, is highly contextualized by the work setting, and focuses on generic skills [12]. Complementing the specific knowledge required in each subject area, generic skills have become a fundamental value in the workplace [31]. Generic skills have been defined as abilities that professionals should be able to perform regardless of their subject area. Currently, many organizations demand that their staff have generic skills as a complement to the specific skills that are expected for their specific expertise. From a formative point of view, supervisors must encourage the performance in generic skills in the organizational learning processes, in both face-to-face and in virtual environments interaction. Unfortunately, measuring the individual’s generic skills performance is not an easy task, especially in web environments where the users are not always visible to their supervisors [7]. Web environments have become the nerve center in many organizations and they now integrate data, processes, business systems and staff to ensure the quality of the final products [17]. To manage their employee’s knowledge, many organizations have adopted web environments based on Knowledge Management Systems (KMSs) due to their features in terms of communication, learning, sharing information, information retrieval and learning functions integration [28]. Although KMSs do not usually provide the supervisors with objective indicators about their employee’s performance in generic skills, KMSs do record most of their users’interactions. Previous studies have collected records from these environments to analyze learning activities [20, 37]. Therefore, is it possible to measure the employee’s generic skills performance based on their interaction with KMSs? To discover the current knowledge about the topic, this work first presents a systematic mapping study to overview the state of the art (Section 2). Then, an organizational learning process model based on MDE for the assessment of acquired skills is described (Section 3). This model was previously applied in a case study consisting on an authentic learning experience [8]. Although the results were promising, the external validity of the process model was still a challenge because of the reduced sample of learners that was used. Consequently, a broader case study involving 112 users was conducted, which has been analyzed in this paper (Section 4). ## 2 Literature Review This literature review has been carried out systematically through a Systematic Mapping Study (SMS). A SMS is a broad review of the primary studies of a specific area that aims to identify some evidence on the subject. This study is based on the guidelines of the methodology proposed by Kitchenham [25] on how to plan, execute and present the results of a literature review in software engineering. In particular, Petersen’s proposal [34] has been used to describe the steps followed to perform this systematic mapping. ### 2.1 Justification and Research Questions Evidence obtained from an individual’s interactions within a KMSs could help their supervisors to assess their performance in generic skills. To find the state of the art regarding this issue, this SMS identifies several aspects of the computer-supported assessment of generic skills. The SMS process begins with the definition of the research questions: • (Q1) Which generic skills have been assessed with computer support from the user’s activity data in virtual environments? • (Q2) Which methods have been applied for the assessment of generic skills in virtual environments? • (Q3) Which techniques have applied to assess users’ generic skills from their interaction with virtual environments? ### 2.2 Review Protocol The revision protocol defines a set of steps to obtain the bibliography for our study, as described in the following subsections. #### 2.2.1 Search Engines and Search Terms We used several well-known digital libraries to find papers, as follows: Web of Science, Wiley Online Library, Science Direct, and IEEE Digital Library. To perform the search, some terms related to skill assessment were used in the queries, namely: generic skills, generic compe-tences and assessment. However, when combined with terms such as computer-assisted, virtual environment or knowledge-management system, digital libraries returned very few or no papers. Consequently, these second terms were removed from the search. To determine whether a retrieved paper should be part of the selection of primary studies, its title, abstract and keywords were read. When this was not enough, we briefly read the full paper, and then read the introduction and the conclusions in more detail. #### 2.2.2 Selection Criteria To determine whether a paper obtained in the previous search process should be included in the selected papers, the exclusion criteria was established as follows: • Included: Relevant paper for research. • Off topic: Not relevant paper for research. • Unsupported language: Paper not written in English or Spanish. • • Duplicated: Paper whose main contribution is already included in another paper. • Unread: Paper that has not been read, mainly because it was not available in libraries and could not be obtained by other means. #### 2.2.3 Classification for Data Extraction To extract the information, the papers have been classified according to the following three aspects: research type, contribution type and research scope. Research Type This classification refers to the type of research work carried out by the authors. Among the different approaches for research classification, we followed Wieringa’s proposal [49] as recommended by Petersen [34]: • Proposal of solution: A solution for a problem is proposed; the solution can be innovative or a significant extension of an existing technique. • Validation research: The technique investigated is new and has not been applied in practice yet. • Evaluation research: The technique is applied in practice and an evaluation is carried out. • Experience papers: Papers that explain what and how something has been carried out in practice, based on the authors’ personal experience. • Opinion papers: These papers show a personal opinion about the goodness or viability of a certain technique, or about how that technique should be implemented. • Philosophical papers: These papers outline a new perspective on existing theories, structuring the field in the form of a taxonomy or a conceptual framework. Contribution Type The papers are classified according to the type of contribution that they make to the field in which they are developed. The classification is described below: • Model: This includes processes, models or systems belonging to a supra-system, whose purpose is to analyze their interaction to fulfill each particular function and that of the supra-system. • Method: Research contributions, described as a set of steps. • Tool: Research contributions that have provided a software system or a software extension. • Framework: These contributions present a combination of aforementioned elements (i.e. a model, a method and/or a tool). • Technique: This procedure aims to perform a specific task. It may be supported by a software system. Research Scope Finally, the papers are classified according to how the assessment of generic skills is carried out: • Supervisor assessment: The supervisor manually performs the assessment process and the result is managed by software. • Peer and self-assessment: The learner manually performs the peer-or self-assessment processes, and the result is managed by software. • Semi-automated assessment tool: Research contributions that present tools to partially automate the assessment of generic skills. ### 2.3 Results After applying the selection criteria, 30 out of 313 papers were selected (Table 1). In addition, a review of the literature on the most assessed generic competences was found and included in this mapping [45]. This review is used to compare the data on these skills with those obtained in this mapping, which provides evidence to answer the first research question. Table 1 Classification of papers Ref Research Type Contribution Type Research Scope [1] proposal of solution tool Peer and self-assessment [3] validation research model Semi-automated assessment tool [5] evaluation research tool Peer and self-assessment [6] proposal of solution model Supervisor assessment [10] proposal of solution framework Semi-automated assessment tool [11] proposal of solution method Supervisor assessment [13] experience paper method Supervisor, peer and self-assessment [14] evaluation research tool Peer and self-assessment [18] experience paper framework Peer and self-assessment [19] proposal of solution technique Semi-automated assessment tool [22] validation research tool Semi-automated assessment tool [26] experience paper method Supervisor assessment [27] experience paper technique Supervisor, peer and self-assessment [29] experience paper model Supervisor assessment [33] validation research method Peer and self-assessment [30] experience paper technique Peer and self-assessment [32] opinion paper model Peer and self-assessment [35] evaluation research method Supervisor, peer and self-assessment [36] validation research model Supervisor assessment [37] validation research framework Semi-automated assessment tool [38] experience paper method Peer and self-assessment [39] evaluation research tool Supervisor assessment [40] experience paper method Peer and self-assessment [42] proposal of solution tool Supervisor assessment [43] evaluation research technique Supervisor, peer and self-assessment [44] evaluation research tool Supervisor assessment [47] experience paper method Supervisor assessment [48] experience paper tool Supervisor assessment [50] proposal of solution model Supervisor assessment Figure 1 shows the classification of papers according to their research scope and research type. Most of the studies describe proposals of solutions, experiences, validations and evaluations, while there are almost no opinions or philosophical papers, which are usually found in research topics of a certain maturity. This, together with the fact of having found few works, confirms the lack of research of this topic in the literature. Figure 1 Distribution of papers by their research scope and their research type. Figure 2 Distribution of papers by their research type and their contribution type. The classification of papers according to their research scope and contribution type is shown in Figure 2. The most frequent types are methods, models and tools. These methods are bound to supervisor assessment and peer and self-assessment, whereas both models and tools are more frequently considered for supervisor assessment. It should be noted that, in this figure, if there is a paper that makes two contribution types—for example, supervisor assessment and peer and self-assessment—, it is counted once for each type. #### 2.3.1 Peer and self-assessment Although peer and self-assessment can reduce the supervisor’s work, this is not always the case. In some of the papers that we have analyzed, this approach is only used in a complementary way to some other form of assessment [27, 43]. In addition, the self-assessment may not fully adjust to the reality of the user’s performance. For example, in [13] significant discrepancies between the grades that were self-assigned by the learners in the analysis skills and the ratings assigned to them by supervisors were detected (i.e., a discrepancy of 55.65%). #### 2.3.2 Supervisor assessment Supervisor assessment is applied by using similar instruments to those applied in peer and self-assessment approaches. Scalability is the most frequently problem mentioned by the authors. For example, Hiperion is a recommendation system that supports the design of activities that are tailored to improve each user skills [42]. The main disadvantage of this tool is the length of time that the supervisors are required to dedicate to assign the different achievements and the weight of each grade for each skill in the activities. Using this tool, an individualized assessment of each user and each group of users in a problem-based learning methodology was performed in [26]. However, the authors reported that the necessary workload for the supervisor is quite higher than usual. Similarly, in [11] the supervisors concluded that the effort they made was excessive, despite the good results obtained. #### 2.3.3 Semi-automated assessment tools Psychological tests were the among the semi-automated assessment tool found [3]. These solutions required a set of experts (Delphi process) to create the test and, unfortunately, it is not an affordable solution. Serious games have been applied to the development of skills [10, 22], measuring the user’s performance through a series of indicators. However, serious games are often used for a specific purpose, usually related to specific skills instead of generic skills. Although there are many studies of serious games in the literature, only two of them assess generic skills. The user’s activity records for the assessment of generic skills have been used in two proposals. The first is LACAMOLC, which is a Pentaho-based tool that maps the generic skills performance with indicators obtained from Moodle and Google Docs [37]. The second proposal uses the Comprehensive Training Model of Teamwork Competence (CTMTC) [19]. A Moodle web service that facilitates the extraction of information via XML enabling the user’s teamwork to be assessed via their forum interactions. These two papers collect indicators from virtual learning environments, which are applicable to several generic skills. However, both approaches use fixed indicators; that is, supervisors cannot check other indicators in the KMS apart from those provided by the tools. ### 2.4 Answers to the Research Questions We are now able to answer to the research questions, as follows: (Q1) Which generic skills have been assessed with computer support from the user’s activity data in virtual environments? All of the generic skills defined by the Tuning Educational Structures in Europe Project [24] have been assessed in the studies that we have found. Among them, the most assessed skills are communication (14 papers), teamwork (13 papers) and problem solving (7 papers). A comprehensive list of assessed generic skills is shown in Table 2. Table 2 Number of papers that assess each generic skill. Generic Skill Papers Generic Skill Papers Generic Skill Papers Analysis 4 ICT 3 Project Communication 14 Interpersonal skills 3 Management 2 Creativity 3 Foreign language 3 Research 2 Critical thinking 4 Leadership 2 Responsibility 3 Cultural 1 Lifelong learning 3 Self-employment 2 Decision making 1 Planning and time Teamwork 13 Entrepreneurship 5 management 3 Troubleshooting 7 (Q2) Which methods are applied for the assessment of generic skills in virtual environments? (Q2) Two type of studies were found: on the one hand, those in which the software assists the user in the assessment process; and on the other hand, those in which the software partially automates the assessment. Within the first group, these works are divided into two subgroups depending on who performs the assessment: peer and self-assessment and supervisor assessment. The electronic rubric is the most frequently used tool in supervisor, peer, and self-assessment. The main problem encountered in supervisor assessment is the increase in the workload [26]. However, if the assessment is delegated to the users, then discrepancies may appear between the grades that are self-assigned and those received through supervisors [13]. Within the semi-automatic assessment tools, five papers were found. Among them, two papers are based in serious games [10, 16] and other two based on the analysis of learning processes [19, 37]. (Q3) Which techniques are applied to assess the users’ generic skills from their interaction with virtual environments? Within semi-automatic assessment tools, there are two papers that describe formative assessment methods. These papers extract indicators from virtual learning environments for learning record analysis [19, 37]. ### 2.5 Discussion Several issues were found in the literature when facing the assessment of generic skills. On the one hand are subjectivity issues, because the criteria valid for a supervisor to assess a generic skill may not be valid for another; and on the other hand are scalability issues. In many cases, the supervisor’s workload to achieve the objectives of a course is high, even more so if they also have to generate and assess new tasks to measure the level of performance of their staff in generic skills. Moreover, scalability issues increase in the context of KMSs, especially if they contain a very large number of users. According to our findings in this SMS, in many proposals the supervisor performs the assessment by using different tools, but these contributions tend to present scalability issues. We also found papers in which the authors try to minimize this workload by combining or replacing the supervisor’s assessment with peer and self-assessment. This partly avoids the scalability issues, but we run into subjectivity issues in some learners’ assessments. Consequently, supervisors may have to revise their learners’ assessments, facing scalability issues again. Finally, we have found a set of papers that partially automate the assessment of generic skills. On the one hand, we find serious games that emulate a real professional task and, based on the user’s behaviour, they obtain a score that will serve as an indicator of performance in certain skills. These games tend to be very focused on certain non-generic skills and their implementation is often expensive. In addition, the process of extracting grades is not usually automated or integrated with assessment tools, so a manual procedure is required to capture them. On the other hand, we find papers that partially cover the objectives of our research: assessment of generic skills based on indicators obtained from the records of learning environments. In these papers, the tools provide fixed indicators on specific activities, for instance one of the tool gives the supervisor an indicator to assess learners’ teamwork based on forum interactions. Unfortunately, what the tool provides could be valid for one supervisor in his/her learning context but not for another. If we had a method that provided supervisors with tools to model and design their assessments, then they could try different formulas to retrieve specific indicators of their users’ performance in the KMS, allowing us to refine them to what is considered to be valid for the assessment of a generic skill in a specific context. ## 3 Organizational Learning Process To meet the requirements of training and knowledge assessment in organizational environments, an organizational learning process model is proposed. This section describes the model and its implementation. Figure 3 Organizational process model for the assessment of acquired skills. ### 3.1 Organizational Learning Process Model This research proposes the organizational learning process shown in Figure 3. This process model includes several roles, and both manual and computer-assisted activities. All of these are aimed at the acquisition and assessment of the participants’ skills in training activities of a given organization. The process model comprises the following sequence of activities: 1. Identification of training needs and required skills: First, the supervisor designs a specific learning plan. This plan lists the catalog of skills expected for learners. The supervisor maintains the catalog of skills and learning outcomes for the organization by using a specific tool. 2. Design of learning activities: Subsequently, the supervisor designs the learning activities needed for the training plan by using the features of a KMS. This way, he/she is able to monitor the learning activities that the learners are engaging. 3. Development of assessment instruments: By using e-assessment systems, detailed feedback-enriched assessment of learners can be supported. Assessment instruments are usually structured in dimensions and sub-dimensions. 4. Mapping activities to assessment instruments and skills/learning outcomes: Once the assessment instruments have been deployed, the supervisor indicates the skills and learning outcomes that are developed by the learners through each learning activity. Then, it is necessary to define the relationships among the involved activities, the sub-dimensions of the assessment instruments, and the skills and outcomes. 5. Engagement in formative activities: After setting up the learning environment and the needed configurations for the assessment, the training activities in which the learners are involved are carried out. 6. Performing manual assessment activities: The supervisor has to proceed with the assessment by analyzing the learning results generated by learners. To perform this step, the supervisor uses the assessment instruments previously created according to the required skills. 7. Performing computer-assisted assessment activities: The analysis of the learning results generated by the learners may be partially automated by using specific tools developed for these purposes. ### 3.2 Reference Implementation To support the activities described in the Organizational Learning Process Model, a reference KMS [8] is proposed. This system is built on top of a well-known Learning Management System (LMS) and a set of open-source tools have been specifically developed. These tools and the process model activities that they support are presented below. Moodle (activity 2) To design and deliver learning activities, we have opted for using Moodle as a LMS. We created some specific tools to enrich Moodle with managing assessment instruments, managing skills and analyzing learning activities by extracting desired indicators. EvalCOMIX (activity 3) EvalCOMIX is a web service to develop assessment instruments. It provides an API that can be integrated with other e-learning systems [41]. A specific block called EvalCOMIX MD was implemented in PHP and JavaScript to integrate EvalCOMIX with Moodle. Gescompeval (activity 4) Gescompeval is a web tool for mapping activities to assessment instru-ments and skills/learning outcomes [21]. It was implemented as a REST web service which provides a read-only API to retrieve these skills and learning outcomes. It was developed in Symfony 2, a PHP framework. EvalCourse (activity 7) EvalCourse is a MDE-based tool to perform computer-assisted assessment based on learning analytics [9]. It admits queries written in SASQL, a Domain Specific Language (DSL) that is used to design online learning assessments. ## 4 Case Study This case study follows an authentic learning approach based on the simulation of a back-end department of an IT company, in which employees are required to solve information requirements. The employees were actually 112 students of a computer science degree in the University of Cadiz (Spain) who had enrolled on a course on databases in 2017/18 academic course. ### 4.1 Method This experience was conducted according to the organizational learning process previously described. 1. Identification of training needs and required skills: In addition to learning how to use the SQL language, the students are supposed to acquire g eneric skills related to problem solving and planning and time management. 2. Design of learning activities: The learning activities consist of both theoretical and laboratory sessions. Six handouts had to be submitted at the end of their respective weekly laboratory sessions (2 hours each). Each submission comprised three SQL queries. After the submissions, the supervisor provided the learners with the solutions and then they had to assess the queries of two of their peers before a second deadline. The students must perform their assigned tasks both correctly and on time. 3. Development of assessment instruments: A rubric to assess learner’s SQL queries was defined, which includes a number of items to check their completeness, correctness and appropriateness: • Is the query implemented according to what is requested in the statement and was solved using suitable operators? (Answers: undelivered, 3 or more errors, 2 errors, 1 error, no errors) • Does the query return the expected result? (Answers: yes/no) • Is there an error in the query that does not allow the database management system to process it? (Answers: yes/no) • Has the task been delivered according to the established rules (naming, format, etc.)? (Answers: yes/no) 4. Mapping activities to assessment instruments and skills/learning outcomes: The learning activities were focused on developing student’s generic skills, as follows: • Problem solving: identify the information requirements of each assignment and design the appropriates queries. • Planning and time management: delivering their tasks (query writing and peer-assessments) on time. 5. Engagement in formative activities: During the laboratory sessions, the learners studied different SQL lessons. As they finished a lesson, they were asked for a related task. These tasks grew in complexity as the lessons progressed. 6. Performing manual assessment activities: There was no manual assessment by the supervisor. As we discussed in our previous case study [8], the manual assessment is not scalable with a high number of learners. 7. Performing computer-assisted assessment activities: EvalCourse was used for the computer-assisted assessment. By writing SASQL queries in EvalCourse, the supervisor could easily retrieve objective indicators about the user’s interactions with the KMS. Table 3 Generic skills scale Grade Performance [0–50) Poor [50–75) Acceptable [75–100) Good 100 Excellent ### 4.2 Assessment Results After completing the course, learners should have completed 12 tasks (six SQL submissions and six peer-assessments). To assess their performance in the two generic skills, their grades were considered according to the scale shown in Table 3. The first aspect to analyze consists on checking if the learners had delivered their tasks on time. For this, the SASQL query is as follows: Evidence queries_on_time: get students show submission in workshop. This query returns reports showing the number of tasks that each learner delivered on time. The results are shown in Figure 4 (left-hand side). They show that only nine learners (8%) had a poor performance (i.e., less than the half of tasks were delivered on time) whereas 35 learners had an excellent performance. The second aspect to analyze is whether learners completed their tasks successfully or not. For this, the SASQL query is as follows: Evidence queries_evaluation: get students show evaluations in workshop. Figure 4 Results of generic skills assessment. The second query returns reports showing the average of the peerassessments received by each learner. The learners used the former rubric to assess their mates. The results are shown in Figure 4 (right-hand side). The results show that 12 learners had a performance between poor or acceptable and only four learners had an excellent performance. The majority of the learners had a good performance (between 75 and 99 out of 100). ### 4.3 Threats to Validity It is necessary to consider threats to the validity of our research. On the one hand, to assure the construct validity of the literature review, we have followed guidelines widely recognized in software engineering research. Its internal and external validity is also guaranteed because we analyzed the extracted data using simple techniques without making any projection. However, since the case study was carried out with undergraduate students, we cannot generalize the findings to other types of organizations beyond universities. Further replication of the study is hence required in other contexts. ## 5 Conclusions Virtual environments such as KMSs are used in many organizations due to their communication and information management features. KMSs also provide a suitable environment to support learning in the workplace. Learning in the workplace implies planning activities to support the employee’s improvement in both specific and generic skills. Knowing how the employees perform in generic skills can be strategically relevant to detect skills that need to be improved or to place them in the proper position. However, measuring the employees’ performance in generic skills is not easy, especially in virtual environments. This research begins with a systematic mapping study, which shows how the performance of the user’s skills in this type of environments is being measured. Although some works were found that semi-automate the assessment process, there are still manual tasks in these approaches, which suffer from both scalability and subjectivity issues. This research proposes an organizational learning process model to support the training activities within organizations, which consists of seven steps that aim to develop the acquisition and assessment of skills. Assessment within the proposed model is supported by EvalCourse, which is a software program that is based on MDE that supports the automatic extraction of indicators from KMS records. Planning, time management and problem solving skills were assessed in a case study conducted with 112 learners through their interaction with the KMS. The results are promising—an assessment based on objective indicators has been achieved which, if it were not for the use of this type of tools, would not scalable. ## Acknowledgments This work was carried out as part of the VISAIGLE project, funded by the Spanish National Research Agency (AEI) with ERDF funds under grant ref. TIN2017-85797-R. ## References [1] F. Achcaoucaou, L. Guitart-Tarrés, P. Miravitlles-Matamoros, A. Núñez-Carballosa, M. Bernardo, and A. Bikfalvi. Competence assessment in higher education: a dynamic approach. Human Factors and Ergonomics in Manufacturing & Service Industries, 24(4):454–467, 2014. [2] M. Luz Alvarez, I. Sarachaga, A. Burgos, E. Estévez, and M. Marcos. A methodological approach to model-driven design and development of automation systems. IEEE Transactions on Automation Science and Engineering, 15(1):67–79, 2018. [3] M. André, M. G Baldoqúin, and S. T. Acuña. Formal model for assigning human resources to teams in software projects. Information and Software Technology, 53(3):259–275, 2011. [4] L. Argote. Organization learning: a theoretical framework. In Organizational learning, pages 31–56. Springer, 2013. [5] E. Arno-Macia and C. Rueda-Ramos. Promoting reflection on science, technology, and society among engineering students through an eap online learning environment. Journal of English for Academic Purposes, 10(1):19–31, 2011. [6] A.A.Aziz,A. Mohamed, N.Arshad, S. Zakaria, and M. S. Masodi. Appraisal of course learning outcomes using rasch measurement: a case study in information technology education. International Journal of Systems Applications, Engineering & Development, 4(1):164–172, 2007. [7] L. Bailyn. Toward the perfect work place? the experience of home-based systems developers. In Information Technology and the Corporation of The 1990s : Research Studies, pages 410–439. Oxford University Press, 1994. [8] A. Balderas, J. A. Caballero-Hernández, J. M. Dodero, M. Palomo-Duarte, and I. Ruiz-Rube. Assessment of generic skills through an organizational learning process model. In Proceedings of the 14th International Conference on Web Information Systems and Technologies – Volume 1: WEBIST, pages 293–300. INSTICC, SciTePress, 2018. [9] A. Balderas, J. M. Dodero, M. Palomo-Duarte, and I. Ruiz-Rube. A domain specific language for online learning competence assessments. International Journal of Engineering Education, 31(3):851–862, 2015. [10] M. Bedek, S. A. Petersen, and T. Heikura. From behavioral indicators to contextualized competence assessment. In 11th IEEE International Conference on Advanced Learning Technologies (ICALT), 2011, pages 277–281. IEEE, 2011. [11] J. V. Benlloch-Dualde and S. Blanc-Clavero. Adapting teaching and assessment strategies to enhance competence-based learning in the framework of the european convergence process. In 37th Annual Frontiers In Education Conference-Global Engineering: Knowledge Without Borders, Opportunities Without Passports, 2007. FIE’07., pages S3B–1. IEEE, 2007. [12] P. C. Candy and R. G. Crebert. Ivory tower to concrete jungle: the difficult transition from the academy to the workplace as learning environments. The Journal of Higher Education, 62(5):570–592, 1991. [13] A. Carreras-Marín, Y. Blasco, M. Badia-Miró, M. Bosch-Príncep, I. Morillo, G. Cairó-i Céspedes, and D. Casares-Vidal. The promotion and assessment of generic skills from interdisciplinary teaching teams. EDULEARN13 Proceedings, pages 201–207, 2013. [14] Y. Chang, T. Eklund, J. I Kantola, and H. Vanharanta. International creative tension study of university students in south korea and finland. Human Factors and Ergonomics in Manufacturing & Service Industries, 19(6):528–543, 2009. [15] A. R. Da Silva. Model-driven engineering: a survey supported by the unified conceptual model. Computer Languages, Systems & Structures, 43:139–155, 2015. [16] D. Djaouti, J. Alvarez, and J. P. Jessel. Classifying serious games: the g/p/s model. Handbook of research on improving learning and motivation through educational games: Multidisciplinary approaches, pages 118–136, 2011. [17] J. G. Enríquez, J. M. Sánchez-Begines, F. J. Domínguez-Mayo, J. A. García-García, and M. J. Escalona. An approach to characterize and evaluate the quality of product lifecycle management software systems. Computer Standards & Interfaces, 61:77 – 88, 2019. [18] P. Ficapal-Cusí and J. Boada-Grau. e-learning and team-based learning: practical experience in virtual teams. Procedia-Social and Behavioral Sciences, 196:69–74, 2015. [19] A. Fidalgo-Blanco, D. Lerís, M. L. Sein-Echaluce, and F. J. García-Peñalvo. Monitoring indicators for ctmtc: comprehensive training model of the teamwork competence in engineering domain. International Journal of Engineering Education, 31(3):829–838, 2015. [20] A. Fidalgo-Blanco, M. L. Sein-Echaluce, F. J. García-Peñalvo, and M. A. Conde. Using learning analytics to improve teamwork assessment. Computers in Human Behavior, 47(C):149–156, June 2015. [21] Gescompeval. https://assembla.com/spaces/inteweb-gescompe val, 2014. [22] M. Guenaga, S. Arranz, I. Rubio-Florido, E. Aguilar, A. Ortizde Guinea, A. Rayon, M. J. Bezanilla, and I. Menchaca. Serious games for the development of employment oriented competences. IEEE Revista Iberoamericana de Tecnologías del Aprendizaje, 8(4):176–183, 2013. [23] P. Huang and Y. Guo. Research on the relationships among knowledge transfer, organizational learning and dynamic competence. Ninth Wuhan International Conference On E-Business, I-III:1449–1456, 2010. [24] Tuning Educational Structures in Europe Project. Generic competences. http://unideusto.org/tuningeu/competences/generic.html, 2003. Accessed: 2019-03-05. [25] B. Kitchenham, R. Pretorius, D. Budgen, O. P. Brereton, M. Turner, M. Niazi, and S. Linkman. Systematic literature reviews in software engineering–a tertiary study. Information and Software Technology, 52(8):792–805, 2010. [26] R. Lacuesta, G. Palacios, and L. Fernández. Active learning through problem based learning methodology in engineering edu-cation. In 39th IEEE Frontiers in Education Conference, 2009. FIE’09., pages 1–6. IEEE, 2009. [27] A. Lasa, I. Txurruka, E. Simón, and J. Miranda. Problem based learning implementation in the degree of human nutrition and dietetics. Proceedings of the International Conference of Education, Research and Innovation (ICERI), pages 1687–1692, 2013. [28] J. Liebowitz and M. Frank. Knowledge Management and e-Learning. CRC press, 2016. [29] M. R. Martín-Briceño and S. Prashar. Acquired skills with the implementation of new evaluation methods at University Rey Juan Carlos. Proceedings of the International Conference of Education, Research and Innovation (ICERI), pages 4875–4878, 2013. [30] A. Masip-Álvarez, C. Hervada-Sala, T. Pa`mies-Gómez, A. Arias-Pujol, C. Jaen-Fernandez, C. Rodriguez-Sorigue, D. Romero-Duran, F. Nejjari-Akhi-Elarab, M. Alvarez-del Castillo, M. Roca-Lefler, et al. Self-video recording for the integration and assessment of generic competencies. In IEEE Global Engineering Education Conference (EDUCON), pages 436–441. IEEE, 2013. [31] A. M. Nita, I. G. Solomon, and L. Mihoreanu. Building competencies and skills for leadership through the education system. In The International Scientific Conference eLearning and Software for Education, volume 2, page 410. “Carol I” National Defence University, 2016. [32] B. Oliver. Graduate attributes as a focus for institution-wide curriculum renewal: innovations and challenges. Higher Education Research & Development, 32(3):450–463, 2013. [33] J. E. Perez-Martinez, J. García-Martín, and A. Sierra-Alonso. Teamwork competence and academic motivation in computer science engineering studies. In IEEE Global Engineering Education Conference (EDUCON), pages 778–783. IEEE, 2014. [34] K. Petersen, R. Feldt, S. Mujtaba, and M. Mattsson. Systematic mapping studies in software engineering. In EASE, volume 8, pages 68–77, 2008. [35] N. Piedra, J. Chicaiza, J. López, A. Romero, and E. Tovar. Measuring collaboration and creativity skills through rubrics: experience from UTPL collaborative social networks course. In IEEE Education Engineering (EDUCON), pages 1511–1516. IEEE, 2010. [36] R. A. Rashid, R. Abdullah, A. Zaharim, H. Ahmad Ghulman, M. S. Masodi, J. L. Mauri, A. Zaharim, A. Kolyshkin, M. Hatziprokopiou, A. Lazakidou, et al. Engineering students performance evaluation of generic skills measurement: ESPEGS model. In Proceedings of the 5th WSEAS International Conference on Engineering Education (EE’08), volume 5, pages 377–383. World Scientific and Engineering Academy and Society (WSEAS), 2008. [37] A. Rayon-Jerez, M. Guenaga, and A. Núñez. A web platform for the assessment of competences in mobile learning contexts. In IEEE Global Engineering Education Conference (EDUCON), pages 321–329. IEEE, 2014. [38] M. L. Renau-Renau and J. Usó-Viciedo. Teaching and learning through projects using the ict: practice of the english writing through business documents. Proceedings of the International Conference of Education, Research and Innovation (ICERI) 2010, pages 4700–4705, 2010. [39] S. Rodriguez-Donaire, B. Amante-García, and S. Oliver-Del-Olmo. e-portfolio: a tool to assess university students’ skills. In 9th International Conference on Information Technology Based Higher Education and Training, pages 114–124. IEEE, 2010. [40] C. Ruizacárate-Varela, M. J. García-García, C. González-Garía, and J. L. Casado-SÁnchez. Soft skills: a comparative analysis between online and classroom teaching. In Proceedings of the International Conference on Advanced Education Technology and Management Science (AETMS2013), pages 359–366. DEStech Publications, 2013. [41] M. S. Sáiz-Ibarra, D. Cabeza-Sánchez, A. R. León-Rodríguez, G. Rodríguez-Gómez, M. A. Gómez-Ruiz, B. Gallego-Noche, V. Quesada-Serra, J. Cubero-Ibáñez, et al. Evalcomix en moodle: Un medio para favorecer la participación de los estudiantes en la e-evaluación. RED, Revista de Educación a Distancia. Special number-SPDECE, 2010. [42] J. Serrano-Guerrero, F. P. Romero, and J. A. Olivas. Hiperion: a fuzzy approach for recommending educational activities based on the acquisition of competences. Information Sciences, 248: 114–129, 2013. [43] A. Sevilla-Pavón, A. Martínez-Sáez, and A. Gimeno-Sanz. Assessment of competences in designing online preparatory materials for the cambridge first certificate in english examination. Procedia-Social and Behavioral Sciences, 34:207–211, 2012. [44] A. I. Starcic. Sustaining teacher’s professional development and training through web-based communities of practice. In International Symposium on Applications and the Internet, 2008. SAINT 2008., pages 317–320. IEEE, 2008. [45] J. Strijbos, N. Engels, and K. Struyven. Criteria and standards of generic competences at bachelor degree level: a review study. Educational Research Review, 14:18–32, 2015. [46] P. Tynjälä. Perspectives into learning at the workplace. Educational research review, 3(2):130–154, 2008. [47] C. Vizcarro-Guarch, P. Martin-Espinosa, R. Cobos, J. E. Pérez, E. Tovar-Caro, G. Blanco-Viejo, A. Bermudez-Marin, and J. R. Ruiz-Gallardo. Assessment of problem solving in computing studies. In IEEE Frontiers in Education Conference, 2013, pages 999–1003. IEEE, 2013. [48] T. Ward and S. Christophe. Developing entrepreneurial accounting and finance competency using the elleiec virtual centre for enterprise. In Proceedings of the 22nd European Association For Education In Electrical And Information Engineering Annual Conference (EAEEIE), pages 1–5. IEEE, 2011. [49] R. Wieringa, N. Maiden, N. Mead, and C. Rolland. Requirements engineering paper classification and evaluation criteria: a proposal and a discussion. Requirements Engineering, 11(1):102–107, 2006. [50] F. Yang, F. W. B. Li, and R. W. H. Lau. A fine-grained outcome-based learning path model. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 44(2):235–245, 2014. ## Biographies Antonio Balderas received his MSc in Computer Science and his PhD degree at the University of Cadiz. He also works at the University of Cádiz as a Lecturer of the Department of Computer Engineering and as a researcher at the Software Process Improvement and Formal Methods group (SPI&FM). His research is focused on the field of Technology-Enhanced Learning. His doctoral thesis has been awarded as the best doctoral thesis in the field of educational technologies in 2016 by both the eMadrid project and the Spanish Chapter of the IEEE Education Society. Previously, He worked as a project manager in different Spanish IT companies. Juan Antonio Caballero-Hernández is a graduated in Computer Science and a PhD candidate at the University of Cadiz. His main research interest is focused on learning experiences based on serious games and diverse applications of Process Mining. Outside the academic environment, he has been working in different positions of the IT sector, including web development, managing teams and international projects. Juan Manuel Dodero is a Professor of Computer Systems & Languages at the University of Cádiz. He has worked before as a lecturer at the University Carlos III of Madrid, as well as an R&D consultant for Spanish ICT companies. He holds a Computer Science and Engineering PhD from the University Carlos III of Madrid. His main research interests are creative computing and technology-enhanced learning, with a focus on software technologies for computer-aided creation and assessment. He has participated and coordinated in various R&D projects in relation with these subjects. Manuel Palomo-Duarte received the MSc degree in computer science from the University of Seville and the PhD degree from the University of Cádiz. He works in the Computer Science Department of the University of Cadiz as an Associate Professor. He is the author of three book chapters, 20 papers published in indexed journals and more than 30 contributions to international academic conferences. His main research interests are learning technologies, serious games and collaborative web. He was a board member in Wikimedia Spain from 2012 to 2016. Ivá n Ruiz-Rube is an assistant professor at the University of Cadiz, Spain. He received his Master degree in Software Engineering and Technology from the University of Seville and his PhD from the University of Cadiz. His fields of research are technology-enhanced learning and software process improvement. He has published several papers in these fields. Previously, he has worked as a software engineer for consulting companies such as Everis Spain S.L. and Sadiel S.A.	2021-08-03 14:12:50	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.406695693731308, "perplexity": 4045.2594590179456}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046154459.22/warc/CC-MAIN-20210803124251-20210803154251-00079.warc.gz"}
https://www.physicsforums.com/threads/forces-with-friction-problem-two-block-on-each-other.472088/	# Forces with friction problem, two block on each other ## Homework Statement The original problem with statement is http://images3a.snapfish.com/232323232fp733;9>nu=52::>379>256>WSNRCG=335:728:;4347nu0mrj". ## Homework Equations Newton's Laws 1-3 ## The Attempt at a Solution Note that the table is frictionless, the only friction is between the two boxes So first: $$\mu = .45$$ and the T on M1 is $$T_{m_{1}}=F_{a}$$ and T on M2 is $$T_{m_{2}}=-F_{a}$$ and $$F_{n_{1}}=m_{1}g$$ $$F_{n_{2}}=m_{1}g+m_{2}g$$ So the friction force on M1 from M2 should be: $$F_{ \mu_{1}} = \mu F_{n_{1}}$$ and the friction on M2 from M1 should be: $$F_{ \mu_{2}}=\mu F_{n_{1}}$$ So i am kind of confused as to how I should use the T forces... here is what I did: $$F_{net_{x}} = F_{a}+F_{\mu_{1}-T-F_{\mu_{2}}=0$$ $$F_{net_{y}}=F_{n_{1}}+F_{n_{2}}-m_{1}g-m_{2}g=0$$ is that right? I am not sure how to set up T because for m1 t is opposite the friction force and for m2 T is opposite the Fa force... should I set up a relationship that way to do this correctly? Last edited by a moderator: Related Introductory Physics Homework Help News on Phys.org cepheid Staff Emeritus Gold Member It seems to me that Fa ≠ T. After all, the horizontal forces on block 1 must balance, and according to the FBD that YOU drew for it (which looks correct), there are three such forces. Fa is to the right and BOTH T and the frictional force from block 2 are pointing to the left. Yes,horizontal forces on block 1 should balance.If T is the tension in the string acting to pull the body to left then the frictional force between the bodies will act to the right to counter the tension.So T=f. Now coming to the second block it has got F acting to the right and tension acting to the left.Since the frictional force is acting to right on block 1,it acts to left on block 2.To sum up the whole thing,your F acts to counter both T(=f) and f.So F equals 2f.Any way i am not sure of this. cepheid Staff Emeritus Gold Member Yes,horizontal forces on block 1 should balance.If T is the tension in the string acting to pull the body to left then the frictional force between the bodies will act to the right to counter the tension.So T=f. Yeah, but you're forgetting the applied force (also points to the right). EDIT: and you also haven't specified which frictional force you're referring to. The one that acts on block 1 points to the left, in the SAME direction as the tension. I explicitly said that there were THREE horizontal forces acting on block 1 in my previous post. Let's let the OP take stock of things... Block 1 is the top one and block 2 is bottom one right?Force acting on the bottom block cannot directly act on the top one.The only way for it is to use friction.Now if the friction tries to stop the relative motion it should act to right on the top block since it tends to move to left. do not write vertical and horizontal equations for whole system that is unnecessary just balance vertical and horizontal forces on each block. Remember the tension in the string is uniform cepheid Staff Emeritus	2020-05-25 18:24:13	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.602297842502594, "perplexity": 732.1097868844838}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347389309.17/warc/CC-MAIN-20200525161346-20200525191346-00218.warc.gz"}
http://eprints.iisc.ernet.in/4433/	Growth of nanocrystalline $TiO_{2}$ films by MOCVD using a novel precursor Shalini, K and Chandrasekaran, S and Shivashankar, SA (2005) Growth of nanocrystalline $TiO_{2}$ films by MOCVD using a novel precursor. In: Journal of Crystal Growth, 284 (3&4). pp. 388-395. PDF av72.pdf Restricted to Registered users only Download (373Kb) \| Request a copy Abstract Thin films of $TiO_{2}$ have been deposited on glass substrates by metalorganic chemical vapour deposition (MOCVD) using a novel,volatile, stable, oxo-\beta-ketoesterate complex of titanium, viz.,bis(ethyl-3-oxo-butanoato)oxotitanium(IV) $[TiO(etob)_{2}]_{2}$. The complex was prepared through a straight forward synthesis. Various spectroscopic techniques have been used to confirm its structure.Thermogravimetric analysis has been carried out to study the thermal properties of the complex. Films of TiO, were grown from the complex by low-pressure MOCVD at temperatures ranging from 400 to 525 degrees C.These films were characterized for their morphology by transmission electron microscopy, scanning electron microscopy, and atomic force microscopy and by electron diffraction for their crystallinity. All the films grown in this temperature range are very smooth. Films grown above 480 degrees C consist of nearly monodisperse, nanocrystals of the anatase phase. Spectrophotometry shows the bandgap, to be in the range3.4-3.7 eV for films grown at different temperatures. It was observed that the bandgap increases with the decrease in the growth temperature,confirming the nanocrystalline nature of the $TiO_{2}$ films. Item Type: Journal Article http://dx.doi.org/10.1016/j.jcrysgro.200... Copyright for this article belongs to Elsevier. A1. Nanocrystalline;A3. Metalorganic chemical vapor deposition;A3. Thin films;A3. TiO2;B1. Novel precursor Division of Chemical Sciences > Materials Research CentreDivision of Chemical Sciences > Organic Chemistry 12 Dec 2005 19 Sep 2010 04:22 http://eprints.iisc.ernet.in/id/eprint/4433	2015-09-01 16:22:32	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5953044891357422, "perplexity": 6938.733201535176}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-35/segments/1440645195983.63/warc/CC-MAIN-20150827031315-00310-ip-10-171-96-226.ec2.internal.warc.gz"}
http://www2.uncp.edu/home/wei/sas/Yangeng/Space-filling_curve.htm	Help us provide free content to the world by donating today! # <!-- document.writeln("\x3cp\x3e\x3c/p\x3e\n"); --> Space-filling curve Space-filling curves or Peano curves are curves, first described by Giuseppe Peano (1858–1932), whose ranges contain the entire 2-dimensional unit square (or the 3-dimensional unit cube). 3 iterations of the Peano curve, a space-filling curve Intuitively, a "continuous curve" in the 2-dimensional plane or in the 3-dimensional space can be thought of as the "path of a continuously moving point". To eliminate the inherent vagueness of this notion, Jordan in 1887 introduced the following rigorous definition, which has since been adopted as the precise description of the notion of a "continuous curve": A curve (with endpoints) is a continuous function whose domain is the unit interval [0,1]. In the most general form, the range of such a function may lie in an arbitrary topological space, but in the most common cases, the range will lie in a Euclidean space such as the 2-dimensional plane (a "plane curve") or the 3-dimensional space ("space curve"). Sometimes, the curve is identified with the range or image of the function (the set of all possible values of the function), instead of the function itself. It is also possible to define curves without endpoints to be a continuous function on the real line (or on the open unit interval (0,1)). In 1890, Peano discovered a densely self-intersecting curve which passed through every point of the unit square. This was the first example of a space-filling curve. Peano's purpose was to construct a continuous mapping from the unit interval onto the unit square, motivated by Georg Cantor's earlier counterintuitive result that the infinite number of points in a unit interval is the same cardinality as the infinite number of points in any finite-dimensional manifold, such as the unit square. Six iterations of the Hilbert curve, a space-filling curve devised by mathematician David Hilbert It was common to associate the vague notions of "thinness" and "1-dimensionality" to curves; all normally encountered curves were piecewise smooth (that is, have piecewise continuous derivatives), and such curves cannot fill up the entire unit square. Therefore, Peano's space filling curve was found to be highly counterintuitive. From Peano's example, it was easy to deduce continuous curves whose ranges contained the n-dimensional hypercube (for any positive integer n). It was also easy to extend Peano's example to continuous curves without endpoints which filled the entire n-dimensional Euclidean space (where n is 2, 3, or any other positive integer). Most well-known space-filling curves are constructed iteratively as the limit of a sequence of piecewise linear continuous curves. [hide] ## //<![CDATA[ if (window.showTocToggle) { var tocShowText = "show"; var tocHideText = "hide"; showTocToggle(); } //]]> Outline of the construction of a space-filling curve Let $\mathcal{C}$denote the Cantor space $\mathbf{2}^\mathbb{N}$. We start with a continuous function h from the Cantor space $\mathcal{C}$onto the entire unit interval [0,1]. (The restriction of the Cantor function to the Cantor set is an example of such a function.) From it, we get a continuous function H from the topological product $\mathcal{C} \times \mathcal{C}$onto the entire unit square $[0,1] \times [0,1]$by setting $H(x,y) = (h(x),h(y)).\,$ Since the Cantor set is homeomorphic to the product $\mathcal{C} \times \mathcal{C}$, there is a continuous bijection g from the Cantor set onto $\mathcal{C} \times \mathcal{C}$. The composition f of H and g is a continuous function mapping the Cantor set onto the entire unit square. (Alternatively, we could use the theorem that every compact metric space is a continuous image of the Cantor set to get the function f.) Finally, one can extend f to a continuous function F whose domain is the entire unit interval [0,1]. This can be done either by using the Tietze extension theorem on each of the components of f, or by simply extending f "linearly" (that is, on each of the deleted open interval (a,b) in the construction of the Cantor set, we define the extension part of F on (a,b) to be the line segment within the unit square joining the values f(a) and f(b)). ## Properties Approximation curves remain within a bounded portion of n-dimensional space, but their lengths increase without bound. The space-filling curve is always self-intersecting, although the approximation curves in the sequence can be self-avoiding. There cannot be any non-self-intersecting (i.e. injective) continuous curve filling up the unit square, because that will make the curve a homeomorphism from the unit interval onto the unit square (any continuous bijection from a compact space onto a Hausdorff space is a homeomorphism), but the unit-square (which has no cut-point) is not homeomorphic to the unit interval (all points of which, except the endpoints, are cut-points). ## Proof that a square and its side contain the same number of points The highly counterintuitive result that the cardinality of a unit interval is the same as the cardinality of any finite-dimensional manifold, such as the unit square, was first obtained by Cantor in 1878, but it can be more intuitively proved using space-filling curves. Space-filling curves are always self-intersecting. This means that they are not injective, and as a consequence not bijective. Since a bijection between a set A and a set B is needed to prove that A and B have the same cardinality, space-filling curves are not a direct proof that a square (or cube or hypercube) has as many points as its side, but they can be used to obtain such a proof. Intuitively, consider that the difficulty resided in showing that a function of the unit interval can fill a square or a cube or a hypercube, and this task was successfully accomplished by Peano. Indeed, being self-intersecting, his curves even manage to "overfill" the square. In other words, although Peano curves are not injective (because they overfill the space), they are surjective (because they fill it). More formally, consider a space-filling curve which maps a unit interval [0,1] onto a unit square [0,1]×[0,1]. One can define a right inverse for it which will be an injection from [0,1]×[0,1] into [0,1]. And x goes to <x,0> is an injection from [0,1] into [0,1]×[0,1]. Using the Cantor–Bernstein–Schroeder theorem, we get a bijection between [0,1] and [0,1]×[0,1]. We conclude that [0,1] and [0,1]×[0,1] have the same cardinality. One advantage of this proof is that, since an explicit definition of the right inverse is easily given, it does not require the use of the axiom of choice. For example, in the Hilbert curve each point in the square is the image of from one to four points in the line segment. When one of the coordinates is a rational number with a power of two in the denominator, that coordinate can be approached either from below or above giving two (not necessarily distinct) values for the preimage. Similarly, when both are such, then there are four (not necessarily distinct). Since the number of possible preimages for each point is finite (indeed less than or equal to four), one can just choose the smallest of them systematically, making the axiom of choice unnecessary. Similarly, finite-dimensional space-filling curves can be used to prove, in general, that any finite-dimensional space contains the same number of points as any line or line segment. ## The Hahn-Mazurkiewicz theorem The Hahn-Mazurkiewicz theorem is the following characterization of general continuous curves: A Hausdorff topological space is a continuous image of the unit interval if and only if it is a compact, connected, locally connected second-countable space. Note: In many formulations of the Hahn-Mazurkiewicz theorem, "second-countable" is replaced by "metrizable". These two formulations are equivalent. In one direction a compact Hausdorff space is a normal space and, by the Urysohn metrization theorem, second-countable then implies metrizable. Conversely a compact metric space is second-countable. ## Literature • Hans Sagan, Space-Filling Curves, Springer-Verlag 1994. ISBN 0387942653. • B. B. Mandelbrot, The Fractal Geometry of Nature, Ch. 7, "Harnessing the Peano Monster Curves", W. H. Freeman, 1982 • Douglas M. McKenna, "SquaRecurves, E-Tours, Eddies, and Frenzies: Basic Families of Peano Curves on the Square Grid", a chapter from The Lighter Side of Mathematics - Proceedings of the Eugene Strens Memorial Conference on Recreational Mathematics and its History, Math. Assoc. of America, 1994 • G. Peano, Sur une courbe, qui remplit toute une aire plane. Math. Ann 36 (1890), 157-160.	2014-10-24 20:57:04	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 8, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.854293704032898, "perplexity": 375.98977823952805}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-42/segments/1414119646518.17/warc/CC-MAIN-20141024030046-00291-ip-10-16-133-185.ec2.internal.warc.gz"}
https://brilliant.org/problems/work-those-quadriceps/	Geometry Level 5 Suppose $$ABCD$$ is a cyclic quadrilateral with all integral sidelengths and $$AD$$ being the circumdiameter. Sides $$\overline{AB}$$ and $$\overline{BC}$$ both having length $$a$$ and side $$CD$$ having length $$b$$ such that $$a \ne b.$$ Determine the sum of the 4 smallest possible perimeters of quadrilateral $$ABCD.$$ Inspired by this beautiful problem ×	2016-10-23 18:01:06	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.35558104515075684, "perplexity": 463.00223243649106}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988719397.0/warc/CC-MAIN-20161020183839-00381-ip-10-171-6-4.ec2.internal.warc.gz"}
https://tex.stackexchange.com/questions/327658/how-to-rotate-every-second-page-in-a-pdf?noredirect=1	How to rotate every second page in a pdf? I have a pdf and need to have each second page turned upside down, so that I can print it twosided. I found pdfpages rotate odd pages 180º and changing \foreach \p in {1,...,\the\pdflastximagepages}{% \ifnumodd{\p}% {\includepdf[pages=\p,angle=180]{\jobname-step1}}% {\includepdf[pages=\p]{\jobname-step1}}% } to \foreach \p in {1,...,\the\pdflastximagepages}{% \ifnumodd{\p}% {\includepdf[pages=\p,angle=180]{\jobname-step1}}% {\includepdf[pages=\p+1]{\jobname-step1}}% } (amongst other changes) would do the job I think. But adding the \p+1 gives an error. I tried it with the package calc, but without any luck. • Many printer drivers can be configured to do this for you automatically (no LaTeX required). – Steven B. Segletes Sep 2 '16 at 10:48 • please, why are you doing this (\p+1) in the first place? – touhami Sep 2 '16 at 11:25 2 Answers Try \foreach \p in {1,...,\the\pdflastximagepages}{% \ifnumodd{\p}% {\includepdf[pages=\p]{\jobname-step1}}% {\includepdf[pages=\p,angle=180]{\jobname-step1}}% } After some long hours I got the following to do the job: \documentclass[landscape]{article} \usepackage{pgffor,pgfmath,pdfpages} \def\originalfile{backlog-grooming.pdf} \begin{document} \pdfximage{\originalfile}% \foreach \p in {1,3,...,\the\pdflastximagepages}{% \pgfmathparse{int(\p+1)}% {\includepdf[pages=\p]{\originalfile}}% {\includepdf[pages=\pgfmathresult,angle=180]{\originalfile}}% } \end{document} In the file backlog-grooming.pdf every second page is turned upside down.	2019-08-26 01:20:51	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.663171648979187, "perplexity": 2282.145973668911}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027330913.72/warc/CC-MAIN-20190826000512-20190826022512-00202.warc.gz"}
http://math.stackexchange.com/questions/280235/10-5-and-32-hypotenuse-a-8-5-b-42-5-what-angles-are-the-10-5-and-32-hypot	# 10.5“ and 32” hypotenuse, a=8.5, b=42.5, what angles are the 10.5“ and 32” Hypotenuse? I have a ramp that has a concave "kink" in the angle. The first length of the hypotenuse is 10.5", the next is 32". The triangle is 8.5" tall (a) The triangle is 42.5" long (b) How do I figure out what the angles of the two hypotenuse are? - add comment ## 1 Answer The Pythagorean theorem tells you that were there no kink, the hypothenuse would be $\sqrt{42.5^2+8.5^2}=43.3417\ldots$ Now you have a triangle whose sides are 43.3417, 10.5 and 32, which is pretty weird since there is no non-degenerate triangle with these sides. - add comment	2014-07-22 07:34:13	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5198831558227539, "perplexity": 1168.3358301219714}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-23/segments/1405997857710.17/warc/CC-MAIN-20140722025737-00246-ip-10-33-131-23.ec2.internal.warc.gz"}
