text:
# error LNK2019: unresolved external symbol _WSInitialize

I tried to run very simple example of connecting to WSTP. I checked a few links in this site but none of them could resolved my issue. I added three .lib files to visual studio location from this link and also linked to my program on visual studio. Also i did it for wstp.h and .exe. each one as explained in documentation developer tutorial. I modified the linker on C++ project and added all these files to current project on visual studio. But still i am getting this problem. I wish they had better documentation. Can someone help me , thanks
error LNK2019: unresolved external symbol _WSInitialize
error LNK2019: unresolved external symbol _WSDeinitialize
error LNK2019: unresolved external symbol _WSOpenString
error LNK2019: unresolved external symbol _WSClose

#include "wstp.h"
#include<iostream>
using namespace std;
int main()
{
WSENV env;
int error;

env = WSInitialize((WSEnvironmentParameter)0);
if (env == (WSENV)0)
{ /* unable to initialize WSTP environment */
}

{ /* unable to create link to the Kernel */
}

/* ... */

WSDeinitialize(env);

return 0;
}

EDITED Solved: beside the right answer, i should have compile as x64 because my system is 64bit, but i ran the program as x86 and got those errors

Those particular linker errors mean that the input library was not added under the linker settings. I put together an example project on GitHub that you can use for reference. The paths are currently setup for the default installation location for Mathematica 12.2.

• that really helped me, one more mistake which i did, I compiled the code as x86 but my system is 64 bits, so i had to change it to x64. thanks – Azzurro94 Mar 3 at 14:50
• could you tell me what should be instead of -mathlink? is that mathlink.exe? thanks – Azzurro94 Mar 3 at 15:06
• In newer versions, -wstp is preferred. But -mathlink still exists for compatibility reasons. – ihojnicki Mar 3 at 19:26


text:
Sinus Surgery (Round 2 — Sub Surface Mucosal Resectioning)

I’m not going to break this into several posts because I wasn’t ontop of things enough to keep a diary.

The Day of Surgery
The advantage of going in for round two is that I wasn’t nearly as nervous this time. That is lucky because there was a teenage girl who was in right before me to get her tonsils out. I could hear freaking out and crying from near complete panic. I saw a woman get this procedure done live on the Dr. Oz show using local anesthesia. Dr. Dawson does it under general anesthesia which I’m thankful for.

The procedure itself took less than 30 minutes. I went in. The anesthesiologist gave me happy drugs. I went to sleep. I woke up. It was easy with no muss or fuss.

I woke up with no packing and the ability to breath out of my nose. I had a mild headache but that was the only pain. Just in case I ate two puddings (which were delicious) and then popped some hydros.

As the day wore on, I stayed pretty comfortable. There was no pain in my nose. I could breathe. There was a little drippyness from my nose which went away within hours.  All in all, this was nothing compared to the deviated septum correction.

Days 2-3
My only symptom was a very bad headache. It didn’t feel like it was in any way connected with the surgery. In fact, at first I just figured it was caffeine withdrawal. After a couple cups of coffee didn’t help, I gave up and took my pain pills. That helped.

Because I’m paranoid, I called Dr. Dawson who assured me that a headache was one of the potential side effects.

Day 4
My headache was completely gone. I went in for my post op. Dr. Dawson used the snot-O-vac to remove some blood clots. I also had a very small amount of packing he put in there during the surgery removed.

I COULD BREATH! The right side was a little more restricted than the left, but nowhere close to where it was before.

I was told I could resume ALL normal activities in another 10 days. I could also start blowing my nose gently immediately.

Day 7
I was feeling a little disappointed because my right sinus remained a bit plugged up. To put a number to it, I would call it 80% of where I want it to be. Then I blew my nose one day.

Stop reading now if you are squeamish and move on to the next bolded text.

Something came out of my head. It was bloody and gross and completely awesome. It was the sort of thing that little kids giggle about. All of a sudden, I could breath perfectly out of both sides. PERFECTLY.

Day 14
As I was told, I could resume all normal activity 10 days after my post op. I really tested it here. The morning of day 14 saw me riding a chair lift up to the top of a cold snowy mountain for a skiing vacation. I have had no complications. No blood….nothing. I can breathe perfectly.

Conclusion
Some would call going in twice a failure. I don’t agree. I’m glad that Dr. Dawson was conservative his first time in. It is comforting that he treats surgery as a last resort and only does the minimum. I’ve read about Empty Nose Syndrome and would rather they take too little out than too much.

For anybody in the same boat I was in, I cannot recommend these procedures enough. My quality of life has improved immensely. I no longer have to go through a nightly regiment of nose sprays and allergy pills just to hope for sleep. I can breath and well. Recovery from surgery wasn’t bad.

Sinus Surgery (One Year Update)

Unfortunately, I can’t call mission accomplished. It has been more than a year since I went under the knife (err chisel).  Before anybody sees this as a reason not to get the procedure done, let me be clear: I am far better than I was before.

The problem is that I am still congested at night. Interestingly, almost all of the problem is in the right side. Before it was the left. The congestion is better than it was, but still obnoxious enough to interfere with my sleeping. While I suffered complete blockage before, I would say that I have half blockage now. My ENT and I have tried several medicines in an attempt to head off a second round of surgery. While the results are better than before, they still don’t work well.

A second CT scan showed the problem. My deviated septum was straightened from intruding into the left side. When this happened, it decreased the space in the left side. My Doctor’s work to shrink the turbinates wasn’t aggressive enough on the right. We decided together that the best option was to go in for a second round or surgery. Luckily, we decided this while there was still time to get in before my insurance deductible recycled.

The recommendation was to have a “sub surface” mucosal resection. In short, he goes inside the mucosal tissue of the turbinate and removes tissue but more importantly causes scarring inside the turbinate. The effect of this is that the turbinate is slightly smaller than before and cannot swell due to the internal scarring. While this sounds invasive, he promised that it is really not very invasive. Because all of the work happens inside the mucous tissue it heals quickly and results in little pain.

Fix: Internet Explorer 9 Freezes After Resuming from Sleep

IE started freezing on my Win8 x64 PC whenever I resumed the machine from sleeping.  The GUI would load completely, but would freeze as soon as I tried to load a web page.  It would lock up for about 60 seconds and then come back like nothing was wrong.

1. Try disabling all add-ons: http://windows.microsoft.com/is-IS/windows7/How-to-manage-add-ons-in-Internet-Explorer-9.  This didn’t work for me, but it is always the first step for troubleshooting IE.
2. If that doesn’t work, try resetting IE settings: http://windows.microsoft.com/en-us/windows7/Reset-Internet-Explorer-settings-in-Internet-Explorer-9.  This will require you to restart the computer.  It worked like a charm for me.
3. If that doesn’t work, check the error logs.  Reproduce the error and make note of the exact time.  Go to start > run and type eventvwr.msc.  Run through the different error lists and look for errors which occurred at the same time as IE froze.  If you can find a suspicious error, try searching for that.

Green Chili (AKA Chili Verde) is probably second only to Coors Beer as the ubiquitous food of the state of Colorado.  Never mind that Colorado means red colored.  In Colorado, green is king.  It is the perfect meal for a cold rainy (or to be more authentic: snowy) day.  I may have moved west of the Rockies, but I still have Green Chili in the blood.

Prep time: 1 hour

Cook time: 3 hours

Ingredients

4-6 Green Chili Peppers — I’ve used both Anaheim, Poblano or Ancho Chili peppers.  Poblanos are hotter, but I’m limited to what I can get at the supermarket.  Anaheim peppers are bigger so I use 4.

10 medium (2in) Tomatillos — If you can’t get tomatillos, tomatoes work.  Your green chili just won’t be green.  Many people make chili verde with tomatoes.

1 medium yellow onion — diced

1 head of garlic, minced — go big or go home.

2lbs Pork roast — Pork shoulder tastes best but has the most fat.  I’ve had good luck with pork loin.

1 cup fresh cilantro, diced —  If fresh cilantro isn’t available, double up on the ground coriander.

1 Green Pepper, diced

0-2 Jalapeños — if you don’t like spice, go with 0.  If you are a fire-breather, go for 2 or upgrade to serranos.   I put in 1.5.

