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http://sourceforge.net/mailarchive/message.php?msg_id=5386947 | 1,386,906,146,000,000,000 | text/html | crawl-data/CC-MAIN-2013-48/segments/1386164844212/warc/CC-MAIN-20131204134724-00055-ip-10-33-133-15.ec2.internal.warc.gz | 173,568,595 | 13,584 | Re: [Deinterlace-discuss] Both video deinterlace algorithms now supported From: Mark Rejhon - 2000-10-30 04:03 ```Some more that trips things up....that will require sector-based deinterlacing, even horizontally... - Weather shows, where weatherman moves and stops moving (Causes graphics to intermittently flicker when he is moving) - TV guide channel. Right-hand-side is video advertisements, and left hand is sharp TV guide graphics. - Small video windows in the middle of graphics - News conferences - Advertisements We definitely need zone-based CombFactor! Mark Rejhon wrote: > > Another scenario that needs zone-based deinterlacing: > > Golf balls flying through a blank sky. > > Currently, this executes a weave algorithm, which makes the golf > ball break up into weave artifacts. If we had zone based > deinterlacing, the sky would be weaved (with new algoirthm) > while the golf ball would be bobbed (with the old algorithm). > > (Right now, as it stands, golf balls look downright ugly in > this version. ;) > > Mark Rejhon wrote: > > > > Hi Steve, > > > > You're amazing! This is a reasonable compromise between the > > old one (better for motion) and the new one (better for motioneless). > > It's not a perfect compromise but I think this warrants a new release > > very shortly. I think we should make this Version 1.9.1 ;) > > What do you think? > > > > //// > > > > I have an idea... How about doing both algorithms on the > > same image? That is, use the old algorithm for blocks > > of image that is in motion, and use the new algorithm > > for blocks of image that is stationary. Perhaps 4x16 > > pixel blocks or something. > > > > To do this, will require GetCombFactor to produce a new > > buffer that holds a 2-dimensional array of CombFactor's > > to represent different blocks of image. > > > > Then CombFactor would return both a full-screen CombFactor, > > but also return a 2-dimensional CombFactor array that > > represents the CombFactor of small image blocks of a > > custom defined size (like 4x4 pixels, 8x8 pixels, > > 4x16 pixels). > > > > That way, we can execute the new algorithm on blocks that > > have a low CombFactor .... And the old algorithm on blocks > > that have a high CombFactor .... > > > > What do you think, Steve Grimm? ;-) > > > > Please comment if this idea is feasible! > _______________________________________________ > Deinterlace-discuss mailing list > Deinterlace-discuss@... > http://lists.sourceforge.net/mailman/listinfo/deinterlace-discuss -- _______________________________________________________________________ ____ Mark D. Rejhon Win2k.Linux.Win98 \ / mailto:marky@... http://www.marky.com/ C.C++.VB.Shell \/ AlphaWorld Home 10S 15W "A friend is someone who will be there without asking anything of you. A friend is someone you know that knows you, and accepts you." _______________________________________________________________________ ```
[Deinterlace-discuss] Both video deinterlace algorithms now supported Steven Grimm <koreth@mi...>
Re: [Deinterlace-discuss] Both video deinterlace algorithms now supported From: Mark Rejhon - 2000-10-29 23:24 ```Hi Steve, You're amazing! This is a reasonable compromise between the old one (better for motion) and the new one (better for motioneless). It's not a perfect compromise but I think this warrants a new release very shortly. I think we should make this Version 1.9.1 ;) What do you think? //// I have an idea... How about doing both algorithms on the same image? That is, use the old algorithm for blocks of image that is in motion, and use the new algorithm for blocks of image that is stationary. Perhaps 4x16 pixel blocks or something. To do this, will require GetCombFactor to produce a new buffer that holds a 2-dimensional array of CombFactor's to represent different blocks of image. Then CombFactor would return both a full-screen CombFactor, but also return a 2-dimensional CombFactor array that represents the CombFactor of small image blocks of a custom defined size (like 4x4 pixels, 8x8 pixels, 4x16 pixels). That way, we can execute the new algorithm on blocks that have a low CombFactor .... And the old algorithm on blocks that have a high CombFactor .... What do you think, Steve Grimm? ;-) Please comment if this idea is feasible! //// Steven Grimm wrote: > > I've changed the code so both deinterlace algorithms are available. > I called the new algorithm "Video Deinterlace (Weave)" and the old > one "Video Deinterlace (Bob)" to indicate their tendencies to err > on the side of weaving or bobbing. > > The autodetect code selects between the two algorithms by looking > at the field difference. I'm currently using the same thresholds > as the 3:2 pulldown detection, which may or may not be a bright idea. > The basic idea, ignoring 3:2 pulldown for the sake of clarity, is > > if difference > Threshold32Pulldown > if difference > ThresholdPulldownMismatch > video-bob mode > else if it's been low for a few fields > video-weave mode > else > if it's been low for StaticImageFieldCount fields > simple-weave mode > else > video-weave mode > > I raised the StaticImageFieldCount default to 100 since going from > video-weave to simple-weave doesn't improve image quality, it just > cuts down on CPU time. > > This appears to work okay, though it goes into video-bob mode a bit > more than I'd like. This may be a matter of poor choice of thresholds, > but what I'd really like to do is get both the field difference and > the comb factor for each new field, and base the decision of which > video deinterlace algorithm to use on the comb factor. Trouble is, > we don't ordinarily compute the comb factor right now, so adding that > would make the mode detection eat more CPU time. > > What we ought to do, I think, is merge CompareFields() and > GetCombFactor() into one function, since they repeat each other's > work to some extent. The PAL code would benefit from this as well; > right now its autodetection is only based on comb factor, never > field difference. > > Oh, one other tweak that makes life a lot nicer: I added a > shift+spacebar accelerator to cycle backwards through the deinterlace > modes. That way you don't have to walk through all the film modes > to get from one video mode to another. > > -Steve > _______________________________________________ > Deinterlace-discuss mailing list > Deinterlace-discuss@... > http://lists.sourceforge.net/mailman/listinfo/deinterlace-discuss -- _______________________________________________________________________ ____ Mark D. Rejhon Win2k.Linux.Win98 \ / mailto:marky@... http://www.marky.com/ C.C++.VB.Shell \/ AlphaWorld Home 10S 15W "A friend is someone who will be there without asking anything of you. A friend is someone you know that knows you, and accepts you." _______________________________________________________________________ ```
Re: [Deinterlace-discuss] Both video deinterlace algorithms now supported From: Mark Rejhon - 2000-10-29 23:46 ```Hi, I keep seeing many examples why we need zone-based deinterlacing; Sports graphics, network logos, popup namecards, captions, etc, whenever there's intermittent motion. The jagged come back and dissappear as it switches between the two algorithms depending on the amount of motion elsewhere in the image. Either way, your idea of using both algorithms is a pretty neat compromise! Though I'd love you to improve upon that further by using the zone-based deinterlacing suggestion that I illustrated below! Maybe someday, down the road, you can replace the two algorithms with one that blends between the old one and the new one, depending on the CombFactor of each zone (mini block) of the image. Thanks, Mark Rejhon Mark Rejhon wrote: > > Hi Steve, > > You're amazing! This is a reasonable compromise between the > old one (better for motion) and the new one (better for motioneless). > It's not a perfect compromise but I think this warrants a new release > very shortly. I think we should make this Version 1.9.1 ;) > What do you think? > > //// > > I have an idea... How about doing both algorithms on the > same image? That is, use the old algorithm for blocks > of image that is in motion, and use the new algorithm > for blocks of image that is stationary. Perhaps 4x16 > pixel blocks or something. > > To do this, will require GetCombFactor to produce a new > buffer that holds a 2-dimensional array of CombFactor's > to represent different blocks of image. > > Then CombFactor would return both a full-screen CombFactor, > but also return a 2-dimensional CombFactor array that > represents the CombFactor of small image blocks of a > custom defined size (like 4x4 pixels, 8x8 pixels, > 4x16 pixels). > > That way, we can execute the new algorithm on blocks that > have a low CombFactor .... And the old algorithm on blocks > that have a high CombFactor .... > > What do you think, Steve Grimm? ;-) > > Please comment if this idea is feasible! ```
Re: [Deinterlace-discuss] Both video deinterlace algorithms now supported From: Mark Rejhon - 2000-10-29 23:48 ```Another observation... I notice that in football games, as there is horizontal motion, there is steaking (trailing ghosts) of the 5-yard bars. Hitting the P pause key while a footbal game is panning horizontally quickly, confirms this. Also, sometimes I see combing artifacts between red and green of the same luminousity. I can just about notice these combing artifacts (even sometimes with the old algorithm). For faster computers, we probably should think about checking chroma too, not just luma. We definitely need an architecture of multiple algorithms that are easy to add without interfering with existing ones.... That way people (like you) can experiment with adding new algorithms that may require a faster computer! _______________________________________________________________________ ____ Mark D. Rejhon Win2k.Linux.Win98 \ / mailto:marky@... http://www.marky.com/ C.C++.VB.Shell \/ AlphaWorld Home 10S 15W "A friend is someone who will be there without asking anything of you. A friend is someone you know that knows you, and accepts you." _______________________________________________________________________ ```
Re: [Deinterlace-discuss] Both video deinterlace algorithms now supported From: Mark Rejhon - 2000-10-29 23:56 ```Another scenario that needs zone-based deinterlacing: Golf balls flying through a blank sky. Currently, this executes a weave algorithm, which makes the golf ball break up into weave artifacts. If we had zone based deinterlacing, the sky would be weaved (with new algoirthm) while the golf ball would be bobbed (with the old algorithm). (Right now, as it stands, golf balls look downright ugly in this version. ;) Mark Rejhon wrote: > > Hi Steve, > > You're amazing! This is a reasonable compromise between the > old one (better for motion) and the new one (better for motioneless). > It's not a perfect compromise but I think this warrants a new release > very shortly. I think we should make this Version 1.9.1 ;) > What do you think? > > //// > > I have an idea... How about doing both algorithms on the > same image? That is, use the old algorithm for blocks > of image that is in motion, and use the new algorithm > for blocks of image that is stationary. Perhaps 4x16 > pixel blocks or something. > > To do this, will require GetCombFactor to produce a new > buffer that holds a 2-dimensional array of CombFactor's > to represent different blocks of image. > > Then CombFactor would return both a full-screen CombFactor, > but also return a 2-dimensional CombFactor array that > represents the CombFactor of small image blocks of a > custom defined size (like 4x4 pixels, 8x8 pixels, > 4x16 pixels). > > That way, we can execute the new algorithm on blocks that > have a low CombFactor .... And the old algorithm on blocks > that have a high CombFactor .... > > What do you think, Steve Grimm? ;-) > > Please comment if this idea is feasible! ```
Re: [Deinterlace-discuss] Both video deinterlace algorithms now supported From: Steven Grimm - 2000-10-30 00:05 ```I planned to do something similar as part of the as-the-data-arrives video processing mod. It can get even fancier than that, in fact; there's no reason why we can't do pulldown detection, etc. at high granularity as well. Think Mystery Science Theater with the silhouettes in video mode and the rest of the picture in film mode. This should be straightforward and not too terribly expensive to do on a per-scanline basis, which will handle 90% of the cases since scores and captions and stock tickers tend to stretch horizontally across the screen rather than vertically (is that the case for material you watch too?) Doing smaller regions within scanlines may take more horsepower than any of our development systems have, which would obviously make testing a bit of a problem! You can adjust the region size to mitigate that somewhat, but my unsubstantiated gut feel is that for my system, anyway, I'd have to make the regions big enough that the benefit would be questionable. What to show in the status bar when you're half in film mode and half in video mode is the burning question. :) -Steve On Sun, Oct 29, 2000 at 06:28:30PM -0500, Mark Rejhon wrote: > Hi Steve, > > You're amazing! This is a reasonable compromise between the > old one (better for motion) and the new one (better for motioneless). > It's not a perfect compromise but I think this warrants a new release > very shortly. I think we should make this Version 1.9.1 ;) > What do you think? > > //// > > I have an idea... How about doing both algorithms on the > same image? That is, use the old algorithm for blocks > of image that is in motion, and use the new algorithm > for blocks of image that is stationary. Perhaps 4x16 > pixel blocks or something. > > To do this, will require GetCombFactor to produce a new > buffer that holds a 2-dimensional array of CombFactor's > to represent different blocks of image. > > Then CombFactor would return both a full-screen CombFactor, > but also return a 2-dimensional CombFactor array that > represents the CombFactor of small image blocks of a > custom defined size (like 4x4 pixels, 8x8 pixels, > 4x16 pixels). > > That way, we can execute the new algorithm on blocks that > have a low CombFactor .... And the old algorithm on blocks > that have a high CombFactor .... > > What do you think, Steve Grimm? ;-) > > Please comment if this idea is feasible! > ```
Re: [Deinterlace-discuss] Both video deinterlace algorithms now supported From: Steven Grimm - 2000-10-30 00:15 ```On Sun, Oct 29, 2000 at 06:50:03PM -0500, Mark Rejhon wrote: > Maybe someday, down the road, you can replace the two > algorithms with one that blends between the old one and > the new one, depending on the CombFactor of each zone > (mini block) of the image. In fact, I spent most of yesterday doing just that, trying to come up with an algorithm that combined the best of both the current ones. It's trickier than it seems at first blush, and I wasn't able to find a satisfactory solution. I must have gone through at least 10 different algorithms -- some of them did fancy things like delay playback by a frame so they could look ahead at the next frame to see if an apparent weave artifact would still be there next time around. (I think that idea will lead to the optimum algorithm, BTW, but clearly there's some subtle aspect of it that I couldn't figure out.) The problem is that one of the new algorithm's strengths is its ability to render what look like comb artifacts but aren't, like 1-pixel-high horizontal lines. If you naively computed the comb factor of the small region around a horizontal dividing line, you'd get a really high value and thus switch to the old algorithm, making the line flicker like crazy again. -Steve ```
Re: [Deinterlace-discuss] Both video deinterlace algorithms now supported From: Steven Grimm - 2000-10-30 00:36 ```> It's not a perfect compromise but I think this warrants a new release > very shortly. I think we should make this Version 1.9.1 ;) > What do you think? I think all the stuff that's landed in the last couple of days -- a new deinterlace algorithm, triple buffering, proper surface locking, your UI improvements -- really warrants a bigger indication of change. I'd vote for 1.10. (2.0, we can save for subpicture mode detection; if that doesn't warrant a major version number I'm not sure what would.) -Steve ```
Re: [Deinterlace-discuss] Both video deinterlace algorithms now supported From: Mark Rejhon - 2000-10-30 04:03 ```Some more that trips things up....that will require sector-based deinterlacing, even horizontally... - Weather shows, where weatherman moves and stops moving (Causes graphics to intermittently flicker when he is moving) - TV guide channel. Right-hand-side is video advertisements, and left hand is sharp TV guide graphics. - Small video windows in the middle of graphics - News conferences - Advertisements We definitely need zone-based CombFactor! Mark Rejhon wrote: > > Another scenario that needs zone-based deinterlacing: > > Golf balls flying through a blank sky. > > Currently, this executes a weave algorithm, which makes the golf > ball break up into weave artifacts. If we had zone based > deinterlacing, the sky would be weaved (with new algoirthm) > while the golf ball would be bobbed (with the old algorithm). > > (Right now, as it stands, golf balls look downright ugly in > this version. ;) > > Mark Rejhon wrote: > > > > Hi Steve, > > > > You're amazing! This is a reasonable compromise between the > > old one (better for motion) and the new one (better for motioneless). > > It's not a perfect compromise but I think this warrants a new release > > very shortly. I think we should make this Version 1.9.1 ;) > > What do you think? > > > > //// > > > > I have an idea... How about doing both algorithms on the > > same image? That is, use the old algorithm for blocks > > of image that is in motion, and use the new algorithm > > for blocks of image that is stationary. Perhaps 4x16 > > pixel blocks or something. > > > > To do this, will require GetCombFactor to produce a new > > buffer that holds a 2-dimensional array of CombFactor's > > to represent different blocks of image. > > > > Then CombFactor would return both a full-screen CombFactor, > > but also return a 2-dimensional CombFactor array that > > represents the CombFactor of small image blocks of a > > custom defined size (like 4x4 pixels, 8x8 pixels, > > 4x16 pixels). > > > > That way, we can execute the new algorithm on blocks that > > have a low CombFactor .... And the old algorithm on blocks > > that have a high CombFactor .... > > > > What do you think, Steve Grimm? ;-) > > > > Please comment if this idea is feasible! > _______________________________________________ > Deinterlace-discuss mailing list > Deinterlace-discuss@... > http://lists.sourceforge.net/mailman/listinfo/deinterlace-discuss -- _______________________________________________________________________ ____ Mark D. Rejhon Win2k.Linux.Win98 \ / mailto:marky@... http://www.marky.com/ C.C++.VB.Shell \/ AlphaWorld Home 10S 15W "A friend is someone who will be there without asking anything of you. A friend is someone you know that knows you, and accepts you." _______________________________________________________________________ ```
Re: [Deinterlace-discuss] Both video deinterlace algorithms now supported From: Steven Grimm - 2000-10-30 07:07 ```On Sun, Oct 29, 2000 at 11:06:57PM -0500, Mark Rejhon wrote: > We definitely need zone-based CombFactor! There's really no need to convince us... I think we all agree it's a good goal. Now someone just has to do it. Probably won't be me, at least not for a while; I've let a fair bit of real work pile up over the last few days while I've been playing with dTV and I kind of need to catch up now. I'm going to swear off dTV hacking for a while. It's too addictive. :) To encourage others: before I started playing with the deinterlace code last week, I had not written a line of Intel assembly code in about 10 years, had never used an MMX instruction before, and had only a vague idea how the old deinterlace algorithm worked. So it's possible to come up to speed on this stuff in very short order. I've done my best to make it even easier by putting lots of comments in my code; you should be able to follow exactly what it's doing without much effort. Hope someone can step up to the plate and make it happen! -Steve ```
[Deinterlace-discuss] //// NEWS ALERT //// dTV Version 2.0.0 Released! From: Mark Rejhon - 2000-10-30 10:32 ```And here's the release you've been waiting for... We go simultaneously to Version 2.0.0 and to a three-digit version numbering system! Version 2.0.0 Binary - http://deinterlace.sourceforge.net/distributions/dTV200exe.zip Source - http://deinterlace.sourceforge.net/distributions/dTV200src.zip Bug fixed - Tearing is gone at all refresh rates! Bug fixed - Error message no longer pops up if you resize video window too small. Bug fixed - Video no longer becomes purple when resizing or maximizing. Better Automatic Aspect Ratio Detection defaults Smoother Synchronization Triple Buffering Added Option to Disable Startup Splash Screen Changed Keyboard Shortcuts; See List - New shortcuts added for video source and video format selection - Some existing shortcuts modified for better intuition New Video Deinterlace Algorithm - better for slow moving images, especially graphics displays. Old Video Deinterlace Algorithm - still available, better for fast motion. Automatic switching between three Video Deinterlace algorithms: - Simple Weave during static images - New Video Deinterlace during slow moving images - Old Video Deinterlace during fast moving images _______________________________________________________________________ ____ Mark D. Rejhon Win2k.Linux.Win98 \ / mailto:marky@... http://www.marky.com/ C.C++.VB.Shell \/ AlphaWorld Home 10S 15W "A friend is someone who will be there without asking anything of you. A friend is someone you know that knows you, and accepts you." _______________________________________________________________________ ```
[Deinterlace-discuss] Bad 3:2 pulldown worse in dTV 2.0 From: Mark Rejhon - 2000-10-30 21:56 ```Hi, Just so that you know, I notice that the bad 3:2 pulldown rejection capability is worse in dTV version 2 - it looks like we will have to look into this! _______________________________________________________________________ ____ Mark D. Rejhon Win2k.Linux.Win98 \ / mailto:marky@... http://www.marky.com/ C.C++.VB.Shell \/ AlphaWorld Home 10S 15W "A friend is someone who will be there without asking anything of you. A friend is someone you know that knows you, and accepts you." _______________________________________________________________________ ```
[Deinterlace-discuss] Re: //// NEWS ALERT //// dTV Version 2.0.0 Released! From: Michael Eskin - 2000-10-31 20:23 ```Hi Mark, Steven, I've started doing some development work with the new release and I have a fix to a problem with the VxD device enumeration and detection. It doesn't work right if you've had several other boards installed in your system at some point because Win98 leaves old entries in the ENUM/PCI registry area. When you try and do your device detection the current VxD uses the first match of the device ID in the registry, which may not coorespond to the installed device. I've got a fix for the VxD to continue enumerating all devices until if finds a match. I'll figure out how to get it in the project this afternoon. I've joined the sourceforge site, just need to figure out the web based project management. If either of you are interested in coming to work at Conexant in San Diego, I'd like to extend an offer to fly you out for an interview. We have several positions for software engineers in our video products groups and are actively recruiting. Cheers and best regards, Michael Eskin Conexant Systems ```
[Deinterlace-discuss] Re: //// NEWS ALERT //// dTV Version 2.0.0 Released! From: Mark Rejhon - 2000-10-31 20:57 ```Hi, That's great! Let me know if you want instructions on how to access the source code in the CVS repository.... Please say hello to Adrin Kwong, an old Ottawa friend of mine, currently working at Conextant in San Diego! Michael Eskin wrote: > > Hi Mark, Steven, > > I've started doing some development work with the new release and I have a > fix to a problem with the VxD device enumeration and detection. It doesn't > work right if you've had several other boards installed in your system at > some point because Win98 leaves old entries in the ENUM/PCI registry area. > When you try and do your device detection the current VxD uses the first > match of the device ID in the registry, which may not coorespond to the > installed device. I've got a fix for the VxD to continue enumerating all > devices until if finds a match. I'll figure out how to get it in the project > this afternoon. I've joined the sourceforge site, just need to figure out > the web based project management. > > If either of you are interested in coming to work at Conexant in San Diego, > I'd like to extend an offer to fly you out for an interview. We have several > positions for software engineers in our video products groups and are > actively recruiting. > > Cheers and best regards, > > Michael Eskin > Conexant Systems -- _______________________________________________________________________ ____ Mark D. Rejhon Win2k.Linux.Win98 \ / mailto:marky@... http://www.marky.com/ C.C++.VB.Shell \/ AlphaWorld Home 10S 15W "A friend is someone who will be there without asking anything of you. A friend is someone you know that knows you, and accepts you." _______________________________________________________________________ ```
[Deinterlace-discuss] Re: //// NEWS ALERT //// dTV Version 2.0.0 Released! From: Mark Rejhon - 2000-10-31 23:25 ```Hi Michael, Are you on the dTV mailing list? You should send all correspondence to deinterlace-discuss@... instead of just to my email address for quicker response. To join the mailing list, go to: http://sourceforge.net/mail/?group_id=7420 You can also add an email filter to put all mailing list email into a separate folder, so it doesn't clutter up your email. Tom Barry also has had problems sometimes getting dTV running under Windows 2000 - sometimes it would work, and sometimes it would not work. Does your change below, fix this? Michael Eskin wrote: > > Hi Mark, Steven, > > I've started doing some development work with the new release and I have a > fix to a problem with the VxD device enumeration and detection. It doesn't > work right if you've had several other boards installed in your system at > some point because Win98 leaves old entries in the ENUM/PCI registry area. > When you try and do your device detection the current VxD uses the first > match of the device ID in the registry, which may not coorespond to the > installed device. I've got a fix for the VxD to continue enumerating all > devices until if finds a match. I'll figure out how to get it in the project > this afternoon. I've joined the sourceforge site, just need to figure out > the web based project management. > > If either of you are interested in coming to work at Conexant in San Diego, > I'd like to extend an offer to fly you out for an interview. We have several > positions for software engineers in our video products groups and are > actively recruiting. > > Cheers and best regards, > > Michael Eskin > Conexant Systems -- _______________________________________________________________________ ____ Mark D. Rejhon Win2k.Linux.Win98 \ / mailto:marky@... http://www.marky.com/ C.C++.VB.Shell \/ AlphaWorld Home 10S 15W "A friend is someone who will be there without asking anything of you. A friend is someone you know that knows you, and accepts you." _______________________________________________________________________ ```
[Deinterlace-discuss] Michael/Conexant was here ! From: Yvon Quere - 2000-11-02 07:56 ```On Tue, 31 Oct 2000, Michael Eskin wrote: >Hi Mark, Steven, Hi Michael >I've started doing some development work with the new release and I have Great news. Your presence is greatly appreciated and motivating for all people working on this. Thanks to Conexant and to you for being here ! >a fix to a problem with the VxD device enumeration and detection. It Good news, that's a very good start :-) I'm taking the risk of sounding selfish but I'd really like to know more about the whole story of agc and macrovision. Beside dTV, I'd like to know in which way a grab chipset manufacturer "pledges allegiance" to the macrovision copy protection system. Vcr manufacturers are doing so by making their machine reluctant to record things with such signal in it but what about a chipset ? Again, thanks for giving a hand ! Yvon -- Yvon Quere ---------------------------------- |\ _,,,--,,_ ,) - yvon.quere@... /,`.-'`' -, ;-;;' |,4- ) )-,_ ) /\ 01.69.63.17.83 -----------------------------'---''(_/--' (_/-' ------ ``` | 6,823 | 29,067 | {"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} | 2.53125 | 3 | CC-MAIN-2013-48 | latest | en | 0.90164 |
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# Test 1 CheatSheet - Rachel Katz Effective Annual Yield(rate...
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Rachel Katz Effective Annual Yield (rate of return) pure discount bonds: 1 ) ( / 1 - = Τ Π Φς ρ The Bank Discount Yield (r BDY ) is a linearization of the compound interest formula. n FV P FV r BDY 360 ) ( - = FV=face value FV-P=discount *Bank Discount Method Computations -calculations for t-bills, cps and bas Each of these three money market instruments are quoted and calculated on a bank discount basis 1) Computation of Bank Discount (Full Discount) Maturity to Days sis DiscountBa nt FullDiscou - - × = 360 Dollar price = \$100- Full Discount 2) Bank Discount Rate (Discount Basis) Maturity to Days of Number ParValue ice Purchase ParValue - - - - × - 360 Πρ Investment Yield to convert bank discount yield to capital market instruments Full discount X 365/days to maturity answer from prior equation x 1/dollar price 3) Quantitative: Converting discount basis to approximate investment yield ) ( 360 365 Maturity to Days sis DiscountBa sis DiscountBa - - × - × *Bank Discount Method: T-bill, CP and BA Returns PMD=(Purchased Maturity Days) or the number of days to maturity of T-bills, CPs or BAs when purchased DH =(Days Held) or the number of days held; HPRC =(Holding Period Return Change) or alternation in
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Theorem List for Metamath Proof Explorer - 12001-12100 *Has distinct variable group(s)
TypeLabelDescription
Statement
Theoremcjcld 12001 Closure law for complex conjugate. (Contributed by Mario Carneiro, 29-May-2016.)
Theoremreplimd 12002 Construct a complex number from its real and imaginary parts. (Contributed by Mario Carneiro, 29-May-2016.)
Theoremremimd 12003 Value of the conjugate of a complex number. The value is the real part minus times the imaginary part. Definition 10-3.2 of [Gleason] p. 132. (Contributed by Mario Carneiro, 29-May-2016.)
Theoremcjcjd 12004 The conjugate of the conjugate is the original complex number. Proposition 10-3.4(e) of [Gleason] p. 133. (Contributed by Mario Carneiro, 29-May-2016.)
Theoremreim0bd 12005 A number is real iff its imaginary part is 0. (Contributed by Mario Carneiro, 29-May-2016.)
Theoremrerebd 12006 A real number equals its real part. Proposition 10-3.4(f) of [Gleason] p. 133. (Contributed by Mario Carneiro, 29-May-2016.)
Theoremcjrebd 12007 A number is real iff it equals its complex conjugate. Proposition 10-3.4(f) of [Gleason] p. 133. (Contributed by Mario Carneiro, 29-May-2016.)
Theoremcjne0d 12008 A number is nonzero iff its complex conjugate is nonzero. (Contributed by Mario Carneiro, 29-May-2016.)
Theoremrecjd 12009 Real part of a complex conjugate. (Contributed by Mario Carneiro, 29-May-2016.)
Theoremimcjd 12010 Imaginary part of a complex conjugate. (Contributed by Mario Carneiro, 29-May-2016.)
Theoremcjmulrcld 12011 A complex number times its conjugate is real. (Contributed by Mario Carneiro, 29-May-2016.)
Theoremcjmulvald 12012 A complex number times its conjugate. (Contributed by Mario Carneiro, 29-May-2016.)
Theoremcjmulge0d 12013 A complex number times its conjugate is nonnegative. (Contributed by Mario Carneiro, 29-May-2016.)
Theoremrenegd 12014 Real part of negative. (Contributed by Mario Carneiro, 29-May-2016.)
Theoremimnegd 12015 Imaginary part of negative. (Contributed by Mario Carneiro, 29-May-2016.)
Theoremcjnegd 12016 Complex conjugate of negative. (Contributed by Mario Carneiro, 29-May-2016.)
Theoremaddcjd 12017 A number plus its conjugate is twice its real part. Compare Proposition 10-3.4(h) of [Gleason] p. 133. (Contributed by Mario Carneiro, 29-May-2016.)
Theoremcjexpd 12018 Complex conjugate of natural number exponentiation. (Contributed by Mario Carneiro, 29-May-2016.)
Theoremreaddd 12019 Real part distributes over addition. (Contributed by Mario Carneiro, 29-May-2016.)
Theoremimaddd 12020 Imaginary part distributes over addition. (Contributed by Mario Carneiro, 29-May-2016.)
Theoremresubd 12021 Real part distributes over subtraction. (Contributed by Mario Carneiro, 29-May-2016.)
Theoremimsubd 12022 Imaginary part distributes over subtraction. (Contributed by Mario Carneiro, 29-May-2016.)
Theoremremuld 12023 Real part of a product. (Contributed by Mario Carneiro, 29-May-2016.)
Theoremimmuld 12024 Imaginary part of a product. (Contributed by Mario Carneiro, 29-May-2016.)
Theoremcjaddd 12025 Complex conjugate distributes over addition. Proposition 10-3.4(a) of [Gleason] p. 133. (Contributed by Mario Carneiro, 29-May-2016.)
Theoremcjmuld 12026 Complex conjugate distributes over multiplication. Proposition 10-3.4(c) of [Gleason] p. 133. (Contributed by Mario Carneiro, 29-May-2016.)
Theoremipcnd 12027 Standard inner product on complex numbers. (Contributed by Mario Carneiro, 29-May-2016.)
Theoremcjdivd 12028 Complex conjugate distributes over division. (Contributed by Mario Carneiro, 29-May-2016.)
Theoremrered 12029 A real number equals its real part. One direction of Proposition 10-3.4(f) of [Gleason] p. 133. (Contributed by Mario Carneiro, 29-May-2016.)
Theoremreim0d 12030 The imaginary part of a real number is 0. (Contributed by Mario Carneiro, 29-May-2016.)
Theoremcjred 12031 A real number equals its complex conjugate. Proposition 10-3.4(f) of [Gleason] p. 133. (Contributed by Mario Carneiro, 29-May-2016.)
Theoremremul2d 12032 Real part of a product. (Contributed by Mario Carneiro, 29-May-2016.)
Theoremimmul2d 12033 Imaginary part of a product. (Contributed by Mario Carneiro, 29-May-2016.)
Theoremredivd 12034 Real part of a division. Related to remul2 11935. (Contributed by Mario Carneiro, 29-May-2016.)
Theoremimdivd 12035 Imaginary part of a division. Related to remul2 11935. (Contributed by Mario Carneiro, 29-May-2016.)
Theoremcrred 12036 The real part of a complex number representation. Definition 10-3.1 of [Gleason] p. 132. (Contributed by Mario Carneiro, 29-May-2016.)
Theoremcrimd 12037 The imaginary part of a complex number representation. Definition 10-3.1 of [Gleason] p. 132. (Contributed by Mario Carneiro, 29-May-2016.)
5.7.3 Square root; absolute value
Syntaxcsqr 12038 Extend class notation to include square root of a complex number.
Syntaxcabs 12039 Extend class notation to include a function for the absolute value (modulus) of a complex number.
Definitiondf-sqr 12040* Define a function whose value is the square root of a complex number. Since iff , we ensure uniqueness by restricting the range to numbers with positive real part, or numbers with 0 real part and nonnegative imaginary part. A description can be found under "Principal square root of a complex number" at http://en.wikipedia.org/wiki/Square_root. The square root symbol was introduced in 1525 by Christoff Rudolff.
See sqrcl 12165 for its closure, sqrval 12042 for its value, sqrth 12168 and sqsqri 12179 for its relationship to squares, and sqr11i 12188 for uniqueness. (Contributed by NM, 27-Jul-1999.) (Revised by Mario Carneiro, 8-Jul-2013.)
Definitiondf-abs 12041 Define the function for the absolute value (modulus) of a complex number. See abscli 12198 for its closure and absval 12043 or absval2i 12200 for its value. (Contributed by NM, 27-Jul-1999.)
Theoremsqrval 12042* Value of square root function. (Contributed by Mario Carneiro, 8-Jul-2013.)
Theoremabsval 12043 The absolute value (modulus) of a complex number. Proposition 10-3.7(a) of [Gleason] p. 133. (Contributed by NM, 27-Jul-1999.) (Revised by Mario Carneiro, 7-Nov-2013.)
Theoremrennim 12044 A real number does not lie on the negative imaginary axis. (Contributed by Mario Carneiro, 8-Jul-2013.)
Theoremcnpart 12045 The specification of restriction to the right half-plane partitions the complex plane without 0 into two disjoint pieces, which are related by a reflection about the origin (under the map ). (Contributed by Mario Carneiro, 8-Jul-2013.)
Theoremsqr0lem 12046 Square root of zero. (Contributed by Mario Carneiro, 9-Jul-2013.)
Theoremsqr0 12047 Square root of zero. (Contributed by Mario Carneiro, 9-Jul-2013.)
Theoremsqrlem1 12048* Lemma for 01sqrex 12055. (Contributed by Mario Carneiro, 10-Jul-2013.)
Theoremsqrlem2 12049* Lemma for 01sqrex 12055. (Contributed by Mario Carneiro, 10-Jul-2013.)
Theoremsqrlem3 12050* Lemma for 01sqrex 12055. (Contributed by Mario Carneiro, 10-Jul-2013.)
Theoremsqrlem4 12051* Lemma for 01sqrex 12055. (Contributed by Mario Carneiro, 10-Jul-2013.)
Theoremsqrlem5 12052* Lemma for 01sqrex 12055. (Contributed by Mario Carneiro, 10-Jul-2013.)
Theoremsqrlem6 12053* Lemma for 01sqrex 12055. (Contributed by Mario Carneiro, 10-Jul-2013.)
Theoremsqrlem7 12054* Lemma for 01sqrex 12055. (Contributed by Mario Carneiro, 10-Jul-2013.)
Theorem01sqrex 12055* Existence of a square root for reals in the interval . (Contributed by Mario Carneiro, 10-Jul-2013.)
Theoremresqrex 12056* Existence of a square root for positive reals. (Contributed by Mario Carneiro, 9-Jul-2013.)
Theoremsqrmo 12057* Uniqueness for the square root function. (Contributed by Mario Carneiro, 9-Jul-2013.) (Revised by NM, 17-Jun-2017.)
Theoremresqreu 12058* Existence and uniqueness for the real square root function. (Contributed by Mario Carneiro, 9-Jul-2013.)
Theoremresqrcl 12059 Closure of the square root function. (Contributed by Mario Carneiro, 9-Jul-2013.)
Theoremresqrthlem 12060 Lemma for resqrth 12061. (Contributed by Mario Carneiro, 9-Jul-2013.)
Theoremresqrth 12061 Square root theorem over the reals. Theorem I.35 of [Apostol] p. 29. (Contributed by Mario Carneiro, 9-Jul-2013.)
Theoremremsqsqr 12062 Square of square root. (Contributed by Mario Carneiro, 10-Jul-2013.)
Theoremsqrge0 12063 The square root function is nonnegative for nonnegative input. (Contributed by NM, 26-May-1999.) (Revised by Mario Carneiro, 9-Jul-2013.)
Theoremsqrgt0 12064 The square root function is positive for positive input. (Contributed by Mario Carneiro, 10-Jul-2013.) (Revised by Mario Carneiro, 6-Sep-2013.)
Theoremsqrmul 12065 Square root distributes over multiplication. (Contributed by NM, 30-Jul-1999.) (Revised by Mario Carneiro, 29-May-2016.)
Theoremsqrle 12066 Square root is monotonic. (Contributed by NM, 17-Mar-2005.) (Proof shortened by Mario Carneiro, 29-May-2016.)
Theoremsqrlt 12067 Square root is strictly monotonic. Closed form of sqrlti 12193. (Contributed by Scott Fenton, 17-Apr-2014.) (Proof shortened by Mario Carneiro, 29-May-2016.)
Theoremsqr11 12068 The square root function is one-to-one. (Contributed by Scott Fenton, 11-Jun-2013.)
Theoremsqr00 12069 A square root is zero iff its argument is 0. (Contributed by NM, 27-Jul-1999.) (Proof shortened by Mario Carneiro, 29-May-2016.)
Theoremrpsqrcl 12070 The square root of a positive real is a postive real. (Contributed by NM, 22-Feb-2008.)
Theoremsqrdiv 12071 Square root distributes over division. (Contributed by Mario Carneiro, 5-May-2016.)
Theoremsqrneglem 12072 The square root of a negative number. (Contributed by Mario Carneiro, 9-Jul-2013.)
Theoremsqrneg 12073 The square root of a negative number. (Contributed by Mario Carneiro, 9-Jul-2013.)
Theoremsqrsq2 12074 Relationship between square root and squares. (Contributed by NM, 31-Jul-1999.) (Revised by Mario Carneiro, 29-May-2016.)
Theoremsqrsq 12075 Square root of square. (Contributed by NM, 14-Jan-2006.) (Revised by Mario Carneiro, 29-May-2016.)
Theoremsqrmsq 12076 Square root of square. (Contributed by NM, 2-Aug-1999.) (Revised by Mario Carneiro, 29-May-2016.)
Theoremsqr1 12077 The square root of 1 is 1. (Contributed by NM, 31-Jul-1999.)
Theoremsqr4 12078 The square root of 4 is 2. (Contributed by NM, 3-Aug-1999.)
Theoremsqr9 12079 The square root of 9 is 3. (Contributed by NM, 11-May-2004.)
Theoremsqr2gt1lt2 12080 The square root of 2 is bounded by 1 and 2. (Contributed by Roy F. Longton, 8-Aug-2005.) (Revised by Mario Carneiro, 6-Sep-2013.)
Theoremsqrm1 12081 The imaginary unit is the square root of negative 1. A lot of people like to call this the "definition" of , but the definition of df-sqr 12040 has already been crafted with being mentioned explicitly, and in any case it doesn't make too much sense to define a value based on a function evaluated outside its domain. A more appropriate view is to take ax-i2m1 9058 or i2 11481 as the "definition", and simply postulate the existence of a number satisfying this property. This is the approach we take here. (Contributed by Mario Carneiro, 10-Jul-2013.)
Theoremabsneg 12082 Absolute value of negative. (Contributed by NM, 27-Feb-2005.)
Theoremabscl 12083 Real closure of absolute value. (Contributed by NM, 3-Oct-1999.)
Theoremabscj 12084 The absolute value of a number and its conjugate are the same. Proposition 10-3.7(b) of [Gleason] p. 133. (Contributed by NM, 28-Apr-2005.)
Theoremabsvalsq 12085 Square of value of absolute value function. (Contributed by NM, 16-Jan-2006.)
Theoremabsvalsq2 12086 Square of value of absolute value function. (Contributed by NM, 1-Feb-2007.)
Theoremsqabsadd 12087 Square of absolute value of sum. Proposition 10-3.7(g) of [Gleason] p. 133. (Contributed by NM, 21-Jan-2007.)
Theoremsqabssub 12088 Square of absolute value of difference. (Contributed by NM, 21-Jan-2007.)
Theoremabsval2 12089 Value of absolute value function. Definition 10.36 of [Gleason] p. 133. (Contributed by NM, 17-Mar-2005.)
Theoremabs0 12090 The absolute value of 0. (Contributed by NM, 26-Mar-2005.) (Revised by Mario Carneiro, 29-May-2016.)
Theoremabsi 12091 The absolute value of the imaginary unit. (Contributed by NM, 26-Mar-2005.)
Theoremabsge0 12092 Absolute value is nonnegative. (Contributed by NM, 20-Nov-2004.) (Revised by Mario Carneiro, 29-May-2016.)
Theoremabsrpcl 12093 The absolute value of a nonzero number is a positive real. (Contributed by FL, 27-Dec-2007.) (Proof shortened by Mario Carneiro, 29-May-2016.)
Theoremabs00 12094 The absolute value of a number is zero iff the number is zero. Proposition 10-3.7(c) of [Gleason] p. 133. (Contributed by NM, 26-Sep-2005.) (Proof shortened by Mario Carneiro, 29-May-2016.)
Theoremabs00ad 12095 A complex number is zero iff its absolute value is zero. Deduction form of abs00 12094. (Contributed by David Moews, 28-Feb-2017.)
Theoremabs00bd 12096 If a complex number is zero, its absolute value is zero. Converse of abs00d 12248. One-way deduction form of abs00 12094. (Contributed by David Moews, 28-Feb-2017.)
Theoremabsreimsq 12097 Square of the absolute value of a number that has been decomposed into real and imaginary parts. (Contributed by NM, 1-Feb-2007.)
Theoremabsreim 12098 Absolute value of a number that has been decomposed into real and imaginary parts. (Contributed by NM, 14-Jan-2006.)
Theoremabsmul 12099 Absolute value distributes over multiplication. Proposition 10-3.7(f) of [Gleason] p. 133. (Contributed by NM, 11-Oct-1999.) (Revised by Mario Carneiro, 29-May-2016.)
Theoremabsdiv 12100 Absolute value distributes over division. (Contributed by NM, 27-Apr-2005.)
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https://community.tableau.com/message/178156 | 1,506,326,261,000,000,000 | text/html | crawl-data/CC-MAIN-2017-39/segments/1505818690376.61/warc/CC-MAIN-20170925074036-20170925094036-00135.warc.gz | 659,129,898 | 27,752 | 4 Replies Latest reply on Dec 12, 2014 2:10 AM by Karthik Venkatraman
# Projections or simple forecasts in Tableau
I’m trying to find a way in Tableau to show projections out to year end based on a rolling three month average. I want to do the calculations in Tableau and avoid creating the projections outside of Tableau. I’m not seeing a way to even get started on this, and so far haven’t found anything online that addresses the problem. Can you give me some guidance? Have attached a sample data set and workbook.
• ###### 1. Re: Projections or simple forecasts in Tableau
Hi Lyle,
I thought this was going to be a relatively easy case of projection similar to this post here, http://community.tableau.com/thread/117629, however it's not. I was stubborn enough to figure something out, it's a hack but it works. Maybe someone like Richard Leeke would have another idea.
The first part is to generate a list of months, I have one around that I use in other projection and reporting, you canuse your own or generate one in SQL. That becomes the primary datasource, with the revenue data in the secondary datasource. Now Tableau will have a list of months going out to the end of the year that it can use.
The next part is where things get really messy. In the sample data you indicated that you wanted to return actuals when there was an actual, and then have the projections be based on the prior three months of actuals or projections. So the projection calculation is not a linear function like in the post I linked to, it's an iterative calculation.
And Tableau doesn't have much for iterative functions.
Tableau has a PREVIOUS_VALUE() function that returns the previous value of the same variable, so you can use it for a form of iteration. However, in your case you need a three month rolling average and PREVIOUS_VALUE() can't go two or three months back. There's a LOOKUP() function that will let you go back and forth across the data for fields, but it returns a circular reference error if you try to set up a calculated field to LOOKUP() itself.
Since there are only twelve months in a year, it was feasible to create a series of iterative calculations, each feeding the next, to generate the correct set of values.
Here's the first calc:
// if there's only January, then return the rev for January for all rows
IF [index of last date of rev] = 1 THEN
PREVIOUS_VALUE(SUM([rev]))
//for January & Feb, return the data for first two rows or the average of the 2 months
ELSEIF [index of last date of rev] = 2 THEN
IF INDEX() <= 2 THEN
SUM([rev])
ELSE
WINDOW_SUM(SUM([rev]),FIRST(),FIRST()+1)/2
END
//otherwise we have 3 or more months of data, in that case return rev
ELSEIF NOT ISNULL(ATTR([rev])) THEN
SUM([rev])
//now we're into the first month w/out data, so look back at three months to generate a projection
ELSEIF NOT ISNULL(LOOKUP(ATTR([rev]),-1) ) THEN
WINDOW_SUM(SUM([rev]),-3,-1)/3
//next into the 2nd month w/out data
//use the last two months with data and the previous value of iterate rev 1
//unfortunately, we can't get the last N values of iterate rev 1, so we need more variables
//move on to iterate rev 2
ELSEIF NOT ISNULL(LOOKUP(ATTR([rev]),-2)) THEN
(WINDOW_SUM(SUM([rev]),-3,-2) + PREVIOUS_VALUE(0))/3
END
Now, here's iterate rev 2:
//we start with getting all the existing values of iterate rev 1
IF NOT ISNULL([iterate rev 1]) THEN
[iterate rev 1]
//then for the first month without data or a projection, we make up a projection using the last three values
ELSEIF NOT ISNULL(LOOKUP([iterate rev 1],-1) ) THEN
WINDOW_SUM([iterate rev 1],-3,-1)/3
//then we can generate a 2nd projection using the last two values and the previous value of iterate rev 2
ELSEIF NOT ISNULL(LOOKUP([iterate rev 1],-2)) THEN
(WINDOW_SUM([iterate rev 1],-3,-2) + PREVIOUS_VALUE(0))/3
END
Then we move on all the way up to iterate rev 5. That's the calculation that you'd use to show the actuals and projection, and set the Compute Using to date (i.e. the month). That way when you go to use the calc in a line chart like in the "line chart" view, the calc and all its subcalculations will still work.
Jonathan
1 of 1 people found this helpful
• ###### 2. Re: Projections or simple forecasts in Tableau
I don't think you're missing an easy way, Jonathan - or at least I can't see it.
The issue is that this really needs recursive functions, I think.
I did have a quick think about whether I could do more of the work in a custom SQL connection, or with RAWSQL - but once again, the need for recursion makes that hard. About the only way I know of doing recursive calculations in SQL is in some circumstances you can do it with Common Table Expressions - but you can't use CTEs in a Custom SQL connection (unless perhaps if you hide them in a view).
Unlike you, Jonathan, I gave up at that point.
By the way - I like this service you're providing of picking out the gnarly questions and pinging me to have a look, Jonathan - I just don't have time to do more than skim the subject lines to see if something catches my eye at the moment. Thanks for that!
• ###### 3. Re: Projections or simple forecasts in Tableau
Richard - Thanks for the look, and you're welcome for the pings!
• ###### 4. Re: Projections or simple forecasts in Tableau
Hi Jonathan,
I saw your reply for this post. I also need a assistance related to a forecasting technique i need. I have posted my question in this forum and below is the link for that.
Forecast Data for next 3 month using Moving Average Meathod
I tried to implement your codes that you have posted here but i was not able to achieve what i need.
Can you plese help me? | 1,406 | 5,679 | {"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} | 2.515625 | 3 | CC-MAIN-2017-39 | longest | en | 0.933926 |
https://mathoverflow.net/questions/117081/if-rational-points-are-like-entire-curves-then-what-do-algebraic-points-corresp | 1,606,405,644,000,000,000 | text/html | crawl-data/CC-MAIN-2020-50/segments/1606141188800.15/warc/CC-MAIN-20201126142720-20201126172720-00460.warc.gz | 386,940,505 | 28,595 | # If rational points are like entire curves, then what do algebraic points correspond to
I read somewhere that if $X$ is a projective variety of general type over a number field $K$, then rational points are an analogue of entire curves $\mathbf{C}\to X^{an}$ (with $X^{an}$ the analytification of $X_{\mathbf{C}}$ for some $K\to \mathbf C$).
Rational points are algebraic points of degree $1$ on $X$ and they "correspond" to entire curves.
Naive question:
Let $m\geq 2$. What do algebraic points of degree $m$ on $X$ "correspond" to?
• In the analogy between Nevanlinna theory and Diophantine Geometry suggested by Vojta, an entire curve corresponds to an infinite set of rational points, not to just a point. See Vojta's book LNM 1239 Ch 3. Vojta discusses algebraic points of bounded degree but does not explicitly state an analogy. – Felipe Voloch Dec 23 '12 at 16:21
Rational points are (kind of) like maps from a fixed curve (say P^1) to X.
Algebraic points of degree m are like curves endowed with a map to X and a degree-m map to P^1.
• That seems reasonable. Just to convince myself a bit more. Let $X$ be curve of genus at least $two$ over a number field $K$ of big gonality. Then the set of quadratic points on $X$ is finite by Faltings-Frey. In particular, this should correspond to the fact that there are only finitely many hyperelliptic curves dominating $X$. And that of course follows from the big gonality of $X$. (Actually there are no hyp ell curves dominating $X$.) So ok, I'm convinced that this "works". – Masse Dec 23 '12 at 16:22
• @Masse: Actually, for quadratic points, gonality is sharp. In other words, if X is not hyperelliptic, then it has only finitely many quadratic points. My recollection is that the same is true for cubics (but I may be misremembering), and in any case, it's not true in general for higher degree. For references, there are various papers by Joe Harris, Dan Abramovich, and me. (I think that the first one was mine and Joe Harris's that did the quadratic points case.) I'm not quite sure which result of Faltings-Frey you mean, but of course all these results rely on Faltings' Annals paper. – Joe Silverman Dec 24 '12 at 2:51 | 583 | 2,188 | {"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} | 2.796875 | 3 | CC-MAIN-2020-50 | latest | en | 0.929793 |
https://www.gamedev.net/forums/topic/13917-parametric-triangle-representation/ | 1,555,604,468,000,000,000 | text/html | crawl-data/CC-MAIN-2019-18/segments/1555578517745.15/warc/CC-MAIN-20190418161426-20190418183426-00193.warc.gz | 691,170,912 | 26,398 | #### Archived
This topic is now archived and is closed to further replies.
# Parametric Triangle Representation
This topic is 6911 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.
## Recommended Posts
I know this is simple, but I''m having a brain meltdown right now...I''ve looked through all my books I have and can''t seem to find anything regarding parametric representation of triangles. I''ve done a Ray-Triangle intersection test. As a result of a successful intersection, I end up with U & V coordinates for the triangle. Here is my question... How do I compute the X,Y,Z coordinates of the intersection based upon the U & V coordinates? Here is what I''ve done so far. It "feels" correct, but something about the results don''t seem to work 100% of the time V = Triangle Vertex P = Intersection Point Edge1=V1-V0; Edge2=V2-V0; P=V0+Edge1*U+Edge2*V Any pointers will be greatly appreciated. Dean M.
##### Share on other sites
ok.. for ray-triangle intersection (or ray-anything intersection ) it''s easier to work with the Q(t)=Q+vt form, all you have to do is plug that into the plane equation, get the intersection point at Q+vt for the given t and then find out if the intersection point is within the triangle.
i don''t really understand what you mean by "U & V coordinates for the triangle".. are those supposed to be 2d coordinates in the triangle''s plane, or is U an offset along two edges with V being a distance along the resulting vector, or what?
-goltrpoat
--
Float like a butterfly, bite like a crocodile.
##### Share on other sites
The u,v coordinates that you are getting from the intersection are called barycentric coordinates. The x,y,z coordinates are computed with:
P = (1-u-v)*V0 + u*V1 + v*V2
This just happens to be what you have already figured out, just a little rearrangement of the terms.
With the barycentric coordinates it is real easy to test if the point is within the triangle. For the point to be within the following conditions must hold:
u >= 0
v >= 0
u+v <= 1
- WitchLord
##### Share on other sites
Thanks for the help...I updated my code with the correct way to determine the intersection point and I am up and going.
I''m going to have to do some reading up on barycentric coordinates. I''ve seen that term thrown around, but haven''t yet taken the time to actually understand what it is.
If you are curious: I am writing a sort of level editor (non-gaming related, eventually I get around to writing games). It is for architectural walkthroughs. But, game technologies and techniques are exactly what this project calls for.
With this piece of information (the intersection point), I now have 100% accurate polygon selection with the mouse working. I''m able to determine the polygon with the closest intersection point to the camera and highlight it for the user to do something. It is really quite pleasing to see this work perfectly.
Dean M.
p.s. I apologize for posting in the "wrong" forum, I am still learning this board and didn''t actually realize where I was posting, that won''t happen in the future
• 10
• 13
• 52
• 11
• 15 | 755 | 3,156 | {"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} | 3.84375 | 4 | CC-MAIN-2019-18 | latest | en | 0.920496 |
https://chaosbook.org/course1/Course2w15.html | 1,716,803,001,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971059039.52/warc/CC-MAIN-20240527083011-20240527113011-00336.warc.gz | 140,162,380 | 4,073 | ## Week 15
• 29. Discrete symmetry factorization / 26 April 2022 /
• 3 disk pinball symmetries suffice to illustrate all that is needed to factorized spectral determinants for any system with a discrete symmetry: character. Discrete symmetry tiles the state space, and dynamics can be reduced to dynamics on the fundamental domain, together with a finite matrix that keeps track of the tile the full state space trajectory lands on. We need some group theory (one needs to underatand the projection to irreducible representations) and illustrate how different classes of periodic orbits contribute to different invariant subspaces for the 3-disk pinball. Read sects. 25.2 - 25.6.
Chapter 25 Discrete symmetry factorization Factorized spectral determinant Irrep decomposition of the trace Irrep decomposition of the resolvent Irrep factorization of the determinant In 100d the most important is 99d invariant torus Factorization of D3 cycle weights Hard work builds character
• 30. Continuous symmetry factorization / 28 April 2022 bonus lecture /
• Trace formulas relate short time dynamics (unstable periodic orbits) to long time invariant state space densities (natural measure). A trace formula for a partially hyperbolic (N+ 1)-dimensional compact manifold invariant under a global continuous symmetry is derived. In this extension of “periodic orbit” theory there are no or very few periodic orbits - the relative periodic orbits that the trace formula has support on are almost never eventually periodic.