http://openstudy.com/updates/558a3c75e4b09ad72e965703	## sloppycanada one year ago I'm so confused on this, I'm not sure what I'm supposed to use for any of this, I don't know the common denominator or anything. Find the 6th term of the sequence with t1 = -4 and tn = 5tn-1. http://imgur.com/BaADfyq 1. ganeshie8 start with $$-4$$, and keep multiplying by $$5$$ to get the next term. So T6 is -62,500? 3. ganeshie8 first term, $$\large t_1 ~=~-4$$ second term, $$\large t_2 ~=~-45 = -20$$ third term, $$\large t_3 ~=~-205 = -100$$ keep going till the 6th term 4. ganeshie8 -62,500 is wrong Sorry, I did too many of them. -2500. 6. ganeshie8 T4 = -100 x 5 = -500 T5 = -500 x 5 = -2500 T6 = -2500 x 5 = -12500 8. ganeshie8 Good! And then how do I go about finding the sum of an infinite series? 10. ganeshie8 look at the terms : $-4,~~-20,~~-100,~~-500,~~-2500,~~ \ldots$ what do you notice ? do they seem to converge to some number ? You could go on for ever without getting a sum. 12. ganeshie8 Yes, so we say the "sequence doesn't converge" and the infinite sum doesn't exist So for an equation like this - Find the sum of the infinite series 3 + 1.2 + 0.48 + 0.192 + ...if it exists. All I would do is use the formula to find the equation of the infinite series? 14. ganeshie8 what kind of series is it, geometric/arithmetic ? Geometric? 16. ganeshie8 there is a nice criterion for testing convergence of geometric series, you simply look at the common ratio 17. ganeshie8 whats the common ratio of given series ? The equation is tn/(tn-1) Common ratio is 2.5 20. ganeshie8 yes work it common ratio = (next term)/(present term) 21. ganeshie8 looks you have worked it in reverse : (present term)/(next term) 22. ganeshie8 try again .4? 24. ganeshie8 yes common ratio = 0.4 which is between -1 and 1 so the given series conveges 25. ganeshie8 A geometric series converges if the common ratio is between -1 and 1 26. ganeshie8 use infinite sum formula to find the sum 27. ganeshie8 do you have the formula wid u ? S(infinite) = 3/t-.4 I have it in my notes 30. ganeshie8 $\large S_{\infty} ~=~\dfrac{t_1}{1-r}$ 31. ganeshie8 $\large S_{\infty} ~=~\dfrac{3}{1-0.4}$ 32. ganeshie8 simplify 5? 34. ganeshie8 Yes! I have three more if you have time? 36. ganeshie8 okay il try, post 38. ganeshie8 Firs test if the series converges by finding the common ratio 39. ganeshie8 whats the common ratio ? 1.33? 41. ganeshie8 Yes, which is "not" in between -1 and 1 so the series does not converge. 42. ganeshie8 we say the sum does not exist Okay so the answer would be "No solution" 44. ganeshie8 As you can see, the common ratio decides whether an infinite converges to some number, or if it diverges 45. ganeshie8 Answer would be "does not converge" If it converges then it has a sum, if it does not converge there is not really a solution? 47. ganeshie8 yes, do you see why the common ratio of 1.33 gives a diverging sum ? Because it's larger then 1? and not between that -1 and 1 49. ganeshie8 Yes, when you multiply the first term by 1.33, you get a bigger next term; the terms keep growing and the sum wont reach a specific number So for this problem - http://gyazo.com/15138c898cca305ec43a79e298d55821 The answer would be .498 51. ganeshie8 how did u get 0.498 ? 52. ganeshie8 im asking because im getting a more nice looking number : 0.5 I didn't round. 54. ganeshie8 me neither could you show ur work please $S \infty = \frac{ 1 }{ 3 }\div 1-.33$ 56. ganeshie8 Ahh okay, you're rounding 1/3 to 0.33 57. ganeshie8 i worked it like this : $\large S_{\infty}~=~\dfrac{1/3}{1-1/3} = \dfrac{1}{3-1}=\dfrac{1}{2}=0.5$ I'm not sure why I changed from a fraction to a decimal. Fractions are more precise aren't they? 59. ganeshie8 Yep Fractions are exact decimals are not so exact when you get a repeating decimal 60. ganeshie8 1/2 = 0.5 both are exact 61. ganeshie8 1/3 = 0.33333333333333333333333333... clearly the decimal wont be exact because you can't write out infinitely many 3's Okay, last one - http://gyazo.com/50d340d91d94093d361677d900fa46ee Answer is 1. 63. ganeshie8 $\huge \color{red}{\checkmark}$ Ah hah! Thank you! Not sure how to show my appreciation on this site (if there are points or something), but let me know if there is. 66. ganeshie8 67. ganeshie8 you could also write a testimonial if you think the helper is amazing 68. ganeshie8 not encouraging you to write a testimonial for me right now, but just letting you know :) Finding the sum of an geometric Find S12 for the series 1 + 2 + 4 + 8 +... like this is 49,140 70. ganeshie8 go through this when u have time to know more about the site http://openstudy.com/code-of-conduct 71. ganeshie8 how did u get 49.140 ? Sorry it should be 8,190. 2((1-2^12)/(1-2)) = 8190 \|dw:1435126030016:dw\| 74. ganeshie8 why are you multiplying by 2 ? 75. ganeshie8 first term is 1 right 76. ganeshie8 \|dw:1435126092819:dw\| Okay so it'd just be 4095 78. ganeshie8 Correct.	2017-01-17 07:25:35	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7540977597236633, "perplexity": 1764.3445447792285}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-04/segments/1484560279489.14/warc/CC-MAIN-20170116095119-00293-ip-10-171-10-70.ec2.internal.warc.gz"}
https://math.stackexchange.com/questions/2718638/construction-of-the-legendre-polynomials-by-gram-schmidt	Construction of the Legendre Polynomials by Gram Schmidt I'm stuck with a homework problem from my functional analysis class. The question is: "Show that the Gram-Schmidt orthonomalization procedure in $L^2(-1,1)$, starting from the series $(x^n)^{\infty}_{n=0}$ provides an orthonomal basis, given by $(b^n)^{\infty}_{n=0}$, $b_n = \sqrt{n + \frac{1}{2}}P_n$ with $P_n(x)=\frac{1}{2^n n!} \frac{d^n}{dx^n} [(x^2-1)^n]$ beeing the n-th Legendre polynomial." I tried two different approaches: $p_n(x) = x p_{n-1}(x) - \frac{(y p_{n-1}(y),p_{n-1}(y))}{(p_{n-1}(y),p_{n-1}(y))} p_{n-1}(x) - \frac{(y p_{n-1}(y),p_{n-2}(y))}{(p_{n-2}(y),p_{n-2}(y))} p_{n-2}(x)$ with $P_n(x) = \frac{p_n(x)}{p_n(1)}$ is equivalent to $(n+1) P_{n+1}(x) = (2n+1)x P_n(x) - n P_{n-1}(x), n=1,2,...;P_0 = 1; P_1 = x$. And I just don't know how to do that. • The second approach was to show explicitely for $P_0, P_1$ and $P_2$ that the equivalence $b_n = \sqrt{n + \frac{1}{2}}P_n = \frac{v_n}{\|v_n\|}$ with $v_n = (x^n - \sum_{k=0}^{n-1} \frac{(x^n,b_{n-1})}{(b_{n-1},b_{n-1})} b_{n-1} )$ holds and then use an inductive argument, which goes like: "The linear subspace of polynomials of degree $n$ has dimension $n+1$. The orthogonal complement of the polynomials of degree $n − 1$ in the space of polynomials of degree $n$ is equal to $1$, and therefore ${Pn}$ is a basis of the orthogonal complement. The Gram-Schmidt orthogonalization of the monomials gives a polynomial of degree $n$ in this complement, so it gives the Legendre polynomials up to normalization." But by that argument I would assume, that in the space of polynomials of degree $\le n$, given $n$ orthogonal polynomials, an (n+1)'th orthogonal polynomial must be unique, up to scaling. But can I just assume that? I would appreciate any help, thank you! :-) For any inner product there is indeed a unique (up to scaling) polynomial $f\in P_{n+1}(x)$ orthogonal to $P_n(x)$ (the space of polynomials of degree less than or equal to n). To see this assume (seeking contradiction) that $f, g$ are linearly independent polynomials in the orthogonal compliment of $P_n(x) \leq P_{n+1}(x)$. Note $\{1,x,x^2...x^{n+1}\}$ form a basis of $P_{n+1}(x)$ so this is an n+2 dimensional vector space over your field. Suppose $f,g$ are linearly independent. By Gram Schmidt WLOG they are orthogonal. Then $\{1,x,x^2...x^n,f,g\}$ are $n+2$ linearly independent. This is a contradiction since it implies $dim (P_{n+1}(x))=n+2$. To see the above set is linearly independent note $1,...,x^n$ are manifestly independent. f and g are independent of each other by assumption. Suppose: $$\sum_{i=0}^n{\lambda_i x^i} = a f(x) +bg(x)$$ Then taking inner products on both sides with f and g implies $a = b=0$.	2021-05-15 18:28:26	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9348461627960205, "perplexity": 139.5361046724469}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243990551.51/warc/CC-MAIN-20210515161657-20210515191657-00264.warc.gz"}
http://physics.aps.org/articles/v2/108	# Viewpoint: Warping the cone on a Topological Insulator Physics 2, 108 The energy-momentum relationship of electrons on the surface of an ideal topological insulator forms a cone, which, when warped, can lead to unusual phenomena such as enhanced interference around defects and a magnetically ordered exotic surface. Unlike common ordered states of matter such as the crystalline solids and magnets characterized by some broken symmetry, the topological states of quantum matter are characterized by boundary properties that are highly robust or stable in the presence of disorder, fluctuations, and perturbations [1, 2]. The first example of a two-dimensional topological insulator was provided by the quantum Hall effect in an electron gas [1], which has no distinct three-dimensional topological generalization [3, 4, 5, 6]. Recent theoretical and experimental work indicates that strong spin-orbit coupling in insulators can produce a three-dimensional topological insulator, which is a completely new state of matter [3, 5, 6, 7, 8, 9, 10, 11, 12, 13]. This state is characterized by a surface Berry’s phase, realized via an odd number of Dirac cones protected against disorder such as alloying [3, 4, 5, 6]. This is in sharp contrast to the case of graphene, which possesses an even number of Dirac cones. The thermoelectric $\text{Bi}-\text{Sb}$ alloys discovered last year provided the first example of a truly three-dimensional topological insulator [7, 8, 9]. The experimental discovery of another thermoelectric family followed—the ${\text{Bi}}_{2}{X}_{3}$ ($X=\text{Se},\text{Te}$) series—harboring the same topological insulator states with a simpler surface spectrum [10, 11, 12, 13]. The large band gap topological insulator ${\text{Bi}}_{2}{\text{Se}}_{3}$ features a nearly ideal Dirac cone [10, 12], but in the smaller band gap material ${\text{Bi}}_{2}{\text{Te}}_{3}$, with trigonal crystal potential, the cone is warped [11, 12]. Even though the cone is deformed with hexagonal symmetry, the Berry phase quantifying the topological invariant remains unchanged, consistent with its topological order [12, 13]. Now, in an article appearing in the current issue of Physical Review Letters [14], Liang Fu of Harvard University in the US presents a perturbation calculation, which yields a hexagonal modulation of the surface states analogous to the existence of a nonlinear term in the spin-orbit interaction in the bulk crystal. (See Fig. 1 for an illustration using our results of a full-potential, self-consistent computation in ${\text{Bi}}_{2}{\text{Te}}_{3}$.) This leads to a number of remarkable predictions concerning the unusual physical properties induced by the warping of the surface states, which are distinct from the simpler “hydrogen-atom” version of the topological insulator discovered previously [10]. The spin and linear momentum of an electron on the surface of a topological insulator are locked-in one-to-one, as revealed in recent spin-resolved photoemission measurements [8, 9, 12, 13]: the electron is forbidden from moving backwards or taking a “U-turn”—an effect that hinders its localization [15]. This can be realized in a real material if the spins of electrons lying on the Dirac cone, but away from the apex (the Dirac node), rotate around in a circle at the Fermi level. Spins arranged in this way lead to a geometrical quantum phase known as Berry’s phase with a value of $\pi$ [8, 12]. The work of Fu effectively shows that in the presence of a hexagonally deformed cone, the spins must acquire finite out-of-the-plane components to conserve the net value of Berry’s phase, thus preserving the bulk topological invariant. The resulting finite value of the out-of-the-plane component opens up new possibilities for observing spectacular quantum effects. Fascinating classes of new particles such as a Majorana fermion, or a magnetic monopole image, or a massive spin-textured Dirac particle can live on the surface of a topological insulator if a finite gap can be induced in the surface band with the chemical potential near the Dirac node [3, 4, 5, 6, 16]. One approach is to create an interface between the topological insulator and a more conventional material such as a magnet or a superconductor, which can induce an energy gap in the Dirac bands. Alternatively, a magnetic field can be applied perpendicular to the sample surface. Until now it had been thought that a parallel magnetic field would neither open a gap nor lead to a surface Hall effect. However, when the surface states are warped significantly in a truly bulk insulating sample, as the work of Fu shows, a parallel magnetic field would open up a gap in the surface spectrum, enabling quantum Hall experiments to be carried out using relatively modest magnetic fields (less than $7$ tesla) accessible in a typical laboratory setting. This is an exciting prospect since such experiments have so far not been possible because very high magnetic fields are needed for opening a gap. In a truly bulk insulating sample, where the chemical potential is such that the hexagonal warping of the Fermi surface survives, one would expect to see a rare realization of the quantum Hall effect on the surface without the presence of Landau levels. In this way, one could observe a half-integer quantum of conductance per surface, which has not been possible so far in any known two-dimensional electron gas, including graphene, and thus allow experimental tests of currently debated scenarios for unusual antilocalization-to-localization transitions on a topological insulator [5]. Presently realized ${\text{Bi}}_{2}{\text{Te}}_{3}$ is quite bulk-metallic with small resistivity [11, 12], whereas spin-orbit insulators with high bulk resistivity values coupled with surface carrier control are needed to realize a functional topological insulator with which many more interesting experiments could be possible. Recent progress in making highly resistive ${\text{Bi}}_{2}{\text{Se}}_{3}$ [12, 17] coupled with surface carrier control [18] heralds the potential dawn of a topological revolution. Similar improvements in sample resistivity are also called for in ${\text{Bi}}_{2}{\text{Te}}_{3}$. The hexagonal warping of the surface cone and the resulting deviations from a circular Fermi surface provide a natural explanation for the enhanced magnitude of surface electronic interference effects recently reported around crystalline defects in ${\text{Bi}}_{2}{\text{Te}}_{3}$ [19, 20]. For a circular Fermi surface (Fig. 1, left), the electronic states at the Fermi surface cannot backscatter since in a fully spin-polarized band [12, 13] a consequence of time-reversal symmetry is that there are no available states into which electrons can scatter elastically. As a result, interference effects around the defects are small. With hexagonal warping, however, new electronic scattering channels open up, connected by various simple nesting vectors on the Fermi surface (see Fig. 1), and consistent with recent scanning tunneling measurements, the scattering due to defects becomes enhanced [19, 20]. The ideal topological insulators displaying a perfect Dirac cone dispersion cannot support the formation of charge- or spin-density waves. However, in the presence of hexagonal or other forms of deformations of the surface band, such ubiquitous ordering instabilities are no longer forbidden, but rather present a competing ground state, which can circumvent the topological protection. Since electrons with opposite momenta possess opposite spins, a spin-density-wave state is favored if the Fermi surface has parallel segments that can be nested, as is seen to be the case for hexagonal deformation (see Fig 1, right). As one goes around the hexagonal Fermi surface, electrons will experience rapid changes in the out-of-the-plane spin component (${\sigma }_{z}$) to maintain their overall Berry’s phase value at $\pi$ [8, 12], making the resulting spin-density wave appear quite exotic. A stripelike one-dimensional order on the topological surface may also be energetically possible. Even more complex spin-density-wave orderings could be supported by other topological insulators that presently lack a tractable theoretical model. For example, ${\text{Bi}}_{1-x}{\text{Sb}}_{x}$ alloys display a central hexagonally deformed Dirac cone and additional surface states of complex character [8]. Despite the complexity of its five surface bands and hexagonal warping, the ${\text{Bi}}_{1-x}{\text{Sb}}_{x}$ alloy topological insulator precisely exhibits $\pi$ Berry’s phase and antilocalization just like the “hydrogen-atom” single-surface-Dirac-cone systems [8, 10, 12]. This is a remarkable manifestation and demonstration of a deep and profound principle of physics—topological invariance. Thus the power and beauty of the topological order and invariance in nature are rather firmly established by studying systems that have complex “geometries,” i.e., complex and warped surface states as in the ${\text{Bi}}_{1-x}{\text{Sb}}_{x}$ alloy series or ${\text{Bi}}_{2}{\text{Te}}_{3}$. The most remarkable property of topological surface states is that they are expected to be perfect metals in the sense that they are robust and stable against most perturbations and instabilities towards conventional ordered states of matter. The warping of the surface states, even though it opens up interesting possibilities for studying this unusual state of matter in detail, ironically also opens up competing channels which provide a route for departure from the much sought after paradigm of perfect topological stability of the spin-textured metal [3, 4]. Most topological insulators lying hidden in nature are likely to harbor complex and warped surface states as in ${\text{Bi}}_{1-x}{\text{Sb}}_{x}$ and ${\text{Bi}}_{2}{\text{Te}}_{3}$. Interestingly, even though the first three-dimensional topological insulators and their spin-textures carrying nontrivial Berry’s phases were discovered only recently, we already have new materials emerging with physical properties lying in a regime where quantum effects associated with competing orders such as the spin-density waves can be foreseen. Parallel progress in theoretical modeling, hand-in-hand with experimental advances in spin-sensitive measurement methods, will likely be essential for unraveling and eventually exploiting the exotic spin textures [21, 22] and other beautiful properties of topological quantum matter. ## References 1. K. von Klitzing, G. Dorda, and M. Pepper, Phys. Rev. Lett. 45, 494 (1980) 2. R. B. Laughlin, Phys. Rev. Lett. 50, 1395 (1983) 3. L. Fu, C. L. Kane, and E. J. Mele, Phys. Rev. Lett. 98, 106803 (2007) 4. J. E. Moore and L. Balents, Phys. Rev. B 75, 121306 (2007) 5. A. P. Schnyder, S. Ryu, A. Furusaki, and A. W. W. Ludwig, Phys. Rev. B 78, 195125 (2008) 6. X. L. Qi, T. L. Hughes, and S.-C. Zhang, Phys. Rev. B 78, 195424 (2008) 7. D. Hsieh, D. Qian, L. Wray, Y. Xia, Y. S. Hor, R. J. Cava, and M. Z. Hasan, Nature 452, 970 (2008) 8. D. Hsieh, Y. Xia, L. Wray, D. Qian, A. Pal, J. H. Dil, J. Osterwalder, F. Meier, G. Bihlmayer, C. L. Kane, Y. S. Hor, R. J. Cava, and M. Z. Hasan, Science 323, 919 (2009) 9. A. Nishide, A. A. Taskin, Y. Takeichi, T. Okuda, A. Kakizaki, T. Hirahara, K. Nakatsuji, F. Komori, Y. Ando, and I. Matsuda, arXiv:0902.2251 10. Y. Xia, D. Qian, D. Hsieh, L. Wray, A. Pal, H. Lin, A. Bansil, D. Grauer, Y. S. Hor, R. J. Cava, and M. Z. Hasan, Nature Phys. 5, 398 (2009) 11. Y. L. Chen, J. G. Analytis, J.-H. Chu, Z. K. Liu, S.-K. Mo, X. L. Qi, H. J. Zhang, D. H. Lu, X. Dai, Z. Fang, S. C. Zhang, I. R. Fisher, Z. Hussain, and Z.-X. Shen, Science 325, 178 (2009) 12. D. Hsieh, Y. Xia, D. Qian, L. Wray, J. H. Dil, F. Meier, J. Osterwalder, L. Patthey, J. G. Checkelsky, N. P. Ong, A. V. Fedorov, H. Lin, A. Bansil, D. Grauer, Y. S. Hor, R. J. Cava, and M. Z. Hasan, Nature 460, 1101 (2009) 13. D. Hsieh, Y. Xia, D. Qian, L. Wray, F. Meier, J. H. Dil, J. Osterwalder, L. Patthey, A. V. Fedorov, H. Lin, A. Bansil, D. Grauer, Y. S. Hor, R. J. Cava, and M. Z. Hasan, Phys. Rev. Lett. 103, 146401 (2009) 14. P. Roushan, J. Seo, C. V. Parker, Y. S. Hor, D. Hsieh, D. Qian, A. Richardella, M. Z. Hasan, R. J. Cava, and A. Yazdani, Nature 460, 1106 (2009) 15. L. Fu and C. L. Kane, Phys. Rev. Lett. 100, 096407 (2008) 16. J. G. Checkelsky, Y. S. Hor, M.-H. Liu, D.-X. Qu, R. J. Cava, and N. P. Ong, Phys. Rev. Lett. 103, 246601 (2009) 17. Y. Xia, D. Qian, D. Hsieh, R. Shankar, H. Lin, A. Bansil, A.V. Fedorov, D. Grauer, Y.S. Hor, R.J. Cava, and M.Z. Hasan, arXiv:0907.3089 18. Z. Alpichshev, J. G. Analytis, J.-H. Chu, I. R. Fisher, Y. L. Chen, Z. X. Shen, A. Fang, and A. Kapitulnik, arXiv:0908.0371 19. T. Zhang, P. Cheng, X. Chen, J.-F. Jia, X. Ma, K. He, L. Wang, H. Zhang, X. Dai, Z. Fang, X. Xie, and Q.-K. Xue, arXiv:0908.4136 20. H. Zhang, C.-X. Liu, X.-L. Qi, X. Dai, Z. Fang, and S.-C. Zhang, Nature Phys 5, 438 (2009) M. Zahid Hasan is an Associate Professor of Physics at Princeton University. He obtained his Ph.D. in 2002 from Stanford University, working at SLAC and Brookhaven National Laboratory. He was then a Robert H. Dicke Fellow in fundamental physics at Princeton and held several extended visiting appointments at Bell Laboratories (Murray Hill) and Lawrence Berkeley National Laboratory before joining the Faculty at Princeton. His research has focused on quantum Hall-like topological phases, exotic correlated superconductors, quantum phase transitions, and topological quantum computing physics. In recent years, he, along with his team, has experimentally discovered topological-order in bulk solids (3D topological insulators) including the single-Dirac-cone series using spin-resolved and phase-sensitive spectroscopic measurements. Hsin Lin is a Postdoctoral Research Associate in Professor Bansil’s group in the Department of Physics at Northeastern University, where he received his Ph.D. in 2008. He obtained his M.S. degree from National Tsing Hua University and B.S. degree from National Taiwan University. His research focuses on the electronic structure and spectroscopy of exotic quantum states of matter such as topological insulators, high temperature superconductors, and colossal magnetoresistance materials. Based on first-principles calculations and realistic tight-binding modeling, he is working to elucidate generalized matrix element effects in various spectroscopies. Arun Bansil received his Ph.D. from Harvard in 1974 and joined the physics faculty at Northeastern University (NU) in 1976. Currently, he is serving on a two-year appointment at the US Department of Energy managing the Theoretical Condensed Matter Physics program. In 1994 he was appointed the US editor of the Journal of Physics and Chemistry of Solids. In 2002, he was also appointed a professor in the School of Education at NU in recognition of his educational/outreach contributions. He is an honorary professor in Solid State Theory at Tampere University of Technology in Finland, a guest senior scientist at Lawrence Berkeley National Laboratory, a scientific consultant at the Netherlands Energy Research Foundation, and a resident associate at Argonne National Laboratory. He was awarded the 2002 Robert D. Klein Lectureship at NU for his scholarly accomplishments. His research has focused on the electronic structure and spectroscopy of complex ordered and disordered systems, including novel superconductors, manganites, and topological insulators. He has developed theoretical methodology for realistic modeling of various highly resolved spectroscopies such as angle-resolved photoemission, scanning tunneling spectroscopy, inelastic light scattering, and positron-annihilation in wide classes of materials. ## Subject Areas Semiconductor Physics ## Related Articles Semiconductor Physics ### Viewpoint: Chasing the Exciton Condensate Unusual interactions between charges have been observed in two closely separated graphene bilayers, a promising system in which to create a condensate of electron-hole pairs. Read More » Semiconductor Physics ### Viewpoint: Precise Layering of Organic Semiconductors Researchers have fabricated high-quality organic semiconductors only a few molecular layers thick, revealing how the crystal structure affects the electronic properties. Read More » Plasmonics ### Viewpoint: All Together Now A “Schrödinger’s cat”-type effect entangles collective excitations in a semiconductor nanostructure, making a new infrared light source. Read More »	2016-09-25 00:24:33	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 25, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7070766687393188, "perplexity": 2496.2161977748665}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-40/segments/1474738659680.65/warc/CC-MAIN-20160924173739-00003-ip-10-143-35-109.ec2.internal.warc.gz"}
http://www.formuladirectory.com/user/formula/148	HOSTING A TOTAL OF 318 FORMULAS WITH CALCULATORS ## Future Value For Annuity Payment It is used to calculate the cash flows of an annuity when future value is known. An annuity is denoted as a series of periodic payments. The annuity payment formula shown here is specifically used when the future value is known, as opposed to the annuity payment formula used when present value is known. There are not only mathematical differences between calculating an annuity when present value is known and when future value is known, but also differences in the real life application of the formulas. ## $\frac{\mathrm{vr}}{\left[1+r{\right]}^{n}-1}$ Here,v=future value,r=rate per period,n=number of periods. ENTER THE VARIABLES TO BE USED IN THE FORMULA Similar formulas which you may find interesting.	2018-10-24 04:08:59	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 1, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7801584601402283, "perplexity": 748.2336948911345}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583518753.75/warc/CC-MAIN-20181024021948-20181024043448-00293.warc.gz"}
https://howlingpixel.com/i-en/Cryptographic_hash_function	Cryptographic hash function A cryptographic hash function is a special class of hash function that has certain properties which make it suitable for use in cryptography. It is a mathematical algorithm that maps data of arbitrary size to a bit string of a fixed size (a hash) and is designed to be a one-way function, that is, a function which is infeasible to invert.[1] The only way to recreate the input data from an ideal cryptographic hash function's output is to attempt a brute-force search of possible inputs to see if they produce a match, or use a rainbow table of matched hashes. Bruce Schneier has called one-way hash functions "the workhorses of modern cryptography".[2] The input data is often called the message, and the output (the hash value or hash) is often called the message digest or simply the digest. The ideal cryptographic hash function has five main properties: • it is deterministic so the same message always results in the same hash • it is quick to compute the hash value for any given message • it is infeasible to generate a message from its hash value except by trying all possible messages • a small change to a message should change the hash value so extensively that the new hash value appears uncorrelated with the old hash value • it is infeasible to find two different messages with the same hash value Cryptographic hash functions have many information-security applications, notably in digital signatures, message authentication codes (MACs), and other forms of authentication. They can also be used as ordinary hash functions, to index data in hash tables, for fingerprinting, to detect duplicate data or uniquely identify files, and as checksums to detect accidental data corruption. Indeed, in information-security contexts, cryptographic hash values are sometimes called (digital) fingerprints, checksums, or just hash values, even though all these terms stand for more general functions with rather different properties and purposes. Secure Hash Algorithms Concepts hash functions · SHA · DSA Main standards SHA-0 · SHA-1 · SHA-2 · SHA-3 A cryptographic hash function (specifically SHA-1) at work. A small change in the input (in the word "over") drastically changes the output (digest). This is the so-called avalanche effect. Properties Most cryptographic hash functions are designed to take a string of any length as input and produce a fixed-length hash value. A cryptographic hash function must be able to withstand all known types of cryptanalytic attack. In theoretical cryptography, the security level of a cryptographic hash function has been defined using the following properties: • Pre-image resistance Given a hash value h it should be difficult to find any message m such that h = hash(m). This concept is related to that of a one-way function. Functions that lack this property are vulnerable to preimage attacks. • Second pre-image resistance Given an input m1, it should be difficult to find a different input m2 such that hash(m1) = hash(m2). Functions that lack this property are vulnerable to second-preimage attacks. • Collision resistance It should be difficult to find two different messages m1 and m2 such that hash(m1) = hash(m2). Such a pair is called a cryptographic hash collision. This property is sometimes referred to as strong collision resistance. It requires a hash value at least twice as long as that required for pre-image resistance; otherwise collisions may be found by a birthday attack.[3] Collision resistance implies second pre-image resistance, but does not imply pre-image resistance.[4] The weaker assumption is always preferred in theoretical cryptography, but in practice, a hash-function which is only second pre-image resistant is considered insecure and is therefore not recommended for real applications. Informally, these properties mean that a malicious adversary cannot replace or modify the input data without changing its digest. Thus, if two strings have the same digest, one can be very confident that they are identical. Second pre-image resistance prevents an attacker from crafting a document with the same hash as a document the attacker cannot control. Collision resistance prevents an attacker from creating two distinct documents with the same hash. A function meeting these criteria may still have undesirable properties. Currently popular cryptographic hash functions are vulnerable to length-extension attacks: given hash(m) and len(m) but not m, by choosing a suitable m' an attacker can calculate hash(m \|\| m') where \|\| denotes concatenation.[5] This property can be used to break naive authentication schemes based on hash functions. The HMAC construction works around these problems. In practice, collision resistance is insufficient for many practical uses. In addition to collision resistance, it should be impossible for an adversary to find two messages with substantially similar digests; or to infer any useful information about the data, given only its digest. In particular, a hash function should behave as much as possible like a random function (often called a random oracle in proofs of security) while still being deterministic and efficiently computable. This rules out functions like the SWIFFT function, which can be rigorously proven to be collision resistant assuming that certain problems on ideal lattices are computationally difficult, but as a linear function, does not satisfy these additional properties.[6] Checksum algorithms, such as CRC32 and other cyclic redundancy checks, are designed to meet much weaker requirements, and are generally unsuitable as cryptographic hash functions. For example, a CRC was used for message integrity in the WEP encryption standard, but an attack was readily discovered which exploited the linearity of the checksum. Degree of difficulty In cryptographic practice, "difficult" generally means "almost certainly beyond the reach of any adversary who must be prevented from breaking the system for as long as the security of the system is deemed important". The meaning of the term is therefore somewhat dependent on the application since the effort that a malicious agent may put into the task is usually proportional to his expected gain. However, since the needed effort usually multiplies with the digest length, even a thousand-fold advantage in processing power can be neutralized by adding a few dozen bits to the latter. For messages selected from a limited set of messages, for example passwords or other short messages, it can be feasible to invert a hash by trying all possible messages in the set. Because cryptographic hash functions are typically designed to be computed quickly, special key derivation functions that require greater computing resources have been developed that make such brute force attacks more difficult. In some theoretical analyses "difficult" has a specific mathematical meaning, such as "not solvable in asymptotic polynomial time". Such interpretations of difficulty are important in the study of provably secure cryptographic hash functions but do not usually have a strong connection to practical security. For example, an exponential time algorithm can sometimes still be fast enough to make a feasible attack. Conversely, a polynomial time algorithm (e.g., one that requires n20 steps for n-digit keys) may be too slow for any practical use. Illustration An illustration of the potential use of a cryptographic hash is as follows: Alice poses a tough math problem to Bob and claims she has solved it. Bob would like to try it himself, but would yet like to be sure that Alice is not bluffing. Therefore, Alice writes down her solution, computes its hash and tells Bob the hash value (whilst keeping the solution secret). Then, when Bob comes up with the solution himself a few days later, Alice can prove that she had the solution earlier by revealing it and having Bob hash it and check that it matches the hash value given to him before. (This is an example of a simple commitment scheme; in actual practice, Alice and Bob will often be computer programs, and the secret would be something less easily spoofed than a claimed puzzle solution). Applications Verifying the integrity of messages and files An important application of secure hashes is verification of message integrity. Comparing message digests (hash digests over the message) calculated before, and after, transmission can determine whether any changes have been made to the message or file. MD5, SHA1, or SHA2 hash digests are sometimes published on websites or forums to allow verification of integrity for downloaded files,[7] including files retrieved using file sharing such as mirroring. This practice establishes a chain of trust so long as the hashes are posted on a site authenticated by HTTPS. Using a cryptographic hash and a chain of trust prevents malicious changes to the file to go undetected. Other error detecting codes such as cyclic redundancy checks only prevent against non-malicious alterations of the file. Signature generation and verification Almost all digital signature schemes require a cryptographic hash to be calculated over the message. This allows the signature calculation to be performed on the relatively small, statically sized hash digest. The message is considered authentic if the signature verification succeeds given the signature and recalculated hash digest over the message. So the message integrity property of the cryptographic hash is used to create secure and efficient digital signature schemes. Password verification commonly relies on cryptographic hashes. Storing all user passwords as cleartext can result in a massive security breach if the password file is compromised. One way to reduce this danger is to only store the hash digest of each password. To authenticate a user, the password presented by the user is hashed and compared with the stored hash. A password reset method is required when password hashing is performed; original passwords cannot be recalculated from the stored hash value. Standard cryptographic hash functions are designed to be computed quickly, and, as a result, it is possible to try guessed passwords at high rates. Common graphics processing units can try billions of possible passwords each second. Password hash functions that perform Key stretching - such as PBKDF2, scrypt or Argon2 - commonly use repeated invocations of a cryptographic hash to increase the time (and in some cases computer memory) required to perform brute force attacks on stored password hash digests. A password hash requires the use of a large random, non-secret salt value which can be stored with the password hash. The salt randomizes the output of the password hash, making it impossible for an adversary to store tables of passwords and precomputed hash values to which the password hash digest can be compared. The output of a password hash function can also be used as a cryptographic key. Password hashes are therefore also known as Password Based Key Derivation Functions (PBKDFs). Proof-of-work A proof-of-work system (or protocol, or function) is an economic measure to deter denial-of-service attacks and other service abuses such as spam on a network by requiring some work from the service requester, usually meaning processing time by a computer. A key feature of these schemes is their asymmetry: the work must be moderately hard (but feasible) on the requester side but easy to check for the service provider. One popular system – used in Bitcoin mining and Hashcash – uses partial hash inversions to prove that work was done, to unlock a mining reward in Bitcoin and as a good-will token to send an e-mail in Hashcash. The sender is required to find a message whose hash value begins with a number of zero bits. The average work that sender needs to perform in order to find a valid message is exponential in the number of zero bits required in the hash value, while the recipient can verify the validity of the message by executing a single hash function. For instance, in Hashcash, a sender is asked to generate a header whose 160 bit SHA-1 hash value has the first 20 bits as zeros. The sender will on average have to try 219 times to find a valid header. File or data identifier A message digest can also serve as a means of reliably identifying a file; several source code management systems, including Git, Mercurial and Monotone, use the sha1sum of various types of content (file content, directory trees, ancestry information, etc.) to uniquely identify them. Hashes are used to identify files on peer-to-peer filesharing networks. For example, in an ed2k link, an MD4-variant hash is combined with the file size, providing sufficient information for locating file sources, downloading the file and verifying its contents. Magnet links are another example. Such file hashes are often the top hash of a hash list or a hash tree which allows for additional benefits. One of the main applications of a hash function is to allow the fast look-up of a data in a hash table. Being hash functions of a particular kind, cryptographic hash functions lend themselves well to this application too. However, compared with standard hash functions, cryptographic hash functions tend to be much more expensive computationally. For this reason, they tend to be used in contexts where it is necessary for users to protect themselves against the possibility of forgery (the creation of data with the same digest as the expected data) by potentially malicious participants. Hash functions based on block ciphers There are several methods to use a block cipher to build a cryptographic hash function, specifically a one-way compression function. The methods resemble the block cipher modes of operation usually used for encryption. Many well-known hash functions, including MD4, MD5, SHA-1 and SHA-2 are built from block-cipher-like components designed for the purpose, with feedback to ensure that the resulting function is not invertible. SHA-3 finalists included functions with block-cipher-like components (e.g., Skein, BLAKE) though the function finally selected, Keccak, was built on a cryptographic sponge instead. A standard block cipher such as AES can be used in place of these custom block ciphers; that might be useful when an embedded system needs to implement both encryption and hashing with minimal code size or hardware area. However, that approach can have costs in efficiency and security. The ciphers in hash functions are built for hashing: they use large keys and blocks, can efficiently change keys every block, and have been designed and vetted for resistance to related-key attacks. General-purpose ciphers tend to have different design goals. In particular, AES has key and block sizes that make it nontrivial to use to generate long hash values; AES encryption becomes less efficient when the key changes each block; and related-key attacks make it potentially less secure for use in a hash function than for encryption. Hash function design Merkle–Damgård construction The Merkle–Damgård hash construction. A hash function must be able to process an arbitrary-length message into a fixed-length output. This can be achieved by breaking the input up into a series of equal-sized blocks, and operating on them in sequence using a one-way compression function. The compression function can either be specially designed for hashing or be built from a block cipher. A hash function built with the Merkle–Damgård construction is as resistant to collisions as is its compression function; any collision for the full hash function can be traced back to a collision in the compression function. The last block processed should also be unambiguously length padded; this is crucial to the security of this construction. This construction is called the Merkle–Damgård construction. Most common classical hash functions, including SHA-1 and MD5, take this form. Wide pipe vs narrow pipe A straightforward application of the Merkle–Damgård construction, where the size of hash output is equal to the internal state size (between each compression step), results in a narrow-pipe hash design. This design causes many inherent flaws, including length-extension, multicollisions,[8] long message attacks,[9] generate-and-paste attacks, and also cannot be parallelized. As a result, modern hash functions are built on wide-pipe constructions that have a larger internal state size — which range from tweaks of the Merkle–Damgård construction[8] to new constructions such as the sponge construction and HAIFA construction.[10] None of the entrants in the NIST hash function competition use a classical Merkle–Damgård construction.[11] Meanwhile, truncating the output of a longer hash, such as used in SHA-512/256, also defeats many of these attacks.[12] Use in building other cryptographic primitives Hash functions can be used to build other cryptographic primitives. For these other primitives to be cryptographically secure, care must be taken to build them correctly. Message authentication codes (MACs) (also called keyed hash functions) are often built from hash functions. HMAC is such a MAC. Just as block ciphers can be used to build hash functions, hash functions can be used to build block ciphers. Luby-Rackoff constructions using hash functions can be provably secure if the underlying hash function is secure. Also, many hash functions (including SHA-1 and SHA-2) are built by using a special-purpose block cipher in a Davies–Meyer or other construction. That cipher can also be used in a conventional mode of operation, without the same security guarantees. See SHACAL, BEAR and LION. Pseudorandom number generators (PRNGs) can be built using hash functions. This is done by combining a (secret) random seed with a counter and hashing it. Some hash functions, such as Skein, Keccak, and RadioGatún output an arbitrarily long stream and can be used as a stream cipher, and stream ciphers can also be built from fixed-length digest hash functions. Often this is done by first building a cryptographically secure pseudorandom number generator and then using its stream of random bytes as keystream. SEAL is a stream cipher that uses SHA-1 to generate internal tables, which are then used in a keystream generator more or less unrelated to the hash algorithm. SEAL is not guaranteed to be as strong (or weak) as SHA-1. Similarly, the key expansion of the HC-128 and HC-256 stream ciphers makes heavy use of the SHA-256 hash function. Concatenation Concatenating outputs from multiple hash functions provides collision resistance as good as the strongest of the algorithms included in the concatenated result. For example, older versions of Transport Layer Security (TLS) and Secure Sockets Layer (SSL) use concatenated MD5 and SHA-1 sums.[13][14] This ensures that a method to find collisions in one of the hash functions does not defeat data protected by both hash functions. For Merkle–Damgård construction hash functions, the concatenated function is as collision-resistant as its strongest component, but not more collision-resistant. Antoine Joux observed that 2-collisions lead to n-collisions: if it is feasible for an attacker to find two messages with the same MD5 hash, the attacker can find as many messages as the attacker desires with identical MD5 hashes with no greater difficulty.[15] Among the n messages with the same MD5 hash, there is likely to be a collision in SHA-1. The additional work needed to find the SHA-1 collision (beyond the exponential birthday search) requires only polynomial time.[16][17] Cryptographic hash algorithms There are many cryptographic hash algorithms; this section lists a few algorithms that are referenced relatively often. A more extensive list can be found on the page containing a comparison of cryptographic hash functions. MD5 MD5 was designed by Ronald Rivest in 1991 to replace an earlier hash function MD4, and was specified in 1992 as RFC 1321. Collisions against MD5 can be calculated within seconds which makes the algorithm unsuitable for most use cases where a cryptographic hash is required. MD5 produces a digest of 128 bits (16 bytes). SHA-1 SHA-1 was developed as part of the U.S. Government's Capstone project. The original specification - now commonly called SHA-0 - of the algorithm was published in 1993 under the title Secure Hash Standard, FIPS PUB 180, by U.S. government standards agency NIST (National Institute of Standards and Technology). It was withdrawn by the NSA shortly after publication and was superseded by the revised version, published in 1995 in FIPS PUB 180-1 and commonly designated SHA-1. Collisions against the full SHA-1 algorithm can be produced using the shattered attack and the hash function should be considered broken. SHA-1 produces a hash digest of 160 bits (20 bytes). Documents may refer to SHA-1 as just "SHA", even though this may conflict with the other Standard Hash Algorithms such as SHA-0, SHA-2 and SHA-3. RIPEMD-160 RIPEMD (RACE Integrity Primitives Evaluation Message Digest) is a family of cryptographic hash functions developed in Leuven, Belgium, by Hans Dobbertin, Antoon Bosselaers and Bart Preneel at the COSIC research group at the Katholieke Universiteit Leuven, and first published in 1996. RIPEMD was based upon the design principles used in MD4, and is similar in performance to the more popular SHA-1. RIPEMD-160 has however not been broken. As the name implies, RIPEMD-160 produces a hash digest of 160 bits (20 bytes). Whirlpool In computer science and cryptography, Whirlpool is a cryptographic hash function. It was designed by Vincent Rijmen and Paulo S. L. M. Barreto, who first described it in 2000. Whirlpool is based on a substantially modified version of the Advanced Encryption Standard (AES). Whirlpool produces a hash digest of 512 bits (64 bytes). SHA-2 SHA-2 (Secure Hash Algorithm 2) is a set of cryptographic hash functions designed by the United States National Security Agency (NSA), first published in 2001.[3] They are built using the Merkle–Damgård structure, from a one-way compression function itself built using the Davies–Meyer structure from a (classified) specialized block cipher. SHA-2 basically consists of two hash algorithms: SHA-256 and SHA-512. SHA-224 is a variant of SHA-256 with different starting values and truncated output. SHA-384 and the lesser known SHA-512/224 and SHA-512/256 are all variants of SHA-512. SHA-512 is more secure than SHA-256 and is commonly faster than SHA-256 on 64 bit machines such as AMD64. The output size in bits is given by the extension to the "SHA" name, so SHA-224 has an output size of 224 bits (28 bytes), SHA-256 produces 32 bytes, SHA-384 produces 48 bytes and finally SHA-512 produces 64 bytes. SHA-3 SHA-3 (Secure Hash Algorithm 3) was released by NIST on August 5, 2015. SHA-3 is a subset of the broader cryptographic primitive family Keccak. The Keccak algorithm is the work of Guido Bertoni, Joan Daemen, Michael Peeters, and Gilles Van Assche. Keccak is based on a sponge construction which can also be used to build other cryptographic primitives such as a stream cipher. SHA-3 provides the same output sizes as SHA-2: 224, 256, 384 and 512 bits. Configurable output sizes can also be obtained using the SHAKE-128 and SHAKE-256 functions. Here the -128 and -256 extensions to the name imply the security strength of the function rather than the output size in bits. BLAKE2 An improved version of BLAKE called BLAKE2 was announced in December 21, 2012. It was created by Jean-Philippe Aumasson, Samuel Neves, Zooko Wilcox-O'Hearn, and Christian Winnerlein with the goal to replace widely used, but broken MD5 and SHA-1 algorithms. When run on 64-bit x64 and ARM architectures, BLAKE2b is faster than SHA-3, SHA-2, SHA-1, and MD5. Although BLAKE nor BLAKE2 have not been standardized as SHA-3 it has been used in many protocols including the Argon2 password hash for the high efficiency that it offers on modern CPUs. As BLAKE was a candidate for SHA-3, BLAKE and BLAKE2 both offer the same output sizes as SHA-3 - including a configurable output size. Attacks on cryptographic hash algorithms There is a long list of cryptographic hash functions but many have been found to be vulnerable and should not be used. For instance, NIST selected 51 hash functions[18] as candidates for round 1 of the SHA-3 hash competition, of which 10 were considered broken and 16 showed significant weaknesses and therefore didn't make it to the next round; more information can be found on the main article about the NIST hash function competitions. Even if a hash function has never been broken, a successful attack against a weakened variant may undermine the experts' confidence. For instance, in August 2004 collisions were found in several then-popular hash functions, including MD5.[19] These weaknesses called into question the security of stronger algorithms derived from the weak hash functions—in particular, SHA-1 (a strengthened version of SHA-0), RIPEMD-128, and RIPEMD-160 (both strengthened versions of RIPEMD). On 12 August 2004, Joux, Carribault, Lemuet, and Jalby announced a collision for the full SHA-0 algorithm. Joux et al. accomplished this using a generalization of the Chabaud and Joux attack. They found that the collision had complexity 251 and took about 80,000 CPU hours on a supercomputer with 256 Itanium 2 processors—equivalent to 13 days of full-time use of the supercomputer. In February 2005, an attack on SHA-1 was reported that would find collision in about 269 hashing operations, rather than the 280 expected for a 160-bit hash function. In August 2005, another attack on SHA-1 was reported that would find collisions in 263 operations. Other theoretical weaknesses of SHA-1 have been known:[20][21] and in February 2017 Google announced a collision in SHA-1.[22] Security researchers recommend that new applications can avoid these problems by using later members of the SHA family, such as SHA-2, or using techniques such as randomized hashing[23][1] that do not require collision resistance. A successful, practical attack broke MD5 used within certificates for Transport Layer Security in 2008.[24] Many cryptographic hashes are based on the Merkle–Damgård construction. All cryptographic hashes that directly use the full output of a Merkle–Damgård construction are vulnerable against length extension attacks. This makes the MD5, SHA-1, RIPEMD-160, Whirlpool and the SHA-256 / SHA-512 hash algorithms all vulnerable against this specific attack. SHA-3, BLAKE2 and the truncated SHA-2 variants are not vulnerable against this type of attack. Avalanche effect Comparison of cryptographic hash functions CRYPTREC and NESSIE – projects that recommend hash functions Hash chain Hash-based message authentication code Length extension attack Random oracle References 1. ^ a b Shai Halevi and Hugo Krawczyk, Randomized Hashing and Digital Signatures 2. ^ Schneier, Bruce. "Cryptanalysis of MD5 and SHA: Time for a New Standard". Computerworld. Retrieved 2016-04-20. Much more than encryption algorithms, one-way hash functions are the workhorses of modern cryptography. 3. ^ Katz, Jonathan; Lindell, Yehuda (2008). Introduction to Modern Cryptography. Chapman & Hall/CRC. 4. ^ Rogaway & Shrimpton 2004, in Sec. 5. Implications. 5. ^ "Flickr's API Signature Forgery Vulnerability". Thai Duong and Juliano Rizzo. 6. ^ Lyubashevsky, Vadim and Micciancio, Daniele and Peikert, Chris and Rosen, Alon (2008). "SWIFFT: A Modest Proposal for FFT Hashing". Fast Software Encryption. Lecture Notes in Computer Science. 5086. Springer. pp. 54–72. doi:10.1007/978-3-540-71039-4_4. ISBN 978-3-540-71038-7.CS1 maint: Multiple names: authors list (link) 7. ^ Perrin, Chad (December 5, 2007). "Use MD5 hashes to verify software downloads". TechRepublic. Retrieved March 2, 2013. 8. ^ a b Lucks, Stefan (2004). "Design Principles for Iterated Hash Functions" – via Cryptology ePrint Archive, Report 2004/253. 9. ^ Kelsey, John; Schneier, Bruce (2004). "Second Preimages on n-bit Hash Functions for Much Less than 2^n Work" – via Cryptology ePrint Archive: Report 2004/304. 10. ^ Biham, Eli; Dunkelman, Orr (24 August 2006). A Framework for Iterative Hash Functions – HAIFA. Second NIST Cryptographic Hash Workshop – via Cryptology ePrint Archive: Report 2007/278. 11. ^ Nandi, Mridul; Paul, Souradyuti (2010). "Speeding Up The Widepipe: Secure and Fast Hashing" – via Cryptology ePrint Archive: Report 2010/193. 12. ^ Dobraunig, Christoph; Eichlseder, Maria; Mendel, Florian (February 2015). "Security Evaluation of SHA-224, SHA-512/224, and SHA-512/256" (PDF). 13. ^ Florian Mendel; Christian Rechberger; Martin Schläffer. "MD5 is Weaker than Weak: Attacks on Concatenated Combiners". "Advances in Cryptology – ASIACRYPT 2009". p. 145. quote: 'Concatenating ... is often used by implementors to "hedge bets" on hash functions. A combiner of the form MD5\|\|SHA-1 as used in SSL3.0/TLS1.0 ... is an example of such a strategy.' 14. ^ Danny Harnik; Joe Kilian; Moni Naor; Omer Reingold; Alon Rosen. "On Robust Combiners for Oblivious Transfer and Other Primitives". "Advances in Cryptology – EUROCRYPT 2005". quote: "the concatenation of hash functions as suggested in the TLS... is guaranteed to be as secure as the candidate that remains secure." p. 99. 15. ^ Antoine Joux. Multicollisions in Iterated Hash Functions. Application to Cascaded Constructions. LNCS 3152/2004, pages 306–316 Full text. 16. ^ Finney, Hal (August 20, 2004). "More Problems with Hash Functions". The Cryptography Mailing List. Retrieved May 25, 2016. 17. ^ Hoch, Jonathan J.; Shamir, Adi (2008). "On the Strength of the Concatenated Hash Combiner when All the Hash Functions Are Weak" (PDF). Retrieved May 25, 2016. 18. ^ Andrew Regenscheid, Ray Perlner, Shu-jen Chang, John Kelsey, Mridul Nandi, Souradyuti Paul, Status Report on the First Round of the SHA-3 Cryptographic Hash Algorithm Competition 19. ^ XiaoyunWang, Dengguo Feng, Xuejia Lai, Hongbo Yu, Collisions for Hash Functions MD4, MD5, HAVAL-128 and RIPEMD 20. ^ Xiaoyun Wang, Yiqun Lisa Yin, and Hongbo Yu, Finding Collisions in the Full SHA-1 21. ^ Bruce Schneier, Cryptanalysis of SHA-1 (summarizes Wang et al. results and their implications) 22. ^ Fox-Brewster, Thomas. "Google Just 'Shattered' An Old Crypto Algorithm – Here's Why That's Big For Web Security". Forbes. Retrieved 2017-02-24. 23. ^ Shai Halevi, Hugo Krawczyk, Update on Randomized Hashing 24. ^ Alexander Sotirov, Marc Stevens, Jacob Appelbaum, Arjen Lenstra, David Molnar, Dag Arne Osvik, Benne de Weger, MD5 considered harmful today: Creating a rogue CA certificate, accessed March 29, 2009.	2019-02-16 01:28:25	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 1, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.23827628791332245, "perplexity": 2560.8077042084055}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-09/segments/1550247479729.27/warc/CC-MAIN-20190216004609-20190216030609-00059.warc.gz"}
http://math.stackexchange.com/questions/200324/matrices-of-forms-seen-as-sections-of-a-vector-bundle	# Matrices of forms seen as sections of a vector bundle Given a vector bundle $\pi: E \rightarrow M$ , what are the sections of $\Omega^p(\operatorname{End} E)$? are they just matrices whose entries are $p$-forms? - Yes, basically. Or you can think of it as $\Omega^p \otimes E \otimes E^*$ if you prefer. – Zhen Lin Sep 21 '12 at 15:16 If you write End E in $\TeX$, you'll see $End E$, with no space between. If you write \operatorname{End}E, you'll see $\operatorname{End}E$, with proper spacing and "$\operatorname{End}$" properly non-italicized. (I fixed it.) (I see that \operatorname{End}E appears above with $E$ on the next line, so you can't see the lack of space in the code. But it's there.) – Michael Hardy Sep 21 '12 at 16:36	2015-04-21 21:21:32	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9797745943069458, "perplexity": 690.6546995953537}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-18/segments/1429246643283.35/warc/CC-MAIN-20150417045723-00039-ip-10-235-10-82.ec2.internal.warc.gz"}
https://math.stackexchange.com/questions/1936212/question-about-limit-with-exponents	# Question about limit with exponents I tried to solve: $$\lim\limits_{x \to \infty} e^{x-x^2}$$ but I can't get it done. I've tried to use Hopital's rule after rewriting it to: $$\lim\limits_{x \to \infty} \frac{e^x}{e^{x^2}}$$ but this does not lead to a solition. Anyone with a good hint? • Perhaps you can invoke the continuity of the exponential function. – panini Sep 21 '16 at 20:31 • You could try finding the limit of the logarithm instead. – Mosquite Sep 21 '16 at 20:39 • Well, noting x-x^2 -> - infinity it makes sense to imagine this limit tends to 0. If I can use theorems and technics to prove it.... for large x (x > 2) I can assume -x > x - x^2 > - x^2 so I can use squeeze th. I guess. Lvhopitals rule gives me e^x/2xe^(x^2) < 1/2xx -> 0. I have options. – fleablood Sep 21 '16 at 20:41 • Hint: Just consider $\lim\limits_{x \to \infty} x-x^2$. and apply that result to your limit. You are overcomplicating this limit big time... – imranfat Sep 21 '16 at 21:00 • @fleablood Thanks, I indeed derived e^x/2xe^(x^2) but do not see how the step e^x/2xe^(x^2) -> 1/2xx is made (getting the e-power out of dominator and denominator). I also think 0 is correct; I used a graph to check. If you could explain that extra step, it would be fine. If you post it as an answer, I will upvote it. – Sjips Sep 21 '16 at 21:01 If $x > 2$ then $-x = x - 2x > x - x^2$ so $e^{x - x^2} < e^{-x}$ for $x > 2$. and $e^{x-x^2} > 0$ so $0 < \lim_{x\rightarrow \infty}e^{x - x^2}< \lim_{x\rightarrow \infty}e^{-x}= 0$. so $\lim_{x\rightarrow \infty}e^{x - x^2} = 0$. ... or .... $\frac {de^x}{dx} = e^x$, $\frac {de^{x^2}}{dx} = 2xe^{x^2} > 2x e^{x}$ for $x > 1$ So by l'hopitals rule $\lim \frac {e^x}{e^{x^2}} = \lim \frac {e^x}{2xe^2} \le \lim \frac 1{2x} = 0$. So $e^{x - x^2} > 0$, $\lim e^{x- x^2} \ge 0$ so $\lim e^{x-x^2} = 0$. .... or .... For $\epsilon > 0$ and $x > 1 + \sqrt{\ln 1/{\epsilon}}$ then $\|e^{x - x^2} - 0\|= 1/e^{x^2 - x} < 1/e^{(x - 1)^2} < 1/e^{\sqrt{\ln 1/\epsilon}^2}= \epsilon$. .... or as $e^x$ is continuous $\lim e^{x- x^2} = e^{\lim x - x^2 = \lim -y} = 0$. As long as you realize $x-x^2 \rightarrow -\infty$ and $\lim_{y\rightarrow -\infty} e^y = 0$ you have many options to prove it. Note a polynomial is equivalent at infinity to its highest degree term, i.e. here: $\;x-x^2\sim_\infty -x^2$, hence $\lim_{x\to\infty}(x-x^2)=\lim_{x\to\infty}(-x^2)=-\infty$. By continuity $\;\mathrm e^{x-x^2}$ tends to $0$. • This argument should be made more precise. If they're equivalent at infinity, then naively one could argue $\lim \ (x - x^2) - (-x^2) = \lim \ (-x^2) - (-x^2) = 0$ which is wrong. – MathematicsStudent1122 Sep 21 '16 at 23:52 • Every one has seen equivalence is not compatible with addition or subtraction, only with multiplication and division (and composition with logarithm, to a certain extent). I suppose students know the precise meaning of equivalence, and at least the main rules. – Bernard Sep 21 '16 at 23:57 You can mind in this way: since $$x^2 > x$$ as $x\to \infty$, then $x - x^2 = x(1-x) \approx x\cdot(-x) = -x^2$ hence $$e^{x -x^2} \approx e^{-x^2} = 0$$ One way forward uses only the elementary inequality $$\bbox[5px,border:2px solid #C0A000]{e^x\ge 1+x} \tag 1$$ along with the squeeze theorem. Proceeding, we write $$e^{x-x^2}=e^{-(x-1/2)^2}e^{1/4}=\frac{e^{1/4}}{e^{(x-1/2)^2}}$$ Then, applying $(1)$ reveals $$0\le \frac{e^{1/4}}{e^{(x-1/2)^2}}\le \frac{e^{1/4}}{1+(x-1/2)^2}$$ whereupon application of the squeeze theorem yields the coveted limit $$\lim_{x\to \infty}e^{x-x^2}=0$$ • Please let me know how I can improve my answer. I really want to give you the best answer I can. -Mark – Mark Viola Oct 5 '16 at 23:35	2019-08-22 04:01:29	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9235779643058777, "perplexity": 536.9046801305997}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027316718.64/warc/CC-MAIN-20190822022401-20190822044401-00262.warc.gz"}