1 Quart chicken broth

1 Tbs ground cumin

2 tsp ground coriander

1 tsp cinnamon

1 tsp oregano

2 Tbs brown sugar

salt and pepper

2 Tbs olive oil

Optional Ingredients

1 Can white kidney beans — beans aren’t authentic to chili verde, but I like them anyway.

1 Denver Broncos football game — preferably when winning.

1+ Bottle of Coors or Fat TIre, for the chef — Any beer is acceptable as long as it isn’t Yuengling

1. Roast and skin the green chilies

It is best to roast your green chilies on the BBQ grill, but that isn’t often a possibility during green chili season.  Here is an alternative

1. Turn on the oven broiler and let it preheat.
2. Cut in a circle around the stem of the pepper.  If done right, you can pull out the stem and 90% of the seeds at once.
3. Half or quarter the chilies.  The goal is to get them to lay as flat as possible.  You may be able to smash them down flat.
4. Lay down a layer of aluminum foil on a large cookie sheet.
5. Lay out the chilies so they don’t overlap
6. Place the whole thing 6-10 in from the broiler
7. Broil until most of the chili skin is blackened and starting to bubble off, then remove the chilies from the oven.
8. Fold the aluminum foil over on itself making an airtight package and sealing the chillies inside.  The steam will help loosen the skins even more.
9. Don’t touch until they are cool enough to handle
10. We will return to the chilies after the rest of the prep work.

2. Cut the pork roast into bite-sized cubes.  Liberally salt and pepper the cubes.

3. Prep the rest of the vegetables

1. Dice the onion and put in a bowl.
2. Smash and mince the garlic and put in a bowl
3. Dice and de-seed the jalapeños.
4. Dice the green pepper and mix with the jalapeños in a bowl.

4. Prepare the tomatillos and cilantro

1. Remove the husks from the tomatillos.
2. Half them and put in a blender
3. Rince and cut the bottom half of the stems off of approximately 1/2 bunch of cilantro.  You should have about a cup of the leafy part left.  Toss that in the blender
5. Blend for a few seconds until smooth.

5. Skin the Chilies

The chilies should be cool enough to handle now.  Open the aluminum foil packet.  The skins should be almost falling off the chillies.  They will peal off in sheets.  Get off as much of the chili skin as possible.  You don’t have to get all of the skin off.  Just try to get most of it off.

Dice the skinned chilies and set aside.

6. Start frying

1. Heat 2 Tbs of olive oil in a very large skillet over high heat
2. Get out a Dutch oven or large stewpot and set aside.
3. Dump in the diced pork into the skillet.
4. Brown the pork stirring occasionally.
5. Once all of the pork is browned — not necessarily completely cooked — poor in a bowl and set aside.  Try to keep the oil and drippings in the skillet.
6. Lower the heat to medium.  Sweat the onions until clear
7. Lower the heat again.  Add the garlic.
8. Once the garlic is brown, dump the whole thing into your Dutch oven or stewpot.
9. Deglaze the skillet with some chicken broth then pour it in with the onions and garlic.

7. Put it all together

Dump the pork and all of the remaining vegetables into the pot.  Pour in enough chicken broth that everything is mostly submerged.  Add all spices and stir to combine.  Turn up the heat until the mixture is simmering.  Make sure to stir regularly.  You don’t want this to burn to the bottom.  Turn down the heat to low and cover.

8.  Wait for 2-3 hours.

After 2-3 hours, the pork should be nice and soft.  All of the vegetables should have cooked down.  Add the beans (if you want beans) and stir to combine.

You’re done.  Add salt to taste (I had to add 2tsp).  If the chili tastes too acidic, try adding a little brown sugar.

Serving suggestions

Serve in a bowl with flour tortillas

Serve over fried eggs for breakfast

Serve over ‘smothered’ burritos

Schedule A Task In Windows 8 (the easy way)

1. Hold down the Windows Key and hit R
2. Type ‘mmc’ in the open field and hit okay
3. Click ‘yes’ on the User Account Control security prompt
4. Click File > Add/Remove Snap-in
5. Scroll to the bottom of the list of available snap-ins.
7. Choose local computer and hit OK
8. Hit OK again
9. Click Task Scheduler (Local) in the left-side snap-in tree.

Now you can either click ‘Create Basic Task’ or ‘Create Task’ under the right side ‘Actions’ menu

Create Basic Task: Gives you a wizard which is easiest if you are less of a power user or want to be walked through the process.

Here is the end of the Basic Task Process:

Powershell scripts can’t be automatically executed by Tasks alone.  They have to be executed by powershell.exe with arguments which run the script.

1. Open the ‘Action’ tab of the task
2. Click ‘Edit’
3. Type powershell as the Program/Script (yes it does say script but don’t actually put a script there.)
4. for the arguments, type (including quotes) -command “& C:\path\to\script.ps1” NOTE: I’m having trouble if there are spaces in the script path. The normal tricks aren’t working.  Best to avoid spaces altogether.
5. Click okay

If you want the task to expire automatically — I do because I don’t want this thing to run forever — Make sure ‘open the properties dialog’ checkbox is checked from the wizard.  Then click finish

If you went the advanced route, start here:

1. Click the triggers tab
2. Click the first trigger in the list (ie the one which says how often your task runs) There should only be one.  Mine says weekly.
3. Check the box next to expire
4. Set the time/date
5. Click OK

2. Expand the tree under task scheduler — click the arrow to the left of ‘Task Scheduler (Local)’
4. Click the ‘History’ tab below
5. You’re looking for a line which says ‘Action completed’

Sinus Surgery Cost

How much did it cost?

Billed to Insurance: $32,012.21 Cost after Insurance’s negotiated rate:$9,130.04

Price I paid: $(significantly significantly less than that) This doesn’t include any of the pre-op, or post-op visits. Thank you Primera BCBS! How to automatically update TFS workitems from the command line A lot of my life is lived according to bugs filed on a Team Foundation Server somewhere. One of my particular projects of late has been requiring weekly updates to a number of TFS workitems. I guess they want to make sure we’re still paying attention to them. I set out to find a solution where I could automatically bulk update my work items at the click of the button. Stretch goal: I wanted to have this happen automatically without any interaction. Step 1: download TFS Powertools from: (make sure you get the version which matches your copy of Visual Studio Command line tool documentation is located at: C:\Program Files (x86)\Microsoft Team Foundation Server 2012 Power Tools\Help\TFPTCommandLineTool.mht NOTE: I will write this assuming you are using VS 2012. Assume the path to other versions will be different. Step 2: Make sure your connection to TFS is configured. cd "C:\Program Files (x86)\Microsoft Team Foundation Server 2012 Power Tools" .\TFPT.exe connections Verify that the correct TFS server is listed. If the correct version of TFS is not configured: 1. Open Visual Studio (2012) 2. Click Team > Connect To Team Foundation Server 3. Click Servers 4. Click Add 5. Configure the server Step 3: Create a query for the items you want to update. The cron script will automatically update anything from a particular query. You could just as easy specify work item IDs on the command line instead of using a query. I decided against that because I wanted the flexibility to change the work items which get edited without having to change my code. 1. Navigate to your TFS server in the browser (you could do this from Visual Studio Too) 2. Click New > Query 3. Build the query you want 4. Save the query and make note of the location. In this case: Shiproom/My Queries/WeeklyAutoUpdate NOTE: this query should actually say Changed Date < @Today – 6. Not =. Note that the last line is searching for @Today – 6. I did that so that any work item I’ve updated within the last week isn’t touched by this query. Step 4: Verify that you are getting the correct work items IDs on the command line: (replace http://tfsserver:8080/tfs with the server’s URL and the query name with your full query path) PS C:\...> .\TFPT.exe query /collection:http://tfsserver: 8080/tfs /format:id "Shiproom/My Queries/WeeklyAutoUpdate" 942 945 946 947 948 PS C:\...> Step 5: Try editing an item through the command line. Replace 942 with one of your work item IDs and once again replace http://tfsserver:8080/tfs with your server’s URL. PS ...> .\TFPT.exe workitem /collection:http://tfsserver:8080/tfs /update 942 /fields:"History=." Work item 942 updated. Check to make sure your work item was updated. It should now show a new entry in the history which merely contains a period. Step 6: Put it all together into a nice PowerShell script $SERVER = "http://server:port/path" #Full URL to the server
$QUERY = "PATH/My Queries/QueryName" #Query of items to update$UPDATECMD = '/fields:"History=."' #Command you want to run against them
$TFSPTPATH = "C:\Program Files (x86)\Microsoft Team Foundation Server 2012 Power Tools" Set-Location$TFSPTPATH

$idlist = .\TFPT.exe query /collection:$SERVER /format:id $QUERY #could avoid the loop and send all IDs at once foreach($id in $idlist) {$result = .\TFPT.exe workitem /collection:$SERVER /update$id $UPDATECMD Write-Host$result
}

pause  #remove this to run without an end prompt

I chose to nest the work item update in a for loop.  This isn’t necessary.  TFPT will take a list of work item IDs and perform the same operation on all of them.  I general feel safer when I wrap something like that in my own loop.  That way one failure doesn’t necessarily kill everything.  Additionally, you get instant progress if there are a large number of workitems which must be updated.

The program as it is above has a call to pause on the last line.  If you want to run this as a scheduled task, that line should be commented out.

Step 7:

Winning!