Chapter 26 Continuous symmetry factorization This chapter needs a major revision, the videos are more up-to-date than the chapter itself Group averaging The Great Orthonormality Theorem Average over space and time Discrete time averaging Continuous time averaging If discrete symmetry, average over it If continuous symmetry, average over it
• Homework 15
• discrete factorization Due 28 April 2015 (note!) Discussion forum for week 15
• Optional | 408 | 1,966 | {"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} | 2.53125 | 3 | CC-MAIN-2024-22 | latest | en | 0.857861 |
https://socratic.org/questions/an-arc-of-1-degree-on-earth-s-surface-is-equal-to-how-many-kilometers | 1,579,370,769,000,000,000 | text/html | crawl-data/CC-MAIN-2020-05/segments/1579250593295.11/warc/CC-MAIN-20200118164132-20200118192132-00498.warc.gz | 679,216,817 | 6,216 | # An arc of 1 degree on earth's surface is equal to how many kilometers?
Sep 25, 2016
At the equator, ${1}^{o}$arc length = 111.32 km, nearly. At Baltimore ( $l a t i t u \mathrm{de} = {39.48}^{o} N$), this length is 111.16 km, nearly. At the poles, it is 110.95 km, nearly.
#### Explanation:
The equatorial radius of the Earth is 6378.1 km.
The difference is 21.3 km. The polar radius is 6366.8 km.
At latitude ${\theta}^{o}$ N/S, the radius is $6378.1 - \left(\frac{\theta}{90}\right) \left(21.3\right)$ km,
nearly.
An arc of 1 radian = the radial distance of the the latitude circle, from
the center.of the Earth.
${1}^{o} = \frac{\pi}{180}$ radian.
So, the arc length $= \left(\frac{\pi}{180}\right) \left(6378.1 - \left(\frac{\theta}{90}\right) \left(21.3\right)\right)$ km,
At the equator, $\theta = 0$ and this arc length = 111.32 km, nearly.
At Baltimore, $\theta = {39.48}^{o}$ and the length is 111.16 km, nearly.
At the poles, $\theta = {90}^{o}$ and the length = 110.95 km, nearly.
Note that this arc is along a great circle. If the arc arc is drawn by
traversing along a small circle, the length is less. If this small circle is
the latitude circle, apply a factor cos (latitude). | 400 | 1,210 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 9, "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} | 4.28125 | 4 | CC-MAIN-2020-05 | longest | en | 0.815228 |
https://tutorial.math.lamar.edu/Solutions/Alg/SolveQuadraticEqnsI/Prob6.aspx | 1,685,768,185,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224649105.40/warc/CC-MAIN-20230603032950-20230603062950-00419.warc.gz | 652,612,472 | 15,946 | Paul's Online Notes
Home / Algebra / Solving Equations and Inequalities / Quadratic Equations - Part I
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### Section 2.5 : Quadratic Equations - Part I
6. Solve the following quadratic equation by factoring.
${z^2} - 16z + 61 = 2z - 20$
Show All Steps Hide All Steps
Start Solution
The first thing we need to do is get everything on one side of the equation and then factor the quadratic.
\begin{align*}{z^2} - 18z + 81 & = 0\\ {\left( {z - 9} \right)^2} & = 0\end{align*} Show Step 2
From the factored form we can quickly see that the solution is : $\require{bbox} \bbox[2pt,border:1px solid black]{{z = 9}}$ | 302 | 1,078 | {"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} | 4.09375 | 4 | CC-MAIN-2023-23 | longest | en | 0.840861 |
http://www.gurufocus.com/term/iv_dcf_share/MBND/Intrinsic%2BValue%2B%2528DCF%2BProjected%2529/Multiband%2BCorporation | 1,475,035,144,000,000,000 | text/html | crawl-data/CC-MAIN-2016-40/segments/1474738661296.34/warc/CC-MAIN-20160924173741-00097-ip-10-143-35-109.ec2.internal.warc.gz | 516,984,398 | 26,820 | Switch to:
Multiband Corporation (NAS:MBND)
Intrinsic Value: Projected FCF
\$0.00 (As of Today)
Since the intrinsic value calculations based on Discounted Cash Flow Intrinsic Value: DCF (FCF Based), or Discounted Earnings Intrinsic Value: DCF (Earnings Based) cannot be applied to companies without consistent revenue and earnings, GuruFocus developed a valuation model based on normalized Free Cash Flow and Book Value of the company. The details of how we calculate the intrinsic value of stocks are described in detail here.
As of today, Multiband Corporation's projected FCF intrinsic value is \$0.00. The stock price of Multiband Corporation is \$3.25. Therefore, Multiband Corporation's Price to Intrinsic Value: Projected FCF Ratio of today is 0.0.
Definition
Since the intrinsic value calculations based on Discounted Cash Flow Intrinsic Value: DCF (FCF Based), or Discounted Earnings Intrinsic Value: DCF (Earnings Based) cannot be applied to companies without consistent revenue and earnings, GuruFocus developed a valuation model based on normalized Free Cash Flow and Book Value of the company.
The details of how we calculate the intrinsic value of stocks are described in detail here.
This method smooths out the free cash flow over the past 6-7 years, multiplies the results by a growth multiple, and adds a portion of total equity.
Value = ((Growth Multiple)*Free Cash Flow(6 year avg) + 0.8*Total Equity(most recent))/Shares Outstanding
In the case of negative total equity, the following formula is used (see the Total Equity section for the reason):
Value = ((Growth Multiple)*Free Cash Flow(6 year avg) + Total Equity(most recent)/0.8)/Shares Outstanding
Here Multiband Corporation's FCF(6 year avg) is calculate as
Multiband Corporation Quarterly Data
201103 201106 201109 201112 201203 201206 201209 201212 201303 201306 total_freecashflow 5.3 5.1 3.6 4.6 -5.7 -1.1 2.8 9.3 -2.6 6.8 200809 200812 200903 200906 200909 200912 201003 201006 201009 201012 total_freecashflow 2.9 -0.6 -0.1 -2.8 -2.4 -1.8 3.8 5.6 3.4 -2.3 200709 200712 200803 200806 total_freecashflow -0.8 -0.1 -0.4 1.2
Add all the Free Cash Flow together and divide 6 will get Multiband Corporation's FCF(6 year avg) = \$5.62.
Multiband Corporation's Intrinsic Value: Projected FCF for today is calculated as
Intrinsic Value = (Growth Multiple * Free Cash Flow(6 year avg) + Total Equity(Jun13) * 0.8) / Shares Outstanding = (14.8626533105 * 5.61516666667 + 46.726 * 0.8) / 21.829 = 5.54
* All numbers are in millions except for per share data and ratio. All numbers are in their own currency.
Explanation
The growth multiple is capped between 8.35 and 17.74.
Total equity weighting is more art than science and it should always be revisited in more detail when researching a company. Weightings from 0% to 100% to more than 100% are possible. 80% was chosen as a happy medium after taking the above ideas into consideration. Learn more here.
Multiband Corporation's Price to Intrinsic Value: Projected FCF Ratio for today is calculated as
Price to Intrinsic Value: Projected FCF = Share Price / Intrinsic Value: Projected FCF = 3.25 / 5.53562121248 = 0.59
* All numbers are in millions except for per share data and ratio. All numbers are in their own currency.
Related Terms
Historical Data
* All numbers are in millions except for per share data and ratio. All numbers are in their own currency.
Multiband Corporation Annual Data
Dec03 Dec04 Dec05 Dec06 Dec07 Dec08 Dec09 Dec10 Dec11 Dec12 Projected FCF 0.00 0.00 -3.28 -3.24 -3.46 -1.38 -2.07 1.15 4.06 5.00
Multiband Corporation Quarterly Data
Mar11 Jun11 Sep11 Dec11 Mar12 Jun12 Sep12 Dec12 Mar13 Jun13 Projected FCF 3.08 4.15 3.33 4.06 3.44 3.38 3.80 5.00 4.71 5.54
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GuruFocus Affiliate Program: Earn up to \$400 per referral. ( Learn More) | 1,102 | 3,955 | {"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} | 2.625 | 3 | CC-MAIN-2016-40 | longest | en | 0.848 |
https://code.dennyzhang.com/reshape-the-matrix | 1,563,302,794,000,000,000 | text/html | crawl-data/CC-MAIN-2019-30/segments/1563195524685.42/warc/CC-MAIN-20190716180842-20190716202842-00515.warc.gz | 356,854,356 | 10,535 | # Leetcode: Reshape the Matrix
Reshape the Matrix
Similar Problems:
In MATLAB, there is a very useful function called ‘reshape’, which can reshape a matrix into a new one with different size but keep its original data.
You’re given a matrix represented by a two-dimensional array, and two positive integers r and c representing the row number and column number of the wanted reshaped matrix, respectively.
The reshaped matrix need to be filled with all the elements of the original matrix in the same row-traversing order as they were.
If the ‘reshape’ operation with given parameters is possible and legal, output the new reshaped matrix; Otherwise, output the original matrix.
```Example 1:
Input:
nums =
[[1,2],
[3,4]]
r = 1, c = 4
Output:
[[1,2,3,4]]
Explanation:
The row-traversing of nums is [1,2,3,4]. The new reshaped matrix is a 1 * 4 matrix, fill it row by row by using the previous list.
```
```Example 2:
Input:
nums =
[[1,2],
[3,4]]
r = 2, c = 4
Output:
[[1,2],
[3,4]]
Explanation:
There is no way to reshape a 2 * 2 matrix to a 2 * 4 matrix. So output the original matrix.
```
Note:
1. The height and width of the given matrix is in range [1, 100].
2. The given r and c are all positive.
Github: code.dennyzhang.com
Credits To: leetcode.com
Leave me comments, if you have better ways to solve.
```## Blog link: https://code.dennyzhang.com/reshape-the-matrix
## Baisc Ideas: If r*c != count of original matrix, we can't reshape it.
## Trasverse the original matrix, and use index as a counter.
## (i2, j2) is the position of the new matrix
## i2 = index/c, j2 = index%c
##
## Complexity: Time O(n*m), Space O(1)
class Solution(object):
def matrixReshape(self, nums, r, c):
"""
:type nums: List[List[int]]
:type r: int
:type c: int
:rtype: List[List[int]]
"""
row_count = len(nums)
if row_count == 0: return nums
col_count = len(nums[0])
if r*c != row_count*col_count: return nums
res = [None]*r
for i in xrange(r): res[i] = [None]*c
index = 0
for i in xrange(row_count):
for j in xrange(col_count):
i2 = index/c
j2 = index%c
res[i2][j2] = nums[i][j]
index += 1
return res
```
Share It, If You Like It. | 624 | 2,171 | {"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} | 3.59375 | 4 | CC-MAIN-2019-30 | longest | en | 0.814772 |
https://oeis.org/A199102 | 1,568,852,582,000,000,000 | text/html | crawl-data/CC-MAIN-2019-39/segments/1568514573385.29/warc/CC-MAIN-20190918234431-20190919020431-00394.warc.gz | 625,496,777 | 3,911 | This site is supported by donations to The OEIS Foundation.
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A199102 G.f. satisfies: A(x) = exp( Sum_{n>=1} x^n/n * Sum_{k=0..n} C(n,k)*A(x^(n+k)) ). 1
1, 2, 6, 20, 63, 213, 719, 2505, 8864, 31948, 116725, 432074, 1616022, 6100775, 23214144, 88949045, 342899474, 1329020016, 5175758820, 20243197030, 79480515302, 313155710230, 1237771800135, 4906616164195, 19502048947616, 77703941363599, 310305199056779 (list; graph; refs; listen; history; text; internal format)
OFFSET 0,2 LINKS EXAMPLE G.f.: A(x) = 1 + 2*x + 6*x^2 + 20*x^3 + 63*x^4 + 213*x^5 + 719*x^6 +... where log(A(x)) = (A(x)+A(x^2))*x + (A(x^2)+2*A(x^3)+A(x^4))*x^2/2 + (A(x^3)+3*A(x^4)+3*A(x^5)+A(x^6))*x^3/3 + (A(x^4)+4*A(x^5)+6*A(x^6)+4*A(x^7)+A(x^8))*x^4/4 +... Explicitly, log(A(x)) = 2*x + 8*x^2/2 + 32*x^3/3 + 100*x^4/4 + 387*x^5/5 + 1370*x^6/6 + 5315*x^7/7 + 20444*x^8/8 + 80897*x^9/9 + 320883*x^10/10 +... PROG (PARI) {a(n)=local(A=1+x); for(i=1, n, A=exp(sum(m=1, n, x^m/m*sum(k=0, m, binomial(m, k)*subst(A, x, x^(m+k)+x*O(x^n)))))); polcoeff(A, n)} CROSSREFS Cf. A073063. Sequence in context: A247076 A177792 A193235 * A053730 A220874 A273902 Adjacent sequences: A199099 A199100 A199101 * A199103 A199104 A199105 KEYWORD nonn AUTHOR Paul D. Hanna, Nov 03 2011 STATUS approved
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Last modified September 18 20:22 EDT 2019. Contains 327181 sequences. (Running on oeis4.) | 705 | 1,658 | {"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} | 3.578125 | 4 | CC-MAIN-2019-39 | latest | en | 0.47706 |
http://forumserver.twoplustwo.com/25/probability/pokerdope-poker-variance-calculator-1666905/?s=b9a719b97cd898d02747ef0e77dbd1cb | 1,501,209,948,000,000,000 | text/html | crawl-data/CC-MAIN-2017-30/segments/1500549436321.71/warc/CC-MAIN-20170728022449-20170728042449-00384.warc.gz | 121,627,995 | 20,957 | Two Plus Two Poker Forums Pokerdope Poker Variance Calculator
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05-14-2017, 05:12 AM #1 Mason Malmuth Top Dog Join Date: Aug 2002 Location: @MasonMalmuth Posts: 9,989 Pokerdope Poker Variance Calculator Hi Everyone: I was looking at the Pokerdope Poker Variance Calculator. which can be found at: http://pokerdope.com/poker-variance-calculator/ In the example he has a winrate in BB / 100 of 2.5BB and a standard deviation per 100 of 100BB. And this gives him a minimum bankroll for less than 5% risk of ruin (»?«) of 5991 BB. Does anyone know how he calculates (or estimates) this number. Also, given that he's showing a 95 percent confidence interval isn't he actually calculating a bankroll for a 2.5 percent risk of ruin? or is he getting the calculated/estimated bankroll another way and is actually getting the 5 percent number? Thanks and best wishes, Mason
05-14-2017, 02:22 PM #2 nickthegeek centurion Join Date: Sep 2011 Posts: 174 Re: Pokerdope Poker Variance Calculator They are using the formula: R(b) = exp(-2*mu*b/sigma^2), where mu is your expected win, sigma is the standard deviation, b is the bankroll and R is the risk of ruin. For derivation and assumptions, see Mathematics of Poker, pp 274-284. In the page you linked, they set R(b) = 0.05 (since they want a 95% survival probability) and solve for b. The 95% confidence interval shown has little to do with the RoR. That interval indicates the range you are expected to finish in if you play all the hands. However, if you start with a finite bankroll, you might not be able to end all the hands, since sometimes you lose it all along the path.
05-14-2017, 04:32 PM #3 whosnext Pooh-Bah Join Date: Mar 2009 Location: California Posts: 3,676 Re: Pokerdope Poker Variance Calculator So the 95% confidence interval that is displayed is not really a 95% confidence interval if you start with a finite bankroll (and cannot 'rebuy')?
05-14-2017, 05:12 PM #4
Mason Malmuth
Top Dog
Join Date: Aug 2002
Location: @MasonMalmuth
Posts: 9,989
Re: Pokerdope Poker Variance Calculator
Quote:
Originally Posted by nickthegeek They are using the formula: R(b) = exp(-2*mu*b/sigma^2), where mu is your expected win, sigma is the standard deviation, b is the bankroll and R is the risk of ruin. For derivation and assumptions, see Mathematics of Poker, pp 274-284. In the page you linked, they set R(b) = 0.05 (since they want a 95% survival probability) and solve for b. The 95% confidence interval shown has little to do with the RoR. That interval indicates the range you are expected to finish in if you play all the hands. However, if you start with a finite bankroll, you might not be able to end all the hands, since sometimes you lose it all along the path.
Hi Nick:
BruceZ pointed this out to me many years ago and in the 2004 edition of my Gambling Theory book the following was added:
Quote:
Special Note: It has been pointed out to me by Bruce Zastera, one of the most knowledgeable posters on our forums at www.twoplustwo.com, that it is also possible to go broke before reaching the number of hours at which we evaluate the probability of a loss, as well as after that time, and this problem is more acute at the 95 percent level than I originally realized. This means that these tables are significantly underestimating by a factor of about 2 the amount of bankroll needed to only have a 5 percent chance of going broke. Fortunately, this problem mitigates as the probability of going broke is reduced. Thus the Bankroll Required to Assure a Win tables do contain solid estimates and produce a risk of ruin of approximately 1.1 percent, but the 95 percent tables should probably not be used.
However, in the PokerDope case, which by the way is an excellent tool for showing players the power of the short term luck factor, it seemed strange to me that he would have a 95 percent confidence interval on his graph which actually cprresponds (without regard to exactly how accurate it is when related to a required bankroll) with a 2.5 percent risk of ruin when he was giving a number for a 5 percent risk of ruin.
However, it has now been explained that his 5 percent risk of ruin number was calculated from a formula (which came from the excellent The Mathematics of Poker by Chen and Ankenman) and has nothing to do with the graph. I suggest that PokerDope make this more clear on his site.
05-14-2017, 05:19 PM #5
nickthegeek
centurion
Join Date: Sep 2011
Posts: 174
Re: Pokerdope Poker Variance Calculator
Quote:
Originally Posted by whosnext So the 95% confidence interval that is displayed is not really a 95% confidence interval if you start with a finite bankroll (and cannot 'rebuy')?
These are completely different concepts.
The 95% confidence interval (although what shown in the page is actually a 2-sigma, 95.4% interval, and the 70% is a one-sigma 68% interval) says that if many players with same EV play 100000 hands each, 95% of them will finish inside that range. It doesn't consider the initial bankroll: each player is assumed to be able to finish all the hands. So the interval doesn't depend on the bankroll, while it depends on the number of hands played (of course the range will change depending on it, since if you play just a few hands, you can't neither win nor lose big amounts).
The risk of ruin expresses the probability of being able to play forever starting with a given bankroll. Even if you play a +EV game, you might incurr in a bad run and lose all your bankroll, making you unable to continue to play (the "ruin"). If you look at the formula, you'll easily realize that it doesn't depend on the number of hands (the assumption is that you survive forever), since both mu and sigma^2 increase linearly with N. So, RoR depends on the bankroll, but not on the number of hands played.
05-14-2017, 07:44 PM #6 whosnext Pooh-Bah Join Date: Mar 2009 Location: California Posts: 3,676 Re: Pokerdope Poker Variance Calculator I understand the math and I appreciate you describing it (again) for the forum viewers. But I think it goes a little too far to say that the two concepts are "completely different".
05-15-2017, 01:53 AM #7 nickthegeek centurion Join Date: Sep 2011 Posts: 174 Re: Pokerdope Poker Variance Calculator I actually can't see many similarities between the two. Try putting a big number of hands, say 1 billion. The 95% range is [24367544 BB, 25632456 BB], hugely on the positive side. The 95% RoR bankroll stays at 5991 BB. It has to be stressed that the RoR can't be calculated by simulating an arbitrary big number of hands and seeing how negative are the bad case scenarios.
05-19-2017, 03:49 AM #8
masque de Z
Carpal \'Tunnel
Join Date: Aug 2009
Location: Stanford, CA USA
Posts: 8,576
Re: Pokerdope Poker Variance Calculator
Quote:
Originally Posted by Mason Malmuth Hi Everyone: I was looking at the Pokerdope Poker Variance Calculator. which can be found at: http://pokerdope.com/poker-variance-calculator/ In the example he has a winrate in BB / 100 of 2.5BB and a standard deviation per 100 of 100BB. And this gives him a minimum bankroll for less than 5% risk of ruin (»?«) of 5991 BB. Does anyone know how he calculates (or estimates) this number. Also, given that he's showing a 95 percent confidence interval isn't he actually calculating a bankroll for a 2.5 percent risk of ruin? or is he getting the calculated/estimated bankroll another way and is actually getting the 5 percent number? Thanks and best wishes, Mason
The correct way to do this is to use a probability density function for the outcome of a typical hand of poker in ones typical game of poker if one had such distribution f(x) available (and was well defined under fixed conditions or well averaged out). Then consider the result of repeated summation of this distribution for a given bankroll and find the first return to 0 distribution of position as function of time. Then integrate that over all times.
That is actually better than seeing poker as a game of winrate m and sd s (especially for small bankrolls where one can easily find themselves all in after a few hands something the standard sd/m treatment doesnt anticipate so fast).
One can even consider the identical Wiener process that has m and s like poker ie Dx=m*Dt+W*s (W standard normal random variable) https://en.wikipedia.org/wiki/Wiener_process
However due to law of large numbers probably it wont be very bad to do the following thing;
Lets say one uses the standard risk of ruin expression for fixed unit risked step d. So p, q=1-p and d and bankroll B define that process.
Now avg is m=p*d-(1-p)*d=(2p-1)*d and s^2 = (p*(d-(2p-1)*d)^2+(1-p)*(-d-(2p-1)d)^2=4 d^2 p*(1-p) so s=2d*(p*(1-p))^(1/2)
Sow fix s to poker sd per hand and m to winrate. This yields d=(m^2+s^2)^(1/2), p=1/2+1/2*m/(m^2+s^2)^(1/2).
if B= bankroll
and z= B/d (how many bet step units left)
Then q(ruin)=((1-p)/p)^(z) from standard risk of ruin expression of position z times the bet risked each time against an infinite wealth adversary (eg see classic book by W. Feller for derivation)
So Risk of Ruin =(s/((s^2+m^2)^(1/2)+m))^(2*B/(m^2+s^2)^(1/2)
Notice that if s>>m (so m/s<<1) the above becomes (but only then)
(1-m/s)^(2*B/s)~ Exp[log(1-m/s)*2*B/s)=Exp[-m/s*2*B/s]=Exp[-2*m*B/s^2]
which is the earlier quoted expression.
This gives the same 5% risk of ruin for the m=0.025 and s=10bb/h for the 5991bb example.
Only posted this because it shows how to get there using the standard risk of ruin result.
For anyone interested see these pages too for more understanding of topics involved.
https://en.wikipedia.org/wiki/Gambler%27s_ruin
http://www.columbia.edu/~ks20/FE-Not...7-Notes-GR.pdf
05-19-2017, 04:44 AM #9 masque de Z Carpal \'Tunnel Join Date: Aug 2009 Location: Stanford, CA USA Posts: 8,576 Re: Pokerdope Poker Variance Calculator By the way see here from the archives too when that result was also derived first time long time ago in a more thorough manner by BruceZ; http://archives2.twoplustwo.com/show...st682045683150
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Copyright © 2008-2010, Two Plus Two Interactive | 3,443 | 13,844 | {"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} | 3.390625 | 3 | CC-MAIN-2017-30 | latest | en | 0.871652 |
http://spotidoc.com/doc/662360/assignment-20 | 1,566,121,658,000,000,000 | text/html | crawl-data/CC-MAIN-2019-35/segments/1566027313747.38/warc/CC-MAIN-20190818083417-20190818105417-00347.warc.gz | 176,074,811 | 7,975 | # Assignment 20
```PROBLEM 5.67
For the beam and loading shown, determine (a) the magnitude
and location of the resultant of the distributed load, (b) the
reactions at the beam supports.
SOLUTION
1
(150lb/ft)(9 ft) = 675 lb
2
1
RII = (120 lb/ft)(9ft) = 540lb
2
R = RI + RII = 675 + 540 = 1215 lb
RI =
XR = Σ x R: X (1215) = (3)(675) + (6)(540)
X = 4.3333 ft
R = 1215 lb
(a)
(b)
Reactions:
X = 4.33 ft
Σ M A = 0: B (9 ft) − (1215 lb) (4.3333 ft) = 0
B = 585.00 lb
B = 585 lb
Σ Fy = 0: A + 585.00 lb − 1215 lb = 0
A = 630.00 lb
A = 630 lb
PROPRIETARY MATERIAL. © 2013 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual may be displayed,
reproduced or distributed in any form or by any means, without the prior written permission of the publisher, or used beyond the limited
distribution to teachers and educators permitted by McGraw-Hill for their individual course preparation. If you are a student using this Manual,
you are using it without permission.
631
PROBLEM 5.69
Determine the reactions at the beam supports for the given loading.
SOLUTION
R I = (200 lb/ft)(15 ft)
R I = 3000 lb
1
(200 lb/ft)(6 ft)
2
R II = 600 lb
R II =
ΣM A = 0: − (3000 lb)(1.5 ft) − (600 lb)(9 ft + 2 ft) + B(15 ft) = 0
B = 740 lb
B = 740 lb
ΣFy = 0: A + 740 lb − 3000 lb − 600 lb = 0
A = 2860 lb
A = 2860 lb
PROPRIETARY MATERIAL. © 2013 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual may be displayed,
reproduced or distributed in any form or by any means, without the prior written permission of the publisher, or used beyond the limited
distribution to teachers and educators permitted by McGraw-Hill for their individual course preparation. If you are a student using this Manual,
you are using it without permission.
633
PROBLEM 5.76
Determine (a) the distance a so that the vertical reactions at
supports A and B are equal, (b) the corresponding reactions at
the supports.
SOLUTION
(a)
We have
Then
1
(a m)(1800 N/m) = 900a N
2
1
RII = [(4 − a ) m](600 N/m) = 300(4 − a) N
2
RI =
ΣFy = 0: Ay − 900a − 300(4 − a ) + B y = 0
or
Ay + B y = 1200 + 600a
Now
Ay = B y
Also,
ΣM B = 0: − (4 m) Ay +
+
or
Ay = B y = 600 + 300a (N)
4−
(1)
a
m [(900a) N]
3
1
(4 − a ) m [300(4 − a) N] = 0
3
Ay = 400 + 700a − 50a 2
Equating Eqs. (1) and (2),
600 + 300a = 400 + 700a − 50a 2
or
a 2 − 8a + 4 = 0
(2)
8 ± (−8) 2 − 4(1)(4)
2
Then
a=
or
a = 0.53590 m
Now
a≤4m
a = 7.4641 m
a = 0.536 m
PROPRIETARY MATERIAL. © 2013 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual may be displayed,
reproduced or distributed in any form or by any means, without the prior written permission of the publisher, or used beyond the limited
distribution to teachers and educators permitted by McGraw-Hill for their individual course preparation. If you are a student using this Manual,
you are using it without permission.
640
PROBLEM 5.76 (Continued)
(b)
We have
From Eq. (1):
ΣFx = 0: Ax = 0
Ay = By
= 600 + 300(0.53590)
= 761 N
A = B = 761 N
PROPRIETARY MATERIAL. © 2013 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual may be displayed,
reproduced or distributed in any form or by any means, without the prior written permission of the publisher, or used beyond the limited
distribution to teachers and educators permitted by McGraw-Hill for their individual course preparation. If you are a student using this Manual,
you are using it without permission.
641
PROBLEM 5.81
The cross section of a concrete dam is as shown. For a 1-m-wide
dam section, determine (a) the resultant of the reaction forces
exerted by the ground on the base AB of the dam, (b) the point of
application of the resultant of part a, (c) the resultant of the
pressure forces exerted by the water on the face BC of the dam.
SOLUTION
(a)
Consider free body made of dam and triangular section of water shown. (Thickness = 1 m.)
p = (7.2 m)(103 kg/m3 )(9.81m/s 2 )
2
(4.8 m)(7.2 m)(1 m)(2.4 × 103 kg/m3 )(9.81 m/s 2 )
3
= 542.5 kN
1
W2 = (2.4 m)(7.2 m)(1 m)(2.4 × 103 kg/m3 )(9.81 m/s 2 )
2
= 203.4 kN
1
W3 = (2.4 m)(7.2 m)(1 m)(103 kg/m3 )(9.81 m/s 2 )
2
= 84.8 kN
1
1
P = Ap = (7.2 m)(1 m)(7.2 m)(103 kg/m3 )(9.81 m/s 2 )
2
2
= 254.3 kN
W1 =
ΣFx = 0: H − 254.3 kN = 0
H = 254 kN
ΣFy = 0: V − 542.5 − 203.4 − 84.8 = 0
V = 830.7 kN
V = 831 kN
PROPRIETARY MATERIAL. © 2013 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual may be displayed,
reproduced or distributed in any form or by any means, without the prior written permission of the publisher, or used beyond the limited
distribution to teachers and educators permitted by McGraw-Hill for their individual course preparation. If you are a student using this Manual,
you are using it without permission.
647
PROBLEM 5.81 (Continued)
5
x1 = (4.8 m) = 3 m
8
1
x2 = 4.8 + (2.4) = 5.6 m
3
2
x3 = 4.8 + (2.4) = 6.4 m
3
(b)
ΣM A = 0: xV − Σ xW + P(2.4 m) = 0
x(830.7 kN) − (3 m)(542.5 kN) − (5.6 m)(203.4 kN)
− (6.4 m)(84.8 kN) + (2.4 m)(254.3 kN) = 0
x(830.7) − 1627.5 − 1139.0 − 542.7 + 610.3 = 0
x(830.7) − 2698.9 = 0
x = 3.25 m (to right of A)
(c)
Resultant on face BC:
Direct computation:
P = ρ gh = (103 kg/m3 )(9.81 m/s 2 )(7.2 m)
P = 70.63 kN/m 2
BC = (2.4) 2 + (7.2) 2
= 7.589 m
θ = 18.43°
1
PA
2
1
= (70.63 kN/m 2 )(7.589 m)(1 m)
2
R=
R = 268 kN
18.43°
− R = 268 kN
18.43°
R = 268 kN
18.43°
Alternate computation: Use free body of water section BCD.
PROPRIETARY MATERIAL. © 2013 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual may be displayed,
reproduced or distributed in any form or by any means, without the prior written permission of the publisher, or used beyond the limited
distribution to teachers and educators permitted by McGraw-Hill for their individual course preparation. If you are a student using this Manual,
you are using it without permission.
648
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https://classroomsecrets.co.uk/multiply-by-100-year-4-multiplication-and-division-learning-video-clip/ | 1,660,906,333,000,000,000 | text/html | crawl-data/CC-MAIN-2022-33/segments/1659882573667.83/warc/CC-MAIN-20220819100644-20220819130644-00572.warc.gz | 182,810,249 | 65,146 | Multiply by 100 Year 4 Multiplication and Division Learning Video Clip | Classroom Secrets
Maths Resources & WorksheetsYear 4 Maths LessonsAutumn Block 4 (Multiplication and Division)02 Multiply by 100 › Multiply by 100 Year 4 Multiplication and Division Learning Video Clip
# Multiply by 100 Year 4 Multiplication and Division Learning Video Clip
## Step 2: Multiply by 100 Year 4 Multiplication and Division Learning Video Clip
Hamish and Syeda have landed in Japan and make their way to their hotel. They will need to convert between GBP (£) and Japanese Yen (¥) to pay for their stay. After the long trip they decide to buy some WiFi to help them relax before the games begin.
More resources for Autumn Block 4 Step 2.
(0 votes, average: 0.00 out of 5)
You need to be a registered member to rate this.
Discussion points for teachers
1. Help Syeda to complete Hamish’s challenge by converting the length from metres to centimetres.
Discuss how to convert between metres and centimetres. Discuss which parts of the dimensions need to be multiplied and which do not.
Length = 1,200cm; width = 255cm; height = 381cm
2. Help Hamish and Syeda to convert the price into Japanese yen by multiplying the price by 100.
Discuss efficient strategies for multiplying by 100. Discuss potential misconceptions with the place holder 0 when multiplying by 100.
£94 = ¥9,400
3. Help Syeda and Hamish calculate how much they need to pay for their WiFi by multiplying by 100.
Discuss efficient strategies for multiplying by 100. Discuss how much Hamish actually wants to pay for, not what the game normally needs.
Syeda = 78MB = ¥7,800; Hamish = 70MB = ¥7,000
4. If the hotel has 90 rooms, how many boxes will the hotel need each week if they change the soap in each room every day?
Discuss how many days there are in a week. Discuss how many boxes the hotel would need to restock the rooms each day.
630 soaps would be needed over the whole week so the hotel will need 7 boxes in total in a week.
5. This hotel is at least half full of athletes, so how many tickets must have been sold?
Discuss how to work out half of the number of rooms in the hotel. Discuss what the term at least means. Discuss the possible number of athletes and how to multiply that number by 100. This question is open-ended for the children to explore.
Various answers, for example: 5,000 tickets.
Optional discussion points:
Discuss with children if they notice a pattern between multiplying by 10 and multiplying by 100. Discuss the differences between the Japanese and English coins and notes, especially in their denominations and size/shapes.
National Curriculum Objectives
Mathematics Year 4: (4C6a) Recall multiplication and division facts for multiplication tables up to 12 × 12
This resource is available to play with a Premium subscription. | 652 | 2,827 | {"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} | 4.46875 | 4 | CC-MAIN-2022-33 | latest | en | 0.933498 |
https://developer.openinventor.com/refmans/10.3/RefManCpp/group___image_analysis_individual_measures.html | 1,571,043,726,000,000,000 | text/html | crawl-data/CC-MAIN-2019-43/segments/1570986649841.6/warc/CC-MAIN-20191014074313-20191014101313-00195.warc.gz | 485,982,115 | 3,250 | # Individual Measures [Image Analysis]
The Individual Measures category contains analysis engines applying a measurement on each label of the input image. More...
## Classes
class SoFilterAnalysisQuantification
SoFilterAnalysisQuantification engine removes from the input label analysis labels whose measure does not fulfill a filter formula. More...
class SoFilterByMeasureProcessing
SoFilterByMeasureProcessing engine allows filtering objects given a target measure and a filter criterion. More...
class SoLabelAnalysisQuantification
SoLabelAnalysisQuantification engine performs measurements on objects from a label image. More...
class SoLabelFilteringAnalysisQuantification
SoLabelFilteringAnalysisQuantification engine computes measurements on objects from a label image and filters the result according to a given formula. More...
class SoLabelFilteringProcessing
SoLabelFilteringProcessing engine filters objects from a label image according to a given formula. More...
class SoMeasureImageProcessing
SoMeasureImageProcessing engine allows to replace all labels of the input image by the result of an individual measure. More...
class SoSieveLabelingProcessing
SoSieveLabelingProcessing engine produces a new label image by grouping labels of the input label image. More...
## Detailed Description
The Individual Measures category contains analysis engines applying a measurement on each label of the input image.
For an introduction, see section Image Analysis
Most of these engines have a field to set one or several input measurements.
## Label filtering from an image
Object filtering allows removing or keeping shapes from a binary or label image according to measurement criteria. Some engines need a formula to define the filter to apply.
### How to define a filter formula
Following engines filter an image with criteria defined in a formula:
The formula syntax accepts the following list of available mathematical and logical operators:
• + - / * ** : The basic mathematical operators (addition, subtraction, division, multiplication, power)
• ! : Unary negation
• < > <= >= != == : Comparison operators less, greater, less or equal, greater or equal, not equal and equal
• && || and or : Logical operators and, or, and and or
• Moreover an element of a distribution can be accessed by the operator []
• FeretInputX[2] : The third element of the distribution FeretInputX
e.g., : To define a filter the equivalent diameter measurement for an analysis:
``` labelFilter->inFilter = SoDataMeasurePredefined::getName(SoDataMeasurePredefined::EQUIVALENT_DIAMETER_2D) + "< 50"
```
Open Inventor Toolkit reference manual, generated on 12 Sep 2019 | 548 | 2,679 | {"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} | 2.609375 | 3 | CC-MAIN-2019-43 | longest | en | 0.742536 |
https://nl.mathworks.com/matlabcentral/cody/problems/28-counting-money/solutions/960876 | 1,611,129,299,000,000,000 | text/html | crawl-data/CC-MAIN-2021-04/segments/1610703519923.26/warc/CC-MAIN-20210120054203-20210120084203-00369.warc.gz | 481,190,359 | 17,080 | Cody
# Problem 28. Counting Money
Solution 960876
Submitted on 6 Sep 2016 by steph26
This solution is locked. To view this solution, you need to provide a solution of the same size or smaller.
### Test Suite
Test Status Code Input and Output
1 Pass
a = {'\$12,001.87','\$0.04','\$103,887.55','\$0.32'}; b = 115889.78; assert(abs(moneySum(a)-b) < 1e-4)
b = 1.1589e+05
2 Pass
a = {'\$0.02'}; b = 0.02; assert(abs(moneySum(a)-b) < 1e-4)
b = 0.0200
3 Pass
a = {'\$81.47','\$12.69','\$91,337.60'}; b = 91431.76; assert(abs(moneySum(a)-b) < 1e-4)
b = 9.1432e+04
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Start Hunting! | 259 | 699 | {"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} | 2.8125 | 3 | CC-MAIN-2021-04 | latest | en | 0.725921 |
https://it.scribd.com/document/172699938/Synopsis-of-power-factor-docx | 1,586,088,953,000,000,000 | text/html | crawl-data/CC-MAIN-2020-16/segments/1585371604800.52/warc/CC-MAIN-20200405115129-20200405145629-00090.warc.gz | 508,466,218 | 79,069 | Sei sulla pagina 1di 10
Synopsis of:
Digital Power Factor Controller
A Project To be submitted by: Abhishek Jain Amit Thapliyal Gaurav Khanduri Himanshu Nautiyal
Under the Guidance Of Mr. Ashish Pandey Sr. Lecturer (Deptt. Of Electrical & Electronics Engineering)
Introduction:
Abstract:
Power Factor Correction:
Capacitive Power Factor correction is applied to circuits which include inductive components as a means of reducing the inductive component of the current and thereby reduce the losses in the supply. There should be no effect on the operation of the motor itself. An inductive load draws current from the supply that is made up of resistive components and inductive components. The resistive components are: 1) Load current. 2) Loss current. and the inductive components are: 3) Leakage reactance. 4) Magnetizing current.
The current due to the leakage reactance is dependant on the total current drawn by the motor, but the magnetizing current is independent of the load on the motor. The magnetizing current will typically be between 20% and 60% of the rated full load current of the motor. The magnetizing current is the current that establishes the flux in the iron and is very necessary if the motor is going to operate. The magnetizing current does not actually contribute to the actual work output of the motor. It is the catalyst that allows the motor to work properly. The magnetizing current and the leakage reactance can be considered passenger
components of current that will not affect the power drawn by the motor, but will contribute to the power dissipated in the supply and distribution system. Take for example a motor with a current draw of 100 Amps and a power factor of 0.75 The resistive component of the current is 75 Amps and this is what the KWh meter measures. The higher current will result in an increase in the distribution losses of (100 x 100) /(75 x 75) = 1.777 or a 78% increase in the supply losses. In the interest of reducing the losses in the distribution system, power factor correction is added to neutralize a portion of the magnetizing current of the motor. Typically, the corrected power factor will be 0.92 - 0.95 Some power retailers offer incentives for operating with a power factor of better than 0.9, while others penalize consumers with a poor power factor. There are many ways that this is metered, but the net result is that in order to reduce wasted energy in the distribution system, the consumer will be encouraged to apply power factor correction. Power factor correction is achieved by the addition of capacitors in parallel with the connected motor circuits and can be applied at the starter, or applied at the switchboard or distribution panel. The resulting capacitive current is leading current and is used to cancel the lagging inductive current flowing from the supply.
Capacitors connected at each starter and controlled by each starter is known as "Static Power Factor Correction" while capacitors connected at a distribution board and controlled independently from the individual starters is known as "Bulk Correction". Bulk Correction. The Power factor of the total current supplied to the distribution board is monitored by a controller which then switches capacitor banks In a fashion to maintain a power factor better than a preset limit. (Typically 0.95) Ideally, the power factor should be as close to unity as possible. There is no problem with bulk correction operating at unity.
Static Correction. As a large proportion of the inductive or lagging current on the supply is due to the magnetizing current of induction motors, it is easy to correct each individual motor by connecting the correction capacitors to the motor starters. With static correction, it is important that the capacitive current is less than the inductive magnetizing current of the induction motor. In many installations employing static power factor correction, the correction capacitors are connected directly in parallel with the motor windings. When the motor is Off Line, the capacitors are
also Off Line. When the motor is connected to the supply, the capacitors are also connected providing correction at all times that the motor is connected to the supply. This removes the requirement for any expensive power factor monitoring and control equipment. In this situation, the capacitors remain connected to the motor terminals as the motor slows down. An induction motor, while connected to the supply, is driven by a rotating magnetic field in the stator which induces current into the rotor. When the motor is disconnected from the supply, there is for a period of time, a magnetic field associated with the rotor. As the motor decelerates, it generates voltage out its terminals at a frequency which is related to it's speed. The capacitors connected across the motor terminals, form a resonant circuit with the motor inductance. If the motor is critically corrected, (corrected to a power factor of 1.0) the inductive reactance equals the capacitive reactance at the line frequency and therefore the resonant frequency is equal to the line frequency. If the motor is over corrected, the resonant frequency will be below the line frequency. If the frequency of the voltage generated by the decelerating motor passes through the resonant frequency of the corrected motor, there will be high currents and voltages around the motor/capacitor circuit. This can result in severe damage to the capacitors and motor. It is imperative that motors are never over corrected or critically corrected when static correction is employed. Static power factor correction should provide capacitive current equal to 80% of the magnetizing current, which is essentially the open shaft current of the motor. The magnetizing current for induction motors can vary considerably. Typically, magnetizing currents for large two pole machines can be as low as 20% of the rated current of the motor while smaller low speed motors can have a magnetizing current as high as 60% of the rated full load current of the motor. It is not practical to use a "Standard table" for the correction of induction motors giving optimum correction on all motors. Tables result in under correction on most motors but can result in over correction in some cases. Where the open shaft current can not be measured, and the magnetizing current is not quoted, an approximate level for the maximum correction that can be applied can be calculated from the half load characteristics of the motor. It is dangerous to base correction on the full load characteristics of the motor as in some cases, motors can exhibit a high leakage reactance and correction to 0.95 at full load will result in over correction under no load, or disconnected conditions.
Static correction is commonly applied by using one contactor to control both the motor and the capacitors. It is better practice to use two contactors, one for the motor and one for the capacitors. Where one contactor is employed, it should be up sized for the capacitive load. The use of a second contactor eliminates the problems of resonance between the motor and the capacitors.
Circuit layout: | 1,448 | 7,179 | {"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} | 2.90625 | 3 | CC-MAIN-2020-16 | latest | en | 0.911383 |
https://mcmahonspublichouse.com/blog/how-many-oz-glass-of-wine/ | 1,721,745,758,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763518058.23/warc/CC-MAIN-20240723133408-20240723163408-00776.warc.gz | 332,709,833 | 32,130 | # How Many Oz Glass Of Wine?
Welcome to the official blog of How Many Oz Glass of Wine! Here you will find everything you need to know about our delicious wine products. From new arrivals to special offers, we will keep you updated on all the latest news and information. So sit back, relax, and enjoy a glass of our finest wine.
## How Many Oz Glass Of Wine?
A standard wine glass holds 8.5 ounces of fluid, but it is not unusual for a glass to hold as much as 12 ounces.
How many ounces of wine should you pour? That depends on the type of wine, the occasion, and your personal preference. If you’re pouring red wine, you may want to pour a little less than if you’re pouring white wine. Red wines tend to be more robust and full-bodied, so a smaller glass will do. If you’re having a casual gathering with friends, you may want to pour a little more than if you’re having a formal dinner party. And if you like your wine really strong, you may want to pour more than if you prefer your wine on the lighter side.
In general, though, most people pour around 4 ounces of wine into their glass. This gives you enough to enjoy the flavor of the wine without getting too drunk too quickly. Of course, if you’re only having one glass of wine, you may want to pour a little less so that it lasts longer!
## How Many Glasses Are in a Bottle of Wine?
Now that you know how many oz in a wine glass, you may be wondering how many glasses are in a bottle of wine. Well, this all depends on the size of the bottle and the size of the glass.
The most common size of wine bottle is 750 ml, which is equivalent to 25.4 ounces. This means that there are approximately 3 glasses of wine in a 750 ml bottle.
But if you are using a smaller glass, such as a four-ounce glass, then there would be approximately 6 glasses of wine in a 750 ml bottle. And if you are using a larger glass, such as an eight-ounce glass, then there would be approximately 12 glasses of wine in a 750 ml bottle.
Of course, these are all estimates. The actual number of glasses will depend on the size of the bottle and the size of the glass.
## How Many Oz in a Bottle of Wine?
The most common size of wine bottle is 750 ml, which is equivalent to 25.4 ounces. This means that there are approximately 25 ounces of wine in a 750 ml bottle.
But if you are using a smaller bottle, such as a 187 ml bottle, then there would be less than 25 ounces of wine in the bottle. And if you are using a larger bottle, such as a 1.5 L bottle, then there would be more than 25 ounces of wine in the bottle.
Of course, these are all estimates. The actual amount of wine will depend on the size of the bottle.
## Wine Bottle Sizes and their Pour Sizes
Now that you know how many glasses are in a bottle of wine, you may be wondering about the different sizes of wine bottles and their pour sizes. Here is a quick overview of the most common wine bottle sizes and their pour sizes:
• champagne split (187 ml): 4 ounces
• half bottle (375 ml): 8 ounces
• standard bottle (750 ml): 12-16 ounces
• magnum (1.5 L): 24-32 ounces
• double magnum (3 L): 48-64 ounces
• jeroboam (4.5 L): 72-96 ounces
• rehoboam (6 L): 96-128 ounces
• methuselah (9 L): 144-192 ounces
• salmanazar (12 L): 192-256 ounces
• balthazar (16 L): 256-384 ounces
• nebuchadnezzar (20 L): 384-512 ounces
As you can see, there is a wide range of wine bottle sizes. And the pour size will depend on the size of the bottle and the size of the glass.
So, if you are ever unsure about how much wine to pour, just remember that it is always better to pour too little than too much. This way, you can always top off your glass if needed.
## Wine Bottle Sizes and their Contents
Now that you know how many oz in a bottle of wine, you may be wondering about the different sizes of wine bottles and their contents. Here is a quick overview of the most common wine bottle sizes and their contents:
• champagne split (187 ml): 5 ounces
• half bottle (375 ml): 10-12 ounces
• standard bottle (750 ml): 20-24 ounces
• magnum (1.5 L): 40-48 ounces
• double magnum (3 L): 80-96 ounces
• jeroboam (4.5 L): 120-144 ounces
• rehoboam (6 L): 160-192 ounces
• methuselah (9 L): 240-288 ounces
• salmanazar (12 L): 320-384 ounces
• balthazar (16 L): 480-512 ounces
• nebuchadnezzar (20 L): 640-768 ounces
As you can see, there is a wide range of wine bottle sizes. And the amount of wine will depend on the size of the bottle.
So, if you are ever unsure about how much wine to pour, just remember that it is always better to pour too little than too much. This way, you can always top off your glass if needed.
## What Is The Ideal Wine Serving?
The perfect wine serving size depends on a few factors, including the type of wine, the occasion, and your personal preference. But in general, a good rule of thumb is to pour four ounces for red wine and two ounces for white wine. This will allow you to enjoy the full flavor of the wine without getting too drunk too quickly.
Of course, if you are planning on drinking wine with dinner, you may want to pour a bit more. And if you are attending a wine tasting event, you will probably want to pour even less so that you can sample a variety of wines.
## How Many Oz is the Ideal Serving of Wine?
So, how many oz should you pour for the perfect wine serving? Again, it depends on the type of wine and the occasion. But as a general rule, four ounces for red wine and two ounces for white wine is a good place to start.
If you are planning on drinking wine with dinner, you may want to pour a bit more. And if you are attending a wine tasting event, you will probably want to pour even less so that you can sample a variety of wines.
No matter how much wine you ultimately decide to pour, be sure to enjoy it!
## Variations in Wine Glass Oz Serving Sizes
Now that you know the ideal wine serving size, you may be wondering if there are any variations. Well, there definitely are!
For example, some people prefer to pour a bit more wine when they are drinking it with food. This is because the food can help to enhance the flavors of the wine. And if you are drinking wine with a strong-flavored dish, you may want to pour a bit less so that the wine doesn’t get lost in the food.
Another common variation is to pour different amounts of wine depending on the type of wine. For example, many people believe that red wines should be poured in larger glasses than white wines. And some people believe that sparkling wines should be poured in even smaller glasses than red or white wines.
Ultimately, it’s up to you to decide how much wine to pour. Just be sure to pour what feels right for you and the occasion.
### Dessert Wines: A Special Case
Dessert wines are a bit of a special case when it comes to wine serving sizes. This is because they are often served in much smaller glasses than other types of wines.
This is because dessert wines are usually very sweet and rich, so you don’t need to drink as much of them to get the full flavor. In general, a good rule of thumb is to pour two ounces of dessert wine per person.
Of course, you may want to pour a bit more or less depending on the sweetness of the wine and your personal preference.
### Fortified Wines: Another Special Case
Fortified wines are another type of wine that is often served in smaller glasses than other types of wines. This is because they are very strong and can be quite overwhelming if you drink too much of them.
In general, a good rule of thumb is to pour one ounce of fortified wine per person. But again, you may want to pour a bit more or less depending on the strength of the wine and your personal preference.
### Wine Tastings: A Special Occasion
Wine tastings are a special occasion where you will want to pour very small amounts of wine. This is because you will want to be able to sample a variety of wines without getting too drunk.
In general, a good rule of thumb is to pour one ounce of wine per person. But you may want to pour even less so that you can really savor the flavor of each wine.
## The Importance of Knowing the Oz in Wine Glasses
As you can see, there is no “correct” answer when it comes to how many oz in a wine glass. It all depends on the type of wine, the occasion, and your personal preference.
But it is important to know the ideal serving size for each type of wine. This way, you can be sure that you are pouring the right amount of wine for the occasion.
And if you are ever unsure, just remember that it is always better to pour too little wine than too much. This way, you can always top off your glass if needed.
## How Many Calories in a Bottle of Wine?
Now that you know how many oz in a bottle of wine, you may be wondering about the calories in a bottle of wine. Well, this all depends on the type of wine and the size of the bottle.
For example, a bottle of red wine generally has more calories than a bottle of white wine. And a magnum (1.5 L) bottle generally has more calories than a standard (750 ml) bottle.
Of course, these are all estimates. The actual number of calories will depend on the type of wine and the size of the bottle.
Wine Bottle Sizes and their Calories
Now that you know how many calories in a bottle of wine, you may be wondering about the different sizes of wine bottles and their calories. Here is a quick overview of the most common wine bottle sizes and their calories:
• champagne split (187 ml): 100 calories
• half bottle (375 ml): 200 calories
• standard bottle (750 ml): 400 calories
• magnum (1.5 L): 800 calories
• double magnum (3 L): 1600 calories
• jeroboam (4.5 L): 2400 calories
• rehoboam (6 L): 3200 calories
• methuselah (9 L): 4800 calories
• salmanazar (12 L): 6400 calories
• balthazar (16 L): 8400 calories
• nebuchadnezzar (20 L): 10400 calories
As you can see, there is a wide range of wine bottle sizes. And the number of calories will depend on the size of the bottle.
So, if you are ever unsure about how many calories are in a glass of wine, just remember that it is always better to pour too little than too much. This way, you can always top off your glass if needed.
## FAQs
### How many glasses are in a bottle of wine?
A standard bottle of wine contains approximately six glasses of wine. But this all depends on the size of the glass and how much wine you pour.
### How many oz in a bottle of wine?
The most common size of wine bottle is 750 ml, which contains approximately 25 ounces of wine. But if you are using a smaller bottle, such as a 187 ml bottle, then there would be less than 25 ounces of wine in the bottle. And if you are using a larger bottle, such as a 1.5 L bottle, then there would be more than 25 ounces of wine in the bottle.
### What is the difference between a champagne split and a standard bottle of wine?
A champagne split is a small bottle of wine that contains187 ml, or about 6 ounces, of wine. A standard bottle of wine is a 750 ml bottle that contains about 25 ounces of wine. So, a champagne split is smaller than a standard bottle of wine.
### How Big is a Standard Bottle of Wine?
A standard bottle of wine is 750 ml, which is about 25 ounces. But the actual size of the bottle may vary slightly depending on the type of wine. For example, a magnum (1.5 L) bottle is slightly larger than a standard bottle of wine.
### What is the Difference Between a Wine Bottle and a Champagne Bottle?
A wine bottle is a 750 ml bottle that contains about 25 ounces of wine. A champagne bottle is a larger bottle that typically contains 1.5 L, or about 50 ounces, of champagne. So, a champagne bottle is twice the size of a standard wine bottle.
### How Many Grapes Does it Take to Make a Bottle of Wine?
It takes approximately 2.5 pounds of grapes to make a standard bottle of wine. But this will vary depending on the type of grape and the size of the grape. For example, it takes more Cabernet Sauvignon grapes to make a bottle of wine than it does Chardonnay grapes. And it takes more Pinot Noir grapes to make a bottle of wine than it does Cabernet Sauvignon grapes.
### How Much Alcohol is in a Bottle of Wine?
The amount of alcohol in a bottle of wine will depend on the type of wine and the alcohol content. For example, a bottle of red wine typically has an alcohol content of 12%, while a bottle of white wine typically has an alcohol content of 10%. So, a bottle of red wine would have more alcohol than a bottle of white wine.
### How Many Calories are in a Bottle of Wine?
A standard bottle of wine contains approximately 400 calories. But this all depends on the type of wine and the size of the bottle. For example, a magnum (1.5 L) bottle of red wine would contain approximately 600 calories. And a double magnum (3 L) bottle of white wine would contain approximately 1200 calories.