https://www.physicsforums.com/threads/ml-inequality-estimation-of-line-integrals.709429/	# ML-inequality, Estimation of Line Integrals 1. Sep 9, 2013 ### wifi Problem: Let $\vec{F}$ be a vector function defined on a curve C. Let $\|\vec{F}\|$ be bounded, say, $\|\vec{F}\| ≤ M$ on C, where $M$ is some positive number. Show that $\|\int\limits_C\ \vec{F} \cdot d\vec{r}\| ≤ ML$ (L=Length of C). Attempt at a Solution: I honestly have no idea where to start with this one. It's not really clear to me exactly what the question is asking me to show. I understand we have this vector function $\vec{F}=F_1 \hat{i} + F_2 \hat{j} + F_3 \hat{k}$, and that's about it... What does it mean to say that the magnitude $\|\vec{F}\|$ is "bounded" in such a way that $\|\vec{F}\| ≤ M$? Are we imposing a restriction here? Last edited: Sep 9, 2013 2. Sep 9, 2013 ### dirk_mec1 Bring the absolute values within the integral then this \|F\| in the integral is smaller than $$\|\|F\|\|_\infty$$. What remains is a simple line integral. 3. Sep 9, 2013 ### wifi Is this what you're saying? $\|\int\limits_C\ \vec{F} \cdot d\vec{r}\| ≤ \int\limits_C\ \| \vec{F} \| \cdot d\vec{r}$ 4. Sep 9, 2013 ### wifi Any help guys? 5. Sep 9, 2013 ### wifi Wouldn't $\|\vec{F}\|$ be a scalar? In which case taking the dot product is undefined in $\int \|\vec{F}\| \cdot d\vec{r}$? 6. Sep 9, 2013 yes, the norm of ${\mathbf{F}}$ is a scalar, so your comment about the dot product with $d {\mathbf{r}}$ is correct. If the norm of ${\mathbf{F}}$ is a scalar, what can you do to simplify $$\int_C {\mathbf{F}} \, d{\mathbf{r}} \text{ ?}$$ and what remains when you do simplify it? (Hint: it is here where you'll use the assumption that $\|\mathbf{F}\| \le M$.) 7. Sep 9, 2013 ### wifi I'm not really sure how $\int_C {\mathbf{F}} \, d{\mathbf{r}}$ can be simplified. Can you be more specific? 8. Sep 9, 2013 ### CAF123 From calculus, you can prove that for smooth $f(x)$ defined on the curve C, (which is in the domain of f(x)) then $$\left\|\int f(x)\, dx \right\| \leq \int \left\| f(x) \right\|\,dx$$ Apply this to your problem. 9. Sep 9, 2013 ### wifi I understand that $\left\|\int f(x)\, dx \right\| \leq \int \left\| f(x) \right\| dx\,$, I don't see how that can be applied to this line integral. 10. Sep 9, 2013 ### CAF123 $\|\underline{F}\|$ is a scalar. How can you reexpress $\int \|\underline{F}\|\,d\underline{r}$? 11. Sep 9, 2013 ### wifi In the integral $\int \|\vec{F}\| \cdot d\vec{r}$, isn't $\|\vec{F}\| \cdot d\vec{r}$ undefined since the dot product is an operation between two vectors? 12. Sep 9, 2013 ### CAF123 It is, but the integral in my last post does not include a dot product. If $k$ is a scalar, then $\int k f(x) dx = ?$ Once you make this step, use the condition of the boundedness of f. 13. Sep 9, 2013 ### wifi $\int k f(x) dx = k\int f(x)dx$. So I think you're trying to say $\int \|\vec{F}\| d\vec{r} = \|\vec{F}\| \int d\vec{r}$. Right? 14. Sep 9, 2013 ### CAF123 Right. Now use the boundedness of $\|\underline{F}\|$ and evaluate $\int_C d \underline{r}$ 15. Sep 9, 2013 ### wifi So since we know that $\|\vec{F}\| \leq M$ and $\int d\vec{r}=L$ , we have $\int \|\vec{F}\| d\vec{r} = \|\vec{F}\| \int d\vec{r} \leq M \int d\vec{r} = ML$. Yes? 16. Sep 9, 2013 ### CAF123 Yes, you are done. 17. Sep 9, 2013 ### wifi CAF123, you're the best!	2017-08-20 22:02:44	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8726727962493896, "perplexity": 949.1844129895272}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886106990.33/warc/CC-MAIN-20170820204359-20170820224359-00024.warc.gz"}
http://www.chegg.com/homework-help/questions-and-answers/consider-simple-alternating-current-generator-ashippolyte-pixii-s-dynamo-current-generated-q413167	Consider a simple alternating current generator such asHippolyte Pixii's dynamo. The current generated by such dynamo canbe described as simple oscillating cosine signal. Assuming forsimplicity that the max current generated each time a pole ofPixii's magnet passed the coil is (2/π)0.5 amperesand that the magnet rotate with a characteristic angular frequencyω0. Write the mathmatical expression for the time-domain signal(current vs. time) from such AC generator. For simplicity, assumethat the magnet was already spinning at the beginning of theobservation and the magnet's poled happened to be just below thecoils at time zero. THANK YOU FOR THE HELP! WILL RATE ASAP	2014-07-31 12:43:32	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8111174702644348, "perplexity": 3822.55211361928}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-23/segments/1406510273012.22/warc/CC-MAIN-20140728011753-00423-ip-10-146-231-18.ec2.internal.warc.gz"}
http://uwdigital.uwyo.edu/aggregator/sources/1?page=4	Recent documents in Wyoming Scholars Repository Updated: 13 hours 30 min ago ### The Fisheries Crisis and its People: An econometric Sustainable Livelihoods application for low-income artisanal fishers in Sierra Leone Wed, 2018-05-09 19:31 The global fisheries crisis is a topic of significant research across fields, including economics. It is evident that the current global fish stocks are declining, which has motivated environmental protection measures to be implemented. Low-income countries and their inhabitants are unevenly harmed by these environmental impacts, as artisanal fishing villages are dependent on fisheries for subsistence and livelihood. This case is particularly true in Sierra Leone, where poverty is evident, artisanal fishing communities exist, and dependence on fisheries is high (Kassam, et al. 2017; Teh, et al. 2016). Policy makers in these countries are faced with the challenge of mitigating environmental disasters while still ensuring that livelihoods of local people are protected. The present paper argues that an econometric model would provide useful, empirical evidence to these policy makers as to the specific factors of livelihood, responding to the question: which factors in the livelihoods of low-income artisanal fishers are most significant, and therefore should be considered in policy decisions? The econometric model in this paper follows the Sustainable Livelihoods Approach to environmental protection and poverty reduction (Krantz 2001). Livelihood, measured by the United Nations Development Programme Human Development Index, is explained by economic, social, and environmental variables in a sustainable livelihoods framework. Results and viability of this model are discussed, followed by a discussion of further research to sharpen these results. The model is then tested to show its practical application for policy-makers in maximizing poverty alleviation outcomes. Research concluded that insufficient data has caused present results to be relatively inconclusive for Sierra Leone today, but the model design and rationale can be useful given a substantially larger dataset. ### Empty Promises: The IOC Olympic Games, FIFA Men’s World Cup, the Displacement of the Disadvantaged and the Illusion of Economic Advancement Wed, 2018-05-09 19:31 The International Olympic Committee (IOC) and the Federation Internacionale de Football Association (FIFA) represent the legacy of premier athletics, economic development, and globalization. Cities around the world fight to host these premier events and showcase the beauty and robustness of their community. The construction of venues for these games adversely affects local populations. This paper attempts to address the arguments for showcasing such events, despite the local population displacement they cause. Using an examination of current literature on the topic, I attempt to provide a picture of the local impact of mega sporting events. I will look at how three forms of legitimacy provided by states as justification for hosting are often not based in reality. I will argue that economic legitimacy influences a state to host games based on perceived benefits that do not reach the majority of the population, especially the poor. The second form of legitimacy, inherent legitimacy, focuses on the way that different types of spending are legitimized or not legitimized by the international community, and how spending on sports has an inherent legitimacy that for example, military spending does not. Finally, I will argue that legitimacy through terminology, such as marketing the perceived benefits to the community of the event, has adverse effects on local populations that are often ignored. ### Stage Management Website Wed, 2018-05-09 19:30 One of the major challenges in the theatre is communication. With casts of over 20 and design teams of almost 15, making sure everyone is in contact with everyone else is a feat to say the least. Of course, we all have email, Facebook, text messages, etc., but for the University of Wyoming’s production of The Tender Land by Aaron Copland, I wanted to find a better way to help bridge the gap between the actors, the design team, and the stage management team. I have created a website to act as the hub of communication for everyone involved with the production. It includes pages for schedules, photos, announcements, reports, and everything else involved in the mounting of a production. My goal was to see if creating a website would help everyone involved be more informed about the rehearsal process, and to create a sort of time capsule of the production that the designers, actors, and other faculty could access long after the production closes. In this presentation, I will explain how I made the website, how I chose what got put on it, and whether I accomplished my goals or not. ### The History of U.S. Copyright Law and Disney’s Involvement in Copyright Term Extension Wed, 2018-05-09 19:30 ### Cornelia de Lange Syndrome: In the Realm of Caregivers and Surviving Wed, 2018-05-09 19:30 Cornelia de Lange Syndrome (CdLS) is a rare congenital disorder that occurs in 1 in 10,000 live births. The goal of this research project was to further understand the impact of caregivers on children with disabilities, specifically CdLS. The purpose of this research project was to critically analyze the caregivers of those with Cornelia de Lange Syndrome, using the social model of disabilities as a theory and Derrida’s “structure” as a method; I argued caretakers of those with disabilities, specifically CdLS need to be given support, as well as resources, in order to maintain a healthy environment and family for the individual with special needs. In the study, it was found that caregivers would like more resources for their child, whether that be awareness, respite, or long-term care facilities. Key words: caregiver, Cornelia de Lange Syndrome (CdLS), disability, resources, respite ### Impacts of Place-Based Professional Development on Teachers Sat, 2018-05-05 00:55 The qualitative case study investigated the relationship between high-quality professional development for place-based education and long-term impacts on teacher practices. The case study focused on a small subset of teachers who attended all four years of the PLACE (Place-based Learning and Civic Engagement) program from 2011-2014. This study was built off a previous program evaluation of PLACE. The purpose of this research study was to evaluate the PLACE professional development's long-term impact on teachers' perceptions and practices and the teachers' implementation of place-based education. The data collection methods for this study involved interviews, observations, and surveys. Based on the data collected from the small sample of teachers, the evidence suggested that the program impacted the teachers' practices to various degrees and their implementation of place-based education varied by teachers. The results identified the continuous, experiential, and collaborative structure of the PLACE program as factors for the program's long-term impact on teaching practices. Recommendations and limitations are included. ### The Long-Term Effects on Conceptual Change and Affect for Preservice Teachers One Year After a Cave Automatic Virtual Environment (CAVE) Experience Sat, 2018-05-05 00:55 The current research evaluated the long-term effects of a cave automatic virtual environment (CAVE) experience on preservice teachers’ conceptual change and affect. To evaluate the lasting effects, four students from a physical science class were interviewed one year following their experience in a CAVE simulation in which they learned about molecular density. For each participant the interview produced a transcript of his/her spoken responses and a drawing that was compared to the drawing s/he had done the year before. The results of the research showed that participants manifested both positive and negative affect in regard to their CAVE experience. Positive affect was most common in recalling the CAVE experience itself, while negative affect was most prevalent when recalling specific content learned. All four participants retained changes in conceptions from their time in the CAVE. However, these conceptual understandings consisted of both accurate information and misconceptions. ### The Effect of Dancers’ Clothing on Perception of Performance Ability Fri, 2018-05-04 08:29 The Effect of Dancers’ Clothing on Perception of Performance Ability Mariah Brewer, Jennifer Deckert Department of Theatre and Dance University of Wyoming Oral and Poster Presentation Honors Program Rapid City, South Dakota Dancers spend several hours a day training in studios where mirrors are present. Observations in the mirror serve as feedback for establishing line, unison, and clarity, and may also impact their perceived performance. As such, clothing may also influence perception of performance ability. This study explores clothing as a potential contributing factor to a dancer’s perceived self-confidence and performance ability while executing movement. This descriptive research study is expected to have 8-10 participants and will ask participants to perform a two movement phases in a dance studio with mirrors under two different clothing conditions. Immediately following each of the participant’s performances with each clothing condition, they will be asked to take a questionnaire to evaluate their perceived performance. Participants will be asked to arrive a week later to view a video of each phrase for each condition and given the questionnaire again, after viewing their performance. Although usable data has not been collected, a pilot study has been conducted. The hypothesis of the study is that the tighter fitting clothing option, compared to the loose-fitting clothing, and regardless of movement type, will have a negative effect on dancer’s perception of their performance ability. The data from this research will enhance current knowledge and promotion of dancer wellness, regarding psychological health and overall dancer well-being. This research has been approved for use of human subjects by the University of Wyoming IRB. ### Schizophrenia: A Scientific and Artistic Review Fri, 2018-05-04 08:28 Schizophrenia is a neurodevelopmental psychiatric disorder affecting approximately 0.5-1% of the world’s population. The symptoms of schizophrenia are positive, negative, and cognitive in nature, but the effects of schizophrenia have far more widespread effects than these. There are several causative theories of schizophrenia, including the dopamine hypothesis, glutamate hypothesis, dendritic spine abnormalities, and immune system involvement. These theories have provided proposed pharmacological targets, giving rise to numerous antipsychotic drugs. Despite the modest effectiveness of antipsychotic drugs, their systemic side effects are severe and plentiful. These side effects only add to the countless, inherent side effects that accompany this disease, the most notable of which are described in this review. Quality of life is severely impaired in schizophrenia patients, with stigma being a significantly contributing factor. This review, as well as the accompanying dance video, aim to portray the large extent to which schizophrenia affects the whole person. ### I'd Strike the Son if He Insulted Me: Milton's and Melville's Flawed Revolutionaries Fri, 2018-05-04 08:28 John Milton and Herman Melville, despite 184 years and an ocean of separation, created two of Western literature’s grandest rebels in Satan and Ahab. I propose that these two characters are blueprints for a literary type, that of the fallen revolutionary. Both assert their own equality and try to overthrow the power structures that they feel oppress them in their respective settings, but both, instead of destroying the inequality that drove them to rebel, betray their own cause and comrades by serving only themselves. Both Milton and Melville advocated for increasing political democratization within their societies; Milton fought against the monarchy, while Melville was a whole-hearted believer in the American democratic experiment. In Paradise Lost, Milton creates Satan as an opponent to the monarchical Father in Heaven, but who fails to carry out his revolution completely, as he becomes a tyrant in hell obsessed with destruction rather than a liberator intent on creation and freedom. In Moby Dick, Ahab is rebelling against what he feels is the metaphysical inequality of the universe that manifests itself in the white while; he too rails against divine oppression, but he too establishes himself as a tyrant aboard the Pequod seeking only to raise himself above his peers rather than enable the freedom of all. Neither rebel’s principles can be wholly discounted, but we also must move beyond their example and recognize the need to fully free ourselves from tyranny and embrace our collective humanity through more communitarian and compassionate philosophies. ### An argument for Sociocultural, and Economic Awareness for WWOOF Volunteers before their Farm Stay in Latin America. Fri, 2018-05-04 08:28 Tourism in Latin America has exponentially increased in the past couple of decades. Two major sectors of this tourism boom have been voluntourism and ecotourism. Voluntourism is defined as “a form of tourism in which travelers participate in voluntary work” (Oxford, Dictionary, 2018). Of course, as its name implies, ecotourism is the form of tourism focused on sustainability. These forms of tourism intersect with World-Wide Opportunities on Organic Farms (WWOOF). In its essence, WWOOF is an online forum that serves as a route for volunteers to connect with local farm owners, leading to a stint of voluntourism on an organic farm (FoWo, 2018). Although WWOOFing is not the most frequent form of either ecotourism, nor voluntourism it is prevalent enough that an in-depth analysis of its effects economically and socioculturally, is imperative to understanding the entire picture of ecotourism/voluntourism in rural Latin America and the Caribbean (LAC). ### Fostering Empowerment for Incarcerated Women: Wild: From Lost to Found on the Pacific Crest Trail; A Book Study Curriculum Thu, 2018-05-03 10:06 Incarcerated women historically have prior membership in marginalized communities, resulting in high rates of under-education, unemployment, single parenthood, poverty, intimate partner abuse, and low self-esteem. This 6 week-long book study curriculum, grounded in transformative learning theory, is designed to wholeheartedly foster the educational growth of female inmates through development of self-competence and specific life skills in areas of literacy, oral communication, and critical thinking. Through engaging, collaborative, and critical exploration of a woman’s memoir entitled Wild: From Lost to Found on the Pacific Crest Trail, incarcerated women will reflect on their lived experiences and their place in family and society. Regarding these female inmates as life-long learners, this book study curriculum consists of five thematic parts: The Ten Thousand Things, Tracks, Range of Light, Wild, and Box of Rain This self-inquiry learning, coupled with empathic group discussions, will bring awareness to shared experiences, social struggles, personal conflicts, and reflective thinking. The ultimate outcome of this book study curriculum that the author hopes for is empowerment for incarcerated women to develop new habits of heart and mind on life, family, and the world in which we live. ### The Perceptions of Principals Regarding the Formative Supervision of Teachers Thu, 2018-05-03 10:05 Educational scholars commonly identify teachers as the primary in-school influence for increasing student achievement therefore, principals need to focus on improving teacher effectiveness through formative supervision. The purpose of this study was to explore differences in perceptions towards the formative supervision of teachers between more experienced and less experienced principals. Formative supervision allows principals to monitor, assess, and systemically address teacher performance with the intent of improving their practice. Guided by current literature, different aspects of formative supervision were constructed, the analyses indicated that certain sets of formative supervision constructs had no significant differences when comparing the grouping variables of principal experience. However, principals with more than three years of experience had a significantly different perception about their abilities to improve teaching through formative supervision than principals with less than three years of experience. More experienced principals indicated a higher level of confidence in improving instruction, as well as a preference for written feedback typically found in performance evaluations and not necessarily in walkthroughs where the principal has the option for oral feedback. ### Norm Inequalities Related to Clarkson Inequalities Thu, 2018-05-03 04:49 ### Denver Student Teaching Practicum Tue, 2018-05-01 23:48 During my research semester, I have had the opportunity to work with a group of thirty, third-grade students to improve and grow in my teaching before I have my own classroom. My practicum experience was in the heart of Denver at Teller Elementary School. My cooperating teacher is in her 34th year of teaching; she has taught and guided me through additional ways to research. The purpose of this practicum experience was to learn how to support and grow future students in their needs academically and social-emotionally. The capstone project assigned is a project that is assigned countrywide and purposed to measure student teachers before they enter the classroom. Some states require a passing grade on this assessment in order to become a licensed teacher in that state. This process is called ed-TPA (Education Teachers Performance Assessment). The overall process of ed-TPA is to have pre-service teachers learn how to best enter the classroom and practice, through research, planning, and reflection. Within this project, I was instructed to reflect on my teaching using extensive research and planning. Through this project, I was able to learn how to best meet the needs of a large group of students that have a great range of comprehension of varying content areas. Presenting in Undergraduate research day, I would like to share and reflect on my time being a student teacher. I would like to share what I had the opportunity to learn throughout my entire semester planning, researching, and teaching. ### Comparing Perceived and Actual Cognitive Lateral Bias in University Dance Majors Tue, 2018-05-01 01:05 Lateral bias (also referred to as lateral preference) is defined as an “innate bias for one side or the other” (Kimmerle, 2010). “Side” of the body is a reference to whether a movement is right dominant or left dominant in its execution. Although all human beings develop a functional lateral bias that is reinforced by the habits in their daily lives, it has been suggested that dance training increases asymmetry because of its over-emphasis on the right side of the body (Mertz et al., 2011). Despite this hypothesis that dance training could be a proponent of lateral bias toward right dominant movement, dancers are encouraged to be symmetrically proficient in their ability to perform movements that are both right dominant and left dominant to avoid choreographic limitation and injury. While it is difficult to determine if asymmetries are pre-existing in a dancer, there is strong evidence that dancers have a highly-developed proprioceptive sense that allows them to accurately identify relatively minute differences in their own laterality (Jola et al., 2011). The objective of this research was to determine if university dance students’ perception of their lateral bias correlates with their actual lateral bias. This information will help dance researchers to understand the effect of lateral bias on dance training and performance, as well as assist dance teachers in making informed choices about how to develop well-rounded dancers. ### Sensational Service Through Transformational Travel Tue, 2018-05-01 01:05 Travel and service are two fundamental activities for me. One way I have been able to combine these experiences and cultivate my love for them is through the University of Wyoming’s Alternative Breaks Program. The mission of this program is, “to engage the University of Wyoming community in service and experiential learning while promoting global citizenship”. The goals for students include, but are not limited to, “enact positive change through service, develop a stronger community between students, empower student leaders, becoming further educated on social justice issues, as well as encourage students to become active citizens”. It is through the Alternative Breaks program that I have been able to see positive changes in myself, as I have reached some of the goals outlined for students. My first exposure to Alternative Breaks was during my sophomore year, when I went to Kanab, Utah. We worked with Best Friends Animal Sanctuary while focusing on animal wellness for this trip. One year later, I went to Matelot, Trinidad. The focus of this trip was community development and women’s education. The two trips were drastically different, while remaining equally impactful. This year, I have the tremendous opportunity to co-lead a trip to Arizona in March 2018. The goal for this trip is to learn about, and provide service for immigration rights and reform. To do so, we will work with non-profit organizations in Tucson and Phoenix, getting exposure to people whose lives are affected by immigration rights on a daily basis. ### Autoerotic Asphyxiation: The Killer Cocktail of Taboos Mon, 2018-04-23 20:20 This analysis examines the trends of fifty years of forensic rhetoric regarding autoerotic asphyxiation (AEA) in Judeo-Christian society and discusses how taboos influence this society’s perception of the act. Each component mechanism of the AEA taboo is separately analyzed; both for its own effects on society and for its influence on the overarching AEA taboo. A recommendation is made about ways to combat the effects of the taboo. Emphasis is placed on why these changes are important. ### Whiteness Isn't an Accident: How My Irish Family Became White Wed, 2018-04-18 14:49 During her ten day trip to Ireland and Northern Ireland, scholar and creative writer Sarah Duncan examined, through exploring her own Irish family history, the connections between Irish migration and the construction of whiteness in what's known as the United States.	2018-07-21 03:41:30	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.20058514177799225, "perplexity": 4632.539038208546}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676592309.94/warc/CC-MAIN-20180721032019-20180721052019-00619.warc.gz"}
http://mathhelpforum.com/calculus/137893-convergence-problem.html	Math Help - Convergence problem 1. Convergence problem Determine whether the series converges absolutely, converges conditionally or diverges: (The sum as k > infinity) (-1)^k+1 (1/((k^3) - 1)) This test is inconclusive on the ratio test for abs. convergence and I'm not certain it can be used with the alternating series test because a1=0. Can anyone help me out here? 2. Anyone know what to do here? I'm trying the integral test, but I'm not sure how to integrate: 1 ------- k^3 - 1 3. Originally Posted by TripleHelix Determine whether the series converges absolutely, converges conditionally or diverges: (The sum as k > infinity) (-1)^k+1 (1/((k^3) - 1)) This test is inconclusive on the ratio test for abs. convergence and I'm not certain it can be used with the alternating series test because a1=0. Can anyone help me out here? First compare the series $\sum_{k = 2}^{\infty} \frac{1}{k^3-1}$ with $\sum_{k = 2}^{\infty} \frac{1}{k^3}$ (limit comparison test) to check for absolute convergence.	2015-09-01 00:40:54	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 2, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8310214281082153, "perplexity": 776.9028068470163}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-35/segments/1440644068184.11/warc/CC-MAIN-20150827025428-00279-ip-10-171-96-226.ec2.internal.warc.gz"}
http://mathoverflow.net/revisions/90134/list	I am always impressed by proofs that reach outside the obvious tool-kit. For example, the proof that the dimensions of the irreducible representations of a finite group divide the order of the group relies on the fact that the character values are algebraic integers. In particular, given a finite group $\|G\|$ and an irreducible character $\chi$ of dimension $n,$ $$\frac{1}{n} \sum_{s \in G} \chi(s^{-1})\chi(s) = \frac{\|G\|}{n}.$$ However, since $\frac{\|G\|}{n}$ is an algebraic integer (it is the image of an algebra homomorphism) lying in $\mathbb{Q},$ it in fact lies in $\mathbb{Z}.$	2013-05-24 12:06:21	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9563760757446289, "perplexity": 71.83921379924699}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368704655626/warc/CC-MAIN-20130516114415-00082-ip-10-60-113-184.ec2.internal.warc.gz"}
http://www.gradesaver.com/textbooks/math/calculus/calculus-early-transcendentals-8th-edition/chapter-2-review-concept-check-page-165/7	## Calculus: Early Transcendentals 8th Edition (a) $f$ is continuous at $a$ by definition means that $$\lim\limits_{x\to a}f(x)=f(a)$$ (b) $f$ is continuous on the interval $(-\infty,\infty)$ means $f$ is continuous at any point $x\in R$. The graph of such a function stretches from $-\infty$ to $\infty$ and is a continuous line from $-\infty$ to $\infty$. (a) $f$ is continuous at $a$ by definition means that $$\lim\limits_{x\to a}f(x)=f(a)$$ This also means that $f(a)$ is defined and $\lim\limits_{x\to a}f(x)$ exists. In the graph, $f$ is continuous at $a$ is shown as a unbroken line at point $a$ We can intuitively think that since the line is continuous at point $x=a$, as $x$ approaches $a$, the graph of $f$ would approach continuously towards $f(a)$. So $\lim\limits_{x\to a}f(x)=f(a)$ (b) $f$ is continuous on the interval $(-\infty,\infty)$ means $f$ is continuous at any point $x\in R$. The graph of such a function stretches from $-\infty$ to $\infty$ and is a continuous line from $-\infty$ to $\infty$. According to definition, $f$ is continuous on an interval if it is continuous at any number in the interval. That means if $f$ is continuous on the interval $(-\infty,\infty)$, it is continuous at any number on $(-\infty,\infty)$, which is the whole set of rational numbers $R$.	2017-05-23 12:46:00	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9161784052848816, "perplexity": 46.02758140109552}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-22/segments/1495463607636.66/warc/CC-MAIN-20170523122457-20170523142457-00359.warc.gz"}
https://jeopardylabs.com/play/delta-sigma-theta-sorority-inc-33	Pins Colors/Flowers Seals Motto/Vow/Secret Bonus Questions ### 100 This Pin was designed by the Epsilon Chapter, at The Ohio State University, and adopted in 1920 at the Second National Convention. It's three sides represent mind, body and spirit. What is the Pyramid Pin. ### 100 What are the Sorority's official colors? What is crimson and cream. ### 100 This official seal is a circular engraving with "Delta Sigma Theta Grand Chapter" surrounding the crest. It is displayed on the front of the podium used by the presiding officer when the Grand Chapter is in session at the national conventions and at regional conferences as well as ritualistic ceremonies. What is the Sorority Seal. ### 100 What is the Sorority emblem? What is goddess Minerva (Pallas Athena), the Goddess of Wisdom. ### 100 This Pin was created as recognition when a Delta member contributed $2,200 or more toward the$1 Million Dollar Howard University Endowment Scholarship. What is the Millennium Pin. ### 200 This Pin is a replica of the sculpture at Howard University. What is the Fortitude Pin. ### 200 What are the Pyramid Colors? What is white and red are the official Pyramid colors. ### 200 This seal is displayed in the entrance to the National President's suite during a national convention. What is the Presidential Seal. ### 200 What is "Intelligence is the Torch of Wisdom". What is The Sorority's Public Motto. ### 200 What colors robes do Jewels wear? What are crimson or red robes. ### 300 This pin was designed by Founder Madree Penn White. This pin is worn over the heart, only by a duly initiated member of the Sorority and is pinned to the wearer's first outer garment. Describe what it looks like and what each part symbolizes or represents. What is the Sorority Pin. It is comprised of three Greek letters, Delta, Sigma and Theta. The nine jewels in the Sigma represent the Nine Cardinal Virtues. Each corner of the Sigma contains a pearl dedicated to the Founders of Delta Sigma Theta. ### 300 What is the Sorority Flower? What is the African violet. ### 300 This is the official coat of arms of the Sorority. It was designed by Delta member F. Ailene Marks and Past National President Jeanette Triplett Jones. What is the Sorority Crest. ### 300 The Pyramid public motto is... What is "Scholarship, Fellowship, Service and a desire to attain all that would ennoble". ### 300 What does the Torch of Wisdom symbolize? What color is this candle and when do we use the candle? What is the public motto; represented by the red candle used during ritualistic ceremonies. ### 400 This handmade Pin was created in recognition of contributions of \$1000 or more to Delta Research and Educational Foundation (DREF). This pin can be worn as a pendant. What is the Diamond Jubilee Pin. ### 400 What is the Pyramid Flower? What is a peppermint carnation. ### 400 When was the Sorority Crest authorized? Who authorized it? What is 1934 and the National Executive Committee. ### 400 The Sorority vow is? What is "Membership in Delta Sigma Theta is a Lifetime Commitment." ### 400 Who speaks for the Grand Chapter of Delta Sigma Theta? Who is the National President. ### 500 What is the Sorority Stone, where is it used and what is their signifance to the Founders? What is the Pearl, it is used only in the official sorority pin, when in four corners of Sigma are dedicated to the Founders. ### 500 All Deltas sing the official songs? They are never song as what? What are solos and renditions. ### 500 What are the parts of the Sorority Crest and what do they represent? What is the Minerva (the emblem) the Goddess of Wisdom, the shield bearing the torch, the sword(representing truth), the staff(represents intelligent leadership), the three Greek letters Delta Sigma and Theta, the Laurel Wreath is the symbol of achievement, mark of honor, fame, distinction, glory and victory as used by the Greeks. ### 500 These are never written, but are transmitted orally from one Delta to another. When do you learn these? What are the Secrets, the secret motto, the handshake, the distress signal and the Delta knock. A new member will learn them at the time of initiation into the sorority. ### 500 What are the Fundamental Principals of the organization embodied in? When? What are the nine Jewels and the Delta Oath. In 1913.	2019-03-21 15:32:17	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.19791394472122192, "perplexity": 12393.580378517887}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-13/segments/1552912202526.24/warc/CC-MAIN-20190321152638-20190321174638-00340.warc.gz"}
http://web2.0calc.com/questions/simplify-this-expression-using-positive-exponents-only	+0 simplify this expression, using positive exponents only? 0 84 2 [(p)^-6(p)^2]^-3 Guest Aug 9, 2017 Sort: #1 +1221 0 Okay, I will attempt to simplify the expression of $$(p^{-6p^2})^{-3}$$ with only positive exponents: $$(p^{-6p^2})^{-3}$$ Use the exponent rule that $$a^{-b}=\frac{1}{a^b}$$ $$\frac{1}{(p^{-6p^2})^3}$$ Use the exponent rule that states that $$(a{^b})^c=a^{bc}$$. $$\frac{1}{p^{-6p^23}}$$ Combine like terms in the exponent. $$\frac{1}{p^{-18p^2}}$$ This expression is simplified as much as possible. TheXSquaredFactor Aug 9, 2017 #2 0 [(p)^-6(p)^2]^-3 simplify 1/(p^2/p^6)^3 =1/[p^6 / p^18] Take the reciprocal of it: =p^18 / p^6 =p^(18 - 6) =p^12 Guest Aug 9, 2017 edited by Guest Aug 9, 2017 13 Online Users We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners. See details	2017-10-19 12:53:19	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.895776629447937, "perplexity": 3730.3151322600734}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187823284.50/warc/CC-MAIN-20171019122155-20171019142155-00294.warc.gz"}
https://mathematica.stackexchange.com/questions/7799/mathematica-sec-and-csc/7800	# Mathematica Sec and Csc How can I prevent Mathematica from using the "old fashioned" functions "Sec" and "Csc"? In Germany these functions are "old fashioned" as they are not taught anymore at school. ## migrated from math.stackexchange.comJul 2 '12 at 9:38 This question came from our site for people studying math at any level and professionals in related fields. • What do you mean by prevent? Why do you think sec csc are old fashioned – Nunoxic Jul 2 '12 at 9:09 • Those functions are no more "old fashioned" than logarithms and cotangents. – Siminore Jul 2 '12 at 9:12 • @Nunoxic: I don't know about the "old fashioned" bit, but I perhaps Klaus (like myself) would simply prefer seeing expressions like "$\frac{x + y}{\sin x \cos y}$" rather than "$(x+y)\csc x \sec y$". – Day Late Don Jul 2 '12 at 9:17 • @Siminore Your statement is not true. At least here in Germany, nowadays nobody will use Sec or Csc. – user1642 Jul 2 '12 at 10:17 • I want to add my voice to those who do not like Ccs and sec. Whenever I see them I have in my mind convert them to normal sin/cos. I wish Mathematica does not use them either. – Nasser Apr 7 '17 at 4:21 This is similar to my Log question and similar methods can be used. $PrePrint = # /. { Csc[z_] :> 1 / Defer@Sin[z], Sec[z_] :> 1 / Defer@Cos[z] } &; Example: (x + y) Csc[x] Sec[y] (x + y)/(Cos[y] Sin[x]) • why not close then? – rm -rf Jul 2 '12 at 13:42 • @R.M well I meant similar in the generic sense. I see this as a closely related but at present different question, and someone may post an answer that goes much deeper than my simple one. Perhaps if that doesn't happen this question can be merged with mine and become a second example. – Mr.Wizard Jul 2 '12 at 14:07 • This was useful. Some, like me, will want to extend this to Cot, as follows. $PrePrint = # /. { Csc[z_] :> 1 / Defer@Sin[z], Sec[z_] :> 1 / Defer@Cos[z], Cot[z_] :> Defer@Cos[z] / Defer@Sin[z] } &; – Rico Picone Mar 10 '15 at 3:10 Using the neat trick Chip showed in this answer: SetSystemOptions["SimplificationOptions" -> "AutosimplifyTrigs" -> False]; TrigFactor[(x + y) Csc[x] Sec[y]] (x + y)/(Cos[y] Sin[x]) TrigFactor[Sec[t]^2] 1/Cos[t]^2 According to this MathGroup post, it's possible to get rid of the superfluous Csc and Sec by doing the following: Unprotect[Csc, Sec]; Format[Csc[x_]] := HoldForm[1/Sin[x]]; Format[Sec[x_]] := HoldForm[1/Cos[x]]; Protect[Csc, Sec]; That old solution at least gives you the following: Csc[t] $\frac{1}{\sin(t)}$ Sec[t] $\frac{1}{\cos(t)}$ but it still won't be able to print out $\frac{1}{\cos^2(t)}$ if you type in Sec[t]^2. Instead you get $\left(\frac{1}{\cos(t)}\right)^2$ But maybe that's OK for your taste. If not, then Mr. Wizard's solution is better because it does put the square in the denominator. • +1, this method is only one that worked for me actually since I was using print[] to print an expression with Csc. For example, Print[Csc[x]] and only this method will print 1/Sin[x] – Nasser Apr 7 '17 at 4:19	2019-11-18 05:51:40	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.23427428305149078, "perplexity": 3783.791291368948}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496669454.33/warc/CC-MAIN-20191118053441-20191118081441-00314.warc.gz"}
http://www.abouttajweed.com/kb/print/401/	## Do we have to make a gunna for the waw letter? Question Do we have to make a gunna for the waw letter? On what letters do we have to make gunna? Do we have to make gunna only when tashjid (little waw) is present? The only two letters that have a ghunnah (nasalization) in them are the noon and meem; this is an intrinsic characteristic of these letters, and the ghunnah never leaves them. When a saakinah or tanween meet a or a between two words, there is an incomplete merging of the saakinah or tanween into the wow. The ghunnah (nasalization) is what remains of the saakinah. So in this merging, the merges into the or , so that we do not hear the as far as the letter, but we hear the ghunnah (nasalization) of the . Since this merging is incomplete, most copies of the Qur'an do not have a shaddah on the or when this idghaam (merging) happens, there are a few copies printed that put a shaddah, but the more accepting way is without the shaddah.	2015-09-01 10:06:05	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8130663633346558, "perplexity": 4348.800073293079}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-35/segments/1440645171365.48/warc/CC-MAIN-20150827031251-00088-ip-10-171-96-226.ec2.internal.warc.gz"}
https://includestdio.com/477.html	# 问题内容: I’m creating a program in C as a homework for college. In this project the user has to add packages and vehicles for a company. I need the user to enter a unique license plate for each vehicle, but the license plate can only have 2 letters and 4 numbers. I’m thinking this should be done with a do..while… But I’m not really sure how to verify letters. I do know that for numbers it’s gotta be x < 0. It’s killing me because I don’t have a clue on how to do it with standard functions. ## 问题评论: Any code you’ve attempted so far would be helpful. As @MatthewDarnell said, try writing some code first, then if you come across a specific issue, post it here. Correct. That’s something like do { scanf in var, if var contains 2L+4N ok=1 else ok = 0 } while ( ok == 0) then for uniqueness, you need an array of strings, and compare the new value with all currently in array. Do it!	2020-12-04 20:06:37	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.20193079113960266, "perplexity": 558.6156638241706}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141743438.76/warc/CC-MAIN-20201204193220-20201204223220-00112.warc.gz"}
https://tex.stackexchange.com/questions/185149/how-to-insert-the-x-is-a-subset-of-y-but-is-not-equal-to-y-symbol	# How to insert the "X is a subset of Y, but is not equal to Y" symbol? [duplicate] How can I insert the "X is a subset of Y, but is not equal to Y" symbol? I have tried using $\subsetneq$, as in $X \subsetneq Y$, but this yields the error message: Undefined control sequence. There is no problem using $\subseteq$. Code: \title{Subset-Not-Equal-To} \author{} \date{} \documentclass[8pt]{article} \usepackage{amsmath} \usepackage{amsfonts} \usepackage{amsthm} \begin{document} \maketitle $X \subsetneq Y$ \end{document} • Could you provide a minimal example from \documentclass to \end{document}. I think that may be amssymb is the package that provides that symbol, but there is no option to see what you actually loaded. Jun 16, 2014 at 16:31 • A tip: You can use backticks to mark your inline code as I did in my edit. Jun 16, 2014 at 17:45 You have to load the amssymb package. Here is a possible solution: \documentclass{article} \usepackage{amssymb} \begin{document} Type \verb\|$A \subsetneq B$\|'' to get $A \subsetneq B$''. Type \verb\|$A \subsetneqq B$\|'' to get $A \subsetneqq B$''. \end{document} `	2023-03-20 13:34:04	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8658364415168762, "perplexity": 1227.6071972653544}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296943483.86/warc/CC-MAIN-20230320114206-20230320144206-00629.warc.gz"}
http://eprints.iisc.ernet.in/762/	# Photon Total Cross-sections Godbole, RM and Grau, A and Pancheri, G and Srivastava, YN (2004) Photon Total Cross-sections. In: Nuclear Physics B - Proceedings Supplements, 126 . pp. 94-99. PDF 0311211.pdf - Published Version Restricted to Registered users only Download (220Kb) \| Request a copy ## Abstract We discuss present predictions for the total $\gamma \gamma$ and $\gamma p$ cross-sections, highlighting why predictions differ. We present results from the Eikonal Minijet Model and improved predictions based on soft gluon resummation. Item Type: Journal Article Copyright of this article belongs to Elsevier Division of Physical & Mathematical Sciences > Centre for Theoretical Studies 31 Jul 2004 19 Sep 2010 04:13 http://eprints.iisc.ernet.in/id/eprint/762	2014-09-30 16:05:38	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5179012417793274, "perplexity": 9264.850952485402}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-41/segments/1412037663036.27/warc/CC-MAIN-20140930004103-00262-ip-10-234-18-248.ec2.internal.warc.gz"}
https://tex.stackexchange.com/questions/630364/dynamometer-ask-for-improvement-suggestions	# Dynamometer - ask for improvement suggestions \documentclass{standalone} \usepackage{tkz-euclide} \begin{document} \begin{tikzpicture}[scale=1, transform shape,every node/.style={scale=1.0}] %argola \definecolor{meu_cinzento}{RGB}{116, 123, 129} \tkzDefPoint(02,25){O1} \tkzDefPoint(02,23){O2} \tkzDefPoint(02,20){O3} \tkzDrawArc[R,line width = 6pt,color=meu_cinzento](O1,2)(0,360) \tkzDrawSegment[line width = 3pt,color=meu_cinzento](O2,O3) %gancho \definecolor{meu_cinzento}{RGB}{116, 123, 129} \tkzDefPoint(02,5){O1} \tkzDefPoint(02,7){O2} \tkzDefPoint(02,9){O3} \tkzDrawArc[R,line width = 6pt,color=meu_cinzento](O1,2)(90,360) \tkzDrawSegment[line width = 6pt,color=meu_cinzento](O2,O3) %espelho do dinamómetro \definecolor{meu_cinzento}{RGB}{175, 191, 196} \tkzDefPoint(02,10){O} \tkzDrawCircle[R,meu_cinzento!20,fill=meu_cinzento,opacity=1](O,2) \tkzDrawArc[R,line width = 3pt,color=black](O,2)(180,0) \tkzDefPoint(02,20){O} \tkzDrawCircle[R,meu_cinzento!20,fill=meu_cinzento,opacity=1](O,2) \tkzDrawArc[R,line width = 3pt,color=black](O,2)(0,180) \tkzDefPoint(00,10){P1} \tkzDefPoint(00,20){P2} \tkzDefPoint(04,20){P3} \tkzDefPoint(04,10){P4} \tkzDrawPolygon[fill=meu_cinzento!20,color=meu_cinzento](P1,P2,P3,P4) \tkzDrawSegment[line width = 3pt,color=black](P1,P2) \tkzDrawSegment[line width = 3pt,color=black](P3,P4) %ranhura do ponteiro \tkzDefPoint(02,10){P1} \tkzDefPoint(02,20){P2} \tkzDrawSegment[line width = 3pt,color=black](P1,P2) %escala \foreach \i in {0,...,20}{% \tkzDefPoint(1.5,{10+0.5\i}){O\i}} \foreach \i in {0,...,20}{% \tkzDefPoint(2.5,{10+0.5\i}){P\i}} \foreach \i in {0,...,20}{% \tkzDrawSegment[line width = 0.5pt,color=black](O\i,P\i)} %ponteiro \tkzDrawSegment[line width = 5pt,color=red](O5,P5) \end{tikzpicture} \end{document} • You don't need to use \definecolor multiple times if you don't re-define the color. Also, you don't need to repeat the same \foreach expression three times. Apart from that, I would probably just use plain tikz to draw this ... But: what exactly is your question? Jan 16 at 11:45 • I don't like the way the segments join each other Jan 16 at 11:48 • I agree with @JasperHabicht you need to use tikz-pgf and not tkz-euclide. Jan 16 at 12:04 There may be a way to connect tkz-euclide macros so that they join nicely (which I am not aware of), or you could use the line cap option. But, I think it is much easier to draw this with plain tikz and not load tkz-euclide. The code would be a lot shorter then: \documentclass{standalone} \usepackage{tikz} \begin{document} \begin{tikzpicture} \definecolor{meu_cinzento-1}{RGB}{116, 123, 129} \definecolor{meu_cinzento-2}{RGB}{175, 191, 196} %argola \draw[line width=6pt, meu_cinzento-1] (2,25) circle (2); \draw[line width=3pt, meu_cinzento-1] (2,23) -- ++(0,-3); %gancho \draw[line width=6pt, meu_cinzento-1] (2,9) -- ++(0,-2) arc (90:360:2); %espelho do dinamómetro \draw[line width=3pt, fill=meu_cinzento-2] (4,20) arc (0:180:2) -- ++(0,-10) arc (180:360:2) -- cycle; %ranhura do ponteiro \draw[line width=3pt] (2,20) -- ++(0,-10); %escala (com ponteiro) \foreach \i in {0,...,20}{ \ifnum\i=5 \draw[line width=5pt, red] \else \draw[line width=0.5pt] \fi (1.5,{10+0.5\i}) -- ++(1,0); } \end{tikzpicture} \end{document} • You don't need to define a color multiple times, and I would suggest that you name different colors differently. • You can include more than just one drawing command in a \foreach macro. So, there is no need to repeat the very same \foreach definition multiple times here. • Thank you all. I've found that my classes adapt better to TKZ, with a smaller set of commands, than to TikZ-pgf. You're right, but I think I should go for the simpler solution and hope that they'll then evolve into a more labor-intensive solution, from their point of view. Jan 16 at 13:01 You need to add : line cap=round,line join=round and it is better to use TikZ, tkz-euclide is for euclidean geometry. \documentclass{standalone} \usepackage{tkz-euclide} \begin{document} \begin{tikzpicture}[scale=1, transform shape,every node/.style={scale=1.0},line cap=round,line join=round] %argola \definecolor{meu_cinzento}{RGB}{116, 123, 129} \tkzDefPoint(02,25){O1} \tkzDefPoint(02,23){O2} \tkzDefPoint(02,20){O3} \tkzDrawArc[R,line width = 6pt,color=meu_cinzento](O1,2)(0,360) \tkzDrawSegment[line width = 3pt,color=meu_cinzento](O2,O3) %gancho \tkzDefPoint(02,5){O1} \tkzDefPoint(02,7){O2} \tkzDefPoint(02,9){O3} \tkzDrawArc[R,line width = 6pt,color=meu_cinzento](O1,2)(90,360) \tkzDrawSegment[line width = 6pt,color=meu_cinzento](O2,O3) %espelho do dinamómetro \definecolor{meu_cinzento}{RGB}{175, 191, 196} \tkzDefPoint(02,10){O} \tkzDrawCircle[R,meu_cinzento!20,fill=meu_cinzento,opacity=1](O,2) \tkzDrawArc[R,line width = 3pt,color=black](O,2)(180,0) \tkzDefPoint(02,20){O} \tkzDrawCircle[R,meu_cinzento!20,fill=meu_cinzento,opacity=1](O,2) \tkzDrawArc[R,line width = 3pt,color=black](O,2)(0,180) \tkzDefPoint(00,10){P1} \tkzDefPoint(00,20){P2} \tkzDefPoint(04,20){P3} \tkzDefPoint(04,10){P4} \tkzDrawPolygon[fill=meu_cinzento!20,color=meu_cinzento](P1,P2,P3,P4) \tkzDrawSegments[line width = 3pt,color=black](P1,P2 P3,P4) %ranhura do ponteiro \tkzDefPoint(02,10){P1} \tkzDefPoint(02,20){P2} \tkzDrawSegment[line width = 3pt,color=black](P1,P2) %escala \foreach \i in {0,...,20}{% \tkzDefPoint(1.5,{10+0.5\i}){O\i} \tkzDefPoint(2.5,{10+0.5*\i}){P\i} \tkzDrawSegment[line width = 0.5pt,color=black](O\i,P\i) } %ponteiro \tkzDrawSegment[line width = 5pt,color=red](O5,P5) \end{tikzpicture} Try this (minimalist): \documentclass[border=10pt]{standalone} \usepackage{tikz,calc} \begin{document} \begin{tikzpicture}[scale=1] \draw[gray,line width=12pt] (0,0) arc (180:0:2); \filldraw[brown] (-1,0) rectangle (5,-22); \node[white] at (2.1,-.5) (a) {\bfseries \large Range: 0-18.5 kg}; \draw[cyan,line width=20pt,centered] (2.1,-1)--(2.1,-21); \foreach \i in {0,1,...,18}{ \pgfmathsetmacro\h{-2-\i}; \pgfmathsetmacro\j{-2.5-\i}; \pgfmathsetmacro\k{.5+\i}; \draw[white,line width=3pt] (1.6,\h)--(1.2,\h) node[left] (\i) {\bfseries \large $\i$}; \draw[white,line width=3pt] (2.6,\j)--(3.0,\j) node[right] (\i) {\bfseries \large $\k$}; } \draw[red,line width=3] (1.5,-2)--(2.7,-2); \draw[gray,line width=12pt] (2.1,-22)--(2.1,-23) arc (90:360:2); \end{tikzpicture} \end{document} Output:	2022-05-24 16:05:43	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8684059381484985, "perplexity": 9076.105085322219}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662573053.67/warc/CC-MAIN-20220524142617-20220524172617-00427.warc.gz"}
http://www.ccdanza.com/battle-of-bnaqyjj/35e444-thermodynamics-formulas-pdf-physics	Print pdf and hang near your desk for quick reference. Chapter 12 :- Thermodynamics The branch of physics which deals with the study of transformation of heat energy into other forms of energy and vice-versa. Share this with your friends, they will love it! Equilibrium thermodynamics is the branch of physics which studies the equilibrium properties of bulk matter using macroscopic variables. One of the most powerful tool, not only for remembering formulas but also for solving typical Physics questions in … I. 1. Past papers, exam questions by topic, revision notes, worksheets and solution banks. . The key concept is that heat is a form of energy corresponding to a definite amount of mechanical work. Applied Thermodynamics By: Mr. Adnan Qamar Lecturer-Mech-KSK Factor Prefix Symbol Factor Prefix Symbol 1012 tera T 10-2 centi c 109-giga G 10 3 milli m 106 mega -M 10 6 micro μ 103 - kilo k 10 9 nano n 102-hecto h 10 12 pico p Pressure: Pressure is the normal force exerted by a system against unit area of the boundary surface. Joules mechanical equivalent of heat -4-186 J cal-I. by on 11/11/2020 . ME 211 and ME312 Thermodynamics Equation Sheet D. Abata, April 1, 2020 Conservation of mass: where Boundary work any system: and flow work (open system) , assuming ideal gas and since T=C then and For the polytropic process, that is : Open system work: , , Chemistry formula sheet for chapter-Thermodynamics is prepared by expert of entrancei and consist of all-important formula use in Thermodynamics chapter , this formula sheet consists of all-important chemistry formula of chapter-Thermodynamics with facts … Part of Thermodynamics For Dummies Cheat Sheet . ... First law of thermodynamics Q U W (2). It can be possible that your LATEX version has problems compiling the ﬁle. The behaviour of these quantities is governed by the four laws of thermodynamics, irrespective of the composition or specific properties of the material or system in question. Exams, IIT JAM, 15.8k … The zeroth law of thermodynamics states that if two thermodynamic systems are each in thermal equilibrium with a third, then they are in thermal equilibrium with each other. The strength of the discipline is its ability to derive general relationships based upon a few funda- mental postulates and a relatively small amount of empirical information without the need to investigate microscopic structure on the atomic scale. First law of thermodynamics – Energy can neither be created nor destroyed. All physics formulas pdf (11 pg, recommended). Thermodynamics has innumerable applications not only in physics but also in chemistry, biology and engineering and as such , it is an important course in all fields of science. Physics Basic Thermodynamic Formulas (Exam Equation Sheet) Control Mass (no mass flow across system boundaries) Conservation of mass: = . CONTENTS v 6.3 All Reversible Heat Engines are Equally E cient . The four laws of thermodynamics [according to Prof. Yosi Avron]: 0th Law: You have to play the game. Physics formulas from Mechanics, Waves and Oscillations, Optics, Heat and Thermodynamics, Electricity and Magnetism and Modern Physics. Helps in quick revision for CBSE, NEET, JEE Mains, and JEE Advanced. Physics Thermodynamics: Official, Free, No Login, Fast PDF Download Get top class preparation for UGC right from your home: Get detailed illustrated notes covering entire syllabus : … Last but not least, statistical physics is much more than thermodynamic equilibrium and if time permits, a course on statistical physics should also cover the basics of non-equilibrium physics, including the Boltzmann equation, Langevin dynamics and the Fokker-Planck equation. Efficiency of Carnot engine, . Statistical physics. [PDF] Download Mathematics JEE Main Question bank with solutions Part1 December 7, 2020 [Videos] Rapid crash course for JEE Main 2020 November 16, 2020 [Videos] Complete Etoos Videos series for free MPC November 11, 2020 [PDF] Download S.B.Mathur solved problems in Physics November 4, 2020 [PDF] Read JH Sir Physical chemistry Notes for class 11 JEE October 28, 2020 Below are useful results from the Maxwell–Boltzmann distribution for an ideal gas, and the implications of the Entropy quantity. Forinstance,whytheskyisblue,whyraindropsarespherical,whywedonotfallthrough the ﬂoor, et cetera. In thermodynamics, the interaction whose external system could be viewed as the raising of mass through a distance against gravitational force is defined as work done by a system on the surroundings during a process. Thermodynamics, science of the relationship between heat, work, temperature, and energy. By Mike Pauken . Also, you can print physics formulae and place them near your study desk as ready reference. thermodynamic principles and can be derived from kinetic theory) ... necessary for the equations that relate system properties to one-another to be valid. H�b">�wB ��X �0� PH=�戫4�]0j�=��u@��+�� Q2.��3l. . Solutions: see ex1-14-solns.pdf posted in class website Slides directory 4/21/14 Physics 115 3 . %PDF-1.3 %�� . Chapter 3: Thermodynamics, rst pass Lecturer: McGreevy Reading: CJ Adkins, Equilibrium Thermodynamics, Chapters 1, 2, 3.1-3.7. qP &7 8. Chapter. Print pdf and hang near your desk for quick reference. This is related to degrees Celsius ℃by The other courses in the 9-series each have a … 1 Classical Thermodynamics: 1st law 1.1 Introduction We ﬁrst review related year 1 courses (such as PHYS 10352 - Properties of Matter) and introduce some basic concepts in thermodynamics. zeroth law. Efficiency of heat engine,. Physics; Important Thermodynamic Equations and Formulas; Important Thermodynamic Equations and Formulas. Physics 9B introduces general principles and analytical methods used in a variety of fields of physics: Waves, Sound, Optics, Thermodynamics, and Fluids. Hence it should come as no surprise that initially thermodynamics constituted the main impetus for its establishment. Thermodynamics is filled with equations and formulas. Formula sheet Thermodynamics key facts (1/9) • Heatis an energy [measured in ] which flows from high to low temperature • When two bodies are in thermal equilibrium they have the same temperature • The S.I. Manypeople are drawntophysicsbecause theywishto understandwhythe worldaround us is likeitis. Helps in quick revision for CBSE, NEET, JEE Mains, and JEE Advanced. Physics formulas from Mechanics, Waves, Optics, Heat and Thermodynamics, Electricity and Magnetism and Modern Physics. The processes will … Thermodynamics deals with the macroscopic states of matter. View Physics 71 Formulas.pdf from PHYSICS 71 at University of the Philippines Diliman. UNIT II: THERMODYNAMICS, LIQUEFACTION OF GASES - AND NON CONVENTIONAL ENERGY 2.1 THERMODYNAMICS 5Hrs First law of thermodynamics – Statement—Isothermal and Adiabatic changes - Explanation – Equations for isothermal and adiabatic changes (No derivation) Simple problems based on equations P1V1 = P2V2 and P1V1 γ= P 2V2 γ Second law of Kindly note that some of these notes are not written by us and they are borrowed from student community. Prerequisites Conservation of energy (1st Law): −= ∆ = ∆+ ∆+ ∆ = ∆+ 2 2− 1 2 2 + (2−1) Entropy Balance (2nd Law): ∆= ∫ + . thermodynamics physics formulas pdf. Super 10 mock test for nta jee main 2019 by disha download free pdf oswaal cbse sample question papers for class 12 biology download free pdf reasoning sample questions series for bank and ssc download free pdf. This summarizes most important formulae, concepts, in form of notes of Thermodynamics which you can read for JEE, NEET preparation. Control Volu Combustion equations: Air-fuel ratio: … Thermodynamics Worksheet Fill the blanks in the following sentences with the correct thermodynamics term: 1) The thing we measure when we want to determine the average kinetic energy of random motion in the particles of a substance is temperature. Thermodynamics Formulas are listed below. This formula book is in pdf format and it can prove to be very helpful when you want to revise all your concepts on the go. There are 4 laws to thermodynamics, and they are some of the most important laws in all of physics. CBSE Class 11 Physics Chapter 12 - Thermodynamics Formulas - Free PDF Free PDF download of Physics Class 11 Chapter 12 - Thermodynamics Formula Prepared by Subject Expert Teacher at Vedantu. 100000+ pdf downloads. The Physics Formulary is made with teTEX and LATEX version 2.09. Buy the print book Check if you have access via personal or institutional login . Remembering Physics formulas seems tough to a lot of students. . The Zeroth Law of Thermodynamics . 2) The specific heat is the energy needed to raise the temperature of one gram of a In this blog, I wish to share you the pdf of my HANDWRITTEN physics formula sheet and the most important high yielding chapters for physics Neet High weight age chapters in physics for Neet : Semiconductors Kinematics Rotational motion Magnetic effects of current Modern physics Heat and thermodynamics Electrostatics Optics Fundamental Units Quantity Length Mass Time Electric Charge Thermodynamic Temperature Amount of These physics formulae helps class 11 and class 12 students in quick revision for CBSE, NEET, IIT JEE Mains, and IIT JEE Advanced. The laws are as follows 1. Changing the State of a System : Heat (VW, S & B: 4.7-4.9) A. unit of temperature is Kelvin (). Physics Notes Class 11 CHAPTER 12 THERMODYNAMICS The branch dealing with measurement of temperature is called thremometry and the devices used to … The distribution is valid for atoms or molecules constituting ideal gases. This states: If two systems are in thermal equilibrium with a third system, they are also in thermal equilibrium with each other. As molecules move or “vibrate”, they release energy in the form of heat energy that varies according to its temperature. Thermodynamics:-It is the branch of physics which deals with process involving heat, work and internal energy. Microscopic systems: one or few particle systems, e.g., a hydrogen atom with one electron moving about one proton, a water molecule (H2O), etc. Energy can be viewed as the ability to cause changes. THERMAL PHYSICS . Basic Terminology:- System. Also includes the value of Physical constants. Energy (1st law of thermodynamics), the 2nd law of thermodynamics and the property relations. . Finally, it should be noted that coincidentally statistical physics … Thermodynamics is a branch of Physics, which deals with the processes that involve heat transfer, work, and internal energy. For this we have included Pdf notes of each Chapter (still updating….). Here are complete Thermodynamics important notes and summary. It can only change forms. n z ds l 1 " = n z ds l 2 " =h "n z ds=0. . Please Do Not Write on This Sheet 1 2 I1 R01 2 + 1 2 I2 R02 2 = 1 2 I1 R 1 2 + 1 2 I2 R 2 2 I1 R1= I1 R1 1+ I2 R2 2 0= I1 R1′ 1+ I2 R2′ 2 1 2 I R12= 1 2 I R1′2+ 1 2 I R2′2 + I R1′ R2′ ( 1 − 2) R I − R = R1 I1+ R2 I2 I1+ I2 Chapter 9: Statics and Torque Open System. Thermodynamics:-It is the branch of physics which deals with process involving heat, work and internal energy.Thermodynamics is concerned with macroscopic behavior rather than microscopic behavior of the system. Chemistry formula for class 11 chapter- Thermodynamics . Thermodynamics For Dummies Cheat Sheet. A system which can exchange both energy and matter with its surroundings. second law. Physics; Thermodynamics For Dummies Cheat Sheet; Cheat Sheet. the well-known hydrostatic formula P = P0 − ˆgz. At times, you may find some difference between video lecture & Pdf Handwritten Notes. We shall be considering what happens when we perform certain processes on various systems. It shows how heat energy can be converted into other forms of energy while affecting the matter as well. heat engines & pumps . The branch of physics that deals with heat and temperature and their relation to energy work radiation and properties of matter. But we made it easy for you. Skip Adkins x3.5.4. Chapter; Aa; Aa; Get access. Thermodynamics is a branch of physics concerned with heat and temperature and their relation to energy and work. Indian Polity by M Laxmikanth 6th Edition Pdf download 22.1k views \| posted on January 26, 2020; NET/JRF,GATE TIFR, JEST, IIT JAM PHYSICS NOTES 19.2k views \| posted on May 28, 2019; Indian Polity by M Laxmikanth 5th Edition Download pdf 18k views \| posted on January 26, 2020; PHYSICS HAND WRITTEN NOTES FOR NET/JRF, GATE, JEST, TIFR, Other M.Sc. Thermodynamics deals with the transfer of energy from one place to another and from one form to another. This would help in proper revision and a quick glance whenever required. There are 4 laws to thermodynamics, and they are some of the most important laws in all of physics. Thermodynamics is the ﬁeld of physics describing thermal ef-fects in matter in a manner which is independent of the microscopic details of the material. How to prepare Thermodynamics. Notice that! first law. Zeroth law of thermodynamics – If two thermodynamic systems are each in thermal equilibrium with a third, then they are in thermal equilibrium with each other. This, and a Dutch version of this ﬁle, can be obtained from the author, Johan Wevers Physics Formulas for Class 11 and Class 12 Author: Jitender Singh Subject: Physics formulas from Mechanics, Waves and Oscillations, Optics, Heat and Thermodynamics, Electricity and Magnetism and Modern Physics. . First law of thermodynamics: one of the most fundamental laws of nature is the conservation of energy principle. Physics Formulas PDF for Class 11 and Class 12 Physics formulas from Mechanics, Waves, Optics, Heat and Thermodynamics, Electricity and Magnetism and Modern Physics. For quasi-static and reversible processes, the first law of thermodynamics is: d U = δ Q − δ W {\displaystyle dU=\delta Q-\delta W} where δ Q is the heat supplied to the system and δ W is the work done by the system. Closed System. Zeroth law of thermodynamics – If two thermodynamic systems are each in thermal equilibrium with a third, then they are in thermal equilibrium with each other. Physics Important Formula. For composite systems, the number of independent intensive parameters (thermodynamic degrees of freedom) is the number of components plus one. physics, but thermodynamics is an integral, and very important, part of their degree courses. These physics formulae helps class 11 and class 12 students in quick revision for CBSE, NEET, IIT JEE Mains, and IIT JEE Advanced. It simply states that during an interaction, energy can . It is intended to be a short reference for anyonewho works with physics and often needs to look up equations. 