Thanks to:

This guy: http://ravendra.wordpress.com/2010/06/02/bulk-edit-tfs-work-items/ for giving me a lot of the concept.

Sinus Surgery (3 Weeks)

I’m feeling great.  The only difficult part appears to have been the first 10 days.  Most of that was due to the unexpected bleeding.  I would have probably been feeling pretty good about a week out if that hadn’t happened.  All in all, I would say that the whole experience wasn’t nearly as bad as I was anticipating.

The surgery appears to have been a resounding success.  I can breath better than I ever could before.  As Dr. Dawson promised, my turbinates were a bit swollen at first, but they have shrunk down.  I can breath better now than I could even with judicious snorting of Afrin before.  I was worried a couple times, but it always turned out to be a clot or temporary irritation due to blowing my nose too hard.

I’m still seeing a little blood when I gently blow my nose.  Every day there is a little less.  I’m no longer coughing up things that look like they came out of a horror movie.  That’s probably for the best.  Emily was getting sick of me saying, “hey babe, wanna see something really gross?”  TMI…

In my 3-week post op yesterday, Dr. Dawson said I could go back to normal activities.  He just suggested taking it easy for a while.  No neti pot yet.

An unintended consequence of the surgery is that my neck and back feel a lot better.  I was doing a lot of stomach sleeping presumably because that was when breathing was easiest.  I can now sleep on my back (WITHOUT SNORING!) or my side comfortably.

My advice to anybody contemplating this surgery: do it.  Breathing at night is well worth a week of moderate discomfort.  Next checkin with the doctor is in another 3 weeks.

Securing THE CLOUD

One of the primary purposes for this blog is to talk about information security.  An appropriate first post on the topic is Securing THE CLOUD.

Cloud is one of those words I don’t like to use.  It was drummed up by marketing gurus to make an old idea sound new.  All the cloud means to me is putting your stuff on somebody else’s servers.  Generally that stuff is accessible from anywhere on the internet, although they have coined the term ‘private cloud’ to describe a scenario where access is more limited.  I digress.

As a developer for the cloud, the stakes are high for you.  Customers are entrusting you to protect their stuff which is logically connected every internet user on the planet (potentially sans N. Korea, Iran, China, et al.).

Here is a checklist that I like to think of when I’m evaluating the security of a cloud product.  I suppose you could turn it around and use it as a howto guide.  Just a quick caveat.  I am not a programmer.  I stopped programming as soon as I realized just how bad I am at it.  You know what they say, “those who can’t do manage”.

1. Guard the front gates with everything you have.  Every restricted-access cloud service sits behind an authentication layer.  That is your first line of defense.  The first line of code on every page (figuratively) should be an authentication/authorization check.
2. Don’t even think of writing your own authentication system.  Let somebody else do that for you.  Trust me, they are much better at it than you are.  Use Microsoft ID (aka LiveID), Open ID, Google ID, Facebook ID.  Better yet, let them pick.  Your customers will thank you because that is one less password they have to remember.http://msdn.microsoft.com/en-us/library/bb676633.aspx
3. Don’t let the bad guy pretend to be a legitimate user.  How do they do that?  Cross-site scripting (XSS) is the most common vulnerability I run across in the wild.  That is followed closely by cross-site request forgery (CSRF).  Both of these can be leveraged by an attacker to cause a user to shoot themselves in the foot.   This is a huge topic which probably warrants its own post.  I’ll try to break it down.
• sanitize! sanitize! sanitize! Consider every piece of data which is ever in a user’s possession as evil. This includes cookies, form variables, url parameters, and uploaded files. They are all evil and must be stopped.  I do mean everything.  Use somebody else’s form sanitization library.  Again, they have thought of things you haven’t.  http://blogs.msdn.com/b/securitytools/archive/2010/09/30/antixss_2d00_4_2d00_0_2d00_release_2d00_notes.aspx
• Canaries are your friend.  This is the only effective way to prevent cross-site request forgery.  Multi-step forms don’t work.  Cookies don’t work.  Use a challenge-response system with canaries to validate that a user really just came from one of your pages.
https://www.owasp.org/index.php/Cross-Site_Request_Forgery_(CSRF)
_Prevention_Cheat_Sheet
• Use HTTP commands as designed.  Never change state with an HTTP GET.  Use a POST.  It may take some extra JavaScript foo, but it is much harder to attack.
• Scan every version of your code.  There are a number of automated XSS scanners on the market.  They are pretty good at finding script kiddie vulnerabilities.  If you are a juicy enough of a target to warrant attention by ‘advanced’ researchers’, you may want to invest in a second set of eyes.  Trust me, an expert pentest crew is a whole lot cheaper than getting horribly owned.
4. Don’t do dumb things with SQL.  It never ceases to amaze me that SQL injection still works. Use stored procedures for everything.  Also, building an SQL string in a stored procedure and EXECing it is just as bad as parameterized SQL.  Don’t do it.
5. SSL is good.  If the data is important enough to put behind a login page, it is important enough to protect with SSL.  Period.
6. Protect data in storage.  This is a topic I am planning on writing a dedicated post about.  The news is full of companies whose data has been stolen and put on pastebin or similar.  If it shouldn’t be shown to the world, it should be encrypted.  Stay tuned for the specifics of this.

As I write this, you may notice that none of these items are specific to the cloud.  These are all best practices for developing on the internet in general.  That is because they are the same thing.  Cloud == internet, internet == cloud.  Marketing will say what marketing will say.  For the rest of us, nothing has changed.  The web is still the web.  If you can secure one, you can secure the other.

Sinus Surgery (Days 7-10)

7 Days Post Surgery

I started bleeding again last night.  It was worse this time.  It went right around the packing he added after yesterday’s cauterization.  I did eventually manage to get it stopped.

I set up an appointment to go back into Dr. Dawson.  He poked around again and couldn’t figure out which area had been bleeding and couldn’t find any obvious contenders for more cauterization.

Very apologetically, he said that he would have to completely pack that side with gauze just like it was right after surgery.  He also said that this sort if thing happens very rarely.  I went home with a packed left sinus.

8 Days Post Surgery

I got almost no sleep.  My right sinus is flowing 49% of normal air.  It turns out it takes 50% in order to sleep comfortably.  It was another night of mouth breathing.

Other than that, I can say I feel great.  For a person who doesn’t have unusual bleeding problems, I can anticipate that a week after surgery they would be feeling right as rain.  Everything is still a bit swollen and tender, but I’m no longer bleeding and feel pretty much normal.

I went back to work today too.  I am a little worn down, but I’m able to get things done.

9 Days Post Surgery

Need Sleep.  My right side has completely rebelled and decided that it wants to swell closed.  4 days without sleep…  Is this what it’s like to have children?  I can’t blame it.  I’ve been trying to use it for 100& of my oxygen intake needs.  It is probably just inflamed.

I went in to Dr. Dawson’s office to have the packing removed.  It came out easily, but it was still a strange feeling.  He vacuumed out both sides again and said that everything is healing up nicely.  Some of the cauterizations are still angry.  He put some Polysporin on them and used a little dissolvable gauze for protection.  He was able to place the gauze in such a way that I can still breath around it.

10 Days Post Surgery

I slept 10 hours last night.  Both sides are wide open and happy.  No bleeding.  I feel fantastic!

format: plain


text:
# Metric prefix

A metric prefix is a unit prefix that precedes a basic unit of measure to indicate a multiple or submultiple of the unit. All metric prefixes used today are decadic. Each prefix has a unique symbol that is prepended to any unit symbol. The prefix kilo-, for example, may be added to gram to indicate multiplication by one thousand: one kilogram is equal to one thousand grams. The prefix milli-, likewise, may be added to metre to indicate division by one thousand; one millimetre is equal to one thousandth of a metre.

Decimal multiplicative prefixes have been a feature of all forms of the metric system, with six of these dating back to the system's introduction in the 1790s. Metric prefixes have also been used with some non-metric units. The SI prefixes are metric prefixes that were standardized for use in the International System of Units (SI) by the International Bureau of Weights and Measures (BIPM) in resolutions dating from 1960 to 1991. Since 2009, they have formed part of the International System of Quantities. They are also used in the Unified Code for Units of Measure (UCUM)

## List of SI prefixes

The BIPM specifies twenty prefixes for the International System of Units (SI).