### How Long Does it Take to Make a Bottle of Wine?
It takes approximately four to six weeks to make a bottle of wine. But this all depends on the type of grape and the fermentation process. For example, it takes longer to make a bottle of red wine than it does to make a bottle of white wine. And it takes longer to make a sparkling wine than it does to make a still wine.
### How Many Fluid Ounces in 750mL?
There are approximately 25 fluid ounces in 750mL. But this all depends on the size of the glass and how much wine you pour.
### How Many Calories are in a Glass of Wine?
A standard glass of wine contains approximately 120 calories. But this all depends on the type of wine and the size of the glass. For example, a glass of red wine would contain more calories than a glass of white wine. And a large glass of wine would contain more calories than a small glass of wine.
### How Long Does Wine Last Once Opened?
Wine typically lasts for about three to five days after it is opened. But this all depends on the type of wine and how you store it. For example, red wine will last longer than white wine. And wine that is stored in a cool, dark place will last longer than wine that is stored in a warm, light place.
### What is the Best Way to Store Wine?
The best way to store wine is in a cool, dark place. But this all depends on the type of wine and how long you plan on storing it. For example, red wine will last longer if it is stored in a cool, dark place. And white wine will last longer if it is stored in a cool, dark place.
### What is the Best Way to Serve Wine?
The best way to serve wine is at room temperature. But this all depends on the type of wine and what you are serving it with. For example, red wine should be served at room temperature. And white wine should be served chilled.
### How Much Wine Should I Buy?
This all depends on how much you plan on drinking and how many people you are buying for. For example, if you are buying wine for a party of eight, you should buy two bottles of wine. But if you are buying wine for a party of ten, you should buy three bottles of wine.
### Can I Freeze Wine?
Wine can be frozen, but it will change the taste of the wine. For example, red wine that is frozen will taste sweeter. And white wine that is frozen will taste more tart.
### How Many Fluid Ounces in a Bottle of Wine?
There are approximately 25 fluid ounces in a bottle of wine. But this all depends on the size of the glass and how much wine you pour.
### Can I Reuse Wine Bottles?
Yes, you can reuse wine bottles. But you will need to clean them first. And you will need to remove the labels from the bottles.
### What is the Best Way to Clean Wine Bottles?
The best way to clean wine bottles is with hot soapy water. But you can also use a bottle brush.
### Can I Recycle Wine Bottles?
Yes, you can recycle wine bottles. But you will need to remove the labels from the bottles first.
### What is the Best Way to Remove Labels from Wine Bottles?
The best way to remove labels from wine bottles is with hot soapy water. But you can also use a bottle brush.
### What is the Best Way to Cut Wine Bottles?
The best way to cut wine bottles is with a glass cutter. But you can also use a utility knife.
### What is the Best Way to Drill Holes in Wine Bottles?
The best way to drill holes in wine bottles is with a drill bit. But you can also use a utility knife.
### What is the Best Way to Make a Candle Holder from a Wine Bottle?
The best way to make a candle holder from a wine bottle is to cut the bottom off of the bottle with a glass cutter. Then, use a utility knife to make a hole in the center of the bottom of the bottle. Next, insert a candle into the hole. Finally, light the candle and enjoy your new candle holder!
### What is the Best Way to Make a Vase from a Wine Bottle?
The best way to make a vase from a wine bottle is to cut the bottom off of the bottle with a glass cutter. Then, use a utility knife to make a hole in the center of the bottom of the bottle. Next, insert flowers into the hole. Finally, enjoy your new vase!
### What is the Best Way to Make a Wind Chime from Wine Bottles?
The best way to make a wind chime from wine bottles is to cut the bottom off of each bottle with a glass cutter. Then, use a utility knife to make a hole in the center of the bottom of each bottle. Next, thread a string through each hole. Finally, tie the strings together and enjoy your new wind chime!
### How Many Fluid Ounces in a Wine Glass?
There are approximately six fluid ounces in a wine glass. But this all depends on the size of the glass.
### What is the Best Way to Store Wine Glasses?
The best way to store wine glasses is in a cool, dark place. But this all depends on the type of wine and how long you plan on storing the glasses.
### What is the Best Way to Clean Wine Glasses?
The best way to clean wine glasses is with hot soapy water. But you can also use a glass cleaner.
### Can I Recycle Wine Glasses?
Yes, you can recycle wine glasses. But you will need to remove the labels from the glasses first.
### What is the Best Way to Remove Labels from Wine Glasses?
The best way to remove labels from wine glasses is with hot soapy water. But you can also use a glass cleaner.
### What is the Best Way to Cut Wine Glasses?
The best way to cut wine glasses is with a glass cutter. But you can also use a utility knife.
### What is the Best Way to Drill Holes in Wine Glasses?
The best way to drill holes in wine glasses is with a drill bit. But you can also use a utility knife.
### What is the Best Way to Make a Candle Holder from a Wine Glass?
The best way to make a candle holder from a wine glass is to cut the bottom off of the glass with a glass cutter. Then, use a utility knife to make a hole in the center of the bottom of the glass. Next, insert a candle into the hole. Finally, light the candle and enjoy your new candle holder!
### What is the Best Way to Make a Vase from a Wine Glass?
The best way to make a vase from a wine glass is to cut the bottom off of the glass with a glass cutter. Then, use a utility knife to make a hole in the center of the bottom of the glass. Next, insert flowers into the hole. Finally, enjoy your new vase!
### What is the Best Way to Make a Wind Chime from Wine Glasses?
The best way to make a wind chime from wine glasses is to cut the bottom off of each glass with a glass cutter. Then, use a utility knife to make a hole in the center of the bottom of each glass. Next, thread a string through each hole. Finally, tie the strings together and enjoy your new wind chime!
### How Many Fluid Ounces in a Wine Bottle?
There are approximately 25 fluid ounces in a wine bottle. But this all depends on the size of the bottle.
### What is the Best Way to Store Wine Bottles?
The best way to store wine bottles is in a cool, dark place. But this all depends on the type of wine and how long you plan on storing the bottles.
### How Many Fluid Ounces in Each Glass of Wine?
There are approximately six fluid ounces in each glass of wine. But this all depends on the size of the glass.
### How Many Calories in a Glass of Wine?
There are approximately 120 calories in a glass of wine. But this all depends on the type of wine and the serving size.
### Is Wine Good for You?
Yes, wine is good for you. But this all depends on the type of wine and how much you drink.
### What is the Best Way to Open a Wine Bottle?
The best way to open a wine bottle is with a corkscrew. But you can also use a utility knife.
### Can I Recycle Wine Bottles?
Yes, you can recycle wine bottles. But you will need to remove the labels from the bottles first.
### How Many mL in a Wine Glass?
There are approximately 177 mL in a wine glass. But this all depends on the size of the glass.
### How Many Grams in a Bottle of Wine?
There are approximately 1,000 grams in a bottle of wine. But this all depends on the size of the bottle.
### Can You Freeze Wine?
Yes, you can freeze wine. But this all depends on the type of wine and how long you plan on storing the wine.
### Can I Recycle Wine Corks?
Yes, you can recycle wine corks. But you will need to remove them from the bottles first.
### What is the Best Way to Remove Corks from Wine Bottles?
The best way to remove corks from wine bottles is with a corkscrew. But you can also use a utility knife.
### 17 Different Wine Bottle Sizes
There are 17 different wine bottle sizes. But this all depends on the type of wine and how much you plan on drinking.
## Conclusion
So, how many ounces are in a glass of wine? It depends on the size of the glass and the alcohol content of the wine. A typical restaurant wineglass holds about six ounces, while a standard shot glass holds one and a half ounces. Of course, you can always make your own measurements at home with a kitchen scale or measuring cup. Now that you know how to measure wine in both volume and weight measurements, you’re ready to start cooking some delicious salmon recipes! | 5,142 | 21,857 | {"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} | 2.640625 | 3 | CC-MAIN-2024-30 | latest | en | 0.949288 |
https://fr.mathworks.com/matlabcentral/cody/problems/14-find-the-numeric-mean-of-the-prime-numbers-in-a-matrix/solutions/234112 | 1,600,961,094,000,000,000 | text/html | crawl-data/CC-MAIN-2020-40/segments/1600400219221.53/warc/CC-MAIN-20200924132241-20200924162241-00567.warc.gz | 379,059,407 | 16,858 | Cody
# Problem 14. Find the numeric mean of the prime numbers in a matrix.
Solution 234112
Submitted on 22 Apr 2013 by Githin
This solution is locked. To view this solution, you need to provide a solution of the same size or smaller.
### Test Suite
Test Status Code Input and Output
1 Pass
%% x = 3; y_correct = 3; assert(isequal(meanOfPrimes(x),y_correct))
p_avg = 3
2 Pass
%% x = [1 2 3]; y_correct = 2.5; assert(isequal(meanOfPrimes(x),y_correct))
p_avg = 2.5000
3 Pass
%% x = [3 3; 3 3]; y_correct = 3; assert(isequal(meanOfPrimes(x),y_correct))
p_avg = 3
4 Pass
%% x = [7 3 8 8]'; y_correct = 5; assert(isequal(meanOfPrimes(x),y_correct))
p_avg = 5 | 235 | 673 | {"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} | 2.796875 | 3 | CC-MAIN-2020-40 | latest | en | 0.541736 |
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GMAT Prep, goal 750, feedback appreciated
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GMAT Prep, goal 750, feedback appreciated [#permalink]
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02 Sep 2009, 22:13
Hello everyone,
These forums have been very helpful, and I was wondering what people thought about my planned study program.
I am still finishing up my undergraduate degree so I am starting slowly.
Because i have a perceived quantitative weakness, I am going to start with basic math, Math Review for Standardized Tests
and then use the Manhattan GMAT guides for strategies on everything else.
For the verbal, which I tend to do better on, I have the Manhattan GMAT SC review, the PowerScore CR Bible, and LSAT Logical Reasoning Bible to help with that portion of the test. I have heard this is overkill, but I plan on taking the LSAT as well.
After doing the strategy guides, I plan on working through the OG 11, the OG verbal review, and the OG math review. I read somewhere that there is varying content in OG 10, and 12. Since I think the Manhattan GMAT guides have you work through the book, would it be a good idea to get one of those and work through it as well?
I am going to use an error log as detailed on one of the forums on this site. I plan on taking the test sometime after summer next year.
My first Kaplan practice test was a 550, and then I took the Knewton one two weeks later and got a 640. What do you think of this plan as a method of preparation?
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Re: GMAT Prep, goal 750, feedback appreciated [#permalink]
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02 Sep 2009, 23:00
Welcome to GMAT Club.
The plan sounds good. You can use OG 12 with the MGMAT Guides. Don't think you need OG 10 - you are already going the extra mile, and since your head is a lot younger and fresher than most here, you should get a pretty good score just with half the materials you mentioned (700+). So, don't worry about having enough materials, rather worry about getting burnt out.
One piece of advice - don't drag it out too long. Don't spend more than 4-6 months prepping. Otherwise you will waste a lot of good materials and still end up with 650.
Does that make sense?
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Re: GMAT Prep, goal 750, feedback appreciated [#permalink]
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03 Sep 2009, 22:46
bb wrote:
One piece of advice - don't drag it out too long. Don't spend more than 4-6 months prepping. Otherwise you will waste a lot of good materials and still end up with 650.
Does that make sense?
Why's that?
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Re: GMAT Prep, goal 750, feedback appreciated [#permalink] 03 Sep 2009, 22:46
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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®. | 1,159 | 4,583 | {"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} | 2.578125 | 3 | CC-MAIN-2017-47 | latest | en | 0.942719 |
https://statinfer.com/203-5-14-neural-network-appendix/ | 1,632,375,778,000,000,000 | text/html | crawl-data/CC-MAIN-2021-39/segments/1631780057417.10/warc/CC-MAIN-20210923044248-20210923074248-00129.warc.gz | 572,438,152 | 278,686 | • No products in the cart.
# 203.5.14 Neural Network Appendix
In previous section, we studied about Neural Networks Conclusion
In this post we will discuss the math behind a few steps of Neural Network algorithms.
#### Math- How to update the weights?
• We update the weights backwards by iteratively calculating the error.
• The formula for weights updating is done using gradient descent method or delta rule also known as Widrow-Hoff rule.
• First we calculate the weight corrections for the output layer then we take care of hidden layers.
• $$W_(jk) = W_(jk) + \Delta W_(jk)$$
• where $$\Delta W_(jk) = \eta . y_j \delta_k$$
• $$\eta$$ is the learning parameter
• $$\delta_k = y_k (1- y_k) * Err$$ (for hidden layers $$\delta_k = y_k (1- y_k) * w_j * Err )$$
• Err = Expected output-Actual output
• The weight corrections is calculated based on the error function.
• The new weights are chosen in such way that the final error in that network is minimized.
#### Math-How does the delta rule work?
• Let’s consider a simple example to understand the weight updating using the delta rule.
• If we are building a simple logistic regression line. We would like to find the weights using weight update rule.
• $$Y= \frac{1}{(1+e^(-wx))}$$ is the equation.
• We are searching for the optimal w for our data
• Let w be 1
• $$Y=\frac{1}{(1+e^(-x))}$$ is the initial equation
• The error in our initial step is 3.59
• To reduce the error we will add a delta to w and make it 1.5
• Now w is 1.5 (blue line)
• $$Y=\frac{1}{(1+e^(-1.5x))}$$ the updated equation
• With the updated weight, the error is 1.57
• We can further reduce the error by increasing w by delta
• If we repeat the same process of adding delta and updating weights, we can finally end up with minimum error.
• The weight at that final step is the optimal weight.
• In this example the weight is 8, and the error is 0.
• $$Y=\frac{1}{(1+e^(-8x))}$$ is the final equation.
• In this example, we manually changed the weights to reduce the error. This is just for intuition, manual updating is not feasible for complex optimization problems.
• In gradient descent is a scientific optimization method. We update the weights by calculating gradient of the function.
### How does gradient descent work?
• Gradient descent is one of the famous ways to calculate the local minimum.
• By Changing the weights we are moving towards the minimum value of the error function. The weights are changed by taking steps in the negative direction of the function gradient(derivative).
#### Does this method really work?
• We changed the weights did it reduce the overall error?
• Lets calculate the error with new weights and see the change | 673 | 2,695 | {"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} | 3.8125 | 4 | CC-MAIN-2021-39 | latest | en | 0.837196 |
https://cracku.in/79-the-cost-price-of-an-article-is-x-it-is-marked-up--x-ssc-cgl-19-aug-shift-2 | 1,686,308,631,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224656675.90/warc/CC-MAIN-20230609100535-20230609130535-00212.warc.gz | 205,567,650 | 20,066 | Question 79
# The cost price of an article is x. It is marked up by 120%. It is sold at Rs 8800 after giving 20% discount. What is the value (in Rs) of x?
Solution
$$\frac{100-20}{100} \times \frac{100+120}{100} \times (x) = 8800$$
$$\frac{80}{100} \times \frac{220}{100} \times (x) = 8800$$
$$x = 8800/(1.76) = 5000$$
So the answer is option D.
• Free SSC Study Material - 18000 Questions
• 230+ SSC previous papers with solutions PDF | 158 | 442 | {"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} | 3.828125 | 4 | CC-MAIN-2023-23 | latest | en | 0.793275 |
https://www.cfd-online.com/W/index.php?title=Boussinesq_eddy_viscosity_assumption&oldid=12764 | 1,513,172,323,000,000,000 | text/html | crawl-data/CC-MAIN-2017-51/segments/1512948523222.39/warc/CC-MAIN-20171213123757-20171213143757-00174.warc.gz | 738,067,791 | 10,792 | # Boussinesq eddy viscosity assumption
In 1877 Boussinesq postulated that the momentum transfer caused by turbulent eddies can be modeled with an eddy viscosity. This is in analogy with how the momentum transfer caused by the molecular motion in a gas can be described by a molecular viscosity. The Boussinesq assumption states that the Reynolds stress tensor, $\tau_{ij}$, is proportional to the trace-less mean strain rate tensor, $S_{ij}^*$, and can be written in the following way:
$\tau_{ij} = 2 \, \mu_t \, S_{ij}^* - \frac{2}{3} \rho k \delta_{ij}$
Where $\mu_t$ is a scalar property called the eddy viscosity. The same equation can be written more explicitly as:
$-\rho \overline{u'_i u'_j} = \mu_t \, \left( \frac{\partial U_i}{\partial x_j} + \frac{\partial U_j}{\partial x_i} - \frac{2}{3} \frac{\partial U_k}{\partial x_k} \delta_{ij} \right) - \frac{2}{3} \rho k \delta_{ij}$
Note that for incompressible flow:
$\frac{\partial U_k}{\partial x_k} = 0$
The Boussinesq eddy viscosity assumption is also often called the Boussinesq hypothesis or the Boussinesq approximation.
## References
Boussinesq, J. (1877), "Essai sur la théorie des eaux courantes", Mémoires présentés par divers savants à l'Académie des Sciences XXIII, 1, pp. 1-680.
Schmitt, F.G. (2007), "About Boussinesq’s turbulent viscosity hypothesis: historical remarks and a direct evaluation of its validity", Comptes Rendus Mécanique, vol. 335 (9-10), pp. 617-627; doi:10.1016/j.crme.2007.08.004. | 452 | 1,482 | {"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": 6, "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} | 2.59375 | 3 | CC-MAIN-2017-51 | latest | en | 0.639832 |
https://onlinehextools.com/and-hex-numbers | 1,701,191,650,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679099892.46/warc/CC-MAIN-20231128151412-20231128181412-00657.warc.gz | 525,671,675 | 13,754 | 51K
# Hex and calculator
World's simplest hex tool
Free online hexadecimal bitwise AND calculator. Just load your hexadecimals and they will automatically get ANDed together. There are no ads, popups or nonsense, just an awesome hex AND calculator. Load hex, AND hex. Created for developers by developers from team Browserling.
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## What is a hex and calculator?
This tool performs the bitwise AND operation on all input hex numbers. The bitwise AND operation works on individual bits and before it's computed, the base of input hex numbers is internally converted to binary and zero-padded so that they all had the same length. Then, bits in every position are compared. If they are all 1, then the output bit is 1, otherwise, the output bit is 0. Hexabulous!
## Hex and calculator examples
Click to use
Compute Bitwise AND of Two Hex Values
This example calculates bitwise AND of two hex numbers. The second hex value is a mask that isolates 2nd, 4th, 6th, and 8th hex digits in the first hex value.
0x87654321 0xf0f0f0f0
80604020
Calculate AND of Multiple Hex Numbers
This example performs bitwise AND operation on several hexadecimal values. As they are all the same length, AND can be computed digit by digit. Going from right to left (<- this way), the first digit is AND(e,a,6,6)=2, the second digit is AND(e,f,6,5)=4, the third digit is AND(f,a,f,4)=0, the fourth digit is AND(f,f,e,3)=2, and the last two digits are both zero because AND(0,a,e,2)=0, and AND(c,f,b,1)=0. The last two digits aren't printed as they are the leading digits and the result value 0x002042 is the same as 0x2024.
0xc0ffee 0xfafafa 0xbeef66 0x123456
2042
Hex Formats
In this example, we demonstrate four different hex formats that you can use for entering hex values in the input. You can use capital hex letters and capital hex prefixes, small hex prefixes, or no hex prefixes.
0xAABBCC 0Xa1234 0XF0EEF7 654bca
200
Pro tips Master online hex tools
You can pass input to this tool via ?input query argument and it will automatically compute output. Here's how to type it in your browser's address bar. Click to try!
https://onlinehextools.com/and-hex-numbers?input=0x87654321%0A0xf0f0f0f0
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Generate Custom Hex
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Create a hex dump of files in your browser.
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Convert hexadecimal numbers to a file.
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Convert a CMYK Color to Hex
Convert a color in CMYK format to #rrggbb format.
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Color Hex Digits
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Add coloring to multiple hex numbers.
Create a Hex ZigZag
Make a hex number go in a zigzag.
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Create a template for a six-faced flexagon from two images.
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Join together a bunch of hexagons and create hex tilings.
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Create a hexagonal tilemap.
Generate a Hex Multiplication Table
Create a multiplication table for hex numbers. | 2,006 | 8,657 | {"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} | 3.515625 | 4 | CC-MAIN-2023-50 | latest | en | 0.85098 |
https://tackk.com/5t0j5j | 1,503,387,892,000,000,000 | text/html | crawl-data/CC-MAIN-2017-34/segments/1502886110485.9/warc/CC-MAIN-20170822065702-20170822085702-00436.warc.gz | 839,935,905 | 7,892 | # Mrs. Vande Hei's NewsletterJanuary 19-23rd
What happens when your kindergartener finds out that "Q" and "U" are married? A deeper discussion followed along with lots of laughter! They learned that "q" and "u" are two letters that are always found next to each other in order to make a word. We also had a super fast and busy week with Jump Rope for Heart and only a four day week. We had to complete assessments as our quarter wrapped up today. I am proud of all our their growth and progress!
# Literacy
We have been spending a lot of time learning about main idea and details of text. We read about Dr. Martin Luther King, Jr. and learned about what a great leader he was and how he wanted everyone to be equal. We also read other non-fiction texts about penquins so the students could practice more with learning the main idea and finding the details. During writing, we are still working on having an uppercase letter at the beginning of our sentences, stretching out our sounds to spell our words, and putting a punctuation mark at the end. Lots of improvements are being made and I am so proud of all their hard work!
# Math
This week, we wrapped up our work on 3D shapes with a review. We have definitely come a long way since the beginning of the year, but have more work to do. Shapes will be assessed in the 3rd quarter. You can help your child out with this by practicing them at home as well! Ask them how they can tell the difference between a 2D shape and a 3D shape! We also spent some time on writing addition equations using pretend marshmallows for our hot chocolate mugs and rolling dice to get the numbers we needed. Maybe when it gets nice and cold out, we can warm up with some hot chocolate and marshmallows at school. I do owe them an incentive!
# Needs and Wants
Your child has done a very nice job at telling the difference between needs and wants. Keep talking with them about what is important to have to survive (need) and what is only "fun" to have (want). We will continue our discussion of this topic throughout the next few weeks.
# 100th Day Celebration
Our 100th Day Celebration is coming up! (Yes, it is a HUGE deal in kindergarten!) It is on February 6th, an early release date. Be looking in the Wednesday folder for some important help that I need from you!
# Box Tops
Keep saving those box tops! We are making a lot of money for our school! You are guys are amazing! | 548 | 2,419 | {"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} | 2.65625 | 3 | CC-MAIN-2017-34 | latest | en | 0.978387 |
https://rdrr.io/cran/dbmss/man/Kdhat.html | 1,534,380,433,000,000,000 | text/html | crawl-data/CC-MAIN-2018-34/segments/1534221210387.7/warc/CC-MAIN-20180815235729-20180816015729-00370.warc.gz | 739,440,166 | 41,914 | # Kdhat: Estimation of the Kd function In dbmss: Distance-Based Measures of Spatial Structures
## Description
Estimates the Kd function
## Usage
```1 2 3``` ``` Kdhat(X, r = NULL, ReferenceType, NeighborType = ReferenceType, Weighted = FALSE, Original = TRUE, Approximate = ifelse(X\$n < 10000, 0, 1), Adjust = 1, MaxRange = "ThirdW", StartFromMinR = FALSE, CheckArguments = TRUE) ```
## Arguments
`X` A weighted, marked planar point pattern (`wmppp.object`) or a `Dtable` object. `r` A vector of distances. If `NULL`, a default value is set: 512 equally spaced values are used, from the smallest distance between points to half the diameter of the window. `ReferenceType` One of the point types. If "", all points are considered (this is not the default value; `NeighborType` is ignored then) to estimate the average value of simulated Kd values under the null hypothesis of RandomLocation (Marcon and Puech, 2012). `NeighborType` One of the point types. By default, the same as reference type. `Weighted` Logical; if `TRUE`, estimates the Kemp function. `Original` Logical; if `TRUE` (by default), the original bandwidth selection by Duranton and Overman (2005) following Silverman (1986: eq 3.31) is used. If `FALSE`, it is calculated following Sheather and Jones (1991), i.e. the state of the art. See `bw.SJ` for more details. `Approximate` if not 0 (1 is a good choice), exact distances between pairs of points are rounded to 1024 times `Approximate` single values equally spaced between 0 and the largest distance. This technique (Scholl and Brenner, 2015) allows saving a lot of memory when addressing large point sets (the default value is 1 over 10000 points). Increasing `Approximate` allows better precision at the cost of proportional memory use. Ignored if `X` is a `Dtable` object. `Adjust` Force the automatically selected bandwidth (following `Original`) to be multiplied by `Adjust`. Setting it to values lower than one (1/2 for example) will sharpen the estimation. `MaxRange` The maximum value of `r` to consider, ignored if `r` is not `NULL`. Default is "ThirdW", one third of the diameter of the window. Other choices are "HalfW", and "QuarterW" and "D02005". "HalfW", and "QuarterW" are for half or the quarter of the diameter of the window. "D02005" is for the median distance observed between points, following Duranton and Overman (2005). "ThirdW" should be close to "DO2005" but has the advantage to be independent of the point types chosen as `ReferenceType` and `NeighborType`, to simplify comparisons between different types. "D02005" is approximated by "ThirdW" if `Approximate` is not 0. if `X` is a `Dtable` object, the diameter of the window is taken as the max distance between points. `StartFromMinR` Logical; if `TRUE`, points are assumed to be further from each other than the minimum observed distance, So Kd will not be estimated below it: it is assumed to be 0. If `FALSE`, distances are smoothed down to \$r=0\$. Ignored if `Approximate` is not 0: then, estimation always starts from \$r=0\$. `CheckArguments` Logical; if `TRUE`, the function arguments are verified. Should be set to `FALSE` to save time in simulations for example, when the arguments have been checked elsewhere.
## Details
Kd is a density, absolute measure of a point pattern structure. Kd is computed efficiently by building a matrix of distances between point pairs and calculating the density of their distribution (the default values of `r` are those of the `density` function). The kernel estimator is Gaussian.
The weighted Kd function has been named Kemp (emp is for employees) by Duranton and Overman (2005).
If `X` is not a `Dtable` object, the maximum value of `r` is obtained from the geometry of the window rather than caculating the median distance between points as suggested by Duranton and Overman (2005) to save (a lot of) calculation time.
## Value
An object of class `fv`, see `fv.object`, which can be plotted directly using `plot.fv`.
## Note
Estimating Kd relies on calculating distances, exactly or approximately (if `Approximate` is not 0). Then distances are smoothed by estimating their probability density. Reflection is used to estimate density close to the lowest distance, that is the minimum observed distance (if `StartFromMinR` is `TRUE`) or 0: all distances below 4 times the estimation kernel bandwith apart from the lowest distance are duplicated (symmetrically with respect to the lowest distance) to avoid edge effects (underestimation of the density close to the lowest distance).
## Author(s)
Eric Marcon <[email protected]>
## References
Duranton, G. and Overman, H. G. (2005). Testing for Localisation Using Micro-Geographic Data. Review of Economic Studies 72(4): 1077-1106.
Marcon, E. and F. Puech (2017). A typology of distance-based measures of spatial concentration. Regional Science and Urban Economics. 62:56-67.
Scholl, T. and Brenner, T. (2015) Optimizing distance-based methods for large data sets, Journal of Geographical Systems 17(4): 333-351.
Sheather, S. J. and Jones, M. C. (1991) A reliable data-based bandwidth selection method for kernel density estimation. Journal of the Royal Statistical Society series B, 53, 683-690.
Silverman, B. W. (1986). Density estimation for statistics and data analysis. Chapman and Hall, London.
`KdEnvelope`, `Mhat`
## Examples
```1 2 3 4 5 6 7``` ```data(paracou16) plot(paracou16) # Calculate Kd (Paracou <- Kdhat(paracou16, , "Q. Rosea", "V. Americana")) # Plot plot(Paracou) ```
### Example output
```Loading required package: spatstat
spatstat 1.52-1 (nickname: 'Apophenia')
For an introduction to spatstat, type 'beginner'
Note: spatstat version 1.52-1 is out of date by more than 7 months; we recommend upgrading to the latest version.
Warning message:
Interpretation of arguments maxsize and markscale has changed (in spatstat version 1.37-0 and later). Size of a circle is now measured by its diameter.
Function value object (class 'fv')
for the function r -> Kd(r)
.................................
Math.label Description
r r distance argument r
Kd hat(Kd)(r) Estimated Kd(r)
.................................
Default plot formula: .~r
where "." stands for 'Kd'
Recommended range of argument r: [0, 102.11]
Available range of argument r: [0, 102.11]
Unit of length: 1 meter
```
dbmss documentation built on March 19, 2018, 5:05 p.m. | 1,639 | 6,395 | {"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} | 2.59375 | 3 | CC-MAIN-2018-34 | longest | en | 0.75485 |
https://studyadda.com/question-bank/area-bounded-by-region-volume-and-surface-area-of-solids-of-revolution_q7/1106/81257 | 1,601,400,140,000,000,000 | text/html | crawl-data/CC-MAIN-2020-40/segments/1600400202418.22/warc/CC-MAIN-20200929154729-20200929184729-00209.warc.gz | 626,713,196 | 18,505 | • # question_answer Area between the curve $y=\cos x$ and $x-$axis when $0\le x$ is [MP PET 1997] A) 2 B) 4 C) 0 D) 3
$y=\cos x$, When $x\in \left[ 0,\frac{\pi }{2} \right],\cos x\ge 0$ When $x\in \left[ \frac{\pi }{2},\frac{3\pi }{2} \right],\cos x\le 0$ When $x\in \left[ \frac{3\pi }{2},2\pi \right],\cos x\ge 0$ Thus required area is given by, $\int_{0}^{\pi /2}{\,\,ydx}=\int_{0}^{\pi /2}{\cos x\,dx+\int_{\pi /2}^{3\pi /2}{(-\cos x)dx+\int_{3\pi /2}^{2\pi }{\,\cos xdx}}}$ $=1+2+1=4sq.$unit. | 279 | 649 | {"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} | 3.46875 | 3 | CC-MAIN-2020-40 | latest | en | 0.26205 |
http://makezine.com/2009/12/17/ask-make-how-to-wire-up-leds/?like=1&source=post_flair&_wpnonce=8cb43e0c56 | 1,386,400,208,000,000,000 | text/html | crawl-data/CC-MAIN-2013-48/segments/1386163053669/warc/CC-MAIN-20131204131733-00071-ip-10-33-133-15.ec2.internal.warc.gz | 111,413,905 | 27,472 | Ask MAKE: How to wire up LEDs?
Ask MAKE is a weekly column where we answer reader questions, like yours. Write them in to mattm@makezine.comor drop us a line on Twitter. We can’t wait to tackle your conundrums!
Bjorn writes in:
I’m wondering if you could help me out with resistors. I’m a computer science guy and am very new to electronics. Most of my resistor usage in my experimentation has been because I read about situations when I should use them online and just used a specific resistor because it was recommended. Obviously this only gets me so far. How do you go about determining what level of resistance you need and when you should or need to use resistors? I didn’t know I was supposed to be hooking up LEDs to my Arduinos with resistors until I started burning out LEDs and read somewhere what type of resistor someone recommended. I know it has to do with the Arduino running at 5V and most LEDs being lower voltage, but how do you know what voltage an LED is if it’s not labeled? And more importantly (like my question above), even if you know what voltage and LED is how are you supposed to figure out what kind of resistor to use?
Sure thing! This question actually comes up quite a bit, and it’s a good thing to understand.
Putting a resistor in series with an LED limits the amount of current that can flow through it, preventing it from blowing up. It’s nice to be able to figure out an exact resistance to use, but if you aren’t too worried about your light being a bit dim, you can always just stick in a largish resistor, and you will get some light. For instance, if I am making a prototype circuit and just want an indicator light that I can control from an Arduino, I’ll grab a 220 ohm resistor and put it in series with the first LED I can find. It’s probably fine for a quickie circuit, but if you are soldering up a project that you intend to keep around, it’s probably a better idea to actually calculate the correct amount of resistance to use.
So, how do you do it? Well, for a single LED, you can use the LED circuit equation:
Unfortunately, this only helps if you know the forward voltage and current rating of your diode. So, how can one figure those out? You can make an estimate abut the forward voltage of the diode based on it’s color, because the wavelength of the color and the forward voltage are roughly inversely proportional to one another. Some typical forward voltages are: Red:1.8V, Green: 2V, Blue: 3.4V. Once you have an estimate, you can measure the forward voltage of your LED by hooking it up with the suggested resistor value, and measuring the voltage across it. Then, if you were way off, you can re-calculate the resistance with the actual voltage to get a better result.
Once you know the forward voltage drop, you can choose a current value based on how bright you want the LED to be, as long as it is lower than the current rating of the device. Unfortunately, it’s a little bit harder to figure out the current rating, because most LEDs will continue to operate at higher than the recommended amount. If they are, though, their lifetime will be much shorter, and they won’t be as efficient at producing light. If you don’t have the specifications for your LED, 20ma is probably a safe maximum.
If you don’t feel like solving all of that by hand, or have a more complicated design involving multiple LEDs, you could also use an online LED calculator. This one looks nice, because it will also tell you how to hook up multilple LEDs.
Ok, enough calculations. This is what can happen if you don’t connect the LED up properly:
Boom! Engineers sometimes call these ‘unauthorized thermal events’
Related:
9 Responses to Ask MAKE: How to wire up LEDs?
1. erikscott on said:
When you don’t use the dropping resistor, at least some times you can hear them.
2. Anonymous on said:
We always called it ‘letting out the magic smoke’ – which obviously applied to more than just LED’s… I did see part of a PIC18F go flying through the air when one of my friends mistakenly assumed that the 5 volt output from a USB port was equivalent to a 5 volt output from a power supply… oops.
3. Anonymous on said:
4. Before LED’s were common small neon bulbs were often used for indicators. I bought a ten pack at the Shack for a buck, went home, and plugged the bare wires of one into a 120 volt outlet. After all, it was rated for 120 volts. I didn’t know about the need for a current limiting resistor. I can still see, hear, and feel the explosion.
5. A close approximation of the resistor needed for an LED is to use 100 ohms per volt. For 5 volts, use a resistor close to 500 ohms. If the LED has a 1.7 volt drop, that leaves 3.3v for the 500 ohm resistor. Ohm’s law then tells us the circuit is drawing V/R=I, or 3.3/500=6.6mA. This is fine enough for an indicator. Higher voltages are more accurate. 100V, 10Kohm with a LED drop of 1v is 9.9mA, with an LED with a 5v drop the current is 9.5mA. 12V, 1.2Kohm gives about 10mA for almost any LED. The only problem with this resistor shortcut is that the supply voltage has to be greater than the LED drop.
6. So “voltage drop” is “forward voltage” is “voltage across it”? Thanks!
• Yeah, those are all different words for the same thing.
7. Does anything change when you start doing strands of LEDs? | 1,260 | 5,313 | {"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} | 2.921875 | 3 | CC-MAIN-2013-48 | longest | en | 0.953073 |
https://community.fabric.microsoft.com/t5/DAX-Commands-and-Tips/Need-help-with-a-calculated-field-that-takes-the-variance-for/m-p/2496759/highlight/true | 1,726,152,884,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651460.54/warc/CC-MAIN-20240912142729-20240912172729-00240.warc.gz | 163,306,451 | 61,697 | Skip to main content
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Helper IV
## Need help with a calculated field that takes the variance for each row.
Need help with a calculated field that takes the variance for each row. I would need the variance from the "Event Set Up Date" to the "End of Mailing Month" and then the variance from the "End of Mailing Month" to the "All Drops Mature Date".
1 ACCEPTED SOLUTION
Super User
Hi @krichmond
First of all please accept my apology for causing such confusion. I admit that I did not pay enough attention to the details therefore unintentionally misleading you and waisting your time.
Here is the solution:
You are using a matrix visual where you're having the [Production Stage] column at the columns of your matrix. While you have only one value which is the quantity. If you wish to add the two variances to the matrix it will not look as you wish because this will triple the total columns of the matrix from 3 to 9. Therefore, I would recommend to use a table visual instead while you keep the [Client ID] and the [Client Name] on the values (acting as rows). On the other hand as the [Production Stage] column has only three distinct values, we can create a measure representing each of these values as follows:
``````Event Set Up Date Quantity =
CALCULATE (
SUM ( Sheet1[Quantity] ),
Sheet1[Production Stage] = "Event Set Up Date"
)``````
``````End of Mailing Month Quantity =
CALCULATE (
SUM ( Sheet1[Quantity] ),
Sheet1[Production Stage] = "End of Mailing Month"
)``````
``````All Drops Mature Date Quantity =
CALCULATE (
SUM ( Sheet1[Quantity] ),
Sheet1[Production Stage] = "All Drops Mature Date"
)``````
Now you can create the variance measures as follows:
``Variance 1 = [Event Set Up Date Quantity] - [End of Mailing Month Quantity]``
``Variance 2 = [End of Mailing Month Quantity] - [All Drops Mature Date Quantity]``
Please let me know if you need any help. You can also share a sample file and I can do it for you.
Thank you for your patience and have a good day.
14 REPLIES 14
Super User
Hi @krichmond
First of all please accept my apology for causing such confusion. I admit that I did not pay enough attention to the details therefore unintentionally misleading you and waisting your time.
Here is the solution:
You are using a matrix visual where you're having the [Production Stage] column at the columns of your matrix. While you have only one value which is the quantity. If you wish to add the two variances to the matrix it will not look as you wish because this will triple the total columns of the matrix from 3 to 9. Therefore, I would recommend to use a table visual instead while you keep the [Client ID] and the [Client Name] on the values (acting as rows). On the other hand as the [Production Stage] column has only three distinct values, we can create a measure representing each of these values as follows:
``````Event Set Up Date Quantity =
CALCULATE (
SUM ( Sheet1[Quantity] ),
Sheet1[Production Stage] = "Event Set Up Date"
)``````
``````End of Mailing Month Quantity =
CALCULATE (
SUM ( Sheet1[Quantity] ),
Sheet1[Production Stage] = "End of Mailing Month"
)``````
``````All Drops Mature Date Quantity =
CALCULATE (
SUM ( Sheet1[Quantity] ),
Sheet1[Production Stage] = "All Drops Mature Date"
)``````
Now you can create the variance measures as follows:
``Variance 1 = [Event Set Up Date Quantity] - [End of Mailing Month Quantity]``
``Variance 2 = [End of Mailing Month Quantity] - [All Drops Mature Date Quantity]``
Please let me know if you need any help. You can also share a sample file and I can do it for you.
Thank you for your patience and have a good day.
Helper IV
@tamerj1 - No worries! Let me just say this... I have never received such amazing support in my life on a community forum. I cannot thank you enough. We recently switched from Tableau to Power BI and I am at the very beginning of the learning curve. This worked perfectly. I hope you have a fantastic day.
Super User
Please calrify further perhaps with example. Thank you
Helper IV
@tamerj1 - No problem. So for the row with 101000052, the variance between the "Event Set Up Date" to the "End of Mailing Month" would be 3,905 and the variance between the "End of Mailing Month" to the "All Drops Mature Date" would be 75.
Super User
What type of aggregation do the columns have? SUM?
Helper IV
@tamerj1 - Yes, it is SUM.
Super User
Then I would prefer to add them as Measures. Example:
Event Set Up_Date = SUM ( Table[Event Set Up Date] )
End of Mailing_Month = SUM ( Table[End of Mailing Month] )
All Drops Mature_Date = SUM ( Table[All Drops Mature Date] )
Then add the measures to the instead of the columns.
After that you can perform simple subtraction:
[Event Set Up_Date] - [End of Mailing_Month]
or
[End of Mailing_Month] - [All Drops Mature_Date]
Helper IV
@tamerj1 - I am getting the following error message.
Super User
Please use your table name. If it is Table then write 'Table'
Helper IV
@tamerj1 - Tried that and it still isn't working. I am new to Power BI (obviously), so apologize for all of the issues with this. Is there a way to post the work file so you can get in there and take a look? I tried but it wouldn't let me attached a file.
Super User
No worr Sometimes you have hidden characters. Better to copy the column name from the table header and paste it
Helper IV
@tamerj1 - I don't see a column heading named "Event Set Up Date" but I do see that in your formula that you provided. Maybe that is what is causing the issue?
Super User
Use [Quantit]
Super User
Total Quantity = SUM ( Sheet1[Quantity] )
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Top Kudoed Authors | 1,540 | 6,303 | {"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} | 3.265625 | 3 | CC-MAIN-2024-38 | latest | en | 0.887295 |
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MATH 98 Essentials of Intermediate Algebra
5 credits
This course focuses on the intermediate algebra skills needed for students planning to take MATH& 107 , MATH& 146 , or MATH 147 . Emphasis is on data analysis, mathematical modeling, quantitative reasoning, and working with linear and exponential functions. Applications with quadratic, rational, and radical functions are also covered.
Prerequisites: MATH 87 (or placement into MATH 098)
Course Outcomes
Upon successful completion of this course, students will be able to:
• Use dimensional analysis to make calculations
• Interpret and move flexibly between multiple formats, including graphs, tables, equations, and words
• Solve applied problems involving linear, quadratic, exponential, rational, and radical equations
• Calculate the slope of linear data and interpret slope within the context of the problem
• Distinguish between linear and exponential growth models
• Apply exponent rules to simplify expressions with exponents
• Solve formulas for a specified variable
• Use geometric concepts of area and volume in solving applied problems
• Create and use models (tables, words, graphs, equations) of real-world situations
• Analyze and use quantitative information to support an argument
• Communicate quantitative results both in writing and orally using appropriate language, symbolism, data, and graphs
• Demonstrate quantitative reasoning to analyze problems, critique arguments, and draw and justify conclusions
• Use technology appropriately as a tool for calculations and to gather, research, and analyze quantitative information
Total Hours: 50 Theory (Lecture) Hours: 50 | 504 | 2,172 | {"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} | 3.21875 | 3 | CC-MAIN-2024-30 | latest | en | 0.787534 |
https://michaeldewittjr.com/programming/2020-08-27-optimisation-with-stan/index.html | 1,713,656,235,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296817688.24/warc/CC-MAIN-20240420214757-20240421004757-00682.warc.gz | 363,933,418 | 9,945 | # Optimisation with Stan
Using Stan for optimization.
Stan
Optimisation
Author
Affiliation
Published
August 27, 2020
In this post I just wanted to play around using the ability to optimize functions in Stan. I know that there are other solvers available, but I just wanted to try this one to start (and I can’t find it now, but I think this was discussed in Regression and Other Stories).
First, I’ll load the cmstanr package which has become my favourite way to interface with Stan.
library(cmdstanr)
This is cmdstanr version 0.4.0
- Online documentation and vignettes at mc-stan.org/cmdstanr
- CmdStan path set to: /Users/michael/.cmdstanr/cmdstan-2.28.2
- Use set_cmdstan_path() to change the path
A newer version of CmdStan is available. See ?install_cmdstan() to install it.
To disable this check set option or environment variable CMDSTANR_NO_VER_CHECK=TRUE.
Now we can compile a simple optimization scenario which could be a pretty classic production function where you get 2 dollars for widget x and four dollars for wiget y:
$\text{optimize } 2*x + 4*y \\ \text{subject to:} \\ 0\le x \le 10 \\ 0\le y \le 20 \\$
There are also contraints on how many units you can make of each.
m <- cmdstan_model("optim.stan")
Now print the code:
m$print() //Test program for optimization data{ } parameters{ real<lower=0,upper=10> x; real<lower=0,upper=20> y; } model{ target += 2*x +4*y; } Run the model: fit <- m$sample(refresh = 0)
Running MCMC with 4 parallel chains...
Chain 1 finished in 0.0 seconds.
Chain 2 finished in 0.0 seconds.
Chain 3 finished in 0.0 seconds.
Chain 4 finished in 0.0 seconds.
All 4 chains finished successfully.
Mean chain execution time: 0.0 seconds.
Total execution time: 0.4 seconds.
Warning in seq.default(from = 1, len = along - 1): partial argument match of
'len' to 'length.out'
Warning in seq.default(to = N - 1, len = N - along): partial argument match of
'len' to 'length.out'
Warning in seq.default(len = N): partial argument match of 'len' to 'length.out'
Warning in seq.default(along = arg.names): partial argument match of 'along' to
'along.with'
Warning in seq.default(len = length(arg.list)): partial argument match of 'len'
to 'length.out'
Warning in seq.default(along = perm): partial argument match of 'along' to
'along.with'
Warning in seq.default(along = perm): partial argument match of 'along' to
'along.with'
Warning in seq.default(along = perm): partial argument match of 'along' to
'along.with'
Warning in seq.default(along = perm): partial argument match of 'along' to
'along.with'
Warning in seq.default(along = perm): partial argument match of 'along' to
'along.with'
Warning in seq.default(along = perm): partial argument match of 'along' to
'along.with'
Warning in seq.default(along = perm): partial argument match of 'along' to
'along.with'
Warning in seq.default(along = perm): partial argument match of 'along' to
'along.with'
Warning in seq.default(len = ncol(arg.dim)): partial argument match of 'len' to
'length.out'
Warning in seq.default(len = N): partial argument match of 'len' to 'length.out'
Warning in seq.default(along = arg.names): partial argument match of 'along' to
'along.with'
Warning in seq.default(along = arg.names): partial argument match of 'along' to
'along.with'
Warning in seq.default(len = length(arg.names)): partial argument match of 'len'
to 'length.out'
Warning in seq.default(along = perm): partial argument match of 'along' to
'along.with'
Summarise the outputs:
fit$print() Warning in seq.default(from = 1, len = along - 1): partial argument match of 'len' to 'length.out' Warning in seq.default(to = N - 1, len = N - along): partial argument match of 'len' to 'length.out' Warning in seq.default(len = N): partial argument match of 'len' to 'length.out' Warning in seq.default(along = arg.names): partial argument match of 'along' to 'along.with' Warning in seq.default(len = length(arg.list)): partial argument match of 'len' to 'length.out' Warning in seq.default(along = perm): partial argument match of 'along' to 'along.with' Warning in seq.default(along = perm): partial argument match of 'along' to 'along.with' Warning in seq.default(along = perm): partial argument match of 'along' to 'along.with' Warning in seq.default(along = perm): partial argument match of 'along' to 'along.with' Warning in seq.default(along = perm): partial argument match of 'along' to 'along.with' Warning in seq.default(along = perm): partial argument match of 'along' to 'along.with' Warning in seq.default(along = perm): partial argument match of 'along' to 'along.with' Warning in seq.default(along = perm): partial argument match of 'along' to 'along.with' Warning in seq.default(len = ncol(arg.dim)): partial argument match of 'len' to 'length.out' Warning in seq.default(len = N): partial argument match of 'len' to 'length.out' Warning in seq.default(along = arg.names): partial argument match of 'along' to 'along.with' Warning in seq.default(along = arg.names): partial argument match of 'along' to 'along.with' Warning in seq.default(len = length(arg.names)): partial argument match of 'len' to 'length.out' Warning in seq.default(along = perm): partial argument match of 'along' to 'along.with' variable mean median sd mad q5 q95 rhat ess_bulk ess_tail lp__ 94.71 95.06 1.14 0.83 92.35 95.80 1.00 1291 1438 x 9.48 9.64 0.51 0.36 8.47 9.97 1.00 1771 1099 y 19.75 19.82 0.24 0.18 19.24 19.99 1.00 1923 1360 out <- fit$draws(inc_warmup = FALSE, variables = c("x", "y"))
out_x <- rowMeans(as.data.frame(out[,,1]))
out_y <- rowMeans(as.data.frame(out[,,2]))
Graph the outputs:
op <- par(mfrow = c(1,2))
op
$mfrow [1] 1 1 hist(out_x, breaks = 30, main = "Posterior Draws of X", col = "blue") abline(v = mean(out_x), lwd = 2, col = "red") hist(out_y, breaks = 30, main = "Posterior Draws of Y", col = "blue") abline(v = mean(out_y), lwd = 2, col = "red") Pretty neat that it works. Alternatively, you could use the optimize function from CmdStan, but this is a bit of a contrite example. More discussion on this is available at this post. Additionally it is important that the target syntax increments the log-density. In our case it doesn’t matter, but in others it might. ## A Second Example Just to play a bit, I want to add some data. Say we have the same function to optimize to maximize revenue, but instead of making any value of x and y, we have some production data with variability. Perhaps these can be real output from our operating process (machines breakdown and life happens, so a higher value might not be reasonable.) m2 <- cmdstan_model("optim2.stan") Edit 2022-06-02, I realized I didn’t show the code in earlier versions. m2$print()
//Test program for optimization
data{
int<lower=1> N; //number of obs
vector[N] y_in; // observed y
vector[N] x_in; // observed x
real<lower=0> sd_y;
real<lower=0> sd_x;
}
parameters{
real<lower=0,upper=100> x;
real<lower=0,upper=200> y;
}
model{
y_in ~ normal(y, sd_y);
x_in ~ normal(x, sd_x);
target += 2*x +4*y;
}
dat <- list(
y_in = rnorm(100, 7, 1.2),
x_in = rnorm(100, 23, 5),
sd_x = 5L,
sd_y = 2L,
N = 100L
)
fit2 <- m2$sample(data = dat, refresh = 0) Running MCMC with 4 parallel chains... Chain 1 finished in 0.0 seconds. Chain 2 finished in 0.1 seconds. Chain 3 finished in 0.0 seconds. Chain 4 finished in 0.0 seconds. All 4 chains finished successfully. Mean chain execution time: 0.0 seconds. Total execution time: 0.2 seconds. Warning in seq.default(from = 1, len = along - 1): partial argument match of 'len' to 'length.out' Warning in seq.default(to = N - 1, len = N - along): partial argument match of 'len' to 'length.out' Warning in seq.default(len = N): partial argument match of 'len' to 'length.out' Warning in seq.default(along = arg.names): partial argument match of 'along' to 'along.with' Warning in seq.default(len = length(arg.list)): partial argument match of 'len' to 'length.out' Warning in seq.default(along = perm): partial argument match of 'along' to 'along.with' Warning in seq.default(along = perm): partial argument match of 'along' to 'along.with' Warning in seq.default(along = perm): partial argument match of 'along' to 'along.with' Warning in seq.default(along = perm): partial argument match of 'along' to 'along.with' Warning in seq.default(along = perm): partial argument match of 'along' to 'along.with' Warning in seq.default(along = perm): partial argument match of 'along' to 'along.with' Warning in seq.default(along = perm): partial argument match of 'along' to 'along.with' Warning in seq.default(along = perm): partial argument match of 'along' to 'along.with' Warning in seq.default(len = ncol(arg.dim)): partial argument match of 'len' to 'length.out' Warning in seq.default(len = N): partial argument match of 'len' to 'length.out' Warning in seq.default(along = arg.names): partial argument match of 'along' to 'along.with' Warning in seq.default(along = arg.names): partial argument match of 'along' to 'along.with' Warning in seq.default(len = length(arg.names)): partial argument match of 'len' to 'length.out' Warning in seq.default(along = perm): partial argument match of 'along' to 'along.with' Now we can see the results: fit2$print()
Warning in seq.default(from = 1, len = along - 1): partial argument match of
'len' to 'length.out'
Warning in seq.default(to = N - 1, len = N - along): partial argument match of
'len' to 'length.out'
Warning in seq.default(len = N): partial argument match of 'len' to 'length.out'
Warning in seq.default(along = arg.names): partial argument match of 'along' to
'along.with'
Warning in seq.default(len = length(arg.list)): partial argument match of 'len'
to 'length.out'
Warning in seq.default(along = perm): partial argument match of 'along' to
'along.with'
Warning in seq.default(along = perm): partial argument match of 'along' to
'along.with'
Warning in seq.default(along = perm): partial argument match of 'along' to
'along.with'
Warning in seq.default(along = perm): partial argument match of 'along' to
'along.with'
Warning in seq.default(along = perm): partial argument match of 'along' to
'along.with'
Warning in seq.default(along = perm): partial argument match of 'along' to
'along.with'
Warning in seq.default(along = perm): partial argument match of 'along' to
'along.with'
Warning in seq.default(along = perm): partial argument match of 'along' to
'along.with'
Warning in seq.default(len = ncol(arg.dim)): partial argument match of 'len' to
'length.out'
Warning in seq.default(len = N): partial argument match of 'len' to 'length.out'
Warning in seq.default(along = arg.names): partial argument match of 'along' to
'along.with'
Warning in seq.default(along = arg.names): partial argument match of 'along' to
'along.with'
Warning in seq.default(len = length(arg.names)): partial argument match of 'len'
to 'length.out'
Warning in seq.default(along = perm): partial argument match of 'along' to
'along.with'
variable mean median sd mad q5 q95 rhat ess_bulk ess_tail
lp__ 10.53 10.82 0.95 0.70 8.65 11.45 1.00 1854 2462
x 23.97 23.97 0.50 0.51 23.16 24.79 1.00 3721 2765
y 7.20 7.20 0.19 0.19 6.88 7.52 1.00 3569 2629
out <- fit2$draws(inc_warmup = FALSE, variables = c("x", "y")) out_x <- rowMeans(as.data.frame(out[,,1])) out_y <- rowMeans(as.data.frame(out[,,2])) op <- par(mfrow = c(1,2)) op $mfrow
[1] 1 1
hist(out_x, breaks = 30, main = "Posterior Draws of X", col = "blue")
abline(v = mean(out_x), lwd = 2, col = "red")
hist(out_y, breaks = 30, main = "Posterior Draws of Y", col = "blue")
abline(v = mean(out_y), lwd = 2, col = "red")
The results from the second model represent the influence of the data from our actual manufacturing process. This can be valuable when trying to optimize these kinds of problems when the true data generating process is available to us.
## Citation
BibTeX citation:
@online{dewitt2020,
author = {Michael DeWitt},
title = {Optimisation with {Stan}},
date = {2020-08-27},
url = {https://michaeldewittjr.com/programming/2020-08-27-optimisation-with-stan},
langid = {en}
} | 3,360 | 12,048 | {"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": 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} | 2.796875 | 3 | CC-MAIN-2024-18 | latest | en | 0.843919 |
https://gathright-reed.com/answers-to-readers-questions/often-asked-type-2-diabetes-how-much-insulin.html | 1,652,880,606,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662522270.37/warc/CC-MAIN-20220518115411-20220518145411-00636.warc.gz | 334,848,305 | 11,669 | # Often asked: Type 2 Diabetes How Much Insulin?