226 0 obj << /Linearized 1 /O 228 /H [ 782 1168 ] /L 423896 /E 26550 /N 52 /T 419257 >> endobj xref 226 17 0000000016 00000 n 0000000691 00000 n 0000001950 00000 n 0000002108 00000 n 0000002239 00000 n 0000003089 00000 n 0000003967 00000 n 0000004630 00000 n 0000005175 00000 n 0000006941 00000 n 0000007149 00000 n 0000007333 00000 n 0000015028 00000 n 0000015092 00000 n 0000022060 00000 n 0000000782 00000 n 0000001927 00000 n trailer << /Size 243 /Info 225 0 R /Root 227 0 R /Prev 419246 /ID[] >> startxref 0 %%EOF 227 0 obj << /Type /Catalog /Pages 209 0 R /JT 224 0 R /PageLabels 207 0 R >> endobj 241 0 obj << /S 1386 /L 1491 /Filter /FlateDecode /Length 242 0 R >> stream Rise in temperature of body when it falls throu height h gh 100 180 80 100 - 32) TF - —Tc + 32 4. Waves and thermodynamics – 3 – FORMULAE SHEET (continued) Electricity and magnetism Quantum, special relativity and nuclear – 4 – Title: Physics Data Sheet, Formulae Sheet and Periodic Table for HSC exams from 2019 Author: NSW Education Standards Authority Created Date: Heat is energy transferred between a system and its surroundings by virtue of a temperature difference only. . Thermodynamics sounds intimidating, and it can be. Also includes the value of Physical constants. In addition, statistical physics may be used to shed some light on the origin of the well-known laws of thermodynamics. Without the ability of a system to use energy within the system to do work — the heart of thermodynamics — there would be nothing for physicists to study. Forinstance,whytheskyisblue,whyraindropsarespherical,whywedonotfallthrough the ﬂoor, et cetera. These notes are aligned with our Channel’s Video Lectures. 1. Heat Heat is a form of energy called thermal energy which flows from a higher temperature body to a lower temperature body when they are placed in contact. In any process, the total energy of the universe remains the same. The laws are as follows. Keywords . Download physics formulas and concept pdf for class 11, 12, IITJEE, PMT and other competitive exams. Thermodynamics is concerned with macroscopic behavior rather than microscopic behavior of the system. For list of math notation used in these equations, see mathematical notation. Revision Notes on Thermodynamics. Here’s a list of the most important ones you need to do the calculations necessary for solving thermodynamics problems. You can download all physics formulas pdf and view on your smart devices. 1st Law: You can’t win. Particularly important questions 1. Also includes the value of Physical Constants. 2. Some thermodynamic functions cannot be calculated directly. To Register Online Physics Tuitions on CoolGyan.org to clear your doubts from our expert teachers and solve the problems easily to score more marks in your CBSE Class 11 Physics … II! Thermodynamics function: a macroscopic quantity that depends only on the state of a system but not on the process (or path) that has been used to reach the state itself (e.g. Make a handmade note of all the formulas being highlighted. Formulas for Thermodynamics . The first law of Thermodynamics. physics, but thermodynamics is an integral, and very important, part of their degree courses. Before moving to physics formula pdf sheet of chapter Thermodynamics Complete the theory form your text book than read the physics formula sheet of entrancei for effective revision do practice the questions from entrancei physics sections of chapter Thermodynamics. Download the free Pdf of chapter-Thermodynamics formula for class 11 chemistry . . Statistical mechanics starts at a microscopic model and derives conclusions for the macroscopic world, based on these microscopic details. Thermodynamics . It is concise and contains all formulas. Physics classes by Pradeep Kshetrapal FORMULA BANK THERMODYNAMICS . Thermodynamics Cheat Sheet - Free download as Word Doc (.doc), PDF File (.pdf), Text File (.txt) or read online for free. The laws of thermodynamics are explained in terms of microscopic constituents by … physics. Equilibrium thermodynamics is the branch of physics which studies the equilibrium properties of bulk matter using macroscopic variables. To Register Online Physics Tuitions on Vedantu.com to clear your doubts from our expert teachers and solve the problems easily to score more marks in your CBSE Class 11 Physics Exam. The most probable source of problems would be the use of large bezier curves and/or emTEX specials in pictures. Changing the value of a thermodynamics variable changes the value of state functions. Indian Polity by M Laxmikanth 6th Edition Pdf download 22.1k views \| posted on January 26, 2020; NET/JRF,GATE TIFR, JEST, IIT JAM PHYSICS NOTES 19.2k views \| posted on May 28, 2019; Indian Polity by M Laxmikanth 5th Edition Download pdf 18k views \| posted on January 26, 2020; PHYSICS HAND WRITTEN NOTES FOR NET/JRF, GATE, JEST, TIFR, Other M.Sc. The strength of the discipline is its ability to derive general relationships based upon a few funda- Revise GCSE/IGCSEs and A-levels! Coefficient of Performance, . pV=nRT Ideal gas state law! Physics Notes Class 11 CHAPTER 12 THERMODYNAMICS The branch dealing with measurement of temperature is called thremometry and the devices used to measure temperature are called thermometers. By Mike Pauken . Physics formulas from mechanics waves and oscillations optics heat and thermodynamics electricity and magnetism and modern physics. . Relation between different scales of temperature "IF -32 TR-o TK-273-15 18. . The Cambridge Handbook of Physics Formulas; Thermodynamics; The Cambridge Handbook of Physics Formulas. Thermodynamics and Statistical Mechanics Book: Heat and Thermodynamics (Tatum) Expand/collapse global location ... Last updated; Save as PDF Page ID 7241; Contributed by Jeremy Tatum; Emeritus Professor (Physics & Astronomy) at University of Victoria; No headers. Thermodynamics is a crucial chapter because 3-4 questions with a weightage of … — 400C has same value on Celcius and Fahrenheit 20. 2. The important notes of Physics for Thermodynamics pdf … Free PDF download of Physics Class 11 Chapter 12 - Thermodynamics Formula Prepared by Subject Expert Teacher at CoolGyan. The Cambridge Handbook of Physics Formulas. While thermodynamics is fundamentally about states it is also used for describing processes that connect states. E-Book D/L (pdf) Home >> Thermal, thermodynamics . A thermodynamic system includes anything whose thermodynamic properties are of interest. Thermodynamics touches on virtually every field of physics, from astrophysics to biophysics, because they all deal in some fashion with the change of energy in a system. . This transfer of energy can change the state of the system. . 5. Also includes the value of Physical Constants. Manypeople are drawntophysicsbecause theywishto understandwhythe worldaround us is likeitis. Part of the universe under investigation. : heat ( VW, s & B: 4.7-4.9 ) a Maxwell–Boltzmann distribution for an ideal gas, JEE..., Waves, Optics, heat and thermodynamics Electricity and Magnetism and Modern physics constituted main... Important ones you need to do the calculations necessary for solving thermodynamics problems the ability to cause changes is! ’ s Video Lectures Charge thermodynamic temperature Amount of Revise GCSE/IGCSEs and A-levels past papers, Exam questions topic! Your smart devices book Check if you have to play the game near. For Dummies Cheat Sheet Conservation of Mass: = thermodynamic temperature Amount of Revise GCSE/IGCSEs and A-levels Control! And the implications of the universe remains the same, et cetera virtue of a system can. The physics Formulary is made with teTEX and LATEX version has problems compiling the ﬁle Maxwell–Boltzmann. Flow across system boundaries ) Conservation of energy can be converted into other forms of energy to. A given state, there is a branch of physics which studies the relationship between energy and matter its! And they are also in thermal equilibrium with each other various systems freedom ) is branch. Same value on Celcius and Fahrenheit 20 as ready reference as the ability to changes... Mechanics Waves and Oscillations, Optics, heat and temperature and their relation to energy and work! Process, the number of independent intensive parameters ( thermodynamic degrees of freedom ) is the number of plus. System which can exchange both energy and the implications of the universe remains the same: 4.7-4.9 ).. Whenever required make a handmade note of all the formulas being highlighted desk as ready reference = z... In pictures problems compiling the ﬁle on these microscopic details to a definite Amount thermodynamics formulas pdf physics Revise and... That connect states derives conclusions for the macroscopic world, based on these microscopic details Philippines.... For class 11, 12, IITJEE, PMT and other competitive exams from the Maxwell–Boltzmann distribution for ideal! Will love it specials in pictures ( 2 ) thermodynamics ), the 2nd law of thermodynamics you. Oscillations Optics heat and thermodynamics, Electricity and Magnetism and Modern physics are with... Into other forms of energy can be converted into other forms of energy from one place to another ’ a... And matter with its surroundings E-Book D/L ( pdf ) Home > > thermal, thermodynamics website Slides directory physics. At University of the most important laws in all of physics which studies the relationship between energy and.! Main impetus for its establishment important formulae, concepts, in form of heat energy can be..., work and internal energy different scales of temperature if -32 TK-273-15... In any process, the number of components plus one Slides directory physics... In form of energy corresponding to a definite Amount of mechanical work to do the necessary... The total energy of the most probable source of problems would be the use of bezier... To play the game pdf of chapter-Thermodynamics formula for class 11 chemistry by us and they are borrowed student... They release energy in the form of notes of thermodynamics and the work a... Difference between Video lecture & pdf Handwritten notes to thermodynamics, Electricity and Magnetism and Modern physics used these. Cbse, NEET preparation see ex1-14-solns.pdf posted in class website Slides directory physics! Same value on Celcius and Fahrenheit 20 microscopic details weightage of … a system. With teTEX and LATEX version 2.09 system includes anything whose thermodynamic properties point. And LATEX version has problems compiling the ﬁle for quick reference (,! Constituting ideal gases law of thermodynamics which you can download all physics formulas a branch of physics that with... Revision and a quick glance whenever required starts at a microscopic model and derives conclusions for the macroscopic world based. Philippines Diliman notes of thermodynamics Q U W ( 2 ) but thermodynamics is with. Form of heat energy thermodynamics formulas pdf physics be possible that your LATEX version has problems compiling the ﬁle the use large! Number of components plus one Home > > thermal, thermodynamics of Revise GCSE/IGCSEs and!. System, they release energy in the form of heat energy can be into. Each other n z ds l 1 = n z ds l 1 = n z l... Are point functions, since for a given state, there is a form of energy principle ) of... Hydrostatic formula P = P0 − ˆgz formulas from mechanics, Waves and,! And Fahrenheit 20 has same value on Celcius and Fahrenheit 20 this would help proper! Some light on the origin of the system Yosi Avron ]: 0th law you! For solving thermodynamics problems microscopic constituents by … the well-known hydrostatic formula =. Work radiation and properties of bulk matter using macroscopic variables make a note. Have access via personal or institutional login helps in quick revision for,. A list of the well-known hydrostatic formula P = P0 − ˆgz formulae and place near. Electric Charge thermodynamic temperature Amount of Revise GCSE/IGCSEs and A-levels hence it should be noted that coincidentally statistical physics be. Freedom ) is the Conservation of Mass: = Yosi Avron ] 0th... -It is the branch of physics that deals with heat and thermodynamics Electricity and Magnetism and Modern physics thermodynamics... Intensive parameters ( thermodynamic degrees of freedom ) is the number of plus! Remains the same of mechanical work their relation to energy and the of! From the Maxwell–Boltzmann distribution for an ideal gas, and very important, of. To shed some light on the origin of the system on various systems TK-273-15 18 they energy. The main impetus for its establishment manypeople are drawntophysicsbecause theywishto understandwhythe worldaround us is likeitis called.! Be created nor destroyed thermodynamics problems = n z ds l 2 =h n! In thermal equilibrium with each other states it is also used for describing processes that states! Thermodynamics ), the 2nd law of thermodynamics Q U W ( 2 ) you may find some difference Video. This summarizes most important formulae, concepts, in form of energy can viewed... Coincidentally statistical physics may be used to shed some light on the origin of Philippines! Be used to shed some light on the origin of the well-known laws of nature is the of. By topic, revision notes, worksheets and solution banks is that heat is a chapter! Thermodynamic formulas ( Exam Equation Sheet ) Control Mass ( no Mass flow across system boundaries ) Conservation Mass! Lecture & pdf Handwritten notes Magnetism and Modern physics recommended ) Mass flow across boundaries! The Maxwell–Boltzmann distribution for an ideal gas, and very important thermodynamics formulas pdf physics of. Concerned with heat and temperature and their relation to energy and the relations... As well Mass: = which you can print physics formulae and place them near your desk quick...	2022-10-07 00:34:37	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.547747790813446, "perplexity": 1982.5252839148236}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030337889.44/warc/CC-MAIN-20221006222634-20221007012634-00261.warc.gz"}
http://tex.stackexchange.com/questions/100038/resizing-image-and-losing-quality?answertab=active	# Resizing image and losing quality I want to create a pdf document from images of different size and I fit each image to the text dimensions to include them in the document, with ``````\includegraphics[width=\textwidth, height=\textheight, keepaspectratio]{file.jpg} `````` The problem is that these images are very enormous: 160MB in total; and this size is kept in the pdf output (160.9MB), but I don't need so much pixel information since I resize each image. How can I exploit the resizing of each image to earn space? - Instinct tells me that LaTeX is not an image/graphics editor, and usually just dumps the image content in the output without modification. As such, some preprocessing using an external application is your best bet (for example, GIMP or Imagemagick). – Werner Feb 26 '13 at 17:29 In addition to resample/resizing (using external tools as Werner suggested) I would also change the jpeg quality. Reducing it to 75% is usually few noticeable (specially on screen), and reduces dramatically the image size. – JLDiaz Feb 26 '13 at 17:41 As the other suggested you can do some pre-processing on your images. This can be done with any tool you're comfortable with that can batch-process several files at once. If you use ConTeXt you can hook this into the graphic inclusion routine very easily. Probably you can do this in LaTeX as well. Here is an example which uses graphicsmagick to reduce the image size and compress the image. ``````\startluacode figures.converters.jpg = { os.execute(string.format('gm convert -size 80%% -quality 20%% "%s" "%s"',oldname,newname)) end } \stopluacode \starttext %% unmodified inclusion \externalfigure [hacker] %% reduced size and higher compression	2014-08-01 07:48:34	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8391786217689514, "perplexity": 2776.239526750611}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-23/segments/1406510274866.27/warc/CC-MAIN-20140728011754-00490-ip-10-146-231-18.ec2.internal.warc.gz"}
https://llvm.org/doxygen/classllvm_1_1FileCollector_1_1PathCanonicalizer.html	LLVM 16.0.0git llvm::FileCollector::PathCanonicalizer Class Reference Helper utility that encapsulates the logic for canonicalizing a virtual path and a path to copy from. More... #include "llvm/Support/FileCollector.h" Classes struct PathStorage Public Member Functions PathStorage canonicalize (StringRef SrcPath) Canonicalize a pair of virtual and real paths. More... Detailed Description Helper utility that encapsulates the logic for canonicalizing a virtual path and a path to copy from. Definition at line 73 of file FileCollector.h. ◆ canonicalize() FileCollector::PathCanonicalizer::PathStorage FileCollector::PathCanonicalizer::canonicalize ( StringRef SrcPath ) Canonicalize a pair of virtual and real paths. Definition at line 103 of file FileCollector.cpp.	2022-10-06 03:33:44	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3868480622768402, "perplexity": 13114.399380601915}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030337723.23/warc/CC-MAIN-20221006025949-20221006055949-00203.warc.gz"}
https://socratic.org/questions/why-are-alkenes-more-reactive-than-other-functional-groups	# Why are alkenes more reactive than other functional groups? Feb 13, 2017 #### Explanation: Alkenes are more reactive than some functional groups, but less reactive than others. It all depends on the functional groups and the specific reactions. The alkene double bond is reactive because the π electrons are “off to the side” of the two carbon atoms. They are further away from the two nuclei, so the nuclear attractions are not as strong. Thus, it is easy for an electrophilic reagent like ${\text{Br}}_{2}$ to attack the π electrons. However, a functional group like $\text{OH}$ does not react with bromine. Thus, only the double bond of 3-chloreprop-1-ene reacts with bromine to give 1,2-dibromo-3-chloropropane. $\text{H"2"C=CHCH"_2"Cl" + "Br"_2 → "BrCH"_2"CHBrCH"_2"Cl}$ The π bond is relatively unreactive toward nucleophiles like $\text{OH"^"-}$. $\text{H"_2"C=CHCH"_2"-Cl" + "HO"^"-" → "H"_2"C=CHCH"_2"-OH" + "Cl"^"-}$ In this case, the $\text{C-Cl}$ bond is more reactive than the $\text{C=C}$ π bond. Thus, the relative reactivity depends on the reaction and the functional groups you are comparing.	2021-06-21 22:56:50	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 7, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7455272674560547, "perplexity": 3989.8213233300617}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623488504838.98/warc/CC-MAIN-20210621212241-20210622002241-00120.warc.gz"}
https://studyadda.com/sample-papers/jee-main-sample-paper-43_q15/297/302786	• # question_answer A body is projected vertically upwards. If ${{t}_{1}}$ and ${{t}_{2}}$ be the instants at which it is at a height h above the point of projection, while ascending and descending respectively, then A) $h=g{{t}_{1}}{{t}_{2}}$ B) $h=2g{{t}_{1}}{{t}_{2}}$ C) $h=\frac{1}{2}\,g{{t}_{1}}{{t}_{2}}$ D) $h=\frac{1}{4}g{{t}_{1}}{{t}_{2}}$ Taking downward direction as positive, we get $\therefore$ ?(i) $f$ ?(ii) From Eqs. (i) and (ii), we get $\|M\|=\alpha$ ${{M}^{-1}}adjM)=kI$ ?(iii) Substituting value of u from Eq. (iii) in Eq. (i), we get $\Rightarrow$	2022-01-18 16:23:32	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9415541291236877, "perplexity": 1451.3369784920176}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320300934.87/warc/CC-MAIN-20220118152809-20220118182809-00254.warc.gz"}
https://keplerlounge.com/neural-computation/2020/01/26/partial-derivatives.html	## Introduction: The typical deep neural network tutorial introduces deep networks as compositions of nonlinearities and affine transforms. In fact, a deep network with relu activation simplifies to a linear combination of affine transformations with compact support. But, why would affine transformations be useful for nonlinear regression? After some reflection it occurred to me that the reason why they work is that they are actually first-order Taylor approximations and by this logic partial derivatives, i.e. Jacobians, are computational primitives for both inference and learning. ## Approximating continuous functions with piece-wise linear functions: A piece-wise linear function $f:\mathbb{R} \rightarrow \mathbb{R}$ is defined as follows: $$f(x) = \sum_i \lambda_i(x) \cdot 1_{X_i}(x)$$ where $1_{X_i}$ is the indicator function and the $\lambda_i$ are affine functions. Clearly, every polynomial $p: \mathbb{R} \rightarrow \mathbb{R}$ may be approximated using piecewise linear functions since they are locally Lipschitz. Now, let’s consider a nonlinear continuous function with compact domain and compact co-domain $X,Y \subset \mathbb{R}^3$: $$F: X \rightarrow Y$$ Since the polynomials are dense in the space of continuous functions, due to Stone-Weierstrass, we may substitute $F$ with a polynomial of degree $n$, $F_n \in P_n$ such that if we define the functional: $$\mathcal{L}[F_n] = \int_X \left\lVert F(x)-F_n(x) \right\rVert^2 dx$$ the sequence $\{\hat{F}_n\}_{n=1}^\infty$ converges uniformly to $F$: $$\hat{F}_n = \underset{F_n \in P_n}{\arg\min} \mathcal{L}[F_n]$$ $$\lim_{n \to \infty} \mathcal{L}[\hat{F}_n] = 0$$ Moreover, due to the Lipschitz condition (3) also allows us to define the maximum local error with respect to a ball $B(x_0,r)$: $$\exists C > 0, E_n(r)= \underset{x_0 \in X}{\max} \int_{B(x_0,r)} \left\lVert F(x)-\hat{F}_n(x) \right\rVert^2 dx \leq C \frac{4}{3}\pi r^5$$ which then allows us to introduce the first-order Taylor approximation: $$\forall x \in B(x_0,r), \phi(x) = \frac{\partial \hat{F}_n}{\partial x} \Big\rvert _{x=x_0}(x-x_0) + x_0$$ where $\frac{\partial \hat{F}_n}{\partial x}$ is a Jacobian. This will allow us to construct a linear basis of $\phi_i$ for $F$. ## Constructing a linear basis for continuous functions: We may construct a linear basis of $\phi_i$ for $F$ using (7) where the number of piece-wise linear $\phi_i$ that allows us to approximate $F$ is given by: $$N(r) = \frac{,74 \cdot \text{Vol}(X)}{\frac{4}{3}\pi r^3} \approx \frac{\text{Vol}(X)}{3} \cdot r^{-3}$$ where $,74$ is the density of closely-packed spheres in $\mathbb{R}^3$. Furthermore, the $\phi_i$ have compact support and pairwise disjoint domains by construction so we have: $$\forall i,j\neq i, \langle \phi_i,\phi_j \rangle = \int_X \phi_i(x) \cdot \phi_j(x) dx = 0$$ and therefore we may approximate $F$ as follows: $$F(x) \approx \hat{F_r}(x) = \sum_{i=1}^{N(r)} \phi_i(x)$$ We also find the following useful upper-bound using (6) and (8): $$\mathcal{L}[\hat{F_r}] = \int_X \left\lVert F(x)-\hat{F_r}(x) \right\rVert^2 dx \leq C \cdot \text{Vol}(X) \cdot r^2$$ Now, the challenge is essentially to find the first-order Taylor approximations and I will try to show that this is basically what is being done by a deep neural network. ## Fully-connected deep rectifier networks: Let’s consider a fully-connected deep network with fixed width, relu activation and compact domain $X \subset \mathbb{R}^n$ and co-domain $Y \subset \mathbb{R}^n$: $$F_\theta: X \rightarrow Y$$ $$F(x;\theta) = f \circ h_L \circ … \circ h_1(x) = f \circ \phi(x)$$ where $relu(x)=\max(0,x)$ and the parameters of $F_\theta$ are given by: $$\theta = \{W_l \in \mathbb{R}^{n_l \times n_{l-1}}, b_l \in \mathbb{R}^{n_l}: I \in [L]\}$$ Now, let’s note that if $F_\theta$ has $N$ layers and $n$ nodes per layer there are: $$(n!)^N$$ layer-wise permutations that result in functions equivalent to $F_\theta$ so it’s more useful to think in terms of function spaces than particular parameterisations of a network. We may also observe that similar to (11) $F_\theta$ is a linear combination of functions $\phi_i$ that are affine on $X_i$ and zero on $X \setminus X_i$. Since $\phi_i$ is characterised by the activation patterns of $F_\theta$ and $\phi_i$ is continuous on $X_i$, $X_i$ must be compact and $X_i$ and $X_j$ must be pair-wise disjoint so: $$\forall i,j\neq i, X_i \cap X_{j \neq i} = \emptyset$$ $$\forall i,j\neq i, \langle \phi_i,\phi_j \rangle = \int_X \phi_i(x) \cdot \phi_j(x) dx = 0$$ $$\exists A \in \mathbb{R}^{n \times n} B \in \mathbb{R}^{n}, \phi_i(x) = Ax+B$$ Now, if the reader is wondering about (16) let’s suppose that there exists $x \in X$ such that $x \in X_i$ and $x \in X_j$. Since $\phi_i$ and $\phi_j$ correspond to different activation patterns in $F_\theta$ there must be a node in $F_\theta(x)$ with value $\alpha \in \mathbb{R}$ such that $\alpha > 0$ and $\alpha \leq 0$. ## Function Approximation with Neural Networks: If we are trying to approximate a continuous function $F:X \rightarrow Y$ by means of $F_\theta$ we may use the results developed earlier and define: $$\mathcal{L}[F_{\theta}] = \int_X \left\lVert F(x)-F_{\theta}(x) \right\rVert^2 dx$$ and given a suitable vector-valued polynomial approximation $\tilde{F}$ such that: $$\mathcal{L}[\tilde{F}] \approx 0$$ it is sufficient to choose the $\phi_i$ in $F_\theta$ such that: $$\forall x \in B(x_0,r), \phi_i(x) = \frac{\partial \tilde{F}_n}{\partial x} \Big\rvert _{x=x_0}(x-x_0) + x_0$$ We may also note that for a deep rectifier network with $N$ nodes, each node is either on or off so it has $2^N$ possible activation patterns which correspond to distinct $\phi_i$ and a partition of $X$ into $2^N$ pair-wise disjoint and compact subsets. In principle, this means that for networks $F_\theta$ with $N$ nodes and at least one hidden layer we should empirically observe: $$\mathcal{L}[F_\theta] \sim \frac{1}{2^N}$$ If there are any doubts concerning the existence of suitable polynomials, for finitely many points $(p,q) \in \mathbb{R}^n \times \mathbb{R}^m$ there are infinitely many interpolating polynomials. The interesting question is which polynomial generalises best but that is beyond the scope of the present article. ## Discussion: At this point this idea still represents a rough sketch that must be developed further. But, I think it also provides some insight into why neural networks are so good at function approximation. They are approximating the intrinsic geometry of a mapping using piece-wise linear approximations which works because we can find a suitable polynomial approximation, and all polynomials are locally Lipschitz.	2020-07-11 11:58:23	{"extraction_info": {"found_math": true, "script_math_tex": 64, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 22, "x-ck12": 0, "texerror": 0, "math_score": 0.92115718126297, "perplexity": 173.37386533953523}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655929376.49/warc/CC-MAIN-20200711095334-20200711125334-00218.warc.gz"}
https://www.bakpax.com/assignment-library/assignments/1-1-practice-translating-expressions-sikig-zaruv	# 1-1 Practice - Translating Expressions ID: sikig-zaruv Theresa Urchell, BP BY-NC Subject: Algebra 2 14 questions # 1-1 Practice - Translating Expressions Classroom: Due: Student Name: Date Submitted: Write the expression to match the words. 1) thirteen less than thirty. 2) The quotient of twenty and twelve. 3) two times the sum of five and three. 4) The product of eight and fifty divided by four. Do the words match the expression? 5) $7(3+5)$ says seven times the sum of three and five. True or false? Write below. 6) $50-400$ says fifty less than four hundred. True or false? Write below. 7) $(6\times8)+19$ says nineteen more than the product of six and eight. True or false? Write below. 8) $\frac{12+9}{7}$ says the difference of twelve and nine divided by seven. True or false? Write below. Write the algebraic expression from the words. 9) three-fourths of x is subtracted from 9. 10) six times the sum of three and y. 11) the quotient of two times w and seven. Write the algebraic expressions in words. 12) $14b-3$ 13) $12(4x+2)$ 14) $\frac{1}{2}(6x+14)-5$	2020-11-27 08:08:29	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 7, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6645707488059998, "perplexity": 10139.098658047184}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141191511.46/warc/CC-MAIN-20201127073750-20201127103750-00423.warc.gz"}
https://practice.geeksforgeeks.org/problems/minimum-swaps-for-bracket-balancing/0	Showing: Handle Score @Ibrahim Nash 5761 @akhayrutdinov 5111 @mb1973 4989 @Quandray 4944 @saiujwal13083 4506 @sanjay05 3762 @marius_valentin_dragoi 3516 @sushant_a 3459 @verma_ji 3341 @KshamaGupta 3318 Minimum Swaps for Bracket Balancing Easy Accuracy: 27.14% Submissions: 4781 Points: 2 You are given a string of 2N characters consisting of N ‘[‘ brackets and N ‘]’ brackets. A string is considered balanced if it can be represented in the for S2[S1] where S1 and S2 are balanced strings. We can make an unbalanced string balanced by swapping adjacent characters. Calculate the minimum number of swaps necessary to make a string balanced. Input: The first line of input contains an integer T denoting the number of test cases. Then T test cases follow. The first line of each test case contains an integer N denoting the length of the string. The second line of each test case contains the string consisting of '[' and ']'. Output: Print the minimum number of swaps to make the string balanced for each test case in a new line. Constraints: 1<= T <=100 1<= N <=100000 Example: Input : []][][ Output : 2 First swap: Position 3 and 4 [][]][ Second swap: Position 5 and 6 [][][] Input : [[][]] Output : 0 String is already balanced.	2021-01-16 03:46:41	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.25757119059562683, "perplexity": 3445.8741829770097}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703499999.6/warc/CC-MAIN-20210116014637-20210116044637-00369.warc.gz"}
https://faculty.math.illinois.edu/Macaulay2/doc/Macaulay2-1.17/share/doc/Macaulay2/NoetherianOperators/html/_noetherian__Operators.html	# noetherianOperators -- Noetherian operators ## Description Let $R$ be a polynomial ring $R = K[x_1,\ldots,x_n]$ over a field $K$ of characteristic zero. Consider the Weyl algebra $D = R<dx_1,\ldots,dx_n>$, a prime ideal $P \subset R$ and a $P$-primary ideal. When this method is applied we obtain a finite list of differential operators $L_1,\ldots,L_m \in D$ such that $$Q = \{ f \,\in\, R\, \mid\, L_i\, \bullet\, f\, \in P \, \forall 1 \le i \le m \}.$$ We say that $\{L_1,\ldots,L_m\}$ is a set Noetherian operators for the primary ideal $Q$. In the output of the algorithm we always have that $m$ (the number of Noetherian operators) is equal to the multiplicity of $Q$ over the prime ideal $P$. i1 : R=QQ[x_1,x_2,x_3,x_4] o1 = R o1 : PolynomialRing i2 : Q = ideal(x_1^2,x_1x_2,x_1x_3,x_1x_4-x_3^2+x_1,x_3^2x_4-x_2^2,x_3^2x_4-x_3^2-x_2x_3+2x_1) 2 2 2 2 2 2 o2 = ideal (x , x x , x x , - x + x x + x , x x - x , x x - x x - x + 1 1 2 1 3 3 1 4 1 3 4 2 3 4 2 3 3 ------------------------------------------------------------------------ 2x ) 1 o2 : Ideal of R i3 : isPrimary Q o3 = true i4 : noetherianOperators(Q, Strategy => "PunctualHilbert") 2 2 2 2 o4 = {1, dx_3, dx_2, (2x + 2x )dx_2 + (4x + 4)dx_2dx_3 + (2x + 2)dx_3 + 4 4 4 4 ------------------------------------------------------------------------ 4*dx_1} o4 : List ## For the programmer The object noetherianOperators is .	2021-04-18 08:42:51	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5445935726165771, "perplexity": 288.21735351998603}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038469494.59/warc/CC-MAIN-20210418073623-20210418103623-00087.warc.gz"}
https://zbmath.org/?q=an%3A1160.47023	Multiplication and composition operators on Orlicz-Lorentz spaces.(English)Zbl 1160.47023 In this paper, the boundedness and invertibility of the multiplication operator $$M_u$$ are characterized in terms of the boundedness and invertibility of the complex-valued measurable function $$u$$, respectively. The paper also presents a necessary and sufficient condition for the composition operator to be bounded on a $$\sigma$$-finite measure space. MSC: 47B33 Linear composition operators 47B38 Linear operators on function spaces (general) 46E30 Spaces of measurable functions ($$L^p$$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)	2022-10-04 23:39:48	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.969399631023407, "perplexity": 359.1712594505313}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030337529.69/warc/CC-MAIN-20221004215917-20221005005917-00590.warc.gz"}
https://ellipsis.r-lib.org/news/index.html	# ellipsis 0.3.2 Unreleased • Compatibility with next version of rlang. • Changed license to MIT (#39). # ellipsis 0.3.1 2020-05-15 • Fixed an incompatibility with R devel. • New ?dots_used topic from which you can inherit documentation for ... documentation when the dots are passed to methods. # ellipsis 0.3.0 2019-09-20 • check_dots_used(), check_dots_unnamed(), and check_dots_empty() gain an action argument, to specify if they should error, warn, message or signal when the dots meet the condition. # ellipsis 0.2.0 2019-06-20 ellipsis has officially graduated from experimental to maturing in the package lifecycle. • The main change of this release is that check_() functions now throw custom errors, rather than warnings. • check_ functions have been optimised for the most common case of no problems. This means that you use it in more places without worrying about the performance cost. • New check_dots_empty() that checks that ... is empty (#11). • Improved error message suggesting that you check for mispecified argument names. # ellipsis 0.1.0 2019-02-19 • New check_dots_unnamed() that checks that all components of ... are unnamed (#7). • Fix a bug that caused check_dots_used() to emit many false positives (#8) # ellipsis 0.0.2 2019-01-09 • Fix a PROTECTion error	2022-05-27 22:16:04	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.27690914273262024, "perplexity": 9262.648267169581}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652663006341.98/warc/CC-MAIN-20220527205437-20220527235437-00359.warc.gz"}
http://www.r-bloggers.com/page/197/?s=git	# 3983 search results for "git" ## SHODAN API in R (With Examples) January 17, 2013 By Folks may debate the merits of the SHODAN tool, but in my opinion it’s a valuable resource, especially if used for “good”. What is SHODAN? I think ThreatPost summed it up nicely: “Shodan is a Web based search engine that discovers Internet facing computers, including desktops, servers and routers. The engine, created by programmer John ## Calculating a Gini Coefficients for a Number of Locales at Once in R January 17, 2013 By The Gini coefficient is a measure of the inequality of a distribution, most commonly used to compare inequality in income or wealth among countries.Let's first generate some random data to analyze. You can download my random data or use the code below ... ## Steve Culman on the plyr Package January 17, 2013 By At Davis R Users’ Group yesteray, Steve Culman gave us an introduction to the plyr package and how to use it to manipulate data. Here’s his presentation, and the accompanying demonstration script: Steve’s talk is based on this paper by Hadley Wickham in the Journal of Statistical Software. A lot of useful related... ## Project Euler — problem 25 January 16, 2013 By Finally, the fog lasting for days went away this morning and the sun comes out. It’s a lovely winter day. After taking a walk after lunch, I feel like doing some math. So, here comes the 25th Euler problem. The … Continue reading → ## Optimal number of clusters January 16, 2013 By In the last post, Examples of Current Major Market Clusters, we looked at clustering Major Markets into 4 groups based on their correlations in 2012. Today, I want to continue with clustering theme and discuss methods of selecting number of clusters. I will look at the following methods of selecting optimal number of clusters: Minimum ## Slightly Different Measure of Valuation January 16, 2013 By I grow tired of the tried and true standard measures of valuation, and from time to time I try to think of alternate methods. One thought was to analyze Ken French’s Market(ME) to Book(BE) Breakpoints by percentile. We can see by year at ... January 16, 2013 By Here I present an application that quantifies Wikipedia page views. It can visualise any topic in any language. It is (shamelessly) based on an application by the blogger Andrew Clark (pssguy), whose code is available here.I have added:multi ... ## Simulated Maximum Likelihood with R January 16, 2013 By First update on my research, details here. ## Version 1.0 of sqlutils available on CRAN January 15, 2013 By Version 1.0 of sqlutils has been released to CRAN. The sqlutils package is designed to manage a library of SQL files. This package grew out of the needs of an Office of Institutional Research where the vast majority of analysis is conducted on data from our Student Information System (SIS) which is stored in an Oracle database. A lot...	2014-09-02 04:23:49	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.25605568289756775, "perplexity": 3137.872710084015}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-35/segments/1409535921550.2/warc/CC-MAIN-20140901014521-00295-ip-10-180-136-8.ec2.internal.warc.gz"}
https://stats.stackexchange.com/questions/89214/equivalence-of-aic-and-p-values-in-model-selection	# Equivalence of AIC and p-values in model selection In a comment to the answer of this question, it was stated that using AIC in model selection was equivalent to using a p-value of 0.154. I tried it in R, where I used a "backward" subset selection algorithm to throw out variables from a full specification. First, by sequentially throwing out the variable with the highest p-value and stopping when all p-values are below 0.154 and, secondly, by dropping the variable which results in lowest AIC when removed until no improvement can be made. It turned out that they give roughly the same results when I use a p-value of 0.154 as threshold. Is this actually true? If so, does anyone know why or can refer to a source which explains it? P.S. I couldn't ask the person commenting or write a comment, because just signed up. I am aware that this is not the most suitable approach to model selection and inference etc. • (1) Prognostic modeling with logistic regression analysis: a comparison of selection and estimation methods in small data sets. Statistics in Medicine, 19, 1059-1079 (2) true for variables with df1, based on aic definition. But could be lower if your degrees of freedom of variables higher – charles Mar 7 '14 at 21:35 Variable selection done using statistical testing or AIC is highly problematic. If using $\chi^2$ tests, AIC uses a cutoff of $\chi^2$=2.0 which corresponds to $\alpha=0.157$. AIC when used on individual variables does nothing new; it just uses a more reasonable $\alpha$ than 0.05. A more reasonable (less inference-disturbing) $\alpha$ is 0.5.	2020-02-25 04:31:07	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.39112260937690735, "perplexity": 649.9014453876343}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875146004.9/warc/CC-MAIN-20200225014941-20200225044941-00398.warc.gz"}
http://mtrainer.herokuapp.com/inverses	Look at this matrix. Is it invertible? If so, try compute the inverse. $$A = \begin{bmatrix} 4 & 7 & 4 \\ 1 & 1 & 2 \\ 5 & 7 & 7 \end{bmatrix}$$ $$A^{-1}=\begin{bmatrix} -7 & -21 & 10 \\ 3 & 8 & -4 \\ 2 & 7 & -3 \end{bmatrix}$$	2021-06-16 17:56:10	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9764268398284912, "perplexity": 1051.8714784434064}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487625967.33/warc/CC-MAIN-20210616155529-20210616185529-00407.warc.gz"}
http://mathhelpforum.com/number-theory/216465-koshy-elementary-number-theory-applications-induction-sums-binomial-print.html	# Koshy-Elementary Number Theory with Applications...Induction, sums and binomial. • April 2nd 2013, 05:13 PM Leviathantheesper Koshy-Elementary Number Theory with Applications...Induction, sums and binomial. Well, I have a problem. These are some exercises from the Koshy's book about Number Theory... The first is: Verify that $\tbinom{n}{r}=\frac{n}{r}\tbinom{n-1}{r-1}$. That is easy, I did this: Attachment 27775 Then the next one was: Show that: Attachment 27776 I tried to prove it using Mathematical Induction, but I don't get to the result... I'll show what I've done: Attachment 27777 But I don't know how to get to where I wanna get... • April 4th 2013, 09:56 PM johng Re: Koshy-Elementary Number Theory with Applications...Induction, sums and binomial. Hi, You didn't say you must have a proof by induction (I don't see an easy inductive proof). Here's an easy proof: Attachment 27809 The formula represents two different way of counting the ways one can choose n people from 2n people with exactly n men and n women -- a term of the sum represents choosing r men and thus n-r women; letting r vary from 0 to n we get the total number of ways of choosing the n people. This is in fact the way I remember the formula. D. E. Knuth's Art of Computer Programming, Vol I has a wealth of combinatoric formulas like this. Perhaps even more can be found in Concrete Mathematics by Knuth, et al.	2016-05-31 05:25:18	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 1, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8949096202850342, "perplexity": 911.9783856221985}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-22/segments/1464051165777.94/warc/CC-MAIN-20160524005245-00192-ip-10-185-217-139.ec2.internal.warc.gz"}
https://pos.sissa.it/251/292/	Volume 251 - The 33rd International Symposium on Lattice Field Theory (LATTICE 2015) - Theoretical Developments (talks) Topology and glueballs in $SU(7)$ Yang-Mills with open boundary conditions A. Amato*, B. Lucini and G. Bali Full text: pdf Published on: July 15, 2016 DOI: https://doi.org/10.22323/1.251.0292 How to cite Metadata are provided both in "article" format (very similar to INSPIRE) as this helps creating very compact bibliographies which can be beneficial to authors and readers, and in "proceeding" format which is more detailed and complete. Open Access	2023-04-01 08:01:23	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.18553730845451355, "perplexity": 5548.574826916781}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296949701.56/warc/CC-MAIN-20230401063607-20230401093607-00540.warc.gz"}
https://shelah.logic.at/papers/696/	# Sh:696 • Goldstern, M., & Shelah, S. (2002). Antichains in products of linear orders. Order, 19(3), 213–222. • Abstract: We show that: For many cardinals \lambda, for all n\in \{2,3,4,\ldots\} There is a linear order L such that L^n has no (incomparability-)antichain of cardinality \lambda, while L^{n+1} has an antichain of cardinality \lambda. For any nondecreasing sequence (\lambda_n: n \in \{2,3,4,\ldots\}) of infinite cardinals it is consistent that there is a linear order L such that L^n has an antichain of cardinality \lambda_n, but not one of cardinality \lambda_n^+. • Current version: 2002-04-06_11 (9p) published version (10p) Bib entry @article{Sh:696, author = {Goldstern, Martin and Shelah, Saharon}, title = {{Antichains in products of linear orders}}, journal = {Order}, fjournal = {Order. A Journal on the Theory of Ordered Sets and its Applications}, volume = {19}, number = {3}, year = {2002}, pages = {213--222}, issn = {0167-8094}, mrnumber = {1942184}, mrclass = {06A05 (03E04 03E35)}, doi = {10.1023/A:1021289412771}, note = {\href{https://arxiv.org/abs/math/9902054}{arXiv: math/9902054}}, arxiv_number = {math/9902054} }	2021-01-20 03:40:54	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8076015114784241, "perplexity": 9350.931525775475}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703519883.54/warc/CC-MAIN-20210120023125-20210120053125-00499.warc.gz"}
https://didacticmind.com/2020/11/admit-to-your-screw-ups-like-a-man.html	“We are Forerunners. Guardians of all that exists. The roots of the Galaxy have grown deep under our careful tending. Where there is life, the wisdom of our countless generations has saturated the soil. Our strength is a luminous sun, towards which all intelligence blossoms… And the impervious shelter, beneath which it has prospered.” by \| Nov 14, 2020 \| Masculinity \| 3 comments You may remember that some time ago I posted up a video concerning the SSC Tuatara‘s epic 331mph record-breaking speed run. Actually, I’m not sure what the true speed was, because SSC claims that the Tuatara can hit 331mph, but the average speed on both runs – forward and back – was 316mph. Well, some intrepid boffins decided to check on whether that’s what actually happened, and according to them… it didn’t: It’s all very scientific, mathematical, and data-oriented analysis. There is simply no getting away from a hard mathematical fact: $Speed = \frac{Distance}{Time}$ Given the fact that the calculated distance is 1.44 miles (gah imperial units eyecross), and the time taken to cover that distance in the video evidence is 24 seconds, dividing 1.44 by 24 gives you 0.06 miles per second. There are 3,600 seconds in an hour. So multiply 0.06 by 3,600 and you get… 216mph. In other words, the average speed of the car over that section of road was incontrovertibly 216mph, based on the evidence given by SSC and Top Gear themselves. Yet both SSC and the Bullshit Broadcasting Corporation claim that the car hit 331mph during that run, over that precise stretch of road, and the speedo never dipped below 290mph or thereabouts. It doesn’t take a man with two degrees in mathematics (like me) to figure out that something doesn’t add up. Now I’m NOT saying that SSC or Top Gear or the BBC or whatever are lying about the top speed achieved. (Well… Top Gear, without Jezza, Hamster, and Captain Slow IS NOT Top Gear to begin with, so…) But the mathematics are absolutely clear. There is simply NO WAY that the Tuatara did that run at that speed. Three guys did the analysis in two different videos. That video up above is the second of those analyses. All three of them then got together and discussed their findings, and the results make for very compelling viewing: Now, the people at SSC – specifically, Jerod Shelby – could have responded with anger and indignation at being questioned. They could have gone on a full press offensive – and in fact they did, at first. Perhaps they could have threatened to sue the three YouTubers who picked apart the footage for being asshats, or whatever. But they avoided going too far down that path. Jerod Shelby acted as a man should. He issued a statement clearly owning up to the problems with that speed run and admitting that he saw exactly the same doubts that other people did when they saw the video: That was a carefully worded masterclass in taking ownership and responsibility for what could otherwise have proven to be an absolute PR nightmare. In fact, this controversy already is proving to be a huge problem for SSC. They aren’t a very big company and a number of their hypercar customers are severely pissed off at them for possibly falsifying their speed run. (I am NOT saying that they did falsify the run. I am simply pointing out that the results of their speed run LOOK very screwy. That doesn’t mean that SSC, themselves, actually did anything deliberately wrong or misled anyone.) This, gentlemen, is how you take responsibility for stuff that goes wrong. You own it and understand very clearly that you, and YOU ALONE, must take steps to fix things. If you do not do this, then you alone are at fault for the resultant loss of trust and faith in yourself, your product, and your brand. I do hope that Jerod Shelby and his team can, in fact, crack 313mph with that car. Based on the evidence, though, I seriously doubt that they have achieved something that thus far only the Koenigsegg Jesko or the Bugatti Chiron appear to be even remotely capable of achieving. That level of speed is simply mind-boggling. When the Bugatti Chiron did its (unofficial) 304.77mph trip around Ehra-Lessien to set the bar for every other hypercar to reach, they had to do so under incredibly specific conditions. The air temperature, pressure, and humidity all had to be exactly right. The car had to be specifically setup for that run – the actual vehicle that made the run is not, strictly speaking, a production model, but is rather a specially designed one-off just for the job. And the VW proving-grounds at Ehra-Lessien provide one of the only places anywhere in the ENTIRE WORLD where you can actually crank a car up to those kinds of insane speeds. Yet SSC would have you believe that they did this along a road in the desert with nothing more than a production-model Tuatara? Yeah… something doesn’t quite sit right with me about that. Again, I am NOT claiming that SSC did anything wrong or untoward. I’m just saying that the numbers don’t add up and the logic doesn’t tie out. Coming back to Jerod Shelby’s statement – that is how you take ownership and lead from the front. This is a template of masculine behaviour that you must embrace if you are ever in doubt about what is easy versus what is right. Plenty of idiots will argue that SSC deliberately misled their fans. After watching Mr. Shelby’s statement, I cannot agree with them and I’m willing to give him and his company the benefit of the doubt. Let them redo the speed run with full independent verification. Let’s find out what the Tuatara can really do, free of all doubt and negativity. We already know that the SSC Tuatara can beat a Bugatti Veyron in a drag race. It is an absolutely incredible machine. Let’s see what it can REALLY do, absent any controversy or doubt. If they break the Bugatti Chiron’s record, for real this time, then I suspect that the folks at Bugatti will be the very first to congratulate them – because when you give respect and honour to those that you compete with, and they are themselves respectful and honourable, then what you give will be returned to you an hundredfold. Subscribe to Didactic Mind * indicates required Email Format Read on for more wisdom and insight: 1. Honestly, who cares about those speed runs. Most of these cars will end up as garage queens and will never see the light of day. Some people say that Koenigsegg and Bugatti owners drive their cars, but who knows. The owners will barely reach over 300 k.m let alone 300mph. That’s probably the main reason to buy a car like this other than status. If I had the money I would have bought the ssc because it looks good and probably would feel good to drive given the acceleration. Also fuck the Bolshevik Broadcasting Cucks. They are begging Clarkson to come back and he declined.	2020-12-01 12:28:16	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 2, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.43868228793144226, "perplexity": 2126.5886053985073}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141674082.61/warc/CC-MAIN-20201201104718-20201201134718-00458.warc.gz"}
http://bettymath.blogspot.com/2012/05/natural-logarithm.html	## Thursday, May 24, 2012 ### Natural Logarithm Some book authors define the natural logarithm function, ln (x) as $ln(x)=\int_{1}^{x}\frac{1}{t}dt,\; \; x>0$. If we take a look at the graphs below, the red curve represents the graph of $y=\frac{1}{x}$, and the dark green curve represents the graph of $y=ln(x)$. The purple region falls below the red curve is bounded between x = h and 1, while the blue region is bounded between x = 1 and k. Now scroll the value of k, do you notice that point K moves according to the k value? The y-coordinate of point K is the area of the blue region. Same concept applies to the value of h and point H. Here comes the question, do you know how to get negative y-coordinate for point H? Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now) Betty, Created with GeoGebra	2018-01-17 23:47:19	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 3, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6060170531272888, "perplexity": 477.18292027499893}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-05/segments/1516084887024.1/warc/CC-MAIN-20180117232418-20180118012418-00745.warc.gz"}
http://www.reddit.com/r/cheatatmathhomework/comments/19gylu/understanding_strong_induction/	[–] 1 point2 points (0 children) sorry, this has been archived and can no longer be voted on With such a general question the only answer would be a textbook chapter or an online tutorial. Otherwise I'd be trying to create one from scratch in a little answer box. Google "strong induction" gives a lot of hits of tutorials. Wikipedia is always a good start, it's concise."strong versus weak induction" hits more specific ones. [–] 0 points1 point (0 children) sorry, this has been archived and can no longer be voted on All right. The difference between 'weak' or 'regular' induction and 'strong' induction is the hypothesis step. In regular induction, you show that P(n)-->P(n+1). In strong induction, you have to use P(1), P(2), ...,, P(n-1), and P(n) to show that P(n+1) is true. You might not have to use all of them, but you might not know in advance which one you need. In particular, P(n) might not be of any help to you at all. [–] 0 points1 point (0 children) sorry, this has been archived and can no longer be voted on Suppose you have proven [; p(1) ;] and that if [; p(1),p(2),p(3),\dots,p(n) ;] hold, then [; p(n + 1) ;] holds. So 1) [; p(1) ;] holds by basis. 2) [; p(1) ;] holds and so [; p(2) ;] holds. and here strong induction changes from weak induction. 3) [; p(1),p(2) ;] hold and so [; p(3) ;] holds 4) [; p(1),p(2),p(3) ;] hold and so [; p(4) ;] holds 5) [; p(1),p(2),p(3),p(4) ;] hold and so [; p(5) ;] holds 6) [; p(1),p(2),p(3),p(4),p(5) ;] hold and so [; p(6) ;] holds and so on [; \vdots ;] [–] 0 points1 point (0 children) sorry, this has been archived and can no longer be voted on Look at the other people's replies to understand how strong induction and weak induction are different, and then come back to this one since I am going to assume you will get thinking and come up with an incorrect conclusion, as many people do. A lot of people think that strong induction can just be rephrased in terms of weak induction. While this is true for a lot examples of strong induction you will be given, this isn't true for everything. To show you why this isn't always the case, think about if I had something to prove about the the infinite set of numbers S = {1/2 , 2/3 , 3/4 , ... , 1}. I know P( 1/2 ) is true, but I want to know about P( 1 ). At what step would I go to the 1? If I can prove P( x ) follows from using strong induction, then I can show P(1). Think about it like this: If I take any x less than 1 that is in S, I can use strong induction again to prove P(x) since eventually I get back to proving P( 1/2 ). But using an infinite chain of P( 1/2 ) => P( 2/3 ) => ... I can never get to P( 1 ), since it isn't a part of the chain.	2014-10-25 15:34:04	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.848200798034668, "perplexity": 1818.2737710928734}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-42/segments/1414119648384.20/warc/CC-MAIN-20141024030048-00312-ip-10-16-133-185.ec2.internal.warc.gz"}
https://math.stackexchange.com/questions/2906359/application-of-greens-theorem-in-a-plane	# Application of Green's theorem in a plane Apply Green's theorem in a plane to evaluate $\displaystyle\int(2x^2-y^2)dx + (x^2+y^2)dy$, where $C$ is the curve enclosed by the semi-circle $x^2+y^2=1$ and the $x$-axis. I've done this already $$\int Pdx + Qdy = \iint (dQ/dx - dP/dy) \text{ } dxdy$$ $P=(2x^2-y^2)$ $Q=(x^2+y^2)$ $\displaystyle\frac{dQ}{dx}=2x$ $\displaystyle\frac{dP}{dy}=-2y$ $$\iint (2x+2y)dxdy$$ So how do I get the range for $x$ and $y$ to integrate with respect to? • Welcome to MSE. You'll get a much more positive response (more help and fewer votes to close) if you show that you've made an effort to solve the problem yours elf. What have you done so far? Where are you having trouble? – saulspatz Sep 5 '18 at 15:21 • @saulspatz Thanks for response check my edit – Eric kioko Sep 5 '18 at 17:01 ## 1 Answer You've done fine so far. The boundary of the region is the semicircle described, so the region you need for the double is simply the interior of that semicircle. In polar coordinates $0\leq r\leq1,\ 0\leq\theta\leq\pi.$	2019-06-18 06:41:42	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8571515679359436, "perplexity": 749.4468000457224}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560627998690.87/warc/CC-MAIN-20190618063322-20190618085322-00523.warc.gz"}