Prefix Base 10 Decimal English word Adoption Etymology
Name Symbol Short scale Long scale Language Source word
yotta Y 1024 1000000000000000000000000 septillion quadrillion 1991 Latin eight
zetta Z 1021 1000000000000000000000 sextillion trilliard 1991 Latin seven
exa E 1018 1000000000000000000 quintillion trillion 1975 Greek six
peta P 1015 1000000000000000 quadrillion billiard 1975 Greek five
tera T 1012 1000000000000 trillion billion 1960 Greek four, monster
giga G 109 1000000000 billion milliard 1960 Greek giant
mega M 106 1000000 million 1873 Greek great
kilo k 103 1000 thousand 1795 Greek thousand
hecto h 102 100 hundred 1795 Greek hundred
deca da 101 10 ten 1795 Greek ten
100 1 one
deci d 10−1 0.1 tenth 1795 Latin ten
centi c 10−2 0.01 hundredth 1795 Latin hundred
milli m 10−3 0.001 thousandth 1795 Latin thousand
micro μ 10−6 0.000001 millionth 1873 Greek small
nano n 10−9 0.000000001 billionth milliardth 1960 Greek dwarf
pico p 10−12 0.000000000001 trillionth billionth 1960 Spanish peak, a little bit
femto f 10−15 0.000000000000001 quadrillionth billiardth 1964 Danish fifteen, Fermi
atto a 10−18 0.000000000000000001 quintillionth trillionth 1964 Danish eighteen
zepto z 10−21 0.000000000000000000001 sextillionth trilliardth 1991 Latin seven
yocto y 10−24 0.000000000000000000000001 septillionth quadrillionth 1991 Latin eight
1. ^ Prefixes adopted before 1960 already existed before SI. The introduction of the CGS system was in 1873.
2. Part of the beginning of the prefix was modified from the word it was derived from, e.g.: "peta" (prefix) vs "penta" (source word).
3. ^ The abbreviation mcg is often used in medicine instead of μg to prevent confusion with mg, which can lead to overdoses. A lower case u is often used instead of μ where the latter character is unavailable.
4. ^ The fermi was introduced earlier with the symbol "fm", which prompted the reinterpretation of the "f" as a prefix to "m", with femto being derived from the Danish word femten.

Each prefix name has a symbol that is used in combination with the symbols for units of measure. For example, the symbol for kilo- is k, and is used to produce km, kg, and kW, which are the SI symbols for kilometre, kilogram, and kilowatt, respectively. Except for the early prefixes of kilo-, hecto-, and deca-, the symbols for the multiplicative prefixes are uppercase letters, and those for the fractional prefixes are lowercase letters. There is a Unicode symbol for micro µ for use when the Greek letter μ is unavailable. When both are unavailable, the visually similar lowercase Latin letter u is commonly used instead. SI unit symbols are never italicised.

Prefixes corresponding to an integer power of one thousand are generally preferred. Hence 100 m is preferred over 1 hm (hectometre) or 10 dam (decametres). The prefixes deci-, and centi-, and less frequently hecto- and deca-, are commonly used for everyday purposes, and the centimetre (cm) is especially common. Some modern building codes require that the millimetre be used in preference to the centimetre, because "use of centimetres leads to extensive usage of decimal points and confusion".

Prefixes may not be used in combination. This also applies to mass, for which the SI base unit (kilogram) already contains a prefix. For example, milligram (mg) is used instead of microkilogram (μkg).

In the arithmetic of measurements having units, the units are treated as multiplicative factors to values. If they have prefixes, all but one of the prefixes must be expanded to their numeric multiplier, except when combining values with identical units. Hence:

• 5 mV × 5 mA = 5×10−3 V × 5×10−3 A = 25×10−6 V⋅A = 25 μW.
• 5.00 mV + 10 μV = 5.00 mV + 0.01 mV = 5.01 mV.

When powers of units occur, for example, squared or cubed, the multiplicative prefix must be considered part of the unit, and thus included in the exponentiation:

Examples
• 5 cm5×10−2 m5 × 0.01 m = 0.05 m.
• 9 km29 × (103 m)29 × (103)2 × m29×106 m29 × 1000000 m29000000 m2.
• 3 MW = 3×106 W = 3 × 1000000 W = 3000000 W.

## Application to units of measurement

The use of prefixes can be traced back to the introduction of the metric system in the 1790s, long before the 1960 introduction of the SI. The prefixes, including those introduced after 1960, are used with any metric unit, whether officially included in the SI or not (e.g., millidynes and milligauss). Metric prefixes may also be used with non-metric units.

The choice of prefixes with a given unit is usually dictated by convenience of use. Unit prefixes for amounts that are much larger or smaller than those actually encountered are seldom used.

### Metric units

#### Mass

The units kilogram, gram, milligram, microgram, and smaller are commonly used for measurement of mass. However, megagram, gigagram, and larger are rarely used; tonnes (and kilotonnes, megatonnes, etc.) or scientific notation are used instead. Megagram and teragram are occasionally used to disambiguate the tonne from other units with the name "ton".[citation needed]

The kilogram is the only base unit of the International System of Units that includes a metric prefix.

#### Volume

The litre (equal to a cubic decimetre), millilitre (equal to a cubic centimetre), microlitre, and smaller are common. In Europe, the centilitre is often used for liquids, and the decilitre is used less frequently. Bulk agricultural products, such as grain, beer and wine, are often measured in hectolitres (each 100 litres in size).

Larger volumes are usually denoted in kilolitres, megalitres or gigalitres, or else in cubic metres (1 cubic metre = 1 kilolitre) or cubic kilometres (1 cubic kilometre = 1 teralitre). For scientific purposes, the cubic metre is usually used.

#### Length

The kilometre, metre, centimetre, millimetre, and smaller units are common. The decimetre is rarely used. The micrometre is often referred to by the older non-SI name micron. In some fields, such as chemistry, the ångström (0.1 nm) has been used commonly instead of the nanometre. The femtometre, used mainly in particle physics, is sometimes called a fermi. For large scales, megametre, gigametre, and larger are rarely used. Instead, ad hoc non-metric units are used, such as the solar radius, astronomical units, light years, and parsecs; the astronomical unit is mentioned in the SI standards as an accepted non-SI unit.

#### Time

Prefixes for the SI standard unit second are most commonly encountered for quantities less than one second. For larger quantities, the system of minutes (60 seconds), hours (60 minutes) and days (24 hours) is accepted for use with the SI and more commonly used. When speaking of spans of time, the length of the day is usually standardized to 86400 seconds so as not to create issues with the irregular leap second.

Larger multiples of the second such as kiloseconds and megaseconds are occasionally encountered in scientific contexts, but are seldom used in common parlance. For long-scale scientific work, particularly in astronomy, the Julian year or annum is a standardized variant of the year, equal to exactly 31557600 SI seconds (365 days, 6 hours). The unit is so named because it was the average length of a year in the Julian calendar. Long time periods are then expressed by using metric prefixes with the annum, such as megaannum or gigaannum.

#### Angle

The SI unit of angle is the radian, but degrees, as well as arc-minutes and arc-seconds, see some scientific use.

#### Temperature

Official policy also varies from common practice for the degree Celsius (°C). NIST states: "Prefix symbols may be used with the unit symbol °C and prefix names may be used with the unit name degree Celsius. For example, 12 m°C (12 millidegrees Celsius) is acceptable." In practice, it is more common for prefixes to be used with the kelvin when it is desirable to denote extremely large or small absolute temperatures or temperature differences. Thus, temperatures of star interiors may be given in units of MK (megakelvins), and molecular cooling may be described in mK (millikelvins).

#### Energy

In use the joule and kilojoule are common, with larger multiples seen in limited contexts. In addition, the kilowatt-hour, a composite unit formed from the kilowatt and hour, is often used for electrical energy; other multiples can be formed by modifying the prefix of watt (e.g. terawatt-hour).

There exist a number of definitions for the non-SI unit, the calorie. There are gram calories and kilogram calories. One kilogram calorie, which equals one thousand gram calories, often appears capitalized and without a prefix (i.e. Cal) when referring to "dietary calories" in food. It is common to apply metric prefixes to the gram calorie, but not to the kilogram calorie: thus, 1 kcal = 1000 cal = 1 Cal.

### Non-metric units

Metric prefixes are widely used outside the metric SI system. Common examples include the megabyte and the decibel. Metric prefixes rarely appear with imperial or US units except in some special cases (e.g., microinch, kilofoot, kilopound). They are also used with other specialized units used in particular fields (e.g., megaelectronvolt, gigaparsec, millibarn). They are also occasionally used with currency units (e.g., gigadollar), mainly by people who are familiar with the prefixes from scientific usage.[citation needed] In astronomy, geology, and paleontology, the year, with symbol a (from the Latin annus), is commonly used with metric prefixes: ka, Ma, and Ga.

Official policies about the use of SI prefixes with non-SI units vary slightly between the International Bureau of Weights and Measures (BIPM) and the American National Institute of Standards and Technology (NIST). For instance, the NIST advises that 'to avoid confusion, prefix symbols (and prefix names) are not used with the time-related unit symbols (names) min (minute), h (hour), d (day); nor with the angle-related symbols (names) ° (degree), ′ (minute), and ″ (second), whereas the BIPM adds information about the use of prefixes with the symbol as for arcsecond when they state: "However astronomers use milliarcsecond, which they denote mas, and microarcsecond, μas, which they use as units for measuring very small angles."