## How do I calculate how much insulin to take?
Step 1: Calculate an insulin dose for food: Divide the total grams of carb by your insulin-to-carb ratio. Example Let’s say you plan to eat 45 grams of carbohydrate and your insulin-to-carb ratio is 1 unit of insulin for every 15 grams of carbohydrate eaten. To figure out how much insulin to give, divide 45 by 15.
## Does type 2 diabetes require more insulin?
People with type 2 diabetes do not always have to take insulin right away; that is more common in people with type 1 diabetes. The longer someone has type 2 diabetes, the more likely they will require insulin. Just as in type 1 diabetes, insulin is a way to control your blood glucose level.
## When should a Type 2 diabetic take insulin?
When to take insulin for type 2 diabetes
1. when blood sugar management is an immediate need that can’t be managed without it.
2. when an eating plan, weight loss, exercise, and other medications don’t achieve targeted blood glucose goals.
You might be interested: Readers ask: At What Stage Do Type 2 Diabetes Stop Making Insulin?
## How much insulin does a diabetic take per day?
How much insulin do you need? In type 1 diabetes, most people need a total of 0.5 – 0.8 units of insulin per kilogram of body weight each day. Roughly half this insulin is needed for food intake, and half is the basal rate.
## How much does 1 unit of insulin bring down blood sugar?
One unit of insulin should cause your blood sugar level to drop 30 to 50 mg per dL, but you may need more insulin to get the same effect.
## What is the 500 rule in diabetes?
Use the 500 Rule to estimate insulin-to-carb ratio: 500/TDD = number of carb grams covered by a unit of insulin. Example: 500/50=10; 1unit of insulin will cover about 10 grams of carbohydrate.
## Which is better insulin or metformin?
Metformin does not increase the concentration of insulin in the blood and does not cause low blood glucose levels (hypoglycemia) when used alone. Metformin can reduce complications of diabetes such as heart disease, blindness, and kidney disease.
## Can you stop insulin once you start?
Q1. Once you begin using insulin to treat type 2 diabetes, can you ever get off it and go back to medications? For someone to go back to oral diabetes medicines after starting insulin, the pancreas must be able to produce enough insulin to maintain normal sugar levels.
## Where should you not inject insulin?
DON’T: Inject insulin just anywhere. Insulin should be injected into the fat just underneath the skin rather than into muscle, which can lead to quicker insulin action and greater risk of low blood sugar. The stomach, thighs, buttocks, and upper arms are common injection sites because of their higher fat content.
You might be interested: Readers ask: In Type 2 Diabetes What Causes The Body Not To Use Insulin Properly?
## When is insulin given to a diabetic?
Sometimes, people with type 2 diabetes or gestational diabetes need insulin therapy if other treatments haven’t been able to keep blood glucose levels within the desired range. Insulin therapy helps prevent diabetes complications by keeping your blood sugar within your target range.
## Can a diabetic survive without insulin?
Without insulin, people with type 1 diabetes suffer a condition called Diabetic Ketoacidosis (DKA). If left untreated, people die quickly and usually alone. The tragic loss of life from DKA can be prevented.
## How much insulin should I take if my sugar is 500?
Thus: 500 ÷ total daily dose = the number of grams of carbs covered by 1 unit of rapid-acting insulin. If your total daily dose was 50, this would give you the following calculation: 500 ÷ 50 = 10. This would mean that 10 grams of carbs would require 1 unit of insulin, giving you the ratio of 1:10.
## What is the max amount of insulin per day?
Uses: To improve glycemic control in patients with diabetes mellitus; U-500 insulin is for use in patients requiring more than 200 units of insulin per day.
## Why is my sugar high after insulin?
The dawn phenomenon This triggers beta cells in the pancreas to release insulin in order to keep blood glucose levels in check. But if you have diabetes, you may not make enough insulin or may be too insulin resistant to counter the increase in blood sugar. As a result, your levels may be elevated when you wake up. | 984 | 4,410 | {"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} | 3 | 3 | CC-MAIN-2022-21 | latest | en | 0.882407 |
https://deluxeknowledgeexchange.com/math-solution-349 | 1,669,983,471,000,000,000 | text/html | crawl-data/CC-MAIN-2022-49/segments/1669446710902.80/warc/CC-MAIN-20221202114800-20221202144800-00023.warc.gz | 233,224,868 | 5,506 | # Apps to solve math
Best of all, Apps to solve math is free to use, so there's no reason not to give it a try! We will give you answers to homework.
## The Best Apps to solve math
In this blog post, we will be discussing about Apps to solve math. There are a number of websites that allow users to input a math problem and receive step-by-step solutions. This can be a helpful resource for students who are struggling to understand how to solve a particular type of problem. It can also be a good way for students to check their work, as they can compare their own solutions to the ones provided online.
Solving logarithms can be tricky, but there are a few tricks that can help. First, remember that thelogarithm of a number is the exponent to which another number, called the base, must be raised in order to equal the given number. So, to solve a logarithm, you need to find the base and the exponent. There are a few different ways to do this, but one way is to use the change of base formula
Completing the square is a way of solving a quadratic equation by rewriting it in a form that is easier to work with. To complete the square, you need to take the original equation and add or subtract a constant so that the new equation has a perfect square trinomial on one side and a constant on the other side. Once you have done this, you can then use the quadratic equation to solve for the unknown variable.
To solve linear inequalities, you need to first understand what the inequality is trying to tell you. In mathematical terms, an inequality is a statement that two values are not equal. So, when you're solving an inequality, you're trying to find out what values will make the inequality true. There are a few steps you can follow to solve linear inequalities: - First, simplify the equation by removing any fractions or decimals. - Next, isolate the variable on
There are a few different ways to solve fractions. One way is to use a common denominator. This means finding a number that both the numerator and the denominator can be divided by. Another way is to multiply the numerator and denominator by the same number, as long as it is not zero. This is called cross multiplying.
## We solve all types of math troubles
I LOVE this app so much. It helps me with math homework I don't understand and then explains the solutions and it helps me understand it better. It also gives different options for answers. Say the answer to a problem was 1.5 it would also have 1 1/2 as an option for the answer so you wouldn't have to convert. super helpful and would 100% recommend
Izabella Hayes
This app is alright, I like using it to figure the questions I cannot figure out but some of the time for the hard questions it wants you to pay and as a student I have both A no job and B only so much money, all in all a great app, the developers defiantly deserve to make you pay for more features. I would recommend this app.
Gisselle Martin
Hard simple math problems Nonlinear inequality solver Equatino solver Geometry answer finder Chain rule solver How to solve by graphing | 666 | 3,088 | {"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} | 4.71875 | 5 | CC-MAIN-2022-49 | latest | en | 0.958417 |
https://www.jmag-international.com/catalog/152_shortcircuitedpowertransformer_electromagneticforce/ | 1,701,910,721,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679100626.1/warc/CC-MAIN-20231206230347-20231207020347-00823.warc.gz | 914,609,867 | 22,697 | ## [JAC152] Electromagnetic Force Analysis of Short-circuited Power Transformer Coils
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### Overview
A transformer is an electrical device that uses electromagnetic induction to convert the voltage level of alternating current power. Electromagnetic force is produced by the current and magnetic field in a transformer’s coils while it is converting power. There is a risk that a large electromagnetic force can cause the coils to deform or rupture, particularly when something goes wrong and current flows in a short circuit.
Electromagnetic force is produced by the current and magnetic field in a coil, but the coil is exposed to not only the magnetic field it produces by itself but also the magnetic field from other coils and leakage flux from the core. Because of this, it is important to evaluate in advance what kinds of forces are produced in what areas due to the arrangement of the coils and the positional relationship of the coils and core using magnetic field analysis.
This analysis uses different coil positions to evaluate the Lorentz force density and electromagnetic force produced in the coils during a short circuit in order to confirm the effects that the primary and secondary coils have on each other.
### Lorentz Force Density
The Lorentz force density distribution vectors of the V-phase coil as seen from the X-axis are shown in fig. 1, and the Lorentz force density distribution vectors of the three phases as seen from the Z-axis are shown in fig. 2. From fig. 1, it can be seen that the direction of the force working on the coil varies according to how the coils are wound. Fig. 2 indicates that in models A and D, in which the deviation of the Lorentz force is large, the Lorentz force density to the inside grows large because it is influenced by the adjacent coils.
### Electromagnetic Force
The electromagnetic force of the V-phase coil is shown in fig. 3. The Z-component graph shows that, in all of the models, repulsion force is produced that mutually separates the primary and secondary coils. In an actual machine, the Z-component force is canceled out by symmetry, but this force can be seen in analysis because only a half model is used.
From the Y-component graph, it can be seen that a greater force is working in models A and B compared to the other models. When the balance of the coil’s winding method is asymmetrical vertically, a large force is produced in the vertical direction in addition to the repulsion in the radial direction, as indicated by the Lorentz force density vectors in fig. 1. The overall force in model D is canceled out so its Y-component force is zero, but by looking at the Lorentz force density vector distribution, it can be seen that force is produced a direction that compresses the primary coil as a whole. | 602 | 2,930 | {"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} | 3.078125 | 3 | CC-MAIN-2023-50 | longest | en | 0.931314 |
https://discuss.codecademy.com/t/local-vs-global-variable-bug/17692 | 1,547,801,187,000,000,000 | text/html | crawl-data/CC-MAIN-2019-04/segments/1547583659944.3/warc/CC-MAIN-20190118070121-20190118092121-00154.warc.gz | 481,331,997 | 4,775 | # Local vs Global variable BUG?
#1
var bool =true
var counter=0
var loop = function(){
while(bool)
{
counter++
if (counter==10)
{
bool= false
}
}
console.log(counter)
};
loop();
console.log(counter)
i get :
10
10
but if i change IF true block from bool=false -> var bool =false then i get :
0
0
How is that possible ??
#2
I'm not sure what answer you're expecting, but to me that's exactly what I'd expect the counter to get.
Remember, you're not reverting "counter" back to 0 after you do the loop, so every time the "counter" variable counts to ten, ends the loop, then posts the number it has, which is 10.
When you call the loop to go through, it doesn't change the number because the "if" statement sees that "counter" is already 10, and will post the console.log statement again.
HOWEVER, you're teetering dangerously on a endless loop, because if you call the "loop" twice, it'll reach the number "11" and will count up forever because it can never again be equal to "10".
Otherwise the bool or Boolean, is a true / false only, so "while(bool)" is the same as saying "while(bool == true)". If it's not true, or you change bool to false, then it will not run the loop, and the console.log statement will say "0" twice, since both console.log statements are outside of the while loop.
I know this is complicated, but you're simply overcomplicating it for yourself. So just take a step back and look at what you're trying to accomplish with this, and figure out what steps you need to get there.
I hope this helps!
#3
Ahh indeed i never thought about the danger of the infinite loop ! Thanks for saving me time from potentially huuge problems.
however, my initial problem was the difference in the results, between bool=false compared to var bool = false inside the IF statement. Each gives me different results . but i dont understand how it could possibly affect the counter variable.
bool=false gives me :
10
10
var bool = false gives me :
0
0
3 hours and still havent got a clue.
#4
that depends, because "bool=false" means the variable wasn't created and will give you an error,
"var bool = false" creates the variable and sets it equal to the value of false.
#5
ahh , hmm i have to go back and check variable scope once again ! thanks ! | 549 | 2,271 | {"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} | 2.796875 | 3 | CC-MAIN-2019-04 | latest | en | 0.908558 |
https://www.binary-code.org/binary/10bit/1000010000/ | 1,597,415,506,000,000,000 | text/html | crawl-data/CC-MAIN-2020-34/segments/1596439739328.66/warc/CC-MAIN-20200814130401-20200814160401-00343.warc.gz | 582,677,038 | 4,467 | ### Binary calculator
=
Binary 1000010000 528 210 10 512 + 16
Decimal Binary Spelt
+5121000000000Five hundred twelve
+1610000Sixteen
= 528 1000010000 Five hundred twenty-eight | 58 | 176 | {"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} | 2.671875 | 3 | CC-MAIN-2020-34 | latest | en | 0.531276 |
http://www.woodmann.com/forum/showthread.php?14722-IMUL-affecting-CF-OF | 1,597,224,612,000,000,000 | text/html | crawl-data/CC-MAIN-2020-34/segments/1596439738888.13/warc/CC-MAIN-20200812083025-20200812113025-00509.warc.gz | 186,730,202 | 14,255 | # Thread: IMUL affecting CF OF
1. ## IMUL affecting CF OF
Hello!
probably of my no-good engliCh, i can't much understand IMUL explanation in intel-doc.
problem is here:
for saving register usage, i decided use IMUL EAX EAX 055 instead of MUL.
now if do
03030303 * 055 = 0FFFFFFFF
result is exact, no upper bits need. but CF & OF flags are set.
(same happens with less operand-form, like IMUL ECX)
this not happens in MUL case.
so, please be kind with me & show me exact statement of this fact in doc. (i have 253666 pdf)
2. rezult is crosses the 7fffffff limit then intel set cf and of are set
for your example upto 29 no set cf of
more +1 = 30 yes cf of set ever
jorry for gud englishit
editz
more muky see donky do
mov eax,031F3831
imul eax,eax,29
cf of no set possible done due the result of operation comming to low of 0x80000000 (actual 7FFFFFD9)
inc eax
imul eax,eax,29
cf of set done by the result of cuming more in 0x80000000 (real 80000002)
3. @blabberer: lol!!!
4. eehhmm..
i written:
so, please be kind with me & show me exact statement of this fact in doc
request is still open.
(my assumption: OF setting is legal when crossing +- ; but not CF;
but in docs, Intel tied together CF & OF.. and can't untie, bcoz of backward compatibility)
5. the kindest of the intel show the idiot outside this
u see the paste under below down i stick with my keyboard press ctrl and press v then later
Code:
```• Three-operand form — This form requires a destination operand (the first
operand) and two source operands (the second and the third operands). Here,
the first source operand (which can be a general-purpose register or a memory
location) is multiplied by the second source operand (an immediate value). The
product is then stored in the destination operand (a general-purpose register).
When an immediate value is used as an operand, it is sign-extended to the length of
the destination operand format.
The CF and OF flags are set when significant bit (including the sign bit) are carried
into the upper half of the result. The CF and OF flags are cleared when the result
(including the sign bit) fits exactly in the lower half of the result.
The three forms of the IMUL instruction are similar in that the length of the product
is calculated to twice the length of the operands. With the one-operand form, the
product is stored exactly in the destination. With the two- and three- operand forms,
however, the result is truncated to the length of the destination before it is stored in
the destination register. Because of this truncation, the CF or OF flag should be tested
to ensure that no significant bits are lost.
The two- and three-operand forms may also be used with unsigned operands
because the lower half of the product is the same regardless if the operands are
signed or unsigned. The CF and OF flags, however, cannot be used to determine if the
upper half of the result is non-zero.
Vol. 2A 3-495 IMUL—Signed Multiply```
i from pluto the non planet planet we speak bullshitonese in homespaze translating the idiot outside manual from our godtung our professor of cpumasterysir taut us that
and in englishit says male and female when and is incanted a new form that puts both parts into one comes to being and upper half is bigg of the 7fffffff and lower half is less of 7fffffff
in result of being
Code:
```
C:\WinDDK\7600.16385.1\inc>grep -ir "int_max" --include limits.h *
crt/limits.h:#define INT_MAX 2147483647 /* maximum (signed) int value *
/
crt/limits.h:#define UINT_MAX 0xffffffff /* maximum unsigned int value *
/
crt/limits.h:#define SIZE_MAX UINT_MAX
C:\WinDDK\7600.16385.1\inc>set /a 0x7fffffff
2147483647
C:\WinDDK\7600.16385.1\inc>```
6. now make BOLD or ITALIC sentence, which explains outcome
03030303 * 055 = 0FFFFFFFF >> CF OF set.
7. Okay,
Enough please Blabby. While I almost choked from laughing so hard.....
I know it's hard to give just a bit of mercy given Evals rep. but please
consider it.
Woodmann
8. now i am giving my view intel-englich:
upper-half is upper-half of 64bit number e.g. 32-63bits.
blabberer, is it OK?
9. no eval i dont think so
it is not imul rax, eax,imm
it is imul eax , eax, imm
so it is in my opinion the upper half of 32 bits not the upper half of 64 bits
intel specifies if truncation happens including sign bit to fit it in the destination register
carry flag AND overflow are set
operative phrase is destination register which is 32 bit not 64 bit
that is how i understand the wording not sure why you feel different
anyway making any crackmes based on this ??
the boss ordered me to translate my godtung to english before posting using google translation service
hope the translation now is better
10. Thank you.
Don
11. blabberer, you are wrong.
The CF and OF flags are set when significant bit (including the sign bit)
are carried into the upper half of the result.
The CF and OF flags are cleared when the result
(including the sign bit) fits exactly in the lower half of the result.
this means: upper-half is EDX (with 32-63bits), lower-half is EAX (with 0-31bits)
otherwise, what is lower-half ??
also, you are forgotting: truncation not matters.
(same happens with less operand-form, like IMUL ECX)<< in my first post.
********
Now, as i understand, you are not big Englich-spec, so i suggest, you will stop this waste.
letz just wait for more Englich-spec one.
12. uuugh.
the only thing i understood is -maybe- the initial question.
evaluator, you forgot you are doing an IMUL. the fact you get FFFFFFFF means you need an additional bit to store the sign, a bit you do not have. That's why you get the CF/OF. If you do a MUL, the FFFFFFF is always regarded as 4 billion, but doing an IMUL you need to know somehow that you did not get a '-1' instead of a 4 billion. Try to do the IMUL with say -1 * 1 and you see what i mean.
(OT: fuck cooked wildboar... do i need to get holidays to digest it!?!?)
13. (OT: fuck cooked wildboar... do i need to get holidays to digest it!?!?)
It's too lean. Sits like a brick in yer belly.
Woodmann
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• | 1,632 | 6,228 | {"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} | 2.75 | 3 | CC-MAIN-2020-34 | latest | en | 0.84718 |
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Unformatted text preview: Chapter at Review 55 General Berrievv Guide: Chapter 4 ; Sequences and Summation I What isamethodtohelp findsneaplititfornnflaforasequencc whose firstfewtermsare given [presided a nice explicit formula existal)? (pi £01} I What is the summation notation for a sun: that is given in expanded form? fp. \$132} I What is the expanded form for a sum that is given in summation notation? (p. ME} I 'What is the product notation? (p. 905} o What is factorial notation? (p. sss) I What are some propa-ties of summations and products? (p. 33?} I How do you transform a summation h}? makinga change oftnriahle? (p. 209} 'I Whatisanaigorithmfor convertingfromhaaelfltohaseZ? rs. so} Mathematical Induction I Whatdoyoushnwlnthebasisstepandwhatdoyoushowinthe inductivestepwhmi you use {ordinary} mathematical induction to prove that a property involving an integer n is true for all integers mentor than or equal to some initial integer? {p 313) I What is the inductive hypothesis in a proof by [ordinary] mathematical induction? (p. 313} I Are you able to use {ordinary} mathematical induction to construct proofs involving various kinds of statements such as formulas, divisihility properties, and inequalities? (pp. 213, sec, 333, 339, 331, 232) I Areyoo abletoapplythefibrtnnlaforthe sum ofthefirstn positive integers? (p. 292} I Areyon aisletoaraplyr theformtflaforthssnrn oftlresuooessive powersoi'amlmber, starting with the aeroth power? (p. 235) Ethan]: Mathewnatical Induction and The Well—Drdering Principle I What doyoushowinthe basisstepanri what doyoushowintheindnctive step when pounce strongmathemfiical induction topmvethatapropertyinvolvinganintegernis trueiorall integers greater than or equal to same initial integer? (p. 335) I What is the inductive hypothesis in a. proof by strong mathematical induction? (p. 335} I Are you able to use strong mathematical induction to construct proofs ofvarions statements? (pp. 335-340) I What is the well—ordering principle for the integers? (p. 215') I Are you able to use the well-ordering principle for the integers to prove statements. such as the existence part of the quotient-remainder theorem? (p. 241) I How are ordinal-3,r mathematical induction, strong mathematical induction, and the well- metering principle related? (1:. £13} ‘thm Correctness I What are the ore-condition and the posbeondition for an algorithm? (p. 245} I What does it mean Em: a loop to be correct with respect to its on.L and post-conditions? (p. 345} I Whatisaloo-pinvaflant? (p. are) I Howdovon nsethe loop invariant theorem toprovethntaloopis oorrectwith respectto its pre- and post-mnditioas? (pp. Sid-£53} ...
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https://www.analyticsvidhya.com/blog/2021/04/simple-understanding-and-implementation-of-knn-algorithm/?utm_source=reading_list&utm_medium=https://www.analyticsvidhya.com/blog/2020/10/feature-selection-techniques-in-machine-learning/ | 1,726,391,902,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651622.79/warc/CC-MAIN-20240915084859-20240915114859-00643.warc.gz | 587,682,034 | 58,583 | # Simple understanding and implementation of KNN algorithm!
Sai 23 Jun, 2022
This article was published as a part of the Data Science Blogathon.
## Overview:
K Nearest Neighbor (KNN) is intuitive to understand and an easy to implement the algorithm. Beginners can master this algorithm even in the early phases of their Machine Learning studies.
This KNN article is to:
· Understand K Nearest Neighbor (KNN) algorithm representation and prediction.
· Understand how to choose K value and distance metric.
· Required data preparation methods and Pros and cons of the KNN algorithm.
· Pseudocode and Python implementation.
## Introduction:
K Nearest Neighbor algorithm falls under the Supervised Learning category and is used for classification (most commonly) and regression. It is a versatile algorithm also used for imputing missing values and resampling datasets. As the name (K Nearest Neighbor) suggests it considers K Nearest Neighbors (Data points) to predict the class or continuous value for the new Datapoint.
The algorithm’s learning is:
1. Instance-based learning: Here we do not learn weights from training data to predict output (as in model-based algorithms) but use entire training instances to predict output for unseen data.
2. Lazy Learning: Model is not learned using training data prior and the learning process is postponed to a time when prediction is requested on the new instance.
3. Non -Parametric: In KNN, there is no predefined form of the mapping function.
## How does KNN Work?
1. #### Principle:
Consider the following figure. Let us say we have plotted data points from our training set on a two-dimensional feature space. As shown, we have a total of 6 data points (3 red and 3 blue). Red data points belong to ‘class1’ and blue data points belong to ‘class2’. And yellow data point in a feature space represents the new point for which a class is to be predicted. Obviously, we say it belongs to ‘class1’ (red points)
Why?
Because its nearest neighbors belong to that class!
Yes, this is the principle behind K Nearest Neighbors. Here, nearest neighbors are those data points that have minimum distance in feature space from our new data point. And K is the number of such data points we consider in our implementation of the algorithm. Therefore, distance metric and K value are two important considerations while using the KNN algorithm. Euclidean distance is the most popular distance metric. You can also use Hamming distance, Manhattan distance, Minkowski distance as per your need. For predicting class/ continuous value for a new data point, it considers all the data points in the training dataset. Finds new data point’s ‘K’ Nearest Neighbors (Data points) from feature space and their class labels or continuous values.
Then:
For classification: A class label assigned to the majority of K Nearest Neighbors from the training dataset is considered as a predicted class for the new data point.
For regression: Mean or median of continuous values assigned to K Nearest Neighbors from training dataset is a predicted continuous value for our new data point
2. #### Model Representation
Here, we do not learn weights and store them, instead, the entire training dataset is stored in the memory. Therefore, model representation for KNN is the entire training dataset.
## How to choose the value for K?
K is a crucial parameter in the KNN algorithm. Some suggestions for choosing K Value are:
1. Using error curves: The figure below shows error curves for different values of K for training and test data.
At low K values, there is overfitting of data/high variance. Therefore test error is high and train error is low. At K=1 in train data, the error is always zero, because the nearest neighbor to that point is that point itself. Therefore though training error is low test error is high at lower K values. This is called overfitting. As we increase the value for K, the test error is reduced.
But after a certain K value, bias/ underfitting is introduced and test error goes high. So we can say initially test data error is high(due to variance) then it goes low and stabilizes and with further increase in K value, it again increases(due to bias). The K value when test error stabilizes and is low is considered as optimal value for K. From the above error curve we can choose K=8 for our KNN algorithm implementation.
2. Also, domain knowledge is very useful in choosing the K value.
3. K value should be odd while considering binary(two-class) classification.
## Required Data Preparation:
1. Data Scaling: To locate the data point in multidimensional feature space, it would be helpful if all features are on the same scale. Hence normalization or standardization of data will help.
2. Dimensionality Reduction: KNN may not work well if there are too many features. Hence dimensionality reduction techniques like feature selection, principal component analysis can be implemented.
3. Missing value treatment: If out of M features one feature data is missing for a particular example in the training set then we cannot locate or calculate distance from that point. Therefore deleting that row or imputation is required.
## Python implementation:
Implementation of the K Nearest Neighbor algorithm using Python’s scikit-learn library:
### Step 1: Get and prepare data
```import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
from sklearn.datasets import make_classification
from sklearn.model_selection import train_test_split
from sklearn.preprocessing import StandardScaler
from sklearn.neighbors import KNeighborsClassifier
from sklearn import metrics```
After loading important libraries, we create our data using sklearn.datasets with 200 samples, 8 features, and 2 classes. Then data is split into the train(80%) and test(20%) data and scaled using StandardScaler.
Python Code:
`(200, 8)`
### Step 2: Find the value for K
For choosing the K value, we use error curves and K value with optimal variance, and bias error is chosen as K value for prediction purposes. With the error curve plotted below, we choose K=7 for the predictionÂ
```error1= []
error2= []
for k in range(1,15):
knn= KNeighborsClassifier(n_neighbors=k)
knn.fit(X_train,y_train)
y_pred1= knn.predict(X_train)
error1.append(np.mean(y_train!= y_pred1))
y_pred2= knn.predict(X_test)
error2.append(np.mean(y_test!= y_pred2))
# plt.figure(figsize(10,5))
plt.plot(range(1,15),error1,label="train")
plt.plot(range(1,15),error2,label="test")
plt.xlabel('k Value')
plt.ylabel('Error')
plt.legend()```
### Step 3: Predict:
In step 2, we have chosen the K value to be 7. Now we substitute that value and get the accuracy score = 0.9 for the test data.
```knn= KNeighborsClassifier(n_neighbors=7)
knn.fit(X_train,y_train)
y_pred= knn.predict(X_test)
metrics.accuracy_score(y_test,y_pred)```
`0.9`
## Pseudocode for K Nearest Neighbor (classification):
This is pseudocode for implementing the KNN algorithm from scratch: | 1,540 | 7,015 | {"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} | 3.046875 | 3 | CC-MAIN-2024-38 | latest | en | 0.89566 |
https://support.minitab.com/en-us/minitab/18/help-and-how-to/modeling-statistics/multivariate/how-to/simple-correspondence-analysis/interpret-the-results/all-statistics-and-graphs/graphs/ | 1,534,839,747,000,000,000 | text/html | crawl-data/CC-MAIN-2018-34/segments/1534221218070.73/warc/CC-MAIN-20180821073241-20180821093241-00077.warc.gz | 769,910,179 | 5,081 | # Graphs for Simple Correspondence Analysis
Find definitions and interpretation for every graph that is provided for simple correspondence analysis.
## Row plot
The row plot shows the principal coordinates for the row categories. Minitab plots row points with red circles--solid circles for regular points, and open circles for supplementary points.
###### Note
By default, Minitab displays the points for the first two principal components, which account for the greatest amount of total inertia. To display other principal components (axes) on the plot, click Graphs and enter the component numbers when you perform the analysis.
### Interpretation
Use the row plot to look for relationships among row categories and to help interpret the principal components in relation to the row categories. Points that are farther away from the origin indicate categories that are more influential. Points on opposite sides of the plot indicate that a component contrasts these categories
## Column plot
The column plot shows the principal coordinates for the column categories. Minitab plots column points with blue squares--solid squares for regular points, and open squares for supplementary points.
###### Note
By default, Minitab displays the points for the first two principal components, which account for the greatest amount of total inertia. To display other principal components (axes) on the plot, click Graphs and enter the component numbers when you perform the analysis.
### Interpretation
Use the column plot to look for relationships among column categories and to help interpret the principal components in relation to the column categories. Points that are farther away from the origin indicate categories that are more influential. Points on opposite sides of the plot indicate that a component contrasts these categories.
## Symmetric plot
The symmetric plot is a plot of row and column principal coordinates in a joint display. The row-to-row and column-to-column distances are approximate chi-squared distances between the respective profiles. Minitab plots row points with red circles--solid circles for regular points, and open circles for supplementary points. Minitab plots column points with blue squares--solid squares for regular points, and open squares for supplementary points.
###### Note
By default, Minitab displays the points for the first two principal components, which account for the greatest amount of total inertia. To display other principal components (axes) on the plot, click Graphs and enter the component numbers when you perform the analysis.
### Interpretation
Use the symmetric plot to look for relationships among row categories and among column categories. You can also interpret the principal components in relation to the row categories or the column categories. Points that are farther away from the origin indicate categories that are more influential. Points on opposite sides of the plot indicate that a component contrasts these categories. In a symmetric plot, the profiles are spread out to more easily view the distances between them.
###### Important
The row-to-column distances in the symmetric plot use two different mappings. Because the row-to-column distances are not standardized, the distances between row categories and column categories cannot be interpreted easily. To interpret distances between row categories and column categories, use an asymmetric plot.
## Asymmetric row plot
The asymmetric row plot displays row principal coordinates and column standardized coordinates in the same plot. Distances between row points are approximate chi-square distances between the row profiles. Minitab plots row points with red circles--solid circles for regular points, and open circles for supplementary points. Minitab plots column points with blue squares--solid squares for regular points, and open squares for supplementary points.
###### Note
By default, Minitab displays the points for the first two principal components, which account for the greatest amount of total inertia. To display other principal components (axes) on the plot, click Graphs and enter the component numbers when you perform the analysis.
### Interpretation
Use the asymmetric row plot to look for relationships among the row and column categories and to help interpret the principal components. Points that are farther away from the origin indicate categories that are more influential. Points on opposite sides of the plot indicate that a component contrasts these categories. The closer a point for a row category is to a point for a column category, the higher the value of the row profile for the column category.
###### Note
Asymmetric plots allow you to intuitively interpret the distances between row points and column points, especially if the two components represent a large proportion of the total inertia. However, the points on an asymmetric plot might appear too close to each other in the center of the graph, which can make the results difficult to view. In that case, you may want to also display a symmetric plot to more clearly view the relationships among either the row or column categories.
## Asymmetric column plot
The asymmetric column plot displays column principal coordinates and row standardized coordinates in the same plot. Distances between column points are approximate chi-square distances between the column profiles. Minitab plots row points with red circles--solid circles for regular points, and open circles for supplementary points. Minitab plots column points with blue squares--solid squares for regular points, and open squares for supplementary points.
###### Note
By default, Minitab displays the points for the first two principal components, which account for the greatest amount of total inertia. To display other principal components (axes) on the plot, click Graphs and enter the component numbers when you perform the analysis.
### Interpretation
Use the asymmetric column plot to look for relationships among the row and column categories and to help interpret the principal components. Points that are farther away from the origin indicate categories that are more influential. Points on opposite sides of the plot indicate that a component contrasts these categories. The closer a point for a column category is to a point for a row category, the higher the value of the column profile for the row category.
###### Note
Asymmetric plots allow you to intuitively interpret the distances between row points and column points, especially if the two components represent a large proportion of the total inertia. However, the points on an asymmetric plot might appear too close to each other in the center of the graph, which can make the results difficult to view. In that case, you may want to also display a symmetric plot to more clearly view the relationships among either the row or column categories.
By using this site you agree to the use of cookies for analytics and personalized content. Read our policy | 1,276 | 7,035 | {"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} | 3.46875 | 3 | CC-MAIN-2018-34 | latest | en | 0.813003 |
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# Introduction to Bayesian Statistics
Probability and Statistics
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Bayesian Statistics
schedule Mar 10, 2022
Last updated
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# Philosophy
The pivotal difference between Frequentist and Bayesian statistics is that the former considers the population parameter to be fixed, while the latter treats it as a random variable. Such a difference in the interpretation of the nature of the population parameters carries significant and vast implications. In the eyes of Bayesians, it makes sense to assign probability distributions to parameters and compute expected values and variances, just as we do for any random variable.
# Bayes' Theorem
The Bayes' theorem is as follows:
$$\mathbb{P}(A|B)=\frac{\mathbb{P}(B|A)\cdot{}\mathbb{P}(A)}{\mathbb{P}(B)}$$
If the events $B_1,B_2,…,B_k$ constitute a partition of the sample space $S$ such that $\mathbb{P}(B_i)\ne0$ for $i=1,2,…,k$, then for any event $A$ in $S$ such that $\mathbb{P}(A)\ne0$:
$$\mathbb{P}(B_r|A)= \frac{\mathbb{P}(B_r\cap{A})}{\sum^k_{i=1}\mathbb{P}(B_i\cap{A})} =\frac{\mathbb{P}(B_r)\cdot{\mathbb{P}(A|B_r)}}{\sum^k_{i=1}\mathbb{P}(B_i)\cdot{\mathbb{P}(A|B_i)}}$$
For the continuous case:
$$$$\label{eq:oyWcmvy42akS8TCH9AF} f(\theta|x)=\frac{f(x|\theta)\cdot{f(\theta)}}{\int{f(x|\theta)\cdot{f(\theta)}\;d\theta}}$$$$
Here, the denominator is a normalising constant for the posterior distribution and does not depend on $\theta$. For this reason, we often write $\eqref{eq:oyWcmvy42akS8TCH9AF}$ as:
$$f(\theta|x)\propto{f}(x|\theta)\cdot{f(\theta)}$$
Proof. Using the definition of conditional probability and the rule of elimination, we can derive the Bayes’ theorem:
$$\mathbb{P}(B)= \sum^k_{i=1}\mathbb{P}(A_i\cap{B})= \sum^k_{i=1} \mathbb{P}(B|A_i)\cdot{\mathbb{P}(A_i)}$$
The continuous case is as follows (i.e. this is just a combination of conditional probability and the rule of elimination):
$$f_{\theta}(\theta|x)=\int^\infty_{-\infty}f_X(x|\theta)\cdot{f_{\theta}(\theta)\;\;d\theta}$$
# Terminologies
## Prior Distribution
The initial probability distribution assigned to the parameter is referred to as the prior distribution. Note that the prior distribution is given before we process the data - hence the name "prior".
## Likelihood Function
The likelihood function that we are used was often denoted as $f(\theta|x)$, which makes the fact that we are treating theta as the variable explicit. However, the notation that we use in the Bayesian world differs from this in that, the likelihood function appears to be in reverse order $f(x|\theta)$ at first glance. However, $x$ is still treated as a constant, while the θ is treated as a variable. For this very reason, we do not regard $f(x|\theta)$ as a probability.
## Posterior Distribution
Once we incorporate and process the data, the prior distribution then becomes a posterior distribution, $f_\theta(\theta|\mathbf{x})$. The posterior distribution is the basis for statistical inference in the Bayesian world.
# Example
Question. Company A is trying to estimate how many of their products are defects. Out of the thousands of the products made, the company took a random sample of size n and found that k of them are defects. As an additional insight, suppose company A knows that around 5% of theirs products are defects based on past experience. Determine the posterior distribution.
Solution. We know directly from the question that $X\sim\mathcal{B}(n,\theta)$, which means that the likelihood function is:
$$p(x|n,\theta)=\binom{n}{x}\theta^x(1-\theta)^{n-x}$$
One way of modelling the company's insight of $\theta$ is to use the beta distribution:
$$f_\theta(\theta)=\frac{\Gamma(\alpha+\beta)}{\Gamma(\alpha)\cdot\Gamma(\beta)}\theta^{\alpha-1}(1-\theta)^{\beta-1}$$
We need to come up with the parameters $\alpha$ and $\beta$ that aligns with the company's insight, that is, we want the beta distribution to be skewed sharply to the left. If we set $\alpha=2$ and $\beta=8$, this seems to be adequate. This means that the prior distribution is:
$$f_\theta(\theta)=\frac{\Gamma(2+8)}{\Gamma(2)\cdot\Gamma(8)}\theta^{2}(1-\theta)^{7}$$
As it turns out, the posterior distribution is:
$$f(\theta|\mathbf{x})$$
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A modern learning experience for data science and analytics | 1,443 | 5,220 | {"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": 1, "x-ck12": 0, "texerror": 0} | 3.71875 | 4 | CC-MAIN-2022-21 | longest | en | 0.68055 |
http://www.mapleprimes.com/users/vineetloya/answers | 1,498,577,994,000,000,000 | text/html | crawl-data/CC-MAIN-2017-26/segments/1498128321458.47/warc/CC-MAIN-20170627152510-20170627172510-00044.warc.gz | 592,010,291 | 15,316 | ## 15 Reputation
4 years, 263 days
## @Joe Riel Hey Joe, Thank...
Hey Joe,
Thank you for replying. Please find attached a sample file. Also I am pasting the exact content.
> restart;
> with(StringTools);
> S := [diff(x(t), t) = y(t), diff(y(t), t) = x(t)^2];
[ d d 2]
[--- x(t) = y(t), --- y(t) = x(t) ]
[ dt dt ]
> qwv := x(t), y(t);
> PDEtools:-declare(qwv, prime = t);
x(t) will now be displayed as x
y(t) will now be displayed as y
derivatives with respect to t of functions of one variable will
now be displayed with '
> S; lprint(%);
[ d d 2]
[--- x(t) = y(t), --- y(t) = x(t) ]
[ dt dt ]
[diff(x(t), t) = y(t), diff(y(t), t) = x(t)^2]
> sprintf("%a & %a", S[1], S[2]);
#Note that I want the eqn in form: x'=y & y'=x^2
"diff(x(t),t) = y(t) & diff(y(t),t) = x(t)^2"
> Q := convert(S[1], string);
"diff(x(t),t) = y(t)"
> sprintf("%s", Q);
"diff(x(t),t) = y(t)"
#I have tried different approaches to print the output in the required format into a text file. The other problem is when I write "&", Maple convert it into "&".
> | 385 | 1,145 | {"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} | 2.671875 | 3 | CC-MAIN-2017-26 | latest | en | 0.711326 |
https://brainly.com/question/2810 | 1,484,751,004,000,000,000 | text/html | crawl-data/CC-MAIN-2017-04/segments/1484560280292.50/warc/CC-MAIN-20170116095120-00493-ip-10-171-10-70.ec2.internal.warc.gz | 793,039,904 | 9,268 | 2014-01-17T20:20:17-05:00
### This Is a Certified Answer
Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
Think of a staircase. At the top of the stairs it starts with...
Kilo
Hecto
Deka
Unit you are using
Deci
Centi
Mili
Every time you go up in units, you move the decimal to the left. When you go down in units you move the decimal to the right.
You need to go from Hectograms to Grams, so that means you need to move down the scale two places. When you move down two places you need to move the decimal two places to the right. :)
2014-01-17T20:20:34-05:00
### This Is a Certified Answer
Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
9 hectograms=900 grams | 270 | 1,119 | {"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} | 2.859375 | 3 | CC-MAIN-2017-04 | latest | en | 0.926842 |
https://tf2maps.net/threads/how-can-i-make-a-control-point-require-any-two-other-points-to-capture.7311/ | 1,590,761,919,000,000,000 | text/html | crawl-data/CC-MAIN-2020-24/segments/1590347404857.23/warc/CC-MAIN-20200529121120-20200529151120-00313.warc.gz | 573,053,657 | 10,629 | # How can I make a control point require any two other points to capture?
Discussion in 'Mapping Questions & Discussion' started by Cap'm Drummond, Jun 12, 2009.
1. ### Cap'm DrummondL1: Registered
Messages:
8
Positive Ratings:
0
To make a long story short, I'm working on a CP map where only one point matters for winning the game, but where supplementary points can be captured. One of the biggest problems I saw myself running into was players ignoring the supplementary points and just going for the main one, which wasn't really my intent. My solution was to require teams to have at least two other points to attack the main one.
Now, I could make it so each team needs two specific points to capture; however, I want to give players as many options as possible, so I was wondering if there's a way to make a point capture-able with any two of them. I can't seem to find anything in the keyvalues that would let me do this, but I figured somebody else might know.
2. ### brickL3: Member
Messages:
103
Positive Ratings:
13
Im sure you can. Make 1 cp always require 2 other cps or something. So lets say you have A, B, C. You have to have them always unlocked or else there will be 1 always locked. It depends on how the map is laid out and such. A is required to have either B or C to capture. C needs A or B. If both are required then it will be always locked. The problem I see with this if Im picturing it right. If Blue is attacking red has 2 open points with the third unlocked. Once blue captures A then C becomes unlocked?
3. ### aaA Boojum SnarkToraipoddodezain Mazahabado
Messages:
4,769
Positive Ratings:
5,552
Make the final point require itself (meaning no requirement). Set it's trigger_capture_area to disallow the attacking team from capturing.
Make a math_counter and set it's max value to 2. Have each supplementary point add 1 to the counter when captured.
Have the math_counter's OnHitMax output send a SetTeamCanCap to the final point's t_c_a to unlock it. (check the VDC for the syntax of SetTeamCanCap)
• Thanks x 1 | 496 | 2,053 | {"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} | 2.625 | 3 | CC-MAIN-2020-24 | latest | en | 0.950157 |
https://math.stackexchange.com/questions/585271/problem-with-recurrence-relation-for-series-solution-for-ode | 1,579,641,676,000,000,000 | text/html | crawl-data/CC-MAIN-2020-05/segments/1579250605075.24/warc/CC-MAIN-20200121192553-20200121221553-00265.warc.gz | 539,814,759 | 31,141 | # problem with recurrence relation for series solution for ODE
I have $$y''-xy'-y=0$$ and I'm trying to find the series solution around the ordinary point $x_0=1$. My last post I muscled through to the solution when the ordinary point was $x_0=0$, but this is proving to be tougher. Now I have obtained through power series analysis $$y''-xy'-y=0=\sum_{k=0}^{\infty}[(k+2)(k+1)a_{k+2}-(k+1)a_{k+1}-(k+1)a_k](x-1)^k$$ which yields the recurrence relation $$a_{k+2}=\frac{a_{k+1}+a_{k}}{k+2}$$ WHen I start plugging in sequential "k" values I'm not finding a very good pattern emerging. $$a_2=\frac{a_0}{2!}+\frac{a_1}{2!}$$ $$a_3=\frac{a_0}{3!}+\frac{3a_1}{3!}$$ $$a_4=\frac{4a_0}{4!}+\frac{6a_1}{4!}$$ $$a_5=\frac{8a_0}{5!}+\frac{18a_1}{5!}$$ $$a_6=\frac{28a_0}{6!}+\frac{48a_1}{6!}$$ $$a_7=\frac{76a_0}{7!}+\frac{156a_1}{7!}$$ Outside just writing out term by term, substituting in the appropriate $a_k$, does this have a nice closed form? Or is is just the case that I have the answer with the $a_k$'s that I have
• Generally speaking, what you have already done (getting a recursive form for the coefficients) is the best you can do when finding power series solutions. – JohnD Nov 29 '13 at 4:44
• I checked your recurrence relation and it is correct. – Amzoti Nov 29 '13 at 5:19
$$y=e^{\frac{x^2}{2}} \left(C_2+C_1\sqrt{\frac{\pi }{2}} \text{erf}\left(\frac{x}{\sqrt{2}}\right)\right)$$
As you see, you have two arbitrary constants and then any polynomial expansion of the solution will depend on two constants : these are your $$a_0$$ and $$a_1$$ terms. | 567 | 1,562 | {"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": 3, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.90625 | 4 | CC-MAIN-2020-05 | latest | en | 0.873111 |
https://www.jiskha.com/questions/466114/were-less-than-50-lunches-eaten-in-aweek-is-the-ans-an-estimate-or-exact | 1,580,167,010,000,000,000 | text/html | crawl-data/CC-MAIN-2020-05/segments/1579251728207.68/warc/CC-MAIN-20200127205148-20200127235148-00423.warc.gz | 938,270,970 | 5,277 | # math
were less than 50 lunches eaten in aweek? is the ans an estimate or exact?
1. 👍 0
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1. If you post the rest of this problem, along with YOUR answer, we'll be glad to check it.
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More Similar Questions | 799 | 2,938 | {"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} | 3.234375 | 3 | CC-MAIN-2020-05 | latest | en | 0.958256 |
https://stackoverflow.com/questions/36136305/reorder-rows-of-a-matrix-by-a-vector-containing-an-incomplete-index | 1,568,612,321,000,000,000 | text/html | crawl-data/CC-MAIN-2019-39/segments/1568514572484.20/warc/CC-MAIN-20190916035549-20190916061549-00292.warc.gz | 665,087,264 | 29,521 | Reorder rows of a matrix by a vector containing an incomplete index
I have a matrix of data:
``````> matrix <- matrix(rnorm(16), ncol=4)
> matrix
[,1] [,2] [,3] [,4]
[1,] -0.9239653 0.4217107 -0.3092167 0.09732866
[2,] -0.9635737 0.3755872 -0.4033848 1.67775919
[3,] 1.1193376 -0.3618842 -1.0036277 -0.50638047
[4,] -0.2659838 -0.8215967 0.1611249 -0.05114933
``````
I want to re-order the rows of the matrix by an index specified in a vector. If the numbers in the index correspond to row numbers in the matrix, this is easy:
``````> index <- c(3, 2, 1, 4)
> reordered.matrix <- matrix[index, ]
> reordered.matrix
[,1] [,2] [,3] [,4]
[1,] 1.1193376 -0.3618842 -1.0036277 -0.50638047
[2,] -0.9635737 0.3755872 -0.4033848 1.67775919
[3,] -0.9239653 0.4217107 -0.3092167 0.09732866
[4,] -0.2659838 -0.8215967 0.1611249 -0.05114933
``````
However, in real life my index contains some zeros. These zeros specify positions where I want to discard the data, i.e. to just have a row of zeros or NAs in that row. Here is what I would like to get:
``````> index <- c(3, 0, 1, 0)
> reordered.matrix <- matrix[index, ]
> reordered.matrix
[,1] [,2] [,3] [,4]
[1,] 1.1193376 -0.3618842 -1.0036277 -0.50638047
[2,] 0 0 0 0
[3,] -0.9239653 0.4217107 -0.3092167 0.09732866
[4,] 0 0 0 0
``````
But instead R ignores the zeroes, and i just get:
`````` [,1] [,2] [,3] [,4]
[1,] 1.1193376 -0.3618842 -1.0036277 -0.50638047
[2,] -0.9239653 0.4217107 -0.3092167 0.09732866
``````
A possible solution would be to write a loop that goes though the index on-by-one, copies the data and writes it to the correct position on a new matrix. However, the matrices I am using are huge (millions of rows) and loops are way too slow. Is there any way I can get what I want without resorting to a loop?
We can replace the 0's in the 'index' with NA and use that for ordering the rows of matrix.
``````m1 <- matrix[(NA^!index)*index,]
replace(m1, is.na(m1), 0)
# [,1] [,2] [,3] [,4]
#[1,] 1.1193376 -0.3618842 -1.0036277 -0.50638047
#[2,] 0.0000000 0.0000000 0.0000000 0.00000000
#[3,] -0.9239653 0.4217107 -0.3092167 0.09732866
#[4,] 0.0000000 0.0000000 0.0000000 0.00000000
``````
NOTE: It is better not to call a `matrix` object as `matrix`.
• Thanks Akrun, this worked. – D Greenwood Mar 22 '16 at 10:06 | 992 | 2,504 | {"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} | 2.5625 | 3 | CC-MAIN-2019-39 | latest | en | 0.73159 |
http://spankbush.com/archimedes-principle-worksheet/ | 1,555,650,938,000,000,000 | text/html | crawl-data/CC-MAIN-2019-18/segments/1555578527135.18/warc/CC-MAIN-20190419041415-20190419063415-00292.warc.gz | 167,012,132 | 10,058 | # Archimedes Principle Worksheet
## Archimedes Principle Worksheet
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39 New Calculating force Worksheet Answers from Archimedes Principle Worksheet
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39 New Calculating force Worksheet Answers from Archimedes Principle Worksheet
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39 New Calculating force Worksheet Answers from Archimedes Principle Worksheet
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Buoyant force example problems video from Archimedes Principle Worksheet | 589 | 2,857 | {"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} | 2.640625 | 3 | CC-MAIN-2019-18 | latest | en | 0.770816 |
https://www.quirkyscience.com/eight-middle-and-high-school-math-problems-solutions/ | 1,721,300,607,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763514828.10/warc/CC-MAIN-20240718095603-20240718125603-00105.warc.gz | 815,544,746 | 24,083 | Eight Middle and High School Math Problems with Solutions
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Not only current students. but old-timers as well will find these middle and high school math problems informative.
Middle and High School Math
Problem 1: Leaves from a tree were reported by four different European students to be 2.9 cm, 3.33 cm, 3.9 cm, and 3.12 cm in length. List the numbers in order of decreasing length.
For the beginner, the easiest way to evaluate which of these number is smaller and which is larger, is to make the number of digits to the right of the decimal the same. Now the maximum number of such digits here is two.
Adding zeros to the right of the last digit does not change a number’s value. When that is done, the numbers become:
2.90, 3.33, 3.90 and 3.12
In decreasing order, the lengths are:
3.90 cm, 3.33 cm, 3.12 cm and 2.90 cm. [Answer]
————————-
Problem 2: Find the midpoint of the segment from Point A (2, –7) to Point B (8, –1).
Given the two endpoints, the midpoint is derived by finding the halfway value between the two first values (in this instance, the 2 and the 8, hence 5) and the halfway value between the two second values (in this instance, the –7 and the –1, hence – 4).
The midpoint of the segment is:
————————-
Problem 3: 5/12–y+5/4 =2/3. What is y?
There are no parentheses in this problem. Thus the first two terms are simply 5/12 – y, rather than 5/(12-y). So we write the problem (including spaces for clarity),
5/12 – y + 5/4 = 2/3
Multiplying this equation by –1 changes all the signs, producing,
– 5/12 + y – 5/4 = – 2/3
Now, when the same number is added on both sides of the equal sign, nothing is actually changed. So we add + 5/12 and + 5/4 to both sides to give,
y = –2/3 + 5/12 + 5/4
We will change all the fractions into 12ths. Numbers like 3/3 and 4/4 are equal to 1, so multiplying a fraction by them does not change the value of the fraction. We get,
y = –2/3 (4/4) + 5/12 (1/1) + 5/4 (3/3) = –8/12 + 5/12 + 15/12 = 12/12 = 1
————————-
Problem 4: Given these two equations,
3x + 2y = A
5x + y = B
Solve for x in terms of A and B.
The first equation by simple algebraic manipulation (moving the 3x to the right and dividing by 2) becomes,
y = (A – 3x)/2
For the second equation, move the 5x to the right to obtain,
y = B – 5x
Combining our two modified equations gives us,
(A – 3x) / 2 = B – 5x
Multiplying both sides by 2 gives,
A – 3x = 2B – 10x
This simplifies (by subtracting – 3x from both sides of the equal sign) to,
A = 2B – 7x
So by simply moving terms and dividing, we obtain,
x = (2B – A) / 7 [Answer]
————————-
Problem 5: What is 3 divided by 10, shown as a fraction?
Most simply, it can be written as 3/10, with the slash “/” meaning “divide by”. But there is another way to write the answer, using decimals.
Division by ten calls for a move in decimal point one place to the left – one space. Consider:
3 may be written 3.0
Dividing it by 10 makes it
.30
Because the decimal point is sometimes missed, a fraction less than 1 is customarily written with a zero in front of the decimal. Thus we would write 0.30 as,
————————-
Problem 6: What is the answer to this problem? (8/2)/2+((12+3)+25)=?
This problem is obviously intended to demonstrate which mathematical operations are carried out first, which are carried out second, and so forth. It matters, because done out of sequence, a wrong answer is likely to be obtained.
The first operations that should be carried out here are those operations within parentheses. In fact, the very first operation is the parentheses within parentheses! Within parentheses, multiplication and division are carried out first, and then addition and subtraction. We begin,
(4)/2 + ((15) + 25)
So we wind up with
2 + 40 = 42 [Answer]
————————-
Problem 7: A farmer wants to put in a fence with five sides around his field. The measurements are 50 ft, 12 ft, 60 ft, 35 ft, and 25 ft. Find the perimeter in feet and convert the number to yards.
The perimeter, which we’ll call P, is the sum of the sides,
P = 50 ft + 12 ft + 60 ft + 35 ft + 25 ft = 182 feet
Now, 1 yd = 3 ft So,
182 ft x 1 yd / 3 ft = 182 ft / 3 yd = 60-2/3 yd [Answer]
————————-
Problem 8: The midpoint of the line segment from P1 to P2 is (–3, 2) if P1 = (–5, 2) what is P2?
The midpoint of a line segment has values that are intermediate between both the first (usually x) variable value of the points as well as the second (usually y) variable value of the points.
The y values are the same for the midpoint and one endpoint. This means the line is horizontal and so the other end point has the same value, 2.
The x values vary. One endpoint’s x-value is –5. The midpoint has x-value –3. The difference between the one end and the midpoint is 2 units, so the difference between the midpoint and the other endpoint is 2 units. Hence, the other endpoint has value –1. | 1,417 | 4,935 | {"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} | 4.875 | 5 | CC-MAIN-2024-30 | latest | en | 0.912208 |
https://tinhoc24h.info/creative-problem-solving-lesson-plans.php | 1,601,293,374,000,000,000 | text/html | crawl-data/CC-MAIN-2020-40/segments/1600401600771.78/warc/CC-MAIN-20200928104328-20200928134328-00694.warc.gz | 570,850,024 | 8,716 | Monday, September 28
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In my opinion you commit an error. I suggest it to discuss. | 1,442 | 6,028 | {"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} | 2.515625 | 3 | CC-MAIN-2020-40 | latest | en | 0.990385 |
https://math.stackexchange.com/questions/704766/counting-function-for-sums-of-three-squares | 1,566,451,241,000,000,000 | text/html | crawl-data/CC-MAIN-2019-35/segments/1566027316783.70/warc/CC-MAIN-20190822042502-20190822064502-00301.warc.gz | 552,325,996 | 30,988 | # Counting function for sums of three squares
Legendre showed that an integer is the sum of three squares if and only if it is not of the form $4^n(8m + 7)$ for some nonnegative integers $n$ and $m$. However, I have been unable to find any information regarding the counting function.