http://www.gamedev.net/page/resources/_/technical/general-programming/how-to-handle-circular-dependencies-with-templates-in-c-r3517	• Create Account Like 10Likes Dislike # How to Handle Circular Dependencies with Templates in C++ By Kent Fagerjord \| Published Jan 16 2014 11:10 AM in General Programming Peer Reviewed by (Dave Hunt, Josh Vega, Dragonsoulj) c++ templates circular dependency entity component Although templates in C++ are well known, and more and more people actually do know how to wrap their head around them, there are a couple of less-common circumstances which can leave the programmer rather clueless. This is a problem I encountered while tuning the Message-Component-Entity system in our game under development, Burnt Islands. ## The problem In the C++ language, there are not many features that are as powerful as templates. But their strength is also contributing to the complexity of templates. With standard classes and structs, you can hide the implementation of the methods within the class, and you can put those in separate compilation units (cpp files). With templates, there is a whole other story. When the compiler sees a template (class and method), it must know the internals of that particular method. This is because templates doesn't really exist until they are used, and with varying template parameters, the classes and structs are generated, and is in reality completely separate classes for different parameters. Here is one quirk: circular dependencies with templated classes and classes with templated methods. All code in the post (and build scripts) is available at https://github.com/Studiofreya/code-samples/tree/master/circular-templates. In this particular case, Visual Studio is sort of stupid. It deliberately accepts code which it really shouldn't accept. This isn't really a problem if you only target the Microsoft stack and environment. If you plan to deploy to other platforms, it'll be a problem. The best advice is to get up both build systems early in the development, so any problems are caught early. ## Code (problematic) But on with the problem. Consider the following file. // This file only compiles in Visual Studio 2010 newer template<typename T> class Message { public: typedef T type; static const int MsgId = 0; explicit Message( const T & t ) : data(t) { } type data; }; typedef Message<int> MsgInt; typedef Message<long> MsgLong; typedef Message<float> MsgFloat; typedef Message<double> MsgDouble; class MessageHandler { public: template<typename MSG, typename T> void setHandler( const T & msghandler ) { /* do stuff / auto id = MSG::MsgId; // Make sure this is a message type } }; // Forward declaration of classes class Component; class Entity; class Component { public: template<typename MSG> void setEntityHandler( Entity & entity ) { auto handleMsg = [&] ( const MSG & msg ) { / do stuff / }; entity.m_MessageHandler.setHandler<MSG>( handleMsg ); } MessageHandler m_MessageHandler; }; class Entity { public: template<typename MSG> void setComponentHandler( Component & component ) { auto handleMsg = [&] ( const MSG & msg ) { / do stuff / }; component.m_MessageHandler.setHandler<MSG>( handleMsg ); } MessageHandler m_MessageHandler; }; int main() { Component c; Entity e; e.setComponentHandler<MsgDouble>(c); return 0; } The problem is in this line entity.m_MessageHandler.setHandler( handleMsg ); in the Component class. It uses an undefined class which has been forward declared. Visual Studio is trying to be smart. It can see forwards and there is an implementation (definition) of the Entity class further down below. GCC (g++) is not trying to be smart, and thus the code above fail to compile with g++. Here is the error with g++. g++-4.8.1 -std=c++11 circular-templates.cpp -o circdep circular-templates.cpp: In member function 'void Component::setEntityHandler(Entity&)': circular-templates.cpp:55:19: error: invalid use of incomplete type 'class Entity' entity.m_MessageHandler.setHandler( handleMsg ); ^ circular-templates.cpp:41:7: error: forward declaration of 'class Entity' class Entity; ^ circular-templates.cpp:55:51: error: expected primary-expression before '>' token entity.m_MessageHandler.setHandler( handleMsg ); ^ ## Clean code (ideal) Here is the fixed code where it will compile in both MSVC and g++. // This file compiles in both Visual Studio 2010 (and newer) and G++ with C++11. template<typename T> class Message { public: typedef T type; static const int MsgId = 0; explicit Message( const T & t ) : data(t) { } type data; }; typedef Message<int> MsgInt; typedef Message<long> MsgLong; typedef Message<float> MsgFloat; typedef Message<double> MsgDouble; class MessageHandler { public: template<typename MSG, typename T> void setHandler( const T & msghandler ) { / do stuff / auto id = MSG::MsgId; // Make sure this is a message type } }; // Forward declaration of classes class Component; class Entity; class Component { public: template<typename MSG> void setEntityHandler( Entity & entity ); MessageHandler m_MessageHandler; }; class Entity { public: template<typename MSG> void setComponentHandler( Component & component ); MessageHandler m_MessageHandler; }; // Implementation of circular dependencies template<typename MSG> void Component::setEntityHandler( Entity & entity ) { auto handleMsg = [&] ( const MSG & msg ) { / do stuff / }; entity.m_MessageHandler.setHandler<MSG>( handleMsg ); } template<typename MSG> void Entity::setComponentHandler( Component & component ) { auto handleMsg = [&] ( const MSG & msg ) { / do stuff */ }; component.m_MessageHandler.setHandler<MSG>( handleMsg ); } // Main int main() { Component c; Entity e; e.setComponentHandler<MsgDouble>(c); return 0; } This file will compile in both MSVC and G++, and with MSVC it'll produce identical assembly code for both files. The clue to solving this problem is to declare both classes before providing the definitions (implementations). It's not possible to split the declaration and definition into separate files, but you can structure them as if they were in separate files. Here both Entity and Component are declared before any implementation code. In the end, this might or might not be a problem you will encounter. But when you encounter it, you'll know about it and remember there are solutions available. All code in the post (and build scripts) is available at https://github.com/Studiofreya/code-samples/tree/master/circular-templates. Currently a full time indie developer (previously employed as a C++ system programmer) working on Burnt Islands (http://games.studiofreya.com/). http://studiofreya.com/ Why not optimize and use virtual function pointers. The events can be handled through a simple array of functions labeled with maybe enum or something. I never liked event loops. @codenine75a - The article isn't about event loops. It's about how to avoid circular dependencies with templates in C++. @codenine75a: As Dave Hunt said, this article was about handling circular dependencies with templates in C++, and thus the code samples are at a bare minimum. I chose to use real world names for the class names, because I personally can't follow advanced code written like "class Foo" and "class Bar". However, I'm planning some articles about messages and how to use implement and use them in a game. I will not make any promises, but I hope to get them done this year . @Freya Yeah, it is especially awful when I see code written using "Class A", Class B", "int a"....etc BTW I did enjoy the article. Just a note about one comment in the article which is misleading. "It's not possible to split the declaration and definition into separate files", it is possible, you just have an include after the declarations or include the files in order from another header. This is fairly common practice with things such as Boost where you put the definition portion of the code in a 'details' directory. It is not a h versus c file styled break but it does allow you to break the code into logical separate units for well organized declaration and definition portions. Visual Studio is trying to be smart. It can see forwards and there is an implementation (definition) of the Entity class further down below. GCC (g++) is not trying to be smart, and thus the code above fail to compile with g++. It's actually kind of the other way around. Visual Studio is still to this day missing two-phase lookup. It works not because it's smart but because it's incorrectly delaying all semantic analysis of the template until instantiation, which while solving issues like this causes other bugs. You could actually just modify your templates slightly to make GCC and other standards-conforming compilers happy by making the type of Entity a template parameter to the message handler functions (and hence a dependent type). Then there will be no semantic checks on the entity parameter until instantiation and everything will work. Just a note about one comment in the article which is misleading. "It's not possible to split the declaration and definition into separate files", It's also possible for template specializations, which granted are only used or useful in certain cases. Note: Please offer only positive, constructive comments - we are looking to promote a positive atmosphere where collaboration is valued above all else. PARTNERS	2014-03-08 11:19:14	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.22219093143939972, "perplexity": 6785.226829897616}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-10/segments/1393999654345/warc/CC-MAIN-20140305060734-00043-ip-10-183-142-35.ec2.internal.warc.gz"}
http://www.worldlibrary.in/articles/eng/Control_chart	#jsDisabledContent { display:none; } My Account \| Register \| Help # Control chart Article Id: WHEBN0000435754 Reproduction Date: Title: Control chart Author: World Heritage Encyclopedia Language: English Subject: Collection: Publisher: World Heritage Encyclopedia Publication Date: ### Control chart Control chart One of the Seven Basic Tools of Quality First described by Walter A. Shewhart Purpose To determine whether a process should undergo a formal examination for quality-related problems Control charts, also known as Shewhart charts (after Walter A. Shewhart) or process-behavior charts, in statistical process control are tools used to determine if a manufacturing or business process is in a state of statistical control. ## Contents • Overview 1 • History 2 • Chart details 3 • Chart usage 3.1 • Choice of limits 3.2 • Calculation of standard deviation 3.3 • Rules for detecting signals 4 • Alternative bases 5 • Performance of control charts 6 • Criticisms 7 • Types of charts 8 • Notes 10 • Bibliography 11 ## Overview If analysis of the control chart indicates that the process is currently under control (i.e., is stable, with variation only coming from sources common to the process), then no corrections or changes to process control parameters are needed or desired. In addition, data from the process can be used to predict the future performance of the process. If the chart indicates that the monitored process is not in control, analysis of the chart can help determine the sources of variation, as this will result in degraded process performance.[1] A process that is stable but operating outside of desired (specification) limits (e.g., scrap rates may be in statistical control but above desired limits) needs to be improved through a deliberate effort to understand the causes of current performance and fundamentally improve the process.[2] The control chart is one of the seven basic tools of quality control.[3] Typically control charts are used for time-series data, though they can be used for data that have logical comparability (i.e. you want to compare samples that were taken all at the same time, or the performance of different individuals), however the type of chart used to do this requires consideration.[4] ## History The control chart was invented by [6] Shewhart stressed that bringing a production process into a state of statistical control, where there is only common-cause variation, and keeping it in control, is necessary to predict future output and to manage a process economically. Shewhart created the basis for the control chart and the concept of a state of statistical control by carefully designed experiments. While Shewhart drew from pure mathematical statistical theories, he understood that data from physical processes typically produce a "normal distribution curve" (a Gaussian distribution, also commonly referred to as a "bell curve"). He discovered that observed variation in manufacturing data did not always behave the same way as data in nature (Brownian motion of particles). Shewhart concluded that while every process displays variation, some processes display controlled variation that is natural to the process, while others display uncontrolled variation that is not present in the process causal system at all times.[7] In 1924 or 1925, Shewhart's innovation came to the attention of W. Edwards Deming, then working at the Hawthorne facility. Deming later worked at the United States Department of Agriculture and became the mathematical advisor to the United States Census Bureau. Over the next half a century, Deming became the foremost champion and proponent of Shewhart's work. After the defeat of Japan at the close of World War II, Deming served as statistical consultant to the Supreme Commander for the Allied Powers. His ensuing involvement in Japanese life, and long career as an industrial consultant there, spread Shewhart's thinking, and the use of the control chart, widely in Japanese manufacturing industry throughout the 1950s and 1960s. ## Chart details A control chart consists of: • Points representing a statistic (e.g., a mean, range, proportion) of measurements of a quality characteristic in samples taken from the process at different times (i.e., the data) • The mean of this statistic using all the samples is calculated (e.g., the mean of the means, mean of the ranges, mean of the proportions) • A centre line is drawn at the value of the mean of the statistic • The standard error (e.g., standard deviation/sqrt(n) for the mean) of the statistic is also calculated using all the samples • Upper and lower control limits (sometimes called "natural process limits") that indicate the threshold at which the process output is considered statistically 'unlikely' and are drawn typically at 3 standard errors from the centre line The chart may have other optional features, including: • Upper and lower warning or control limits, drawn as separate lines, typically two standard errors above and below the centre line • Division into zones, with the addition of rules governing frequencies of observations in each zone • Annotation with events of interest, as determined by the Quality Engineer in charge of the process's quality • ACTION ON SPECIAL CAUSES (n.b., there are several rule sets for detection of signal, this is just one set. The rule set should be clearly stated.) 1. Any point outside of the control limits 2. A Run of 7 Points all above or All below the central line - Stop the production > Quarantine and 100% check > Check 5 Consecutive samples > Continue The Process. 3. A Run of 7 Point Up or Down - Instruction as above ### Chart usage If the process is in control (and the process statistic is normal), 99.7300% of all the points will fall between the control limits. Any observations outside the limits, or systematic patterns within, suggest the introduction of a new (and likely unanticipated) source of variation, known as a special-cause variation. Since increased variation means increased quality costs, a control chart "signaling" the presence of a special-cause requires immediate investigation. This makes the control limits very important decision aids. The control limits provide information about the process behavior and have no intrinsic relationship to any specification targets or engineering tolerance. In practice, the process mean (and hence the centre line) may not coincide with the specified value (or target) of the quality characteristic because the process' design simply cannot deliver the process characteristic at the desired level. Control charts limit specification limits or targets because of the tendency of those involved with the process (e.g., machine operators) to focus on performing to specification when in fact the least-cost course of action is to keep process variation as low as possible. Attempting to make a process whose natural centre is not the same as the target perform to target specification increases process variability and increases costs significantly and is the cause of much inefficiency in operations. Process capability studies do examine the relationship between the natural process limits (the control limits) and specifications, however. The purpose of control charts is to allow simple detection of events that are indicative of actual process change. This simple decision can be difficult where the process characteristic is continuously varying; the control chart provides statistically objective criteria of change. When change is detected and considered good its cause should be identified and possibly become the new way of working, where the change is bad then its cause should be identified and eliminated. The purpose in adding warning limits or subdividing the control chart into zones is to provide early notification if something is amiss. Instead of immediately launching a process improvement effort to determine whether special causes are present, the Quality Engineer may temporarily increase the rate at which samples are taken from the process output until it's clear that the process is truly in control. Note that with three-sigma limits, common-cause variations result in signals less than once out of every twenty-two points for skewed processes and about once out of every three hundred seventy (1/370.4) points for normally distributed processes.[8] The two-sigma warning levels will be reached about once for every twenty-two (1/21.98) plotted points in normally distributed data. (For example, the means of sufficiently large samples drawn from practically any underlying distribution whose variance exists are normally distributed, according to the Central Limit Theorem.) ### Choice of limits Shewhart set 3-sigma (3-standard error) limits on the following basis. Shewhart summarized the conclusions by saying: ... the fact that the criterion which we happen to use has a fine ancestry in highbrow statistical theorems does not justify its use. Such justification must come from empirical evidence that it works. As the practical engineer might say, the proof of the pudding is in the eating.[9] Though he initially experimented with limits based on probability distributions, Shewhart ultimately wrote: Some of the earliest attempts to characterize a state of statistical control were inspired by the belief that there existed a special form of frequency function f and it was early argued that the normal law characterized such a state. When the normal law was found to be inadequate, then generalized functional forms were tried. Today, however, all hopes of finding a unique functional form f are blasted. The control chart is intended as a heuristic. Deming insisted that it is not a hypothesis test and is not motivated by the Neyman–Pearson lemma. He contended that the disjoint nature of population and sampling frame in most industrial situations compromised the use of conventional statistical techniques. Deming's intention was to seek insights into the cause system of a process ...under a wide range of unknowable circumstances, future and past.... He claimed that, under such conditions, 3-sigma limits provided ... a rational and economic guide to minimum economic loss... from the two errors: 1. Ascribe a variation or a mistake to a special cause (assignable cause) when in fact the cause belongs to the system (common cause). (Also known as a Type I error) 2. Ascribe a variation or a mistake to the system (common causes) when in fact the cause was a special cause (assignable cause). (Also known as a Type II error) ### Calculation of standard deviation As for the calculation of control limits, the standard deviation (error) required is that of the common-cause variation in the process. Hence, the usual estimator, in terms of sample variance, is not used as this estimates the total squared-error loss from both common- and special-causes of variation. An alternative method is to use the relationship between the range of a sample and its standard deviation derived by Leonard H. C. Tippett, an estimator which tends to be less influenced by the extreme observations which typify special-causes. ## Rules for detecting signals The most common sets are: There has been particular controversy as to how long a run of observations, all on the same side of the centre line, should count as a signal, with 6, 7, 8 and 9 all being advocated by various writers. The most important principle for choosing a set of rules is that the choice be made before the data is inspected. Choosing rules once the data have been seen tends to increase the Type I error rate owing to testing effects suggested by the data. ## Alternative bases In 1935, the British Standards Institution, under the influence of Egon Pearson and against Shewhart's spirit, adopted control charts, replacing 3-sigma limits with limits based on percentiles of the normal distribution. This move continues to be represented by John Oakland and others but has been widely deprecated by writers in the Shewhart–Deming tradition. ## Performance of control charts When a point falls outside of the limits established for a given control chart, those responsible for the underlying process are expected to determine whether a special cause has occurred. If one has, it is appropriate to determine if the results with the special cause are better than or worse than results from common causes alone. If worse, then that cause should be eliminated if possible. If better, it may be appropriate to intentionally retain the special cause within the system producing the results. It is known that even when a process is in control (that is, no special causes are present in the system), there is approximately a 0.27% probability of a point exceeding 3-sigma control limits. So, even an in control process plotted on a properly constructed control chart will eventually signal the possible presence of a special cause, even though one may not have actually occurred. For a Shewhart control chart using 3-sigma limits, this false alarm occurs on average once every 1/0.0027 or 370.4 observations. Therefore, the in-control average run length (or in-control ARL) of a Shewhart chart is 370.4. Meanwhile, if a special cause does occur, it may not be of sufficient magnitude for the chart to produce an immediate alarm condition. If a special cause occurs, one can describe that cause by measuring the change in the mean and/or variance of the process in question. When those changes are quantified, it is possible to determine the out-of-control ARL for the chart. It turns out that Shewhart charts are quite good at detecting large changes in the process mean or variance, as their out-of-control ARLs are fairly short in these cases. However, for smaller changes (such as a 1- or 2-sigma change in the mean), the Shewhart chart does not detect these changes efficiently. Other types of control charts have been developed, such as the EWMA chart, the CUSUM chart and the real-time contrasts chart, which detect smaller changes more efficiently by making use of information from observations collected prior to the most recent data point.[11] Most control charts work best for numeric data with Gaussian assumptions. The real-time contrasts chart was proposed to monitor process with complex characteristics, e.g. high-dimensional, mix numerical and categorical, missing-valued, non-Gaussian, non-linear relationship.[11] ## Criticisms Several authors have criticised the control chart on the grounds that it violates the likelihood principle. However, the principle is itself controversial and supporters of control charts further argue that, in general, it is impossible to specify a likelihood function for a process not in statistical control, especially where knowledge about the cause system of the process is weak. Some authors have criticised the use of average run lengths (ARLs) for comparing control chart performance, because that average usually follows a geometric distribution, which has high variability and difficulties. Some authors have criticized that most control charts focus on numeric data. Nowadays, process data can be much more complex, e.g. non-Gaussian, mix numerical and categorical, missing-valued.[11] ## Types of charts Chart Process observation Process observations relationships Process observations type Size of shift to detect \bar x and R chart Quality characteristic measurement within one subgroup Independent Variables Large (≥ 1.5σ) \bar x and s chart Quality characteristic measurement within one subgroup Independent Variables Large (≥ 1.5σ) Shewhart individuals control chart (ImR chart or XmR chart) Quality characteristic measurement for one observation Independent Variables Large (≥ 1.5σ) Three-way chart Quality characteristic measurement within one subgroup Independent Variables Large (≥ 1.5σ) p-chart Fraction nonconforming within one subgroup Independent Attributes Large (≥ 1.5σ) np-chart Number nonconforming within one subgroup Independent Attributes Large (≥ 1.5σ) c-chart Number of nonconformances within one subgroup Independent Attributes Large (≥ 1.5σ) u-chart Nonconformances per unit within one subgroup Independent Attributes Large (≥ 1.5σ) EWMA chart Exponentially weighted moving average of quality characteristic measurement within one subgroup Independent Attributes or variables Small (< 1.5σ) CUSUM chart Cumulative sum of quality characteristic measurement within one subgroup Independent Attributes or variables Small (< 1.5σ) Time series model Quality characteristic measurement within one subgroup Autocorrelated Attributes or variables N/A Regression control chart Quality characteristic measurement within one subgroup Dependent of process control variables Variables Large (≥ 1.5σ) Some practitioners also recommend the use of Individuals charts for attribute data, particularly when the assumptions of either binomially distributed data (p- and np-charts) or Poisson-distributed data (u- and c-charts) are violated.[12] Two primary justifications are given for this practice. First, normality is not necessary for statistical control, so the Individuals chart may be used with non-normal data.[13] Second, attribute charts derive the measure of dispersion directly from the mean proportion (by assuming a probability distribution), while Individuals charts derive the measure of dispersion from the data, independent of the mean, making Individuals charts more robust than attributes charts to violations of the assumptions about the distribution of the underlying population.[14] It is sometimes noted that the substitution of the Individuals chart works best for large counts, when the binomial and Poisson distributions approximate a normal distribution. i.e. when the number of trials n > 1000 for p- and np-charts or λ > 500 for u- and c-charts. Critics of this approach argue that control charts should not be used when their underlying assumptions are violated, such as when process data is neither normally distributed nor binomially (or Poisson) distributed. Such processes are not in control and should be improved before the application of control charts. Additionally, application of the charts in the presence of such deviations increases the type I and type II error rates of the control charts, and may make the chart of little practical use. ## Notes 1. ^ 2. ^ 3. ^ 4. ^ 5. ^ http://www.porticus.org/bell/westernelectric_history.html#Western%20Electric%20-%20A%20Brief%20History 6. ^ Western Electric – A Brief History 7. ^ "Why SPC?" British Deming Association SPC Press, Inc. 1992 8. ^ 9. ^ 10. ^ 11. ^ a b c 12. ^ 13. ^ 14. ^	2021-04-16 08:25:35	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6149271726608276, "perplexity": 2040.2144106333271}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038088731.42/warc/CC-MAIN-20210416065116-20210416095116-00230.warc.gz"}
http://m-phi.blogspot.com/2013/06/category-of-all-models-isomorphic-to.html	## Saturday, 8 June 2013 ### Category of all models isomorphic to a given one This is a question for aficionados of category theory. Is there, for any given model $\mathcal{A} = (A, \vec{R})$, a category, say $Mod(\mathcal{A})$, of all models isomorphic to $\mathcal{A}$? So, the objects are these models, and the morphisms are the isomorphisms. If so, what properties does this category $Mod(\mathcal{A})$ have? 1. I don't understand your notation. In your email you said A is a 'domain' and R is a 'special relation', but I don't know what you mean by those terms, either. Nonetheless, there is clearly a category of all models isomorphic to a given one, for the simple reason that for any given blah-di-blah, whatever it might be, there's always a category of all blah-di-blahs isomorphic to that one, as long as 1) you have defined the concept of isomorphism of blah-di-blahs, 2) you can compose isomorphisms in an associative way, and 3) the identity morphism is an isomorphism. (And if these 3 conditions don't hold, you shouldn't be talking about isomorphisms of blah-di-blahs!) Whenever you look at category of 'all blah-di-blahs isomorphic to a given one', with isomorphisms as morphism, you're looking a groupoid with one connected component. Such a groupoid is equivalent to a group. And, this group is simply the automorphism group of your given blah-di-blah. An automorphism is an isomorphism from something to itself. In plain English, it's a symmetry of that thing. So: studying the category you're talking about is just a glorified way of studying the symmetry group of your blah-di-blah. So, you might as well just study that symmetry group and drop the category-theoretic terminology. But from a category-theoretic viewpoint, it's much more interesting to study the category of all blah-di-blahs, and not just with isomorphisms between them, but all morphisms. That's when category theory really becomes useful. This is far as I can go without knowing what you're talking about. :-) 2. John, many thanks! Yes, that's what I have in mind indeed. (Since we lack a latex enabled preview here, let's see if the latex works.) The notation is, e.g., $(X,\leq)$ for an order, where $X$ is the domain/carrier set, and $\leq \subseteq X^2$. Or $(X, \circ)$ for a group; etc. I don't want to be to fussy about the signature of the model. Suppose we have, say, an 2-element total strict order $(A, R)$, where $A = \{0,1\}$ and $R = \{(0,1)\}$. The category here is the category of all models $(B,S)$ isomorphic to $(A,R$. That is, all $(B,S)$ such that, for some bijection $f:A \to B$, we have, for all $a_1, a_2 \in A$, $(f(a_1), f(a_2)) \in S$ iff $(a_1, a_2) in R$. But I think this is not quite the automorphism group $Aut(\mathcal{A})$, because automorphisms keep the carrier set fixed. In a sense, it's much bigger, because the carrier set can be changed arbitrarily. It seems like the automorphism group is a kind of canonical subcategory. Cheers, Jeff 1. Okay, now I understand your terminology. Yes, the groupoid of all things isomorphic to a given thing is much bigger than the group of automorphisms of that thing, but they are equivalent in the usual technical sense in category theory. And this means that anything truly interesting you can say about can be translated into a statement about the other. So, you might as well just study whatever is simpler, and that's the group. (This sort of fact is precisely the sort of thing that aficionados of category theory know, that most other people don't.) 2. John, Brilliant - thanks! But I don't really mean the category (i.e., groupoid) of automorphisms of the model $\mathcal{A}$ to itself. I mean the category of all models isomorphic to $\mathcal{A}$. And one can get an isomorphic copy of $\mathcal{A}$ simply by trivially permuting the carrier set ... Consider the 2-element order $(A,R)$ above, with $A = \{0,1\}$ and $R = \{(0,1)\}$. It's rigid, because the transposition swapping $0$ and $1$ flips $R$ to $S = \{(1,0)\}$. So, $R$ is not invariant under this swap. Still, I can simply consider instead the new model $(A, S)$, and this is (trivially) isomorphic to the original! So, any permutation $\pi : A \to A$ gives me an isomorphic copy. So it seems like, at least when we fix a specific domain/carrier set $A$, the group here is $Sym(A)$ not the automorphisms... Cheers, Jeff 3. [Oops - typos.] John, If I get the picture right, when we fix the domain/carrier set $A$ of our given model $\mathcal{A}$, we get a groupoid of all models, with domain $A$, isomorphic to $\mathcal{A}$. But surely this corresponds to any permutation $\pi: A \to A$? In other words, the relevant group is $Sym(A)$, rather than $Aut(\mathcal{A})$? Cheers, Jeff 1. This comment has been removed by the author. 2. No. The main problem here is that you're saying "this corresponds to" without saying precisely what "this" is or precisely how it's supposed to correspond to a permutation of the set A. Given a groupoid where all objects are isomorphic, it's equivalent, in the sense of category theory, to the groupoid containing just one of those objects, and all its automorphisms. So, for example, the groupoid of all 9-element ordered sets is equivalent to the groupoid with any one 9-element ordered set as its only object, and all order-preserving isomorphisms of this ordered set as morphisms. There is just one such isomorphism, the identity. So, the groupoid of all 9-element ordered sets is equivalent to the groupoid with just one object and just one morphism. The latter groupoid is another way of talking about the trivial group. The 'triviality' of the trivial group here is a way of noticing that the structure of a 9-element ordered set is completely 'rigid': it doesn't admit any automorphisms. This is an atypical example: most structures have automorphisms, aka symmetries, and that's when this subject becomes interesting. 4. John, So, what I've got in mind is clearer with the example, say, for the 2-element order example above, $\mathcal{A} = (A,R)$. - there are two isomorphisms (keeping $A$ fixed); - but only one automorphism, as $\mathcal{A}$ is rigid. Cheers, Jeff 5. John, Here's the more exact definition for "corresponds", from a few weeks ago, http://m-phi.blogspot.co.uk/2013/05/quine-transform-of-model.html (This is analogous to applying a diff $\phi : M \to M$ to a spacetime $(M, g, \dots)$, "moving" all the fields along under $\phi$.) Cheers, Jeff 6. It seems that what is necessary is exclusive isomorphism to give an exclusive set, which in turn requires exclusive variables. Otherwise you end up with an infinite set, e.g. automorphisms of automorphisms, with numerous permutations of boundedness. One of the most concise variations of this kind of thing is discussed in David K. Lewis' <>, but I think what he reached was basically a philosophical Klein Bottle. To move beyond that there are several options: 1. Find the exclusive categories of (A, R) however they are defined, in a format similar to (AA, AB, BB, BA), but only if the variables are exclusive. In my view this means that AA is the opposite of BB and AB is the opposite of BA. Other cases are more difficult or else trivial, in a modal sense referring to specific contexts rather than the most general ones. 2. Define an infinite set in a different way than exclusivity. 3. Define a local-boundary set, such as a modal set, e.g. a local permutation of 'available' as opposed to 'definitive' properties. This may be something like 'measurements', or linear descriptions super-imposed on one another. Maybe some of this changes some of the thinking. My strictly qualia approach can be found in the Dimensional Philosopher's Toolkit (2013). If it seems basic, it is also much more useful than average. It has a real method for 'operating' the data, which I believe goes beyond mere permutation. 7. Thanks for your comment, Nathan. Jeff	2017-06-27 03:42:54	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9162542223930359, "perplexity": 512.9285313332543}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-26/segments/1498128320915.38/warc/CC-MAIN-20170627032130-20170627052130-00538.warc.gz"}
https://electronics.stackexchange.com/questions/254562/block-diagram-of-161-mux-using-four-41-mux-only/254569	# Block diagram of 16:1 MUX using four 4:1 MUX only As far as I know we can make a 16:1 MUX using five 4:1 MUX. For four 4:1 MUX, I think we have to apply NOT to different selection lines but I am not getting the correct configuration to do that. • The question is not clear. Also, if you provide a schematic or drawings to your question it will improve your explanation a lot! – Alper91 Aug 28 '16 at 9:44 You could've easily found it on the internet if you searched. The basis: See it this way: You need a combinational logic with 16 input pins, 4 select lines and one output. In a 4:1 mux, you have 4 input pins, two select lines and one output. So, at the least you have to use 4 4:1 MUX, to obtain 16 input lines. But you'd then have a logic with 4 output pins. We can use another 4:1 MUX, to multiplex only one of those 4 outputs at a time. Hence, this would be your final design. There might be other designs methods too, but this is the most common. Image courtesy: www.slideplayer.com EDIT: Yes, we can implement it without using the last 4:1 MUX; but you have to use an OR gate there and also include enable pins for each 4:1 MUX. It utilizes the traditional method; drawing a truth table and then analytically deciding the design. Here is an example of an 8:1 MUX from 2:1 MUX without using a 2:1 MUX at the output. But, to obtain the same for a 16:1 MUX you'll need to make a lot of modifications. Like if you draw the truth table and analyze (compare it with the above 8:1 MUX design), you'll require two enable pins for each MUX, each with different options. For example, the first MUX needs to be enabled only when the two enable pins(say, e1, e0) are low, the second MUS should be enabled only when e1= 0 and e0=1 and so on. As the size of the MUX increases, it'll become too complex to design using this model. Hence, the first approach is utilized; the one with a MUX at the end. There may be other designs, but this is my approach. • This thing i know. I am asking is it possible to make a 16:1 MUX without using that last single 4:1 MUX ? – Debakar Roy Aug 28 '16 at 5:29 • Yes, it is. Check the edited answer. – electronics Aug 28 '16 at 5:55 • Actually I watched that video before I asked the question here. Anyway thank you for the explanation part. I think I get it now. – Debakar Roy Aug 28 '16 at 6:09 Q 16×1 mux by using 4×1mux Ans:. It contains four 4×1mux are used & it is a 16×1 mux 16 i/p are used the selective lines are S0, s1 ,s2, s3 , and 4 not gates are used and o/p are "y". See the given image to verify the logical circuit It is designed by "Krishna .ch" • How is this answer different from the one that was accepted 2 years ago? – Harry Svensson Sep 21 '18 at 13:55	2020-07-14 03:47:39	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4376775324344635, "perplexity": 1452.5683571962022}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593657147917.99/warc/CC-MAIN-20200714020904-20200714050904-00030.warc.gz"}
https://blog.csdn.net/tel_annie/article/details/80346508	# LeetCode-Arranging_Coins You have a total of n coins that you want to form in a staircase shape, where every k-th row must have exactly k coins. Given n, find the total number of full staircase rows that can be formed. n is a non-negative integer and fits within the range of a 32-bit signed integer. Example 1: n = 5 The coins can form the following rows: ¤ ¤ ¤ ¤ ¤ Because the 3rd row is incomplete, we return 2. Example 2: n = 8 The coins can form the following rows: ¤ ¤ ¤ ¤ ¤ ¤ ¤ ¤ Because the 4th row is incomplete, we return 3. n 是一个非负整数，并且符合32位有符号整数的范围。 n = 5 ¤ ¤ ¤ ¤ ¤ n = 8 ¤ ¤ ¤ ¤ ¤ ¤ ¤ ¤ C++代码（Visual Studio 2017）： #include "stdafx.h" #include <iostream> using namespace std; class Solution { public: int arrangeCoins(int n) { int i = 1; while (n >= i) { n = n - i; i++; } return i-1; } }; int main() { Solution s; int n = 6; int result; result = s.arrangeCoins(n); cout << result; return 0; }	2018-11-12 17:47:48	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2194763422012329, "perplexity": 10363.46872461199}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039741016.16/warc/CC-MAIN-20181112172845-20181112194845-00102.warc.gz"}
https://publications.hse.ru/en/articles/226523470	• A • A • A • ABC • ABC • ABC • А • А • А • А • А Regular version of the site ## On interrelations between divergence-free and Hamiltonian dynamics Journal of Geometry and Physics. 2019. Vol. 135. P. 70-79. L. Lerman (., E. Yakovlev. A mathematically correct description is presented on the interrelations between the dynamics of divergence free vector fields on an oriented 3-dimensional manifold M and the dynamics of Hamiltonian systems. It is shown that for a given divergence free vector field Xwith a global cross-section there exist some 4-dimensional symplectic manifold M̃⊃M and a smooth Hamilton function H:M̃→R such that for some c∈R one gets M={H=c}and the Hamiltonian vector field XH restricted on this level coincides with X. For divergence free vector fields with singular points such an extension is impossible but the existence of local cross-section allows one to reduce the dynamics to the study of symplectic diffeomorphisms in some sub-domains of M. We also consider the case of a divergence free vector field X with a smooth integral having only finite number of critical levels. It is shown that such a noncritical level is always a 2-torus and restriction of X on it possesses a smooth invariant 2-form. The linearization of the flow on such a torus (i.e. the reduction to the constant vector field) is not always possible in contrast to the case of an integrable Hamiltonian system but in the analytic case (M and X are real analytic), due to the Kolmogorov theorem, such a linearization is possible for tori with Diophantine rotation numbers.	2019-11-18 18:04:08	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.91700279712677, "perplexity": 610.3819204650913}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496669809.82/warc/CC-MAIN-20191118154801-20191118182801-00336.warc.gz"}
https://roslerer.vn/te4wpmn/ac92ba-github-lifelines-python	smoothing. lifelines is a pure Python implementation of the best parts of survival analysis. These are often denoted T and E The survival function looks like: A priori, we do not know what \lambda and \rho are, but we use the data on hand to estimate these parameters. Cameron Davidson-Pilon @CamDavidsonPilon. The survival functions is a great way to summarize and visualize the An example of this is periodically recording a population of organisms. lifelines can also be used to define your own parametric model. (The Nelson-Aalen estimator has no parameters to fit to). And (apparently) everyone is … lifelines; Edit on GitHub; lifelines¶ lifelines is a complete survival analysis library, written in pure Python. Note the use of calling fit_interval_censoring instead of fit. via elections and natural limits (the US imposes a strict eight-year limit). Of course, we need to report how uncertain we are about these point estimates, i.e., we need confidence intervals. Embed Embed this gist in your website. Work fast with our official CLI. datasets. Learn more, Cannot retrieve contributors at this time, :class:~lifelines.fitters.kaplan_meier_fitter.KaplanMeierFitter, :meth:~lifelines.fitters.kaplan_meier_fitter.KaplanMeierFitter.fit, :attr:~lifelines.fitters.kaplan_meier_fitter.KaplanMeierFitter.survival_function_, :meth:~lifelines.fitters.kaplan_meier_fitter.KaplanMeierFitter.plot, :attr:~lifelines.fitters.kaplan_meier_fitter.KaplanMeierFitter.confidence_interval_, :func:lifelines.statistics.logrank_test, :func:~lifelines.utils.datetimes_to_durations, :class:~lifelines.fitters.nelson_aalen_fitter.NelsonAalenFitter, :meth:~lifelines.fitters.nelson_aalen_fitter.NelsonAalenFitter.cumulative_hazard_, "Cumulative hazard function of different global regimes", :meth:~lifelines.fitters.nelson_aalen_fitter.NelsonAalenFitter.smoothed_hazard_, :meth:~lifelines.fitters.nelson_aalen_fitter.NelsonAalenFitter.smoothed_hazard_confidence_intervals_, :meth:~lifelines.fitters.nelson_aalen_fitter.NelsonAalenFitter.plot_hazard, :meth:~lifelines.fitters.nelson_aalen_fitter.NelsonAalenFitter.plot, "Hazard function of different global regimes \| bandwidth=%.1f", :class:~lifelines.fitters.weibull_fitter.WeibullFitter, :meth:~lifelines.fitters.weibull_fitter.WeibullFitter.plot, "Cumulative hazard of Weibull model; estimated parameters", , coef se(coef) lower 0.95 upper 0.95 p -log2(p), lambda_ 0.02 0.00 0.02 0.02 <0.005 inf, rho_ 3.45 0.24 2.97 3.93 <0.005 76.83, # directly compute the survival function, these return a pandas Series, # by default, all functions and properties will use, "Survival function of Weibull model; estimated parameters", NH4.Orig.mg.per.L NH4.mg.per.L Censored, 1 <0.006 0.006 True, 2 <0.006 0.006 True, 3 0.006 0.006 False, 4 0.016 0.016 False, 5 <0.006 0.006 True, :meth:~lifelines.fitters.kaplan_meier_fitter.KaplanMeierFitter.fit_left_censoring, :attr:~lifelines.fitters.kaplan_meier_fitter.KaplanMeierFitter.cumulative_density_, # plot what we just fit, along with the KMF estimate, # for now, this assumes closed observation intervals, ex: [4,5], not (4, 5) or (4, 5]. with real data and the lifelines library to estimate these objects. For this example, we will be investigating the lifetimes of political Support and discussion about lifelines. The birth event is the start of the individual's tenure, and the death How to access environment variable values? Try predict_percentile with p=0.75 or 0.9. Looking at figure above, it looks like the hazard starts off high and intervals, similar to the traditional :meth:~lifelines.fitters.nelson_aalen_fitter.NelsonAalenFitter.plot functionality. is not how we usually interpret functions. The doctor against another variable – in this case durations. Survival analysis in Python. The function :func:lifelines.statistics.logrank_test is a common not observed -- JFK died before his official retirement. Support for Lifelines. Above, we can see that some subjects' death was exactly observed (denoted by a red ●), and some subjects' deaths is bounded between two times (denoted by the interval between the red ▶︎ ◀︎). n_i is the number of subjects at risk of death just prior to time mark, you probably have a long life ahead. us to specify a bandwidth parameter that controls the amount of called :attr:~lifelines.fitters.kaplan_meier_fitter.KaplanMeierFitter.survival_function_ (again, we follow the styling of scikit-learn, and append an underscore to all properties that were estimated). If you are new to survival analysis, wondering why it is useful, or are interested in lifelines examples, API, and syntax, please read the Documentation and Tutorials page. table of contents. lifelines data format is consistent across all estimator class and Below we compare the parametric models versus the non-parametric Kaplan-Meier estimate: With parametric models, we have a functional form that allows us to extend the survival function (or hazard or cumulative hazard) past our maximum observed duration. Note . here. lifelines is a pure Python implementation of the best parts of survival analysis. is unsure when the disease was contracted (birth), but knows it was before the discovery. Another situation with left-truncation occurs when subjects are exposed before entry into study. Alternatively, there are situations where we do not observe the birth event lifelines/Lobby. You can use plots like qq-plots to help invalidate some distributions, see Selecting a parametric model using QQ plots and Selecting a parametric model using AIC. It is more clear here which group has the higher hazard, and Non-democratic regimes appear to have a constant hazard. they're used to gather information about the pages you visit and how many clicks you need to accomplish a task. lifelines/Lobby. Contribute to CamDavidsonPilon/lifelines development by creating an account on GitHub. includes some helper functions to transform data formats to lifelines Embed. In lifelines, confidence intervals are automatically added, but there is the at_risk_counts kwarg to add summary tables as well: For more details, and how to extend this to multiple curves, see docs here. I was curious however, since in the summary all three coefficients are displayed, what is the baseline? You signed in with another tab or window. the API and functionality is still experimental. If we did manage to observe them however, they would have depressed the survival function early on. An example dataset is below: The recommended API for modeling left-censored data using parametric models changed in version 0.21.0. Piecewise Exponential Models and Creating Custom Models, Selecting a parametric model using QQ plots, Mohammad Zahir Shah.Afghanistan.1946.1952.Monarchy, Sardar Mohammad Daoud.Afghanistan.1953.1962.Civilian Dict, Mohammad Zahir Shah.Afghanistan.1963.1972.Monarchy, Sardar Mohammad Daoud.Afghanistan.1973.1977.Civilian Dict, Nur Mohammad Taraki.Afghanistan.1978.1978.Civilian Dict. upon his retirement, thus the regime's lifespan was eight years, and there was a We model and estimate the cumulative hazard rate instead of the survival function (this is different than the Kaplan-Meier estimator): In lifelines, estimation is available using the :class:~lifelines.fitters.weibull_fitter.WeibullFitter class. Regarding the first question, when I one hot encode the three-level categorical variable and then use it in the model, it work just fine. of dataset compilation (2008), or b) die while in power (this includes assassinations). Based on the above, the log-normal distribution seems to fit well, and the Weibull not very well at all. Lifetimes is my latest Python project. Yes, the time-varying model is harder to interpret. Survival analysis in Python. average 50% of the population has expired, is a property: Interesting that it is only four years. Another example of using lifelines for interval censored data is located here. pipeline import make_pipeline from sklearn. event observation (if any). t. From the lifelines library, we'll need the Sign in Sign up Instantly share code, notes, and snippets. Use Git or checkout with SVN using the web URL. In contrast the the Nelson-Aalen estimator, this model is a parametric model, meaning it has a functional form with parameters that we are fitting the data to. The sum of estimates is much more What would you like to do? functions, but the hazard functions is the basis of more advanced techniques in Visit the LifeLines home page (see end of file for URL) for details on how to obtain pre-compiled or beta (test) copies of these versions. we introduced the applications of survival analysis and the There are alternative (and sometimes better) tests of survival functions, and we explain more here: Statistically compare two populations. the data. The original author of LifeLines is Thomas T. Wetmore IV, who released it to the open source community under a MIT-style licence (see LICENCE). cross_validation import train_test_split from patsylearn import PatsyTransformer data = lifelines. There is a Gitter channel available. I try to use pythons lifelines package Package website and Github. If the curves are more @CamDavidsonPilon: @kpeters I can't give a complete answer without seeing the data - but I'll try: i) the 0.5 represents the median. Thus we know the rate of change stable than the point-wise estimates.) Thus, "filling in" the dashed lines makes us over confident about what occurs in the early period after diagnosis. it is recommended. Documentation and intro to survival analysis. I tried it in a python:3.6 docker container and get the same thing. population, we unfortunately cannot transform the Kaplan Meier estimate leader rarely makes it past ten years, and then have a very short Survival analysis in Python. It's tempting to use something like one-half the LOD, but this will cause lots of bias in downstream analysis. We will run a python code for predicting the survival function at … The property is a Pandas DataFrame, so we can call :meth:~lifelines.fitters.kaplan_meier_fitter.KaplanMeierFitter.plot on it: How do we interpret this? This allows for you to "peer" below the LOD, however using a parametric model means you need to correctly specify the distribution. You will see how Convolutional Neural Networks are being applied to process the visual data, generating some valuable knowledge. All gists Back to GitHub. Learn more. statistical test in survival analysis that compares two event series' New to lifelines in version 0.21.3 is a wrapper that allows you to use lifeline’s regression models with scikit-learn’s APIs. Image Analysis: Introduction to deep learning for computer vision Authors: Nargiz Bakhshaliyeva, Robert Kittel. For readers looking for an introduction to survival analysis, it’s recommended to start at Introduction to survival analysis. The cumulative hazard the more interpretable hazard function our websites so we can build better products only handles data. Relative to the data but knows it was before the discovery, can... And lifeline it ’ s recommended to start at introduction to survival analysis variable values you visit how... Notes, and the Nelson-Aalen non-parametric model, of the individual models in lifelines describes where. Is multi-core parallelized out of the median, you can always update your selection by clicking Cookie Preferences at bottom! Chance of github lifelines python early on in prison, the logrank test will an... Primary distribution tenure, and inspired by, scikit-learn 's fit/predict API ) tempting to something. Study entry are using lifelines for interval censored data above, the log-normal distribution seems to fit to.. Where t years, where t years is on the data integrated the. More here: Statistically compare two survival functions is very obvious, performing! Is not the only way on after diagnosis democratic regimes vs non-democratic regimes appear to have a very short past... Which group has the higher hazard, and we explain more here: compare. S APIs, iv be difficult -- it is more interested in a. Regression – the name implies we regress covariates ( e.g., age, country,.... As the: attr: ~lifelines.fitters.kaplan_meier_fitter.KaplanMeierFitter.cumulative_density_ property after fitting the Kaplan-Meier for. Is below: the recommended API for fit_interval_censoring is different than right left. Size, 59, is small too Jane Wayne and let us know your thoughts on the other hand most..., or some sort of model goodness-of-fit how the code is multi-core parallelized out of the individual an estimate the! ~lifelines.fitters.nelson_aalen_fitter.NelsonAalenFitter.smoothed_hazard_ and: meth: ~lifelines.fitters.nelson_aalen_fitter.NelsonAalenFitter.smoothed_hazard_confidence_intervals_ methods when the underlying data generation is. Analyze their customers ’ repeat purchases number of susceptible individuals: Statistically compare two survival is! Pre-Specified value, then we rule that the series have different generators cumulative density function AIDS. Late entry ) a statistical test lifetime past that a python:3.6 docker container and get the same thing into! To fit well, and performing a statistical test seems pedantic hazards is true to choose is determined by knowledge... Auc to survival data, generating some valuable knowledge lifelines data format is across... That we github lifelines python about these point estimates, i.e., we will work with real and! Conda: conda install -c conda-forge lifelines used the same thing will work with real data and lifelines... Below we will work with real data and github lifelines python Weibull model available the! Can use: let 's segment on democratic regimes vs non-democratic regimes appear to have a constant.. Describes the time between actual birth '' ( or exposure '' ) to entering study... Only handles right-censored data test will give an inaccurate assessment of differences distribution seems to the! To access environment variable values to fit well, and performing a statistical test and sometimes better ) of! The other hand, most survival analysis estimate, \\ ( n_i\\ ) is the model... In our example below we will be investigating the lifetimes of subjects README - gist:023350676604d0a19780 dataset this., but not everyone dies in the figure below, we use analytics to... Is defined by a single individual's time in office who controls the ruling regime a of!, we will now discuss about its basic implementation in python with the cumulative density.! And how many clicks you need to report how uncertain we are estimating cumulative hazard function, knows... Bound is Often called the limit of detection ( LOD ) detection ( ). Lifelines is a pure python implementation of the individual 's tenure, and then have a %! An account on GitHub of cessation in four years or less two event generators! At introduction to survival data is located here CamDavidsonPilon thank you for your answer ten years, where t,. Two survival functions is a special case of the individual the ROC AUC to analysis. < p > lifelines data format is consistent across all estimator class and your coworkers to find share. Using lifelines for interval censored because you know a subject died between two observations periods analysis. Coefficients are displayed, what is the number of susceptible individuals to find share! The prisoners will enter the study at different ages right-censored data run a python code for predicting the survival,. With AIDS, possibly years before version has been integrated into the study hazard... Analyze github lifelines python customers ’ repeat purchases ¶ Often we have been using in the::. Diagnosed with AIDS, possibly years before more similar, or some of..., since in the tail: meth: ~lifelines.fitters.kaplan_meier_fitter.KaplanMeierFitter.cumulative_density_ property after fitting data! A population of organisms stick with the cumulative hazard function primary distribution thoughts on the.. The baseline still around after t years is on the other hand, most survival analysis is clear... Confidence intervals us which model is most appropriate report any bugs or features on GitHub. Survival dataset, however it is not how we usually interpret functions H ( t ) it! Only way we model the survival curves cross, the prisoners will enter the study different... Git or checkout with SVN using the cumulative hazard function github lifelines python implies we regress covariates ( e.g.,,. A common statistical test, however it is not how we usually interpret functions to define your parametric... Available as the: mod: ~lifelines.fitters.nelson_aalen_fitter.NelsonAalenFitter.smoothed_hazard_ and: meth . Too Jane Wayne @ CamDavidsonPilon do n't fill-in '' this value naively derive the more interpretable function... Variable values visual Studio and try again displayed, what is the Weibull not very at! \\ ( n_i\\ ) is the retirement of the best parts of survival functions is a on! Of producing a survival function early on much more stable than the point-wise estimates. when individuals may the! Severely underestimate chance of dying early on after diagnosis or late entry ) may have the opportunity to die entering... Lifelines.Statistics to fit well, and inspired by, scikit-learn 's fit/predict github lifelines python ) before discovery... To fit to tell us which model is most appropriate data, generating some valuable.! Git or checkout with SVN using the web URL only handles right-censored data,. Death of prisoners in prison, the log-normal distribution seems to fit )... The sum of estimates is much more stable than the point-wise estimates. development by creating account... Report how uncertain we are estimating cumulative hazard function, what is the start of the.... Based on the other hand, most survival analysis data generation distribution unknown... Source code on GitHub projects, and the lifelines library to estimate objects! Size, 59, is defined by a single individual's time in office a special of. Survival dataset, however it is not the only way to analyze their ’... About what occurs in github lifelines python summary all three coefficients are displayed, what is number! ( the Nelson-Aalen non-parametric model, of the page 59, is too. My advice: stick with the help of lifelines package test will give an inaccurate assessment of differences of early! ~lifelines.fitters.nelson_aalen_fitter.NelsonAalenFitter your thoughts on the library lifelines contains routines in: mod: ... The cumulative hazard function, so there are alternative ( and sometimes better ) tests of survival analysis more here! On GitHub ; survival regression – the alpha value associated with the interval... For modeling left-censored data analysis is done using the cumulative hazard functions, H t... Download GitHub Desktop and try again an elected president, unelected dictator, monarch, etc. ROC github lifelines python... To perform essential website functions, e.g on our GitHub issue list lifelines documentation lifelines version thomas! Different than right and left censored data ~lifelines.fitters.kaplan_meier_fitter.KaplanMeierFitter.fit to fit well, and snippets study time! Name implies we regress covariates ( e.g., age, country, etc. cumulative density function and censored... Birth ), but knows it was before the discovery web URL resort to measures of fit to ) KMunicate. Fit_Interval_Censoring is different than right and left censored data is located here Often called the Multicenter AIDS study! Account late entries report how uncertain we are about these point estimates, i.e., we need report! Start of the cumulative hazard functions, e.g report how uncertain we estimating! Filling in '' the dashed lines makes us over confident about what occurs in tail... The world, elected leaders have a 50 % chance of cessation in four years or less estimate the... Use github lifelines python ’ s recommended to start at introduction to survival data is here... Start at introduction to survival data, generating some valuable knowledge you to use one situation is when individuals have... The version and reinstall the python and lifeline are other parametric models changed in version 0.21.0 generalization... Lifelines for interval censored data the technique is called left-truncation ( or late entry ) the log-normal seems! The hazard function, so there are situations where we do not observe the birth event the... Working together to host and review code, notes, and the Weibull model are measuring time all-cause. Mode version has been integrated into the primary distribution model, of the cumulative function... Br > how to access environment variable values or late entry ), too pages you visit how! Routines in: mod: lifelines.utils ` sub-library import train_test_split from patsylearn PatsyTransformer! A generalization of the same thing rate of change of this is similar,...	2021-04-17 02:35:55	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4119272828102112, "perplexity": 3356.335632298313}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038098638.52/warc/CC-MAIN-20210417011815-20210417041815-00312.warc.gz"}
https://im.kendallhunt.com/HS/students/2/5/learning_targets.html	Geo.5 Solid Geometry Lesson 1 • I can draw the two-dimensional shape that creates a particular three-dimensional solid when rotated using a given axis. • I can identify the three-dimensional solid created by rotating a two-dimensional figure using a linear axis. Lesson 2 • I can identify the three-dimensional shape that generates a set of cross sections. • I can visualize and draw multiple cross sections of a three-dimensional figure. Lesson 3 • I know that a pyramid’s cross sections are dilations of its base with scale factors ranging from 0 to 1. Lesson 4 • I know that when figures are dilated by a scale factor of $k$, their areas are multiplied by $k^2$. Lesson 5 • I can use square root graphs and do calculations to interpret the relationships between scale factors and areas. Lesson 6 • I know that when a solid is dilated by a scale factor of $k$, its surface area is multiplied by $k^2$ and its volume is multiplied by $k^3$. Lesson 7 • I can create and describe graphs that show relationships between volumes and scale factors. • I can work backwards from a volume or surface area scaling to find a scale factor. Lesson 8 • I can calculate scale factors for lengths, surface areas, and volumes if I’m given any 1 of the 3 factors. Lesson 9 • I can calculate volumes of solids that are composed of cylinders. • I can explain how finding the volume of a prism relates to finding the volume of a cylinder. Lesson 10 • I know that if two solids have equal-area cross sections at all heights, they have the same volumes. Lesson 11 • I can calculate volumes of right and oblique prisms and cylinders and figures composed of prisms and cylinders. Lesson 12 • I can explain the relationships between pyramids, cones, prisms, and cylinders. Lesson 13 • I can explain why the volume formula for pyramids and cones is $V=\frac13Bh$. Lesson 14 • I can calculate volumes of pyramids and cones. • I can work backward from a given volume to find possible dimensions of a pyramid or cone. Lesson 15 • I can use the Pythagorean Theorem and trigonometry to help calculate volumes of prisms, cylinders, cones, and pyramids, including solids of rotation. Lesson 16 • I can use surface area and volume relationships to solve problems. Lesson 17 • I can solve problems involving density and volume. • I know that the density of an object is the ratio between its mass and its volume. Lesson 18 • I can use cube root and square root graphs to solve geometric problems.	2022-06-28 03:01:05	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5697033405303955, "perplexity": 912.5987008580026}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103347800.25/warc/CC-MAIN-20220628020322-20220628050322-00284.warc.gz"}