An advantage of the SI system decimal prefixes is that they make for simplicity of calculation and conversion involving units of different sizes; consider for example the simplicity of buying 13 items of 390 g weight at €12.34 per kilogram, compared with items of 13+34 oz at \$4.79 per pound (or, worse, with old non-decimalized currency: £4/15/9+12). In the units used in the US, combining of units that are not decimal multiples of each other is often avoided by not mixing the units used, e.g., using inches, feet or miles only: 89  inches rather than 7 feet 5 inches (or 2 yards, 1 foot 5 inches).

## Presentation

### Pronunciation

When a metric prefix is affixed to a root word, the prefix carries the stress, while the root drops its stress but retains a full vowel in the syllable that is stressed when the root word stands alone.[citation needed] For example, kilobyte is /ˈkɪlɒbaɪt/, with stress on the first syllable. However, units in common use outside the scientific community may be stressed idiosyncratically. In English-speaking countries, kilometre is the most conspicuous example. It is often pronounced /kɪˈlɒmɪtər/, with reduced vowels on both syllables of metre. This stress is not applied to other multiples or sub-multiples of metre, or to other units prefixed with kilo-.

The prefix giga is usually pronounced in English as /ˈɡɪɡə/, with hard ⟨g⟩ as in get, but sometimes /ˈdʒɪɡə/, with soft ⟨g⟩ as in gin.[citation needed]

### Typesetting

The LaTeX typesetting system features an SIunitx package in which the units of measurement are spelled out, for example, \SI{3}{\tera\hertz} formats as "3 THz".

## Non-standard prefixes

Distance marker on the Rhine: 36 (XXXVI) myriametres from Basel. The stated distance is 360 km; the decimal mark in Germany is a comma.

### Obsolete metric prefixes

Some of the prefixes formerly used in the metric system have fallen into disuse and were not adopted into the SI. The decimal prefix for ten thousand, myria- (sometimes spelled myrio-), and the prefixes double- (2×) and demi- (1/2×) were parts of the original metric system adopted by France in 1795, but were not retained when the SI prefixes were internationally adopted by the 11th CGPM conference in 1960.

Other metric prefixes used historically include hebdo- (107) and micri- (10−14).

### Double prefixes

Double prefixes have been used in the past, such as micromillimetres or millimicrons (now nanometres), micromicrofarads (μμF; now picofarads, pF), kilomegatons (now gigatons), hectokilometres (now 100 kilometres) and the derived adjective hectokilometric (typically used for qualifying the fuel consumption measures). These are not compatible with the SI.

Other obsolete double prefixes included "decimilli-" (10−4), which was contracted to "dimi-" and standardized in France up to 1961.

## Similar symbols and abbreviations

In written English, the symbol K is often used informally to indicate a multiple of thousand in many contexts. For example, one may talk of a 40K salary (40000), or call the Year 2000 problem the Y2K problem. In these cases, an uppercase K is often used with an implied unit (although it could then be confused with the symbol for the kelvin temperature unit if the context is unclear). This informal postfix is read or spoken as "thousand" or "grand", or just "k".

The financial and general news media mostly use m or M, b or B, and t or T as abbreviations for million, billion (109) and trillion (1012), respectively, for large quantities, typically currency and population.

The medical and automotive fields in the United States use the abbreviations cc or ccm for cubic centimetres. 1 cubic centimetre is equivalent to 1 millilitre.

For nearly a century, engineers used the abbreviation MCM to designate a "thousand circular mils" in specifying the cross-sectional area of large electrical cables. Since the mid-1990s, kcmil has been adopted as the official designation of a thousand circular mils, but the designation MCM still remains in wide use. A similar system is used in natural gas sales in the United States: m (or M) for thousands and mm (or MM) for millions of British thermal units or therms, and in the oil industry, where MMbbl is the symbol for "millions of barrels". This usage of the capital letter M for "thousand" is from Roman numerals, in which M means 1000.

### Binary prefixes

In some fields of information technology, it has been common to designate non-decimal multiples based on powers of 1024, rather than 1000, for some SI prefixes (kilo-, mega-, giga-), contrary to the definitions in the International System of Units (SI). This practice was once sanctioned by some industry associations, including JEDEC. The International Electrotechnical Commission (IEC) standardized the system of binary prefixes (kibi-, mebi-, gibi-, etc.) for this purpose.

## Explanatory notes

1. ^ On Microsoft Windows systems, Alt+230 will yield the symbol for micro µ. With macOS systems it is ⌥ Opt+Y or ⌥ Opt+m, and with Linux systems it is Ctrl+⇧ Shift+u b5space.
2. ^ The names and symbols of the binary prefixes proposed by the IEC include
• kibi (Ki) = 210 = 1024,
• mebi (Mi) = 220 = 10242 = 1048576,
• gibi (Gi) = 230 = 10243 = 1073741824,
etc.

This page was last updated at 2022-09-09 22:13 UTC. . View original page.

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text:
How do you solve the polynomial 10x^3-5x^2=0?

Nov 18, 2014

In order to solve the algebraic equation for the variable x we would begin by factoring out the common factor from the equation
$10 {x}^{3} - 5 {x}^{2} = 0$
The common factor between $10 {x}^{3}$ and $5 {x}^{2}$ is $5 {x}^{2}$

$5 {x}^{2} \left(2 x - 1\right) = 0$

Next we would set each value of x equal to 0

$5 {x}^{2} = 0 \mathmr{and} \left(2 x - 1\right) = 0$

$5 {x}^{2} = 0$ divide by 5 and square root each side
${x}^{2} = \frac{0}{5}$
$x = 0$

$\left(2 x - 1\right) = 0$ add 1 and divide by 2 on each side
$2 x = 0 + 1$
$x = \frac{1}{2}$

$x = \left\{0 , \frac{1}{2}\right\}$


text:
# errors

1. ### Limit as x approaches zero

(1) Compute the limit for p(x) = x^2 - 1. lim p(p(p(p(x)))) as x approaches 0. (2) Find all the errors in the following incorrect string of equalities. (a) lim 1/x as x approaches 0 = lim x/x^2 as x approaches 0 = (lim x as x approaches 0) (lim 1/x^2 as x approaches 0) = 0 . ? = 0. (b) lim...
2. ### fitting with individual errors in data

I have two sets of data x and y with individual errors dx and dy. I want to plot a linear line through the data of the form y=ax+b that takes into account the individual errors in x and y and translates this to an error in the fitting parameters a and b. Is there any method to do this?
3. ### Cholesky Roundoff Errors

I am developing a Cholesky algorithm in C++ (a computer language ) and I am using single precision, 32bits. I read that if my matrix is ill conditioned then the main diagonal may turn negative due to round off errors. I can understand that it might be zero, but could someone give an example...
4. ### Help plz with integral approximation error calculation finding K

I'm working on integral approximations and errors. My errors never come out right. My approximations are correct, so I think I'm just misunderstanding how to find K. Q.a) Find the approximations T8 and M8 for ∫(0 to 1) cos(x2)dx I found these to be T8=0.902333 and M8=0.905620 b) Estimate...
5. ### Calculation of type II errors

I am given: $n_1 = 50, \overline{x}_1 = 2.61, s_1 = 0.12$ $n_2 = 40, \overline{x}_2 = 2.38, s_2 = 0.14$ H0 is to be rejected if and only if $\mu_1 - \mu_2 = 0.20$. I need to find $\beta$, the probability of a type II error (false acceptance of H0), when $\mu_1 - \mu_2$ is 0.12 and then 0.16...
6. ### Dealing with subtracting means with margin of errors

Hi all, If i have two means with a margin of error (95% confidence intervals). how can I subtract one from the other, what will the computed margin of error be? e.g. (10 +/-2) - (8 +/-1) Many Thanks
7. ### Type 1 and 2 errors for binomial

I am working on a research project this summer and I'm a bit confused about type 2 errors. The actual scenario I am testing is nonsense to most people so I'll rephrase the problem in a way that makes more sense. There is a bag containing many green balls and 1 red ball. A boy comes to play a...
8. ### Simple Regression - Assessing SSE (sum of square errors)

Hello, I can't figure out how to solve this question: Consider these summary statistics for a random sample: Mean of x=20 Mean of y=10 Sx(variance)=3 Sy=7 Sxy= -18 For which of the following straight lines would the SSE (sum of the squared errors) be SMALLEST? a) y= 4 -6x b) y= 8-6x c) y=...
9. ### Theory of errors and confusion with roundings