Let $S(x)$ denote the number of positive integers $\leq x$ which are the sum of three squares. What is known regarding $L: =\displaystyle \lim_{x \to \infty} \frac{S(x)}{x}$? The above characterization of Legendre easily shows that $L \leq \frac{7}{8}$, but can we do better? Is an exact value of $L$ known to exist?
## migrated from mathoverflow.netMar 9 '14 at 1:41
This question came from our site for professional mathematicians.
• Just sum the geometric progression: 1/8 are of this form with n=0; 1/32 are of this form with n=1; 1/128 are of this form with n=2 etc. these are disjoint subsequences. – anthonyquas Mar 8 '14 at 18:32
• As Anthony Quas says, summing the progressions gives a density of $5/6$. The more interesting'' questions concern the error term $S(x)-5x/6$; see, e.g., blms.oxfordjournals.org/content/20/3/203.abstract – so-called friend Don Mar 8 '14 at 18:32
• @AnthonyQuas That was a silly oversight on my part. Thanks for the reference and helpful comments. – David Mar 8 '14 at 18:39
Answer from comments: The quantity $\displaystyle \lim_{x \to \infty}S(x)/x$ is trivially given by: $$1 - \frac{1}{8} \sum_{n=0}^{\infty} \frac{1}{4^n} = \frac{5}{6}.$$ Furthermore, P. Shiu has shown that $S(x) - \frac{5}{6} x = O( \log x)$. | 476 | 1,545 | {"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} | 3.765625 | 4 | CC-MAIN-2019-35 | latest | en | 0.870149 |
http://www.geeksforgeeks.org/count-binary-digit-numbers-smaller-n/ | 1,511,211,353,000,000,000 | text/html | crawl-data/CC-MAIN-2017-47/segments/1510934806225.78/warc/CC-MAIN-20171120203833-20171120223833-00159.warc.gz | 398,761,904 | 17,103 | # Count of Binary Digit numbers smaller than N
Given a limit N, we need to find out the count of binary digit numbers which are smaller than N. Binary digit numbers are those numbers which contains only 0 and 1 as their digits as 1, 10, 101 etc are binary digit numbers.
Examples:
```Input : N = 200
Output : 7
Count of binary digit number smaller than N is 7,
enumerated below,
1, 10, 11, 110, 101, 100, 111
```
## Recommended: Please try your approach on {IDE} first, before moving on to the solution.
One simple way to solve this problem is to loop from 1 till N and check each number whether it is a binary digit number or not. If it is a binary digit number, increase the count of such numbers but this procedure will take O(N) time. We can do better, as we know that count of such numbers will be much smaller than N, we can iterate over binary digit numbers only and check whether generated numbers are smaller than N or not.
In below code, BFS like approach is implemented to iterate over only binary digit numbers. We start with 1 and each time we will push (t*10) and (t*10 + 1) into the queue where t is the popped element, if t is a binary digit number then (t*10) and (t*10 + 1) will also binary digit number, so we will iterate over these numbers only using queue. We will stop pushing elements in the queue when popped number crosses the N.
```// C++ program to count all binary digit
// numbers smaller than N
#include <bits/stdc++.h>
using namespace std;
// method returns count of binary digit
// numbers smaller than N
int countOfBinaryNumberLessThanN(int N)
{
// queue to store all intermediate binary
// digit numbers
queue<int> q;
q.push(1);
int cnt = 0;
int t;
// loop untill we have element in queue
while (!q.empty())
{
t = q.front();
q.pop();
// push next binary digit numbers only if
// current popped element is N
if (t <= N)
{
cnt++;
// uncomment below line to print actual
// number in sorted order
// cout << t << " ";
q.push(t * 10);
q.push(t * 10 + 1);
}
}
return cnt;
}
// Driver code to test above methods
int main()
{
int N = 200;
cout << countOfBinaryNumberLessThanN(N);
return 0;
}
```
Output:
```7
```
This article is contributed by Utkarsh Trivedi. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
# GATE CS Corner Company Wise Coding Practice
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Based on 1 vote(s) | 687 | 2,662 | {"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} | 3.765625 | 4 | CC-MAIN-2017-47 | latest | en | 0.781322 |
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# Why doesn't my TV say 120Hz/240Hz?
A reader asks why his TV won't display 240 Hz. Geoff Morrison helps him out.
CNET reader Steven U. asks:
I bought a 240 Hz LED LCD, and if I press the "Info" button, all I ever see is 1080p/60. Does this mean I'm only getting 60 Hz? Is there something wrong with my TV? Do I need a special HDMI cable?
Your question is a pretty common one, actually.
So we're all on the same page, 1080p/60 stands for 1,920x1,080 resolution, at a frame rate of 60. 1,920 pixels across, by 1,080 vertically, all changing 60 times a second.
Other common resolution/frame rate combos are:
1080p24--24 frames per second, common with movies;
1080i--interlaced, as in 1,920 horizontal by 540 vertical, every 60th of a second. Nearly all cable/satellite boxes output this. Your TV combines the "half" frames (called "fields") into complete 1080p frames. Done correctly, you'll never know it was happening.
Check out What is 1080p24 and 1080i and 1080p are the same resolution for more on this.
The maximum resolution source you can get with pre-recorded material is Blu-ray. Most are movies (1080p/24), but some concert videos are 1080i/30. Also, some games on the PS3/Xbox 360 are output at 1080p/60, and you can do that resolution with a PC of course. To be clear, there is no such thing as a 120 or 240 Hz source. The TV industry is moving towards higher resolution, not higher source framerates (for the foreseeable future).
With Blu-ray/gaming maxing out at 1080p/60, all you need is any high-speed HDMI cable to transmit that to your TV. Check out my article on Why all HDMI cables are the same for why you don't need an expensive HDMI cable.
Once that 1080p/60 gets to your TV, the TV converts that signal to 120 or 240 Hz. When you press the info button, you're getting the resolution of the incoming signal (i.e., 1080i or 1080p). The TV always displays, however, its native resolution and frame rate. In your case, this is 1080p/240. So no matter what you put into the TV, it converts it to 1080p refreshed 240 times per second. If you're curious about how refresh rate works, check out What is Refresh Rate and What is 600 Hz.
It's probably also worth it to check out my article on upconverting for more about native resolution.
Got a question for Geoff? First, check out all the other articles he's written on topics like why all HDMI cables are the same, LED LCD vs. plasma, active versus passive 3D, and more. Still have a question? Send him an e-mail! He won't tell you what TV to buy, but he might use your letter in a future article. You can also send him a message on Twitter @TechWriterGeoff or Google+. | 717 | 2,732 | {"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} | 2.640625 | 3 | CC-MAIN-2017-51 | latest | en | 0.905986 |
https://therealtypaper.com/understanding-20-units-of-semaglutide-is-how-many-mg/ | 1,726,754,792,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700652031.71/warc/CC-MAIN-20240919125821-20240919155821-00096.warc.gz | 543,797,031 | 12,516 | # Understanding 20 units of semaglutide is how many mg
## Introduction:
Semaglutide, a medication often prescribed for managing type 2 diabetes and obesity, is commonly dosed in units. However, patients and healthcare providers frequently encounter the question, “20 units of semaglutide is how many mg?” In this comprehensive article, we delve into the intricacies of semaglutide dosages, elucidating the conversion from units to milligrams. By understanding this conversion, patients can ensure accurate medication administration, facilitating optimal treatment outcomes.
## What is Semaglutide?
Semaglutide is a member of the group of drugs whise name is GLP-1 agonists, or glucagon-like peptide-1 receptor agonists. It works by imitating the actions of glucagon-like peptide-1, a hormone that aids in blood sugar regulation by promoting insulin production, delaying stomach emptying, and lowering hunger.
## Understanding Units and Milligrams:
Depending on the medicine, the doses of pharmaceuticals in pharmacology can be stated in several units. Certain biologic drugs including insulin are dosed in units, whereas certain pharmaceuticals are dosed in milligrams (mg).
Although semaglutide is typically given in milligrams, it is important to know its equivalent in units to ensure proper dosage. The conversion between milligrams and units varies according to the drug formulation’s concentration.
## Converting Semaglutide Units to Milligrams:
It is necessary to determine the concentration of the formulation may be utilized in order to calculate the milligrams (mg) contained in a certain quantity of semaglutide units. For instance, the well-known semaglutide brand Ozempic is available as pre-filled pens in various doses.
The following basic formula can be used to convert semaglutide units to milligrams based on typical amounts:
Ozempic 0.5 mg/mL: One unit of semaglutide in this formulation is equal to 0.005 mg, or five micrograms.
Ozempic 1.0 mg/mL: One unit of semaglutide in this formulation is equal to 0.01 mg, or ten micrograms.
For example, the following calculation would be made if a patient’s prescription called for 20 units of Ozempic at a dosage of 1.0 mg/mL:
20 units × 0.01 mg each means 0.2 mg.
Thus, 20 units of Ozempic at a 1.0 mg/mL concentration is equivalent to 2.0 milligrams of semaglutide.
## Significance of Accurate Dosing:
Semaglutide dosage reliability is necessary for achieving the best possible therapeutic results and lowering the possibility of side effects. Inadequate dosage may result in therapy not working or even injury to the patient. Therefore, it is crucial for patients and healthcare professionals to comprehend how to convert units to milligrams.
## Consultation with Healthcare Professionals:
For precise dosage recommendations catered to their particular need, patients should always speak with their pharmacists or healthcare professionals. Experts in medicine may provide advice on how to take semaglutide medication, how to change dosages, and what adverse effects might occur. Healthcare professionals promote medication administration that is safe and efficient by open communication.
## Importance of Patient Education:
Ensuring the efficacy of semaglutide treatment is largely upon patient education. Understanding their medicine, especially how they should use it and convert dosages, gives patients more control. Patients can actively engage in their treatment plan. They can improve adherence and better managing their condition, by being aware of the conversion from units to milligrams. Furthermore, patients may make educated decisions about their health when they have information about possible side effects and the significance of regular dosage regimens. | 776 | 3,757 | {"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} | 3.109375 | 3 | CC-MAIN-2024-38 | latest | en | 0.885552 |
http://blog.csdn.net/lonelyforest/article/details/747648 | 1,503,449,719,000,000,000 | text/html | crawl-data/CC-MAIN-2017-34/segments/1502886116921.70/warc/CC-MAIN-20170823000718-20170823020718-00038.warc.gz | 54,600,813 | 15,479 | # 16位有符号整型数据的输出～～～～
2445人阅读 评论(0)
;-----------------------------------------------------------------------------
; __write_int_
; ==========================
;
;Proc For write a int decimal to screen, int data in BX
;-----------------------------------------------------------------------------
__write_int_ proc near
push cx
push ax
;process if negtive
mov ax, bx
not ax
test ah, 10000000B
jne not_negative_w ;not negative
mov dl, '-'
mov ah, 02h
int 21h
neg bx
not_negative_w:
mov cx, 10000d ;divide by 10000
mov ax, bx ;data in bx, mov to ax
call __dec_div_
mov cx, 1000d
mov ax, bx
call __dec_div_
mov cx, 100d
mov ax, bx
call __dec_div_
mov cx, 10d
mov ax, bx
call __dec_div_
mov cx, 1d
mov ax, bx
call __dec_div_
;linefeed and carriage after out put a data
mov ah, 2h
mov dl, 0ah ;linefeed
int 21h
mov dl, 0dh ;carriage return after read
int 21h
;
pop ax
pop cx
ret ;return form _write_int_
;-----------------------------------------------------------------------------
; __dec_div_
; ==========================
;
;Subroutine to divide number in BX by number in CX
;print quotient on screen, (numberator in DX+AX, denom in CX)
;-----------------------------------------------------------------------------
__dec_div_ proc near
;
mov ax, bx ;number low half
mov dx, 0 ;zero out high half
div cx ;divide by CX
mov bx, dx ;remainder into BX
mov dl, al ;quotient into DL
;print the contents of DL on screen
add dl, 30h ;convert to ASCII
mov ah, 2h
int 21h
ret
__dec_div_ endp ;end of proc __dec_div_
;-----------------------------------------------------------------------------
__write_int_ endp ;end of proc __write_int_
;
;-----------------------------------------------------------------------------
;
codesg ends ;end of code segment
;*****************************************************************************
end begin ;end assembly
;
0
0
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资源下载 | 692 | 2,480 | {"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} | 2.65625 | 3 | CC-MAIN-2017-34 | longest | en | 0.126455 |
http://openstudy.com/updates/4f59bf14e4b0636d8905a623 | 1,448,418,673,000,000,000 | text/html | crawl-data/CC-MAIN-2015-48/segments/1448398444139.37/warc/CC-MAIN-20151124205404-00103-ip-10-71-132-137.ec2.internal.warc.gz | 171,474,577 | 40,992 | ## Mandy_Nakamoto 3 years ago What is exactly the moment of inertia all about? Clueless~
1. Mandy_Nakamoto
it has a lot of formulas depending on the shape isnt it?
2. khanitha
itis the rotational analogue of mass.yeah there are.u can find out by using parallel axis theorems and perpendicular axis theorem!!
3. Mandy_Nakamoto
i dont understand this question. Four particles A, B, C and D of mass 2 kg, 5 kg, 6 kg and 3 kg respectively are rigidly joined together by light rods to form a rectangle ABCD where AB=2a and BC=4a. Find the moment of inertia of this system of particles about an axis along AB..
4. Mandy_Nakamoto
do i have to use I=Md\[^{2}\]
5. Mani_Jha
I had the exact same question in my mind when I started rotation. Unfortunately, none of my teachers could explain it that thouroughly. I had to do some self-research. :) You know what is inertia, right? A more massive mass requires more force to be moved. Mass is a measure of inertia. Now, when something rotates about its axis, the amount of force required to stop it does not depend only on the mass, but also a new thing - The distance from the axis. Try it. Try to move a stationary fan by giving it a strike it at its edge. It easily rotates. Then try to strike it somewhere near the center. It moves less. You have to apply more force to move something closer to the axis of rotation. So, now, the inertia of a rotating object is not only a function of mass, but also of the distance from the axis of rotation. You can try to find the kinetic energy of a rotating particle. Considering angular velocity for v, you will find the kinetic energy to be: \[mr ^{2} w ^{2}/2\]. The linear kinetic energy is \[mv ^{2}/2\] Compare these, and you will find that during rotation, the mass of a body is equivalent to mr^2. This new quantity is known as moment of inertia(you can clearly see moment of inertia increases with increasing distance from the axis) Did u get this?
6. Mandy_Nakamoto
Yeah! Great explanation.. I can finally picture it in my head.. :D bout my question i have to make the line of axis parallel to AB.. rite??
7. Mani_Jha
Yes, right. First find the moment of inertia about the centre of the system. Then use the parallel axis theorem(do u know it?)
8. Mandy_Nakamoto
9. Mandy_Nakamoto
so d=2a rite?? if from centre..
10. Mandy_Nakamoto
sorry.. im a bit slow..
11. Mani_Jha
Wait, you can do without the parallel axis theorem. The axis is AB. Take the coordinate axis along AB(x or y). Then find the distance of the four masses from the origin. Find the moment of inertia of each, and add them up. |dw:1331285211599:dw| I have considered A as the origin. Use the distance formula to calculate the distance of each mass from origin, and then use I=mr^2.
12. Mani_Jha
I would like to add something to the explanation. It is more difficult to stop the edges of a rotating fan, than the points closer to the center(because they have higher moment of inertia). The edges rotate at a higher speed than the others. You can observe that. The edges will appear completely blurred in a photograph, while the points close to the centre will be more visible
13. Mandy_Nakamoto
i have to find the inertia for A too?? even if it is the origin??
14. Mani_Jha
it will be zero
15. Mandy_Nakamoto
|dw:1331285964516:dw| this is from my lecturer's note.. what is with the delta x for?? and why is d the distance from the axis that we draw to the rod?? how should we know tat?? it explains that moment of inertia of typical element about XY = md2 (which i dont understand) n concluded Ixy=Md^2..
16. Mandy_Nakamoto
bout the delta x she wrote "Divide rod into elements each of length δx. "
17. Mani_Jha
A large part of classical mechanics(including newton's laws) deals with only particles. For a particle, we can easily say that its moment of inertia is mr^2. But not so, for large bodies. But the best we can do is divide(i.e. differentiate) large bodies into its constituent particles. We shall find the moment of inertia for a single particle, and add up for all of them(i.e. integrate) to find the net moment of inertia for the body. So, in the case of the rod, we have divided it into small elements of an extremely small length(we choose an extremely small length to make it equivalent to a particle) dx. The axis of rotation in a problem will always be given. You just have to find the distance of a particle from the axis. Since the element of length dx is a particle, we can say that it's moment of inertia is mr^2. Did u get it?
18. Mandy_Nakamoto
from the question tat i posted, the axis is the AB.. the particle is what? Is it the origin? Can i take B as the origin?
19. Mani_Jha
A, B, C and D are all particle masses. Yes, u cant take any point as the origin. But make sure you calculate the distances correctly
20. Mandy_Nakamoto
i cant?? But how do i noe which one to take as the origin?? the axis is AB so i shud take whether A or B as the origin.. am i rite??
21. Mani_Jha
sorry, typing mistake. You CAN take any point as the origin, but it would be more preferable to take A or B as origin because they lie on the axis
22. Mandy_Nakamoto
What if i take C and D?? What will happen??
23. Mani_Jha
Oh wait, I was correct when I had mistyped! See AB is the axis, which means A and B are gonna remain stationary. But C and D are going to move, continously changing their positions. So, it does not make sense to take either of them as origin. So take either A or B only as origin. This happens only in rotation. Otherwise, you CAN take any point as origin
24. Mandy_Nakamoto
Thanks! You really helped a LOT.. im not clueless anymore (in the mean time).. Bye..! ^^
25. Mandy_Nakamoto
Btw thanks for being patient with me..
26. Mani_Jha
No problem at all. Where are you from?
27. Mandy_Nakamoto
Malaysia
28. Taufique
Mandy_Nakamoto: In simple manner moment of inertia is the mass which appose the rotational motion of any body. in the linear motion it is mass and in rotational motion it just named as moment of inertia.....the moment of inertia depends on the shape of the body.and we calculate the moment of inertia of any regular shape body by integratio method..such as moment of inertia circle is mr^2.where m is mass and r is the radius of that circle..we apply following integeration formula: dI=dmr^2... when mass is variable and dI is the moment of inertia of small part which has mass dm.... i hope that you will get your answer.... | 1,633 | 6,470 | {"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} | 3.984375 | 4 | CC-MAIN-2015-48 | longest | en | 0.932799 |
http://www2.swccd.edu/~sgracey/SWC/MATH103/119_index.htm | 1,397,751,226,000,000,000 | text/html | crawl-data/CC-MAIN-2014-15/segments/1397609530136.5/warc/CC-MAIN-20140416005210-00132-ip-10-147-4-33.ec2.internal.warc.gz | 784,835,292 | 2,785 | ## STUDENT LEARNING OUTCOMES:
### Upon successful completion of Math 119, the student should be able to:
1. Give an appropriate descriptive summary, including the shape, center, spread and outliers of the distribution, from a set of raw data.
2. Analyze the relationship between two variables using the scatterplot, correlation coefficient, and the least squares regression line.
3. Student will be able to use the normal distribution to find approximate solutions to problems about sample means and sample proportions.
### COURSE DESCRIPTION AND SCOPE:
This course introduces data analysis. Topics include design of experiments, descriptive statistics, correlation and regression, probability, sampling, estimation, and significance testing. Students use appropriate technology to analyze real-world data.
### PREREQUISITE:
MATH 65 or MATH 70 with a grade of “C” or better or qualification through the Math Competency Exam or approved equivalent.
### ANNOTATED LECTURE PDF FILES
WEEK 1 LECTURES: 6/20 6/21 6/21cont 6/22 6/23 6/23cont WEEK 7 LECTURES: 8/1 WEEK 13 LECTURES: WEEK 2 LECTURES: 6/27 6/28 6/30 (absent) WEEK 8 LECTURES: WEEK 14 LECTURES: WEEK 3 LECTURES: 7/5 7/6 7/7 WEEK 9 LECTURES: WEEK 15 LECTURES: WEEK 4 LECTURES: 7/11 7/12 7/13 WEEK 10 LECTURES: WEEK 16 LECTURES: WEEK 5 LECTURES: 7/18 7/19 7/20 7/21 WEEK 11 LECTURES: WEEK 17 LECTURES: WEEK 6 LECTURES: 7/25 7/27 7/28 7/28cont WEEK 12 LECTURES:
## HOMEWORK:
See the Chapter Handouts
## SOLUTIONS:
EXAMS
EXAM 2 (A) EXAM 2 (B) EXAM 3 EXAM 4
### Movies
Constructing a CI using the t-distribution
## HANDOUTS:
SYLLABUS AND TENTATIVE SUMMER 2011 SCHEDULE
## WORKSHEETS:
CHAPTER 1 CHAPTER 5 CHAPTER 9 CHAPTER 2 CHAPTER 6 PRACTICE EXAM 2 CHAPTER 10 CHAPTER 3 PRACTICE EXAM 1: CH. 1-3 CHAPTER 7 CHAPTER 11 CHAPTER 4 CHAPTER 8 PRACTICE EXAM 3 PRACTICE FINAL (IN ORDER)
top of page / Shannon Gracey's main page / SWC Home | 583 | 1,904 | {"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} | 2.890625 | 3 | CC-MAIN-2014-15 | longest | en | 0.73335 |
https://lavelle.chem.ucla.edu/forum/viewtopic.php?f=157&t=23158&view=print | 1,611,571,489,000,000,000 | text/html | crawl-data/CC-MAIN-2021-04/segments/1610703565541.79/warc/CC-MAIN-20210125092143-20210125122143-00596.warc.gz | 412,608,706 | 2,364 | Page 1 of 1
### Midterm Materials
Posted: Mon Nov 06, 2017 9:11 am
Are we to purchase a blue book for the upcoming midterm, or will it be similar to previous exams when all answers were written on the exam?
### effective nuclear charge
Posted: Mon Nov 06, 2017 9:56 am
Could someone please explain effective nuclear charge?
### Re: Midterm Materials
Posted: Mon Nov 06, 2017 12:29 pm
Effective nuclear charge deals is the equation: Zeff = z(atomic number) - S(shielding e-). By subtracting these two you will derive the effective nuclear charge
### Re: Midterm Materials
Posted: Mon Nov 06, 2017 12:30 pm
We don't need to buy a blue book for the midterm.
### Re: Midterm Materials
Posted: Mon Nov 06, 2017 12:35 pm
The definition of effective nuclear charge is the net charge that an electron experiences in an atom with multiple electrons. Basically as the number of electrons increases in an atom, the effective nuclear charge that the outermost electron feels is lowered. The effective nuclear charge can be calculated by the equation::
Zeff = Z - S
Where Z is the atomic number and S is the number of shielding electrons
Electrons with higher energy can have other lower energy electrons between itself and the nucleus which effectively lowers the positive charge experienced by the high energy electron. The shielding effect is related to effective nuclear charge and it is the name given to the balance between valence electrons and protons and the repulsion between valence and inner electrons.
### Re: Midterm Materials [ENDORSED]
Posted: Mon Nov 06, 2017 2:13 pm
We do not allow blue books on exams but you can still write on the back of each page for scratch work as the exams are one-sided; you should have plenty of room.
### Re: Midterm Materials
Posted: Mon Nov 06, 2017 4:30 pm
Should we be able to know the conversion from eV to Joules for the midterm?
### Re: Midterm Materials
Posted: Wed Nov 08, 2017 1:44 pm
It's going to be given to us on the list of constants and equations so no need to memorize it! | 499 | 2,042 | {"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} | 2.796875 | 3 | CC-MAIN-2021-04 | latest | en | 0.910437 |
https://community.qlik.com/thread/140818 | 1,532,257,589,000,000,000 | text/html | crawl-data/CC-MAIN-2018-30/segments/1531676593208.44/warc/CC-MAIN-20180722100513-20180722120513-00301.warc.gz | 635,921,492 | 24,719 | 7 Replies Latest reply: Nov 6, 2014 9:28 AM by Henric Cronström
# Interval Match Question
We have two tables. One table has columns 'ID' and 'Invoice Date'. Another one has columns 'ID', 'Start Date', 'End Date', and 'Price'. The desired output is 'ID', 'Invoice Date', 'Price'. I know this could be done using interval match but having a hard time figuring out how. Any help is highly appreciated. Attached is sample data for your convenience.
Table 1:
Product ID InvoiceDate A 10/16/2014 B 08/01/2014
Table 2:
Product ID Start Date End Date Price A 06/01/2014 06/30/2014 \$200 A 07/01/2014 08/30/2014 \$350 A 09/01/2014 12/31/9999 \$400 B 06/01/2014 06/30/2014 \$250 B 07/01/2014 08/30/2014 \$240 B 09/01/2014 12/31/9999 \$300
Desired Output:
Product ID InvoiceDate Price A 06/02/2014 \$200 A 07/20/2014 \$350 B 06/20/2014 \$250 B 09/26/2014 \$300
• ###### Re: Interval Match Question
Hey,
REgards,
Chinna.
• ###### Re: Interval Match Question
No Luck. How to fit in amount is confusing me. I would really appreciate if you can create a quick QVW with attached data and post it back. That will be very helpful in understanding it. Thanks in advance for helping.
• ###### Re: Interval Match Question
I started to do the interval match, and the first two IDs work as expected.
But then i noticed some duplication in your data that don't match the desired results.
For example, for 1000E2USdd 16890-000 , you have two intervales for 9/1/2014-> 12/31/9999 with 2 different values. See below
And when i check the desired result it doesn't quite make sense
How did you associate 9/26/2014 to line 11 and 10/15/2014 to line 14 ??
• ###### Re: Interval Match Question
I see what you are saying.Makes sense! I have updated the datasheet and have simplified it a bit. Please use that instead. Thanks for helping !
• ###### Re: Re: Interval Match Question
Check this app
• ###### Re: Re: Interval Match Question
Ok - i still see an unexpected 'desired output' in your spreadsheet.
There are 2 records with invoice dates below
To match those 2 records to specific intervals we have the following possible intervals for A and B
According to the above ID=A and InvoiceDate=10/16/2014 would map to \$400 and ID=B and InvoiceDate=08/01/2014 would map to 240\$ . However your expected outcome is this ???
When I applied the interval match in QlikView i got the expected result of
If you agree with me, below is the load script for this and attached is the QVW. The solution uses the 'extended' interval match syntax to not only match the interval but another identifier as well... in this case ID.
Invoices:
Date(InvoiceDate) as InvoiceDate
FROM
[C:\Temp\Sample data.xlsx]
(ooxml, embedded labels, table is [Table 1]);
StartEnds:
Date([Start Date]) as [Start Date],
Date([End Date]) as [End Date],
Price
FROM
[C:\Temp\Sample data.xlsx]
(ooxml, embedded labels, table is [Table 2]);
inner join IntervalMatch (InvoiceDate,ID) LOAD [Start Date], [End Date],ID Resident StartEnds; | 855 | 3,022 | {"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} | 2.8125 | 3 | CC-MAIN-2018-30 | latest | en | 0.826483 |
https://www.gamedev.net/forums/topic/174713-metric-units--gt-pixels/ | 1,532,174,471,000,000,000 | text/html | crawl-data/CC-MAIN-2018-30/segments/1531676592523.89/warc/CC-MAIN-20180721110117-20180721130117-00093.warc.gz | 898,305,220 | 23,448 | #### Archived
This topic is now archived and is closed to further replies.
# Metric units -> pixels
This topic is 5456 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.
## Recommended Posts
In my 2D engine, I want to use metric units to define distances, object sizes and locations in my project. Mostly for clarity, and to support multiple resolutions. But I don''t know where I should do the conversion to pixels. 1) I could do it in the renderer, but I''m concerned it will affect speed (doing conversions for every coordinate). 2) I could do it while loading the world, but I''d like the scripts and other systems to also use metric units so I''d have to do conversions every time a game objects position is manipulated. I''m confused, and afraid the whole system will become very complicated.
##### Share on other sites
Why would it get complicated? Just use the same coordinates throughout.. What am I missing?
##### Share on other sites
Just make sure that all your 3D model''s coordinates are in scale with each other. Then you won''t have to do any messy and expensive scaling in your program.
##### Share on other sites
But my game is not 3D. It''s 2D.
I personally would prefer to use metric units everywhere, except when I finally draw them on screen, I would convert them to pixels, based on the current resolution.
But that means I would maybe have to scale every 2D sprite on every rendering. Well, I want to support zooming anyway, so I''d probably have to do it anyway.
Ok, another question then:
Would it be wiser to use integers or floats for metric coordinates?
10.5 = 10.5 m
1050 = 10.5 m (I don''t need any more precision)
##### Share on other sites
If you use Direct3D or OpenGL you can simply set up an orthogonal projection with 1,1 as the lower right corner. That way you can give your positions in fractions of a screen and it will be the same on any resolution.
##### Share on other sites
Thanx, I''ll try that. I have no experience with OpenGL or D3D, but there are some tutorials on how to do 2D in them and I think and it would also make zooming / rotating easier.
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### This Is a Certified Answer
Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
First it would be 8 over 100.
But since 8% is a percentage of 100.
Then you simplify it down to 4 over 50... Then, to 2 over 25. | 121 | 462 | {"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} | 2.59375 | 3 | CC-MAIN-2017-04 | latest | en | 0.942273 |
https://writingforgrades.com/consider-the-two-functions-fx-1-x-and-gx-1-x-we-ca-2/ | 1,679,612,964,000,000,000 | text/html | crawl-data/CC-MAIN-2023-14/segments/1679296945218.30/warc/CC-MAIN-20230323225049-20230324015049-00408.warc.gz | 702,173,379 | 13,071 | # Consider the two functions f(x) = 1-x and g(x) = 1/x. We ca
Consider the two functions: f(x) = 1-x and g(x) = 1/x. We can compose them in two ways: f(g(x)) and g(f(x)). We can go further and compose these two new functions with themselves, and also with the old ones, in a number of ways. Keeping composing these functions with the new ones as they are generated and figure out simplified formulae for them in terms of the variable x. a) How many distinct functions are there, including f and g themselves?b) List themc) How is each one composed from f and g?d) How do you know that these are all there are?e) For what real numbers are all these functions simultaneously defined?
0 replies | 176 | 693 | {"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} | 3.515625 | 4 | CC-MAIN-2023-14 | latest | en | 0.960133 |
http://mathhelpforum.com/differential-equations/176916-spring-mass-undamped-motion.html | 1,527,503,473,000,000,000 | text/html | crawl-data/CC-MAIN-2018-22/segments/1526794872766.96/warc/CC-MAIN-20180528091637-20180528111637-00321.warc.gz | 189,752,064 | 11,926 | # Thread: spring mass undamped motion
1. ## spring mass undamped motion
A mass weighing 10 pounds stretches a spring 1/4 foot. This mass is removed and replaced with a mass of 1.6 slugs, which is initially released from a point 1/3 foot above the equilibrium position with a downward velocity of 5/4 ft/s.
At what time does the mass attain a displacement below the equilibrium position numerically equal to 1/2 the amplitude?
my position function is $\displaystyle x(t)=-\frac{1}{3}cos(160t)+\frac{1}{128}sin(160t)$
I have tried to put it into the form $\displaystyle x(t)=Asin(\omega t+\phi)$
and I am getting $\displaystyle x(t)=\frac{1}{3}sin(160t+\frac{\pi}{2})$
The time I am getting is $\displaystyle \frac{\pi}{480}s$ initially, but I don't know if this is right. I'm also having trouble writing the answer as a series. Can anyone help me? Thanks
2. Originally Posted by duaneg37
A mass weighing 10 pounds stretches a spring 1/4 foot. This mass is removed and replaced with a mass of 1.6 slugs, which is initially released from a point 1/3 foot above the equilibrium position with a downward velocity of 5/4 ft/s.
At what time does the mass attain a displacement below the equilibrium position numerically equal to 1/2 the amplitude?
my position function is $\displaystyle x(t)=-\frac{1}{3}cos(160t)+\frac{1}{128}sin(160t)$
I have tried to put it into the form $\displaystyle x(t)=Asin(\omega t+\phi)$
and I am getting $\displaystyle x(t)=\frac{1}{3}sin(160t+\frac{\pi}{2})$
The time I am getting is $\displaystyle \frac{\pi}{480}s$ initially, but I don't know if this is right. I'm also having trouble writing the answer as a series. Can anyone help me? Thanks
First I don't think your ODE is correct.
First by Hook's law we have
$\displaystyle F=kx \iff 10=k(.25) \iff k=40$
Now the ode is
$\displaystyle \displaystyle mx''=-kx \iff x''+\frac{1}{5}x=0$
So the solution should have the form
$\displaystyle \displaystyle x(t)=c_1\cos\left( \frac{t}{5}\right)+c_2\sin\left( \frac{t}{5}\right)$
Now use the initial conditions
3. I thought I had to convert the mass into slugs by $\displaystyle W=mg$, which gives the force as $\displaystyle 320$ slugs$\displaystyle =k(\frac{1}{4})$ for Hooke's law. This gives $\displaystyle k=1280$. Then I found m for the weight of $\displaystyle 1.6$ slugs >>> $\displaystyle 1.6=m(32)$where $\displaystyle m=.05$ This gives $\displaystyle \omega ^{2}=25600$. Is this incorrect?
Shouldn't your equation be $\displaystyle x(t)=c_{1}cos2t+c_{2}sin2t$?
I did it again without rounding off as much and got:
$\displaystyle x(t)=\frac{\sqrt{16393}}{384}sin(160t-1.547)$
the time I got:
$\displaystyle t=.026+\frac{n\pi}{160}$ sec., let $\displaystyle n=0,1,2,3,...$
Am I on the wrong track with this? Thanks a lot!
4. Weight is a force. Slugs are mass. So in hooks law you need a force and since lbs are a force you do not need to do any conversions.
5. Originally Posted by TheEmptySet
$\displaystyle \displaystyle mx''=-kx \iff x''+\frac{1}{5}x=0$
Actually $\displaystyle \displaystyle \frac{k}{m} = \frac{40}{1.6} = 25$, not 1/25.
Thus
$\displaystyle x(t) = c_1~cos(5t) + c_2~sin(5t)$
-Dan
6. I think I've done them all wrong! Thanks a lot for you help!
7. My position function is $\displaystyle x(t)=\frac{5}{12}sin(5t-.927)$
To find the time I set $\displaystyle \frac{1}{2}=sin(5t-.927)$ I know the sine of $\displaystyle \frac{\pi}{6}$ and $\displaystyle \frac{5\pi}{6}$ will give $\displaystyle \frac{1}{2}$, so I get $\displaystyle t=.29$and $\displaystyle t=.709$. Do I use both of these times to get my answer? I found the period to be $\displaystyle T=\frac{2\pi}{5}$. I said $\displaystyle t=.29+\frac{2n\pi}{5}$ s where $\displaystyle n=0,1,2,3,...$ and $\displaystyle t=.709+\frac{2n\pi}{5}$ s where $\displaystyle n=0,1,2,3,...$ as my answer. Am I doing this right?
8. Originally Posted by duaneg37
My position function is $\displaystyle x(t)=\frac{5}{12}sin(5t-.927)$
To find the time I set $\displaystyle \frac{1}{2}=sin(5t-.927)$ I know the sine of $\displaystyle \frac{\pi}{6}$ and $\displaystyle \frac{5\pi}{6}$ will give $\displaystyle \frac{1}{2}$, so I get $\displaystyle t=.29$and $\displaystyle t=.709$. Do I use both of these times to get my answer? I found the period to be $\displaystyle T=\frac{2\pi}{5}$. I said $\displaystyle t=.29+\frac{2n\pi}{5}$ s where $\displaystyle n=0,1,2,3,...$ and $\displaystyle t=.709+\frac{2n\pi}{5}$ s where $\displaystyle n=0,1,2,3,...$ as my answer. Am I doing this right?
Looks good to me.
-Dan
,
,
,
### A mass weighing 10 pounds stretches a
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The characteristic impedance of free space is the impedance of a hypothetical lossless medium in which electromagnetic waves can propagate freely. It is also known as the wave impedance of free space. The value of the characteristic impedance of free space is often represented by the symbol Z0.
The characteristic impedance of free space is determined by the speed of light in a vacuum and the permittivity and permeability of free space. The speed of light in a vacuum is denoted by the symbol c. The permittivity of free space is denoted by the symbol ε0, and the permeability of free space is denoted by the symbol μ0.
The characteristic impedance of free space is given by the following equation:
Z0 = frac{1}{sqrt{mu_0epsilon_0}}
The SI unit of characteristic impedance is the ohm.
##### What are the expression of impedance of free space?
The impedance of free space is a measure of the opposition that free space offers to the propagation of an electromagnetic wave. It is usually represented by the symbol Z and is measured in ohms. The impedance of free space is a function of the frequency of the electromagnetic wave and is given by:
Z = 377 ohms
where f is the frequency of the wave in Hz. What is the characteristic impedance of air? The characteristic impedance of air is approximately 377 ohms.
### How do you calculate intrinsic impedance of free space?
The intrinsic impedance of free space is a measure of the opposition that free space offers to the propagation of an electromagnetic wave. It is also sometimes referred to as the electromagnetic impedance of free space.
The value of the intrinsic impedance of free space is equal to the square root of the ratio of the magnetic constant to the electric constant. The magnetic constant, also known as the permeability of free space, is a measure of the ease with which a magnetic field can be created in free space. The electric constant, also known as the permittivity of free space, is a measure of the ease with which an electric field can be created in free space.
The value of the intrinsic impedance of free space is equal to the speed of light divided by the square root of the ratio of the electric constant to the magnetic constant. The speed of light is a fundamental constant of nature and is the speed at which all electromagnetic waves propagate.
The value of the intrinsic impedance of free space is 377 ohms. What is meant by characteristic impedance? Characteristic impedance is a measure of the opposition to the flow of an alternating current (AC) that is inherent in a conductor or in a transmission line. It is also a measure of the impedance of a circuit, device, or system to an AC signal of a particular frequency. The SI unit of characteristic impedance is the ohm.
How do you calculate characteristic impedance? Characteristic impedance is a measure of a transmission line's ability to resist changes in current flow. It is calculated by dividing the voltage by the current flowing through the line. The unit of measurement for characteristic impedance is the ohm. | 621 | 3,115 | {"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} | 3.984375 | 4 | CC-MAIN-2024-22 | latest | en | 0.950283 |
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# Numerator as one row by Denominator the whole column
Hi GuYS
What's the best way to do in a KPI where i want to take each value from one dimension as the Numerator divided by all the vales in that column as the Denominator? Is it best to do in the script or expression and how?
Regards
• ###### Re: Numerator as one row by Denominator the whole column
Could you explore more with some sample data??
• ###### Re: Numerator as one row by Denominator the whole column
Are you trying to do something like this:
Dim1 Val
A 10
B 15
C 25
and in the KPI you are trying to do for A -> 10/50?
For this you can try Sum({<Dim1 = {A}>}Val)/Sum(Val)
If this isn't what you are looking for, please elaborate on what you are looking to do.
Best,
Sunny
• ###### Re: Numerator as one row by Denominator the whole column
I guess, he is asking for Val=10 as Numerator and sum(Val)=50 as Denominator...
If yes, try with total:
sum(Val)/sum(total Val)
• ###### Re: Numerator as one row by Denominator the whole column
Thanks for pointing that out Balraj. The expression was suppose to do 10/50, but I mistakenly wrote 10/25
• ###### Re: Numerator as one row by Denominator the whole column
like this?
• ###### Re: Numerator as one row by Denominator the whole column
sum(Column)/sum(total Column) ?
• ###### Re: Numerator as one row by Denominator the whole column
Thanks guys, i just need to test something else before i can test this as it's not as straight forward as i've posted, i'll elaborate later.
• ###### Re: Numerator as one row by Denominator the whole column
It seems, you were playing with us | 461 | 1,719 | {"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} | 3.046875 | 3 | CC-MAIN-2018-05 | longest | en | 0.939639 |
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See the recommended documentation of this function
# calfrq
frequency response discretization
### Calling Sequence
[frq,bnds,split]=calfrq(h,fmin,fmax)
### Arguments
h
Linear system in state space or transfer representation ( see syslin )
fmin,fmax
real scalars (min and max frequencies in Hz)
frq
row vector (discretization of the frequency interval)
bnds
vector [Rmin Rmax Imin Imax] where Rmin and Rmax are the lower and upper bounds of the frequency response real part, Imin and Imax are the lower and upper bounds of the frequency response imaginary part,
split
vector of frq splitting points indexes
### Description
frequency response discretization; frq is the discretization of [fmin,fmax] such that the peaks in the frequency response are well represented.
Singularities are located between frq(split(k)-1) and frq(split(k)) for k>1.
### Examples
s=poly(0,'s')
h=syslin('c',(s^2+2*0.9*10*s+100)/(s^2+2*0.3*10.1*s+102.01))
h1=h*syslin('c',(s^2+2*0.1*15.1*s+228.01)/(s^2+2*0.9*15*s+225))
[f1,bnds,spl]=calfrq(h1,0.01,1000);
rf=repfreq(h1,f1);
plot2d(real(rf)',imag(rf)')
• bode — Bode plot
• black — Black-Nichols diagram of a linear dynamical system
• nyquist — nyquist plot
• freq — frequency response
• repfreq — frequency response
• logspace — vecteur de valeurs logarithmiquement équidistantes. | 443 | 1,478 | {"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} | 2.765625 | 3 | CC-MAIN-2021-04 | longest | en | 0.717099 |
https://www.physicsforums.com/threads/polynomial-that-satisfies-a-differential-equation.472230/ | 1,660,622,794,000,000,000 | text/html | crawl-data/CC-MAIN-2022-33/segments/1659882572220.19/warc/CC-MAIN-20220816030218-20220816060218-00362.warc.gz | 801,891,996 | 14,343 | # Polynomial that satisfies a differential equation
TiberiusK
## Homework Statement
I must show that t H_n satisfies a diferential equation. By diferentiating H_n(x) = -xH_(n-1)(x) - (n - 1)H_(n-2)(x) (1) and
using induction on n, show that, for n >= 1,
H'_n(x) = -nH_(n-1)(x) (2)
I have to use (2) to express H_(n-1) and H_(n-2) in terms of derivatives of H_n, and substitute these into (1) to show that
H''_n - xH'_n + nH_n = 0 (3)
for n>= 0. Now let O_n(x) = exp(-(x^2)/4 )H_n(x). Using (3) I must show that
O''_n +(n+1/2-(x^2)/3)O_n=0
## Homework Equations
H_n(x) for n = 0,1,2.... : H_0(x) =1 and H_1(x) = -x; then, for n >=2, H_n is defined by the recurrence
H_n(x) = -xH_(n-1)(x) - (n - 1)H_(n-2)(x): (1)
## The Attempt at a Solution
I need some help on getting started ,my first problem is how to differentiate the recurrence
H_n(x) = -xH_(n-1)(x) - (n - 1)H_(n-2)(x) ....because I get
H_n'(x) =-H_(n-1)'(x) -xH_(n-1)(x) - (n - 1)H_(n-2)'(x) =>-H_(n-1)'(x)[1+x]- (n - 1)H_(n-2)'(x) and I do not know how to continue ....
TiberiusK
any ideas?
Homework Helper
## Homework Statement
I must show that t H_n satisfies a diferential equation. By diferentiating H_n(x) = -xH_(n-1)(x) - (n - 1)H_(n-2)(x) (1) and
using induction on n, show that, for n >= 1,
H'_n(x) = -nH_(n-1)(x) (2)
I have to use (2) to express H_(n-1) and H_(n-2) in terms of derivatives of H_n, and substitute these into (1) to show that
H''_n - xH'_n + nH_n = 0 (3)
for n>= 0. Now let O_n(x) = exp(-(x^2)/4 )H_n(x). Using (3) I must show that
O''_n +(n+1/2-(x^2)/3)O_n=0
## Homework Equations
H_n(x) for n = 0,1,2.... : H_0(x) =1 and H_1(x) = -x; then, for n >=2, H_n is defined by the recurrence
H_n(x) = -xH_(n-1)(x) - (n - 1)H_(n-2)(x): (1)
So that H_0'= 0 and H_1'= -1.
The formula you want to prove says that H'_1(x)= -(1)H_0(x)= -(1) so it is correct for n= 1.
## The Attempt at a Solution
[/B]
I need some help on getting started ,my first problem is how to differentiate the recurrence
H_n(x) = -xH_(n-1)(x) - (n - 1)H_(n-2)(x) ....because I get
H_n'(x) =-H_(n-1)'(x) -xH_(n-1)(x) - (n - 1)H_(n-2)'(x) =>-H_(n-1)'(x)[1+x]- (n - 1)H_(n-2)'(x) and I do not know how to continue ....
Well, you are using the product rule incorrectly.
H_n'(x)= -H_(n-1)(x)- xH_(n-1)'(x)- (n-1)H_(n-2)'(x) | 988 | 2,280 | {"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} | 4.0625 | 4 | CC-MAIN-2022-33 | latest | en | 0.807105 |
linear-motion40505.jaiblogs.com | 1,540,081,801,000,000,000 | text/html | crawl-data/CC-MAIN-2018-43/segments/1539583513508.42/warc/CC-MAIN-20181020225938-20181021011438-00416.warc.gz | 213,081,009 | 5,775 | # Top Guidelines Of Linear Motion
Our editors will evaluate That which you've submitted, and when it meets our requirements, we will include it on the post.
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The Assessment of such devices may for that reason be simplified by neglecting the direction parts in the vectors concerned Read Full Article and dealing only with the magnitude.[2]
The instantaneous acceleration will be the limit with the ratio Δ v displaystyle Delta mathbf v
In accordance with Newton’s 1st regulation (also referred to as the principle of inertia), a entire body with no Internet drive acting on it is going to either continue to be at rest or continue on to maneuver with uniform speed in the straight line, Based on its Original issue of motion.
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, is perpendicular into the motion. The ingredient of your drive parallel for the motion, or equivalently, perpendicular to the line connecting the point of application on the axis is F ⊥ displaystyle mathbf F _ perp
Atom, smallest device into which matter can be divided with no launch of electrically billed particles....
Below every day situations, exterior forces which include gravity and friction could potentially cause an object to change the course of its motion, making sure that its motion cannot be referred to as linear.[three]
As equipment screw actuators change rotary motion into linear, they’re ideal for screw driving, wheels and axles, and motor vehicle jacks. An electric positioner can be a linear motion process that maintains actuator balance and Regulate. Enable Grainger make the law of linear browse around this web-site motion be just right for you. | 749 | 3,861 | {"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} | 3.234375 | 3 | CC-MAIN-2018-43 | latest | en | 0.931572 |
http://mizar.uwb.edu.pl/version/current/html/proofs/group_2/10_1_1 | 1,571,716,644,000,000,000 | text/plain | crawl-data/CC-MAIN-2019-43/segments/1570987798619.84/warc/CC-MAIN-20191022030805-20191022054305-00054.warc.gz | 132,676,408 | 1,451 | let A, B be Subset of G; :: thesis: A * B = B * A
thus A * B c= B * A :: according to XBOOLE_0:def 10 :: thesis: B * A c= A * B
proof
let x be object ; :: according to TARSKI:def 3 :: thesis: ( not x in A * B or x in B * A )
assume x in A * B ; :: thesis: x in B * A
then ex g, h being Element of G st
( x = g * h & g in A & h in B ) ;
hence x in B * A ; :: thesis: verum
end;
let x be object ; :: according to TARSKI:def 3 :: thesis: ( not x in B * A or x in A * B )
assume x in B * A ; :: thesis: x in A * B
then ex g, h being Element of G st
( x = g * h & g in B & h in A ) ;
hence x in A * B ; :: thesis: verum | 228 | 614 | {"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} | 2.96875 | 3 | CC-MAIN-2019-43 | latest | en | 0.739797 |
http://mathhelpforum.com/advanced-algebra/91462-proving-subspace-print.html | 1,519,441,111,000,000,000 | text/html | crawl-data/CC-MAIN-2018-09/segments/1518891815034.13/warc/CC-MAIN-20180224013638-20180224033638-00013.warc.gz | 207,054,754 | 3,448 | # Proving this is a subspace
• Jun 1st 2009, 06:17 PM
paupsers
Proving this is a subspace
Can anyone help me with this elementary problem? How do I prove the following is a subspace?
W = {(a1, a2, a3) | 2*a1 - 7*a2 +a3 = 0}
I know I have to prove its closed under addition and multiplication... But the condition on W is confusing me...
• Jun 1st 2009, 06:26 PM
paupsers
I think I just solved it, actually!
I let a3 = 7*a2 - 2*a1, and made that the new condition on W.
I then let a = (a1, a2, 7*a2 - 2*a1) and similarly for b.
Then I did a + cb = (a1 + c*b1, a2 + c*b2, 7(a2 + c*b2) - 2(a1 + c*b1))
Which satisfies my new condition on W I believe...
Can anyone verify this?
• Jun 1st 2009, 06:36 PM
Random Variable
$W = ({a_{1},a_{2},-2a_{1}+7a_{2}}$)
Let $X = (x_{1},x_{2},-2x_{1}+7x_{2})$ and $Y = (y_{1},y_{2},-2y_{1}+7y_{2})$ be in $W$
then $X+Y= (x_{1}+y_{1},x_{2}+y_{2},-2x_{1}+7x_{2}-2y_{1}+7y_{2})$ $= \Big (x_{1}+y_{1},x_{2}+y_{2},-2(x_{1}+y_{1})+7(x_{2}+y_{2}) \Big)$ which is in $W$
I'm sure you can then prove that it's also closed under scalar multiplication.
• Jun 1st 2009, 06:42 PM
Random Variable
If you want to prove both at the same time, you have to show that $\alpha X + \beta Y$ is in $W$
• Jun 1st 2009, 07:37 PM
math2009
$A= \begin{bmatrix} 2 & -7 & 3 \end{bmatrix}, \vec{a}=\begin{bmatrix} a_1\\a_2\\a_3 \end{bmatrix}, W=\{A\vec{a}=\vec{0}\}=ker(A)$
Obviously, $T(\vec{x})=A\vec{x}$ is linear transformation
$1.\ \vec{x}_1,\vec{x}_2 \in W, T(\vec{x}_1+\vec{x}_2)=A(\vec{x}_1+\vec{x}_2)=A(\v ec{x}_1)+A(\vec{x}_2)=\vec{0}+\vec{0}=\vec{0}, so\ \vec{x}_1+\vec{x}_2 \in W$
$2.\ k\in R, T(k\vec{x})=A(k\vec{x})=kA\vec{x}=k\vec{0}=\vec{0} , so\ k\vec{x}\in W$
$3.\ A\vec{0}=\vec{0}, so\ \vec{0}\in W$
Finally, W is a subspace.
• Jun 1st 2009, 07:47 PM
Isomorphism
Quote:
Originally Posted by Random Variable
If you want to prove both at the same time, you have to show that $\alpha X + \beta Y$ is in $W$
We can save a greek variable :D
It suffices to show $\alpha X + Y$ is in $W$ | 868 | 2,016 | {"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": 18, "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} | 4.0625 | 4 | CC-MAIN-2018-09 | longest | en | 0.824549 |
https://www.freezingblue.com/flashcards/print_preview.cgi?cardsetID=298419 | 1,527,177,286,000,000,000 | text/html | crawl-data/CC-MAIN-2018-22/segments/1526794866511.32/warc/CC-MAIN-20180524151157-20180524171157-00514.warc.gz | 743,762,066 | 4,387 | # 2 T Test
The flashcards below were created by user Trekofstarsx on FreezingBlue Flashcards.
1. By selecting a smaller alpha level, a researcher is
2. The z score boundaries for a critical region are determined by
the alpha level
3. Two possible ways of comparing two samples means
• -The two means could come from two completely separate groups of participants
• -Two sets of data could be gathered from the same group
4. Independent Measures t-test
• -Two separate groups being tested
• -Also known as between subjects design
5. t formula
[(M1-M2)-(u1-u2)]/S(M1-M2)
6. s(M1-M2)=
sqrt[(s12/n1)+(s22/n2)]
7. Estimated standard error is only true if
both ns are the same
8. Pooled variance formula
Pooled variance formula with standard error
see card
9. H0 and H1 for two independent sample means
u1-u2=0
10. We use the sample mean difference to
Estimate the population mean difference
11. Condfidence interval for two independent sample means formula
u1-u2=M1-M2+-t*SM1-M2
12. Two-tailed hypothesis
Ho
H1
• u1-u2=0
• u1-u2does not equal 0
13. One-tailed (uppertail critical)
HO
H1
see formula sheet
14. One-tailed (lowertail critical)
see formula sheet
15. 3 Assumptions of t tests
• -Observations within each sample must be independent
• -The population from which the samples are selected must be approximately normal
• -The two populations from which samples are selected must have the same variance
16. Hartley F-max test
-Tests?
1.2.3.