https://ferraricalifornia.org/how-to-write-resign-letter-in-teacher/teaching-assistant-resignation-letter-example-how-to-write-resign-letter-in-teacher-on/	# Teaching Assistant Resignation Letter Example How To Write Resign Letter In Teacher On Teaching Assistant Resignation Letter Example How To Write Resign Letter In Teacher On How To Write Resign Letter In Teacher . How To Write Resign Letter In Teacher . How To Write Resign Letter In Teacher . How To Write Resign Letter In Teacher . How To Write Resign Letter In Teacher . How To Write Resign Letter In Teacher . How To Write Resign Letter In Teacher . How To Write Resign Letter In Teacher . How To Write Resign Letter In Teacher . How To Write Resign Letter In Teacher . How To Write Resign Letter In Teacher . How To Write Resign Letter In Teacher . How To Write Resign Letter In Teacher . How To Write Resign Letter In Teacher . How To Write Resign Letter In Teacher . How To Write Resign Letter In Teacher .	2019-08-24 20:38:05	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8276588320732117, "perplexity": 6655.030288458167}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027321696.96/warc/CC-MAIN-20190824194521-20190824220521-00231.warc.gz"}
https://gmatclub.com/forum/chetan-s-own-252069.html	GMAT Question of the Day - Daily to your Mailbox; hard ones only It is currently 21 Nov 2018, 06:49 # LBS is Calling R1 Admits - Join Chat Room to Catch the Latest Action ### GMAT Club Daily Prep #### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email. Customized for You we will pick new questions that match your level based on your Timer History Track every week, we’ll send you an estimated GMAT score based on your performance Practice Pays we will pick new questions that match your level based on your Timer History ## Events & Promotions ###### Events & Promotions in November PrevNext SuMoTuWeThFrSa 28293031123 45678910 11121314151617 18192021222324 2526272829301 Open Detailed Calendar • ### All GMAT Club Tests are Free and open on November 22nd in celebration of Thanksgiving Day! November 22, 2018 November 22, 2018 10:00 PM PST 11:00 PM PST Mark your calendars - All GMAT Club Tests are free and open November 22nd to celebrate Thanksgiving Day! Access will be available from 0:01 AM to 11:59 PM, Pacific Time (USA) • ### Key Strategies to Master GMAT SC November 24, 2018 November 24, 2018 07:00 AM PST 09:00 AM PST Attend this webinar to learn how to leverage Meaning and Logic to solve the most challenging Sentence Correction Questions. # If represents one of the four basics operation of arithmetic Author Message TAGS: ### Hide Tags Math Expert Joined: 02 Aug 2009 Posts: 7044 If represents one of the four basics operation of arithmetic [#permalink] ### Show Tags 24 Oct 2017, 07:26 1 5 00:00 Difficulty: 45% (medium) Question Stats: 51% (00:52) correct 49% (00:55) wrong based on 138 sessions ### HideShow timer Statistics If @ represents one of the four basics operation of arithmetic - addition, subtraction, division or multiplication, what is $$\frac{1}{3}@\frac{1}{4}$$? 1) $$1@1=1$$ 2) $$\frac{1}{2}@\frac{1}{3}=\frac{1}{6}$$ self made : from a similar but still different Q _________________ 1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html GMAT online Tutor Manager Joined: 21 Jun 2014 Posts: 62 Re: If represents one of the four basics operation of arithmetic [#permalink] ### Show Tags Updated on: 24 Oct 2017, 08:28 B St 1: can be * or / diff answers St 2 : can be - or * same answer 1/12 Sent from my Moto G (5) Plus using GMAT Club Forum mobile app Originally posted by saicharan1191 on 24 Oct 2017, 08:24. Last edited by saicharan1191 on 24 Oct 2017, 08:28, edited 1 time in total. Manager Joined: 21 Jun 2014 Posts: 62 Re: If represents one of the four basics operation of arithmetic [#permalink] ### Show Tags 24 Oct 2017, 08:27 Oh missed it.. It must be B Because * or - yield 1/12 answer. Sent from my Moto G (5) Plus using GMAT Club Forum mobile app Senior Manager Joined: 17 Oct 2016 Posts: 321 Location: India Concentration: Operations, Strategy GPA: 3.73 WE: Design (Real Estate) Re: If represents one of the four basics operation of arithmetic [#permalink] ### Show Tags 24 Oct 2017, 08:46 1 ST1: can be either multiplication or division ST2: can be either multiplication or subtraction Combined-@ is definitely multiplication hence C _________________ Help with kudos if u found the post useful. Thanks Manager Joined: 21 Jun 2014 Posts: 62 Re: If represents one of the four basics operation of arithmetic [#permalink] ### Show Tags 24 Oct 2017, 10:05 Sasindran wrote: ST1: can be either multiplication or division ST2: can be either multiplication or subtraction Combined-@ is definitely multiplication hence C In statement 2 , for either case ( substraction or multiplication) u get 1/3@1/4 = 1/12 so B is sufficient. It's a tricky question. Sent from my Moto G (5) Plus using GMAT Club Forum mobile app Intern Joined: 31 Jul 2017 Posts: 6 Location: United States GMAT 1: 620 Q44 V31 GMAT 2: 710 Q49 V37 GPA: 3.44 WE: Research (Other) Re: If represents one of the four basics operation of arithmetic [#permalink] ### Show Tags 24 Oct 2017, 16:02 Stmt 1: Not sufficient - can be multiplication or Division. If you test these on the prompt you will get 1/12 with multiplication and 4/3 with division - so NS Stmt 2: Sufficient - can be multiplication or subtraction. If you test both on the prompt you will get 1/12 for each, therefore it is sufficient since you will receive one unique answer no matter what the operation is. Note that the question asks specifically what the answer would be. Manager Joined: 07 Jun 2017 Posts: 174 Location: India Concentration: Technology, General Management GMAT 1: 660 Q46 V38 GPA: 3.6 WE: Information Technology (Computer Software) Re: If represents one of the four basics operation of arithmetic [#permalink] ### Show Tags 24 Oct 2017, 21:57 $$1/3@1/4$$ 1/3 - 1/4 = 1/12 1/31/4 = 1/12 So both multiplication and subtraction gives the same answer for the stem. We need to find out whether any of the 2 statement gives the same answer from 1. 11 = 1 1/1 = 1 so 1/3 -1/4 = 1/12 (1/3) / (1/4) = 4/3 From 2. 1/2 - 1/3 = 1/6 1/2 * 1/3 = 1/6 both answer gives same, which is similar the operation used in the question stem. So sufficient. _________________ Regards, Naveen email: nkmungila@gmail.com Please press kudos if you like this post Intern Joined: 21 Oct 2017 Posts: 13 Re: If represents one of the four basics operation of arithmetic [#permalink] ### Show Tags 18 Oct 2018, 17:33 chetan2u wrote: If @ represents one of the four basics operation of arithmetic - addition, subtraction, division or multiplication, what is $$\frac{1}{3}@\frac{1}{4}$$? 1) $$1@1=1$$ 2) $$\frac{1}{2}@\frac{1}{3}=\frac{1}{6}$$ self made : from a similar but still different Q Statement 1: can be multiplication or division yields different values for $$\frac{1}{3}@\frac{1}{4}$$ Statement 2: can be multiplication or subtraction yields same values for $$\frac{1}{3}@\frac{1}{4}$$ Re: If represents one of the four basics operation of arithmetic &nbs [#permalink] 18 Oct 2018, 17:33 Display posts from previous: Sort by # If represents one of the four basics operation of arithmetic Powered by phpBB © phpBB Group \| Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.	2018-11-21 14:49:53	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6088079810142517, "perplexity": 9488.564253625236}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039748901.87/warc/CC-MAIN-20181121133036-20181121155036-00499.warc.gz"}
https://proofwiki.org/wiki/Mathematician:Charles_Proteus_Steinmetz	# Mathematician:Charles Proteus Steinmetz ## Mathematician Prussian-born American mathematician and electrical engineer and professor at Union College. Fostered development of alternating current that enabled expansion of electric power industry in United States. Formulated mathematical theories for engineers. Explained the phenomenon of hysteresis. ## Nationality Prussian (Hanoverian) ## History • Born: April 9, 1865 in Breslau, Province of Silesia, Prussia • Died: October 26, 1923 in Schenectady, New York, United States ## Notable Quotes Mathematics is the most exact science, and its conclusions are capable of absolute proof. But this is so only because mathematics does not attempt to draw absolute conclusions. All mathematical truths are relative, conditional. ($1923$) -- Quoted in 1937: Eric Temple Bell: Men of Mathematics: They Say: What Say They? : Let Them Say ## Also known as Steinmetz was born Karl August Rudolph Steinmetz. He changed his name to Charles on applying to enter the US in $1889$, and adopted the middle name Proteus after a character from Homer's The Odyssey.	2023-03-24 21:54:45	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2588966190814972, "perplexity": 9373.738672556457}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296945289.9/warc/CC-MAIN-20230324211121-20230325001121-00446.warc.gz"}
https://eanshub.com/community/introduction-to-euclid-geometry/in-figure-if-ac-bd-then-prove-that-ab-cd/	# Forum In Figure, if AC = ... Notifications Clear all # In Figure, if AC = BD, then prove that AB = CD. 1 Posts 2 Users 0 Likes 76 Views 0 Topic starter In Figure, if AC = BD, then prove that AB = CD. Topic Tags 1 Answer 0 It is given, AC = BD From the given figure, we get, AC = AB + BC BD = BC + CD ⇒ AB + BC = BC + CD [AC = BD, given] We know that, according to Euclid’s axiom, when equals are subtracted from equals, remainders are also equal. Subtracting BC from the L.H.S and R.H.S of the equation AB + BC = BC + CD, we get, AB + BC - BC = BC + CD - BC AB = CD Hence Proved. Share:	2023-03-27 08:25:25	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8584504723548889, "perplexity": 5998.574590958691}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296948609.41/warc/CC-MAIN-20230327060940-20230327090940-00693.warc.gz"}
http://systems-sciences.uni-graz.at/etextbook/sw2/lyapunov.html	# Lyapunov exponent An essential aspect of deterministic chaos is the fact that small differences in the initial values of a system's development over time can grow into very large differences. The reason for this is the exponential growth of these differences, which in principle is once more a feedback effect. Differences grow in respect to the size they have reached in the previous moment of time. The larger they are, the faster they grow. This increase in differences measures the so-called Lyapunov exponent, named after the Russian mathematician Aleksandr Mikhailovich Lyapunov. This exponent indicates the speed with which two initially close dynamics diverge - if the L. exponent is positive - or converge - if the L. exponent is negative - in phase space. If the difference of the initial values is $u_0$, the difference at time $t$ can be estimated as $\| u_t \| = e^{\lambda t} * \| u_0 \|$, with $\lambda$ denoting the Lyapunov exponent, which can be calculated as $\lambda = lim \frac{1}{t} * ln \|\frac{u_t}{u_0}\|$. The Lyapunov exponent hence indicates how rapidly a complex system of several interdependent dynamics tends to run up to deterministic chaos. The inverse value of the exponent indicates the so-called Lyapunov time, the time an initial difference needs to reach $e$, thus allowing certain conclusions about the predictability of a system. Knowing Lyapunov time enables to estimate for what time period a system can be expected to be predictable. In more-dimensional developments, there may be a whole spectrum of Lyapunov exponents. Usually only the largest of them is called Lyapunov exponent, or more accurately the Maximal Lyapunov Exponent (MLE). For a time discrete system ($x_{t+1}=f(x_t)$ it is defined as: $\lambda (x_0) = \lim_{n \to \infty} \frac{1}{n} \sum_{i=0}^{n-1} \ln \| f'(x_i)\|$ In respect to the Lorenz equations on weather forecast, for example, reliable predictions for about four days would be possible with an initial accuracy as provided by 1000 weather stations evenly distributed over the earth's surface. For an equally reliable forecast for 11 days the number of required weather stations increases to 100 million stations. And for predictions over a whole month, an amount of 1020 stations would be needed - one per 5 square millimeters earth surface. (The following examples are taken - and slightly varied - from the excellent textbook Introduction to the Modeling and Analysis of Complex Systems of Hiroki Sayama) ## The Lyapunov exponent with Python¶ Basically, the Lyapunov exponent is just a time average of $log\mid f'(x_i) \mid$ at every state the system visits over the course of the simulation. Here is an example of computing the Lyapunov exponent for the time-discrete system $x_{t+1} = x_t + r - x_t^2$ over varying $r$: In [147]: import numpy as np import matplotlib.pyplot as plt # show plots in notebook % matplotlib inline result = [] lambdas = [] maps = [] # define range of r rvalues = arange(0, 2, 0.01) # loop through r for r in rvalues: x = 0.1 result = [] # iterate system 100 times for t in range(100): x = x + r - x*2 # calculate log of the absolute of the derivative result.append(log(abs(1 - 2x))) # take average lambdas.append(mean(result)) # for the map ignore first 100 iterations as transient time and iterate anew for t in range(20): x = x + r - x*2 maps.append(x) fig = plt.figure(figsize=(10,7)) xticks = np.linspace(0, 2, 4000) # zero line zero = [0]4000 ax1.plot(xticks, zero, 'g-') # plot map ax1.plot(xticks, maps, 'r.',alpha = 0.3, label = 'Map') ax1.set_xlabel('r') # plot lyapunov ax1.plot(rvalues, lambdas, 'b-', linewidth = 3, label = 'Lyapunov exponent') ax1.grid('on') ax1.set_xlabel('r') ax1.legend(loc='best') ax1.set_title('Map of x(t+1) = x(t) + r - x(t)^2 versus Lyapunov exponent') Out[147]: <matplotlib.text.Text at 0x1bf18dd0> As can be seen in the above plot, a bifurcation (in the red map) is indicated when the Lyapunov exponent (blue) approches zero (green line). The outbreak of deterministic chaos, i.e. the danger of rapid divergence of two initially close dynamics, is indicated by the Lyapunov exponent becoming positive (crossing the zero line). Those locations in the plot where the Lyapunov exponent diverges to deep negative values (at times even infinite values) indicate extremely stable equilibrium points in the system with $f'(x_t) \approx 0$ for certain $t$. ### Logistic map¶ The following example shows the same simulation for the logisitic difference equation $x_{t+1}= rx_t(1-x_t)$ In [142]: result = [] lambdas = [] maps = [] xmin = 2 xmax = 4 mult = (xmax - xmin)2000 rvalues = arange(xmin, xmax, 0.01) for r in rvalues: x = 0.1 result = [] for t in range(100): x = r x * (1 - x) result.append(log(abs(r - 2rx))) lambdas.append(mean(result)) # ignore first 100 iterations as transient time # then iterate anew for t in range(20): x = r * x * (1 - x) maps.append(x) fig = plt.figure(figsize=(10,7)) xticks = np.linspace(xmin, xmax, mult) # zero line zero = [0]mult ax1.plot(xticks, zero, 'g-') ax1.plot(xticks, maps, 'r.',alpha = 0.3, label = 'Logistic map') ax1.set_xlabel('r') ax1.plot(rvalues, lambdas, 'b-', linewidth = 3, label = 'Lyapunov exponent') ax1.grid('on') ax1.set_ylim(-1, 1) ax1.set_xlabel('r') ax1.legend(loc='best') ax1.set_title('Logistic map versus Lyapunov exponent') Out[142]: <matplotlib.text.Text at 0x1b95f450> ### The cubic map¶ $x_{t+1}=x_t^3-rx_t$ In [149]: result = [] lambdas = [] maps = [] xmin = 0 xmax = 3 mult = (xmax - xmin)2000 rvalues = arange(xmin, xmax, 0.01) for r in rvalues: x = 0.1 result = [] for t in range(100): x = x3 - r x result.append(log(abs(3x2 - r))) lambdas.append(mean(result)) # ignore first 100 iterations as transient time # then iterate anew for t in range(20): x = x3 - r x maps.append(x) fig = plt.figure(figsize=(10,7)) xticks = np.linspace(xmin, xmax, mult) # zero line zero = [0]mult ax1.plot(xticks, zero, 'g-') ax1.plot(xticks, maps, 'r.',alpha = 0.5, label = 'Cubic map') ax1.set_xlabel('r') ax1.plot(rvalues, lambdas, 'b-', linewidth = 3, label = 'Lyapunov exponent') ax1.set_ylim(-4, 2) ax1.grid('on') ax1.set_xlabel('r') ax1.legend(loc='best') ax1.set_title('Cubic map versus Lyapunov exponent') Out[149]: <matplotlib.text.Text at 0x1eeec810> ### The sinusoid map¶ $x_{t+1}=rsin x_t$ In [148]: result = [] lambdas = [] maps = [] xmin = 2 xmax = 3 mult = (xmax - xmin)2000 rvalues = arange(xmin, xmax, 0.01) for r in rvalues: x = 0.1 result = [] for t in range(100): x = r sin(x) result.append(log(abs(rcos(x)))) lambdas.append(mean(result)) # ignore first 100 iterations as transient time # then iterate anew for t in range(20): x = r sin(x) maps.append(x) fig = plt.figure(figsize=(10,7)) xticks = np.linspace(xmin, xmax, mult) # zero line zero = [0]*mult ax1.plot(xticks, zero, 'g-') ax1.plot(xticks, maps, 'r.', alpha = 0.5, label = 'Sinusoid map') ax1.set_xlabel('r') ax1.plot(rvalues, lambdas, 'b-', linewidth = 3, label = 'Lyapunov exponent') ax1.set_xlim(2, 3) ax1.set_ylim(-1, 3) ax1.grid('on') ax1.set_xlabel('r') ax1.legend(loc='best') ax1.set_title('Sinusoid map versus Lyapunov exponent') Out[148]: <matplotlib.text.Text at 0x1ee8e630> In [ ]:	2018-11-17 06:32:59	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 3, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7079578042030334, "perplexity": 3225.7172901961862}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039743294.62/warc/CC-MAIN-20181117061450-20181117083450-00068.warc.gz"}
https://thetensor.space/articles/example-post/	# Post Template ## Create an Article, Event, or other post Posts for Articles and Events are kept in the following directories (as of writing this): • _posts -> Articles Page • _events -> Events Page To create a new post, add a file with the markdown file extension (.md). Jekyll uses Kramdown for processing these files. It is important that you follow Jekyll’s naming conventions for a post as follows: YYYY-MM-DD-YOUR_POST_NAME.md. This is how Jekyll organizes and sorts your posts correctly. For example, this is how you create a new post for the Articles page: 1. Create a file named 2019-12-21-tensors-rock.md in the _posts directory. 2. Insure you have the proper Front Matter for your post. An Article has the following Front Matter: --- # Uses this html: "_layout/post.html" as a template. layout: post title: Post Template # (Optional) Used to sort posts, not supported as of writing this. categories: [ Workshops ] --- 3. Write your article. Use this post template or Kramdown’s documentation for any markdown questions / issues you have. 4. Confirm your article shows up on the site. ## Use KaTex Use KaTex to draw Math formulas directly in Markdown. KaTex uses LaTeX and TeX macros to parse math formulas. See the Katex docs for a full list of LaTeX and TeX macros. Below is a simple example of using Katex: Note: There are new lines before and after display mode (aka centered katex) formulas. _Today we'll go over the Pythagorean Theorem..._ $$a^{2} + b^{2} = c^{2}$$# Inline mode:$ a^{2} + b^{2} = c^{2} $ …Which results in the following output: Today we’ll go over the Pythagorean Theorem…$ a^{2} + b^{2} = c^{2} $Trouble Shooting KaTex Because this is a markdown file and not a latex file there are some competing symbols that can at times cause some problems. 1. * is used in markdown to introudce bold. If used within math mode as a symbol it mostly works, but sometimes the viewer will find two copies * followed by stuff and a later * and missunderstand these to mean bold. The math mode looses. Solutions include using $$...$$ instead of $...$ or changing the symbol to a latex one like \star or \circ as those never conflict with Markdown. 2. Another one is \| which markdown uses to make walls of a table and at times within KaTex the use of \| can get confused. Try latex \mid if you find trouble – it may not be your preferred spacing but notice this is getting math on the internet so what are you complaining about? 3. Keep in mind that $$...$$ will only center the display mode if there si a new line before and after. • Get the source of a video. For Vimeo videos, you can get the source of the video by clicking share then copying the link shown in the popup. For YouTube, right-click a video and choose copy video url. • You can also add videos to the site in the /uploads/videos directory, but it is not recommended to keep videos in your code repository. • Once you have the source of a video, use the code below as a template: {% include video.html src="https://vimeo.com/379509939" title="Tensors & Operators -- James B. Wilson" desc="Introduction to Tensors, Tensor Spaces, and Transverse Operators. TACA 2019. For more visit https://TheTensor.Space/. Creative Commons 2.0 CC-BY 2019 James B. Wilson" %} …which will result in the following output: ### Tensors & Operators -- James B. Wilson Introduction to Tensors, Tensor Spaces, and Transverse Operators. Creative Commons 2.0 CC-BY 2019 James B. Wilson ### Direct Embed Directly embedding a video can avoid issues caused by the theme and / or video provider. To directly embed a video, it’s recommended to follow these instructions: 1. Get the a video’s embed src (often, clicking “share”, then “embed” or “iframe” will lead you here). 2. Use the following component: <div class="iframe-wrapper"> <iframe class="iframe" src="https://sms.cam.ac.uk/media/3155105/embed" scrolling="no"></iframe> </div> …to render this output: You can also copy and paste an iframe directly onto a page, but using this component will make the iframe fit to the page nicely. It is not recommended to keep images in your code repository, but at a small scale it is acceptable (this is because Git tracks every image and slows down version control and for other reasons). Use the following markdown as a template to add an image to a post: Use an image in the /uploads/images directory: Or, use an external image (Be sure the image won't be removed in the future): ![Text that is shown if the image fails to load](https://URL_TO_YOUR_IMAGE) ## Edit a non-post page All non-post pages are mostly located in the root directory. For example, About, Home, and Contact pages can be found in the root directory as about.md, index.md, and contact.md. To make a post a featured post and show up on the home page, add tags: featured to a post. For example: --- layout: post title: Post Template # The "featured" tag will make this post appear on the home page. tags: featured --- ## Documentation A full list of documentation for the site can be found on the documentation page. ## Contributing When you’d like to contribute to the website, you’ll need to follow these steps: 1. Fork our repository, thetensor-space/thetensor-space.github.io. 3. Create a new branch with a descriptive name like article-squid-membranes. 4. Run the site locally: 1. Open a terminal and navigate inside your cloned project. 2. Use Docker (Recommended, Free for linux): docker run --rm \ --volume="\$PWD:/srv/jekyll" \ -p 4000:4000 \ -it jekyll/jekyll \ jekyll serve Then, run jekyll serve or bundle exec jekyll serve to run the site. 3. Now the site is available at http://localhost:4000 it will automagically reload every time a file is saved. 5. Create new changes (Add an article, update the navbar, etc.). • Instructions for common changes are described in the rest of this post. 7. Create a pull request to master on thetensor-space/thetensor-space.github.io. 8. We will review your pull request and either request changes or approve it and merge your changes to master. 9. The site will automatically refresh with any new changes within a few minutes. If you have additional questions, feel free to reach out to a maintainer / contributor on the contact page.	2020-06-03 12:24:48	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 2, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.18856142461299896, "perplexity": 4654.7427899298345}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347434137.87/warc/CC-MAIN-20200603112831-20200603142831-00071.warc.gz"}
https://www.qb365.in/materials/stateboard/12th-maths-chapter-2-complex-numbers-one-mark-question-paper-9195.html	#### Complex Numbers One Mark Question 12th Standard EM Reg.No. : • • • • • • Maths Time : 00:45:00 Hrs Total Marks : 30 24 x 1 = 24 1. The value of $\sum _{ i=1 }^{ 13 }{ \left( { i }^{ n }+i^{ n-1 } \right) }$ is (a) 1+ i (b) i (c) 1 (d) 0 2. If z is a non zero complex number, such that 2iz2=$\bar { z }$ then \|z\| is (a) $\cfrac { 1 }{ 2 }$ (b) 1 (c) 2 (d) 3 3. If \|z-2+i\|≤2, then the greatest value of \|z\| is (a) $\sqrt { 3 } -2$ (b) $\sqrt { 3 } +2$ (c) $\sqrt { 5 } -2$ (d) $\sqrt { 5 } +2$ 4. If \|z\|=1, then the value of $\cfrac { 1+z }{ 1+\overline { z } }$ is (a) z (b) $\bar { z }$ (c) $\cfrac { 1 }{ z }$ (d) 1 5. The solution of the equation \|z\|-z=1+2i is (a) $\cfrac { 3 }{ 2 } -2i$ (b) $-\cfrac { 3 }{ 2 } +2i$ (c) $2-\cfrac { 3 }{ 2 } i$ (d) $2+\cfrac { 3 }{ 2 } i$ 6. If z is a complex number such that $z\varepsilon C/R\quad$and $z+\cfrac { 1 }{ z } \epsilon R$ then\|z\| is (a) 0 (b) 1 (c) 2 (d) 3 7. If z=x+iy is a complex number such that \|z+2\|=\|z−2\|, then the locus of z is (a) real axis (b) imaginary axis (c) ellipse (d) circle 8. The principal argument of $\cfrac { 3 }{ -1+i }$ (a) $\cfrac { -5\pi }{ 6 }$ (b) $\cfrac { -2\pi }{ 3 }$ (c) $\cfrac { -3\pi }{ 4 }$ (d) $\cfrac { -\pi }{ 2 }$ 9. If (1+i)(1+2i)(1+3i)...(1+ni)=x+iy, then $2\cdot 5\cdot 10...\left( 1+{ n }^{ 2 } \right)$ is (a) 1 (b) i (c) x2+y2 (d) 1+n2 10. If $\alpha$ and $\beta$ are the roots of x2+x+1=0, then ${ \alpha }^{ 2020 }+{ \beta }^{ 2020 }$ is (a) -2 (b) -1 (c) 1 (d) 2 11. If $\omega \neq 1$ is a cubic root of unity and $\left\| \begin{matrix} 1 & 1 & 1 \\ 1 & { -\omega }^{ 2 } & { \omega }^{ 2 } \\ 1 & { \omega }^{ 2 } & { \omega }^{ 2 } \end{matrix} \right\|$ =3k, then k is equal to (a) 1 (b) -1 (c) $\sqrt { 3i }$ (d) $-\sqrt { 3i }$ 12. If $\omega =cis\cfrac { 2\pi }{ 3 }$, then the number of distinct roots of $\left\| \begin{matrix} z+1 & \omega & { \omega }^{ 2 } \\ \omega & z+{ \omega }^{ 2 } & 1 \\ { \omega }^{ 2 } & 1 & z+\omega \end{matrix} \right\|$ (a) 1 (b) 2 (c) 3 (d) 4 13. The value of (1+i) (1+i2) (1+i3) (1+i4) is (a) 2 (b) 0 (c) 1 (d) i 14. If $\sqrt { a+ib }$ =x+iy, then possible value of $\sqrt { a-ib }$ is (a) x2+y2 (b) $\sqrt { { x }^{ 2 }+{ y }^{ 2 } }$ (c) x+iy (d) x-iy 15. If a=cosθ + i sinθ, then $\frac { 1+a }{ 1-a }$ = (a) cot $\frac { \theta }{ 2 }$ (b) cot θ (c) i cot $\frac { \theta }{ 2 }$ (d) i tan$\frac { \theta }{ 2 }$ 16. The principal value of the amplitude of (1+i) is (a) $\frac { \pi }{ 4 }$ (b) $\frac { \pi }{ 12 }$ (c) $\frac { 3\pi }{ 4 }$ (d) $\pi$ 17. The least positive integer n such that $\left( \frac { 2i }{ 1+i } \right) ^{ n }$ is a positive integer is (a) 16 (b) 8 (c) 4 (d) 2 18. If z = $\frac { 1 }{ (2+3i)^{ 2 } }$ then \|z\| = (a) $\frac { 1 }{ 13 }$ (b) $\frac { 1 }{ 5}$ (c) $\frac { 1 }{ 12 }$ (d) none of these 19. If z=1-cosθ + i sinθ, then \|z\| = (a) 2 sin$\frac { 1 }{ 3 }$ (b) 2 cos$\frac { \theta }{ 2 }$ (c) 2\|sin$\frac { \theta }{ 2 }$\| (d) 2\|cos$\frac { \theta }{ 2 }$\| 20. If z=$\frac { 1 }{ 1-cos\theta -isin\theta }$, the Re(z) = (a) 0 (b) $\frac{1}{2}$ (c) cot$\frac { \theta }{ 2 }$ (d) $\frac{1}{2}$cot$\frac { \theta }{ 2 }$ 21. The complex number z which satisfies the condition $\left\| \frac { 1+z }{ 1-z } \right\|$ =1 lies on (a) circle x2+y2 =1 (b) x-axis (c) y-axis (d) the lines x+y=1 22. If zn =$cos\frac { n\pi }{ 3 } +isin\frac { n\pi }{ 3 }$, then z1, z2 ..... z6 is (a) 1 (b) -1 (c) i (d) -i 23. If a =cosα + i sinα, b= -cosβ + i sinβ then $\left( ab-\frac { 1 }{ ab } \right)$ is _________ (a) -2i sin(α - β) (b) 2i sin(α - β) (c) 2 cos(α - β) (d) -2 cos(α - β) 24. If x=cosθ + i sinθ, then xn+$\frac { 1 }{ { x }^{ n } }$ is ______ (a) 2 cos nθ (b) 2 i sin nθ (c) 2n cosθ (d) 2n i sinθ 25. 6 x 1 = 6 26. Re(z) 27. (1) 2$\sqrt { 2 }$ 28. Im(z) 29. (2) $\frac { z+\bar { z } }{ 2 }$ 30. z is real 31. (3) z=$\bar { z }$ 32. z is imaginary 33. (4) \|$\bar { z }$\| 34. \|z\| 35. (5) $\frac { z-\bar { z } }{ 2 }$ 36. \|2+2i\| 37. (6) z=-$\bar { z }$	2019-10-16 12:35:51	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9489070177078247, "perplexity": 8822.428665266356}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986668569.22/warc/CC-MAIN-20191016113040-20191016140540-00130.warc.gz"}
https://crypto.ethz.ch/publications/abstract.html?label=Maurer93a	Publications: Abstract # Secret Key Agreement by Public Discussion ## Ueli Maurer The problem of generating a shared secret key $S$ by two parties knowing random variables $X$ and $Y$, respectively, but not sharing a secret key initially, is considered. An enemy who knows the random variable $Z$, jointly distributed with $X$ and $Y$ according to some probability distribution $P_{XYZ}$, and who receives all messages exchanged by the two parties over a public channel, must not obtain more than a negligible amount of information about $S$. Upper bounds on $H(S)$ as a function of $P_{XYZ}$ are presented. Lower bounds on the rate $H(S)/N$ (as $N\rightarrow\infty$) are derived for the case where $X=[X_1\pp X_N]$, $Y=[Y_1\pp Y_N]$ and $Z=[Z_1\pp Z_N]$ result from $N$ independent executions of a random experiment generating $X_i,Y_i$ and $Z_i$, for $i=1\pp N$. The results of this paper suggest to build cryptographic systems that are provably secure against enemies with unlimited computing power under realistic assumptions about the partial independence of the noise on the involved communication channels.	2019-01-19 06:25:41	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.63588547706604, "perplexity": 226.2352830008145}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547583662690.13/warc/CC-MAIN-20190119054606-20190119080606-00554.warc.gz"}
https://www.zbmath.org/?q=an%3A1066.46023	# zbMATH — the first resource for mathematics Discretization and anti-discretization of rearrangement-invariant norms. (English) Zbl 1066.46023 A new method of discretization and anti-discretization of weighted inequalities is developed which is applied to norms in classical Lorentz spaces and to spaces endowed with the so-called Hilbert norm. As an application of these results, some integral conditions characterizing embeddings $$\Gamma^{p}(v)\to \Lambda^{q}(w)$$ and an integral characterization of the associate space to $$\Gamma^{p}(v)$$ are given, where $$p,q\in (0,\infty),$$ $$v,w$$ are weights on $$[0,\infty)$$ and $\\| f\\| _{\Lambda^{p}(v)}=\left(\int_{0}^{\infty}f^{\ast}(t)^{p}v(t) \,dt\right)^{1/p},\qquad \\| f\\| _{\Gamma^{p}(v)}= \left(\int_{0}^{\infty} f^{\ast\ast}(t)^{p}v(t) \,dt\right)^{1/p}.$ ##### MSC: 46E30 Spaces of measurable functions ($$L^p$$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 26D10 Inequalities involving derivatives and differential and integral operators Full Text:	2021-04-22 11:22:45	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8582202792167664, "perplexity": 1577.4512403966044}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618039603582.93/warc/CC-MAIN-20210422100106-20210422130106-00125.warc.gz"}
http://math.stackexchange.com/questions/127725/riemannian-connection-very-basic-question	# Riemannian Connection (Very basic question) We know that a connection $\nabla$ in a manifold M hashas the purpose of performing the same role as the covariant derivative of vector fields of surfaces in $\mathbb{R}^3$. Such analogies are clearly perceived in the connection definition. When M has a Riemannian metric,$~~ g~~$, to make things even more similar to the case in $\mathbb{R}^3$ we introduce the concept of Riemannian connection or Levi-Civita connection, which is a connection satisfying: 1. compatibility with the metric: $Xg(Y,Z)=g(\nabla_X Y,Z)+g(Y,\nabla_X Z)$ 2. torsion-free: $T(X,Y)=\nabla_X Y-\nabla_YX-[X,Y]\equiv 0$ where $X, Y, Z$ are vector fields on $M.$ What I understand is the need / intuition of the second property, torsion-free,what would work well if not we assume this hypothesis? - You might find this mathoverflow thread interesting: mathoverflow.net/questions/20493/…. One motivation for requiring $\nabla$ to have 0 torsion is that this (along with 1) singles out a unique connection. People do however study geometries with torsion (and I've heard these have applications to string theory). – Eric O. Korman Apr 3 '12 at 20:37 One good motivation for choosing a torsion free connection is the fact that it gives you equality of mixed partial derivatives, i.e. if $X$ and $Y$ are coordinate vector fields then $\nabla_X Y = \nabla_Y X$. – treble Apr 3 '12 at 23:24	2015-12-01 22:21:38	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7326252460479736, "perplexity": 483.0348400764126}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-48/segments/1448398471441.74/warc/CC-MAIN-20151124205431-00116-ip-10-71-132-137.ec2.internal.warc.gz"}
https://aakashdigitalsrv1.meritnation.com/ask-answer/question/please-explain-q5-of-ex-12-2-of-ncert-textbook-i-went-throug/introduction-to-three-dimensional-geometry/3640105	# please explain Q5 of Ex:12.2 of NCERT textbook. i went through the solution yet not able to understand......its very important !!!!!!! reply soon In the said question, we have to find the equation of the set of points P, the sum of whose distances from A (4, 0, 0) and B (–4, 0, 0) is equal to 10 i.e., PA + PB = 10. Solution: In order to find the equation of the set of points P, firstly we consider the coordinates of P be (x, y, z). The coordinates of points A and B are (4, 0, 0) and (–4, 0, 0) respectively. It is given that PA + PB = 10. Now, by using distance formula, we get Simply on squaring both sides, we obtain Again, on squaring both sides again, we get 25 (x2 + 8x + 16 + y2 + z2) = 625 + 16x2 + 200x ⇒ 25x2 + 200x + 400 + 25y2 + 25z2 = 625 + 16x2 + 200x ⇒ 9x2 + 25y2 + 25z2 – 225 = 0 Thus, the required equation is 9x2 + 25y2 + 25z2 – 225 = 0. Hope you get it now!! • 0 What are you looking for?	2022-08-13 01:10:43	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8162723183631897, "perplexity": 691.929832593731}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882571847.45/warc/CC-MAIN-20220812230927-20220813020927-00737.warc.gz"}
https://www.esaral.com/q/two-cars-x-and-y-63486	# Two cars X and Y Question: Two cars $\mathrm{X}$ and $\mathrm{Y}$ are approaching each other with velocities $36 \mathrm{~km} / \mathrm{h}$ and $72 \mathrm{~km} / \mathrm{h}$ respectively. The frequency of a whistle sound as emitted by a passenger in car X, heard by the passenger in car $\mathrm{Y}$ is $1320 \mathrm{~Hz}$. If the velocity of sound in air is $340 \mathrm{~m} / \mathrm{s}$, the actual frequency of the whistle sound produced is ........ Hz. Solution: $\mathrm{V}_{\mathrm{x}}=36 \mathrm{~km} / \mathrm{hr}=10 \mathrm{~m} / \mathrm{s}$ $\mathrm{V}_{\mathrm{y}}=72 \mathrm{~km} / \mathrm{hr}=20 \mathrm{~m} / \mathrm{s}$ by doppler's effect $\mathrm{F}^{\prime}=\mathrm{F}_{0}\left(\frac{\mathrm{V} \pm \mathrm{V}_{0}}{\mathrm{~V} \pm \mathrm{V}_{\mathrm{s}}}\right)$ $1320=\mathrm{F}_{0}\left(\frac{340+20}{340-10}\right) \Rightarrow \mathrm{F}_{0}=1210 \mathrm{~Hz}$	2023-02-06 09:59:48	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5998584628105164, "perplexity": 517.5126205683492}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500334.35/warc/CC-MAIN-20230206082428-20230206112428-00722.warc.gz"}
https://granite.phys.s.u-tokyo.ac.jp/wiki/Lab/index.php?VoluntarySeminars	## Journal Club † ### Coming up next † 2013年4月日松本伸之Observation of quantum state collapse and revival due to the single-photon Kerr effectNature 495, 205 (2013) ### Log † 2013年4月22日道村唯太Phase-measurement sensitivity beyond the standard quantum limit in an interferometer consisting of a parametric amplifier and a beam splitterPhys. Rev. A 87, 023825 (2013) 2013年4月18日松本伸之Cognitive neuroscience: Sensory noise drives bad decisionsNature 496, 172 (2013) Rats and Humans Can Optimally Accumulate Evidence for Decision-MakingScience 340, 95 (2013) 2013年4月16日松本伸之Exploiting shot noise correlations in the photodetection of ultrashort optical pulse trainsNature Photonics 7, 290 (2013) 2013年4月11日道村唯太Dispersive Fourier transformation for fast continuous single-shot measurementsNature Photonics 7, 102 (2013) Recovering three-dimensional shape around a corner using ultrafast time-of-flight imagingNature Commun. 3, 745 (2012) 2013年4月8日松本伸之Physiologic brain activity causes DNA double-strand breaks in neurons, with exacerbation by amyloid-βNature Neuroscience (2013) 2013年1月11日松本伸之Optomechanical Transducers for Long-Distance Quantum CommunicationPhys. Rev. Lett. 105, 220501 (2010) 2012年10月25日岡田健志Gravitational-Wave Background as a Probe of the Primordial Black-Hole AbundancePhys. Rev. Lett. 102, 161101 (2009) 2012年10月17日道村唯太The potential for very high-frequency gravitational wave detectionClass. Quantum Grav. 29 095003 (2012) 2012年10月10日渡辺篤史An introduction to signal extraction in interferometric gravitational wave detectorsAm. J. Phys. 71, 365 (2003) 2012年10月9日松本伸之A quantum radiation pressure noise-free optical springarXiv:1210.0309v1 2012年10月2日松本伸之Observation of Radiation Pressure Shot NoisearXiv:1209.6334v1 2012年9月26日道村唯太Laboratory limit on the charge of photons by electric field deflectionarXiv:1209.2052v1 2012年8月15日松本伸之A Technique for In-situ Measurement of Free Spectral Range and Transverse Mode Spacing of Optical CavitiesarXiv:1206.5037v2 2012年8月15日道村唯太Thermo-optic noise in coated mirrors for high-precision optical measurementsPhys. Rev. D 78, 102003 (2008) 2012年7月10日中野雅之Probing Planck-scale physics with quantum opticsNature Physics 8, 393–397 (2012) 2012年6月26日正田亜八香Precision Rotation Measurements with an Atom Interferometer GyroscopePhys. Rev. Lett. 78, 2046–2049 (1997) 2012年6月19日松本伸之Eigenmode changes in a misaligned triangular optical cavity2011 J. Opt. 13 055504 2012年6月12日松本伸之An investigation of coupledresonances in materials suitable for test masses in gravitational wave detectorsPhysics Letters A 161 (1991) 101-110 2012年6月5日松本伸之Thermoelastic effects at low temperatures and quantum limits in displacement measurementsPhys. Rev. D 63, 082003 (2001) 2012年5月29日中野雅之Test of the Gravitational Inverse Square Law at Millimeter RangesPhys. Rev. Lett. 108, 081101 (2012) 2012年5月11日道村唯太Experimental demonstration of a displacement noise free interferometry scheme for gravitational wave detectors showing displacement noise reduction at low frequenciesPhys. Rev. D 81, 062004 (2010) 2012年5月8日正田亜八香Development of a Displacement- and Frequency-Noise-Free Interferometer in a 3D Configuration for Gravitational Wave DetectionPhys. Rev. Lett. 103, 171101 (2009) 2012年5月1日松本伸之Optomechanically Induced TransparencyScience 330, 1520 (2010) 2012年4月27日道村唯太Active noise cancellation in a suspended interferometerRev. Sci. Instrum. 83, 024501 (2012) 2012年4月16日正田亜八香Virgo data characterization and impact on gravitational wave searches (Section 4のみ)arXiv:1203.5613v1 2012年4月9日松本伸之Nanomechanical motion measured with an imprecision below that at the standard quantum limitNature Nanotechnology 4, 820 - 823 (2009) 2012年4月6日道村唯太Locking the frequency of lasers to an optical cavity at the $1.6 \times 10^{-17}$ relative instability levelarXiv:1203.6247v1 ### Interesting Papers † Weak value amplification in a shot-noise limited interferometerarXiv:1201.6039v1 Intensity feedback effects on quantum-limited noiseJ. Opt. Soc. Am. B 12, 1792-1800 (1995) Opportunity to test non-Newtonian gravity using interferometric sensors with dynamic gravity field generatorsPhys. Rev. D 84, 082002 (2011) Damping and local control of mirror suspensions for laser interferometric gravitational wave detectorsRev. Sci. Instrum. 83, 044501 (2012) Resonant Speed Meter for Gravitational-Wave DetectionPhys. Rev. Lett. 101, 081101 (2008) THE SEISMIC NOISE OF THE EARTH'S SURFACEClass. Quantum. Grav. 15, 3339 (1998) Terrestrial gravitational noise on a gravitational wave antennaPhys. Rev. D. 30, 732 (1984) A cryogenic torsion pendulum: progress reportClass. Quantum Grav. 17 2313 (2000) Treatment of Calibration Uncertainty in Multi-Baseline Cross-Correlation Searches for Gravitational WavesarXiv:1205.3112 Pound–Drever–Hall error signals for the length control of three-port grating coupled cavitiesApplied Optics, Vol. 50, Issue 22, pp. 4340-4346 (2011) Many-Wavelength Interferometry with Thousands of Lasers for Absolute Distance MeasurementPhys. Rev. Lett. 108, 183901 (2012) Biological measurement beyond the quantum limitarXiv:1206.6928v1 Serial time-encoded amplified imaging for real-time observation of fast dynamic phenomenaNature 458, 1145-1149 (30 April 2009) Dual-wavelength optical parametric oscillator using antiresonant ring interferometerLaser Photonics Rev., 1–5 (2012) Tunable High-Frequency Gravitational-Wave Detection with optically-levitated sensorsarXiv:1207.5320v1 A New Bound on Excess Frequency Noise in Second Harmonic Generation in PPKTP at the 10^-19 LevelarXiv:1208.2011 Large-angle scattered light measurements for quantum-noise filter cavity design studiesJOSA A, Vol. 29, Issue 8, pp. 1722-1727 (2012) Enhanced Quantum Nonlinearities in a Two-Mode Optomechanical SystemPhys. Rev. Lett. 109, 063601 (2012) Measurement of the Velocity of Neutrinos from the CNGS Beam with the Large Volume DetectorPhys. Rev. Lett. 109, 070801 (2012) Non-classical light generated by quantum-noise-driven cavity optomechanicsNature (2012) Polarization speed meter for gravitational-wave detectionPhys. Rev. D 86, 062001 (2012) Pulsed quantum optomechanicsProc. Natl Acad. Sci. USA 108, 16182-16187 (2011) Development of a high-sensitivity torsion balance to investigate the thermal Casimir forceInt. J. Mod. Phys. Conf. Ser. 14, 337 (2012) Quantum-Enhanced Optical-Phase TrackingScience 21 September 2012: Vol. 337 no. 6101 pp. 1514-1517 Quantum Magnetomechanics: Ultrahigh-Q-Levitated Mechanical OscillatorsPhys. Rev. Lett. 109, 147206 (2012) DC readout experiment in Enhanced LIGOClass. Quantum Grav. 29 065005 (2012) Many-Wavelength Interferometry with Thousands of Lasers for Absolute Distance MeasurementPhys. Rev. Lett. 108, 183901 (2012) Simple Pendulum Determination of the Gravitational ConstantPhys. Rev. Lett. 105, 110801 (2010) A high-resolution microchip optomechanical accelerometerNature Photonics (2012) Measurement of the Instantaneous Velocity of a Brownian ParticleScience 328, 1673 (2010) Trapping of Neutral Mercury Atoms and Prospects for Optical Lattice ClocksPhys. Rev. Lett. 100, 053001 (2008) Controlling advanced gravitational wave detector output mode cleaners acting on the laser frequencyAstroparticle Physics (2012) Squeezing of optomechanical modes in detuned Fabry-Perot interferometerarXiv:1212.2941 Force-insensitive optical cavityOptics Letters, 36, 3572-3574 (2011) Pulsed Sagnac source of polarization entangled photon pairsOptics Express, 20, 25022-25029 (2012) A sub-40-mHz-linewidth laser based on a silicon single-crystal optical cavityNat. Photon. 6, 687–692 (2012) Gravitational bar detectors set limits to Planck-scale physics on macroscopic variablesNature Physics (2012) Measurements of Ω and Λ from 42 High-Redshift Supernovae1999 ApJ 517 565 Long-term stable squeezed vacuum state of light for gravitational wave detectors2012 Class. Quantum Grav. 29 075001 Measurement of mirror birefringence at the sub-ppm level: Proposed application to a test of QEDPhys. Rev. A 62, 013815 (2000) Two-beam interferometer with phase difference magnifiedOptics Letters, 38, 133 (2013) ## 量子光学 † ### テキスト † Marlan O. Scully, M. Suhail Zubairy: Quantum Optics (Cambridge University Press, 1997) ### レジュメ † 1. Quantum theory of radiation 20100423 2. Coherent and squeezed states of the radiation field 20100430 3. Quantum Distribution Theory and Partially Coherent Radiation 20100507 appendix 4. Field-field and photon-photon correlation interferometry 5. Atom-field interaction - semiclassical theory 6. Atom-field interaction - quantum theory 7. Lasing without inversion and other effects of atomic coherence and interference 20100709 20100723 8. Quantum theory of damping - density operator and wave function approach 9. Quantum theory of damping - Heisenberg-Langevin approach 10. Resonance fluorescence 11. Quantum theory of laser - density operator approach 12. Quantum theory of laser - Heisenberg-Langevin approach 13. Theory of the micrometer 14. Correlated emission laser: concept, theory and analysis 15. Phase sensitivity in quantum optical systems: applications 16. Squeezing via non-linear optical processes 17. Atom optics 18. The EPR paradox, hidden variables and Bell's Theorem 19. Quantum non-demolition measurements 20. Quantum optical tests of complementarity 21. Two-photon interferometry and the quantum measurement problem ## Saulsonゼミ † ### テキスト † Peter R. Saulson: Fundamentals of Interferometric Gravitational Wave Detectors (World Scientific Pub Co Inc, 1994) ### レジュメ † 1. The Search for Gravitational Waves 2. The Nature of Gravitational Waves 3. Sources of Gravitational Waves 20091218 4. Linear Systems, Signals and Noise 20100113 supplement 6. Folded Interferometer Arms 7. Thermal Noise 20100127 20100203 8. Seismic Noise and Vibration Isolation 20100210 9. Design Features of Large Interferometers 10. Null Instruments 20100302 11. Feedback Control Systems 20100420 20100427 12. An Interferometer as an Active Null Instrument 20091216 20100511 appendix(麻生さんの資料) 13. Resonant Mass Gravitational Wave Detectors 20100525 14. Detecting Gravitational Wave Signals 20100601 15. Gravitational Wave Astronomy 20100608 16. Prospects ## 参考 † ### ネタの参考にどうぞ。 † フォローやネタ集めなどご自由に使ってください。リプライ歓迎です。 Last-modified: 2013-07-09 (火) 14:50:24	2022-11-28 00:51:39	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3882367014884949, "perplexity": 13997.508072118313}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710462.59/warc/CC-MAIN-20221128002256-20221128032256-00470.warc.gz"}
http://www.vdtek.com/hyperloop-texas-bmn/how-to-prove-a-function-is-continuous-0b44c7	to apply the theorems about continuous functions; to determine whether a piecewise defined function is continuous; to become aware of problems of determining whether a given function is conti nuous by using graphical techniques. This means that the function is continuous for x > 0 since each piece is continuous and the function is continuous at the edges of each piece. We can also define a continuous function as a function … And if a function is continuous in any interval, then we simply call it a continuous function. She is the author of several For Dummies books, including Algebra Workbook For Dummies, Algebra II For Dummies, and Algebra II Workbook For Dummies. The left and right limits must be the same; in other words, the function can’t jump or have an asymptote. Examples of Proving a Function is Continuous for a Given x Value Let C(x) denote the cost to move a freight container x miles. In the second piece, the first 200 miles costs 4.5(200) = 900. 1. In addition, miles over 500 cost 2.5(x-500). You need to prove that for any point in the domain of interest (probably the real line for this problem), call it x0, that the limit of f(x) as x-> x0 = f(x0). My attempt: We know that the function f: x → R, where x ∈ [ 0, ∞) is defined to be f ( x) = x. And remember this has to be true for every v… Both sides of the equation are 8, so ‘f(x) is continuous at x = 4. How to Determine Whether a Function Is Continuous. - [Instructor] What we're going to do in this video is come up with a more rigorous definition for continuity. The function f is continuous at a if and only if f satisﬁes the following property: ∀ sequences(xn), if lim n → ∞xn = a then lim n → ∞f(xn) = f(a) Theorem 6.2.1 says that in order for f to be continuous, it is necessary and suﬃcient that any sequence (xn) converging to a must force the sequence (f(xn)) to converge to f(a). A function f is continuous at a point x = a if each of the three conditions below are met: i. f (a) is defined. Then f ( x) is continuous at c iff for every ε > 0, ∃ δ > 0 such that. In mathematics, a continuous function is a function that does not have any abrupt changes in value, known as discontinuities. The limit of the function as x approaches the value c must exist. If either of these do not exist the function will not be continuous at x=ax=a.This definition can be turned around into the following fact. Let ﷐﷯ = tan⁡ ﷐﷯ = ﷐﷐sin﷮﷯﷮﷐cos﷮﷯﷯ is defined for all real number except cos⁡ = 0 i.e. Please Subscribe here, thank you!!! The function must exist at an x value (c), which means you can’t have a hole in the function (such as a 0 in the denominator). Modules: Definition. Once certain functions are known to be continuous, their limits may be evaluated by substitution. More precisely, sufficiently small changes in the input of a continuous function result in arbitrarily small changes in its output. Continuous functions are precisely those groups of functions that preserve limits, as the next proposition indicates: Proposition 6.2.3: Continuity preserves Limits : If f is continuous at a point c in the domain D, and { x n} is a sequence of points in D converging to c, then f(x) = f(c). Prove that if f is continuous at x0 ∈ I and f(x0)>μ, then there exist a δ>0 such that f(x)>μ for all x∈ I with \|x-x0\|<δ. However, are the pieces continuous at x = 200 and x = 500? Let’s look at each one sided limit at x = 200 and the value of the function at x = 200. In other words, if your graph has gaps, holes or … The first piece corresponds to the first 200 miles. By "every" value, we mean every one … Answer. f(x) = f(x_0) + α(x), where α(x) is an infinitesimal for x tending to x_0. $latex \displaystyle \underset{x\to a}{\mathop{\lim }},f(x)=f(a)$. Consider f: I->R. You can substitute 4 into this function to get an answer: 8. The function is continuous on the set X if it is continuous at each point. Your pre-calculus teacher will tell you that three things have to be true for a function to be continuous at some value c in its domain: f(c) must be defined. Example 18 Prove that the function defined by f (x) = tan x is a continuous function. Can someone please help me? Let c be any real number. ii. The identity function is continuous. For this function, there are three pieces. We can define continuous using Limits (it helps to read that page first):A function f is continuous when, for every value c in its Domain:f(c) is defined,andlimx→cf(x) = f(c)\"the limit of f(x) as x approaches c equals f(c)\" The limit says: \"as x gets closer and closer to c then f(x) gets closer and closer to f(c)\"And we have to check from both directions:If we get different values from left and right (a \"jump\"), then the limit does not exist! Let f (x) = s i n x. All miles over 200 cost 3(x-200). If you look at the function algebraically, it factors to this: Nothing cancels, but you can still plug in 4 to get. is continuous at x = 4 because of the following facts: f(4) exists. Since these are all equal, the two pieces must connect and the function is continuous at x = 200. Step 1: Draw the graph with a pencil to check for the continuity of a function. https://goo.gl/JQ8NysHow to Prove a Function is Uniformly Continuous. Prove that C(x) is continuous over its domain. A function f is continuous at x = a if and only if If a function f is continuous at x = a then we must have the following three … Recall that the definition of the two-sided limit is: For example, you can show that the function. I.e. However, the denition of continuity is exible enough that there are a wide, and interesting, variety of continuous functions. Another definition of continuity: a function f(x) is continuous at the point x = x_0 if the increment of the function at this point is infinitely small. Interior. The function’s value at c and the limit as x approaches c must be the same. Constant functions are continuous 2. Thread starter caffeinemachine; Start date Jul 28, 2012; Jul 28, 2012. Thread starter #1 caffeinemachine Well-known member. Medium. Consequently, if you let M := sup z ∈ U \| \| d f ( z) \| \|, you get. If a function is continuous at every value in an interval, then we say that the function is continuous in that interval. This gives the sum in the second piece. x → c − lim f (x) x → c − lim (s i n x) since sin x is defined for every real number. I asked you to take x = y^2 as one path. Definition 81 Continuous Let a function f(x, y) be defined on an open disk B containing the point (x0, y0). Problem A company transports a freight container according to the schedule below. A function f is continuous at a point x = a if each of the three conditions below are met: ii. Definition of a continuous function is: Let A ⊆ R and let f: A → R. Denote c ∈ A. Alternatively, e.g. Prove that function is continuous. if U is not convex and f ∈ C 1, you can integrate: if γ is a smooth curve joining x and y, f ( x) − f ( y) = f ( γ ( 1)) − f ( γ ( 0)) = ∫ 0 1 ( f ∘ γ) ′ ( t) d t ≤ M ∫ 0 1 \| \| γ ′ ( t) \| \| d t. Let’s break this down a bit. If not continuous, a function is said to be discontinuous. To do this, we will need to construct delta-epsilon proofs based on the definition of the limit. Needed background theorems. But in order to prove the continuity of these functions, we must show that $\lim\limits_{x\to c}f(x)=f(c)$. In the third piece, we need $900 for the first 200 miles and 3(300) = 900 for the next 300 miles. The second piece corresponds to 200 to 500 miles, The third piece corresponds to miles over 500. Each piece is linear so we know that the individual pieces are continuous. f is continuous on B if f is continuous at all points in B. And the general idea of continuity, we've got an intuitive idea of the past, is that a function is continuous at a point, is if you can draw the graph of that function at that point without picking up your pencil. \| f ( x) − f ( y) \| ≤ M \| x − y \|. \| x − c \| < δ \| f ( x) − f ( c) \| < ε. Your pre-calculus teacher will tell you that three things have to be true for a function to be continuous at some value c in its domain: f(c) must be defined. The function must exist at an x value (c), which means you can’t have a hole in the function (such as a 0 in the denominator). To prove a function is 'not' continuous you just have to show any given two limits are not the same. In the first section, each mile costs$4.50 so x miles would cost 4.5x. You are free to use these ebooks, but not to change them without permission. f is continuous at (x0, y0) if lim (x, y) → (x0, y0) f(x, y) = f(x0, y0). To prove these functions are continuous at some point, such as the locations where the pieces meet, we need to apply the definition of continuity at a point. The Applied Calculus and Finite Math ebooks are copyrighted by Pearson Education. I … Transcript. b. At x = 500. so the function is also continuous at x = 500. We know that A function is continuous at x = c If L.H.L = R.H.L= f(c) i.e. For all other parts of this site, $latex \displaystyle \underset{x\to a}{\mathop{\lim }},f(x)$, $latex \displaystyle \underset{x\to a}{\mathop{\lim }},f(x)=f(a)$, Chapter 9 Intro to Probability Distributions, Creative Commons Attribution 4.0 International License. If any of the above situations aren’t true, the function is discontinuous at that value for x. Mary Jane Sterling aught algebra, business calculus, geometry, and finite mathematics at Bradley University in Peoria, Illinois for more than 30 years. The mathematical way to say this is that. x → c lim f (x) = x → c + lim f (x) = f (c) Taking L.H.L. f(x) = x 3. simply a function with no gaps — a function that you can draw without taking your pencil off the paper Note that this definition is also implicitly assuming that both f(a)f(a) and limx→af(x)limx→a⁡f(x) exist. A graph for a function that’s smooth without any holes, jumps, or asymptotes is called continuous. Prove that sine function is continuous at every real number. Up until the 19th century, mathematicians largely relied on intuitive … In the problem below, we ‘ll develop a piecewise function and then prove it is continuous at two points. MHB Math Scholar. $latex \displaystyle \underset{x\to a}{\mathop{\lim }},f(x)$ is defined, iii. To prove these functions are continuous at some point, such as the locations where the pieces meet, we need to apply the definition of continuity at a point. I was solving this function , now the question that arises is that I was solving this using an example i.e. Sums of continuous functions are continuous 4. Health insurance, taxes and many consumer applications result in a models that are piecewise functions. Continuous Function: A function whose graph can be made on the paper without lifting the pen is known as a Continuous Function. Along this path x … The study of continuous functions is a case in point - by requiring a function to be continuous, we obtain enough information to deduce powerful theorems, such as the In- termediate Value Theorem. If your pencil stays on the paper from the left to right of the entire graph, without lifting the pencil, your function is continuous. Free to use these ebooks, but not to change them without permission each mile costs 4.50... Points in B ) denote the cost to move a freight container x would. If L.H.L = R.H.L= f ( c ) \| < ε = 4 of... Continuity of a function f is continuous at x = c if =! F is continuous at x = 500 $is defined, iii = if. Iff for every v… Consider f: I- > R can show that the function is continuous... The pieces continuous at c iff for every ε > 0 such that function and then prove it continuous! As one path 2012 ; Jul 28, 2012 exist the function example 18 prove that c ( )... < ε { x\to a } { \mathop { \lim } }, (... A } { \mathop { \lim } }, f ( x ) is at... Prove a function that ’ s smooth without any holes, jumps, or asymptotes is continuous. Continuous, a function is continuous at x = 200 them without.... Variety how to prove a function is continuous continuous functions costs 4.5 ( 200 ) = s i n x step 1: the. A graph for a function, ∃ δ > 0, ∃ >! For every v… Consider f: I- > R to 500 miles, the first piece corresponds to the 200... Have to show any given two limits are not the same jumps, or asymptotes is called continuous Math! Function defined by f ( c ) \| < ε to change them without permission equation are 8, ‘. Then f ( 4 ) exists are 8, so ‘ f ( x =f., each mile costs$ 4.50 so x miles would cost 4.5x need to construct delta-epsilon proofs based on paper. Pen is known as a continuous function ( y ) \| ≤ M \| x − \|... Function is continuous at x = c if L.H.L = R.H.L= f ( x ) − (... Function ’ s smooth without any holes, jumps, or asymptotes is continuous... In a models that are piecewise functions 0, ∃ δ > 0 that. Health insurance, taxes and many consumer applications result in a models that are piecewise functions its output functions! 4 into this function to get an answer: 8 or have an asymptote without any holes,,. That i was solving this using an example i.e x-200 ) cost 4.5x points. That c ( x ) is continuous at all points in B all in. 200 ) = s i n x then we simply call it a continuous function, taxes and consumer! Function will not be continuous, their limits may be evaluated by substitution to miles. Thread starter caffeinemachine ; Start date Jul 28, 2012 ; Jul 28, 2012 to... An asymptote, sufficiently small changes in the second piece, the first piece corresponds the. First section, each mile costs $4.50 so x miles a freight container x miles prove the. Miles would cost 4.5x =f ( a )$ get an answer: 8 ’. Abrupt changes in the first section, each mile costs $4.50 so x.! Use these ebooks, but not to change them without permission will need to construct delta-epsilon proofs based the. In any interval, then we simply call it a continuous function: a function is 'not ' you! Given two limits are not the same δ > 0, ∃ >! This, we will need to construct delta-epsilon proofs based on the paper without lifting the pen is known a! Are copyrighted by Pearson Education the cost to move a freight container x miles continuous over its domain continuous its! That are piecewise functions and then prove it is continuous over its domain = 4 of... ’ s value at c and the limit as x approaches the value of the equation are 8 so! These are all equal, the how to prove a function is continuous can ’ t jump or have an asymptote,... { \mathop { \lim } }, f ( x ) is continuous at all points B! To construct delta-epsilon proofs based on the definition of the three conditions below are met: ii 8... In other words, the first 200 miles that c ( x ) denote the cost to a... Conditions below are met: ii every v… Consider f: I- > R continuous over domain... Start date Jul 28, 2012 ; Jul 28, 2012 ; Jul 28 2012... Second piece, the two pieces must connect and the value of equation. Into this function, now the question that arises is that i was solving this using example. As x approaches the value c must exist once certain functions are to... Prove it is continuous at x=ax=a.This definition can be made on the definition of the three conditions are. The input of a continuous function δ > 0, ∃ δ > 0, δ! Function is also continuous at every real number first section, each mile costs$ 4.50 so x.... Graph with a pencil to check for the continuity of a continuous.. Smooth without any holes, jumps, or asymptotes is called continuous the second piece corresponds to the first miles. All equal, the denition of continuity is exible enough that there a... That arises is that i was solving this using an example i.e pieces continuous c! Any interval, then we simply call it a continuous function the.... So x miles, known as discontinuities an answer: 8 that ’ s smooth any... − c \| < δ \| f ( x ) =f ( a $! To be discontinuous Calculus and Finite Math ebooks are copyrighted by Pearson Education \lim } } f! Pieces are continuous miles costs 4.5 ( 200 ) = tan x is a function is over. Must exist be continuous at x = 500 the Applied Calculus and Finite Math ebooks are copyrighted by Education. Since these are all equal, the two pieces must connect and the function as x approaches c must the. Graph can be turned around into the how to prove a function is continuous fact are 8, so ‘ f ( )... Of these do not exist the function ’ s look at each how to prove a function is continuous. This, we will need to construct delta-epsilon proofs based on the paper lifting. = 500. so the function defined by f ( c ) i.e is also continuous two! Problem a company transports a freight container x miles would cost 4.5x conditions are! Arbitrarily small changes in its output 200 miles costs 4.5 ( 200 ) = s i x., now the question that arises is that i was solving this function to get an answer 8! Caffeinemachine ; Start date Jul 28, 2012 the three conditions below are met: ii to miles 200! Equation are 8, so ‘ f ( x ) − f ( c ).. Tan⁡ ﷐﷯ = tan⁡ ﷐﷯ = tan⁡ ﷐﷯ = ﷐﷐sin﷮﷯﷮﷐cos﷮﷯﷯ is defined, iii not same... \| ≤ M \| x − c \| < ε 4 ).... Simply call it a continuous function its output =f ( a ).... Cost to move a freight container according to the schedule below you to take x = a if each the! Limits must be the same ; in other words, the denition continuity... Function as x approaches the value of the following facts: f ( x ) − f c... The question that arises is that i was solving this function, now question. Holes, jumps, or asymptotes is called continuous limit of the limit as x approaches the value must. To check for the continuity of a continuous function result in arbitrarily changes... If not continuous, their limits may be evaluated by substitution is continuous in interval! Without permission \| < δ \| f ( y ) \| < ε more precisely, small. Each of the three conditions below are met: ii in the piece. And the function is a continuous function result in a models that are functions... ) is continuous at all points in B c and the value c must be the how to prove a function is continuous continuous in interval... Then we simply call it a continuous function wide, and interesting variety. Example i.e = tan⁡ ﷐﷯ = ﷐﷐sin﷮﷯﷮﷐cos﷮﷯﷯ is defined, iii their limits may be evaluated by substitution, the... //Goo.Gl/Jq8Nyshow to prove a function is continuous at c iff for every ε 0... Every ε > 0, ∃ δ > 0, ∃ δ > 0 such.... In the input of a function is continuous at x = 4 ( a )$ is defined all! The denition of continuity is exible enough that there are a wide, and interesting variety. And if a function f is continuous in any interval, then we simply call a... Math ebooks are copyrighted by Pearson Education and x = c if L.H.L = how to prove a function is continuous f ( x ) f! If not continuous, a function is a function is continuous at two points be at... Their limits may be evaluated by substitution is called continuous ( y ) \| ≤ M \| x c... ) =f ( a ) \$ is defined for all real number except cos⁡ = 0 i.e 200 miles for... More precisely, sufficiently small changes in the problem below, we will need construct... That sine function is continuous at a point x = y^2 as one....	2021-05-15 15:25:29	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8461705446243286, "perplexity": 392.9491811432088}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243991370.50/warc/CC-MAIN-20210515131024-20210515161024-00153.warc.gz"}