With given: k_1 = 37.1\pm0.3 k_2 = 9.87\pm0.11 k_3 = 6.052\pm0.016 estimate the absolute and relative error for w = k_1 \cdot k_2^2 \cdot k_3^3 and round both w and the error in such a way not to lose any precise figures. So my attempt looks like this: We know the absolute errors for the...
10. ### Algebraic Errors

This is sample work of factorising with fractions in an inequality. I've been told that the 3rd line is incorrect, as a^2+b^2 cannot be factored over a real number. Can anyone help me determine if the factoring simply stops at the second line, or is there a correct way to continue? Many...
11. ### Identify errors

Hi guys, the task: Identify the errors a stundent made in the following problems and correct them. Explain your answer. 1. (7x)^1/3 = 1 divided by 7x^3 my answer: it should be = (7x)^1/3 = 7^1/3 x^1/3 Is that right? 2. 2^2 divided by 2^1/4 = 2^2/4 = 2^1/2 = square root of 2 What is wrong...
12. ### Normality plot (no of errors over 2 years)

I am trying to analyse number of errors over a period of 2 years and I run a normality test for my data via minitab. it shows Can i conclude that the graphical representation show non-normal data ? then what should i do ? Thanks!
13. ### Linear codes: how to construct checkmatrix, localise errors

The problem goes like this. A linear binary code is given by the control matrix H = 1 1 0 1 0 1 0 1 1 0 0 1 1 1 0 0 1 0 a) What codeword can, with at most one error, become 010110? b) Find a word that cannot arise with at most one error in a codeword. First, I don't understand how to...
14. ### probability of DNA sequence errors

I am a molecular biologist with a probability question. Before I get to the question, I will give you a little background information about DNA. As you may know, DNA consists of two long polymers of simple units called nucleotide bases (4 types: A, C, G or T) arranged in an antiparallel double...
15. ### Residuals vs. errors

What is the difference between a residual and an error?
16. ### Correcting errors

Given an error rate and a binary (n,k,d) - code I can find out the probability of making a certain number of errors but how do I work out the probability of correcting such errors if I don't know what the codewords are?
17. ### Probability that 2 errors occur on separate lines

Hi, I have the following problem, but I am stuck on question D. I would really appreciate if someone could give me a hand! I know I have to use Bayes' theorem, but I don't know how :/. Thanks! The problem says: "A page of typescript contains 40 lines, with 80 characters per line. Each...
18. ### Deflection of beam. Efect of % errors in span and load data.

OK so I'm practicsing some of the questions out of my text book for when I start my course in 2 weeks and finding this one pretty difficult, but here it goes. Bestend Properties is refurbishing an old hospital that was built in the 1950's. The building's main structure is a steel frame. The...
19. ### Using the normal approximation interval to calculate number of errors

Hello I have a bit of a problem how to use the normal approximation interval( Binomial proportion confidence interval - Wikipedia, the free encyclopedia ). I would be very happy if anyone could explain further! I am trying to calculate the upper probability of an error, say I have a confidence...
20. ### Type 1 and Type 2 Errors

Hello, I was given the following handout: I know how to get the power, because this is 1 - beta = 1 - .40 = .60. But I just don't get how beta was calculated using the above figures. Plus, if I have the following problem: A sample size of 102 will be sufficient to detect an effect size...


text:
# 6.1 Blackbody radiation  (Page 6/15)

 Page 6 / 15

Check Your Understanding A molecule is vibrating at a frequency of $5.0\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{14}\text{Hz}.$ What is the smallest spacing between its vibrational energy levels?

$3.3\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-19}\text{J}$

## Quantum theory applied to a classical oscillator

A 1.0-kg mass oscillates at the end of a spring with a spring constant of 1000 N/m. The amplitude of these oscillations is 0.10 m. Use the concept of quantization to find the energy spacing for this classical oscillator. Is the energy quantization significant for macroscopic systems, such as this oscillator?

## Strategy

We use [link] as though the system were a quantum oscillator, but with the frequency f of the mass vibrating on a spring. To evaluate whether or not quantization has a significant effect, we compare the quantum energy spacing with the macroscopic total energy of this classical oscillator.

## Solution

For the spring constant, $k=1.0\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{3}\text{N/m},$ the frequency f of the mass, $m=1.0\text{kg},$ is

$f=\frac{1}{2\pi }\sqrt{\frac{k}{m}}=\frac{1}{2\pi }\sqrt{\frac{1.0\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{3}\text{N/m}}{1.0\text{kg}}}\simeq 5.0\phantom{\rule{0.2em}{0ex}}\text{Hz}$

The energy quantum that corresponds to this frequency is

$\text{Δ}E=hf=\left(6.626\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-34}\text{J}·\text{s}\right)\left(5.0\text{Hz}\right)=3.3\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-33}\text{J}$

When vibrations have amplitude $A=0.10\text{m},$ the energy of oscillations is

$E=\frac{1}{2}k{A}^{2}=\frac{1}{2}\left(1000\text{N/m}\right){\left(0.1\text{m}\right)}^{2}=5.0\text{J}$

## Significance

Thus, for a classical oscillator, we have $\text{Δ}E\phantom{\rule{0.1em}{0ex}}\text{/}\phantom{\rule{0.1em}{0ex}}E\approx {10}^{-34}.$ We see that the separation of the energy levels is immeasurably small. Therefore, for all practical purposes, the energy of a classical oscillator takes on continuous values. This is why classical principles may be applied to macroscopic systems encountered in everyday life without loss of accuracy.

Check Your Understanding Would the result in [link] be different if the mass were not 1.0 kg but a tiny mass of 1.0 µ g, and the amplitude of vibrations were 0.10 µ m?

No, because then $\text{Δ}E\phantom{\rule{0.1em}{0ex}}\text{/}\phantom{\rule{0.1em}{0ex}}E\approx {10}^{-21}$

When Planck first published his result, the hypothesis of energy quanta was not taken seriously by the physics community because it did not follow from any established physics theory at that time. It was perceived, even by Planck himself, as a useful mathematical trick that led to a good theoretical “fit” to the experimental curve. This perception was changed in 1905 when Einstein published his explanation of the photoelectric effect, in which he gave Planck’s energy quantum a new meaning: that of a particle of light.

## Summary

• All bodies radiate energy. The amount of radiation a body emits depends on its temperature. The experimental Wien’s displacement law states that the hotter the body, the shorter the wavelength corresponding to the emission peak in the radiation curve. The experimental Stefan’s law states that the total power of radiation emitted across the entire spectrum of wavelengths at a given temperature is proportional to the fourth power of the Kelvin temperature of the radiating body.
• Absorption and emission of radiation are studied within the model of a blackbody. In the classical approach, the exchange of energy between radiation and cavity walls is continuous. The classical approach does not explain the blackbody radiation curve.
• To explain the blackbody radiation curve, Planck assumed that the exchange of energy between radiation and cavity walls takes place only in discrete quanta of energy. Planck’s hypothesis of energy quanta led to the theoretical Planck’s radiation law, which agrees with the experimental blackbody radiation curve; it also explains Wien’s and Stefan’s laws.

## Conceptual questions

Which surface has a higher temperature – the surface of a yellow star or that of a red star?

yellow

Describe what you would see when looking at a body whose temperature is increased from 1000 K to 1,000,000 K.

Explain the color changes in a hot body as its temperature is increased.

goes from red to violet through the rainbow of colors

Speculate as to why UV light causes sunburn, whereas visible light does not.

Two cavity radiators are constructed with walls made of different metals. At the same temperature, how would their radiation spectra differ?

would not differ

Discuss why some bodies appear black, other bodies appear red, and still other bodies appear white.

If everything radiates electromagnetic energy, why can we not see objects at room temperature in a dark room?

human eye does not see IR radiation

How much does the power radiated by a blackbody increase when its temperature (in K) is tripled?

## Problems

A 200-W heater emits a 1.5-µm radiation. (a) What value of the energy quantum does it emit? (b) Assuming that the specific heat of a 4.0-kg body is $0.83\text{kcal}\phantom{\rule{0.1em}{0ex}}\text{/}\phantom{\rule{0.1em}{0ex}}\text{kg}·\text{K},$ how many of these photons must be absorbed by the body to increase its temperature by 2 K? (c) How long does the heating process in (b) take, assuming that all radiation emitted by the heater gets absorbed by the body?

a. 0.81 eV; b. $2.1\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{23};$ c. 2 min 20 sec

A 900-W microwave generator in an oven generates energy quanta of frequency 2560 MHz. (a) How many energy quanta does it emit per second? (b) How many energy quanta must be absorbed by a pasta dish placed in the radiation cavity to increase its temperature by 45.0 K? Assume that the dish has a mass of 0.5 kg and that its specific heat is $0.9\phantom{\rule{0.2em}{0ex}}\text{kcal}\phantom{\rule{0.1em}{0ex}}\text{/}\phantom{\rule{0.1em}{0ex}}\text{kg}·\text{K}.$ (c) Assume that all energy quanta emitted by the generator are absorbed by the pasta dish. How long must we wait until the dish in (b) is ready?