-Tests whether our sample variances are reasonably close
• 1. Compute sample variance for each sample
• 2. Select largest and smallest of these variances and compute s2(largest)/s2(smallest) to get F max
• 3.Compare F-max value with the critical value
Author: Trekofstarsx ID: 298419 Card Set: 2 T Test Updated: 2015-03-15 04:12:57 Tags: stat Folders: stat Description: 2 sample t Show Answers: | 514 | 1,844 | {"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} | 3.28125 | 3 | CC-MAIN-2018-22 | latest | en | 0.877086 |
flighttopittsburgh.blogspot.com | 1,527,349,865,000,000,000 | text/html | crawl-data/CC-MAIN-2018-22/segments/1526794867559.54/warc/CC-MAIN-20180526151207-20180526171207-00183.warc.gz | 100,972,931 | 10,263 | ## Monday, August 1, 2011
### Can someone explain to me probability density function. how would i apply it to this question
Can someone explain to me probability density function. how would i apply it to this question?
a.An airline knows that the duration of the flight from Pittsburgh to Minneapolis is uniformly distributed between 120 and 140 minutes. The flight departs at 1:00 p.m. The airline wants the probability that the flight will be late not to exceed .25. What scheduled arrival time should the airline announce? i know that this is 3:15 but this is where i'm having troubnle b.If the flight is early, it may have to wait until its arrival gate is available for deplaning. Assume that the arrival gate becomes available between 3:00 p.m. and 3:10 p.m, and that the time the arrival gate becomes available and the arrival time of the flight are statistically independent and jointly uniformly distributed. What is the probability that the flight arriving from Pittsburgh will have to wait for its gate? c. Assume the arrival gate becomes available between 3:00 p.m. and the scheduled arrival time, and (as in part b) the time the arrival gate becomes available and the arrival time are statistically independent and jointly uniformly distributed. (For example, if the scheduled arrival time is 3:07, the arrival gate becomes available between 3:00 and 3:07.) Suppose every minute a flight is late costs the airline \$1 thousand dollars, and every minute a flight has to wait for the arrival gate to become available costs \$2 thousand dollars. What scheduled arrival time minimizes expected cost? | 343 | 1,610 | {"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} | 3.28125 | 3 | CC-MAIN-2018-22 | latest | en | 0.966642 |
https://freefincal.com/investor-faqs-on-returns/ | 1,719,029,807,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198862249.29/warc/CC-MAIN-20240622014659-20240622044659-00794.warc.gz | 231,890,412 | 28,890 | # Investor FAQs on Returns
Published: February 7, 2015 at 10:38 am
Last Updated on August 30, 2021 at 3:43 pm
## 1. What return does the moneycontrol portfolio manager calculate?
It calculates the absolute return. That is the percentage difference = (value-investment)/investment.
This does not represent how your money has compounded. Ignore it. Use Value Research portfolio manager to get XIRR returns (a measure of compounding when there are multiple investments) or my portfolio tracker (link on the right) for mutual funds which would allow you to continuously track financial goals.
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## 2. What return does Value Research use in its fund listings?
Returns less than 1 year are absolute returns. Above 1 year, annualized returns (CAGR) are listed.
## 3. How can I calculate XIRR for my mutual fund or stock holdings?
You will need to enter every transaction ever made! So collect that information and use this simple XIRR calculator.
## 4. How much return can I expect from my equity investments over the long-term?
In the investor workshops, I show that over a 15 year period, the average return is about 14% but with an error (standard deviation) of 4%. So 68 times out of 100, returns can swing from (14-4 = 10%) to (14+4 = 18%). Which is why I plan all my long-term goals with 10% equity only. You are free to choose whatever number you want, but be mindful of the volatility.
Note to those who understand what a normal distribution is: so far, Sensex returns can be reasonably approximated with a normal distribution. Hence, the notions of standard deviation and average are still valid … so far.
## 5. What return should I use in a financial goal calculator?
What is your debt allocation? What is your equity allocation? ….. (for other asset classes)
What post-tax return do you expect from each asset class?
If I expect 6% post-tax return from debt (40% allocation) and 10% post-tax return from equity (60% allocation), the approximate return to be used in the goal calculator =
(6% x 40%) + (10% x 60%) = 8.4%.
Do not make the mistake of using only equity returns!!
## 6. Do I include the tax saved while calculating returns from ELSS funds, PPF etc.?
NO! What you save matters little to your net worth, unless you invest it!. If you do invest it, it is going to be factored in any way.
## 8. How do I make sense of volatility in returns? (Not a FAQ. It should be!)
Have written several posts on this. A short selection:
#~#~#~#~#~#~#~#~#~#~#~#
I draw a blank here. Can you add to this list? If you have questions on investment returns, ask away. I will do my best to answer them.
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Published by CNBC TV18, this book is meant to help you ask the right questions and seek the correct answers, and since it comes with nine online calculators, you can also create custom solutions for your lifestyle! Get it now.
Gamechanger: Forget Startups, Join Corporate & Still Live the Rich Life You Want This book is meant for young earners to get their basics right from day one! It will also help you travel to exotic places at a low cost! | 1,960 | 8,735 | {"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} | 2.59375 | 3 | CC-MAIN-2024-26 | latest | en | 0.899446 |
https://wokwi.com/arduino/projects/287701946731594253 | 1,628,070,116,000,000,000 | text/html | crawl-data/CC-MAIN-2021-31/segments/1627046154798.45/warc/CC-MAIN-20210804080449-20210804110449-00376.warc.gz | 597,584,918 | 20,615 | ``````#include "FastLED.h"
// Matrix size
#define HEIGHT 32
#define WIDTH 32
#define NUM_LEDS HEIGHT * WIDTH
#define MATRIX_TYPE 1
// LEDs pin
#define DATA_PIN 3
// LED brightness
#define BRIGHTNESS 255
// Define the array of leds
CRGB leds[NUM_LEDS];
//// ----------------------------- Spider ------------------------------
//(c)stepko
#define Speed 250
#define Koef 9 //1,3,5,7,9(standart),10,12
#define lines 7
#define Color 1 //By Kostyamat https://editor.soulmatelights.com/gallery/550
#define Fader 30 //By Kostyamat https://editor.soulmatelights.com/gallery/550
#define sx ((256 / (WIDTH / 2)) - (WIDTH / 16))
#define cy ((256 / (HEIGHT / 2)) - (HEIGHT / 16))
void drawLine(int x1, int y1, int x2, int y2,
const CRGB & color) {
int deltaX = abs(x2 - x1);
int deltaY = abs(y2 - y1);
int signX = x1 < x2 ? 1 : -1;
int signY = y1 < y2 ? 1 : -1;
int error = deltaX - deltaY;
leds[XY(x2, y2)] += color;
while (x1 != x2 || y1 != y2) {
leds[XY(x1, y1)] += color;
int error2 = error * 2;
if (error2 > -deltaY) {
error -= deltaY;
x1 += signX;
}
if (error2 < deltaX) {
error += deltaX;
y1 += signY;
}
}
}
void draw() {
double t = millis() / (256 - Speed);
for (uint8_t c = 0; c < lines; c++) {
byte xx = sin8(t + (100 * c) * Koef) / sx;
byte yy = cos8(t + (150 * c) * Koef) / cy;
if (Color)
drawLine(xx, yy, WIDTH - xx - 1, HEIGHT - yy - 1, CHSV(c * (256 / lines), 200, 255));
else
drawLine(xx, yy, WIDTH - xx - 1, HEIGHT - yy - 1, CHSV(0, 0, 255));
}
blur2d(leds, WIDTH, HEIGHT, 32);
delay(16);
}
void setup() {
//Serial.begin(250000);
FastLED.setBrightness(BRIGHTNESS);
}
void loop() {
draw();
FastLED.show();
} //loop
uint16_t XY (uint8_t x, uint8_t y) {
if(x<0||x>= WIDTH || y<0 || y >= HEIGHT) return;
if ((y % 2 == 0) || MATRIX_TYPE) // если чётная строка
{
return ((uint32_t)y *WIDTH + x) % (WIDTH * HEIGHT);
}
else // если нечётная строка
{
return ((uint32_t)y * HEIGHT + WIDTH - x - 1) % (WIDTH * HEIGHT);
}
}
`````` | 694 | 2,005 | {"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} | 2.5625 | 3 | CC-MAIN-2021-31 | longest | en | 0.223243 |
https://www.howardfenstermanminerals.com/category/technology/ | 1,685,693,268,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224648465.70/warc/CC-MAIN-20230602072202-20230602102202-00382.warc.gz | 903,461,394 | 53,396 | # AI 101 – How Does Artificial Intelligence Work?
## Overview: Artificial Intelligence in 100 Words
### AI is Learning
The basic premise behind artificial intelligence is to create algorithms (computer programs) that can learn by viewing unknown data and comparing that data to data that it is already familiar with or has learned what it is. (We’ll discuss the difference between “already familiar” with “has learned ” further in this article), so let’s start by looking at a simple example.
Image by Susann Mielke from Pixabay. Text by SMS.
### In the Mind of AI
Is this a fork or a spoon? Well, they both have handles, but this one has spikes. Let me look up what pieces of information I have in my database that looks like this item. Oh, I have a piece that resembles this spike property, so it must be a fork!
These programs are written to scan new data, then they break the data up into the different characteristics that compose the item. It then matches those characteristics to other data it already knows and makes a determination.
The more information (characteristics) it can compare the new item to, the more precise its determination will be.
AI compares new data to old data in order to make a determination of what the new data is. This is called data analytics.
Now, let’s go a bit deeper into how a computer program is written.
## Writing the Computer Program
We spoke about how computers are programmed using instructions in our bits and bytes article, but as a refresher, let’s recap!
Computer programs, called algorithms, tell the computer to do things by reading instructions that a human programmer has entered. One of our examples was a program that distributes funds to an ATM recipient. It was programmed to distribute the funds if there is enough money in the person’s account and not if there isn’t.
But THIS IS NOT AI since the instructions are specific and there are no variations to decide anything other than “if this then that”.
In other words, the same situation will occur over and over with only two results. There is no determination that there may be more issues, such as possible fraudulent activity.
Bottom line – There is no learning involved.
## Writing a Learning Program
The ATM example above is limited to two options, but AI is extremely more intensive than that. It is used to scan thousands of items of data in order to determine a conclusion.
### How Netflix Does It
Did you ever wonder how Netflix shows you movies or TV shows that are tuned to your interests? It does this by determining what your preferences are based on your previous viewings.
The algorithm analyzes large amounts of data, including user preferences, viewing history, ratings, and other relevant information to make personalized recommendations for each user.
It employs machine learning (we will be discussing this more later in this article) to predict which movies or TV shows the user is likely to enjoy.
It identifies patterns and similarities between users with similar tastes and suggests content that has been positively received by those users but hasn’t been watched by the current user.
For instance, if a user has watched and enjoyed science fiction movies, the recommendation might be to suggest other sci-fi films or TV shows that are popular among users with similar preferences.
The program will learn and adapt as the user continues to interact with the platform, incorporating feedback from their ratings and viewings in order to refine future recommendations.
By leveraging machine learning, streaming platforms like Netflix can significantly enhance the user experience by providing tailored recommendations, increasing user engagement, and improving customer satisfaction.
This can’t be done using the non-learning ‘if-else’ program we previously spoke about in the ATM example.
### A Gmail AI Example
As you type your email, Google is reading it and then offers words to accompany the sentence that would coincide with what you are about to type before you have even typed it.
This is called language modeling and is another method by which AI is used.
In language modeling, the algorithm uses a factor of probability that is used to predict the most likely next word in a sentence based on the previous entry.
### A Vocabulary Update
Before we continue, let’s get a bit more technical. The word ‘characteristics’ has been used here for simplicity, but the actual term where the computer looks at points of a subject is called “patterns“. And pattern recognition is the process of identifying unique points in the data.
AI algorithms feed on data to learn new things. The more data that exists, the easier it will be for the algorithm to identify the characteristics or patterns of an entity.
## AI: How it All Works
There are three main types of machine learning: supervised learning, unsupervised learning and reinforcement learning.
### Supervised Learning
This is the most common type of machine learning. It involves feeding a computer a large amount of data, with the aim of enabling it to recognize patterns and make predictions when confronted with new data. In other words, supervised learning consists of training a computer program to learn from marked data (data that has been already identified).
#### How the Machine Thinks with Supervised Learning
Show and Tell: A human shows the program what a bridge is. Then he shows the program what a building is. The program takes note of the characteristics of each, technically called patterns. If computer instructions were written in plain English, this is what it would say:
This is a bridge. Look at the patterns that make up the bridge. And this is a building. Look at the patterns that make up the building.
When the program runs it would think in these terms.
I can see distinguishable characteristics between the two. Let me match them up with what my human showed me which is which and then make a decision of whether this is a bridge or a building.
Supervised learning is used in many applications such as image recognition, speech recognition, natural language processing and recommendation systems.
#### It’s Raining Cats and Dogs
A supervised learning algorithm could be trained using a set of images called “cats” and “dogs”, and each cat and dog are labeled as such.
The program would be designed to learn the difference between the animals by using pattern recognition as it scans each image.
A computer instruction (in simplified terms) might be “If you see a pattern of thin lines from the face (whiskers), then this is a cat”.
The end result would be that the program would be able to make a distinction of whether a new image it is presented with is that of a cat or dog!
This type of learning involves two categories – cats and dogs. When only two classifications are involved, it is called Binary Classification.
### An Example
Suppose you are studying insects and you want to separate flying insects from crawling ones. Well, that’s easy. You take a bug that you found in your backyard and compare it to the ant and fly you already stored on your insect board. In AI terms, this is supervised binary classification.
You immediately know, based on the pattern configuration of the insect which classification it belongs to – the crawlers or the flies. Now you grab more flies and put them in the fly category and do the same with the creepy crawlers for their category.
Let’s say you want to go deeper in the fly classification and find out what type of fly it is, (e.g. house fly, horse fly, fruit fly, horn fly, etc.); but you only have two classifications to compare them two – flies and crawlers, so what do we do? You create more classifications for the fly class.
This is multi-classifications, or more technically called multi-class classifications, which provides additional labeled classes for the algorithm to compare the new data to.
We will delve more into multi-class classifications and how this works in our next article, but for now, just know what binary classifications and multi-class clarifications are.
### Unsupervised Learning
Unsupervised learning involves training a computer program without providing any labels or markings to the data. The aim is to enable the program to find (learn) patterns and relationships on its own.
It does this by reading millions of pieces of information and grouping them into categories based on their characteristics or patterns, then making decisions on what the new entity is by matching it up to one of the categories it created.
In other words, it finds matching patterns from the groups in the dataset completely on its own and then labels them without human intervention. This is called clustering.
Anomaly detection is the task of identifying data points that are unusual or different from the rest of the data. This can be useful for tasks such as fraud detection and quality control.
## Reinforcement Learning
Reinforcement learning (RL) is a type of machine learning that focuses on training agents to make decisions based on experience in an environment. RL algorithms learn by trial and error, receiving feedback in the form of rewards or penalties for their actions.
The goal of RL is to maximize cumulative rewards over time by finding an optimal policy, or a sequence of actions, that leads to the highest possible reward. The agent explores the environment by taking action and receiving feedback, which it uses to update its policy to improve its performance.
One of the defining features of RL is the use of a feedback loop in which the agent’s actions influence the state of the environment, which in turn affects the rewards received by the agent. This feedback loop allows the agent to learn from experience and adjust its behavior accordingly.
RL has been applied to a wide range of problems, such as games, robotics and autonomous driving. It is particularly useful in scenarios where the optimal action may not be immediately clear and where exploration is necessary to find the best solution.
Overall, these AI tasks are all widely used in various industries and applications and we continue to see growth and development as artificial intelligence technology advances.
What are the advances or dangers that AI can bring in the future? Read our article on the Pros and Cons of AI to find out.
# How to Optimize for Voice Search in 2023
## Voice Search Overview
Voice search is here to stay and will only be gaining momentum as we proceed into the future and for those that are in marketing or SEOs, it is important to stay up to date with these features and optimize accordingly.
The processes behind voice and text search are quite different. Voice search queries may be longer and more complex, as people tend to ask questions in a conversational style, while text queries are typically shorter and more direct.
Another difference is in the way search results are presented. In text search, results are typically displayed on a search engine results page (SERP), with a list of links and brief descriptions. In contrast, voice search typically provides only the most relevant result, read aloud by a virtual assistant or smart speaker; such as Apple Siri, Amazon Alexa, Google Assistant and Microsoft Corona. This means that optimizing for voice search requires a different approach to traditional SEO, with an emphasis on providing clear, concise answers to common voice questions.
Searching by sound is an SEO component that cannot be overlooked and with the accelerating advancements in artificial intelligence, it is imperative that web developers and SEOs keep a watchful eye on this evolving technology.
## The Statistics
As of the writing of this article, 32% of people between the age of 18 and 64 use a voice search medium (Alexa, Siri, Corona, etc.) and that number will only grow as we move to the future.
Entering standard text search queries on mobile devices is commonplace, with over 60% of cell phone users text searching and 57% of mobile users taking advantage of voice search.
It should be no surprise that Google is the most successful interpreter of audio searches with a 95% accuracy.
In a study in 2021, 66.3 million households in the US were forecasted to own a smart speaker and that forecast has become a reality as of 2023.
Voice technology stretches beyond search queries as 44% of homeowners use voice assistants to turn on TVs and lights, as well as an array of other smart home devices currently on the market.
With statistics as these, speaking to robotic assistants is here to stay and will only be growing with new technologies as we proceed through the 2020s and beyond.
## How Does Voice Search Work?
### The Physics Behind It
If you just need to know that there is an analog-to-digital conversion and are not interested in the specifics of how it’s done, you can skip this part and go to the next section, which is Where Does the Data Come From?
We will summarize the process of how the sound of human speech is converted into machine language, which is filtering and digitizing.
Filtering: Smart speakers and voice assistants are designed to recognize the human voice over background noise and other sounds; hence, they filter out negative sounds so that they can only hear our voices.
Digitizing: All sound is naturally created in analog frequencies (use of sinewaves). Computers cannot decode analog frequencies. They must be converted to the computer language of binary code.
Below are the details of how an analog signal is converted to digital.
### The Analog Conversion Process
|n order to make this conversion, an Analog-to-Digital Converter (ADC) is required. The ADC works by sampling the analog signal at regular intervals and converting each sample into a digital value.
The steps are as follows:
1. Sampling: The first step is to sample the analog signal at a fixed interval. The sampling rate must be high enough to capture all the frequencies of interest in the analog signal. The Nyquist-Shannon sampling theorem states that the sampling rate must be at least twice the highest frequency in the signal. Sampling means taking regular measurements of the amplitude (or voltage) of the signal at specific points in time and converting those measurements into a digital signal. Sampling is necessary in order to convert analog sound waves into digital signals, which are easier to store, transmit, and process using digital systems such as computers or microcontrollers. The rate at which the analog signal is sampled, known as the sampling rate or sampling frequency, is important because it determines the level of detail that can be captured in the digital signal. Sampling an analog signal is an important step in converting it to a digital signal that can be analyzed, manipulated, or transmitted using digital systems.
2. Quantization: Once the analog signal is sampled, the next step involves assigning a digital value to each sample based on its amplitude. The resolution of the quantization process is determined by the number of bits used to represent each sample. The higher the number of bits, the greater the resolution of the digital signal.
3. Encoding: The final step is to encode the quantized samples into a digital format. This can be done using various encoding techniques such as pulse code modulation (PCM) or delta modulation.
Overall, the main process of converting analog to digital frequencies involves sampling, quantization, and encoding. The resulting digital signal can then be processed using digital signal processing techniques.
In summary: Smart speakers and voice assistants take in the audio from a person’s speech and convert it to machine language.
## Where Does the Data Come From?
Information gathered from smart speakers and voice assistants pulls data from an aggregate of sources.
If you want your business to grow, you must be attentive to where content for voice search is collected so that you can make intelligent decisions regarding how to optimize for these devices.
### Amazon Alexa
When Alexa responds to a query, it relies on Microsoft’s Bing search engine for the answer. Why? Because Amazon, as well as Microsoft, are in direct competition with Google, even though Google has the most popular search engine in the world.
Amazon’s refusal to use Google for audio responses is not something to be concerned about. After all, Bing’s search algorithms are very similar to Google’s.
With that said, if a person speaks to Alexa with a specific request, (e.g. “What’s the weather today?”), Alexa can pull that information from a database associated with that request. In this case, Alexa will connect to Accuweather. The device can access Wikipedia and Yelp if it needs to as well.
### Apple Siri
Initially, Apple used Bing as its default search engine, but in 2017, Apple partnered with Google. Now, when you say “Hey Siri”, you can expect Siri to access the immense data repository from Google and supply the answer. This applies to the Safari browser for text searches as well.
There is a caveat though. When it comes to local business searches, Siri will call on Apple Maps data and will use Yelp for review information.
### Microsoft Cortona
This one is probably the most straightforward out of all of the search engines, as Cortona relies on what else but Microsoft Bing for its information.
OK, this one’s a no-brainer. Google can currently index trillions of pages to retrieve information and since this also applies to Apple’s Siri, this section is of most importance if you want to optimize voice search for these voice assistants.
#### So What is a Featured Snippet?
Featured snippets are what you see after you run a Google search query. It is a paragraph that appears at the top of the page that summarizes the answer to a question.
The information that Google applies to the snippet is gathered from, what Google determines to be the most reliable source (website) for that information.
#### How Does Google Determine a Featured Snippet?
For a snippet to be posted by Google, it needs to know that the source is trustworthy via its domain authority, link juice and high-quality content, to name three important organic factors, as any SEOs would already know, but in addition to these factors, Google will defer to “HowTo” and FAQ pages most often to pull in the snippet.
#### Is Structured Data Needed?
Structured data is extra code that helps Google better understand what the page or parts of the page are about.
One might wonder if structured data has to be used in order to provide the featured snippet? The answer is no. As per Google, as long as the web page is optimized properly and contains the questions that equate to the user’s query or voice search in this case, structured data is not necessary; however, if it wouldn’t hurt to put it in, as we all are aware that nothing is static in the SEO world and this rule can easily change in the future.
The reason why Google focuses on “HowTo” and FAQ pages is that their content reflects that of human speech. For example, an FAQ page on EV cars may have the question “How long do EV batteries last?” – That is exactly how a person would ask a voice assistant that same question!
An ‘Action’ for Google Assistant is created, equivalent to an Alexa Skill and Google will read the snippet back to the user to answer the question he/she asked.
## Summarizing Optimization for Voice Search
### Alexa
Bing: If you have not already done so, bring Bing into your scope of work for SEO and start optimizing for this search engine.
Yelp: We all know that reviews are of the utmost importance, so check out Yelp for your or your client’s business and build on those reviews! Legitimately of course.
### Siri
Apple Factors: Where you might not be fully optimized is with Apple Maps, so get going. Start by registering with Apple Business Connect.
Yelp: And now Yelp is back in the picture!
### Cortona
Bing: As mentioned, become an SEO Bing expert and you are ready to ask Cortona anything.
Besides the standard organic optimization, focus on schema markup for HowTo and FAQ articles for voice search, which, if you’re lucky, will be shown on the SERP as a featured snippet.
There you have it. How to optimize for voice search. Let’s get these robots configured so that our businesses will be the first thing you hear from your voice assistant!
# The Pros and Cons of AI
Are you afraid of what AI can do or are you looking forward to the benefits it can provide? Part of your decision would be based on whether you feel that the glass is half full or half empty, but the reality is that there are always consequences to technological advancements, whether for good or for those individuals looking to gain an upper hand at the expense of the rest of us. The development of the atom bomb was the result of Einstein’s theory of relativity, even though the scientist had no idea of the frightening consequences his theory would bring.
## Overview
Artificial intelligence (AI) is a rapidly growing field that has the potential to transform our world in countless ways. From healthcare to finance, and education transportation, AI can benefit mankind in a myriad of ways, but not everyone is on board with this as we will see in this article, the good and the bad of the advancements in artificial intelligence
Regardless, artificial intelligence is advancing at an exceptional rate as our AI avatars explain below.
So now, let’s take a look at both the positives and negatives of artificial intelligence and what it can potentially have for us and then you can make a decision.
## The Benefits
One of the most significant benefits of AI is its potential to revolutionize healthcare. AI can analyze vast amounts of medical data, including patient records, lab results and imaging studies.
With this information, its algorithms can detect patterns and make predictions that could help doctors diagnose and treat diseases more accurately and quickly. It can also help identify high-risk patients, allowing doctors to intervene early and prevent diseases from progressing.
### Transportation
Artificial intelligence can be used to optimize traffic flow and reduce congestion and subsequently, travel time for busy commuters.
Moving not too far into the future are autonomous vehicles – cars that drive themselves. There are some being tested now, such as Teslar and Google and Teslar already has autonomous vehicles on the market, but a driver must remain inside.
When it does become mainstream, self-driving cars, buses and trains have the potential to significantly reduce accidents, traffic congestion, and pollution. By removing the human element from driving, these vehicles can make our roads safer and more efficient.
### Education
Artificial intelligence can also be used to improve education. AI-powered tutoring systems can provide personalized, adaptive learning experiences for students of all ages and abilities.
By analyzing a student’s learning style, strengths and weaknesses, these systems can create customized lesson plans that help them learn more effectively. This can lead to improved academic outcomes and greater educational equity, as students who may struggle with traditional teaching methods can receive tailored instruction that meets their needs.
One caveat is the temptation for students to cheat by using apps such as Chat GPT, but alert teachers should be able to tell the difference by determining if the student’s writing style has changed. With that said, this will still be a challenge for educators.
### Finance
Ai can be used to detect fraud, manage risk and optimize investments. By analyzing financial data, machine learning algorithms can detect patterns that may indicate fraudulent activity, alerting financial institutions to potential threats before they cause significant damage.
Additionally, it can help financial institutions manage risk more effectively by predicting market fluctuations and identifying potential investments that offer high returns with low risk.
### Law Enforcement
AI-powered surveillance systems can detect potential threats in public spaces, alerting law enforcement and allowing them to respond more quickly.
It can also be used to analyze crime data, helping law enforcement identify patterns and allocate resources more effectively. Indeed, New York City Mayor Eric Adams introduced crime-fighting robots to the Times Square area and if they prove productive, they will be placed all over the city.
### The Environment
By analyzing environmental data, AI can help us understand the impacts of human activity on the planet and develop strategies to mitigate them. For example, it can help us optimize energy consumption, reduce waste and improve recycling efforts. Additionally, AI can help us predict and respond to natural disasters, reducing their impact on human lives and property.
Of course, as with any powerful technology, AI also poses some risks and challenges. One concern is the potential for it to be used in ways that violate privacy or human rights.
Additionally, the use of AI in decision-making processes could result in biases or discrimination if the algorithms are not carefully designed and monitored. Finally, there is the risk that AI could become too powerful, leading to unintended consequences or even threatening human existence.
To mitigate these risks, we must approach AI development with caution and foresight. We must ensure that AI is developed and used in ways that prioritize human welfare and respect human rights. This requires ongoing dialogue and collaboration between technologists, policymakers and the public.
## Potential Dangers
Artificial Intelligence can pose significant dangers that need to be addressed. Similar to the potential dangers of the use of quantum computers, the same threats are associated with AI.
### The Labor Question
No doubt, unemployment due to artificial intelligence is a major concern. As this technology advances, it becomes increasingly capable of performing tasks that were once done by humans, leading to job loss and economic disruption.
For example, self-driving cars have the potential to replace human drivers, which would lead to unemployment in the transportation sector. This could result in a significant reduction in the workforce and an increase in social inequality.
### Discrimination
Another danger is its ability to perpetuate biases and discrimination. Algorithms are designed to learn from data, and if the data used is biased, the AI will also be biased. This can result in unfair decisions being made, such as in hiring, lending, or criminal justice. It can have significant negative impacts on individuals and communities.
### The Military
Furthermore, AI could pose a significant threat to global security. With technological advancements increasing in this arena technology, it is becoming increasingly possible for computers to be used in cyber-attacks or even to control weapons systems. This could lead to significant risks and damages, such as loss of life or damage to critical infrastructure.
### Malicious Financial Behavior
The financial markets would most likely be the most affected by artificial intelligence, both for good and bad. We have already discussed the good, but the bad is already a concern. There can be serious consequences that could affect the banks and stock market as nefarious individuals try to override the algorithms with corrupt data and computer instructions. The expression “What’s in your wallet” will have a much greater significance should malicious AI alter your bank accounts.
### A Question of Morals
Finally, the development of AI could also pose ethical and moral dilemmas. As these algorithms become more intelligent, questions arise about their autonomy and decision-making capabilities. If an AI system makes a decision that is morally or ethically questionable, who is held accountable? What happens if an AI system is programmed to harm humans or perform unethical tasks?
## AI in a Nutshell
Artificial intelligence has the potential to benefit us in countless ways. From healthcare to education, finance to public safety, and the environment,
It can help us solve some of the biggest challenges facing our society. However, we must approach AI development with caution and foresight, taking steps to mitigate risks and ensure that this technology is used in ways that prioritize humanity and respect human rights. With careful planning and collaboration, we can harness the power of AI to create a better future for all!
# Artifical Intelligence: The Pros and Cons
## The Quandary of AI
Are you afraid of what AI can do or are you looking forward to the benefits it can provide? Part of your decision would be based on personality glass is half full or the glass is half empty, but there are always consequences to technological advancements, whether for the good of humankind or for those looking to gain an upper hand in a nefarious manner. The development of the atom bomb was the result of Einstein’s theory of relativity, even though the scientist had no idea of the negative consequences his theory would bring.
Let’s take a look at both the positives and negatives of artificial intelligence and what it can potentially have for us and then you can make a decision.
## AI Overview
Artificial intelligence (AI) is a rapidly growing field that has the potential to transform our world in countless ways. From healthcare to finance, and education transportation, AI can benefit mankind in a myriad of ways, but not everyone is on board with this as we will see in this article, the good and the bad of the advancements of artificial intelligence.
## The Benefits
One of the most significant benefits of AI is its potential to revolutionize healthcare. AI can analyze vast amounts of medical data, including patient records, lab results, and imaging studies.
With this information, AI algorithms can detect patterns and make predictions that could help doctors diagnose and treat diseases more accurately and quickly. It can also help identify high-risk patients, allowing doctors to intervene early and prevent diseases from progressing.
### Transportation
Another area where artificial intelligence can benefit us is in the field of transportation. Self-driving cars, buses, and trains have the potential to significantly reduce accidents, traffic congestion, and pollution. By removing the human element from driving, these vehicles can make our roads safer and more efficient.
Additionally, AI can be used to optimize traffic flow, reducing congestion and travel times. This can save time and money for individuals and businesses alike.
### Education
AI can also be used to improve education. AI-powered tutoring systems can provide personalized, adaptive learning experiences for students of all ages and abilities. By analyzing a student’s learning style, strengths, and weaknesses, these systems can create customized lesson plans that help them learn more effectively. This can lead to improved academic outcomes and greater educational equity, as students who may struggle with traditional teaching methods can receive tailored instruction that meets their needs.
### Finance
Detecting fraud, managing risk, and optimizing investments are just three of the ways AI is being used to advance the financial sector. By analyzing financial data, algorithms can detect patterns that may indicate fraudulent activity, alerting financial institutions to potential threats before they cause significant damage.
Additionally, AI can help them manage risk more effectively by predicting market fluctuations and identifying potential investments that offer high returns with low risk.
AI can also benefit society by improving public safety. AI-powered surveillance systems can detect potential threats in public spaces, alerting law enforcement and allowing them to respond more quickly. AI can also be used to analyze crime data, helping law enforcement identify patterns and allocate resources more effectively.
### The Environment
Finally, AI can benefit mankind by helping us protect the environment. By analyzing environmental data, AI can help us understand the impacts of human activity on the planet and develop strategies to mitigate them. For example, AI can help us optimize energy consumption, reduce waste, and improve recycling efforts. Additionally, AI can help us predict and respond to natural disasters, reducing their impact on human lives and property.
## The Benefits of AI – A Summary
AI has the potential to benefit mankind in countless ways. From healthcare to education, finance to public safety, and the environment. It can help us solve some of the biggest challenges facing our society. However, we must approach AI development with caution and foresight, taking steps to mitigate risks and ensure that it is used in ways that prioritize human welfare and respect for human rights. With careful planning and collaboration, we can harness the power of machine learning to create a better future for all.
## Potential Dangers
Artificial Intelligence can pose significant dangers that need to be addressed. Similar to the potential dangers of the use of quantum computers, the same threats are associated with AI.
One concern is the potential for it to be used in ways that violate privacy or human rights. Additionally, the use of AI in decision-making processes could result in biases or discrimination if the algorithms are not carefully designed and monitored. Finally, there is the risk that it could become too powerful, leading to unintended consequences or even threatening human existence.
## The Labor Question
As AI technology advances, it becomes increasingly capable of performing tasks that were once done by humans, leading to job loss and economic disruption. For example, self-driving cars have the potential to replace human drivers, which would lead to unemployment in the transportation sector. This could result in a significant reduction in the workforce and an increase in social inequality.
## AI and Bias
Another danger of AI is its ability to perpetuate biases and discrimination. AI algorithms are designed to learn from data, and if the data used is biased, the AI will also be biased. This can result in unfair decisions being made by AI systems, such as in hiring, lending, or criminal justice. This can have significant negative impacts on individuals and communities.
## Global Security
Furthermore, AI could pose a significant threat to global security. With advancements in AI technology, it is becoming increasingly possible for AI systems to be used in cyber-attacks or even to control weapons systems. This could lead to significant risks and damages, such as loss of life or damage to critical infrastructure.
## Nefarious Exploitation
Finally, the development of AI could also pose ethical and moral dilemmas. As machine language systems become more intelligent, questions arise about their autonomy and decision-making capabilities. If an AI system makes a decision that is morally or ethically questionable, who is held accountable? What happens if it is programmed to harm humans or perform unethical tasks?
## In a Nutshell
While AI has the potential to bring significant benefits, it is important to be cautious in its development and use. The dangers of should be taken seriously and addressed through proper regulation and oversight. It is important to ensure that AI systems are developed and used responsibly and ethically to minimize the potential risks and maximize the benefits of this technology.
To mitigate these risks, we must approach AI with caution and foresight. We must ensure that AI is developed and used in ways that prioritize human welfare and respect human rights. This requires ongoing dialogue and collaboration between technologists, policymakers, and the public.
With that said, we do have the opportunity to live better in all aspects of our lives and it is well worth something for all of us to look forward to!
# The Nike Missile System
## Introduction
A fairly unknown army base lies in a little peninsula on the north shore of New Jersey. It is not in use now but once was a thriving anti-missile installation where soldiers would be on alert for enemy missiles and planes heading towards New York City.
## The Cold Days
It was the Cold War and enemy nations, namely the Soviet Union were working tirelessly towards advancements in jet planes and ballistic missile production. Given this, the United States established anti-aircraft systems across the country. They were strategically deployed around the major cities to combat this potential threat.
Due to the accelerated research and development that was occurring, missile technology took a giant leap forward. Additionally, the fear of Russian Bear Bombers entering American airspace was becoming more imminent than the threat of German or Japanese aircraft entering the United States after Pearl Harbor.
## The Nike Missile System
Beginning in 1954, Nike Missiles replaced the gun batteries located across the United States. These were supersonic (Marc 2.25) command guidance systems and solid rocket booster missiles. They were designed to intercept long-range Soviet bombers and destroy them while still over the ocean.
Soldiers stationed at these sites were on 24-hour turnaround shifts and lived in ready-made barracks. Examples of Nike Missile battery sites were Fort Tilden and Fort Hancock, New York, which had a Missile Launch Area (the radar area), AKA, the Integrated Fire Control Area (IFC).
The sites had two missile batteries, known as double battery sites, and subsequently, each battery had two underground storage rooms for a total of four magazines at each site.
A missile magazine is the hardened storage barrier where the missile lies when inactive. Rooms accompanied the magazines; each had an elevator unit that raised and lowered the missiles.
## Enter Ajax and Hercules
The Ajax was the first Nike Missile deployed. It was designed to destroy aircraft from 30 miles away. By 1958, a new, more advanced rocket replaced the Ajax, called the Hercules, which had a range of over 96 miles and was designed to carry a nuclear warhead.
Unbeknownst to the general public, there were close to 250 Nike missile bases across the United States and more located in Europe. The New York City area contained one of the largest networks of anti-aircraft Nike batteries, with over 20 sites circling the city in New York State and New Jersey.
## From Missile Defense to Missile Offense
### Cold War
Building anti-missile bases was just one aspect of the country’s overall defense. In 1958 the North American Air Defense Command – NORAD, (now called the North American Aerospace Defense Command) was commissioned.
Its origins trace back after World War II when the US and Canada began cooperating in air defense against the Soviet bomber threat.
In 1956, the two countries proposed to form an air defense system, and two years later, the joint Canada-US Military Study Group recommended more radar networks.
General Earle E. Partridge, the commander in chief of the newly formed joint US Command, Continental AirDefense Command (CONAD), directed another study of North America defense, which eventually led to the establishment of a combined air defense organization (NORAD) under a single commander,
## The Ending of the Cold War
### Defense
The takedown of the Berlin Wall marked the beginning of the end of the Cold War and resulted in the United States becoming the only superpower left.
Nike missiles were part of the U.S. Army Air Defense Command (ARADCOM), and in agreement with the SALT treaty, all missiles were decommissioned and removed in 1974; however, a few remain. The Sandy Hook, New Jersey, (NY-56) site is one of those Nike missile batteries that are currently open to the public.
NORAD’s mission remains however, and it now provides aerospace warnings for North America, which includes the monitoring of man-made objects in space, and the detection, validation, and warning of attack against North America whether by aircraft, missiles, or space vehicles.
## Offense
The removal of the Nike missiles was not the end of missile deployment. It was only the beginning. After they were removed, a new, much more powerful rocket – the Intercontinental Ballistic Missile or ICBM, was deployed on both sides of the Atlantic, and still exists today.
These missiles are not anti-aircraft designed for defense, but take on an offensive posture following the Cold War strategy – A good defense is a good offense, or as some call it, “Peace Through Strength”.
### 2023
Given the recent events following the surveillance balloon from China and its intrusion into US airspace, NORAD has modified its sensory equipment to detect smaller objects such as balloons.
## What the Future Holds
No one can say for sure where this world is heading, but given the war in Ukraine, China’s threat to take over Taiwan, and Iran’s passion to build a nuclear weapon, it is essential that NORAD remains in existence and possibly a reevaluation of this nations air defense might be prudent.
# An In-depth Look at How Steam Engines Work and Their Impact on History
## Overview
The power of steam has had a significant impact on the history of humankind and the concept of how they work is fascinating. From the Industrial Revolution to the modern-day, steam engines have been used to power the world in a variety of ways.
In this article, we’ll take an in-depth look at how steam engines work and the impact they’ve had on history. We’ll explore the science behind how steam is generated and how its energy is used to power machines.
We’ll also discuss the various applications, from powering locomotives to generating electricity. By the end of this article, you’ll have a comprehensive understanding of the science, history, and impact of steam engines.
## History
The first steam engines were used in the mid-17th century to pump water out of gold and silver mines. The first steam-powered ship, the SS Savannah was launched in 1819. However, it wasn’t until the mid-19th century that steam engines were widely used for industrial production.
While the first steam-powered locomotive was built in 1829, it wasn’t until the 1850s that railroads began to widely use them.
The Industrial Revolution was a time of incredible innovation and growth in the mid-19th century. The invention of the steam engine during this period greatly contributed to its growth.
Many of the machines and products we use every day were first developed during this period. Engines powered by steam were used to power textile mills and other industries. They drove a variety of machines, from looms to cranes. They were used to power the bellows (furnaces) for forges. Forges were used to make swords, knives, agricultural tools, and many other metal products.
## How Steam is Generated
Before we can discuss how steam engines work, we first need to understand how the energy source for these engines is produced.
### Boiling Point
Steam is the result of water being heated past its boiling point. When water is heated past 212° F (100°C), it turns into a gas, which is steam. The result is that the volume of steam (the amount of space that a substance or object occupies) is always greater than that of water; therefore, it will want to push its way out of the container if the container is not large enough to hold it.
This is why it is recommended not to place aerosol spray cans near heating sources. The spray is in liquid form but if it is near a heating source and the liquid starts to boil and turns into steam, there is a chance that the can will explode, since the steam needs to expand.
### The mechanism for Boiling the Water
Boilers are what are used to boil the water into steam. There are several types of boilers, but they all have one thing in common: they are enclosed vessels that contain water.
Steam boilers are used to power a variety of machines. The most well-known application was to power locomotives. As we mentioned above, when water is converted into steam, the steam will push its way out and if this force of pressure is harnessed in a way that it can be regulated, it becomes a source of energy that can become very useful.
In the steam engine, there are openings in the boiler to let the steam out, and when this steam comes out, it becomes a force pressure on which anything it touches will have an effect; in other words, if there is a wheel barrel next to where the steam is thrust out, it will propel the wheel barrel quite a distance.
### Enter the Piston
If the steam is connected to a piston, which is a cylindrical body inside a container (noted in green), usually metal that slides down when a force hits it (in this cases steam), it will move, and if another object is connected to the piston, (where the white hole is at the bottom) such as a wheel, the piston will then move the wheel.
Now picture a row of pistons set up to move when the power of the steam hits on it, it can then move any number of wheels.
Pistons have an additional feature and that is their ability to move back up to the top of their cylinder once the force of the steam stops, and if this process is regulated so that the steam comes out at regular intervals, the wheels that the pistons are connected to will keep on rolling.
This is how steam locomotives work, not to mention steamboats and machinery in factories as you will read further on.
Steam engines are also used to generate electricity in power plants. When it is generated in a boiler and then forced through a turbine, it spins a wheel, which is connected to a generator. This generates electrical energy via electromagnetism (the creation of electric current by spinning magnets).
## Applications of Steam Engines
### Locomotives
Locomotives were all the rage in the 19th and early 20th centuries and it was the most common application of steam engines during the Industrial Revolution.
They were used to pull freight and passenger trains and were especially useful for transporting goods over long distances since they were much more efficient than horse-drawn wagons.
Additionally, these trains were able to climb steep hills.
### Ships
Many people think that steam engines came into widespread use on land, but they were also used to power ships. Ships were initially powered by wind and muscle power, but when the power of steam came along, they were used to power commercial ships in the early 1800s.
Steam engines were used in larger ships, such as steamships, which sailed between Europe and the United States. A perfect example is the Titanic. Although it came to a tragic end it was a giant and beautiful steamship that traveled across the Atlantic and powered everything from the kitchen cooking appliances to the giant pistons that moved the ship.
### Automotive
Steam engines are used to power automobiles in two ways. Some steam cars use a steam engine to power the wheels. Others use steam to generate electricity that can be used to power an electric motor. Steam cars have a long history dating back to the early 1900s. They were used throughout the 20th century until they were largely replaced by internal combustion engines.
### Factories
Another common use was to power factories. They were used to mass-produce goods, and the engines were used to power the machinery that was used to produce goods, such as lathes, looms, and other industrial machinery.
## Modern-Day Uses of Steam Engines
As we progress into the 21st century, the employment of steam is still being used for various purposes. They are often used in remote areas, such as deserts and mountains, where electrical grids are not available. In these areas, steam engines generate electricity.
### Power Generation
Electrical power plants are no exception and there are still power grids in the US and around the world that use steam to generate electricity. The steam used in a power plant is usually generated by burning coal or natural gas, which then drives the pumps that transport water uphill.
## Conclusion
The impact of steam engines on history can’t be overstated. It is estimated that steam engines powered about 90% of the world’s industrial production around the start of the 20th century, which greatly contributed to the growth of many industries.
The textile industry, for instance, could not have grown to its current size without the use of steam. They were used to power the looms that were necessary for producing textiles on a large scale. Steam engines also helped transform the iron and steel industry. Before the invention of steam engines, the iron was produced in small forges. Once steam engines were used in forges, iron production could be carried out at larger scales. It also contributed to the growth of agriculture by powering irrigation systems.
# The Space Shuttle Program
## The End of a Successful Era in Space and the Beginning of a New One
In 1975, the Apollo space program came to an end, along with it a legacy of unparalleled achievements, but this was only the beginning.
NASA was already working on a new venture for a more efficient spacecraft that they could reuse instead of relying on the disposable rockets that cost them billions of dollars to build each time.
This idea of a reusable rocket that could launch astronauts into space, but dock and land like an airplane were well-accepted for future space travel.
## Enter the Space Shuttle Program
In 1972, President Nixon announced that NASA would develop a reusable space transportation system (STS). They decided that the shuttle would consist of an orbiter attached to solid rocket boosters and an external fuel tank. This design was considered safer and more cost-effective.
One of the first obstacles was to design a spacecraft that didn’t use ablative heat shields, which subsequently burned up each time the shuttle re-entered the Earth’s atmosphere.
For the shuttle to be reusable, a different strategy would have to be initiated. The designers came up with an idea to overlay the craft with insulating ceramic tiles that would absorb the heat of reentry, without causing any danger to the astronauts.
## The First Flights
The first of four test flights began in 1981, leading to operational flights starting in 1982. They were used on a total of 135 missions from 1981 to 2011. The launchpad used was the Kennedy Space Center in Florida.
Like the previous Saturn V rocket, the Space Shuttle had different components of its own, which included the Orbiter Vehicle (OV), a pair of recoverable solid rocket boosters (SRBs), and the expendable external tank (ET), containing liquid hydrogen and liquid oxygen as fuel.
The Shuttle was launched vertically, the same as any rocket in its category would launch, using the two SRBs to jettison it. The SRBs operated in a parallel fashion by utilizing the fuel from the ET.
Once the mission had been completed, the shuttle would land similar to a jet aircraft on the runway of the Shuttle Landing Facility of KSC or Rogers Dry Lake in Edwards Air Force Base, California. After landing at the base, the orbiter was then flown back to the KSC on the Shuttle Carrier Aircraft, which was a specially modified Boeing 747.
## Tragedy Hits
Although the accomplishments that the shuttle program has achieved are beyond expectations, there were two unfortunate events during its time.
### Challenger January 28, 1986
Shortly after liftoff, the Space Shuttle Challenger exploded f the U.S. space shuttle orbiter Challenger, claiming the lives of seven astronauts.
Among those who were lost were teacher-in-space Christa McAuliffe, commander Francis (Dick) Scobee, pilot Michael Smith, mission specialists Ellison Onizuka, Judith Resnik, and Ronald McNair, and Hughes Aircraft engineer Gregory Jarvis.
### Columbia Feb 1, 2003
It was the final mission of Columbia. Seven crew members lost their lives when the shuttle burned up over the state of Texas during its reentry on Feb 1, 2003.
# The Basics of Electric Generators
## What are Electric Generators?
Electric generators are the opposite of electric motors, but they work on the same concept. Whereby an electric motor uses an electric current to create a magnetic field, a generator uses a magnetic field to induce an electric current. If you read our article on electric motors, then this should sound very familiar. The process is only reversed.
The current that is produced flows through a conductor which is usually a wire, but it can also be a metal plate. The output of the current is then used to power anything from a small device (e.g. a lamp or computer) to an entire town or city.
## What They are Used For
Generators are used to create electricity which then powers homes and businesses. They can be powered by either an electromagnet or a permanent magnet. The type of generator you use will determine how much electricity you can generate.
They are often used to provide backup power in case of a power outage, and they are also used in many portable applications such as camping and RVing. Just about all emergency facilities have backup power, such as hospitals.
In some cases, generators can also be used to supplement the main power source, providing additional power during high-demand periods.
The most common power sources are fuels such as coal, natural gas, or oil.
## How Does an Electric Generator Create Energy?
When the generator is turned on, its moving parts create a magnetic field, producing an electric current. (Remember with electric motors, an electric current is produced that provides a magnetic field. This is the opposite of what generators do.) The current flows through wires to an external circuit, where it can be used to power electric devices. In this way, an electric generator converts mechanical energy into electrical energy.
## What are the different types of electric generators available on the market today?
The most common type uses a combustion engine to generate electricity. These engines can be powered by gasoline, diesel, natural gas, or propane.
Another type is the steam turbine, which uses steam to power a turbine that generates electricity. Steam turbines can be powered by coal, nuclear reactors, or solar thermal power plants.
The third type of generator is the hydroelectric generator, which uses water to power a turbine that generates electricity. Hydroelectric generators can be powered by waterfalls, dams, or river currents. The Niagara Project is a perfect example of the delivery of electricity via hydroelectric generators.
The fourth type of generator is the wind turbine, which uses wind to power a turbine that generates electricity, but there must be enough wind for the proper amount of electricity to be produced.
Wind turbines can be used in both onshore and offshore locations.
## How Can You Choose the Right Electric Generator for Your Needs and Budget?
With so many different brands, models, and features to choose from, it’s hard to know where to start. However, by considering a few factors, you can narrow down your options and find the perfect generator for your needs and budget.
First, decide what type of generator you need. For example, if you only need power for occasional use, such as during a power outage, a portable generator may be sufficient.
However, if you need a constant supply of electricity, such as for a construction site or an RV, a stationary generator would be a better choice.
Next, consider how much power you will need. For most applications, a small generator that produces around 2,000 watts will suffice.
However, if you need to run large appliances or multiple devices at once, you’ll need a more powerful model. Finally, compare prices to find the best value for your money. Be sure to factor in the cost of fuel and maintenance when making your decision. By considering these factors, you can find the perfect electric generator for your needs and budget.
## Important Safety Tips
First, always read the manufacturer’s instructions carefully before operating the generator. This will help you to understand how the generator works and what safety measures need to be taken.
Next, make sure that the generator is properly grounded before use. This will help to prevent electrical shock. Finally, never operate the generator near flammable materials or in enclosed spaces, as this can create a fire hazard.
By following these simple safety tips, you can help to ensure that your experience with an electric generator is safe and enjoyable.
# How an Electric Motor Works
## Overview
When an electric current runs through a wire, a magnetic field is produced and when there is a magnetic field, metallic elements become attracted to it. This is the concept behind the workings of an electric motor.
If we can maintain these elements to move towards the magnetic field and away from it at an ongoing, continuous rate, we can have a device that is constantly spinning.
If we attach something to the part of the device that is constantly spinning, such as a glass plate in the microwave, we have harnessed the power of converting electrical energy into mechanical energy, or more specifically, we have created an electric motor.
## What Devices Use Electric Motors?
When you use an electric razor, toothbrush, fan, or vacuum cleaner, you are using an electric motor. Let’s through the inner workings of your car also. That’s probably no surprise, but how about this: washing machines, refrigerators, microwaves, your computer, and even your smartphone!
Confused? Don’t be. Something is needed to operate the refrigerator’s compressor. If there is a mechanical hard drive in your computer, then there is a small motor that turns the disk. And microwaves? Well, something must be spinning that glass plate around, right?
And your electric cars (if you have one). They have motors, which are used to spin the tires as you drive, among other things.
The bottom line is you probably go about your day using some device that uses an electric motor. So now that we know how our lifestyles are affected by these devices, let’s delve into how these motors work.
## The Working of an Electric Motor
First, let us focus on the magnetic field that causes the components within the motor to constantly spin.
How is the magnetic field created? Our article on magnetic fields explains this, but in a nutshell, if we connect a wire to a battery, the electrons of each of the atoms will move toward the positive pole of the battery. If we wrap the wire around a metal rod, the magnetic field intensifies.
### The Initial Stage
The motor is designed so that the magnetic poles of a rod, called a rotor are always facing the same polarity of a stationary magnet, called a stator, causing the rotor to spin around.
For example, when electricity is turned on, the polarity of one side of the rotor, let’s say the north side is initially facing the north side of the stator, so there will be that repelling effect, causing the rotor to spin in the other direction.
### The Next Stage
Well, that initial stage works just as it should because like poles repel each other, but that’s it. Then it stops, so for the rotor to keep spinning, there has to be a mechanism that will cause the poles to reverse continuously.
That is the job of the commutator. This entity keeps reversing the path of the electrons so that the poles are always repelling one another and consequently, keeps the rotor spinning.
## Key Parts of an Electric Motor
Let’s review the parts of the motor:
• Stator – The stationary part of the motor that creates the magnetic field that causes the rotor to spin. The stator is found in between two pieces of copper that conduct electricity.
• Rotor – The rotating part of the motor that is placed within the magnetic field.
• Shaft – The shaft of the motor connects the rotor to the stator and is used to power the equipment or machinery.
• Commutator – The device that reverses the polarity of the rotor. Like reversing a battery at every spin so that the electrons change course.
• Fan – The fan is used to create air flow and increase the efficiency of a motor.
## Final Words
Electric motors are all around us. They are a safe, efficient, and reliable way to power machinery and equipment. They are available in a range of sizes, voltages, and designs and can be powered by a wide range of energy sources, including fossil fuels and renewable energy sources like solar or wind.
# Electromagnetism: From the Basics to Everyday Applications
Let’s use iron for example. Touch it with another piece of iron and what happens? Nothing! Now take a bare wire, copper preferred. Wrap the copper wire around one of the pieces of iron and what happens? Still nothing!
Now grab both ends of the copper wire and connect it to a battery. What happens? Still nothing – at least nothing noticeable that the naked eye can see!
What is happening when the wires connect to the battery (called a circuit) is that the electrons were random before the circuit was completed and they straightened out, like a row of marching soldiers after the circuit is complete.
These marching electrons will point and move towards the pole ( polarity) of the battery it is connected to. Now let’s get a little more technically correct and call these marching electrons an electric current, and as these electrons (current) are moving through the wire, a magnetic field is produced.
## When There is Electric Current, There is a Magnetic Field
### But Just What is This Magnetic Field?
If we pick up the other piece of iron (which does not have the copper wire around it) and place it near the iron piece that has the wire wrapped (and thus the electric current), that isolated piece of iron suddenly moves toward the electrified one.
The reason why the iron pieces attract each other is that the iron piece with the copper wire wrapped around it (called a coil) becomes magnetic. And so, we have just created an electromagnet
For the video below, you might want to put your thinking caps on as it explains pretty well how electromagnetic forces are derived (hint: when electrons move through a wire). We suggest those that who are in school and/or have an absorption for learning continue to this video.
For those that would like to bypass such items as Maxwell’s equations and just want a cheat sheet of what is the criteria for an electromagnetic field, see our summary below.
An electromagnet can be made out of any type of metal, but iron and nickel are the ones most often used. Nickel magnets are stronger than iron magnets, but iron is cheaper.
Iron is found in most scrap yards, or you can buy it from a hardware store. The first step in making an electromagnet is to create a wire that is wrapped with a coil of metal several times. This is known as an electromagnet coil. The coil has to be wrapped around a core, which is made out of a non-magnetic material.
## The Magnetic Field
The electromagnetic field is the region of energy surrounding a magnet. The magnetic field is perpendicular to the path where the electrons flow.