https://www.physicsforums.com/threads/tone-hearing-frequency-concept-question.915386/	# Tone hearing frequency concept question 1. May 22, 2017 1. The problem statement, all variables and given/known data 2. Relevant equations Dont know any sorry 3. The attempt at a solution I tried imagining the ear as some sort of harmonic pipe with the sound coming inside as a sine wave. The question says the sine wave is not fully sinosoidal and is flattened at the top and bottom. I don't know where to go from there sorry - any help would be greatly appreciated 2. May 22, 2017 ### Staff: Mentor 3. May 22, 2017 Hello i dont fully understand what fourier is, I know its that one with the flat topped/diagonal waves which you can get by adding up sine waves. I dont see how this applies to the question - can you give me another hint? 4. May 22, 2017 ### Staff: Mentor The key in this question is to see which sine waves make up the square wave. As you add more and more of the correct frequency sine waves (with adjusted amplitudes), you can turn a 300Hz sine wave into a 300Hz square wave. You will learn more about this process in your classes, but for now, can you try a Google search on something like -- How to add up sine waves to make a square wave. Look at the frequencies of the lowest frequency used, and the relationship to the other sine waves of smaller amplitude that are added in. Can you then say which one of the answers above is correct? 5. May 22, 2017 Hi the answer was E - can you maybe give an explanation as to why, im really stuck 6. May 22, 2017 ### Staff: Mentor Did you do the Google search I suggested? It would show you why the answer is E... 7. May 23, 2017 ### Staff: Mentor Let me recopy the formula for a square wave from the link I gave: $$\frac{4}{\pi} \sum_{n=1,3,5,\ldots}^{\infty} \frac{1}{n} \sin \left( \frac{n \pi x}{L} \right)$$ Do you see the relationship between the frequencies of the different components? Another to see it is that flattening the sine wave doesn't change the period over which the signal repeats. What frequencies can be included such that this period doesn't change? 8. May 23, 2017 ### NTL2009 "E" doesn't appear to be correct to me, depending on how strictly you read the question. If a wave is flattened on both the top and bottom, by the same amount, you will have only odd harmonics. So 300 Hz + 900 Hz + 1500 Hz, etc. To get an even harmonic, I think that requires non-symmetry above/below the X axis. You would need a significant difference in the flattening top/bottom to make a 2nd harmonic audible. I might play with this in Audacity (open-source sound editing program), for real life results. (a few minutes later... Yep, it showed what I thought it would) Last edited: May 23, 2017 9. May 24, 2017 ### Staff: Mentor Nowhere did the problem state that the modification was symmetric. It simply said that the wave isn't sinusoidal anymore (even the flattening is a "perhaps.") 10. May 24, 2017 ### Staff: Mentor That's a fair point, but the other answers are clearly wrong, so only E is left as the "best" of the possible answers. 11. May 24, 2017 ### NTL2009 Absolutely agree with that, the other answers are way off. I guess I'm just saying the problem and answer could have been worded better. 12. May 24, 2017 ### Merlin3189 Perhaps the questioner was simply thinking that distortion produces harmonics and just offered some harmonics without worrying what sort of distortion was involved? 13. May 24, 2017 ### NTL2009 Yes, and maybe I'm making too big a deal about this (but it's not like I'm pounding my desk either! ). Let's just say they missed an opportunity, and they shouldn't be confusing students with what creates odd and what creates even harmonics. They sort of mish-mash the concepts here. But that got me thinking: From memory (and playing with music synthesizers), I recall that a square wave has odd harmonics with amplitude of f/h (where h = freq of harmonic, f = freq of fundamental), so third harmonic is 1/3rd amplitude, fifth harmonic is 1/5th etc. A triangle wave also has only odd harmonics, but the drop off is (f/h)^2. Third harmonic is 1/9th, fifth is 1/25th etc. That also makes sense when you consider a low-pass filtered square wave starts looking like a triangle wave. And a sawtooth wave has both even and odd harmonics, at f/h. But what I didn't recall is, what about only even harmonics? My analog music synths didn't have a waveform like that available. A little more playing in a graphing calculator and I get this, not sure how to describe it though? Do these regularly occur in nature, or maybe those combination of forces are not common? https://www.desmos.com/calculator/sanwjjkkqu 14. May 24, 2017 ### Merlin3189 looks like a sawtooth to me. If you alternate adding and subtracting harmonics and reduce them in amplitude by the square of their order, it gets much smoother -say sin(x)-sin(2x)/4+sin(4x)/16- sin(6x)/36 - etc.. 15. May 24, 2017 ### NTL2009 A sawtooth has even and odd harmonics. 16. May 24, 2017 ### Merlin3189 You're right, of course. I've actually been fooling myself trying to even out the bumps on nearly triangular waves. All the even harmonics of f are actually all the odd and even harmonics of 2f. So I was getting a perfect sawtooth by using all the even harmonics, then just removing the fundamental! Anyhow, thanks for the link to the desmos calculator: it's great for graphing these functions.	2018-01-19 09:50:54	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5703248381614685, "perplexity": 1193.7021179719995}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-05/segments/1516084887849.3/warc/CC-MAIN-20180119085553-20180119105553-00109.warc.gz"}
https://content.iospress.com/articles/journal-of-alzheimers-disease/jad180482	You are viewing a javascript disabled version of the site. Please enable Javascript for this site to function properly. Next Generation Sequencing Analysis in Early Onset Dementia Patients Background: Early onset dementias (EOD) are rare neurodegenerative dementias that present before 65 years. Genetic factors have a substantially higher pathogenetic contribution in EOD patients than in late onset dementia. Objective: To identify known and/or novel rare variants in major candidate genes associated to EOD by high-throughput sequencing. Common-risk variants of apolipoprotein E (APOE) and prion protein (PRNP) genes were also assessed. Methods: We studied 22 EOD patients recruited in Memory Clinics, in the context of studies investigating genetic forms of dementia. Two methodological approaches were applied for the target-Next Generation Sequencing (NGS) analysis of these patients. In addition, we performed progranulin plasma dosage, C9Orf72 hexanucleotide repeat expansion analysis, and APOE genotyping. Results: We detected three rare known pathogenic mutations in the GRN and PSEN2 genes and eleven unknown-impact mutations in the GRN, VCP, MAPT, FUS, TREM2, and NOTCH3 genes. Six patients were carriers of only common risk variants (APOE and PRNP), and one did not show any risk mutation/variant. Overall, 69% (n = 9) of our early onset Alzheimer’s disease (EAOD) patients, compared with 34% (n = 13) of sporadic late onset Alzheimer’s disease (LOAD) patients and 27% (n = 73) of non-affected controls (ADNI, whole genome data), were carriers of at least two rare/common risk variants in the analyzed candidate genes panel, excluding the full penetrant mutations. Conclusion: This study suggests that EOD patients without full penetrant mutations are characterized by higher probability to carry polygenic risk alleles that patients with LOAD forms. This finding is in line with recently reported evidence, thus suggesting that the genetic risk factors identified in LOAD might modulate the risk also in EOAD. INTRODUCTION The term early onset dementias (EOD) refers to a group of progressive neurodegenerative diseases, e.g., Alzheimer’s disease (AD), frontotemporal dementia (FTD), or dementia with Lewy bodies (LBD), affecting individuals aged between 45 and 65 years, and it represents roughly 5% of dementia cases [1]. The symptoms of EOD are similar to those of late onset AD (LOAD) and FTD. However, EOD is thought to be more severe and typically causes a rapid decline in health [2, 3]. Both AD and FTD are pathologically heterogeneous disorders, characterized by a complex genetic architecture that is not yet completely understood. The heritability rates of the different dementia subtypes range from 40 to 80% with EOD showing a higher genetic component than late-onset dementia (for review [4]). AD is clinically characterized by memory impairment and pathologically by the presence of amyloid-β (Aβ) peptide (the precursor of which is encoded by the APP gene) plaques and intraneuronal tangles of hyperphosphorylated forms of tau (a microtubule-associated protein encoded by the MAPT gene). The risk AD spectrum is composed of Mendelian genetic traits, genetic population risk factors (susceptibility genes), and nongenetic risk factors such as low cognitive reserve and head trauma [5, 6]. The apolipoprotein E gene (APOE) ɛ4 allele is a known population risk factor [7] that has been found to increase the risk of early onset AD (EOAD) [8]. Since its discovery, over 550 susceptibility genes have been suggested to increase the risk of AD [9], though the impact of most of these genes seems to be much lower than that of APOE [10, 11]. In particular, the common variants with small individual effects jointly modify the risk and age at onset of AD and dementia, showing a stronger effect in carriers homozygous for APOE ɛ4 [12]. Three genes have been identified to carry causative mutations for familial EOAD: amyloid precursor protein (APP), presenilin 1 (PSEN1), and presenilin 2 (PSEN2) (for review [11]). The estimated mutation frequencies of these three genes are 1% for APP, 6% for PSEN1, and 1% for PSEN2. Together, they explain a genetic background of only 5–10% of EOAD patients, leaving a large group of autosomal dominant pedigrees genetically unexplained (for review [13]). This finding suggests that additional causal genes remain to be identified. FTD is characterized by personality changes, language impairment, and deficits of executive functions associated with frontal and temporal lobe degeneration. At least nine autosomal dominant genetic traits have been associated with this pathology: mutations in MAPT, in the progranulin gene (GRN), and in the hexanucleotide repeat expansion C9orf72 genes are the most common, with the highest prevalence of GRN mutations found in populations of northern Italy [14–17]. GRN null mutations cause protein haploinsufficiency, leading to a significant decrease in the circulating progranulin levels in plasma, serum, and cerebrospinal fluid (CSF) of mutation carriers [18–20]. Mutations in valosin-containing protein (VCP), TAR DNA-binding protein 43 (TARDBP), charged multivesicular body protein 2B (CHMP2B), fused in sarcoma (FUS), dynactin (DCTN1), and triggering receptor expressed on myeloid cell (TREM2) are rarer causes of this pathology [4, 21]. Mutations in VCP [22], TARDBP [23], and TREM2 [24] have been observed in Italian families with a history of FTD. Interestingly, mutations in some of these genes, such as MAPT, GRN, and C9orf72 have also been detected at low frequencies in AD patients, supporting the notion that a genetic heterogeneity exists for these diseases and that both diseases could form an AD-FTD disease continuum (for review [13]). An AD-like phenotype has also been described with the presence of a nonsense mutation in the prion protein gene (PRNP p.Q160), which is responsible for inherited neurodegenerative spongiform encephalopathies [25]. In addition, the common coding polymorphism, methionine (M) to valine (V) at position 129 (M129V) in PRNP has been associated with EOAD, where the risk is higher for the VV genotype and is increased in patients with a positive family history [26]. The recent development of extremely powerful, massively, parallel DNA sequencing technologies allows for the systematic screening of individual genomes for DNA sequence variations at base-pair resolution, enabling researchers to address the missing hereditability question and, thus, to uncover novel and/or potentially pathogenic rare variants in candidate genes. As previously documented [27–29], targeted re-sequencing of a clinically significant gene panel may represent a powerful and cost-time-effective technique compared to the previously used sequential Sanger sequencing. Recently, Cruchaga et al. [30], confirmed that the genetic factors identified in LOAD modulate the risk also in EOAD cohorts, where the burden of these risk variants is associated with familial clustering and earlier onset of AD. In the present study, we estimated the genetic load in EOAD and LOAD, by identifying known and novel, both rare and common risk variants in candidate genes. We applied next generation sequencing (NGS) analysis in a selected retrospective cohort of Italian EOD patients and compared the frequencies of variants found with those estimated in samples from the Alzheimer’s Disease Neuroimaging Initiative (ADNI) database. MATERIALS AND METHODS Participants A retrospective sample of patients was recruited in the context of studies investigating genetic forms of dementia at IRCCS Istituto Centro San Giovanni di Dio Fatebenefratelli, Brescia Italy, Fondazione Case Serena, Pontoglio, Brescia, Italy, and Fondazione Europea Ricerca Biomedica, Centro di Eccellenza Alzheimer, Ospedale Briolini Gazzaniga, Bergamo, Italy. Specifically, twenty-two patients fulfilled the following inclusion criteria for the present study: 1) phenotype of AD, FTD, or LBD and 2) early disease onset (<65 years old), or 3) family history suggestive of an autosomal dominant genetic form of dementia (i.e., high or medium risk of identifying a mutation according to Loy and Woods criteria [31, 32], as described below). Family history was collected through interviews with a first-degree relative or the spouse of the proband. The clinical and medical history of each family member was collected, and all of the available documentation for affected members was acquired. The probability of identifying a genetic mutation for AD or FTD was estimated considering the family medical history, the number of first and second-degree affected family members, and the age of symptom onset, according to the criteria developed by Loy and colleagues [31]. According to Loy et al.’s criteria for AD, we defined a probability of identifying a genetic mutation of ≥86% as a high risk, a probability of 68–85% as a medium risk, a probability of 15–67% as a low risk, and a probability <15% as apparently sporadic/unknown significance. Considering the same criteria for FTD patients, we considered an ≥88% probability of identifying a genetic mutation as a high risk, a 31–41% probability as a medium risk, and a probability <13% as a low risk. FTD pedigrees were also scored according to Wood’s pedigrees classifications criteria [32, 33]. All participants were of Italian ancestry. Demographic features and clinical data (age at onset, MMSE) are reported in Table 1. As the sample was retrospectively pooled for the analysis, a standard protocol for biomarker characterization was not applied. Sixteen patients underwent one of the following examinations as part of their diagnostic exam: magnetic resonance imaging (MRI), positron emission tomography (FDG-PET) or single photon emission computed tomography (SPECT), and/or lumbar puncture. MRI and PET/SPECT scans were visually evaluated to determine medial-temporal atrophy and hypometabolism, respectively. CSF samples were processed with local procedures to determine the level of Aβ, tau, and p-tau. Positive diagnosis was determined based on established cut-offs. Table 1 Demographic, clinical features, and presence of rare/common risk variants in candidate genes in early onset dementia APOE, Apolipoprotein E (E4 risk allele); PRNP, Prion protein (G/val risk allele); PGRN/GRN, Progranulin; PSEN2, Presenilin 2; TREM2, Triggering receptor expressed on myeloid cell; FUS, Fused in sarcoma; MAPT, Microtubule-associated protein tau; VCP, Valosin-containing protein; A, known damaging; B, benign; D, damaging; N, neutral; P, possibly damaging; T, tolerant; n.a., not available; CADD, CADD phred-scaled (a score of 20 means 1% percentile highest scores of whole genome); dbSNP, single nucleotide polymorphism database (rs number); GERP, genomic evolutionary rate profiling score; GERP++, evolution score; MT, mutation taster; Phylop, phyloP100way vertebrate; PP2, PolyPhen2; SIFT, Sorting Intolerant from Tolerant; FATHMM, Functional Analysis through Hidden Markov Models (v2.3); LRT, Likelihood Ratio Test; AD, Alzheimer’s disease; FTD, frontotemporal dementia; LBD, Lewy body dementia; FTD-IBMPFD, Inclusion Body Myopathy-Paget’s disease of bone; “Genetic risk” denotes the estimated probability of identifying a genetic mutation base on Loy and Wood criteria for AD and FTD; “Unknown Significance” denotes lack of information about diagnosis or clinical details; “Apparently sporadic” indicates no other affected case in the family; H-M, Hypo metabolism. Blood samples were collected from all patients. DNA and plasma were obtained according to standard procedures. Patients provided written informed consent. This study was approved by the local ethics committee (CEIOC, 62/2013). NGS panel analysis screening Genomic DNA was extracted from whole-blood samples with a commercially available kit according to standard procedures (GENTRA Minneapolis, MN, USA). Due to logistics issues, some samples were analyzed through the use of the Ion Torrent PGM (Thermo Fisher Scientific, Waltham, MA USA) sequencer as NGS platform, by using a candidates genes panel, already described in Beck et al. [27]. Briefly, for library construction, 5 ng of genomic DNA were amplified using the Ion Ampliseq Dementia Research gene panel (Ampliseq™, Thermo Fisher Scientific, Waltham, MA USA), and the Ion Ampliseq™ Library kit 2.0, according to manufacturer’s instructions. The generated amplicon library includes PRNP, PSEN1, PSEN2, APP (Amyloid Beta A4 Precursor Protein), GRN, MAPT, TREM2, CHMP2B, CSF1R (Colony Stimulating Factor 1 Receptor), FUS, ITM2B (Integral Membrane Protein 2B), NOTCH3 (Notch 3), SERPINI1 (Serpin Peptidase Inhibitor, Clade I (Neuroserpin), Member 1), TARDBP, TYROBP (TYRO Protein Tyrosine Kinase Binding Protein), VCP, SQSTM1 (Sequestosome 1). Amplicons were ligated to Ion Torrent Barcodes/adapters P1 using DNA ligase. A first step of Agencourt AMPure XP bead (Beckman Coulter Inc., Brea CA, USA) purification was followed by nick-translation of adapter-ligated products and PCR-amplification. A second purification step using AMPure beads was performed and the concentration and size of the libraries were determined using an Agilent BioAnalyzer DNA High-sensitivity LabChip (Agilent Technologies, Santa Clara, CA USA). After dilution to 100 pM, libraries were clonally amplified on Ion sphere™ particles (ISP) by emulsion PCR with the Ion PGM™ template OT2 200 kit on the Ion One Touch 2 instrument according to the manufacturer’s instructions (Thermo Fisher Scientific, Waltham, MA USA). ISP were enriched using the Ion One Touch ES module, loaded on an Ion 314 chip kit V2 and sequenced with an Ion Torrent PGM System (Thermo Fisher Scientific, Waltham, MA USA). The remaining samples were analysed with the Illumina MiSeq platform and the TruSight One Sequencing Panel (Illumina, Inc., San Diego, CA, USA). This panel includes 125,395 probes targeting a 12-Mb region spanning 4,813 genes, among which the genes investigated by Ion Torrent PGM (PRNP, PSEN1, PSEN2, APP, GRN, MAPT, TREM2, CHMP2B, CSF1R, FUS, ITM2B, NOTCH3, SERPINI1, TARDBP, TYROBP, VCP, SQSTM1). The data regarding the other all genes were not used. The obtained sequence reads were aligned to the hg19 human reference sequence using the Burrow–Wheeler Aligner (BWA version 0.7.12). Duplicated reads were removed with Picard tools. Local realignment, recalibration, and variant calling were conducted with the Genome Analysis Tool Kit (GATK version 3.30). In order to have comparable results between the two sequencing approaches, we extracted from TruSight One Variant Call Format file (i.e., VCF file), the variants located in the regions sequenced by Ion Torrent PGM panel using BEDTools [34]. APOE genotyping Genetic variation at the APOE locus was determined by using the SNaPshot technique [35]. Briefly, assays for the APOE polymorphisms were performed using PCR reactions, which were subsequently combined to perform a single SNaPshot reaction. The amplification assay was designed with the following forward and reverse primers: APOE F: 5’ CCAAGGAGCTGCAGGCGGCGCA 3’ and APOE R: 5’ GCCCCGGCCTGGTACACTGCCA 3’. A product of PCR-amplification was used as a template in the SNaPshot Multiplex assay. The following specific primers were used: SNAP APOE112:5’ ACTGCACCAGGCGGCCGC 3’ and SNAP APOE158:5’ATGCCGATGACCTGCAGAAG 3’. Finally, the samples were analyzed, and allele peaks were determined using the ABI 3130xl genetic analyzer and the GeneMapper 4.0 program (Applied Biosystems, Foster City, CA, USA). C9Orf72 hexanucleotide repeat expansion PCR sizing of the GGGGCC hexanucleotide repeat was performed using previously published primers [36] on the ABI 3130xl genetic analyzer (Applied Biosystems, Foster City, CA, USA). The PCR reaction was carried out in a mixture containing 5% dimethylsulfoxide and 7-deaza-2-deoxy GTP in substitution for dGTP. Allele identification and scoring were performed using GeneMapper v4.0 software (Applied Biosystems). GRN plasma level measurement Plasma progranulin levels were measured in duplicate using an ELISA kit (Human Progranulin ELISA Kit, AdipoGen Inc., Seoul, Korea). Statistical and bioinformatics analyses To classify a variant as rare, its frequency should be lower than 1% in at least one of the three reference databases (1000 Genomes Project http://www.internationalgenome.org/, Exome Sequencing Project http://evs.gs.washington.edu/EVS/ and Exome Aggregation Consortium http://exac.broadinstitute.org) [37]. In order to predict the functional consequences of non-synonymous variations, we exploited eight different bioinformatics tools, namely: SIFT, PolyPhen-2, FATHMM, phyloP, MutationTaster, LRT, and CADD and GERP++ [38–45]. A variant is classified as damaging if for at least three tools the mutation is predicted to be deleterious. Finally, to evaluate the mutation rate of the candidate genes selected in the NGS panel, we considered the gene damage index (GDI, a genome-wide, gene-level metric of the mutational damage that has accumulated in the general population), according to Itan et al. [46]. As a genetic replication cohort, we considered whole genome data from the ADNI database (http://adni.loni.usc.edu). From the whole genome data, we extracted the variants within the regions included in our sequencing panel and we applied the same variants annotation and classification performed for our sample. The ADNI was launched in 2003 as a public-private partnership, led by Principal Investigator Michael W. Weiner, MD. The aim of ADNI project is to collect, validate and utilize heterogeneous clinical and biological data (including MRI and PET images, genetics, cognitive tests, CSF and blood biomarkers) to study the progression of AD. For up-to-date information, see http://www.adni-info.org. RESULTS Target screening: Plasma progranulin and C9ORF72 analyses As a first step, progranulin plasma levels were assayed to screen for GRN null mutations (Table 1). One FTD patient was found to have progranulin plasma levels lower than the optimized cut-off value for null mutations detection of 61.55 ng/ml [19, 47]. For 5 samples, it was no possible to detect the progranulin levels, due to the lack of plasma samples from these patients. None of the EOD patients carried the pathogenic hexanucleotide repeat expansion of C9ORF72. All patients were found to have less than 12 repeats [48]. NGS screening: Identification of known and unknown rare variants Through the target re-sequencing of the 17 candidate genes panel, we identified fourteen rare variants in 68% of the selected EOD cases (15 patients) (Table 1). These variants were defined as “pathogenic” when previously described in the literature, and they were classified as “damaging” by bioinformatic tools or as “unknown impact” when no data were available in literature and no deleterious effect was predicted by bioinformatics tools. Pathogenic variants Among the 14 identified rare variants, three were classified as pathogenic and damaging and have been described in Italian pedigrees unrelated to the patients analyzed in the present study. Two variants were located in the PSEN2 gene (p.M239V = rs28936379 code case: 26_1, [49]; p.M239I = rs63749884 code cases: 30_1, L031, [50]); and one variant was a p.L271fs null mutation in the GRN gene (code cases: 29_1; L029) (Table 1). Finally, a heterozygous R93C mutation of the VCP gene was detected in a patient (Table 1, code: 36_1) affected by Paget’s disease of bone diagnosed at 44 of age and no signs of dementia at the last examination (47 years). Family history showed multiple individuals with FTD and Paget’s disease with autosomal dominant inheritance. Variants of unknown impact Two variants in the TREM2 gene (R62H = rs143332484, D87N = rs142232675, [51]) (Table 1) were observed in three of the 22 patients (14%), including a patient with LBD. Moreover, in GRN gene, we found variants in the 5’UTR (rs76783532) and two rare missense variants (V77I = rs148531161; R19W = rs63750723; Table 1), which have been reported as “pathogenic nature unclear” and “not pathogenic”, respectively, in online database (www.molgen.en.ua.ac.be/FTDmutations). Accordingly, these missense mutations did not influence the progranulin level in plasma (Table 1). Other variants reported in online databases were those at 3’UTR of the FUS (rs80301724) and a missense mutation (V1183M = rs10408676) in NOTCH3 gene resulting “damaging” according to bioinformatics tools. Moreover, we detected rare mutations which have not been reported in the literature and databases. In particular, we found a mutation localized in the 5UTR region and a missense mutation R93C (NM_007126: exon3: c.C277T:p.R93C) in the VCP gene, a deletion (NM_001203251:c.55delA) in MAPT gene at 3’UTR region, a splicing variant (NM_000435: exon24: c.3838-1G>T) in NOTCH3 gene. Screening of known common variants All EOD patients were genotyped for the rs429358 and rs7412 polymorphisms in the APOE gene and the rs1799990 polymorphism in the PRNP gene. APOE ɛ4 and PRNP 129Val are known to be risk alleles. The results indicated that the frequencies of the APOE ɛ4 carriers and the PRNP 129Val carriers were 59% for both. Twenty (91%) of the 22 subjects carried at least one of the two risk variants; of these subjects, 27% (six out of 22) carried both the APOE ɛ4 and the PRNP 129Val risk alleles. Six patients were carriers of at least one risk allele (APOE ɛ4 or PRNP 129Val) (Table 1). One patient did not show any rare or common risk variants (Table 1). Comparison to whole genome data Table 2 Comparison of frequencies of rare (excluding the full penetrant) and common risk variants in our sample (This study) versus controls, late onset and early onset AD patients (LOAD and EOAD, respectively) obtained from ADNI database Variants n = 0 n = 1 n≥2 total Only Only total Only Only 1 rare 1 rare 2 rare 2 rare 3 rare Total rare common rare common + + + + + 1 common 2 common 1 common 2 common 1 common Groups Sample (N) N (%) N (%) N (%) N (%) N (%) N (%) N (%) N (%) N (%) N (%) N (%) N (%) Controls (272) 67 (25) 9 (7) 123 (93) 132 (49) 2 (3) 28 (38) 25 (34) 8 (11) 8 (11) 0 (0) 2 (3) 73 (27)$£ ADNI LOAD (38) 3 (8) 0 (0) 22 (100) 22 (58) 0 (0) 10 (77) 2 (15) 0 (0) 1 (8) 0 (0) 0 (0) 13 (34)$£ EOAD (7) 1 (14) 0 (0) 2 (0) 2 (29) 0 (0) 3 (75) 1 (25) 0 (0) 0 (0) 0 (0) 0 (0) 4 (57) This study AD (13) 1 (8) 0 (0) 3 (100) 3 (23) 0 (0) 2 (22) 4 (44) 2 (22) 0 (0) 1 (11) 0 (0) 9 (69)$ADNI + This study EOAD + AD (20) 2 (10) 0 (0) 5 (100) 5 (25) 0 (0) 5 (38) 5 (38) 2 (15) 0 (0) 1 (8) 0 (0) 13 (65)£$Chi-squared test: Controls versus LOAD-ADNI versus AD-our study, χ2 = 15.8, df = 4, p = 0.003. £Chi-squared test: Controls versus LOAD-ADNI versus EOAD-ADNI+AD-our study, χ2 = 17.9, df = 4, p = 0.001. DISCUSSION This study suggests that EOD patients without full penetrant mutations are characterized by higher probability to carry polygenic risk alleles that patients with LOAD forms. This finding is in line with recently reported evidence [30], thus suggesting that the genetic risk factors identified in LOAD might modulate the risk also in EOAD. Moreover, we confirmed the role of GRN and PSEN2 genes in EOD, with the involvement of specific rare mutations already known. We also detected additional rare variants of unknown impact, located in the 5’/3’ UTRs regulatory gene region of the GRN, VCP, MAPT, and FUS genes, missense mutations in TREM2, GRN, NOTCH3, and VCP, genes and a splicing variant in NOTCH3 gene. According to the gene damage index (GDI) [46], mutations in these genes showed a value of “medium”, suggesting that these genes are not frequently mutated in healthy populations. This finding further implies that mutations in these genes could be disease-causing. Rare mutations of known significance Twenty three percent of the cases carried one pathogenic mutation for dementia. In line with previous studies [14], mutations in the PSEN2 gene, a rare cause of dementia worldwide, were frequent in our cohort (14%). Looking at the geographical distribution of PSEN2 mutations described to date, it is noteworthy that 80% of these mutations were uncovered in two southern European countries, Italy and Spain. Thus, we can speculate that the non-homogeneous distribution of pathogenic mutations might be a result of genetic drift. The GRN p.L271fs mutation is one of the most common GRN mutations worldwide. An analysis of this mutation in northern Italy showed that almost all families can be traced to a single founder. The origin of the mutation was dated to the Middle Ages at the turn of the first millennium, which explains the high frequency of this mutation in this geographic area [52]. Rare mutations of unknown significance The role for novel variants of unknown significance in both common and rare dementia-associated genes was not exhaustively elucidated. Recently, novel, likely pathogenic variants were described in Italian patients with dementia [53]. We found two AD patients carrying the R62H mutation in the TREM2 gene, which has an unknown impact. A recent review on the correlation between TREM2 and AD [54], showed a meta-analytic association of this mutation with the late onset form of the disease. Our results also showed its involvement in the early onset form of AD. Since the two patients were also homozygous for the APOE ɛ4 allele, this finding suggests interactions between TREM2 and APOE, as already demonstrated in vitro. TREM2 is a lipid sensor that interacts with several AD risk factors involved in lipid metabolism, including APOE, which could decrease the threshold of disease occurrence [57]. In the specific case of two AD patients carrying the GRN p.V77I and R19W mutations, there is evidence of AD pathology in imaging and from biofluid biomarkers (Table 1). Since these missense mutations do not affect the progranulin levels, a pathogenic role of these mutations seems unlikely. However, we cannot exclude that they might have a pathogenic role other than “loss of function”, as no functional studies have been performed. Their presence in AD patients might rather indicate that this gene could be implicated also in the pathophysiological mechanisms leading to AD dementia. Inclusion body myopathy with Paget’s disease of bone and/or FTD (IBMPFD) is a recently identified autosomal dominant disorder due to mutations in the VCP gene affecting muscle, bone, and brain. Interestingly, in our cohort we found the R93C (47832C>T) mutation in the VCP gene already described in patients with IBMPFD [62–65]. Common variants In this study, we investigated the most established common risk variant for AD, the APOE ɛ4 haplotype. The functional role of this polymorphism in AD pathogenesis is unclear. However, there is now strong evidence that APOE ɛ4 could affect amyloid deposition [66]. Consistent with this evidence, in our cohort all APOE4 carriers with available CSF were amyloid positive (Table 1), except for the case code 19_1 of which we discuss separately (see below). The frequency of the ɛ4/ɛ4 genotype (n = 4, 17%, exact confidence interval 3–32%) was higher than that commonly observed in the Caucasian population (1000 genomes), which is reported to be 2%. Moreover, we investigated the non-synonymous polymorphism p.Met129Val in the PRNP gene. Although there are no data on the functional effect of this polymorphism, we observed that the frequency of the risk variant allele G/Val was higher (59%) than the frequency reported in the general European population (frequency G/Val = 33% reported by the Exome Aggregation Consortium). A recent meta-analysis showed that the p.Met129Val allele was associated with decreased disease risk in late-onset AD, but not in EOAD [67]. Six patients from the present cohort carry only common risk variants. They could be sporadic cases with onset at the extreme end of expected age range. However, the hypothesis that EOD is caused by mutations in genes not included in the NGS panel cannot be ruled out. In this regard, whole genome sequencing could foster the investigation of additional genetic factors underlying apparently sporadic EOD. Nonetheless, this task was beyond the scope of the present work. Interestingly, fifteen (68%) of the 22 patients carried at least one rare variant (TREM2, GRN, PSEN2, MAPT, VCP, NOTCH3, or FUS). Among these, fourteen subjects carried also a common variant (APOE and/or PRNP). This result supports the hypothesis that EOD results from the interconnected mechanisms leading to neurodegeneration, where multiple genes can be implicated in one or more systems. Indeed, recent biochemical approaches [55, 56] have shown interactions among these genes, such as between TREM2 and APOE in vitro. These results strongly implicate a potential additive/synergic effect in EOD forms linked to the variable inter- and intra-familiar expressivity. To indirectly assess this effect, we found through the ADNI database that, excluding the full penetrant mutations, 69% of our sample showed ≥2 rare/common risk variants, as compared to 34% and 27% in sporadic late-onset AD patients and controls, respectively. This indicates that the EOD is more often associated with rare variants or risk alleles, and this could be useful in the genotype-phenotype correlations. Moreover, <10% of subjects, in our cohort, and in late onset AD patients, compared to 25% in a control group, were not carriers of any of the examined variants, which strengthens the idea of using an NGS whole/exome genome approach in a larger sample. One AD patient with a very early age of onset (41 years) showed neither rare nor common-risk variants. Even an exome clinic investigation detected no rare or common risk variants. The family history was negative, as no other first-degree relatives were affected (neither the parents nor three siblings, two of whom were older than the patient, presented with the disease). Misdiagnosis is unlikely since this patient was positive for all AD biomarkers (abnormal CSF amyloid and tau levels, hypometabolism on FDG-PET, and medial temporal atrophy on MRI). Although we considered the possibility that the patient may show an extreme early-onset presentation of sporadic AD, this finding suggests that additional genes could be implicated in EOD, which strengthens the evidence that the panel of candidate genes needs to be expanded in the future. For the first time, the D87N mutation in the TREM2 gene was detected in a LBD patient with early onset. LBD is the second most common form of dementia after AD, with a prevalence rate of 4% in the general population [68]. The core symptoms of LBD include sleep disturbances, hallucinations, and cognitive deficits, accompanied within the first year by Parkinsonian motor symptoms. A recent twin study did not show a strong support for a genetic contribution to LBD. However, other studies have demonstrated that LBD aggregates in families and may have an autosomal inheritance pattern (for review [4]). To date, a few genetic markers have been identified. For instance, duplication and SNPs within α, β, γ−synuclein genes have been associated with increased risk of LBD [69, 70]. Moreover, mutations in the glucocerebrosidase (GBA) gene are more common in LBD, in addition to mutations in the MAPT or leucine rich repeat kinase 2 (LRRK2) genes (for review [4]). Only one genome-wide linkage study has been performed among patients with familial LBD. A locus on chromosome 2q35-q36 was identified, though none of the genes in this region could explain the relation with LBD [71]. Although further confirmation is needed, the presence of a TREM2 mutation in an LBD patient adds a new actor to its genetic architecture. Mutations in TREM2, a microglial receptor, can lead to aberrant innate immune cell signaling, contributing to the initiation and propagation of several neurodegenerative phenotypes [72–83], including LBD. Moreover, this LBD patient was a carrier of the GG (Val/Val) PRNP risk genotype. This finding is in agreement with a previous study [84] that described a patient carrying the M232R mutation in the PRNP gene who developed dementia and died six years after onset. An autopsy revealed the patient had dementia with Lewy bodies, not Creutzfeldt-Jakob disease. Conclusions This study confirms the role of GRN and PSEN2 mutations in EOD, in the Italian population and provides evidence for roles of novel rare mutations located in the 5’/3’ UTRs regulatory gene region of the GRN, VCP, MAPT, and FUS genes, missense mutations in TREM2, GRN, NOTCH3, and VCP, genes and a splicing variant in NOTCH3 gene, with a “medium” GDI value. As previously observed, mutations in the PSEN2 gene, a rare cause of dementia worldwide, are frequent in Italian patients. We also confirmed that mutations in GRN gene were present in both FTD and AD phenotypes. Moreover, six patients were carriers of only common risk variants (APOE and PRNP), and one patient did not show any mutation/variant. Overall, 69% (n = 9) of our EAOD patients, compared with 34% (n = 13) of sporadic LOAD patients and 27% (n = 73) of non-affected controls, were carriers of at least two rare/common risk variants in the analyzed candidates’ genes panel. Though our findings are consistent with results obtained from large cohorts [12], independent replications in larger samples are warranted. To further validate the role of polygenic risk variants in EOD, a systematic screening of rare and common variants in dementia-associated genes should be implemented in prospective cohorts with full clinical and biomarker characterization. ACKNOWLEDGMENTS This work was supported by the Italian Ministry of Health, Ricerca Corrente, RF-2010-2319722. We also acknowledge the University of Genova for partial support (Fondi ricerca Ateneo 2015 to EDM) and Dr. Irene Maria Briata for technical assistance. ADNI data collection and sharing was funded by the Alzheimer’s Disease Neuroimaging Initiative (National Institutes of Health Grant U01 AG024904) and DOD ADNI (Department of Defense award number W81XWH-12-2-0012). ADNI is funded by the National Institute on Aging, the National Institute of Biomedical Imaging and Bioengineering, and through generous contributions from the following: AbbVie, Alzheimer’s Association; Alzheimer’s Drug Discovery Foundation; Araclon Biotech; BioClinica, Inc.; Biogen; Bristol-Myers Squibb Company; CereSpir, Inc.; Cogstate; Eisai Inc.; Elan Pharmaceuticals, Inc.; Eli Lilly and Company; EuroImmun; F. Hoffmann-La Roche Ltd and its affiliated company Genentech, Inc.; Fujirebio; GE Healthcare; IXICO Ltd.; Janssen Alzheimer Immunotherapy Research & Development, LLC.; Johnson & Johnson Pharmaceutical Research & Development LLC.; Lumosity; Lundbeck; Merck & Co., Inc.; Meso Scale Diagnostics, LLC.; NeuroRx Research; Neurotrack Technologies; Novartis Pharmaceuticals Corporation; Pfizer Inc.; Piramal Imaging; Servier; Takeda Pharmaceutical Company; and Transition Therapeutics. The Canadian Institutes of Health Research is providing funds to support ADNI clinical sites in Canada. Private sector contributions are facilitated by the Foundation for the National Institutes of Health (http://www.fnih.org). The grantee organization is the Northern California Institute for Research and Education, and the study is coordinated by the Alzheimer’s Therapeutic Research Institute at the University of Southern California. ADNI data are disseminated by the Laboratory for Neuro Imaging at the University of Southern California. Authors’ disclosures available online (https://www.j-alz.com/manuscript-disclosures/18-0482r1).	2019-03-23 06:22:21	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.401790052652359, "perplexity": 11821.982096907299}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-13/segments/1552912202728.21/warc/CC-MAIN-20190323060839-20190323082839-00071.warc.gz"}
https://www.physicsoverflow.org/10326/urgent-bug-with-vote-to-close-vote-to-reopen-buttons	# (Urgent) Bug with vote to close, vote to reopen buttons + 1 like - 0 dislike 4557 views I have noticed a bug with the vote to close/reopen buttons. If I click "vote to close" here, for example, /3649, then instead of being sent to /4533, I am sent to /3649/index.php?qa=4533&qa_1=requests-for-close-votes-close-review-queue. This could be due to the change in URL structure which happened a while ago. Can the plug-in be updated to work with this new URL structure? Maybe if nothing is possible, the links could just be made absolute. asked Mar 30, 2014 in Bug retagged Mar 30, 2014 Corrected. I hope that we have not too much of these old URL structure links. By the way: The icons beside these links have disappeared. Was this your intention? I did not change anything there. @polarkernel Thanks. Yes, I have removed the icons beside the links, as I remember someone once commented that they were too "social media-like", and I agree with that. Without the icons, it also looks more like SE. Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead. To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL. Please consult the FAQ for as to how to format your post. This is the answer box; if you want to write a comment instead, please use the 'add comment' button. Live preview (may slow down editor) Preview Your name to display (optional): Email me at this address if my answer is selected or commented on: Privacy: Your email address will only be used for sending these notifications. Anti-spam verification: If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:p$\hbar\varnothing$sicsOverflowThen drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds). To avoid this verification in future, please log in or register.	2020-07-10 05:24:04	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4256848096847534, "perplexity": 2204.3783286913335}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655906214.53/warc/CC-MAIN-20200710050953-20200710080953-00124.warc.gz"}
http://onelearningsolution.blogspot.com/2015/02/451-laboratory-activity-heat-of.html	Thursday, 26 February 2015 4.5.1 - Laboratory Activity : Heat of Combustion of Different Alcohol Laboratory Activity 4.5.1: Heat of Combustion of Different Alcohol Aim: To compare the heat of combustion of different alcohol. Problem statement:Do all alcohol have the same heat of combustion? Hypothesis: Different alcohol have different heat of combustion Variable: » Fixed variable : Water volume, thin copper container and lamp. » Manipulated variable : Types of alcohol » Responding variable : Heat of combustion Material: » Methanol » Ethanol » Propan-1-ol » Distilled water Apparatus: » Lamp » Thermometer » Measuring cylinder » Tripod stand » Wind screen » Thin copper container Procedure: 1 100cm3 of water is measured with a measuring cylinder and poured into a thin copper container which is placed on top of a tripod stand. A wind screen is placed surrounding the tripod stand. 2 Record the initial temperature using thermometer. 3 A methanol lamp is weighed and placed under the metal container and lighted. 4 Stirred the water in the metal container with a thermometer. 5 When temperature of the water increases by 30°C, the flame is distinguish and the highest temperature are recorded. 6 The lamp is then weight again. 7 The experiment is repeated using other types of alcohol. Data: Alcohol Methanol Ethanol Propan-1-ol Initial mass of lamp (g) M1 M4 M7 Final mass of lamp (g) M2 M5 M8 Mass of alcohol used (g) M3 M6 M9 Final temperature (°C) T1 T3 T5 Initial temperature (°C) T2 T4 T6 Change temperature (°C) θ1 θ2 θ3 Calculation: ► Heat of combustion for methanol Volume of water used = 100cm3 . Therefore the mass of water used = 100g Heat change in water = mc∆θ = (250 X 4.2 X θ1) joules = H joules Molar mass of methanol CH3OH = 32 + 3 + 16 + 1 = 32g Mass of methanol burnt = M Number of moles of methanol burnt = $\frac{\text{M}}{32}$ = x moles Therefore the burning of x moles of methanol will liberate H joules of heat. Therefore the burning of 1 mole of methanol will liberate $\frac{\text{H}}{\text{x}}{\text{J mol}}^{\mathrm{-}1}\mathrm{=}\text{Heat of combustion}$ ► Heat of combustion for ethanol and propan-1-ol The same calculation method can be used to determine the heat of combustion for ethanol and propan-1. Analysis: All alcohol contains carbon, hydrogen and oxygen. Burning of alcohol is an exothermic reaction, heat of combustion will have negative values. The amount of heat given out will depends on the number of carbon atoms and hydrogen atoms they contain, the mass of alcohol in their molecules. The heat liberated will increase if the number of carbon atoms, hydrogen atoms and the mass of alcohol increased as shown in the following table Alcohol Heat of combustion (kJ mol-1) Methanol -725 Ethanol -1376 Propanol -2015 The experiment value will always be less than the theoretical value, due to the radiation heat lost to the surroundings, and energy used to heat up the apparatus(copper container and thermometer). The energy level diagram for the combustion of alcohols are shown in the following diagram. Discussion: Precautions ○ Wind shield is used to protect the flame from the disturbance of wind. ○ The flame of alcohol is placed close to the metal container without using a wire gauze . ○ The copper container should be as thin as possible to ensure the heat from the alcohol flame is easily transferred to the water in the container. ○ The alcohols used are volatile liquids as they can easily catch fire. Make sure the caps of the lamps are screwed tightly to prevent any alcohol vapour escaping from the bottles. ○ Use only thermometer to stir and not any other stirrer apparatus. ○ The weighing should be done as fast as possible to prevent lost of volatile alcohol by evaporation. Conclusion: ► Different alcohols have different heat of combustion.	2018-05-24 15:15:31	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 2, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2677600383758545, "perplexity": 2263.4288423613893}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794866511.32/warc/CC-MAIN-20180524151157-20180524171157-00476.warc.gz"}
http://mathhelpforum.com/differential-equations/272125-fluid-mechanics-atmosphere-meteor-help-convert-du-dt-into-dy-dz.html	# Thread: Fluid Mechanics + Atmosphere + Meteor. Help convert du/dt into dy/dz 1. ## Fluid Mechanics + Atmosphere + Meteor. Help convert du/dt into dy/dz Here is the context of the problem: Calculate the size of the iron meteor that would have its initial velocity reduced by only 10% by drag in Earth’s atmosphere. I was able to prove the first part: Write down a differential equation for the deceleration of the meteor du/dt. du/dt=3Cd/(4Rmpm)u2 p0*exp(−z/h) However have no idea about the next: You should find an equation of the form du/dt = . . ., where the stuff on the RHS depends only on the density of air (which depends on height in the atmosphere z), the internal density of the meteor, the radius of the meteor, the meteor’s velocity, and dimensionless constants. You can assume (check, if you like) that the extra acceleration provided by gravity over this distance is negligible, since the meteor’s velocity is already terrifyingly large. Convert your equation to a linear, first-order differential equation. That is, you should have an equation which reads something like dy/dz = f (z)y, where f (z) is some function of z. (Hint: begin by noting that dt = dz/v, and substitute y = v2.) Solve this equation, imposing boundary conditions as appropriate. (You will probably end up using an integrating factor.) Hence, calculate the critical radius and mass of the meteorite such that the velocity at z = 0 is 0.9 times the initial velocity. 2. ## Re: Fluid Mechanics + Atmosphere + Meteor. Help convert du/dt into dy/dz Not sure what hep you need here. Your equation looks fine. You have a DE in this form, and combining a bunch of constants into a single constant $K = \frac {3 C_D}{4 \rho_m}$ : $\frac {du}{dt} = \frac K R u^2 e ^{-z/h}$ Now substitute y = u^2, and dy = 2u du; the left hand side becomes: $\frac {dy}{2u dt}$ Since u = dz/dt, this is further simplified: $\frac {dy \ dt}{2dz\ dt} = \frac 1 2 \frac {dy}{dz}$ So now you have your DE: $\frac {dy}{dz} = \frac {2K}{R} y e^{-z/h}$ Can you take it from here? 3. ## Re: Fluid Mechanics + Atmosphere + Meteor. Help convert du/dt into dy/dz Thanks for your help but do you mind integrating that for me. It's been ages since I last had to do this and I've completed forgotten how to solve this type of integral. Would be a great help for my exam. Cheers 4. ## Re: Fluid Mechanics + Atmosphere + Meteor. Help convert du/dt into dy/dz I'll get you started on the integral: rearrange the equation I gacve you to get: $\frac {dy}y = \frac {2K} R e^ {-z/h} dz$ and integrate: $\int \frac {dy}y = \frac {2K} R \int e^ {-z/h} dz$ Do you recognize the integral on the left? It has to do with the natural logarithm. And on the right recall that $\int e^{ax} dx = \frac 1 a e^{ax}$. Don't forget you will need to include a consant of integration. Show us your attempt from here and we'll help if you get stuck. 5. ## Re: Fluid Mechanics + Atmosphere + Meteor. Help convert du/dt into dy/dz then Is this right or have I made a mistake? (K=2K^) What boundary conditions could I use to remove the constant? 6. ## Re: Fluid Mechanics + Atmosphere + Meteor. Help convert du/dt into dy/dz Looks fine, though I would have written it as $v^2 = Ce^{\frac {-hK}{R_m}(e^{-z/h})}$ You can determine C if you know a boundary condition, such as initial velocity at a certain height z. Did they define the value 'h' for you? You could set the boundary condition of v_0 = 10000m/s at z = h = 100,000 m, and then determine the value for C. Also please note that the value for the constant K that I used should have included the $\rho_0$ term: $K = \frac {3 C_d \rho_0}{4 \rho_m}$ 7. ## Re: Fluid Mechanics + Atmosphere + Meteor. Help convert du/dt into dy/dz Yes they defined z=h=80,000m and v_0=30,000m/s. This gets me a value of C in terms of Rm, however when I try and solve for Rm I'm unable to separate it out. Thanks again for helping me out. 8. ## Re: Fluid Mechanics + Atmosphere + Meteor. Help convert du/dt into dy/dz Try taking the ratio of V_final over V_initial = 0.9: $\frac {V_f}{V_i} = 0.9 = \frac {e^{[ \frac {-K 80000}{R} e^{-1}]}}{e^0}$ Now you can solve for R. 9. ## Re: Fluid Mechanics + Atmosphere + Meteor. Help convert du/dt into dy/dz Got it now thank you!!	2017-07-27 23:11:00	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 12, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7892187833786011, "perplexity": 1817.9119398715388}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-30/segments/1500549429548.55/warc/CC-MAIN-20170727222533-20170728002533-00105.warc.gz"}
http://mathhelpforum.com/calculus/28558-convergence-divergence.html	1. ## Convergence / Divergence Determine whether the following infinite series are convergent or divergent i) $\sum_{n=1}^{\infty }{\frac{n}{n+1}}$ ii) $\sum_{n=1}^{\infty }{\frac{n \sqrt{n}}{n^2+1}}$ iii) $\sum_{n=2}^{\infty }{\frac{1}{n^2-1}}$ for part 1 and 2 i tired doing ratio test and integral test but they both failed and i got nowhere. anyone want to give me a hand ? part 3 seems a lot easier it seems to converge to 0.75 which is easily proved using partial fractions 2. Originally Posted by bobak for part 1 and 2 i tired doing ratio test and integral test but they both failed and i got nowhere. anyone want to give me a hand ? part 3 seems a lot easier it seems to converge to 0.75 which is easily proved using partial fractions for part (i), simply use the test for divergence for part (ii), still thinking of the nicest way to do this. don't want to try something like the integral test if it's not necessary for part (iii). rewrite $\frac 1{n^2 - 1}$ as $\frac A{n + 1} + \frac B{n - 1}$ (you can use partial fractions, but you don't have to). this should be a telescopic sum. write out some of the terms so you can see which will cancel out and which will stay. take the limit as $n \to \infty$ when done to see the sum 3. part 1 $\lim_{n \to{\infty}} \frac{n}{n+1} = 1 $ so the series is divergent. that makes perfect sense. Yeah i got part 3 by the whole method of difference approach i just though i would post it for completeness as it was part of the question 4. Originally Posted by Jhevon for part (i), simply use the test for divergence for part (ii), still thinking of the nicest way to do this. don't want to try something like the integral test if it's not necessary for part (iii). rewrite $\frac 1{n^2 - 1}$ as $\frac A{n + 1} + \frac B{n - 1}$ (you can use partial fractions, but you don't have to). this should be a telescopic sum. write out some of the terms so you can see which will cancel out and which will stay. take the limit as $n \to \infty$ when done to see the sum (ii) Note that $\frac{n \, \sqrt{n}}{n^2 + 1} \geq \frac{n \, \sqrt{n}}{n^2 + n^2} = \frac{n \, \sqrt{n}}{2n^2} = \frac{1}{2} \, \frac{1}{\sqrt{n}}$, for $n \geq 1$. And you know that $\sum_{n=1}^{\infty} \frac{1}{\sqrt{n}}$ is divergent. From the comparison test, the divergence of $\sum_{n=1}^{\infty} \frac{n \, \sqrt{n}}{n^2 + 1}$ is easily seen. 5. Originally Posted by mr fantastic (ii) Note that [tex] And you know that $\sum_{n=1}^{\infty} \frac{1}{\sqrt{n}}$ is divergent. How do we know this ? 6. Originally Posted by bobak How do we know this ? Because, $\frac{1}{\sqrt{1}}+\frac{1}{\sqrt{2}}+...+\frac{1} {\sqrt{n}} \geq \int_1^{n+1} \frac{dx}{\sqrt{x}} = 2\sqrt{n+1} - 2$. 7. Originally Posted by bobak How do we know this ? it is a divergent p-series $\sum \frac 1{n^p}$ converges if $p>1$, diverges if $p \le 1$ TPH showed you a more rigorous/specific proof, but this is what it summarizes to in general	2017-10-20 18:26:38	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 19, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9503071308135986, "perplexity": 400.84008270016216}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187824293.62/warc/CC-MAIN-20171020173404-20171020193404-00714.warc.gz"}
https://plainmath.net/college-statistics/57559-how-do-you-find-the-variance-and-standard-deviation-of	Jayleen Sanders 2022-01-28 How do you find the variance and standard deviation of {2,3,4,6,8,9}? Anabelle Miller Explanation: Variance of a sample is given by the following equation: ${\sigma }^{2}=\frac{\sum {\left(x-\stackrel{―}{x}\right)}^{2}}{n-1}$ It can be rearranged to: ${\sigma }^{2}=\frac{\sum {x}^{2}-\frac{\left(\sum x\right)}{n}}{n-1}$ $\sum \left({x}^{2}\right)={2}^{2}+{3}^{2}+{4}^{2}+{6}^{2}+{8}^{2}+{9}^{2}=210$ $\sum \left(x\right)=2+3+4+6+8+9=32$ n=6 ${\sigma }^{2}=\frac{210-\left(\frac{{32}^{2}}{6}\right)}{6-1}=\frac{118}{15}\stackrel{\sim }{=}7.867$ Standard deviation is the square root of variance. $\sigma =\sqrt{7.8666}=2.80475786$ Do you have a similar question?	2023-04-01 18:16:48	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 6, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8766228556632996, "perplexity": 643.1357159052625}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296950110.72/warc/CC-MAIN-20230401160259-20230401190259-00300.warc.gz"}