(a) For what temperature is the peak of blackbody radiation spectrum at 400 nm? (b) If the temperature of a blackbody is 800 K, at what wavelength does it radiate the most energy?

a. 7245 K; b. 3.62 μm

The tungsten elements of incandescent light bulbs operate at 3200 K. At what frequency does the filament radiate maximum energy?

Interstellar space is filled with radiation of wavelength $970\text{μ}\text{m.}$ This radiation is considered to be a remnant of the “big bang.” What is the corresponding blackbody temperature of this radiation?

about 3 K

The radiant energy from the sun reaches its maximum at a wavelength of about 500.0 nm. What is the approximate temperature of the sun’s surface?

#### Questions & Answers

plot a graph of MP against tan ( Angle/2) and determine the slope of the graph and find the error in it.
Ime Reply
expression for photon as wave
BARISUA Reply
Are beta particle and eletron are same?
Amalesh Reply
yes
mari
how can you confirm?
Amalesh
sry
Saiaung
If they are same then why they named differently?
Amalesh
because beta particles give the information that the electron is ejected from the nucleus with very high energy
Absar
what is meant by Z in nuclear physic
Shubhu Reply
atomic n.o
Gyanendra
no of atoms present in nucleus
Sanjana
Note on spherical mirrors
Shamanth Reply
what is Draic equation? with explanation
M.D Reply
what is CHEMISTRY
trpathy Reply
it's a subject
Akhter
it's a branch in science which deals with the properties,uses and composition of matter
Eniabire
what is a Higgs Boson please?
FRANKLINE Reply
god particles is know as higgs boson, when two proton are reacted than a particles came out which is used to make a bond between than materials
M.D
bro little abit getting confuse if i am wrong than please clarify me
M.D
the law of refraction of direct current lines at the boundary between two conducting media of
BATTULA Reply
what is the black body of an ideal radiator
Areej Reply
uncertainty principles is applicable to
Areej
fermions
FRANKLINE
what is the cause of the expanding universe?
FRANKLINE
microscopic particles or gases
Areej
Astronomers theorize that the faster expansion rate is due to a mysterious, dark force that is pulling galaxies apart. One explanation for dark energy is that it is a property of space.
Areej
Thanks for your contribution Areej.
FRANKLINE
no problem
Areej
what is photoelectric equation
HIMANSHU Reply
How does fringe intensity depend upon slit width in single slit diffraction?
Abhishek Reply
intensity seems to be directly proportional radius of slit
Mathieu
what are the applications of Bernoulli's equation
Shaukat
VOLTE
Md Reply
what is Draic equation
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text:
Algebra 1

$3y - 5 = 3y-9$ Subtract $3y$ from both sides. $-5 = -9$ This is not possible, so there are no solutions for $y$ that makes $3y-5 = 3y-9.$


text:
# The closure of the set of rational points in the Adeles

Let $X$ be a smooth geometrically integral projective variety over $\mathbb{Q}$. Then we may consider the closure $\overline{X(\mathbb{Q})}$ of $X(\mathbb{Q})$ inside the adelic points $X(\mathbb{A})=\prod_v X(\mathbb{Q}_v)$ of $X$. However, we may also take the closure $\overline{X(\mathbb{Q})}^v$ of $X(\mathbb{Q})$ inside $X(\mathbb{Q}_v)$ for any place $v$ of $\mathbb{Q}$. Obviously we have $$\overline{X(\mathbb{Q})} \subset \prod_v \overline{X(\mathbb{Q})}^v \subset X(\mathbb{A}).$$

My question whether this first inequality is actually an equality?

My motivation is that I am trying to understand better $\overline{X(\mathbb{Q})}$ and what it looks like. I will simply note that the answer to my question is yes in the easy cases where $X$ satisfies weak approximation and when $X(\mathbb{Q})$ is empty.

Edit: To make sure there are not simple counter-examples like the one David pointed out below, I am assuming that $X(\mathbb{Q})$ is Zariski dense. I should also note that I am particularly interested in the case where $X$ is a fano variety.

-
If $X(\mathbb{Q})$ is finite of order $> 1$, as for an elliptic curve of rank 0 with nontrivial torsion, then $\overline{X(\mathbb{Q})}$ is finite, but $\prod_v \overline{X(\mathbb{Q})}^v = X(\mathbb{Q})^{\aleph_0}$ is uncountably infinite, isn't it? –  David Loeffler May 22 '11 at 8:47
@David: Yes of course thanks! I over looked this simple case as the case I have in mind $X$ is fano and $X(\mathbb{Q})$ is Zariski dense. I will edit my question. –  Daniel Loughran May 22 '11 at 9:03
I'm puzzled by the question: isn't true that, because $\mathbb{Q}$ is discrete in $\mathbb{A}$, the set $X(\mathbb{Q})$ is discrete (hence closed) in $X(\mathbb{A})$? (this is certainly the case for affine varieties). –  Alain Valette May 22 '11 at 10:24
@Daniel: WHAT??? –  Alain Valette May 22 '11 at 11:27
@Alain: the projective situation is completely different to the affine situation. $\mathbf{Z}$ is a long way from $\mathbf{Q}$, so $\mathbf{A}^1(\mathbf{Z})$ is a long way from $\mathbf{A}^1(\mathbf{Q})$, but $\mathbf{P}^1(\mathbf{Q})=\mathbf{P}^1(\mathbf{Z)}$ by the valuative criterion for properness. –  Kevin Buzzard May 22 '11 at 18:38

Here's an example where $X(\mathbf{Q})$ is Zariski-dense but the first inequality is not an equality.

Let $X$ be an elliptic curve over the rationals, such that the group $X(\mathbf{Q})$ is isomorphic to $\mathbf{Z}$. Let me first remind you what $X(\mathbf{Q}_p)$ looks like, for $p$ a prime where the curve has good reduction. There's a natural reduction map $X(\mathbf{Q}_p)\to\overline{X}(\mathbf{F}_p)$, with $\overline{X}$ the reduction of $X$, and this reduction map is surjective onto a finite target. Hence $X(\mathbf{Q}_p)$ naturally breaks up as a finite disjoint union of cosets of the kernel of this map, and the kernel is (and hence all the cosets are) clopen.

Now let $P$ be a generator of $X(\mathbf{Q})$, put the curve into minimal form, choose a random large prime $\ell$ and consider $Q:=\ell.P$. It will be easy to find an example where $Q=(x,y)$ and there are two primes $p_1$ and $p_2$ in the denominator of $x$ but not in the denominator of the coordinates of $P$, and such that $X$ has good reduction at these primes. In short it should be easy to find two primes $p_1$ and $p_2$ such that $P$ has order exactly $\ell$ modulo both $p_1$ and $p_2$.

But now the first inclusion must be strict, because even the closure of $X(\mathbf{Q})$ in $X(\mathbf{Q}_{p_1})\times X(\mathbf{Q}_{p_2})$ is easily seen to be strictly smaller than the product of the closures, for the "same reason" that if $P_1$ has order $\ell$ in the finite abelian group $G$ and $P_2$ has order $\ell$ in the finite abelian group $H$, then the group generated by $(P_1,P_2)$ in $G\times H$ is strictly smaller than the product of the subgroups generated by $P_1$ and $P_2$.

-
You must mean $l=14$, as $P=(0,0)$ is a generator of 37A, and $7P=(−{5\over 9},{8\over 27})$. –  Junkie May 23 '11 at 3:09
For example if $X$ is the rank 1 curve of conductor 37 and $P$ is a generator then one can take $\ell=17$ and $p_1=11$ and $p_2=139$. –  Kevin Buzzard May 23 '11 at 7:02
[Junkie: you're right---thanks. I was using $2P$; I just deleted the comment and replaced it with a corrected one.] –  Kevin Buzzard May 23 '11 at 7:03
Great answer thanks! –  Daniel Loughran May 23 '11 at 9:32


text:
In the age of information overload,
brevity is the soul of wit ...