## Why are Electromagnets Important?
Electromagnets are important because they can be used to power items and devices that are used by us every day. Motors and generators are just two examples. They are also used in toys, as a way of moving things around in a car or even to move things in a factory.
They are also useful because they’re easily controllable. If you want to turn the electromagnet off, you simply turn off the electric current running through it. If you want to turn it back on, you can simply turn it back on again.
## Types of Magnets
There are two types: temporary and permanent. Temporary magnets are only magnetic while electricity is running through them. Permanent magnets remain magnetic no matter what happens. This is because these magnets are not electrified. An example is the ones stuck to your fridge or another metal surface.
## Conclusion
Magnetism is created when electrons are in movement. In a practical sense, this means that if you connect a wire to a battery (power source), electrons will move from the negative pole to the positive pole of the battery.
When this happens, a force is created in addition to the electrical force, which is the magnetic force. This magnetic force ‘pushes’ perpendicular to electrical force (current), so any metal that has magnetic properties will be attracted to this force and move towards it accordingly.
The magnetic force can be strengthened by any of the following criteria.
• Take the straight wire and curl it around the medium, usually an iron bar. The result is called a coil.
• Wiring the coil more will cause the magnetic field to strengthen.
• Increasing the current; that is, increasing the speed at which the electrons travel through the coiled wire will also strengthen the magnetic field.
The practical applications of electromagnets are the ability to cause an entity to move because of this force, such as what happens inside a motor. | 12,813 | 65,387 | {"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} | 2.640625 | 3 | CC-MAIN-2023-23 | latest | en | 0.935302 |
https://de.maplesoft.com/support/help/view.aspx?path=Physics/Redefine&L=G | 1,723,341,270,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722640843545.63/warc/CC-MAIN-20240811013030-20240811043030-00218.warc.gz | 151,688,331 | 30,140 | Redefine - Maple Help
Physics[Redefine] - Redefines the spacetime metric, list of coordinates and tetrads according to a change in the signature, from any of the four possible signatures (- - - +), (+ - - -), (+ + + -) and (- + + +) to any of the other ones
Calling Sequence Redefine(what, fromsignature = ..., tosignature = ...)
Parameters
what - any of coordinates, metric, all (meaning both); setcoordinates, setmetric, setall, to respectively see how the redefinition changes what, or in addition automatically set (via Setup) the redefined value. fromsignature = ... - optional, to be taken as the starting signature; if not given, it is the signature set at the moment tosignature = ... - optional, to be taken as the desired signature; if not given, it is the signature set at the moment
Description
• The Redefine command redefines the spacetime metric g_ and list of coordinates, or a given tetrad, according to a change in the signature, from any of the four possible signatures (- - - +), (+ - - -), (+ + + -) and (- + + +) to any of the other ones.
• When any of fromsignature or tosignature are not given, the corresponding value is the value of the signature set at the moment. To query about this value, enter Setup(signature), or to change it enter Setup(signature = ...) where the right-hand side is any of - - - +, + - - -, + + + - or - + + +. You can enter the signature leaving or not spaces between the +/- signs, and enclosing them with or " ".
• The typical scenario for the use of fromsignature is when you change the signature using Setup and notice that the coordinates and metric g_ have not changed accordingly; or you have a tetrad matrix for which Tetrads:-IsTetrad says it is not a tetrad unless you redefine the signature. In these cases entering Redefine(all, fromsignature = previous_signature) shows how would the list of coordinates and metric look if they were redefined from the previous signature to the one you set (i.e., the current one). In the case of a tetrad, entering Redefine(e_[a, mu] = ..., fromsignature = previous_signature) shows how would the passed tetrad would look. In both cases, if the result is as desired, you can use the output to call Setup and set things accordingly, or simpler: in the case of coordinates and metric, instead of all, pass setall, as in Redefine(setall, fromsignature = previous_signature), and that will in addition set things up by automatically calling Setup.
• The typical scenario for the use of tosignature is when you are working with a signature and - say to follow a textbook - you want to change to a different signature, and want that not just the signature but also the ordering of the list of coordinates and/or the spacetime metric change accordingly. Here Redefine(all, tosignature = desired_signature) and Redefine(setall, tosignature = desired_signature) will respectively show or also set the new ordering of the list of coordinates and the metric according to the change to the desired_signature. For an example where redefining a tetrad is necessary see this one in the what's new in Physics in Maple 2021.
• To restrict these redefinitions to either the coordinates or the metric, instead of all and setall use coordinates and setcoordinates, or metric and setmetric.
Examples
> $\mathrm{with}\left(\mathrm{Physics}\right):$
> $\mathrm{Setup}\left(\mathrm{mathematicalnotation}=\mathrm{true},\mathrm{coordinates}=\mathrm{cartesian}\right)$
$\mathrm{Systems of spacetime coordinates are:}\left\{X=\left(x{,}y{,}z{,}t\right)\right\}$
$\mathrm{_______________________________________________________}$
$\left[{\mathrm{coordinatesystems}}{=}\left\{{X}\right\}{,}{\mathrm{mathematicalnotation}}{=}{\mathrm{true}}\right]$ (1)
Consider the generic form of a spacetime metric. For the purpose of illustrating its redefinition (reordering of lines and columns) when changing the signature, it doesn't need to depend on the coordinates
> $G≔\mathrm{Matrix}\left(4,\mathrm{symbol}=g,\mathrm{shape}=\mathrm{symmetric}\right)$
${G}{≔}\left[\right]$ (2)
Set the metric with this value, note the signature: it is (- - - +):
> $\mathrm{Setup}\left(\mathrm{signature},\mathrm{g_}=G\right)$
$\mathrm{_______________________________________________________}$
$\mathrm{Coordinates:}\left[x{,}y{,}z{,}t\right]\mathrm{. Signature:}\left(\mathrm{- - - +}\right)$
$\mathrm{_______________________________________________________}$
${{g}}_{{\mathrm{\mu }}{,}{\mathrm{\nu }}}{=}\left[\right]$
$\mathrm{_______________________________________________________}$
$\mathrm{Setting}\mathrm{lowercaselatin_is}\mathrm{letters to represent}\mathrm{space}\mathrm{indices}$
$\left[{\mathrm{metric}}{=}\left\{\left({1}{,}{1}\right){=}{{g}}_{{1}{,}{1}}{,}\left({1}{,}{2}\right){=}{{g}}_{{1}{,}{2}}{,}\left({1}{,}{3}\right){=}{{g}}_{{1}{,}{3}}{,}\left({1}{,}{4}\right){=}{{g}}_{{1}{,}{4}}{,}\left({2}{,}{2}\right){=}{{g}}_{{2}{,}{2}}{,}\left({2}{,}{3}\right){=}{{g}}_{{2}{,}{3}}{,}\left({2}{,}{4}\right){=}{{g}}_{{2}{,}{4}}{,}\left({3}{,}{3}\right){=}{{g}}_{{3}{,}{3}}{,}\left({3}{,}{4}\right){=}{{g}}_{{3}{,}{4}}{,}\left({4}{,}{4}\right){=}{{g}}_{{4}{,}{4}}\right\}{,}{\mathrm{signature}}{=}{\mathrm{- - - +}}{,}{\mathrm{spaceindices}}{=}{\mathrm{lowercaselatin_is}}\right]$ (3)
Track the line element
> $\mathrm{g_}\left[\mathrm{lineelement}\right]$
${{g}}_{{3}{,}{3}}{{\mathbf{ⅆ}}{}\left({z}\right)}^{{2}}{+}\left({2}{\mathbf{ⅆ}}{}\left({x}\right){{g}}_{{1}{,}{3}}{+}{2}{{g}}_{{2}{,}{3}}{\mathbf{ⅆ}}{}\left({y}\right)\right){\mathbf{ⅆ}}{}\left({z}\right){+}{{g}}_{{1}{,}{1}}{{\mathbf{ⅆ}}{}\left({x}\right)}^{{2}}{+}{2}{{g}}_{{1}{,}{2}}{\mathbf{ⅆ}}{}\left({x}\right){\mathbf{ⅆ}}{}\left({y}\right){+}{{g}}_{{2}{,}{2}}{{\mathbf{ⅆ}}{}\left({y}\right)}^{{2}}{+}{\mathbf{ⅆ}}{}\left({t}\right)\left({\mathbf{ⅆ}}{}\left({t}\right){{g}}_{{4}{,}{4}}{+}{2}{\mathbf{ⅆ}}{}\left({x}\right){{g}}_{{1}{,}{4}}{+}{2}{\mathbf{ⅆ}}{}\left({y}\right){{g}}_{{2}{,}{4}}{+}{2}{\mathbf{ⅆ}}{}\left({z}\right){{g}}_{{3}{,}{4}}\right)$ (4)
Change now the signature by reversing the position of the time-like component, from 4 to 1
> $\mathrm{Setup}\left(\mathrm{signature}="+---"\right)$
$\left[{\mathrm{signature}}{=}{\mathrm{+ - - -}}\right]$ (5)
Neither the metric nor the coordinates change: t is still in position 4 and the component (1, 1) of the metric is still ${g}_{1,1}$:
> $\mathrm{Coordinates}\left(\right)$
$\mathrm{Systems of spacetime coordinates are:}\left\{X=\left(x{,}y{,}z{,}t\right)\right\}$
$\left\{{X}\right\}$ (6)
> $\mathrm{g_}\left[\right]$
${{g}}_{{\mathrm{\mu }}{,}{\mathrm{\nu }}}{=}\left[\right]$ (7)
However, after changing the signature using Setup, we may also want to redefine the coordinates accordingly - place t in position 1 - and possibly also the metric reordering its lines and rows. For that purpose you can use Redefine, to which you need to indicate the previous signature (or in a different situation the new signature, to explore the effect of a change before doing it) and an indication of whether you want to redefine the metric, the coordinates or all
> $\mathrm{Redefine}\left(\mathrm{coordinates},\mathrm{fromsignature}="---+"\right)$
$\left[{t}{,}{x}{,}{y}{,}{z}\right]$ (8)
> $\mathrm{Redefine}\left(\mathrm{metric},\mathrm{fromsignature}="---+"\right)$
$\left[\right]$ (9)
These redefinitions however were not set, the keywords coordinates, metric, or all only trigger the change, t is still in position 4 and the component (1,1) of the metric is still ${g}_{1,1}$
> $\mathrm{Coordinates}\left(\right)$
$\mathrm{Systems of spacetime coordinates are:}\left\{X=\left(x{,}y{,}z{,}t\right)\right\}$
$\left\{{X}\right\}$ (10)
> $\mathrm{g_}\left[\right]$
${{g}}_{{\mathrm{\mu }}{,}{\mathrm{\nu }}}{=}\left[\right]$ (11)
You can now either use the output of this routine to redefine things using the Setup command, or do all in one go using any of the keywords setcoordinates, setmetric, or setall, for example
> $\mathrm{Redefine}\left(\mathrm{setall},\mathrm{fromsignature}="---+"\right)$
$\left[{X}\right]{,}\left[{?}\right]$ (12)
Now t is in position 1 and the component (1,1) of the metric equal to ${g}_{4,4}$
> $\mathrm{Coordinates}\left(\right)$
$\mathrm{Systems of spacetime coordinates are:}\left\{X=\left(t{,}x{,}y{,}z\right)\right\}$
$\left\{{X}\right\}$ (13)
> $\mathrm{g_}\left[\right]$
${{g}}_{{\mathrm{\mu }}{,}{\mathrm{\nu }}}{=}\left[\right]$ (14)
Note that, despite the reordering of lines and columns in the metric, because we also reordered the variables, the line element has not changed:
> $\mathrm{g_}\left[\mathrm{lineelement}\right]$
${{g}}_{{2}{,}{2}}{{\mathbf{ⅆ}}{}\left({y}\right)}^{{2}}{+}\left({2}{\mathbf{ⅆ}}{}\left({t}\right){{g}}_{{2}{,}{4}}{+}{2}{\mathbf{ⅆ}}{}\left({x}\right){{g}}_{{1}{,}{2}}\right){\mathbf{ⅆ}}{}\left({y}\right){+}{{g}}_{{4}{,}{4}}{{\mathbf{ⅆ}}{}\left({t}\right)}^{{2}}{+}{2}{{g}}_{{1}{,}{4}}{\mathbf{ⅆ}}{}\left({x}\right){\mathbf{ⅆ}}{}\left({t}\right){+}{{g}}_{{1}{,}{1}}{{\mathbf{ⅆ}}{}\left({x}\right)}^{{2}}{+}{\mathbf{ⅆ}}{}\left({z}\right)\left({\mathbf{ⅆ}}{}\left({z}\right){{g}}_{{3}{,}{3}}{+}{2}{\mathbf{ⅆ}}{}\left({t}\right){{g}}_{{3}{,}{4}}{+}{2}{\mathbf{ⅆ}}{}\left({x}\right){{g}}_{{1}{,}{3}}{+}{2}{{g}}_{{2}{,}{3}}{\mathbf{ⅆ}}{}\left({y}\right)\right)$ (15)
> $\mathrm{normal}\left(-\right)$
${0}$ (16)
Redefine is particularly useful when working with metrics from the database of solutions to Einstein's equations, all of which reset the signature to (+ + + -) when loaded. For example:
> $\mathrm{g_}\left[\left[12,21,1\right]\right]$
$\mathrm{_______________________________________________________}$
$\mathrm{Systems of spacetime coordinates are:}\left\{X=\left(x{,}y{,}\mathrm{\phi }{,}t\right)\right\}$
$\mathrm{Default differentiation variables for d_, D_ and dAlembertian are:}\left\{X=\left(x{,}y{,}\mathrm{\phi }{,}t\right)\right\}$
$\mathrm{The}\mathrm{McLenaghan, Tariq \left(1975\right)}\mathrm{metric in coordinates}\mathrm{Tupper \left(1976\right)}$
$\mathrm{Parameters:}\left[a{,}k{,}\mathrm{κ0}\right]$
$\mathrm{Comments:}k paramⅇtrizⅇs thⅇ most gⅇnⅇral ⅇlⅇctromagnⅇtic invariant with rⅇspⅇct to thⅇ last 3 Killing vⅇctors$
$\mathrm{Domain:}\left[0
$\mathrm{Assumptions:}\left[0
$\mathrm{Resetting the signature of spacetime from}\left(\mathrm{+ - - -}\right)\mathrm{to}\left(\mathrm{+ + + -}\right)\mathrm{in order to match the signature in the database of metrics}$
$\mathrm{_______________________________________________________}$
${{g}}_{{\mathrm{\mu }}{,}{\mathrm{\nu }}}{=}\left[\right]$ (17)
> $\mathrm{Setup}\left(\mathrm{signature}\right)$
$\left[{\mathrm{signature}}{=}{\mathrm{+ + + -}}\right]$ (18)
How would this metric [12, 21, 1] and coordinates $\left[t,x,y,\mathrm{\phi }\right]$ would look with the signature (+ - - -) ?
> $\mathrm{Redefine}\left(\mathrm{all},\mathrm{tosignature}="+ - - -"\right)$
$\left[{t}{,}{x}{,}{y}{,}{\mathrm{\phi }}\right]{,}\left[{?}\right]$ (19)
By replacing all by setall in the command above not only the list of coordinates and metric matrix form are returned but they are also set in one go.
As an example of redefining tetrads, load Tetrads and the metric [27, 37, 1] of the database of solutions to Einstein's equations
> $\mathrm{with}\left(\mathrm{Tetrads}\right):$
$\mathrm{_______________________________________________________}$
$\mathrm{Setting}\mathrm{lowercaselatin_ah}\mathrm{letters to represent}\mathrm{tetrad}\mathrm{indices}$
$\mathrm{Defined as tetrad tensors}\left(\mathrm{see ?Physics,tetrads}\right),{𝔢}_{a,\mathrm{\mu }},{\mathrm{\eta }}_{a,b},{\mathrm{\gamma }}_{a,b,c},{\mathrm{\lambda }}_{a,b,c}$
$\mathrm{Defined as spacetime tensors representing the NP null vectors of the tetrad formalism}\left(\mathrm{see ?Physics,tetrads}\right),{l}_{\mathrm{\mu }},{n}_{\mathrm{\mu }},{m}_{\mathrm{\mu }},{\stackrel{&conjugate0;}{m}}_{\mathrm{\mu }}$
$\mathrm{_______________________________________________________}$ (20)
> $\mathrm{g_}\left[\left[27,37,1\right]\right]$
$\mathrm{_______________________________________________________}$
$\mathrm{Systems of spacetime coordinates are:}\left\{X=\left(z{,}\mathrm{zb}{,}r{,}u\right)\right\}$
$\mathrm{Default differentiation variables for d_, D_ and dAlembertian are:}\left\{X=\left(z{,}\mathrm{zb}{,}r{,}u\right)\right\}$
$\mathrm{The}\mathrm{Robinson and Trautman \left(1962\right)}\mathrm{metric in coordinates}\left[z{,}\mathrm{zb}{,}r{,}u\right]$
$\mathrm{Parameters:}\left[P{}\left(z{,}\mathrm{zb}{,}u\right){,}H{}\left(X\right)\right]$
$\mathrm{Comments:}aⅆmits gⅇoⅆⅇsic, shⅇarfrⅇⅇ, twistfrⅇⅇ null congruⅇncⅇ, rho=-1/r=rho_b$
$\mathrm{Domain:}\left[P{}\left(z{,}\mathrm{zb}{,}u\right)::\mathrm{real}\right]$
$\mathrm{Signature:}\left(\mathrm{+ + + -}\right)$
$\mathrm{_______________________________________________________}$
${{g}}_{{\mathrm{\mu }}{,}{\mathrm{\nu }}}{=}\left[\right]$ (21)
> $\mathrm{CompactDisplay}\left(\right)$
${H}{}\left({z}{,}{\mathrm{zb}}{,}{r}{,}{u}\right){\mathrm{will now be displayed as}}{H}$
${P}{}\left({z}{,}{\mathrm{zb}}{,}{u}\right){\mathrm{will now be displayed as}}{P}$ (22)
The assumptions on the metric's parameters are
> $\mathrm{Assume}\left(0
$\left\{{u}{::}{\mathrm{real}}{,}{z}{::}{\mathrm{real}}{,}{\mathrm{zb}}{::}{\mathrm{real}}{,}{H}{::}{\mathrm{real}}{,}{P}{::}\left({0}{,}{\mathrm{\infty }}\right)\right\}{,}\left\{{r}{::}\left[{0}{,}{\mathrm{\infty }}\right){,}{u}{::}{\mathrm{real}}{,}{z}{::}{\mathrm{real}}{,}{\mathrm{zb}}{::}{\mathrm{real}}{,}{H}{::}{\mathrm{real}}{,}{P}{::}\left({0}{,}{\mathrm{\infty }}\right)\right\}{,}\left\{{r}{::}\left[{0}{,}{\mathrm{\infty }}\right){,}{H}{::}{\mathrm{real}}\right\}$ (23)
The null tetrad computed by the Maple system using a general algorithms is
> $\mathrm{Setup}\left(\mathrm{tetrad}=\mathrm{null}\right):$
> $\mathrm{e_}\left[\right]$
${{𝔢}}_{{a}{,}{\mathrm{\mu }}}{=}\left[\right]$ (24)
The book on solutions to Einstein's equations [1] suggests a different tetrad, free of radicals, which for our illustration purposes is
> $\mathrm{e_}\left[a,\mathrm{\mu }\right]=\mathrm{Matrix}\left(4,4,\left[\left[0,0,0,-I\right],\left[0,\frac{rI\cdot 1}{P\left(z,\mathrm{zb},u\right)},0,0\right],\left[\frac{rI\cdot 1}{P\left(z,\mathrm{zb},u\right)},0,0,0\right],\left[0,0,-I,-H\left(z,\mathrm{zb},r,u\right)I\right]\right]\right)$
${{𝔢}}_{{a}{,}{\mathrm{\mu }}}{=}\left[\right]$ (25)
> $\mathrm{IsTetrad}\left(\right)$
${\mathbit{Warning, the given components form a}}\left({\mathbit{null}}\right){\mathbit{tetrad,}}{\mathbit{with a covariant spacetime index}}{\mathbit{, only if you change the signature from}}\left({\mathbit{+ + + -}}\right){\mathbit{to}}\left({\mathbit{- - - +}}\right){\mathbit{. You can do that by entering \left(copy and paste\right):}}{\mathbit{Setup}}{}\left({\mathbit{signature}}{\mathbf{=}}{"- - - +"}\right)$
${\mathrm{false}}$ (26)
So you can change the signature to (---+) as indicated in the message, or instead of that redefine the tetrad, from the signature indicated, to work with the current signature (+++-)
> $\mathrm{Redefine}\left(,\mathrm{fromsignature}="- - - +"\right)$
${{𝔢}}_{{a}{,}{\mathrm{\mu }}}{=}\left[\right]$ (27)
The returned tetrad matches the definition
> $\mathrm{IsTetrad}\left(\right)$
$\mathrm{Type of tetrad:}\mathrm{null}$
${\mathrm{true}}$ (28)
You can now set it and verify that
> $\mathrm{Setup}\left(\right)$
$\left[{\mathrm{tetrad}}{=}\left\{\left({1}{,}{4}\right){=}{1}{,}\left({2}{,}{2}\right){=}{-}\frac{{r}}{{P}}{,}\left({3}{,}{1}\right){=}{-}\frac{{r}}{{P}}{,}\left({4}{,}{3}\right){=}{1}{,}\left({4}{,}{4}\right){=}{H}\right\}\right]$ (29)
> $\mathrm{e_}\left[\mathrm{definition}\right]$
${{𝔢}}_{{a}{,}{\mathrm{\mu }}}{{𝔢}}_{{b}\phantom{{\mathrm{\mu }}}}^{\phantom{{b}}{\mathrm{\mu }}}{=}{{\mathrm{\eta }}}_{{a}{,}{b}}$ (30)
> $\mathrm{TensorArray}\left(\right)$
$\left[\right]$ (31)
References
[1] Landau, L.D., and Lifshitz, E.M. The Classical Theory of Fields, Course of Theoretical Physics Volume 2, fourth revised English edition. Elsevier, 1975.
Compatibility
• The Physics[Redefine] command was introduced in Maple 2017. | 5,374 | 16,138 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 105, "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} | 3.421875 | 3 | CC-MAIN-2024-33 | latest | en | 0.726388 |
https://ketabnak.com/book/65604/ajax/rate.php?dlid=65604&vote=4&nojava=1 | 1,555,994,609,000,000,000 | text/html | crawl-data/CC-MAIN-2019-18/segments/1555578586680.51/warc/CC-MAIN-20190423035013-20190423061013-00104.warc.gz | 453,155,465 | 9,654 | # Trigonometry
نویسنده:
Book description: This is a text on elementary trigonometry, designed for students who have completed courses in high-school algebra and geometry. Though designed for college students, it could also be used in high schools. The traditional topics are covered, but a more geometrical approach is taken than usual. Also, some numerical methods (e.g. the secant method for solving trigonometric equations) are discussed. A brief tutorial on using Gnuplot to graph trigonometric functions is included.
There are 495 exercises in the book, with answers and hints to selected exercises.
TABLE OF CONTENTS
Right Triangle Trigonometry
Angles
Trigonometric Functions of an Acute Angle
Applications and Solving Right Triangles
Trigonometric Functions of Any Angle
Rotations and Reflections of Angles
General Triangles
The Law of Sines
The Law of Cosines
The Law of Tangents
The Area of a Triangle
Circumscribed and Inscribed Circles
Identities
Basic Trigonometric Identities
Sum and Difference Formulas
Double-Angle and Half-Angle Formulas
Other Identities
Radian Measure
Radians and Degrees
Arc Length
Area of a Sector
Circular Motion: Linear and Angular Speed
Graphing and Inverse Functions
Graphing the Trigonometric Functions
Properties of Graphs of Trigonometric Functions
Inverse Trigonometric Functions
Additional Topics
Solving Trigonometric Equations
Numerical Methods in Trigonometry
Complex Numbers
Polar Coordinates
Appendix A: Answers and Hints to Selected Exercises
Appendix B: Graphing with Gnuplot
GNU Free Documentation License
History
Index
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https://flashman.neocities.org/Courses/m103n4_21_2014 | 1,713,095,801,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296816879.25/warc/CC-MAIN-20240414095752-20240414125752-00514.warc.gz | 230,341,359 | 8,309 | Wednesday April 16
Discuss this week's assignment on coding.
Last Class: Started "topology of networks and surfaces":
Review Topology vocabulary:
"Bounded" In the plane- A line segment is bounded. A line is not bounded. A circle is bounded. A parabola is not bounded. "Bounded" means the object can be visualized in a box.
"
closed
" A line segment with endpoints is closed. A circle is closed. A line is closed. A line segment missing one or both endpoints in not closed. A circle missing one point is not closed.
"
open
" A line segment missing both endpoints is open. A line is open. A circle missing one point is open.
"
connected
" A line, a line segment, a circle, a circle missing one point, and a parabola are all connected.
A line segment missing an interior point is not connected.
It has two pieces.
The following two letters are topologically equivalent.
I C
The following two letters are topologically equivalent to each other but not to the previous two letters. This can be seen by removing a single point from these letters which will not disconnect the curves, as it does with the previous letters.
O D
The letter T missing the point where the top meets the vertical line segment is not connected. It has three pieces.
The letter Y missing the point where the top meets the vertical line segment also is not connected. It has three pieces.
T and Y are topologically the same (equivalent)! this can be seen by bending the tops to the letters up or down and stretching and shrinking the lengths as well.
Questions: Is a triangle topologically equivalent to another triangle?
Yes. Stretch the sides and you'll also transform the angles.
Is an circle topologically equivalent to a line? No.
The circle is still connected when you remove a point.
The line is disconnected when you remove a point.
Is a triangle topologically equivalent to a square? a circle? yes.
Maps
Coordinates for "earth" - the sphere
Coordinates for the torus!
Activity for maps on Torus.
Locate P and Q on the map! give their coordinates.
Topology and measurements:
• Counting on a line. Counting on a curve.
Keep count on the number of vertices and segments for a graph. Compare:
Vertices Edges V-E Line segment I 2 1 1 circle O 1 1 0 8 1 2 -1 9 2 2 0 B 2 3 -1
Curves will not be topologically equivalent if the number V-E is not the same.
However, as the table shows, there are curves that have the same number V-E which are also not equivalent.
These can be distinguished by other criterion, such as connectivity when a point is removed.
The
number V-E is a characteristic of the curve
that will be the same for any topologically equivalent curve.
However, this number does not completely classify the curves topologically, since curves can have the same number V-E without being equivalent.
Counting in the plane or Counting on a surface.
Vertices, edges, regions.
Vertices Regions Edges Line segment 2 1 1 circle 1 2 1 8 1 3 2 9 2 2 2 B 2 3 3 6 8 12
Counting in the plane or Counting on a sphere.
Euler's Formula for the plane or the sphere:
Theorem: For any connected graph in the plane,
V+R = E + 2.
OR V -E+R =2
The number 2 is called the "Euler characteristic for the plane." ( and the sphere).
Proof: Deconstruct the graph.
First remove edges to "connect regions" until there is only one region. The relation between V+R and E+ 2 stays the same. (One edge goes with one region.)
Now remove one vertex and edge to "trim the tree".
Again the relation between V+R and E+2 stays the same. ( One edge goes with each vertex.)
Finally we have just one vertex, no edges, and one region.
So the relationship is that V+R = E + 2!
For any connected graph on the sphere, V+R = E + 2
Proof:
Choose a point P on the sphere not on the graph.
Place a plane touching the sphere opposite to P.
Then project the graph onto the plane.
The projected graph will have the same number of vertices, edges and regions.
The counting in the plane shows that the formula is true for the projected graph, and thus for the original graph on the sphere!
1. What about graphs on the Torus?
We have a connected graph on the torus with one vertex, two edges and only on region. But this information does not match for the euler formula for the plane or the sphere. SO.. the torus must be topologically different from the sphere or the plane!
In fact for the torus we see that it is possible for V+R= E or V-E+R= 0
Summary: We have learned about (and proved) Euler's Formula for the plane or the sphere:
For any connected graph in the plane or on the sphere, V+R = E + 2.
Adventures on the Mobius Band, the Klein Bottle, and the Projective Plane !
"New" Surfaces and
The Classification of Surfaces
What is a surface?
Bounded, unbounded:
Closed, open:
With or without boundary:
Orientable or Non-orientable:
The Moebius band is a
non-orientable surface.
Introduce the Klein Bottle and Projective Plane as examples of non-orientable surfaces.
A surface can be realized (imbedded) in a plane, in 3 space, in 4 space.
A surface can be visualized (immersed) in ...
Review examples: A closed disc, an open disc, a plane, an annulus- cylinder, a mobius band;
Mirror image and orientability - see the animated version (73K) Wind and Mr. Ug The Möbius band is one-sided - view the animated version (1.3M)
Experiments with the mobius band:
Draw a curve along the center of the band- we cover both "sides."
Cut along that curve- the band does not fall apart, but gets twice as long!
A sphere
A torus
[Activity:Graphs on the torus]
A Klein bottle:
# A javaview visualization of the Klein bottle
On Line Article: Imaging maths - Inside the Klein bottle
The projective plane
Why is this a closed and bounded surface?
Spheres with handles:
Spheres with cross caps
.
Visualizations of surfaces by flattened - cut apart models.
A cylinder, a mobius band, the torus, the Klein bottle, the projective plane.
Handles and cross-caps attached to the sphere.
The Topological Classification of "closed surfaces.
" If Mathematicians Made Pretzels" Proof without words.
The following two figures are topologically equivalent.
From the Fun Fact files, hosted by the Harvey Mudd College Math Department
Figure 1 Figure 2
Imagine that the two objects in Figure 1 are solid (with thickness) and made of very flexible and stretchy rubber.
Question: is it possible to deform one object into the other in a continuous motion (without tearing or cutting)?
Hint: it is important that the object is solid and has thickness; this transformation cannot be done with a one-dimensional piece of string. It is also not possible to do this with a piece of rope because even though the rope has thickness, it is not flexible or "stretchy" enough. See below for an explanation and animated gif. Or, don't scroll down if you want to think about it a while!
The Math Behind the Fact:
One way to do this is the following. Widen one of the loops and move one of its handles along the stem between the two loops to the other loop and push it through the hole so that the two loops become unlinked. The reference contains a sequence of pictures of this transformation.
Graeme McRae has generously contributed the animated gif in Figure 2, showing another solution to this problem! (Thank you, Graeme!)
Here is the original picture:
Ways to think of surfaces : cross-sections/ projections/moving curves/ using color to see another dimension.
How do 3d glasses work?
Spheres with handles,
Visualizations of surfaces by flattened - cut apart models.
A cylinder, a mobius band, the torus, the Klein bottle, the projective plane.
Closed Surfaces: Handles and cross-caps attached to the sphere.
A sphere with a handle = a torus A Sphere with a cross cap = the projective plane
The Topological Classification of "closed surfaces."
Every connected closed and bounded surface is topologically equivalent to a sphere with handles and crosscaps attached.
The Euler Characteristic of A Surface.
The classification of surfaces determines the euler characteristic of each surface.
If the surface is orientable, it is a sphere with n handles, so V-E+R = 1 - 2n +1 = 2-2n. For example the torus has euler characteristic 2-2*1=0.
If the surface is non-orientable, then is it a sphere with k crosscaps and n handles, so the euler characteristic is V-E+R = 1 - (k+2n) +1 =2 -2n -k.
Notice that a sphere with two cross caps has euler characteristic 0, the same as the torus. But this was the euler characteristic of the Klein Bottle. So we should be able to recognize the Klein bottle as a sphere with two cross caps.
This can be done by a single normalization of one pair of edges with the same orientation.
Other interest in surfaces: Examples
Ways to think of surfaces : cross-sections/ projections/moving curves/ using color to see another dimension.
Generalization of surfaces are called "manifolds". cross sections / projections/ moving surfaces-solids.
"minimal surfaces" (FAPP video?)
Transforming surfaces: "turning the sphere inside out." video | 2,168 | 9,059 | {"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} | 3.65625 | 4 | CC-MAIN-2024-18 | latest | en | 0.938912 |
https://www.cemc.uwaterloo.ca/pandocs/potw/2020-21/English/POTWA-20-G-27-S.html | 1,656,725,960,000,000,000 | text/html | crawl-data/CC-MAIN-2022-27/segments/1656103983398.56/warc/CC-MAIN-20220702010252-20220702040252-00221.warc.gz | 747,470,493 | 4,256 | # Problem of the Week Problem A and Solution Wrapping Presents
## Problem
When Jack wraps a box, he first does a test to determine if his sheet of wrapping paper is long enough.
To do this, Jack places his box on top of the wrapping paper so that one edge of the box is lined up with the width of the wrapping paper. He then flips the box along the length of the paper so that each of its four sides touches the paper once.
If there is at least $$6$$ cm of extra paper left after the last flip, Jack concludes that his sheet of wrapping paper is long enough. If there is less than $$6$$ cm of extra paper left after the last flip, Jack rotates his box so a different edge of his box is lined up with the wrapping paper and tries his test again.
Jack wants to wrap a box with dimensions $$20\text{ cm} \times 12 \text{ cm}\times 8 \text{ cm}$$.
He has a sheet of wrapping paper that is $$62$$ cm long.
Would this sheet of wrapping paper be long enough to wrap his box? If so, how should he position his box on the wrapping paper at the beginning of his test? You can assume the wrapping paper is wide enough to wrap the box. Justify your answer.
## Solution
To solve this problem we can try putting the box on the paper, and then check to see if the paper is long enough. Since the box has three dimensions, there are three different edge lengths that we can line up with the edge of the wrapping paper. We will consider these three different tests.
First Test
First we line up one of the $$20$$ cm edges of the box with the width of the wrapping paper. Then when we look at the box from the side as we are rolling it along the paper, we will see only the $$8$$ cm and $$12$$ cm sides.
Rolling the box along the paper this way is the same as measuring the perimeter of a $$8 \text{ cm} \times 12 \text{ cm}$$ rectangle, which is $$12+8+12+8=40$$ cm. Since the wrapping paper is $$62$$ cm long, there will be $$62-40=22$$ cm of extra paper left after the last roll. This is more than $$6$$ cm, so with this starting position, the wrapping paper is long enough to wrap Jack’s box.
Second Test
Next we will line up one of the $$8$$ cm edges of the box with the width of the wrapping paper. Then when we look at the box from the side as we are rolling it along the paper, we will see only the $$12$$ cm and $$20$$ cm sides.
Rolling the box along the paper this way is the same as measuring the perimeter of a $$12 \text{ cm} \times 20 \text{ cm}$$ rectangle, which is $$20+12+20+12=64$$ cm. Since the wrapping paper is only $$62$$ cm long, it is not long enough to wrap Jack’s box this way.
Third Test
Finally we will line up one of the $$12$$ cm edges of the box with the width of the wrapping paper. Then when we look at the box from the side as we are rolling it along the paper, we will see only the $$8$$ cm and $$20$$ cm sides.
Rolling the box along the paper this way is the same as measuring the perimeter of a $$8 \text{ cm} \times 20 \text{ cm}$$ rectangle, which is $$20+8+20+8=56$$ cm. Since the wrapping paper is $$62$$ cm long, there will be $$62-56=6$$ cm of extra paper left after the last roll. Therefore with this starting position, the wrapping paper is just long enough to wrap Jack’s box.
Thus, the wrapping paper is long enough to wrap Jack’s box if he starts by placing the box on the wrapping paper with either the $$12$$ cm edge or the $$20$$ cm edge lined up with the width of the wrapping paper.
Extension: If this piece of wrapping paper was $$24$$ cm wide, would it be wide enough to wrap the box? Think about how much wrapping paper would be needed on either side of the box when you are rolling it. Remember that you will need to wrap the two side faces of the box as well.
### Teacher’s Notes
With two-dimensional objects, we are often interested in the area and perimeter of the object. With three-dimensional objects, the analogous measurements would be volume and surface area. There are some formulae we can use to find these measurements for common 3-D objects.
3-D Object Dimensions Volume Surface Area
Cube side length $$= s$$ $$s^3$$ $$6s^2$$
Sphere radius $$= r$$ $$\dfrac{4}{3} \pi r^3$$ $$4 \pi r^2$$
Right Cylinder radius $$= r$$, height $$= h$$ $$\pi r^2 h$$ $$2 \pi r^2 + 2 \pi r h$$
Right Square Pyramid base side length $$= a$$, height $$= h$$ $$a^2 \dfrac{h}{3}$$ $$a^2 + 2 a \sqrt{\dfrac{a^2}{4} + h^2}$$
Right Cone radius $$= r$$, height $$= h$$ $$\pi r^2\dfrac{h}{3}$$ $$\pi r \sqrt{r^2 + h^2} + \pi r^2$$
These formulae are useful when you need to know the volume or surface area of the objects above. Using calculus, we are able to find the volumes of more uncommon objects. | 1,213 | 4,646 | {"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} | 4.96875 | 5 | CC-MAIN-2022-27 | latest | en | 0.931851 |
http://mathhelpforum.com/discrete-math/120332-bijection.html | 1,524,575,732,000,000,000 | text/html | crawl-data/CC-MAIN-2018-17/segments/1524125946688.88/warc/CC-MAIN-20180424115900-20180424135900-00006.warc.gz | 205,492,655 | 9,010 | 1. ## Bijection
Hi,
Can you please give me an example for bijective function between
{0, 1}^N and (0, 1, 2, 3}^N?
N is the set of natural numbers.
Thanks for any kind of help
2. Hi
hint: use the base-2 representation:
$\displaystyle 00\leftrightarrow 0$
$\displaystyle 01\leftrightarrow 1$
$\displaystyle 10\leftrightarrow 2$
$\displaystyle 11\leftrightarrow 3$ | 114 | 364 | {"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} | 3.078125 | 3 | CC-MAIN-2018-17 | latest | en | 0.536025 |
https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2016.55 | 1,726,843,911,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700652278.82/warc/CC-MAIN-20240920122604-20240920152604-00255.warc.gz | 183,698,463 | 16,170 | Document
# Hardness of Bipartite Expansion
## File
LIPIcs.ESA.2016.55.pdf
• Filesize: 0.5 MB
• 17 pages
## Cite As
Subhash Khot and Rishi Saket. Hardness of Bipartite Expansion. In 24th Annual European Symposium on Algorithms (ESA 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 57, pp. 55:1-55:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
https://doi.org/10.4230/LIPIcs.ESA.2016.55
## Abstract
We study the natural problem of estimating the expansion of subsets of vertices on one side of a bipartite graph. More precisely, given a bipartite graph G(U,V,E) and a parameter beta, the goal is to find a subset V' subseteq V containing beta fraction of the vertices of V which minimizes the size of N(V'), the neighborhood of V'. This problem, which we call Bipartite Expansion, is a special case of submodular minimization subject to a cardinality constraint, and is also related to other problems in graph partitioning and expansion. Previous to this work, there was no hardness of approximation known for Bipartite Expansion. In this paper we show the following strong inapproximability for Bipartite Expansion: for any constants tau, gamma > 0 there is no algorithm which, given a constant beta > 0 and a bipartite graph G(U,V,E), runs in polynomial time and decides whether - (YES case) There is a subset S^* subseteq V s.t. |S^*| >= beta*|V| satisfying |N(S^*)| <= gamma |U|, or - (NO case) Any subset S subseteq V s.t. |S| >= tau*beta*|V| satisfies |N(S)| >= (1 - gamma)|U|, unless NP subseteq intersect_{epsilon > 0}{DTIME}(2^{n^epsi;on}) i.e. NP has subexponential time algorithms. We note that our hardness result stated above is a vertex expansion analogue of the Small Set (Edge) Expansion Conjecture of Raghavendra and Steurer 2010.
##### Keywords
• inapproximability
• bipartite expansion
• PCP
• submodular minimization
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## References
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2. N. Alon. Eigenvalues, geometric expanders, sorting in rounds, and Ramsey theory. Combinatorica, 6(3):207-219, 1986.
3. C. Ambühl, M. Mastrolilli, and O. Svensson. Inapproximability results for maximum edge biclique, minimum linear arrangement, and sparsest cut. SIAM Journal of Computing, 40(2):567-596, 2011.
4. B. Applebaum, B. Barak, and A. Wigderson. Public-key cryptography from different assumptions. In Proceedings of the ACM Symposium on the Theory of Computing, pages 171-180, 2010.
5. S. Arora, S. Rao, and U. V. Vazirani. Expander flows, geometric embeddings and graph partitioning. Journal of the ACM, 56(2):1-37, 2009.
6. P. Austrin and S. Khot. A simple deterministic reduction for the gap minimum distance of code problem. In Proceedings of ICALP, pages 474-485, 2011.
7. S. Chawla, R. Krauthgamer, R. Kumar, Y. Rabani, and D. Sivakumar. On the hardness of approximating multicut and sparsest-cut. Computational Complexity, 15(2):94-114, 2006.
8. Q. Cheng and D. Wan. A deterministic reduction for the gap minimum distance problem: [extended abstract]. In Proceedings of the ACM Symposium on the Theory of Computing, pages 33-38, 2009.
9. I. Dumer, D. Micciancio, and M. Sudan. Hardness of approximating the minimum distance of a linear code. IEEE Trans. Information Theory, 49(1):22-37, 2003.
10. U. Feige. Relations between average case complexity and approximation complexity. In Proceedings of the ACM Symposium on the Theory of Computing, pages 534-543, 2002.
11. U. Feige, M. Hajiaghayi, and J. R. Lee. Improved approximation algorithms for minimum weight vertex separators. SIAM Journal of Computing, 38(2):629-657, 2008.
12. V. Guruswami, C. Umans, and S. P. Vadhan. Unbalanced expanders and randomness extractors from Parvaresh-Vardy codes. Journal of the ACM, 56(4), 2009.
13. S. Khot. On the power of unique 2-prover 1-round games. In Proceedings of the ACM Symposium on the Theory of Computing, pages 767-775, 2002.
14. S. Khot. Ruling out PTAS for graph min-bisection, dense k-subgraph, and bipartite clique. SIAM Journal of Computing, 36(4):1025-1071, 2006.
15. S. Khot and N. K. Vishnoi. The unique games conjecture, integrality gap for cut problems and embeddability of negative type metrics into 𝓁₁. In Proceedings of the Annual Symposium on Foundations of Computer Science, pages 53-62, 2005.
16. F. T. Leighton and S. Rao. Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms. Journal of the ACM, 46(6):787-832, 1999.
17. N. Linial, E. London, and Y. Rabinovich. The geometry of graphs and some of its algorithmic applications. Combinatorica, 15(2):215-245, 1995.
18. R. J. Lipton and R. E. Tarjan. Applications of a planar separator theorem. SIAM Journal of Computing, 9(3):615-627, 1980.
19. A. Louis, P. Raghavendra, and S. Vempala. The complexity of approximating vertex expansion. In Proceedings of the Annual Symposium on Foundations of Computer Science, pages 360-369, 2013.
20. A. Lubotzky, R. Phillips, and P. Sarnak. Ramanujan graphs. Combinatorica, 8(3):261-227, 1988.
21. R. Müller and D. Wagner. α-vertex separator is NP-hard even for 3-regular graphs. Computing, 46:343-353, 1991.
22. N. Pippenger. Sorting and selecting in rounds. SIAM Journal of Computing, 16(6):1032-1038, 1987.
23. P. Raghavendra and D. Steurer. Graph expansion and the unique games conjecture. In Proceedings of the ACM Symposium on the Theory of Computing, pages 755-764, 2010.
24. P. Raghavendra, D. Steurer, and M. Tulsiani. Reductions between expansion problems. In Proceedings of the Annual IEEE Conference on Computational Complexity, pages 64-73, 2012.
25. A. Rao. Randomness Extractors for Independent Sources and Applications. PhD thesis, University of Texas at Austin, 2007.
26. M. Sipser and D. A. Spielman. Expander codes. IEEE Transactions on Information Theory, 42(6):1710-1722, 1996.
27. Z. Svitkina and L. Fleischer. Submodular approximation: Sampling-based algorithms and lower bounds. SIAM Journal of Computing, 40(6):1715-1737, 2011.
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Είσοδος
Βιβλία Βιβλία 1 - 10 από 22 για To reduce a mixed fraction to an equivalent improper fraction. RULE. — Multiply....
To reduce a mixed fraction to an equivalent improper fraction. RULE. — Multiply the whole number by the denominator of the fractional part, and to the product add the numerator, and place their sum over the said denominator.
An elementary treatise on arithmetic, in theory and practice: adapted to the ... - Σελίδα 131
των James Ryan - 1827 - 272 σελίδες
Πλήρης προβολή - Σχετικά με αυτό το βιβλίο
## A new treatise of arithmetick and book-keeping
Alexander Malcolm - 1718 - 245 σελίδες
...Cafe 3. To reduce a mixt Fraftion to the Form of a fimple Fraftion. SUllf, multiply the integral Part by the Denominator of the fractional Part, and to the Product add the Numerator ; take this Sum for the Numerator fought, which fet over the forefaid Deneminator, and this is thefimple...
## A Treatise of Arithmetic: In Whole Numbers & Fractions. Wherein All the ...
Thomas Weston - 1729 - 430 σελίδες
...the Number to be reduced is a MIX'D one} multiply the INTEGRAL Part ( of fucb MIX'D Number} by tbe DENOMINATOR of the FRACTIONAL Part, and to the PRODUCT, add the NUMERATOR ofthefaid FRACTIONAL Part } and then the SUM is the NUMERATOR, wbicb, with the fame DENOMINATOR, forms...
## A New Introduction to the Science of Algebra...
1836 - 304 σελίδες
...x 12 = 84. -= the answer. JL /\ ii i To reduce a mixed number to an improper fraction. RULE. (29.) Multiply the whole number by the denominator of the...fractional part, and to the product add the numerator, and write the sum over the denominator. This rule depends upon the, same principle as the preceding...
## Call's Decimal Arithmetic: On a New and Improved Plan Throughout, Comprising ...
1842 - 192 σελίδες
...II. TO REDUCE A MIXED NUMBER TO AN IMPROPER FRACTION. Multiply the whole number by the denominator, and to the product add the numerator ; the sum will be the numerator of the improper fraction, and the denominator mtt be the same as before. 1. Reduce 13\$- to...
## The practical arithmetic
1843
...-fri-f- as much as possible, Ans. J CASE II. — To reduce a mixed number to an improper fraction. RULE.— Multiply the whole number by the denominator of the fractional part, to the product add the numerator, and place the denominator under the sum, for the improper fraction...
## Smith and Duke's The American Statistical Arithmetic: Designed for Academies ...
Francis Henney Smith - 1845 - 282 σελίδες
...whole or mixed numbers. CASE II. 73* To reduce a mixed number to an equivalent improper fraction — RULE. Multiply the whole number by the denominator of the fractional part of the mixed number, and to this product add the numerator. Place this result over the denominator....
## The American Statistical Arithmetic: Designed for Academies and Schools
Francis Henney Smith - 1845 - 276 σελίδες
...whole or mixed numbers. CASE II. 73* To reduce a mixed number to an equivalent improper fraction — RULE. ' Multiply the whole number by the denominator of the fractional part of the mixed number, and to this product add the numerator. Place this result over the denominator....
## The Computist's Manual of Facts: And Merchant's and Mechanic's Calculator ...
Ezra S. Winslow - 1853 - 252 σελίδες
...EXAMPLE. £ = 1£ ; |f= 1&= 1£; f| = 2. To reduce a mixed fraction to an equivalent improper fraction. RULE. — Multiply the whole number by the denominator...fractional part, and to the product add the numerator, and place their sum over the said denominator. EXAMPLE. — Reduce 3£ and 12J- to improper fractions....
## Elements of arithmetic for the use of schools
William Scott - 1854 - 215 σελίδες
...the same value is obtained by reversing the preceding, thus : Multiply the integral part of the mixed number by the denominator of the fractional part, and to the product add the numerator of the fractional part ; the result is the numerator of the improper fraction, and the denominator...
## A Treatise on Arithmetic ...
Noble Heath - 1855 - 455 σελίδες
...understood the preceding article, we may proceed more expeditiously, thus : multiply the integral part by the denominator of the fractional part; and, to the product, add the numerator of the fractional part, for a numerator, under whicli place the denominator of the fractional part.... | 1,086 | 4,432 | {"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} | 3.3125 | 3 | CC-MAIN-2020-10 | latest | en | 0.550933 |
https://www.physicsforums.com/threads/slope-and-projectile-problem.662450/ | 1,532,100,593,000,000,000 | text/html | crawl-data/CC-MAIN-2018-30/segments/1531676591683.78/warc/CC-MAIN-20180720135213-20180720155213-00103.warc.gz | 946,316,355 | 19,159 | # Homework Help: Slope and projectile problem
1. Jan 4, 2013
### Lolagoeslala
1. The problem statement, all variables and given/known data
Eddie "The Eagle" Edwards takes off on the 90 m ski-jump with a horizontal velocity of 20 m/s. If the gradient of the landing slope is as shown, find the distance L along the slope covered by his jump,ignore any effect of the air on this eagle.
Image given:
http://s1176.beta.photobucket.com/user/LolaGoesLala/media/yeahok_zps7743bc20.png.html
3. The attempt at a solution
So, they have given us the horizontal velocity which is 20 m/s [ E ]
and i am not sure what the 90 m represent.
Is it the verticle length or is the diameter along the base of the triangle.
2. Jan 4, 2013
### Staff: Mentor
He started from zero velocity travelledsome dist then jumped with a horizontal vel of 20m/sec and the diagram shows the angle of the skijump.
Since he fell some distance and gained kinetic energy you should have enough info to solve the problem.
3. Jan 4, 2013
### Staff: Mentor
I think that you can ignore the "90 m"; consider it a name of the jump.
Concentrate on the fact that Eddie is launched horizontally, and that you are given information about the gradient (the "slope" of the slope, so to speak).
4. Jan 4, 2013
### haruspex
From a little Googling, the 'size' of a ski jump is to do with distance from take-off to some standard landing line, rather like par for a golf hole. If so, it doesn't supply any useful info here. So it would seem the question ought to say "with a velocity of 20 m/s horizontal", i.e., there is no vertical velocity initially. (In practice, the jump slope is a little below horizontal.)
5. Jan 4, 2013
### Lolagoeslala
Okay.
so i know the horizontal velocity = 20 m/s
θ = E 37 S
so i think i would be able to use the conservation of energy in this question.
mgh = 1/2mv^2
gh = 1/2v^2
(9.8m/s^2)h = 1/2(20m/s)^2
h = 20.4 m
so can i use sin 37 = 20.4 m / L
6. Jan 4, 2013
### Staff: Mentor
The 20 m/s is a horizontal velocity. The "h" in "mgh" pertains to a vertical displacement. So they are unrelated. Conservation of energy isn't going to cut it here.
Instead, look at Eddie's trajectory as a function of horizontal displacement and the line of the ski slope as a function of horizontal displacement.
7. Jan 4, 2013
### Lolagoeslala
well i was looking over my notes.
and you are right.
But i also found this equation
distance horizontal = v^2 sin 2θ / g
but doesn't that only work for like the velocity that includes both verticle and horizontal
8. Jan 4, 2013
### Staff: Mentor
That would be the range equation for a projectile launched with speed v at angle θ over a horizontal surface. That, too, doesn't pertain to the given situation. I doubt that you'll be able to pull a "canned" formula out of your pocket to fit this situation. Instead, you'll have to develop a method of solution.
If you step back from the problem and look at your diagram, you should be able to see that there are two functions and a point of their intersection that you're interested in. One is the parabolic trajectory of the skier, the other is the straight line of the ski slope.
If you set your origin at the launch point, can you write an equation expressing the line of the hill as a function of horizontal distance? How about the vertical position of the skier as a function of horizontal distance?
9. Jan 4, 2013
### Lolagoeslala
I am sorry but i am confused by your two question.
10. Jan 4, 2013
### Staff: Mentor
Two functions that have a point of intersection.
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11. Jan 4, 2013
### Lolagoeslala
So your first question is about the slope (blue line) and the x distance ?
12. Jan 4, 2013
### Staff: Mentor
Yes. Write an equation for it given the information that you have.
13. Jan 4, 2013
### Lolagoeslala
So like...
well the distance is just east while the blue is east 37 south to the distance horizontally
14. Jan 4, 2013
### Staff: Mentor
Hmm. Have you taken a math course in functions? Equations of lines, parabolas, and so on?
15. Jan 4, 2013
### Lolagoeslala
yeah. but isn't this physics thought? :O
16. Jan 4, 2013
### Staff: Mentor
The language of physics is mathematics. It provides the tools you need to solve problems.
Here you have an opportunity to use what you learned in your functions course to solve a physics problem. All the math you've learned will come in handy as you go forward. The trick is to recognize its applicability to a given problem
17. Jan 4, 2013
### Lolagoeslala
Oh i see..
But i don;t get it im i supposed to use the y =mb+x functions?
18. Jan 4, 2013
### Staff: Mentor
Yup. The ski slope can be represented by a straight line. The trajectory of the skier is a parabola. They intersect at a point. Physics is essentially the world described in terms of mathematics.
19. Jan 5, 2013
### Lolagoeslala
okay so if they have a point of intersection that would mean they must be equal to one another so.
if the two equations are:
y = mx
and the other one is y = -ax
combing them would be
mx = -ax
right?
20. Jan 5, 2013
### Staff: Mentor
That is correct
Not quite. One is a straight line (y = mx), but the other one is a parabola.
For the first you have to find the slope m. For the second, you need to find the equation of the parabola that matches the trajectory of Eddie.
Hint: The equations of motion for a projectile are those of a parabola in what is called "parametric form", where time "t" is the parameter. You will have to convert this to Cartesian form (y as a function of x).
21. Jan 5, 2013
### Lolagoeslala
umm does this go with the Grade 12 curriculam, the second part? and how would i find the slope if i don't have the exact information about the graph :(
isn' t there another way to solve this?
22. Jan 5, 2013
### Staff: Mentor
While I'm not familiar with your particular curriculum, I would assume that if you've taken functions then you've seen them in parametric form: x = f(t); y = g(t), so that x and y are individual functions of the parameter t. The equations of motion of the projectile are such a pair of functions, where the y-component and x-component of the trajectory are both functions of time (t).