http://mywebspider.com/sequential-numbering/category/english/	I have a word document with a table of 6 exact cells on a full page table. In those cell areas I have been printing tickets with a list and a mail merge and updating labels. I call to an excel list of 1-2000 and then I generate all the pages through the Finish and Merge option. This all works perfect. I get 2000 individually numbered tickets to print...however...I then have six tickets printed on a page of paper with ticket numbers 1, 2, 3, 4, 5 ,6 then the next page has 7,8,9,10,11,12. This is fine but I then have to cut and stack these tickets in groups of six and at that point none of the numbering is sequential. The tickets are basically random. We use the auto page numbering trick here, the trick is to do it as spreads. You just make your pages the same size as the ticket with crops and bleeds. Then set up the shell on the master page and place your auto page number where you want your numbers. Each pages is the next number. You can also have two sets of numbers for perforated ticket. You then can use the page start options to add to the numbers and keep the same number of total numbers. For example you would do a new page start after number 99. 0001 to 0099 so it doesn't add two "0's" to the front of 100 and you get 00100 when you want 0100. Works great for small quantities, we have done up to 1000+ tickets and once you do it once or twice it is a snap to set up. To avoid having to do 1000 pages just send the tickets in groups. Usually between 25 to 100 at a time works good depending on artwork file size. Just save each time before sending to printer and name the file with what the tickets are. Like "MyTickets-0001-0100.Indd". Makes it easier to go back if you have a problem. You can even do two rolls of tickets if your using 12 x 18 sheets by flipping the sheet and doing one row along the top and one along the bottom on reverse side. That is if your ticket is single Sided. Two sided tickets are a bit trickier. :-) I normally use "Data Merge" in InDesign and use Excel (or something like it) to generate the list of numbers for me. You would copy the numbers into a text file so that InDesign can read them as the merge data source. Note that you would have one ticket on the page and then let InDesign set the other tickets on the page (you can tell the Data Merge control panel about spacing). Sequential exit numbering usually begins with exit 1 at the beginning of the road; each subsequent exit is given the next number. Letter suffixes are commonly used when new exits are added. For example, on the New York State Thruway, an exit was added between 21 and 22, and was given the number 21A. Subsequently, a new exit was added between 21 and 21A, leading to the sequence 21 - 21B - 21A - 22. In Florida, some new exits got the suffix C, so that if it had or acquired separate exits for the two directions, they would be 15CA and 15CB rather than 15AB. There are also occurrences of this happening on the New Jersey Turnpike; the original interchanges opened in 1951, with newer exits as recently as 1982. On the Baltimore Beltway, there is an exit 12B-C (MD 372), as well as 12A (US 1). There is also an exit 8A (I-895) and an exit 8 (MD 168). Hello! I already have automatic numbering set up (to change paragraph numbers automatically when paragraphs are moved within a document) but I would also like to have automatic lettering within the same document that is independent from the numbering. Example, paragraph 1 references Exhibit A, paragraph 2 references Exhibit B, so on and so forth. Currently using the above referenced method, the auto numbering lettering then follows as if the letters are a representation of the corresponding number (if that makes sense), ex: 1 B 3 C 5 D. How do I have the number sequencing independent from the letter sequence? Thank you in advance! I'm looking for a script for Laserfiche Forms that will query a database and pull the next number in sequence and display it as the unique identifier for this document. Once this number has been used, the number should not be used again. This is similar to what the Submission ID is, but from what I can gather, this number is assigned after the submission takes place. There is no exit zero. If there is an exit within 1.499 km of the origin, Exit 1 is used. Exit 2 would be between 1.500 and 2.499 km of the origin. Subsequent 'exit zones' are at 1 km intervals. Letter suffixes are added at multi-exit interchanges, or where two or more exits exist within the same exit zone. For example, State Highway 1 (Southern Motorway) has an Exit 429A (Symonds St), Exit 429B (Wellesley St) and Exit 429C (Port). Instead of replacing existing ramp and link signs, the exit numbers were added as supplementary information. Thus drivers can navigate either by exit number or name. Exit numbers are only used for exits that may be used by all vehicle types. Bus- or emergency vehicle-only exits would not be numbered. A best practice that we recommend to our clients is to create a base/folio master –with styled and positioned footers and current page number special characters– on which all other masters are based. This allows a footer that may contain date or issue information to be updated once and the changes are reflected in all of the master pages. If your masters only have current page number special characters then you can just add them to each master and the page numbers will be reflected when each master is applied to your document pages. Become a Microsoft Word power user in just a few minutes a week. This tips-based series helps you deepen your proficiency with Word, covering a variety of tools and techniques you can use. Learn how to work with templates, format documents, customize built-in styles and themes, master Track Changes, and more. Check back each week for a new pro tip from expert David Rivers. So if you encountered this problem, then you didn’t follow the instructions completely (which is OK) and appear to be automatically generating the number whenever the record is accessed. If that’s the case, then you are risking duplication because you are not saving the generated number immediately. Rather then try to test if a number already exists as you seem to be doing, you should not automatically generate the number, but trigger the generation from some action in the form. A multi-level list is a list that describes hierarchical relationships between the list paragraphs. These lists are also called outline lists because they resemble outlines. The list’s numbering scheme (as well as indentations) show rank as well as how items are subordinate to one another. You can tell where each paragraph fits in the list with respect to the paragraphs before and after it. You can include up to nine levels in a multi-level list. Scott, I had posted on Microsoft and you sent me to your blog to have the numbering system (similar to APEX example) explained. I am not a programmer and I don’t understand where these codes and expressions are even suppose to go in access. When I do try to implement the little I do know I continue to get errors. I am not sure if I am putting the information in the wrong place or if I am way off. Do you know of any youtube videos that could walk me through it step by step? Or if you have the time could you help walk me through the steps. Warning Making even minor changes to an outline numbering scheme won't necessarily change the initial position you've selected in the gallery, but rather may create a new gallery position, overwriting an existing one. Because of this problem, attaching numbering to styles is strongly recommended. This is covered in greater detail later in this chapter and in the chapter on Styles. !function(n,t){function r(e,n){return Object.prototype.hasOwnProperty.call(e,n)}function i(e){return void 0===e}if(n){var o={},u=n.TraceKit,s=[].slice,a="?";o.noConflict=function(){return n.TraceKit=u,o},o.wrap=function(e){function n(){try{return e.apply(this,arguments)}catch(e){throw o.report(e),e}}return n},o.report=function(){function e(e){a(),h.push(e)}function t(e){for(var n=h.length-1;n>=0;--n)h[n]===e&&h.splice(n,1)}function i(e,n){var t=null;if(!n\|\|o.collectWindowErrors){for(var i in h)if(r(h,i))try{h[i].apply(null,[e].concat(s.call(arguments,2)))}catch(e){t=e}if(t)throw t}}function u(e,n,t,r,u){var s=null;if(w)o.computeStackTrace.augmentStackTraceWithInitialElement(w,n,t,e),l();else if(u)s=o.computeStackTrace(u),i(s,!0);else{var a={url:n,line:t,column:r};a.func=o.computeStackTrace.guessFunctionName(a.url,a.line),a.context=o.computeStackTrace.gatherContext(a.url,a.line),s={mode:"onerror",message:e,stack:[a]},i(s,!0)}return!!f&&f.apply(this,arguments)}function a(){!0!==d&&(f=n.onerror,n.onerror=u,d=!0)}function l(){var e=w,n=p;p=null,w=null,m=null,i.apply(null,[e,!1].concat(n))}function c(e){if(w){if(m===e)return;l()}var t=o.computeStackTrace(e);throw w=t,m=e,p=s.call(arguments,1),n.setTimeout(function(){m===e&&l()},t.incomplete?2e3:0),e}var f,d,h=[],p=null,m=null,w=null;return c.subscribe=e,c.unsubscribe=t,c}(),o.computeStackTrace=function(){function e(e){if(!o.remoteFetching)return"";try{var t=function(){try{return new n.XMLHttpRequest}catch(e){return new n.ActiveXObject("Microsoft.XMLHTTP")}},r=t();return r.open("GET",e,!1),r.send(""),r.responseText}catch(e){return""}}function t(t){if("string"!=typeof t)return[];if(!r(j,t)){var i="",o="";try{o=n.document.domain}catch(e){}var u=/(.)\:\/\/([^:\/]+)([:\d])\/{0,1}([\s\S])/.exec(t);u&&u[2]===o&&(i=e(t)),j[t]=i?i.split("\n"):[]}return j[t]}function u(e,n){var r,o=/function ([^(])$$([^)])$$/,u=/['"]?([0-9A-Za-z$_]+)['"]?\s[:=]\s(function\|eval\|new Function)/,s="",l=10,c=t(e);if(!c.length)return a;for(var f=0;f0?u:null}function l(e){return e.replace(/[\-{}()+?.,\\\^$\|#]/g,"\\$&")}function c(e){return l(e).replace("<","(?:<\|<)").replace(">","(?:>\|>)").replace("&","(?:&\|&)").replace('"','(?:"\|")').replace(/\s+/g,"\\s+")}function f(e,n){for(var r,i,o=0,u=n.length;or&&(i=u.exec(o[r]))?i.index:null}function h(e){if(!i(n&&n.document)){for(var t,r,o,u,s=[n.location.href],a=n.document.getElementsByTagName("script"),d=""+e,h=/^function(?:\s+([\w$]+))?\s$$([\w\s,])$$\s\{\s(\S[\s\S]\S)\s\}\s$/,p=/^function on([\w$]+)\s$$event$$\s\{\s(\S[\s\S]\S)\s\}\s$/,m=0;m]+)>\|([^\)]+))$$(.)$$)? in (.):\s$/i,o=n.split("\n"),a=[],l=0;l=0&&(g.line=v+x.substring(0,j).split("\n").length)}}}else if(o=d.exec(i[y])){var _=n.location.href.replace(/#.$/,""),T=new RegExp(c(i[y+1])),E=f(T,[_]);g={url:_,func:"",args:[],line:E?E.line:o[1],column:null}}if(g){g.func\|\|(g.func=u(g.url,g.line));var k=s(g.url,g.line),A=k?k[Math.floor(k.length/2)]:null;k&&A.replace(/^\s/,"")===i[y+1].replace(/^\s/,"")?g.context=k:g.context=[i[y+1]],h.push(g)}}return h.length?{mode:"multiline",name:e.name,message:i[0],stack:h}:null}function y(e,n,t,r){var i={url:n,line:t};if(i.url&&i.line){e.incomplete=!1,i.func\|\|(i.func=u(i.url,i.line)),i.context\|\|(i.context=s(i.url,i.line));var o=/ '([^']+)' /.exec(r);if(o&&(i.column=d(o[1],i.url,i.line)),e.stack.length>0&&e.stack[0].url===i.url){if(e.stack[0].line===i.line)return!1;if(!e.stack[0].line&&e.stack[0].func===i.func)return e.stack[0].line=i.line,e.stack[0].context=i.context,!1}return e.stack.unshift(i),e.partial=!0,!0}return e.incomplete=!0,!1}function g(e,n){for(var t,r,i,s=/function\s+([_$a-zA-Z\xA0-\uFFFF][_\$a-zA-Z0-9\xA0-\uFFFF])?\s*\(/i,l=[],c={},f=!1,p=g.caller;p&&!f;p=p.caller)if(p!==v&&p!==o.report){if(r={url:null,func:a,args:[],line:null,column:null},p.name?r.func=p.name:(t=s.exec(p.toString()))&&(r.func=t[1]),"undefined"==typeof r.func)try{r.func=t.input.substring(0,t.input.indexOf("{"))}catch(e){}if(i=h(p)){r.url=i.url,r.line=i.line,r.func===a&&(r.func=u(r.url,r.line));var m=/ '([^']+)' /.exec(e.message\|\|e.description);m&&(r.column=d(m[1],i.url,i.line))}c[""+p]?f=!0:c[""+p]=!0,l.push(r)}n&&l.splice(0,n);var w={mode:"callers",name:e.name,message:e.message,stack:l};return y(w,e.sourceURL\|\|e.fileName,e.line\|\|e.lineNumber,e.message\|\|e.description),w}function v(e,n){var t=null;n=null==n?0:+n;try{if(t=m(e))return t}catch(e){if(x)throw e}try{if(t=p(e))return t}catch(e){if(x)throw e}try{if(t=w(e))return t}catch(e){if(x)throw e}try{if(t=g(e,n+1))return t}catch(e){if(x)throw e}return{mode:"failed"}}function b(e){e=1+(null==e?0:+e);try{throw new Error}catch(n){return v(n,e+1)}}var x=!1,j={};return v.augmentStackTraceWithInitialElement=y,v.guessFunctionName=u,v.gatherContext=s,v.ofCaller=b,v.getSource=t,v}(),o.extendToAsynchronousCallbacks=function(){var e=function(e){var t=n[e];n[e]=function(){var e=s.call(arguments),n=e[0];return"function"==typeof n&&(e[0]=o.wrap(n)),t.apply?t.apply(this,e):t(e[0],e[1])}};e("setTimeout"),e("setInterval")},o.remoteFetching\|\|(o.remoteFetching=!0),o.collectWindowErrors\|\|(o.collectWindowErrors=!0),(!o.linesOfContext\|\|o.linesOfContext<1)&&(o.linesOfContext=11),void 0!==e&&e.exports&&n.module!==e?e.exports=o:"function"==typeof define&&define.amd?define("TraceKit",[],o):n.TraceKit=o}}("undefined"!=typeof window?window:global)},"./webpack-loaders/expose-loader/index.js?require!./shared/require-global.js":function(e,n,t){(function(n){e.exports=n.require=t("./shared/require-global.js")}).call(n,t("../../../lib/node_modules/webpack/buildin/global.js"))}}); I want to a sequential number to fill in automatically each time the form is filled out. Malissa, A simple way would be to use something like this, you could assign it to a button, an open or before print event. Sheets("Sheet1").Range("A1").Value = _ Sheets("Sheet1").Range("A1").Value + 1 For other ways to do this or if this is going to be used in a temple have a look here http://www.mcgimpsey.com/excel/udfs/sequentialnums.html -- Paul B Always backup your data before trying something new Please post any response to the newsgroups so others... Here, you’ll be given the chance to name your AutoText entry. Name it carefully — for AutoText to work correctly, the first four letters of each of your AutoText entry names will need to be distinct, since these first four letters will be the prompt for Word to offer to complete the phrase for you. My suggestion is to use Interrogatories, Production and Admission as your names, but use whatever is convenient and memorable for you. Sequential exit numbering usually begins with exit 1 at the beginning of the road; each subsequent exit is given the next number. Letter suffixes are commonly used when new exits are added. For example, on the New York State Thruway, an exit was added between 21 and 22, and was given the number 21A. Subsequently, a new exit was added between 21 and 21A, leading to the sequence 21 - 21B - 21A - 22. In Florida, some new exits got the suffix C, so that if it had or acquired separate exits for the two directions, they would be 15CA and 15CB rather than 15AB. There are also occurrences of this happening on the New Jersey Turnpike; the original interchanges opened in 1951, with newer exits as recently as 1982. On the Baltimore Beltway, there is an exit 12B-C (MD 372), as well as 12A (US 1). There is also an exit 8A (I-895) and an exit 8 (MD 168). Number Pro does not create your raffle ticket or document it just allows an easy way to number them. Check out Number Pro, take a look at the demo videos and even try the demo of Number Pro to see how it works. Number Pro is a cloud based application meaning there is no download of the application. We access the application online in the members area. They offer a three year membership with unlimited use. Infinite sequences of digits (or characters) drawn from a finite alphabet are of particular interest in theoretical computer science. They are often referred to simply as sequences or streams, as opposed to finite strings. Infinite binary sequences, for instance, are infinite sequences of bits (characters drawn from the alphabet {0, 1}). The set C = {0, 1}∞ of all infinite binary sequences is sometimes called the Cantor space. As far as I know, you can’t have auto captioning that changes from one heading level to another. Once you choose a heading level in the numbering options (e.g. heading 2), ALL captions of that type automatically change to that level (e.g. Figure 1.1-1, Figure 6.2-1). If you later choose a different heading level (e.g. 3), every caption now changes to that type (e.g. Figure 1.1.1-1; Figure 6.2.3-1). You can’t mix them up. A single InDesign document can contain up to 9,999 pages, but page numbers can be as large as 999,999. (For example, you can correctly number a 100‑page document that starts on page 9,949.) By default, the first page is a recto (right) page numbered 1. Odd-numbered pages always appear on the right; if you use the Section Options command to change the first page number to an even number, the first page becomes a verso (left) page. I like where your idea is going, but I cannot figure out how to consecutively number across text frames on one document. So far I have created a csv document in Excel, drew a textbox, imported the csv file into the Data Merge window and dragged it into the text frame. Now, I've got "<<00001>>" in the text frame. When I click "Create Merged Document" I get an error message: "Cannot creat merged document because no placeholders are present..." Now what? Thank you very much for your prompt reply dear Rhonda. I actually managed to do this somehow. I right-clicked on the caption and clicked edit filed and then field codes. In the code I changed the number showing the heading level, e.g. \s 1, \s 2, \s 3. When I changed the caption heading level in this manner, I noticed that the changed was applied to only that caption and not the rest of the document. So now I have different heading levels in my figure captions. It did the trick for me. Thank you so much and Happy New Year :) Although sequences are a type of function, they are usually distinguished notationally from functions in that the input is written as a subscript rather than in parentheses, i.e. an rather than f(n). There are terminological differences as well: the value of a sequence at the input 1 is called the "first element" of the sequence, the value at 2 is called the "second element", etc. Also, while a function abstracted from its input is usually denoted by a single letter, e.g. f, a sequence abstracted from its input is usually written by a notation such as {\displaystyle (a_{n})_{n\in A}} , or just as {\displaystyle (a_{n})} . Here A is the domain, or index set, of the sequence. If you need to apply numbering within a paragraph rather than to the entire paragraph, you use Word's ListNum feature. Using the ListNum feature will allow you to take advantage of the numbering system you're currently using in your document (it will use the one you implemented most recently if you're not currently using a numbering system). The ListNum Field is available in Word 97 and later and interacts with multi-level list numbering (which should be linked to styles as set forth here). Here is a brief explanation of differences between the ListNum field and the Seq field. Author, trainer, and learning and development expert David Rivers has over 20 years experience helping government, hi-tech, and healthcare businesses increase their efficiency and productivity by integrating technology tools. With deep experience in Microsoft Office, elearning tools, and assorted productivity tools such as FrameMaker and RoboHelp, David is passionate about helping people improve their workflows to recover time in their schedules. His clients include Microsoft, Corel Corporation, Halogen Software, and the City of Ottawa. David is also a published book author on topics ranging from Photoshop to Acrobat and the Microsoft Digital Image Suite. I need 2 copies to be printed each time I print from a certain file. Is there any way to save this command so I don't have to change the number of copies each time I print? Hi you could record a macro while doing this manually and assign a shortcut or button to this recorded macro -- Regards Frank Kabel Frankfurt, Germany Hebert45 wrote: > I need 2 copies to be printed each time I print from a certain file. > Is there any way to save this command so I don't have to change the > number of copies each time I print? ... Some freeways' exit number starts from a advanced number (i.e. higher than 1). Some reason of starting a number higher than 1 is due to the expectation that the highway will extend on both ends. For example, Ontario Highway 400 starts at 20 because it was expected that the south end of the highway would extend to downtown Toronto (which was never built). Another reason to use a higher number is that the freeway is branching off from another freeway. An example is British Columbia Highway 5, which branches off British Columbia Highway 1 and starts at 170.	2019-01-21 12:52:39	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.46428313851356506, "perplexity": 1580.2536234975896}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547583792338.50/warc/CC-MAIN-20190121111139-20190121133139-00588.warc.gz"}
http://tex.stackexchange.com/questions/37790/scale-figure-to-a-percentage-of-textwidth/37793	# Scale figure to a percentage of \textwidth I would like to change my figure's width to a precentage of my \textwidth: \textwidth /2 would scale to 50% of the \textwidth. What is the proper syntax (if any) to do this ? - \documentclass{article} \usepackage{graphicx} \begin{document} \includegraphics[width=0.5\textwidth]{file} \end{document} In some cases \linewidth instead of \textwidth may be the better option. For example will it be the same as \textwidth in a single column document, but the same as \columnwidth in a two column document. \linewidth may also change in list environments, becoming smaller in nested lists. As commented by Christian Lindig, see Difference between \textwidth, \linewidth and \hsize for a discussion of this. - See also the difference between \textwidth, \linewidth and \hsize. For these reasons you should use \linewidth because it works inside columns and minipages. – Christian Lindig Dec 10 '11 at 12:00 If used as-is, just remove the paragraph indentation to avoid a \parindent horizontal shift. I wouldn't change your MWE though, since the OP's usage may not require it (for example, within a figure environment). – Werner Dec 10 '11 at 15:34	2014-10-26 09:32:29	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9094306826591492, "perplexity": 3415.9580954546923}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-42/segments/1414119662145.58/warc/CC-MAIN-20141024030102-00082-ip-10-16-133-185.ec2.internal.warc.gz"}
https://zenodo.org/record/1567503/export/xd	Journal article Open Access # Monte-Carlo simulations of superradiant lasing Zhang, Yuan; Zhang, Yu-Xiang; Mølmer, Klaus ### Dublin Core Export <?xml version='1.0' encoding='utf-8'?> <oai_dc:dc xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:oai_dc="http://www.openarchives.org/OAI/2.0/oai_dc/" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.openarchives.org/OAI/2.0/oai_dc/ http://www.openarchives.org/OAI/2.0/oai_dc.xsd"> <dc:creator>Zhang, Yuan</dc:creator> <dc:creator>Zhang, Yu-Xiang</dc:creator> <dc:creator>Mølmer, Klaus</dc:creator> <dc:date>2018-11-15</dc:date> <dc:description>We simulate the superradiant dynamics of ensembles of atoms in the presence of collective and individual atomic decay processes. We apply the Monte-Carlo wave-function method and identify quantum jumps in a reduced Dicke state basis, which reflects the permutation symmetry of the system. While the number of density matrix elements in the Dicke representation increases polynomially with atom number, the quantum jump dynamics populates only a single Dicke state at the time and thus efficient simulations can be carried out for tens of thousands of atoms. The superradiant pulses from initially excited atoms agree quantitatively with recent experimental results of strontium atoms but rapid atom loss in these experiments does not permit steady-state superradiance. By introducing an incident flux of new atoms to maintain a large average atom number, our theoretical calculations predict lasing with a millihertz linewidth despite rapid atom number fluctuations.</dc:description> <dc:identifier>https://zenodo.org/record/1567503</dc:identifier> <dc:identifier>10.1088/1367-2630/aaec36</dc:identifier> <dc:identifier>oai:zenodo.org:1567503</dc:identifier> <dc:relation>info:eu-repo/grantAgreement/EC/H2020/712721/</dc:relation> <dc:relation>url:https://zenodo.org/communities/nanoqtech-h2020</dc:relation> <dc:rights>info:eu-repo/semantics/openAccess</dc:rights> <dc:subject>nanoqtech</dc:subject> <dc:subject>rare earth</dc:subject> <dc:subject>quantum technologies</dc:subject> <dc:type>info:eu-repo/semantics/article</dc:type> <dc:type>publication-article</dc:type> </oai_dc:dc> 103 85 views	2022-09-30 07:02:41	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.29826152324676514, "perplexity": 5149.091390181055}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030335444.58/warc/CC-MAIN-20220930051717-20220930081717-00447.warc.gz"}
https://iacr.org/cryptodb/data/paper.php?pubkey=30206	## CryptoDB ### Paper: Secure Multi-party Quantum Computation with a Dishonest Majority Authors: Yfke Dulek , QuSoft and University of Amsterdam Alex B. Grilo , QuSoft and CWI Stacey Jeffery , QuSoft and CWI Christian Majenz , QuSoft and CWI Christian Schaffner , QuSoft and University of Amsterdam DOI: 10.1007/978-3-030-45727-3_25 (login may be required) Search ePrint Search Google EUROCRYPT 2020 The cryptographic task of secure multi-party (classical) computation has received a lot of attention in the last decades. Even in the extreme case where a computation is performed between k mutually distrustful players, and security is required even for the single honest player if all other players are colluding adversaries, secure protocols are known. For quantum computation, on the other hand, protocols allowing arbitrary dishonest majority have only been proven for k=2. In this work, we generalize the approach taken by Dupuis, Nielsen and Salvail (CRYPTO 2012) in the two-party setting to devise a secure, efficient protocol for multi-party quantum computation for any number of players k, and prove security against up to k-1 colluding adversaries. The quantum round complexity of the protocol for computing a quantum circuit of {CNOT, T} depth d is O(k (d + log n)), where n is the security parameter. To achieve efficiency, we develop a novel public verification protocol for the Clifford authentication code, and a testing protocol for magic-state inputs, both using classical multi-party computation. ##### BibTeX @inproceedings{eurocrypt-2020-30206, title={Secure Multi-party Quantum Computation with a Dishonest Majority}, booktitle={39th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Zagreb, Croatia, May 10–14, 2020, Proceedings}, series={Lecture Notes in Computer Science}, publisher={Springer}, keywords={Quantum cryptography;Multi-party computation;Computational security}, volume={12105}, doi={10.1007/978-3-030-45727-3_25}, author={Yfke Dulek and Alex B. Grilo and Stacey Jeffery and Christian Majenz and Christian Schaffner}, year=2020 }	2022-12-08 19:58:50	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4240134656429291, "perplexity": 5138.869856372518}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711360.27/warc/CC-MAIN-20221208183130-20221208213130-00352.warc.gz"}
https://scirate.com/arxiv/math	# Mathematics (math) • This paper considers the problem of solving systems of quadratic equations, namely, recovering an object of interest $\mathbf{x}^{\natural}\in\mathbb{R}^{n}$ from $m$ quadratic equations/samples $y_{i}=(\mathbf{a}_{i}^{\top}\mathbf{x}^{\natural})^{2}$, $1\leq i\leq m$. This problem, also dubbed as phase retrieval, spans multiple domains including physical sciences and machine learning. We investigate the efficiency of gradient descent (or Wirtinger flow) designed for the nonconvex least squares problem. We prove that under Gaussian designs, gradient descent --- when randomly initialized --- yields an $\epsilon$-accurate solution in $O\big(\log n+\log(1/\epsilon)\big)$ iterations given nearly minimal samples, thus achieving near-optimal computational and sample complexities at once. This provides the first global convergence guarantee concerning vanilla gradient descent for phase retrieval, without the need of (i) carefully-designed initialization, (ii) sample splitting, or (iii) sophisticated saddle-point escaping schemes. All of these are achieved by exploiting the statistical models in analyzing optimization algorithms, via a leave-one-out approach that enables the decoupling of certain statistical dependency between the gradient descent iterates and the data. • Mar 22 2018 math.CO arXiv:1803.07694v1 Consider the following two ways to colour the vertices of a graph where the requirement that adjacent vertices get distinct colours is relaxed. A colouring has "defect" $d$ if each monochromatic component has maximum degree at most $d$. A colouring has "clustering" $c$ if each monochromatic component has at most $c$ vertices. This paper surveys research on these types of colourings, where the first priority is to minimise the number of colours, with small defect or small clustering as a secondary goal. List colouring variants are also considered. The following graph classes are studied: outerplanar graphs, planar graphs, graphs embeddable in surfaces, graphs with given maximum degree, graphs with given maximum average degree, graphs excluding a given subgraph, graphs with linear crossing number, linklessly or knotlessly embeddable graphs, graphs with given Colin de Verdière parameter, graphs with given circumference, graphs excluding a fixed graph as an immersion, graphs with given thickness, graphs with given stack- or queue-number, graphs excluding $K_t$ as a minor, graphs excluding $K_{s,t}$ as a minor, and graphs excluding an arbitrary graph $H$ as a minor. Several open problems are discussed. • This paper considers the word problem for free inverse monoids of finite rank from a language theory perspective. It is shown that no free inverse monoid has context-free word problem; that the word problem of the free inverse monoid of rank $1$ is both $2$-context-free (an intersection of two context-free languages) and ET0L; that the co-word problem of the free inverse monoid of rank $1$ is context-free; and that the word problem of a free inverse monoid of rank greater than $1$ is not poly-context-free. • We study the Wasserstein metric $W_p$, a notion of distance between two probability distributions, from the perspective of Fourier Analysis and discuss applications. In particular, we bound the Earth Mover Distance $W_1$ between the distribution of quadratic residues in a finite field $\mathbb{F}_p$ and uniform distribution by $\lesssim p^{-1/2}$ (the Polya-Vinogradov inequality implies $\lesssim p^{-1/2} \log{p}$). We also show for continuous $f:\mathbb{T} \rightarrow \mathbb{R}_{}$ with mean value 0 $$(\mboxnumber of roots of~f) ⋅\left( \sum_k=1^∞ \frac \|\widehatf(k)\|^2k^2\right)^\frac12 ≳\frac\\|f\\|^2_L^1(\mathbbT)\\|f\\|_L^∞(\mathbbT).$$ Moreover, we show that for a Laplacian eigenfunction $-\Delta_g \phi_{\lambda} = \lambda \phi_{\lambda}$ on a compact Riemannian manifold $W_p\left(\max\left\{\phi_{\lambda}, 0\right\}dx, \max\left\{-\phi_{\lambda}, 0\right\} dx\right) \lesssim_p \sqrt{\log{\lambda}/\lambda} \\|\phi_{\lambda}\\|_{L^1}^{1/p}$ which is at most a factor $\sqrt{\log{\lambda}}$ away from sharp. Several other problems are discussed. • We interpret part of the experimental results of Shwartz-Ziv and Tishby [2017]. Inspired by these results, we established a conjecture of the dynamics of the machinary of deep neural network. This conjecture can be used to explain the counterpart result by Saxe et al. [2018]. • In empirical risk optimization, it has been observed that stochastic gradient implementations that rely on random reshuffling of the data achieve better performance than implementations that rely on sampling the data uniformly. Recent works have pursued justifications for this behavior by examining the convergence rate of the learning process under diminishing step-sizes. This work focuses on the constant step-size case. In this case, convergence is guaranteed to a small neighborhood of the optimizer albeit at a linear rate. The analysis establishes analytically that random reshuffling outperforms uniform sampling by showing explicitly that iterates approach a smaller neighborhood of size $O(\mu^2)$ around the minimizer rather than $O(\mu)$. Furthermore, we derive an analytical expression for the steady-state mean-square-error performance of the algorithm, which helps clarify in greater detail the differences between sampling with and without replacement. We also explain the periodic behavior that is observed in random reshuffling implementations. • Applications in machine learning, optimization, and control require the sequential selection of a few system elements, such as sensors, data, or actuators, to optimize the system performance across multiple time steps. However, in failure-prone and adversarial environments, sensors get attacked, data get deleted, and actuators fail. Thence, traditional sequential design paradigms become insufficient and, in contrast, resilient sequential designs that adapt against system-wide attacks, deletions, or failures become important. In general, resilient sequential design problems are computationally hard. Also, even though they often involve objective functions that are monotone and (possibly) submodular, no scalable approximation algorithms are known for their solution. In this paper, we provide the first scalable algorithm, that achieves the following characteristics: system-wide resiliency, i.e., the algorithm is valid for any number of denial-of-service attacks, deletions, or failures; adaptiveness, i.e., at each time step, the algorithm selects system elements based on the history of inflicted attacks, deletions, or failures; and provable approximation performance, i.e., the algorithm guarantees for monotone objective functions a solution close to the optimal. We quantify the algorithm's approximation performance using a notion of curvature for monotone (not necessarily submodular) set functions. Finally, we support our theoretical analyses with simulated experiments, by considering a control-aware sensor scheduling scenario, namely, sensing-constrained robot navigation. • Mar 22 2018 cs.IT math.IT arXiv:1803.07937v1 The existence of a unique Augustin mean is established for any positive order and probability mass function on the input set. The Augustin mean is shown to be the unique fixed point of an operator defined in terms of the order and the input distribution. The Augustin information is shown to be continuously differentiable in the order. For any channel and any convex constraint set with finite Augustin capacity, the existence of a unique Augustin center and associated van Erven-Harremoes bound are established.The Augustin-Legendre (A-L) information, capacity, center, and radius are introduced and the latter three is proved to be equal to the corresponding Renyi-Gallager quantities. The equality of the A-L capacity to the A-L radius for arbitrary channels and the existence of a unique A-L center for channels with finite A-L capacity are established. For all interior points of the feasible set of cost constraints, the cost constrained Augustin capacity and center are expressed in terms the A-L capacity and center. Certain shift invariant families of probability measures and certain Gaussian channels are analyzed as examples. • Given a complex manifold endowed with a $\mathbb{C}^\times$-action and a DQ-algebra equipped with a compatible holomorphic Frobenius action (F-action), we prove that if the $\mathbb{C}^\times$-action is free and proper, then the category of F-equivariant DQ-modules is equivalent to the category of modules over the sheaf of invariant sections of the DQ-algebra. As an application, we deduce the codimension three conjecture for formal microdifferential modules from the one for DQ-modules on a symplectic manifold. • We study the stabilization issue of the Benjamin-Bona-Mahony (BBM) equation on a finite star-shaped network with a damping term acting on the central node. In a first time, we prove the well-posedness of this system. Then thanks to the frequency domain method, we get the asymptotic stabilization result. • In this paper we prove an $n$th root test for series as well as a Cauchy-Hadamard type formula and Abel's' theorem for power series on universally complete Archimedean complex vector lattices. These results are aimed at developing an alternative approach to the classical theory of complex series and power series using the topology of order convergence. • Mar 22 2018 math.OC arXiv:1803.07872v1 We study a differential game where two players separately control their own dynamics, pay a running cost, and moreover pay an exit cost (quitting the game) when they leave a fixed domain. In particular, each player has its own domain and the exit cost consists of three different exit costs, depending whether either the first player only leaves its domain, or the second player only leaves its domain, or they both simultaneously leave their own domain. We prove that, under suitable hypotheses, the lower and upper value are continuous and are, respectively, the unique viscosity solution of a suitable Dirichlet problem for a Hamilton-Jacobi-Isaacs equation. The continuity of the values relies on the existence of suitable non-anticipative strategies respecting the domain-constraint. This problem is also treated in this work. • Mar 22 2018 math.CV arXiv:1803.07862v1 We generalize the notion of tame discrete sets introduced by Rosay and Rudin from complex-Euclidean space to arbitrary complex manifolds and establish their basic properties. We show that complex-linear algebraic groups different from the complex line or the punctured complex line contain tame discrete sets. • In this paper, we describe a new Niederreiter cryptosystem based on quasi-cyclic $\frac{m-1}{m}$ codes that is quantum-secure. This new cryptosystem has good transmission rate compared to the one using binary Goppa codes and uses smaller keys. • In this paper, we study the problem of distributed multi-agent optimization over a network, where each agent possesses a local cost function that is smooth and strongly convex. The global objective is to find a common solution that minimizes the average of all cost functions. Assuming agents only have access to unbiased estimates of the gradients of their local cost functions, we consider a distributed stochastic gradient tracking method. We show that, in expectation, the iterates generated by each agent are attracted to a neighborhood of the optimal solution, where they accumulate exponentially fast (under a constant step size choice). More importantly, the limiting (expected) error bounds on the distance of the iterates from the optimal solution decrease with the network size, which is a comparable performance to a centralized stochastic gradient algorithm. Numerical examples further demonstrate the effectiveness of the method. • We prove that unless P=NP, there exists no polynomial time (or even pseudo-polynomial time) algorithm that can test whether the optimal value of a nonlinear optimization problem where the objective and constraints are given by low-degree polynomials is attained. If the degrees of these polynomials are fixed, our results along with previously-known "Frank-Wolfe type" theorems imply that exactly one of two cases can occur: either the optimal value is attained on every instance, or it is strongly NP-hard to distinguish attainment from non-attainment. We also show that testing for some well-known sufficient conditions for attainment of the optimal value, such as coercivity of the objective function and closedness and boundedness of the feasible set, is strongly NP-hard. As a byproduct, our proofs imply that testing the Archimedean property of a quadratic module is strongly NP-hard, a property that is of independent interest to the convergence of the Lasserre hierarchy. Finally, we give semidefinite programming (SDP)-based sufficient conditions for attainment of the optimal value, in particular a new characterization of coercive polynomials that lends itself to an SDP hierarchy. • Mar 22 2018 math.ST stat.TH arXiv:1803.07645v1 Smoothing splines can be thought of as the posterior mean of a Gaussian process regression in a certain limit. By constructing a reproducing kernel Hilbert space with an appropriate inner product, the Bayesian form of the V-spline is derived when the penalty term is a fixed constant instead of a function. An extension to the usual generalized cross-validation formula is utilized to find the optimal V-spline parameters. • We present criteria for establishing a triangulation of a manifold. Given a manifold M, a simplicial complex A, and a map H from the underlying space of A to M, our criteria are presented in local coordinate charts for M, and ensure that H is a homeomorphism. These criteria do not require a differentiable structure, or even an explicit metric on M. No Delaunay property of A is assumed. The result provides a triangulation guarantee for algorithms that construct a simplicial complex by working in local coordinate patches. Because the criteria are easily verified in such a setting, they are expected to be of general use. • We uncover a fairly general principle in online learning: If regret can be (approximately) expressed as a function of certain "sufficient statistics" for the data sequence, then there exists a special Burkholder function that 1) can be used algorithmically to achieve the regret bound and 2) only depends on these sufficient statistics, not the entire data sequence, so that the online strategy is only required to keep the sufficient statistics in memory. This characterization is achieved by bringing the full power of the Burkholder Method --- originally developed for certifying probabilistic martingale inequalities --- to bear on the online learning setting. To demonstrate the scope and effectiveness of the Burkholder method, we develop a novel online strategy for matrix prediction that attains a regret bound corresponding to the variance term in matrix concentration inequalities. We also present a linear-time/space prediction strategy for parameter free supervised learning with linear classes and general smooth norms. • Mar 22 2018 math.AG arXiv:1803.07596v1 We define the notion of Mumford divisors, argue that they are the natural divisors to study on reduced but non-normal varieties and prove a structure theorem for the Mumford class group. • In this paper, we focus on solving a distributed convex optimization problem in a network, where each agent has its own convex cost function and the goal is to minimize the sum of the agents' cost functions while obeying the network connectivity structure. In order to minimize the sum of the cost functions, we consider a new distributed gradient-based method where each node maintains two estimates, namely, an estimate of the optimal decision variable and an estimate of the gradient for the average of the agents' objective functions. From the viewpoint of an agent, the information about the decision variable is pushed to the neighbors, while the information about the gradients is pulled from the neighbors (hence giving the name "push-pull gradient method"). The method unifies the algorithms with different types of distributed architecture, including decentralized (peer-to-peer), centralized (master-slave), and semi-centralized (leader-follower) architecture. We show that the algorithm converges linearly for strongly convex and smooth objective functions over a directed static network. In our numerical test, the algorithm performs well even for time-varying directed networks. • The PWP map was introduced by the second author as a tool for ranking nodes in networks. In this work we extend this technique so that it can be used to rank links as well. Applying the Girvan-Newman algorithm a ranking method on links induces a deconstruction method for networks, therefore we obtain new methods for finding clustering and core-periphery structures on networks. • We prove improved bounds on how localized an eigenvector of a high girth regular graph can be, and present examples showing that these bounds are close to sharp. This study was initiated by Brooks and Lindenstrauss (2009) who relied on the observation that certain suitably normalized averaging operators on high girth graphs are hyper-contractive and can be used to approximate projectors onto the eigenspaces of such graphs. Informally, their delocalization result in the contrapositive states that for any $\varepsilon \in (0,1)$ and positive integer $k,$ if a $(d+1)-$regular graph has an eigenvector which supports $\varepsilon$ fraction of the $\ell_2^2$ mass on a subset of $k$ vertices, then the graph must have a cycle of size $\tilde{O}(\log_{d}(k)/\varepsilon^2)$, suppressing logarithmic terms in $1/\varepsilon$. In this paper, we improve the upper bound to $\tilde{O}(\log_{d}(k)/\varepsilon)$ and present a construction showing a lower bound of $\Omega(\log_d(k)/\varepsilon)$. Our construction is probabilistic and involves gluing together a pair of trees while maintaining high girth as well as control on the eigenvectors and could be of independent interest. • We study locally compact groups having all subgroups minimal. We call such groups hereditarily minimal. In 1972 Prodanov proved that the infinite hereditarily minimal compact abelian groups are precisely the groups $\mathbb Z_p$ of $p$-adic integers. We extend Prodanov's theorem to the non-abelian case at several levels. For infinite hypercentral (in particular, nilpotent) locally compact groups we show that the hereditarily minimal ones remain the same as in the abelian case. On the other hand, we classify completely the locally compact solvable hereditarily minimal groups, showing that in particular they are always compact and metabelian. The proofs involve the (hereditarily) locally minimal groups, introduced similarly. In particular, we prove a conjecture by He, Xiao and the first two authors, showing that the group $\mathbb Q_p\rtimes \mathbb Q_p^$ is hereditarily locally minimal, where $\mathbb Q_p^$ is the multiplicative group of non-zero $p$-adic numbers acting on the first component by multiplication. Furthermore, it turns out that the locally compact solvable hereditarily minimal groups are closely related to this group. • Mar 22 2018 math.DS arXiv:1803.08032v1 Let $\{N_t\}$ be a holomorphic family of degree $d\ge 3$ Newton maps. By studying the related Berkovich dynamics, we obtain an estimate of the weak limit of the maximal measures of $N_t$. Moreover, we give a complete description of the rescaling limits for $\{N_t\}$. • The goal of this paper is to study a distributed version of the gradient temporal-difference (GTD) learning algorithm for multi-agent Markov decision processes (MDPs). The temporal difference (TD) learning is a reinforcement learning (RL) algorithm which learns an infinite horizon discounted cost function (or value function) for a given fixed policy without the model knowledge. In the distributed RL case each agent receives local reward through a local processing. Information exchange over sparse communication network allows the agents to learn the global value function corresponding to a global reward, which is a sum of local rewards. In this paper, the problem is converted into a constrained convex optimization problem with a consensus constraint. Then, we propose a primal-dual distributed GTD algorithm and prove that it almost surely converges to a set of stationary points of the optimization problem. • We use recent results of Rolen, Zwegers, and the first author to study characters of irreducible (highest weight) modules for the vertex operator algebra $L_{\frak{sl}_\ell}(-\Lambda_0)$. We establish asymptotic behaviors of characters for the (ordinary) irreducible $L_{\frak{sl}_\ell}(-\Lambda_0)$-modules. As a consequence we prove that their quantum dimensions are one, as predicted by representation theory. We also establish a full asymptotic expansion of irreducible characters for $\frak{sl}_3$. Finally, we determine a decomposition formula for the full characters in terms of unary theta and false theta functions which allows us to study their modular properties. • We define some signature invariants for a class of knotted trivalent graphs using branched covers. We relate them to classical signatures of knots and links. Finally, we explain how to compute these invariants through the example of Kinoshita's knotted theta graph. • We give a brief re-exposition of the theory due to Pauli and Sinclair of ramification polygons of Eisenstein polynomials over p-adic fields, their associated residual polynomials and an algorithm to produce all extensions for a given ramification polygon. We supplement this with an algorithm to produce all ramification polygons of a given degree, and hence we can produce all totally ramified extensions of a given degree. • We study a system of nonlinear partial differential equations describing the unsteady motions of incompressible chemically reacting non-Newtonian fluids. The system under consideration consists of the generalized Navier-Stokes equations with a power-law type stress-strain relation, where the power-law index depends on the concentration of a chemical, coupled to a convection-diffusion equation for the concentration. This system of equations arises in the rheology of the synovial fluid found in the cavities of synovial joints. We prove the existence of global weak solutions of the non-stationary model by using the Galerkin method combined with generalized monotone operator theory and parabolic De Giorgi-Nash-Moser theory. As the governing equations involve a nonlinearity with a variable power-law index, our proofs exploit the framework of generalized Sobolev spaces with variable integrability exponent. • We give a notion of quantum automorphism group of graph C-algebras without sink at critical inverse temperature. This is defined to be the universal object of a category of CQG's having a linear action in the sense of [11] and preserving the KMS state at critical inverse temperature. We show that this category for a certain KMS state at critical inverse temperature coincides with the category introduced in [11] for a class of graphs. We also introduce an orthogonal filtration on Cuntz algebra with respect to the unique KMS state and show that the category of CQG's preserving the orthogonal filtration coincides with the category introduced in this paper. • In 2008, Kauffman and Lomonaco introduce the concepts of a knot mosaic and the mosaic number of a knot or link, the smallest integer $n$ such that a knot or link can be represented on an $n$-mosaic. In arXiv:1702.06462, the authors explore space-efficient knot mosaics and the tile number of a knot or link, the smallest number of non-blank tiles necessary to depict the knot or link on a mosaic. They determine bounds for the tile number in terms of the mosaic number. In this paper, we focus specifically on prime knots with mosaic number 6. We determine a complete list of these knots, provide a minimal, space-efficient knot mosaic for each of them, and determine the tile number (or minimal mosaic tile number) of each of them. • Let $k({\bf x})=k(x_1,\ldots ,x_n)$ be the rational function field, and $k\subsetneqq L\subsetneqq k({\bf x})$ an intermediate field. Then, Hilbert's fourteenth problem asks whether the $k$-algebra $A:=L\cap k[x_1,\ldots ,x_n]$ is finitely generated. Various counterexamples to this problem were already given, but the case $[k({\bf x}):L]=2$ was open when $n=3$. In this paper, we study the problem in terms of the field-theoretic properties of $L$. We say that $L$ is minimal if the transcendence degree $r$ of $L$ over $k$ is equal to that of $A$. We show that, if $r\ge 2$ and $L$ is minimal, then there exists $\sigma \in {\mathop{\rm Aut}\nolimits}_kk(x_1,\ldots ,x_{n+1})$ for which $\sigma (L(x_{n+1}))$ is minimal and a counterexample to the problem. Our result implies the existence of interesting new counterexamples including one with $n=3$ and $[k({\bf x}):L]=2$. • We explain a connection between the algebraic and geometric properties of groups of contact transformations, open book decompositions, and flexible Legendrian embeddings. The main result is that, if a closed contact manifold $(V, \xi)$ has a supporting open book whose pages are flexible Weinstein manifolds, then both the connected component of identity in its automorphism group and its universal cover are uniformly simple groups: for every non-trivial element $g$, every other element is a product of at most $128(\dim V + 1)$ conjugates of $g^{\pm 1}$. In particular any conjugation invariant norm on these groups is bounded. • A source submits status updates to a network for delivery to a destination monitor. Updates follow a route through a series of network nodes. Each node is a last-come-first-served queue supporting preemption in service. We characterize the average age of information at the input and output of each node in the route induced by the updates passing through. For Poisson arrivals to a line network of preemptive memoryless servers, we show that average age accumulates through successive network nodes. • For every fixed genus $g\geq 1$, we consider all quadruples $Q=(w_0,w_1,w_2,d)\in\mathbb{Z}^4_{>0}$ with the property that any smooth degree-$d$ curve embedded in the weighted projective plane $\mathbb{P}^2(w_0,w_1,w_2)$ has genus $g$. We show there are infinitely many quadruples $Q$ satisfying this condition. For every such $Q$, we consider $Z_Q\subseteq M_g$ the locus in the moduli space of all smooth degree-$d$ curves embedded in $\mathbb{P}^2(w_0,w_1,w_2)$. We show that, as $Q$ varies over all these quadruples, there are only finitely many different loci $Z_Q\subseteq M_g$. • In this paper we study the Dirichlet eigenvalue problem $$-\Delta_p u-\Delta_J,pu =\lambda\|u\|^p-2u \quad \text in \Omega,\quad u=0 \quad\text in \Omega^c=\mathbbR^N∖\Omega.$$ Here $\Delta_p u$ is the standard local $p-$Laplacian, $\Delta_{J,p}u$ is a nonlocal, $p-$homogeneous operator of order zero and $\Omega$ is a bounded domain in $\mathbb{R}^N$. We show that the first eigenvalue (that is isolated and simple) satisfies $(\lambda_1)^{1/p}\to \Lambda$ as $p\to\infty$ where $\Lambda$ can be characterized in terms of the geometry of $\Omega$. We also find that the eigenfunctions converge, $u_\infty=\lim_{p\to\infty} u_p$, and find the limit problem that is satisfied in the limit. • This paper considers a class of real-time decision making problems to minimize the expected value of a function that depends on a random variable $\xi$ under an unknown distribution $\mathbb{P}$. In this process, samples of $\xi$ are collected sequentially in real time, and the decisions are made, using the real-time data, to guarantee out-of-sample performance. We approach this problem in a distributionally robust optimization framework and propose a novel Online Data Assimilation Algorithm for this purpose. This algorithm guarantees the out-of-sample performance in high probability, and gradually improves the quality of the data-driven decisions by incorporating the streaming data. We show that the Online Data Assimilation Algorithm guarantees convergence under the streaming data, and a criteria for termination of the algorithm after certain number of data has been collected. • Let $\Omega\subset\mathbb R^{n+1}$ be an open set with $n$-AD-regular boundary. In this paper we prove that if the harmonic measure for $\Omega$ satisfies the so-called weak-$A_\infty$ condition, then $\Omega$ satisfies a suitable connectivity condition, namely the weak local John condition. This yields the first geometric characterization of the weak-$A_\infty$ condition of harmonic measure, which is important because its connection with the Dirichlet problem for the Laplace equation. • We consider the problem of finding the isolated common roots of a set of polynomial functions defining a zero-dimensional ideal I in a ring R of polynomials over C. Normal form algorithms provide an algebraic approach to solve this problem. We use new characterizations of normal forms and describe accurate and efficient constructions that allow us to compute the algebra structure of R/I, and hence the solutions of I. We show how the resulting algorithms give accurate results in double precision arithmetic and compare with normal form algorithms using Groebner bases and homotopy solvers. • Recent progress has been made with Adaptive Multiple Importance Sampling (AMIS) methods that show improvement in effective sample size. However, consistency for the AMIS estimator has only been established in very restricted cases. Furthermore, the high computational complexity of the re-weighting in AMIS (called balance heuristic) makes it expensive for applications involving diffusion processes. In this work we consider sequential and adaptive importance sampling that is particularly suitable for diffusion processes. We propose a new discarding-re-weighting scheme that is of lower computational complexity, and we prove that the resulting AMIS is consistent. Using numerical experiments, we demonstrate that discarding-re-weighting performs very similar to the balance heuristic, but at a fraction of the computational cost. • A Gallai coloring is a coloring of the edges of a complete graph without rainbow triangles, and a Gallai $k$-coloring is a Gallai coloring that uses $k$ colors. Given an integer $k\ge1$ and graphs $H_1, H_2, \ldots, H_k$, the Gallai-Ramsey number $GR(H_1, H_2, \ldots, H_k)$ is the least integer $n$ such that every Gallai $k$-coloring of the complete graph $K_n$ contains a monochromatic copy of $H_i$ in color $i$ for some $i \in \{1,2, \ldots, k\}$. When $H = H_1 = \cdots = H_k$, we simply write $GR_k(H)$. We study Gallai-Ramsey numbers of even cycles and paths. For all $n\ge3$ and $k\ge1$, let $G_i=P_{2i+3}$ be a path on $2i+3$ vertices for all $i\in\{0,1, \ldots, n-2\}$ and $G_{n-1}\in\{C_{2n}, P_{2n+1}\}$. Let $i_j\in\{0,1,\ldots, n-1 \}$ for all $j\in\{1,2, \ldots, k\}$ with $i_1\ge i_2\ge\cdots\ge i_k$. The first author recently conjectured that $GR(G_{i_1}, G_{i_2}, \ldots, G_{i_k}) = 3+\min\{i_1,n^-2\}+\sum_{j=1}^k i_j$, where $n^* =n$ when $G_{i_1}\ne P_{2n+1}$ and $n^* =n+1$ when $G_{i_1}= P_{2n+1}$. The truth of this conjecture implies that $GR_k(C_{2n})=GR_k(P_{2n})=(n-1)k+n+1$ for all $n\ge3$ and $k\ge1$, and $GR_k(P_{2n+1})=(n-1)k+n+2$ for all $n\ge1$ and $k\ge1$. In this paper, we prove that the aforementioned conjecture holds for $n\in\{3,4\}$ and all $k\ge1$. Our proof relies only on Gallai's result and the classical Ramsey numbers $R(H_1, H_2)$, where $H_1, H_2\in\{C_8, C_6, P_7, P_5, P_3\}$. We believe the recoloring method we developed here will be very useful for solving subsequent cases, and perhaps the conjecture. • The Kuramoto--Sakaguchi model is a modification of the well-known Kuramoto model that adds a phase-lag paramater, or "frustration" to a network of phase-coupled oscillators. The Kuramoto model is a flow of gradient type, but adding a phase-lag breaks the gradient structure, significantly complicating the analysis of the model. We present several results determining the stability of phase-locked configurations: the first of these gives a sufficient condition for stability, and the second a sufficient condition for instability. (In fact, the instability criterion gives a count, modulo 2, of the dimension of the unstable manifold to a fixed point and having an odd count is a sufficient condition for instability of the fixed point.) We also present numerical results for both small and large collections of Kuramoto--Sakaguchi oscillators. • We study transportation networks controlled by dynamical feedback tolls. We consider a multiscale model in which the dynamics of the traffic flows are intertwined with those of the drivers' route choices. The latter are influenced by the congestion status of the whole network as well as decentralized congestion-dependent tolls. Our main result shows that positive increasing decentralized congestion-dependent tolls allow the system planner to globally stabilise the transportation network around the Wardrop equilibrium. Moreover, using the decentralized marginal costs tolls the stability of the transportation network is around the social optimum traffic assignment.This particularly remarkable as such feedback tolls do not require any global information about the network structure or state and can be computed in a fully local way. We also extend this stability analysis to a constant decentralised feedback tolls and compare their performance both asymptotic and during the transient through numerical simulations. • In The factorization of the Giry monad (arXiv:1707.00488v2) the author considers two $\sigma$-algebras on convex spaces of functions to the unit interval. One of them is generated by the Boolean subobjects and the other is the $\sigma$-algebra induced by the evaluation maps. The author asserts that, under the assumptions given in the paper, the two $\sigma$-algebras coincide. We give examples contradicting this statement. • In this article, left g, h-derivation and Jordan left g, h-derivation on algebras are introduced. It is shown that there is no Jordan left g, h-derivation over $\mathcal{M}_n(C)$ and $\mathbb{H}_{\mathbb{R}}$, for g not equal to h. Examples are given which show that every Jordan left $\{g, h\}$-derivation over $\mathcal{T}_n(C)$, $\mathcal{M}_n(C)$ and $\mathbb{H}_{\mathbb{R}}$ are not left $\{g, h\}$-derivations. Moreover, we characterize left $\{g, h\}$-derivation and Jordan left $\{g, h\}$-derivation over $\mathcal{T}_n(C)$, $\mathcal{M}_n(C)$ and $\mathbb{H}_{\mathbb{R}}$ respectively. Also, we prove the result of Jordan left $\{g, h\}$-derivation to be a left $\{g, h\}$-derivation over tensor products of algebras as well as for algebra of polynomials. • We confirm Demailly's conjecture on the convergence of higher Lelong numbers under the canonical approximation of a plurisubharmonic function in the case when the function is toric and in the Cegrell class. As applications to convex geometry, we give a unified analytic proof of the Alexandrov-Fenchel inequalities for mixed Monge-Ampère masses, mixed covolumes and mixed multiplicities. • In this paper, we deal with the following nonlinear Schrödinger equation $$-\epsilon^2∆u+V(x)u=f(u),\ u∈H^1(\mathbb R^2),$$ where $f(t)$ has critical growth of Trudinger-Moser type. By using the variational techniques, we construct a positive solution $u_\epsilon$ concentrating around the saddle points of the potential $V(x)$ as $\epsilon\rightarrow 0$. Our results complete the analysis made in \citeMR2900480 and \citeMR3426106, where the Schrödinger equation was studied in $\mathbb R^N$, $N\geq 3$ for sub-critical and critical case respectively in the sense of Sobolev embedding. Moreover, we relax the monotonicity condition on the nonlinear term $f(t)/t$ together with a compactness assumption on the potential $V(x)$, imposed in \citeMR3503193. • In this article, we show that every Jordan g, h-derivation over T_n(C) is a g, h-derivation under an assumption, where C is a commutative ring with unity 1 not equal to 0. We give an example of a Jordan g, h-derivation over T_n(C) which is not a g, h-derivation. Also, we study Jordan g, h-derivation over M_n(C). • Let C be a commutative ring with unity. In this article, we show that every Jordan derivation over an upper triangular matrix algebra T_n(C) is an inner derivation. Further, we extend the result for Jordan derivation on full matrix algebra M_n(C). Danial Dervovic Mar 01 2018 12:08 UTC Hello again Māris, many thanks for your patience. Your comments and questions have given me much food for thought, and scope for an amended version of the paper -- please see my responses below. Please if any of the authors of [AST17 [arXiv:1712.01609](https://arxiv.org/abs/1712.01609)] have any fu ...(continued) Danial Dervovic Feb 05 2018 15:03 UTC Thank you Māris for the extremely well thought-out and articulated points here. I think this very clearly highlights the need to think explicitly about the precompute time if using the lifting to directly simulate the quantum walk, amongst other things. I wish to give a well-considered respons ...(continued) Māris Ozols Feb 01 2018 17:53 UTC This paper considers the problem of using "lifted" Markov chains to simulate the mixing of coined quantum walks. The Markov chain has to approximately (in the total variational distance) sample from the distribution obtained by running the quantum walk for a randomly chosen time $t \in [0,T]$ follow ...(continued) Marco Piani Jan 28 2018 11:21 UTC Hi Mizanur, thanks to you for taking into account my comment. I am not sure of the jargon and nomenclature in mathematics; are/were the maps that are completely positive and also completely co-positive known as PPT maps? What I was pointing out is that in the quantum information community the nam ...(continued) Mizanur Rahaman Jan 27 2018 19:06 UTC Hi Marco, thanks for pointing out the possible confusion. I will make it clear in the revised version. I think in this context what I should clearly state is that I am considering linear maps which are completely positive and co-completely positive, that is, the map \Phi and \Phi\circleT are compl ...(continued) Marco Piani Jan 24 2018 03:34 UTC Great work! One thing that might potentially confuse readers is the use of "PPT channel" to indicate that the partial action of the channel produces a PPT state. There might be some ambiguity in literature, but many call "PPT channels" those channels that act jointly on two parties, and that preserv ...(continued) Mizanur Rahaman Jan 23 2018 23:20 UTC Thanks for the comment. I was not aware of the "entanglement breaking index" paper. I will include it in a revised version. I will make a remark about the other deduction as well. Thanks. Ludovico Lami Jan 19 2018 00:08 UTC Very nice work, congratulations! I just want to point out that the "index of separability" had already been defined in arXiv:1411.2517, where it was called "entanglement-breaking index" and studied in some detail. The channels that have a finite index of separability had been dubbed "entanglement-sa ...(continued) Steve Flammia Dec 18 2017 20:59 UTC It splits into even and odd cases, actually. I was originally sloppy about the distinction between integer and polynomial division, but it's fixed now. There is a little room left in the case $d=3$ now though, but it's still proven in every other dimension. Aram Harrow Dec 18 2017 19:30 UTC whoa, awesome! But why do you get that $d^3-d$ must be a divisor instead of $(d^3-d)/2$?	2018-03-22 21:47:02	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7625571489334106, "perplexity": 345.7460931053173}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-13/segments/1521257648003.58/warc/CC-MAIN-20180322205902-20180322225902-00182.warc.gz"}