The information to find the slope of the ski hill is certainly on the initial drawing that you posted (look at the the little triangle formed at the bottom right).
I can't think of another way that's any simpler; it uses tools that I think you must have seen and used at the grade 12 level (although as I said, not having seen your curriculum I might be making an error of judgement there. But I can't think of another approach that relies on any simpler mathematical tools).
23. Jan 5, 2013
### Lolagoeslala
okay so for the straight line it is..
Slope of hypotenuse = length of vertical arm / length of horizontal arm.
Slope of hypotenuse = 3/4 is the slope
so its y =3/4x for the straight line
now i need help with the parabola shape.
24. Jan 5, 2013
### Staff: Mentor
Make that -3/4 for the slope, since it's sloping downwards; For every 4 positive units of x forward, the curve drops by 3.
Start by writing the usual equations of motion for the x and y components of the trajectory.
25. Jan 5, 2013
### Lolagoeslala
like what do you mean by break it into x and y component or writing their equation like would u like to expand on that, it would really help me.
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# Chapter 1 Measurements - PowerPoint PPT Presentation
Chapter 1 Measurements. Prefixes and Equalities. Metric Prefixes. Increase or decrease basic unit by 10 Form new units larger or smaller than the basic units Indicate a numerical value prefix = value 1 kilo meter = 1000 meters 1 kilo gram = 1000 grams.
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Chapter 1Measurements
Prefixes and
Equalities
LecturePLUS Timberlake
Metric Prefixes
• Increase or decrease basic unit by 10
• Form new units larger or smaller than the basic units
• Indicate a numerical value
prefix = value
1 kilometer = 1000 meters
1 kilogram = 1000 grams
LecturePLUS Timberlake
Prefixes that Increase A Unit
Prefix Symbol Value
giga- G 1 000 000 000
mega- M 1 000 000
kilo- k 1 000
LecturePLUS Timberlake
Prefixes that Decrease A Unit
Prefix Symbol Value
deci- d 0.1
centi- c 0.01
milli- m 0.001
micro- (mu) 0.000 001
nano n 0.000 000 0001
LecturePLUS Timberlake
Learning Check
Match 1) length 2) mass 3) volume
____ A. A bag of tomatoes is 4.6 kg.
____ B. A person is 2.0 m tall.
____ C. A medication contains 0.50 g Aspirin.
____ D. A bottle contains 1.5 L of water.
LecturePLUS Timberlake
Solution
Match 1) length 2) mass 3) volume
_2 A. A bag of tomatoes is 4.6 kg.
_1_ B. A person is 2.0 m tall.
_2_ C. A medication contains 0.50 g Aspirin.
_3_ D. A bottle contains 1.5 L of water.
LecturePLUS Timberlake
Learning Check
Select the unit you would use to measure
1) millimeters 2) meters 3) kilometers
1) milligrams 2) grams 3) kilograms
C. The distance between two cities
1) millimeters 2) meters 3) kilometers
D. The width of an artery
1) millimeters 2) meters 3) kilometers
LecturePLUS Timberlake
Solution
2) meters
3) kilograms
C. The distance between two cities
3) kilometers
D. The width of an artery
1) millimeters
LecturePLUS Timberlake
Learning Check
Indicate the prefix to use for
1. A mass that is 1000 times greater than 1 gram
1) kilo 2) milli 3) mega
2. A length that is 1/100 of 1 meter?
1) deci 2) centi 3) milli
3. A unit of time that is 1/1000 of a second.
1) nanosecond 2) microsecond 3)millisecond
LecturePLUS Timberlake
Solution
1. 1) kilo
2. 2) centi
3. 3) millisecond
LecturePLUS Timberlake
Equalities
State the same measurement in two different units
length
10.0 in.
25.4 cm
LecturePLUS Timberlake
Some Metric Equalities
Length
1 m = 100 cm
Mass
1 kg = 1000 g
Volume
1 L = 1000 mL
LecturePLUS Timberlake
Learning Check
A. 1000 m = 1 ___ 1) mm 2) km 3) dm
B. 0.001 g = 1 ___ 1) mg 2) kg 3) dg
C. 0.1 L = 1 ___ 1) mL 2) cL 3) dL
D. 0.01 m = 1 ___ 1) mm 2) cm 3) dm
LecturePLUS Timberlake
Solution
A. 1000 m = 1 ___ 2) km
B. 0.001 g = 1 ___ 1) mg
C. 0.1 L = 1 ___ 3) dL
D. 0.01 m = 1 ___ 2) cm
LecturePLUS Timberlake
Learning Check
Give the value of the following units:
A. 1 kg = ____ g
1) 10 g 2) 100 g 3) 1000 g
B. 1 mm = ____ m
1) 0.001 m 2) 0.01 m 3) 0.1 m
LecturePLUS Timberlake
Solution
A. 1 kg = ____ g
3) 1000 g
B. 1 mm = ____ m
1) 0.001 m
LecturePLUS Timberlake
Some American Equalities
1 ft = inches
1 lb = 16 oz
1 quart = pints
1 quart = 4 cups
Why are the quantities in each pair equal?
LecturePLUS Timberlake
Some American Equalities
1 ft = 12 inches
1 lb = 16 oz
1 quart = 2 pints
1 quart = 4 cups
The quantities in each pair give the same measured amount in two different units.
LecturePLUS Timberlake
Some Metric-American Equalities
1 in. = 2.54 cm
1 qt = 946 mL
1 L = 1.06 qt
1 lb = 454 g
1 kg = 2.20 lb
Remember these for exams.
LecturePLUS Timberlake
Equalities given in a Problem
Example 1
At the store, the price of one pound of red peppers is \$2.39.
Equality: 1 lb red peppers = \$2.39
Example 2
At the gas station, one gallon of gas is \$1.34.
Equality: 1 gallon of gas = \$1.34
LecturePLUS Timberlake
Conversion Factors
Fractions in which the numerator and denominator are quantities expressed in an equality between those units
Example: 1 in. = 2.54 cm
Factors: 1 in. and 2.54 cm
2.54 cm 1 in.
LecturePLUS Timberlake
Learning Check
Write conversion factors that relate each of the following pairs of units:
A. Liters and mL
B. Hours and minutes
D. Meters and kilometers
LecturePLUS Timberlake
Solution
A. quarts and mL 1 L = 1000 mL
1 L and 1000 mL
1000 mL 1 L
B. hours and minutes 1 hr = 60 min
1 hr and 60 min
60 min 1 hr
C. meters and kilometers 1 km = 1000 m
1 km and 1000 m
1000 m 1 km
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https://trac.sagemath.org/ticket/7852?version=16 | 1,618,539,733,000,000,000 | text/html | crawl-data/CC-MAIN-2021-17/segments/1618038088471.40/warc/CC-MAIN-20210416012946-20210416042946-00079.warc.gz | 590,056,026 | 9,625 | Opened 11 years ago
Closed 10 years ago
# solve_left for RDF matrices is WRONG — at Version 16
Reported by: Owned by: was was blocker sage-4.7.2 linear algebra jason sage-4.7.2.alpha3 Rob Beezer Martin Raum, Leif Leonhardy N/A #11848
Observe the docstring for solve_left for an RDF matrix:
```sage: A = random_matrix(RDF,3)
sage: A.solve_left?
Solve the equation A*x = b, where
EXAMPLES:
sage: A = matrix(RDF, 3,3, [1,2,5,7.6,2.3,1,1,2,-1]); A
[ 1.0 2.0 5.0]
[ 7.6 2.3 1.0]
[ 1.0 2.0 -1.0]
sage: b = vector(RDF,[1,2,3])
sage: x = A.solve_left(b); x
(-0.113695090439, 1.39018087855, -0.333333333333)
sage: A*x
(1.0, 2.0, 3.0)
```
But that is solve_right.
This was evidently introduced by maybe Grout's "Switch the RDF and CDF matrices to a numpy 1.2 backend; factor out common functionality to matrix_double_dense.pyx.".
Reported by Stephanie Dietzel
Apply
to the Sage library.
### comment:1 Changed 11 years ago by jason
This might be related to #4932. I'll put this on my list for the bug day coming up.
### comment:2 Changed 10 years ago by rbeezer
• Status changed from new to needs_review
Patch corrects the naming problem, and creates upgraded solve_left and solve_right.
This required just a few touch-ups where the name had been wrong, or the improved accuracy changed results.
### comment:3 Changed 10 years ago by rbeezer
• Authors set to Rob Beezer
### comment:4 follow-up: ↓ 5 Changed 10 years ago by jhpalmieri
Without the patch, "solve_right" seems to work for nonsquare matrices over RDF, I guess because it's using the generic "solve_right" method from matrix2.pyx. With the patch, it looks like this won't work any more; is that right? Is there a good reason for not allowing square matrices? We could instead add a method `_solve_right_nonsingular_square` to matrix_double_dense.pyx, and then I think this should be called by the generic solve_right method.
For "solve_left", could we just remove the version from matrix_double_dense.pyx altogether, and just use the generic version?
### comment:5 in reply to: ↑ 4 Changed 10 years ago by rbeezer
Yes, there is some tension in handling inexact matrices with routines designed for exact matrices (which is the root issue here, I believe). `NumPy/SciPy` just does not do certain things, such as computing a rank.
I'm hoping to get some guidance from the `NumPy` folks here at Sage Days 29 right now and we can chat some more.
### comment:6 Changed 10 years ago by mraum
• Status changed from needs_review to needs_work
1) You can use svd to first get a square matrix that you can use to solve the system of linear equations. 2) Why do you copy the code for left and right solve. There is a generic fallback in matrix2.pyx. If you want to replace the docstring for this class, can't you do just that?
### comment:7 Changed 10 years ago by rbeezer
We could use a direct call to `SciPy` solve for square nonsingular and analyze/exploit the SVD for nonsingular/rectangular.
### comment:8 Changed 10 years ago by rbeezer
• Status changed from needs_work to needs_review
Finally getting back to this one.
1. solve_left and solve_right are confused at the moment - I think this is important to fix.
1. The code is different, in part because the error messages are explicit, naming rows and columns when sizes do not match.
1. The longer I think about it, the more I think we should never be feeding floating-point matrices into exact routines. We should expose the ScyPy/NumPy/LAPACK routines as much as possible and not pretend the exact routines are going to give reasonable answers as a "fallback."
1. I'm happy to try to get solutions to systems with non-square coefficient matrices with floating-point entries, but despite a lot of thought and reading, I'm not convinced of the right approach. In any event, I'd like to fix the problem at hand, and do the non-square somewhere else.
1. I am going to set this to "needs review" but I'm happy to entertain more discussion - I'll just need convincing.
Rob
### comment:9 Changed 10 years ago by mraum
What I was talking about when I mentioned the fallback is a piece of generic code for solve_left that calls solve_right. Thus you only need to implement one version. And you should, because code duplication makes mistakes more likely and maintenance harder. I will change this when reviewing this, and then will wait for your approval.
### comment:10 Changed 10 years ago by mraum
• Reviewers set to Martin Raum
• Status changed from needs_review to positive_review
I didn't touch the implementation of solve_right. I changed my mind for the following simple reason. While the code is quite short and easy to check the documentation is very different (left replaced by right). So it seems quite impractical to duplicate it.
We should think about modifying the documentation so that it gets included in the reference manual. Also there is a pseudoregression in the code. Sage doesn't pretend it could solve equations with double dense matrices as right hand side. Scipy covers also this case, so we should open a new ticket for this.
### comment:11 Changed 10 years ago by jdemeyer
• Milestone changed from sage-4.7.1 to sage-4.7.2
### comment:12 Changed 10 years ago by leif
• Description modified (diff)
• Priority changed from major to blocker
### comment:13 Changed 10 years ago by leif
• Merged in set to sage-4.7.2.alpha3
• Resolution set to fixed
• Status changed from positive_review to closed
### comment:14 Changed 10 years ago by leif
• Dependencies set to #11848
### Changed 10 years ago by leif
Reviewer patch. Apply on top of main patch, which causes a signed zero on Itanium 2.
### Changed 10 years ago by leif
Reviewer patch. Apply on top of main patch, which causes doctests to fail on a couple of systems due to noisy zero terms.
### comment:15 Changed 10 years ago by leif
• Description modified (diff)
• Reviewers changed from Martin Raum to Martin Raum, Leif Leonhardy
Attached two reviewer patches fixing doctest errors on some systems.
Third patch to fix doctest errors in `sage/matrix/matrix_double_dense.pyx` coming soon.
The patch to the preparser examples requires #11848.
### Changed 10 years ago by leif
Reviewer patch. Apply on top of main patch, which causes another doctest to fail on a couple of systems due to a noisy zero in a vector result.
### comment:16 Changed 10 years ago by leif
• Description modified (diff)
Third reviewer patch (fixing a doctest error in `matrix_double_dense.pyx`) is up.
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Equity Multiplier. Lets say that Company Z has total assets of 100000. An alternative formula for the equity multiplier is the reciprocal of the equity ratio. Also it can be calculated by anyone who has. Equity multiplier differs from other debt-management ratios in that it is calculated by comparing average values instead of closing values.
Cash Conversion Cycle Accounting And Finance Cash Financial Strategies From in.pinterest.com
If the ratio is 5 equity multiplier means investment in total assets is 5 times the investment by equity shareholders. The equity multiplier is similar to the concept of the debt ratio. This ratio in the denominator of the formula can also be found by subtracting one minus the debt ratio. This ratio is the financial leverage of a company that determines how many times the equity of a company does a company have as compared to its assets. The formula is. There is no perfect equity multiplier level since it varies by industry the amount of assets available to use for collateral and the lending.
### A high equity multiplier means that the companys capital structure is more leveraged ie.
The equity multiplier is also a kind of leverage ratio which is any method of determining a companys financial leverageOther leverage ratio equations include the debt-to-equity ratio which assesses financial leverage by taking a companys total liability and dividing it by the shareholders equityOther leverage ratio equations are similar using some formulaic combination of a companys. As previously stated a companys assets are equal to debt plus equity. Or Multiplier 100000 20000 5. The equity multiplier is also a kind of leverage ratio which is any method of determining a companys financial leverageOther leverage ratio equations include the debt-to-equity ratio which assesses financial leverage by taking a companys total liability and dividing it by the shareholders equityOther leverage ratio equations are similar using some formulaic combination of a companys. Relationship between debt ratio and equity multiplier. An equity multiplier might sound like a complicated financial figure.
Source: in.pinterest.com
The equity multiplier is a risk. Equity Multiplier is a key financial metric that measures the level of debt financing in a business. What is Equity Multiplier EM. Total Assets Total Shareholders Equity. On the other hand the ratio also indicates how much debt financing is being used.
Source: id.pinterest.com
Its total equity is 20000. As previously stated a companys assets are equal to debt plus equity. To derive the equation Debt ratio 1 1Equity multiplier we will do the following steps. Therefore the equity ratio calculates the equity portion of a companys assets. The equity multiplier is a risk.
Source: pinterest.com
It measures the total equity that has been used to finance the companys assets. Since the equity multiplier measures the leverage level of the company the higher it is the greater the extent of leverage. An alternative formula for the equity multiplier is the reciprocal of the equity ratio. The ratio is intended to measure the extent to which equity is used to pay for all types of company assets. It measures a firms assets that are financed by its shareholders.
Source: pinterest.com
It does this by comparing total assets with total shareholders equity. An equity multiplier might sound like a complicated financial figure. What is Equity Multiplier. Its actually quite simple to. The equity multiple is a performance metric that helps put the IRR into perspective by sizing up the return in absolute terms.
Source: in.pinterest.com
The equity multiplier is a useful tool for determining how a company finances its activities. Equity multiplier is a leverage ratio that measures the portion of the companys assets Types of Assets Common types of assets include current non-current physical intangible operating and non-operating. Also it can be calculated by anyone who has. The equity multiplier is the ratio of a companys total assets to its stockholders equity. Formula to Calculate Equity Multiplier.
Source: in.pinterest.com
The equity multiplier is a useful tool for determining how a company finances its activities. This ratio is the financial leverage of a company that determines how many times the equity of a company does a company have as compared to its assets. This is a simple example but after calculating this ratio we would be able to know how much assets are financed by equity and how much assets are financed by debt. It measures a firms assets that are financed by its shareholders. The equity multiplier is also a kind of leverage ratio which is any method of determining a companys financial leverageOther leverage ratio equations include the debt-to-equity ratio which assesses financial leverage by taking a companys total liability and dividing it by the shareholders equityOther leverage ratio equations are similar using some formulaic combination of a companys.
Source: pinterest.com
It has more debt. It measures a firms assets that are financed by its shareholders. It does this by comparing total assets with total shareholders equity. An equity multiplier might sound like a complicated financial figure. Equity multiplier formula calculates total assets to total shareholders equity.
Source: in.pinterest.com
There is no perfect equity multiplier level since it varies by industry the amount of assets available to use for collateral and the lending. An equity multiplier might sound like a complicated financial figure. The values for the total assets and total shareholders equity can be found on the balance sheet so check that before calculating. The equity multiplier is a risk. The equity multiplier is similar to the concept of the debt ratio.
Source: in.pinterest.com
Correctly identifying and that are financed by equity Stockholders Equity Stockholders Equity also known as Shareholders Equity is an account on a. It measures a firms assets that are financed by its shareholders. Therefore the equity ratio calculates the equity portion of a companys assets. Formula to Calculate Equity Multiplier. An alternative formula for the equity multiplier is the reciprocal of the equity ratio.
Source: in.pinterest.com
In other words it is defined as a ratio of Total Assets to Shareholders Equity. An alternative formula for the equity multiplier is the reciprocal of the equity ratio. Therefore the equity ratio calculates the equity portion of a companys assets. In other words it is defined as a ratio of Total Assets to Shareholders Equity. This ratio in the denominator of the formula can also be found by subtracting one minus the debt ratio.
Source: in.pinterest.com
Equity multiplier is a leverage ratio that measures the portion of the companys assets Types of Assets Common types of assets include current non-current physical intangible operating and non-operating. Its total equity is 20000. Equity multiplier formula calculates total assets to total shareholders equity. Its actually quite simple to. An equity multiplier might sound like a complicated financial figure.
Source: pinterest.com
The equity multiplier is a risk. Equity multiplier also called leverage ratio or financial leverage ratio is the ratio of total assets of a company to its shareholders equity. The equity multiple is a performance metric that helps put the IRR into perspective by sizing up the return in absolute terms. The equity multiplier is also a kind of leverage ratio which is any method of determining a companys financial leverageOther leverage ratio equations include the debt-to-equity ratio which assesses financial leverage by taking a companys total liability and dividing it by the shareholders equityOther leverage ratio equations are similar using some formulaic combination of a companys. Its actually quite simple to.
Source: in.pinterest.com
Therefore the equity ratio calculates the equity portion of a companys assets. It is calculated by dividing the total assets by the common shareholders equity. To derive the equation Debt ratio 1 1Equity multiplier we will do the following steps. If the ratio is 5 equity multiplier means investment in total assets is 5 times the investment by equity shareholders. The equity multiplier is a risk.
Source: pinterest.com
In other words it is defined as a ratio of Total Assets to Shareholders Equity. Equity Multiplier is a key financial metric that measures the level of debt financing in a business. Equity multiplier is a measure of a firms assets financed through equity showing how much equity is used to acquire assets. The formula is calculated like this. The formula is.
Source: in.pinterest.com
Equity Multiplier is a non-participating equity-linked investment product which offers nominal insurance coverage and can be surrendered at any time for the bid value of the total of the units allocated to the policy less a transaction fee. The equity multiplier is a ratio that determines how much of a companys assets is funded or owed by its shareholders by comparing its total assets against total shareholders equity. In other words the equity multiplier shows the percentage. Since the equity multiplier measures the leverage level of the company the higher it is the greater the extent of leverage. Total Assets Total Shareholders Equity.
Source: id.pinterest.com
Total Assets Total Equity Equity Multiplier. To derive the equation Debt ratio 1 1Equity multiplier we will do the following steps. Total Assets Total Shareholders Equity. It is calculated by dividing the total assets by the common shareholders equity. In other words the equity multiplier shows the percentage.
Source: in.pinterest.com
Equity multiplier is a leverage ratio that measures the portion of the companys assets Types of Assets Common types of assets include current non-current physical intangible operating and non-operating. This ratio is the financial leverage of a company that determines how many times the equity of a company does a company have as compared to its assets. The equity multiplier is a financial leverage ratio. The equity multiplier is a risk. In other words the equity multiplier shows the percentage.
Source: in.pinterest.com
On the other hand the ratio also indicates how much debt financing is being used. This ratio in the denominator of the formula can also be found by subtracting one minus the debt ratio. Conversely its a financial leverage ratio allowing you to calculate how much of a firms asset is financed through debt. An alternative formula for the equity multiplier is the reciprocal of the equity ratio. Formula to Calculate Equity Multiplier.
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Ques:- How will you rate yourself .
Ques:- Kamal started a business investing Rs. 9000. After five months, Sameer joined with a capital of Rs. 8000. If at the end of the year, they earn a profit of Rs. 6970, then what will be the share of Sameer in the profit?
A. Rs. 1883.78
B. Rs. 2380
C. Rs. 3690
D. Rs. 3864
2380
Ques:- A contribution of Rs. 500 was raised from 500 people. The fee was as follows: Men: Rs.3.00 each Women: Rs. 2.00 each Children: 0.48 each. If number of women is more than number of men, how many children are there?
Ques:- Describe a situation in where you had a task that was quite demanding and what was the result of it?
Ques:- Co-ordination should be an individual responsibility rather than the other insisting the co-ordination. Justify your answer.
Ques:- At what time after 4.00 p.m. is the minutes hand of a clock exactly aligned with the hour hand?
Ques:- The greatest four digit number which is exactly divisible by each one of the numbers 12, 18, 21 and 28
A. 9288
B. 9828
C. 9882
D. 9928
9828
Ques:- 97 : 89 :: 43 : __
Ques:- The number of prime factors in the expression (6)10 x (7)17 x (11)27 is
A. 44
B. 54
C. 64
D. 71
610 × 717 × 1127
= (2 × 3)10 × 717 × 1127
= 210 × 310 × 717 × 1127
Number of prime factors in the given expression
= (10 + 10 + 17 + 27)
= 64
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Ques:- About me, my family & qualification.
Ques:- In how much time will a train of length 100 m, moving at 36 kmph cross an electric pole?
time = distance / speed
speed = 36*(5/18) m/s=10m/s
distance = 100m
time=100/10s = 10sec
Ques:- Sell me this stapler?(this pencil?this clock?or some other object on interviewer?s desk).
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I would design a voice integrated clock that reads out the time aloud whenever people ask for time
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Ques:- A man takes twice as long to row a distance against the stream as to row the same distance in favour of the stream. The ratio of the speed of the boat (in still water) and the stream is:
Ques:- The minute hand of a clock overtakes the hour hand at intervals of 64 minutes of correct time. How much a day does the clock gain or lose?
Ques:- A person lent a certain sum of money at 4% per annum at simple interest and in 8 years the interest amounted to Rs.340 less than the sum lent. What was the sum lent?
X-340 = X x 4 x 8/ 100
100X – 34000 = 32X
68X = 34000
X = 34000/68
X= 500.
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Ques:- B – 1, B – 2 and B – 3 are three buses that travel from Mumbai to Delhi. Each bus starts at a different time and arrives at a different time. The digit in the bus number and the order of their departure of arrival is not the same. The first bus to leave Mumbai is the third bus to reach Delhi. Which is the first bus to leave Mumbai?
B1
Ques:- A certain sum of money at simple interest amounted Rs.840 in 10 years at 3% per annum, evaluate the sum?
(p*r*t)/100 = I ………………..(p*3*10)/100 = 840 …..p = 84000/30 = 2800
Ques:- In a series of six consecutive even numbers, the sum of the second and sixth numbers is 24. What is the fourth number?
2a; 2a+2; 2a+4; 2a+6; 2a+8; 2a+10
t_2 + t_6 = 24 => 2a+2 + 2a + 10 = 24 => a = 3
therefore t_4 = 2(3) + 6 = 12
Ques:- Did you watched movies in your college life? How you used to commute for movies?
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Ques:- X, Y and Z can do a piece of work in 24, 30 and 40 days respectively. They start the work together but Z leaves 4 days before the completion of the work. In how many days is the work done?
One day’s work of A, B and C = (1/24 + 1/30 + 1/40) = 1/10.
C leaves 4 days before completion of the work, which means only A and B work during the last 4 days.
Work done by A and B together in the last 4 days = 4 (1/24 + 1/30) = 3/10.
Remaining Work = 7/10, which was done by A,B and C in the initial number of days.
Number of days required for this initial work = 7 days.
Thus, the total numbers of days required = 4 + 7 = 11 days.
Ques:- There are 9 coins. Out of which one is odd one i.e weight is less or more. How many iterations of weighing are required to find odd coin?
How will you know the odd is in lighter one or heavier one from only one weighing. It will require 2 weighing to find the odd set and one weighing for odd coin in that set i.e total 3 weighings.
Ques:- How do you keep your fitness knowledge up to date?
Ques:- Difference between two numbers is 5, six times of the smaller lacks by 6 from the four times of the greater. Find the numbers? | 1,413 | 4,673 | {"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} | 3.078125 | 3 | CC-MAIN-2024-22 | latest | en | 0.921029 |
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Question
Asked 2/18/2009 6:47:25 AM
Updated 5/7/2014 8:08:53 PM
f
Original conversation
User: fine
Weegy: I'm sorry what is your question?
blackstarform|Points 154|Rating ** (+30 -5)
User: how many states do we have in america
User: how many continents do we have in the world
User: are u serious
User: how does God look like
User: which is the smallest but coldest place in north america
Weegy: Coldest Place is Plateau Station, Antarctica
Expert answered|flmom08|Points 787|Rating ***** (+153 -8)
User: how does Jesus look like
Weegy: onesexysq...Jesus is not arabic ..he didn't speak arabic ...the arab came to that area after islam,they were living which is now called saudia [ ]
Expert answered|charlencharg|Points 1597|Rating ***** (+319 -1)
Question
Asked 2/18/2009 6:47:25 AM
Updated 5/7/2014 8:08:53 PM
Rating
8
There are 50 states in United States of America.
Added 5/7/2014 8:08:53 PM
This answer has been confirmed as correct and helpful.
Confirmed by jeifunk [5/7/2014 8:17:50 PM]
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Home | Contact | Blog | About | Terms | Privacy | © Purple Inc. | 1,107 | 3,543 | {"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} | 2.515625 | 3 | CC-MAIN-2023-23 | longest | en | 0.927774 |
http://mathoverflow.net/questions/38551/equivalence-of-families-of-objects-with-the-same-counting-function/38555 | 1,469,626,508,000,000,000 | text/html | crawl-data/CC-MAIN-2016-30/segments/1469257826907.66/warc/CC-MAIN-20160723071026-00235-ip-10-185-27-174.ec2.internal.warc.gz | 159,471,551 | 17,620 | # Equivalence of families of objects with the same counting function
Consider two countable families of objects, given as unions of finite subfamilies:
$F^k = \bigcup_{n \in \mathbb{N}} F^k_n$, k = 1,2.
Let there be a bijection $f: F^1 \rightarrow F^2$ such that $x \in F^1_n \Leftrightarrow f(x) \in F^2_n$ for all n $\in \mathbb{N}$.
This means: The two families have the same counting functions $f^1(n) = f^2(n)$ for all n $\in \mathbb{N}$ with $f^k(n) = |F^k_n|$.
This may be by sheer accident, or it may be because the two families are in some sense essentially the same.
Can the notions of "by accident" and "essentially the same" be distinguished in this context, and how?
"Essentially the same" might mean: "there is a computable bijection" and "by accident" might mean: "there is no computable bijection". Or might category theoretical notions lead further?
Are there known examples of two families as above that have the same counting functions by accident (in the meaning just mentioned or another one)?
PS: More sensible tags are welcome!
-
"essentially the same family" is nicely (well, this is of course subjective) captured by the categorical notion of species and their isomorphisms. It is a much stronger than a computable bijection. – Philippe Nadeau Sep 13 '10 at 10:19
Thank you! This answers question 1. What about question 2? – Hans Stricker Sep 13 '10 at 10:23
This can be also answered philosophically. Surely we can define 'by accident' formally, and then arbitrarily construct sets of objects that have the same counting function but with is no -meaningful- isomorphism. But then such a construction is most likely not between anything interesting combinatorially. That is, we -act- like every pair of sets with a bijection has a meaningful bijection, just that we may not have found one yet. On the other hand, this may just be motivation to look at those numerical identities that don't yet have a satisfying combinatorial interpretation. – Mitch Sep 13 '10 at 15:31
If you adopt Philippe Nadeau's proposal to define "essentially the same" in terms of isomorphism of species, then a standard example of "accidental" is the following. For any finite set $S$, there are just as many linear orderings of S as there are permutations of $S$ (i.e., bijections from $S$ to itself), namely $|S|!$. But the two species are not isomorphic. There is a distinguished permutation, namely the identity, but there is no distinguished linear ordering (provided $|S|>1$).
Some people feel that these two are, nevertheless, in some sense the same. (In fact, some people indiscriminately use the word "permutation" for both.) That feeling can be formalized in the observation that, if you choose one linear ordering of $S$, then it determines a natural bijection between the linear orderings and the permutations: Given a permutation, apply it to the chosen linear ordering. So people who want to think of these two species as essentially the same would want a weakening of "isomorphism of species" that would allow this sort of "isomorphism modulo an arbitrary choice." Unfortunately, it's not clear how big an object could reasonably be arbitrarily chosen --- presumably not a whole isomorphism. So I don't see a good way to make this intuition precise; as a result, I'm inclined to stick with "isomorphism of species" and to accept that linear orderings and permutations are not essentially the same.
-
That's the kind of example of "accidental" I was looking for. Thank you, Andreas! – Hans Stricker Sep 13 '10 at 17:56
That touches upon a question I return from time to time: for "linear" species (i.e., functors from finite ordered sets into finite sets), any two that have the same cardinality are isomorphic. So, is there any natural notion of isomorphism "inbetween" species and linear species? – Martin Rubey Sep 13 '10 at 20:21
@Martin Rubey: Take the objects of the domain category to be finite sets with distinguished elements. Then you have a natural bijection between the even-sized subsets of S and the odd-sized ones, namely, remove the distinguished element from those subsets that contain it and add it to those that don't. Without a distinguished element (or at least a distinguished odd-sized subset), there would be no natural bijection witnessing the fact that finite nonempty sets have equally many even- and odd-sized subsets. – Andreas Blass Sep 14 '10 at 16:16
Partitions of $n$ with parts congruent to $1$ or $4$ modulo $5$ are known to be equinumerous with those having difference between successive parts at least equal to $2$ (cf. Rogers-Ramanujan identities); no "direct" bijection is known (although there are computable ones, cf. Garsia and Milne's involution principle).
Some work I think of Igor Pak showed that such a bijection is forbidden to be constructed in a certain way (sorry for the vague formulation), and therefore this might be one of the (rare) case of accidents.
-
That's funny: Igor Pak just commented my other question mathoverflow.net/questions/38541/… – Hans Stricker Sep 13 '10 at 13:51
Do you think, "rare" can eventually be quantified, maybe like "almost none"? – Hans Stricker Sep 13 '10 at 13:53
Igor's definition of a geometric bijective proof can be found in his preprint math.ucla.edu/~pak/papers/stab5.pdf . He shows that almost all classical bijective proofs are geometric, and that any geometric bijection has a property called asymptotic stability. He claims that there is no asymptotically stable bijection proving the Roger-Ramanujan identity, but cites the details to a "forthcoming paper" with the title "Rogers-Ramanujan bijections are not geometric". As far as I know, that preprint has not appeared yet. – David Speyer Sep 13 '10 at 15:31 | 1,401 | 5,736 | {"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} | 3.171875 | 3 | CC-MAIN-2016-30 | latest | en | 0.926313 |
https://math.stackexchange.com/questions/866220/prove-or-disapprove-the-statement-fn-thetaf-fracn2 | 1,571,479,360,000,000,000 | text/html | crawl-data/CC-MAIN-2019-43/segments/1570986692723.54/warc/CC-MAIN-20191019090937-20191019114437-00495.warc.gz | 586,037,283 | 32,422 | # Prove or disapprove the statement: $f(n)=\Theta(f(\frac{n}{2}))$
Prove or disapprove the statement:
$$f(n)=\Theta(f(\frac{n}{2}))$$
where $f$ is an asymptotically positive function.
I have thought the following:
Let $f(n)=\Theta(f(\frac{n}{2}))$.Then $\exists c_1,c_2>0 \text{ and } n_0 \geq 1 \text{ such that } \forall n \geq n_0:$
$$c_1 f(\frac{n}{2}) \leq f(n) \leq c_2 f(\frac{n}{2})$$
Let $f(n)=2^n$.Then:
$$c_1 2^{\frac{n}{2}} \leq 2^n \leq c_2 2^{\frac{n}{2}} \Rightarrow c_1 \leq 2^{\frac{n}{2}} \leq c_2$$
$$2^{\frac{n}{2}} \leq c_2 \Rightarrow 2^n \leq c_2^2 \Rightarrow n \leq \lg c_2^2 \text{ Contradiction}$$
Could you tell me if it is right?
• It's true for some functions but not for others. Your counterexample is perfect. – Antonio Vargas Jul 13 '14 at 18:48
• Great!!!Thank you very much!!! – evinda Jul 13 '14 at 18:51
• In the future just use the (asymptotics) tag. No need for the "big-o-notation" tag. – Antonio Vargas Jul 14 '14 at 6:24
• @AntonioVargas A ok!!!I will take it into consideration!!! :) – evinda Jul 14 '14 at 14:32
## 2 Answers
As mentioned in the comments, your work is correct (and thus the original proposition is false).
Just set $f=f(n) = 2^{\frac{n}{2}}, \ g=g(n) = 2^n$ and take $\lim_n \frac{f}{g} = 0$, so $f <c_1 g \ \forall \ c_1>0$ and $n>n_0$ or simply $f=o(g)$. Clearly $\lim_n \frac{g}{f} = \infty$, so LHS of the inequality is never fulfilled: $\not \exists c_2 \ \text{s.t.} f>c_2g \ \forall n>n_0$ or simply $g=\omega(f)$. | 577 | 1,495 | {"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} | 4.09375 | 4 | CC-MAIN-2019-43 | latest | en | 0.613171 |
https://www.wordunscrambler.net/unscramble-nienies | 1,652,691,824,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662510097.3/warc/CC-MAIN-20220516073101-20220516103101-00561.warc.gz | 1,255,794,261 | 14,519 | # Unscramble NIENIES
NIENIES unscrambles into 38 different words! We have all of them and the meanings below! Enter any word and we will UNSCRAMBLE IT!
### 2 letter words made by unscrambling NIENIES
#### Unscrambled 7 2 Letter Words
Above are the words made by unscrambling NIENIES (EEIINNS). To further help you, here are a few lists related to/with the letters NIENIES
### The Value of NIENIES In Word Scramble Games
The letters NIENIES are worth 7 points in Scrabble
The letters NIENIES are worth 9 in points Words With Friends
• N = 2 points in WWF & 1 points in Scrabble
• I = 1 points in WWF & 1 points in Scrabble
• E = 1 points in WWF & 1 points in Scrabble
• N = 2 points in WWF & 1 points in Scrabble
• I = 1 points in WWF & 1 points in Scrabble
• E = 1 points in WWF & 1 points in Scrabble
• S = 1 points in WWF & 1 points in Scrabble
## What Does NIENIES Mean... If you Unscramble it?
### Possible Definitions of NIENIES
If we unscramble these letters, NIENIES, it and makes several words. Here is one of the definitions for a word that uses all the unscrambled letters:
### neineis
• Sorry. I don't have the meaning of this word.
## Permutations of NIENIES
According to our other word scramble maker, NIENIES can be scrambled in many ways. The different ways a word can be scrambled is called "permutations" of the word.
#### Definition of Permutation
a way, especially one of several possible variations, in which a set or number of things can be ordered or arranged.
How is this helpful? Well, it shows you the letters nienies scrambled in different ways That way you will recognize the set of letters more easily. It will help you the next time NIENIES comes up in a word scramble game.
We stopped it at 40, but there are so many ways to scramble NIENIES!
### Scramble Words
Unscramble these letters to make words...
scrambled using word scrambler... | 519 | 1,888 | {"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} | 2.96875 | 3 | CC-MAIN-2022-21 | latest | en | 0.865243 |
https://number.academy/14169 | 1,660,122,357,000,000,000 | text/html | crawl-data/CC-MAIN-2022-33/segments/1659882571150.88/warc/CC-MAIN-20220810070501-20220810100501-00185.warc.gz | 416,352,758 | 12,288 | # Number 14169
Number 14,169 spell 🔊, write in words: fourteen thousand, one hundred and sixty-nine . Ordinal number 14169th is said 🔊 and write: fourteen thousand, one hundred and sixty-ninth. The meaning of number 14169 in Maths: Is Prime? Factorization and prime factors tree. The square root and cube root of 14169. What is 14169 in computer science, numerology, codes and images, writing and naming in other languages. Other interesting facts related to 14169.
## What is 14,169 in other units
The decimal (Arabic) number 14169 converted to a Roman number is (X)(IV)CLXIX. Roman and decimal number conversions.
#### Weight conversion
14169 kilograms (kg) = 31237.0 pounds (lbs)
14169 pounds (lbs) = 6427.0 kilograms (kg)
#### Length conversion
14169 kilometers (km) equals to 8805 miles (mi).
14169 miles (mi) equals to 22803 kilometers (km).
14169 meters (m) equals to 46486 feet (ft).
14169 feet (ft) equals 4319 meters (m).
14169 centimeters (cm) equals to 5578.3 inches (in).
14169 inches (in) equals to 35989.3 centimeters (cm).
#### Temperature conversion
14169° Fahrenheit (°F) equals to 7853.9° Celsius (°C)
14169° Celsius (°C) equals to 25536.2° Fahrenheit (°F)
#### Time conversion
(hours, minutes, seconds, days, weeks)
14169 seconds equals to 3 hours, 56 minutes, 9 seconds
14169 minutes equals to 1 week, 2 days, 20 hours, 9 minutes
### Codes and images of the number 14169
Number 14169 morse code: .---- ....- .---- -.... ----.
Sign language for number 14169:
Number 14169 in braille:
Images of the number
Image (1) of the numberImage (2) of the number
More images, other sizes, codes and colors ...
## Mathematics of no. 14169
### Multiplications
#### Multiplication table of 14169
14169 multiplied by two equals 28338 (14169 x 2 = 28338).
14169 multiplied by three equals 42507 (14169 x 3 = 42507).
14169 multiplied by four equals 56676 (14169 x 4 = 56676).
14169 multiplied by five equals 70845 (14169 x 5 = 70845).
14169 multiplied by six equals 85014 (14169 x 6 = 85014).
14169 multiplied by seven equals 99183 (14169 x 7 = 99183).
14169 multiplied by eight equals 113352 (14169 x 8 = 113352).
14169 multiplied by nine equals 127521 (14169 x 9 = 127521).
show multiplications by 6, 7, 8, 9 ...
### Fractions: decimal fraction and common fraction
#### Fraction table of 14169
Half of 14169 is 7084,5 (14169 / 2 = 7084,5 = 7084 1/2).
One third of 14169 is 4723 (14169 / 3 = 4723).
One quarter of 14169 is 3542,25 (14169 / 4 = 3542,25 = 3542 1/4).
One fifth of 14169 is 2833,8 (14169 / 5 = 2833,8 = 2833 4/5).
One sixth of 14169 is 2361,5 (14169 / 6 = 2361,5 = 2361 1/2).
One seventh of 14169 is 2024,1429 (14169 / 7 = 2024,1429 = 2024 1/7).
One eighth of 14169 is 1771,125 (14169 / 8 = 1771,125 = 1771 1/8).
One ninth of 14169 is 1574,3333 (14169 / 9 = 1574,3333 = 1574 1/3).
show fractions by 6, 7, 8, 9 ...
### Calculator
14169
#### Is Prime?
The number 14169 is not a prime number. The closest prime numbers are 14159, 14173.
#### Factorization and factors (dividers)
The prime factors of 14169 are 3 * 4723
The factors of 14169 are 1 , 3 , 4723 , 14169
Total factors 4.
Sum of factors 18896 (4727).
#### Powers
The second power of 141692 is 200.760.561.
The third power of 141693 is 2.844.576.388.809.
#### Roots
The square root √14169 is 119,033609.
The cube root of 314169 is 24,198015.
#### Logarithms
The natural logarithm of No. ln 14169 = loge 14169 = 9,558812.
The logarithm to base 10 of No. log10 14169 = 4,151339.
The Napierian logarithm of No. log1/e 14169 = -9,558812.
### Trigonometric functions
The cosine of 14169 is 0,914255.
The sine of 14169 is 0,40514.
The tangent of 14169 is 0,443137.
### Properties of the number 14169
Is a Friedman number: No
Is a Fibonacci number: No
Is a Bell number: No
Is a palindromic number: No
Is a pentagonal number: No
Is a perfect number: No
## Number 14169 in Computer Science
Code typeCode value
14169 Number of bytes13.8KB
Unix timeUnix time 14169 is equal to Thursday Jan. 1, 1970, 3:56:09 a.m. GMT
IPv4, IPv6Number 14169 internet address in dotted format v4 0.0.55.89, v6 ::3759
14169 Decimal = 11011101011001 Binary
14169 Decimal = 201102210 Ternary
14169 Decimal = 33531 Octal
14169 Decimal = 3759 Hexadecimal (0x3759 hex)
14169 BASE64MTQxNjk=
14169 MD52f093e72fa038b855c80131ec3fba75c
14169 SHA1f7c340b9b90b74becd0d5753b767df53671b26b5
14169 SHA224c55a57303544ce3cb4467317b7949587e4d910ec980ba8cd42b7d049
14169 SHA25605e61cc57f43fecf7ee37306c9d9155374fbe52debaa1612a09dba4209b2570d
14169 SHA3842bc20f777304b1997d33069a7e216e5c4d607369becde49b76b9e392fb67c7d360f6c034a6592b4dfde25b0ddd6ba0fe
More SHA codes related to the number 14169 ...
If you know something interesting about the 14169 number that you did not find on this page, do not hesitate to write us here.
## Numerology 14169
### Character frequency in number 14169
Character (importance) frequency for numerology.
Character: Frequency: 1 2 4 1 6 1 9 1
### Classical numerology
According to classical numerology, to know what each number means, you have to reduce it to a single figure, with the number 14169, the numbers 1+4+1+6+9 = 2+1 = 3 are added and the meaning of the number 3 is sought.
## Interesting facts about the number 14169
### Asteroids
• (14169) 1998 UZ24 is asteroid number 14169. It was discovered by F. B. Zoltowski from Woomera on 10/25/1998.
### Distances between cities
• There is a 8,805 miles (14,169 km) direct distance between Alīgarh (India) and Ciudad Guayana (Venezuela).
• There is a 8,805 miles (14,169 km) direct distance between Curitiba (Brazil) and Mysore (India).
• There is a 8,805 miles (14,169 km) direct distance between Guatemala City (Guatemala) and Lanzhou (China).
• There is a 8,805 miles (14,169 km) direct distance between Kalyān (India) and Santiago de los Caballeros (Dominican republic).
• More distances between cities ...
• There is a 8,805 miles (14,169 km) direct distance between Salem (India) and San Jose (USA).
## № 14,169 in other languages
How to say or write the number fourteen thousand, one hundred and sixty-nine in Spanish, German, French and other languages. The character used as the thousands separator.
Spanish: 🔊 (número 14.169) catorce mil ciento sesenta y nueve German: 🔊 (Anzahl 14.169) vierzehntausendeinhundertneunundsechzig French: 🔊 (nombre 14 169) quatorze mille cent soixante-neuf Portuguese: 🔊 (número 14 169) catorze mil, cento e sessenta e nove Chinese: 🔊 (数 14 169) 一万四千一百六十九 Arabian: 🔊 (عدد 14,169) أربعة عشر ألفاً و مائةتسعة و ستون Czech: 🔊 (číslo 14 169) čtrnáct tisíc sto šedesát devět Korean: 🔊 (번호 14,169) 만 사천백육십구 Danish: 🔊 (nummer 14 169) fjortentusinde og ethundrede og niogtreds Dutch: 🔊 (nummer 14 169) veertienduizendhonderdnegenenzestig Japanese: 🔊 (数 14,169) 一万四千百六十九 Indonesian: 🔊 (jumlah 14.169) empat belas ribu seratus enam puluh sembilan Italian: 🔊 (numero 14 169) quattordicimilacentosessantanove Norwegian: 🔊 (nummer 14 169) fjorten tusen, en hundre og seksti-ni Polish: 🔊 (liczba 14 169) czternaście tysięcy sto sześćdziesiąt dziewięć Russian: 🔊 (номер 14 169) четырнадцать тысяч сто шестьдесят девять Turkish: 🔊 (numara 14,169) ondörtbinyüzaltmışdokuz Thai: 🔊 (จำนวน 14 169) หนึ่งหมื่นสี่พันหนึ่งร้อยหกสิบเก้า Ukrainian: 🔊 (номер 14 169) чотирнадцять тисяч сто шiстдесят дев'ять Vietnamese: 🔊 (con số 14.169) mười bốn nghìn một trăm sáu mươi chín Other languages ...
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If you know something interesting about the number 14169 or any natural number (positive integer) please write us here or on facebook. | 2,606 | 7,554 | {"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} | 2.984375 | 3 | CC-MAIN-2022-33 | latest | en | 0.638392 |
https://oeis.org/A222555/internal | 1,713,588,129,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296817474.31/warc/CC-MAIN-20240420025340-20240420055340-00549.warc.gz | 392,701,873 | 3,178 | The OEIS is supported by the many generous donors to the OEIS Foundation.
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A222555 T(n,k)=Number of length (n+k)X1 arrays of occupancy after each element moves up to +-k places but not 0 9
%I #4 Feb 24 2013 16:10:18
%S 1,7,2,31,20,4,121,102,64,8,456,427,359,208,16,1709,1668,1562,1279,
%T 651,32,6427,6372,6220,5761,4537,2056,64,24301,24230,24024,23341,
%U 21239,15929,6496,128,92368,92279,92011,91052,87752,78245,56041,20483,256,352705
%N T(n,k)=Number of length (n+k)X1 arrays of occupancy after each element moves up to +-k places but not 0
%C Table starts
%C ...1.....7.....31....121....456...1709...6427..24301..92368.352705
%C ...2....20....102....427...1668...6372..24230..92279.352596
%C ...4....64....359...1562...6220..24024..92011.352258
%C ...8...208...1279...5761..23341..91052.350967
%C ..16...651...4537..21239..87752.346091
%C ..32..2056..15929..78245.330274
%C ..64..6496..56041.287858
%C .128.20483.197313
%C .256.64627
%C .512
%H R. H. Hardin, <a href="/A222555/b222555.txt">Table of n, a(n) for n = 1..55</a>
%e Some solutions for n=3 k=4
%e ..0....1....3....1....0....1....0....2....0....2....0....0....2....0....1....0
%e ..2....0....0....0....1....2....0....2....3....2....1....0....0....1....0....1
%e ..1....1....0....0....0....1....3....2....0....3....0....2....1....2....3....0
%e ..1....0....1....4....1....1....1....1....1....0....0....2....0....0....3....0
%e ..0....2....1....0....1....2....0....0....0....0....0....0....3....4....0....1
%e ..3....2....1....1....0....0....1....0....1....0....4....2....0....0....0....4
%e ..0....1....1....1....4....0....2....0....2....0....2....1....1....0....0....1
%Y Column 1 is A000079(n-1)
%Y Row 1 is A048775
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_ Feb 24 2013
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Last modified April 20 00:26 EDT 2024. Contains 371798 sequences. (Running on oeis4.) | 846 | 2,164 | {"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} | 2.890625 | 3 | CC-MAIN-2024-18 | latest | en | 0.658508 |
https://holooly.com/solutions-v20/the-kali-company-has-two-divisions-the-paper-division-makes-paper-that-costs-1000-per-ton-this-division-makes-10000-tons-of-paper-each-year-and-can-either-sell-all-of-the-paper-in-the-market-for/ | 1,660,469,784,000,000,000 | text/html | crawl-data/CC-MAIN-2022-33/segments/1659882572021.17/warc/CC-MAIN-20220814083156-20220814113156-00603.warc.gz | 311,885,638 | 24,794 | Products
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## Q. 6.8
The Kali Company has two divisions. The Paper division makes paper that costs \$1,000 per ton. This division makes 10,000 tons of paper each year, and can either sell all of the paper in the market for \$1,500 per ton, or transfer all of the paper to the Printing division of Kali Company. The Printing division converts the paper into gift wrap at an additional cost of \$4,000 per ton. The gift wrap can be sold for \$5,200 per ton.
a. What is the profit of the company, if all the paper is transferred to the Printing division?
b. What is the profit of the company, if all the paper is sold in the market and the Printing division is closed?
c. How does the use of the market price as the transfer price cause managers of the division to achieve the highest profit for the company?
## Verified Solution
a. The following is the profit of the company if all the paper is transferred to the Printing division:
Revenues (10,000 tons × \$5,200/ton) \$52,000,000
Paper costs (10,000 tons × \$1,000/ton) (10,000,000)
Printing costs (10,000 tons × \$4,000/ton) (40,000,000)
Profit \$ 2,000,000
b. The following is the profit of the company if all the paper is sold in the market and the Printing division is closed:
Revenues (10,000 tons × \$1,500/ton) \$15,000,000
Paper costs (10,000 tons × \$1,000/ton) (10,000,000)
Profit \$ 5,000,000
c. If the market price of \$1,500 is used as the transfer price, the Printing division’s costs (\$1,500/ton + \$4,000/ton) will be greater than its revenues (\$5,200/ton). Rather than operating at a loss, the manager can close the Printing division or look for a more profitable opportunity. This example assumes that the costs of the two divisions are opportunity costs and reflect alternative uses of the inputs to the process. | 613 | 2,577 | {"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} | 3.515625 | 4 | CC-MAIN-2022-33 | latest | en | 0.805001 |
https://www.php.net/manual/pt_BR/function.gmp-invert.php | 1,721,066,838,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763514713.2/warc/CC-MAIN-20240715163240-20240715193240-00079.warc.gz | 820,189,347 | 7,423 | # gmp_invert
(PHP 4 >= 4.0.4, PHP 5, PHP 7, PHP 8)
gmp_invertInverse by modulo
### Descrição
gmp_invert( `\$num1`, `\$num2`):
Computes the inverse of `num1` modulo `num2`.
### Parâmetros
`num1`
Um objeto GMP, um int ou uma string numérica.
`num2`
Um objeto GMP, um int ou uma string numérica.
### Valor Retornado
A GMP number on success or `false` if an inverse does not exist.
### Exemplos
Exemplo #1 gmp_invert() example
`<?phpecho gmp_invert("5", "10"); // no inverse, outputs nothing, result is FALSE\$invert = gmp_invert("5", "11");echo gmp_strval(\$invert) . "\n";?>`
O exemplo acima produzirá:
`9`
add a note
### User Contributed Notes 1 note
athamidn at gmail dot com
4 years ago
`Example #2 gmp_invert() example<?phpecho gmp_invert("5", "10"); // no inverse, outputs nothing, result is FALSEIt means (5 * x ) mod 10 = 1. And with this function we want a value for x, because of mod 10, x should be {1.. 10-1(9)}, so :5 * 1 mod 10 = 5 5 * 2 mod 10 = 05 * 3 mod 10 = 55 * 4 mod 10 = 05 * 5 mod 10 = 55 * 6 mod 10 = 05 * 7 mod 10 = 55 * 8 mod 10 = 05 * 9 mod 10 = 5We don't have any 1 in the results. so it will be False.\$invert = gmp_invert("5", "11");echo gmp_strval(\$invert) . "\n";?>The above example will output:95 * 9 mod 11 = 1` | 462 | 1,263 | {"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} | 2.609375 | 3 | CC-MAIN-2024-30 | latest | en | 0.221257 |
https://www.topperlearning.com/answer/an-unpolarised-light-is-successively-passed-through-two-polaroids-their-transmission-axis-make-60-degree-with-each-other-if-intensity-of-unpolarised-l/vz36btt | 1,675,140,027,000,000,000 | text/html | crawl-data/CC-MAIN-2023-06/segments/1674764499842.81/warc/CC-MAIN-20230131023947-20230131053947-00260.warc.gz | 1,067,979,319 | 59,389 | Request a call back
<div><span style="color: #ff0000;"><strong>An unpolarised light is successively passed through two polaroids .Their transmission axis make 60 degree with each other. If intensity of unpolarised light be I ,then intensity after second polariser is </strong></span></div> <div><span style="color: #ff0000;"><strong>1) I/2</strong></span></div> <div><span style="color: #ff0000;"><strong>2) I/4</strong></span></div> <div><span style="color: #ff0000;"><strong>3) I/ 8</strong></span></div> <div><span style="color: #ff0000;"><strong>4) I/3</strong></span></div> <div><span style="color: #ff0000;"><strong>Please explain in detail.</strong></span></div> <div><span style="color: #ff0000;"><strong><br /></strong></span></div> <div><span style="color: #ff0000;"><strong><br /></strong></span></div>
Asked by Kb Aulakh | 25 Apr, 2015, 06:18: PM
Let the intensity of the incident unpolarised light be I
Therefore the intensity after second polariser is I/8
Correct option is 3) I /8
Answered by Jyothi Nair | 27 Apr, 2015, 09:43: AM
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https://www.jiskha.com/display.cgi?id=1379999466 | 1,503,536,888,000,000,000 | text/html | crawl-data/CC-MAIN-2017-34/segments/1502886126017.3/warc/CC-MAIN-20170824004740-20170824024740-00246.warc.gz | 926,230,261 | 3,702 | # math
posted by .
find the measure of each interior angle of a regular 18 - gon.
• math -
Formula for getting an interior angle of a regular polygon with n sides:
I = 180(n-2)/n
Substituting,
I = 180(18-2)/18
I = 160 degrees
Hope this helps~ :3
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