# Topological frequency conversion in Weyl semimetals

By: Frederik Nathan, Ivar Martin, Gil Refael

We theoretically predict a new working principle for optical amplification, based on Weyl semimetals: when a Weyl semimetal is suitably irradiated at two frequencies, electrons close to the Weyl points convert energy between the frequencies through the mechanism of topological frequency conversion from [Martin et al, PRX 7 041008 (2017)]. Each electron converts energy at a quantized rate given by an integer multiple of Planck's constant mul... more

# On the Nature and Types of Anomalies: A Review of Deviations in Data

By: Ralph Foorthuis

Anomalies are occurrences in a dataset that are in some way unusual and do not fit the general patterns. The concept of the anomaly is typically ill-defined and perceived as vague and domain-dependent. Moreover, despite some 250 years of publications on the topic, no comprehensive and concrete overviews of the different types of anomalies have hitherto been published. By means of an extensive literature review this study therefore offers the ... more

# Quantum simulation costs for Suzuki-Trotter decomposition of quantum many-body lattice models

By: Nathan M. Myers, Ryan Scott, Kwon Park, Vito W. Scarola

Quantum computers offer the potential to efficiently simulate the dynamics of quantum systems, a task whose difficulty scales exponentially with system size on classical devices. To assess the potential for near-term quantum computers to simulate many-body systems we develop a model-independent formalism to straightforwardly compute bounds on the number of Trotter steps needed to accurately simulate the system's time evolution based on the fi... more

# The ANITA Anomalous Events as Signatures of a Beyond Standard Model Particle, and Supporting Observations from IceCube

By: Derek B. Fox, Steinn Sigurdsson, Sarah Shandera, Peter Mészáros, Kohta Murase, Miguel Mostafá, Stephane Coutu (Penn State University)

The ANITA collaboration have reported observation of two anomalous events that appear to be $\varepsilon_{\rm cr} \approx 0.6$ EeV cosmic ray showers emerging from the Earth with exit angles of $27^\circ$ and $35^\circ$, respectively. While EeV-scale upgoing showers have been anticipated as a result of astrophysical tau neutrinos converting to tau leptons during Earth passage, the observed exit angles are much steeper than expected in Stand... more

# Evidence of near-ambient superconductivity in a N-doped lutetium hydride

By: Nathan Dasenbrock-Gammon, Elliot Snider, Raymond McBride, Hiranya Pasan, Dylan Durkee, Nugzari Khalvashi-Sutter, Sasanka Munasinghe, Sachith E. Dissanayake, Keith V. Lawler, Ashkan Salamat & Ranga P. Dias

The absence of electrical resistance exhibited by superconducting materials would have enormous potential for applications if it existed at ambient temperature and pressure conditions. Despite decades of intense research efforts, such a state has yet to be realized. At ambient pressures, cuprates are the material class exhibiting superconductivity to the highest critical superconducting transition temperatures (Tc), up to about 133 K. Over th... more

# Motorized actuation system to perform droplet operations on printed plastic sheets

By: Taejoon Kong, Santosh Pandey

We developed an open microfluidic system to dispense and manipulate discrete droplets on planar plastic sheets. Here, a superhydrophobic material is spray-coated on commercially-available plastic sheets followed by the printing of hydrophilic symbols using an inkjet printer. The patterned plastic sheets are taped to a two-axis tilting platform, powered by stepper motors, that provides mechanical agitation for droplet transport. We demonstrat... more
5 SciCasts by Santosh Pandey.

# Effect of magnetic field on the fermentation kinetics of Saccharomyces cerevisiae

By: Santosh Pandey

Published literature has shown conflicting results regarding the effects of magnetic fields on the fermentation kinetics or cellular growth of various Saccharomyces cerevisiae strains. Here, two sets of experiments were conducted to characterize the role of magnetic fields on cell growth and ethanol production during fermentation. The first experiment was completed for 25 h at a 2% dextrose loading rate under influence of homogeneous and non-... more
10 SciCasts by Santosh Pandey.

# Unidirectional, electrotactic-response valve for Caenorhabditis elegans in microfluidic devices

By: Santosh Pandey

We report a nematode electrotactic-response valve (NERV) to control the locomotion of Caenorhabditis elegans (C. elegans) in microfluidic devices. This nonmechanical, unidirectional valve is based on creating a confined region of lateral electric field that is switchable and reversible. We observed that C. elegans do not prefer to pass through this region if the field lines are incident to its forward movement. Upon reaching the boundary of t... more
10 SciCasts by Santosh Pandey.

# COVID-19 Testing and Diagnostics: A Review of Commercialized Technologies for Cost, Convenience and Quality of Tests

By: Ashler Benda, Lukas Zerajic, Ankita Ankita, Erin Cleary, Yunsoo Park, Santosh Pandey

Population-scale and rapid testing for SARS-CoV-2 continues to be a priority for several parts of the world. We revisit the in vitro technology platforms for COVID-19 testing and diagnostics—molecular tests and rapid antigen tests, serology or antibody tests, and tests for the management of COVID-19 patients. Within each category of tests, we review the commercialized testing platforms, their analyzing systems, specimen collection protocols, ... more

# Robotic agricultural instrument for automated extraction of nematode cysts and eggs from soil to improve integrated pest management

By: Christopher M. Legner, Gregory L Tylka, Santosh Pandey

Soybeans are an important crop for global food security. Every year, soybean yields are reduced by numerous soybean diseases, particularly the soybean cyst nematode (SCN). It is difficult to visually identify the presence of SCN in the field, let alone its population densities or numbers, as there are no obvious aboveground disease symptoms. The only definitive way to assess SCN population densities is to directly extract the SCN cysts from s... more

# Video Capsule Endoscopy and Ingestible Electronics: Emerging Trends in Sensors, Circuits, Materials, Telemetry, Optics, and Rapid Reading Software

By: Dylan Miley, Leonardo Bertoncello Machado, Calvin Condo, Albert E. Jergens, Kyoung-Jin Yoon, Santosh Pandey

Real-time monitoring of the gastrointestinal tract in a safe and comfortable manner is valuable for the diagnosis and therapy of many diseases. Within this realm, our review captures the trends in ingestible capsule systems with a focus on hardware and software technologies used for capsule endoscopy and remote patient monitoring. We introduce the structure and functions of the gastrointestinal tract, and the FDA guidelines for ingestible wir... more

# A Runtime Environment for Contract Automata

By: Davide Basile, Maurice H. ter Beek

Contract automata have been introduced for specifying applications through behavioural contracts and for synthesising their orchestrations as finite state automata. This paper addresses the realisation of applications from contract automata specifications. We present {\tt CARE}, a new runtime environment to coordinate services implementing contracts that guarantees the adherence of the implementation to its contract. We discuss how {\tt... more

# Evidence for suppression of growth of structure

By: Nhat-Minh Nguyen, Dragan Huterer, Yuewei Wen

We present evidence for a suppressed growth rate of large-scale structure during the dark-energy dominated era. Modeling the growth rate of perturbations with the growth index'' γ, we find that current cosmological data strongly prefer a higher growth index than the value γ=0.55 predicted by general relativity in a flat ΛCDM cosmology. Both the cosmic microwave background data from Planck and the large-scale structure data from weak lensing... more

# DeepCPG Policies for Robot Locomotion

By: Aditya M Deshpande, Eric Hurd, Ali A. Minai, Manish Kumar

Central Pattern Generators (CPGs) form the neural basis of the observed rhythmic behaviors for locomotion in legged animals. The CPG dynamics organized into networks allow the emergence of complex locomotor behaviors. In this work, we take this inspiration for developing walking behaviors in multi-legged robots. We present novel DeepCPG policies that embed CPGs as a layer in a larger neural network and facilitate end-to-end learning of locomo... more

# A primer on twistronics: A massless Dirac fermion's journey to moiré patterns and flat bands in twisted bilayer graphene

By: Deepanshu Aggarwal, Rohit Narula, Sankalpa Ghosh

The recent discovery of superconductivity in magic-angle twisted bilayer graphene has sparked a renewed interest in the strongly-correlated physics of sp2 carbons, in stark contrast to preliminary investigations which were dominated by the one-body physics of the massless Dirac fermions. We thus provide a self-contained, theoretical perspective of the journey of graphene from its single-particle physics-dominated regime to the strongly-correl... more

# TAU: A Framework for Video-Based Traffic Analytics Leveraging Artificial Intelligence and Unmanned Aerial Systems

Smart traffic engineering and intelligent transportation services are in increasing demand from governmental authorities to optimize traffic performance and thus reduce energy costs, increase the drivers’ safety and comfort, ensure traffic laws enforcement, and detect traffic violations. In this paper, we address this challenge, and we leverage the use of Artificial Intelligence (AI) and Unmanned Aerial Vehicles (UAVs) to develop an AI-integr... more

# Statistical strong lensing. I. Constraints on the inner structure of galaxies from samples of a thousand lenses

By: Alessandro Sonnenfeld

Context. The number of known strong gravitational lenses is expected to grow substantially in the next few years. The combination of large samples of lenses has the potential to provide strong constraints on the inner structure of galaxies. Aims: We investigate the extent to which we can calibrate stellar mass measurements and constrain the average dark matter density profile of galaxies by combining strong lensing data from thousands of lens... more

# Statistical strong lensing. II. Cosmology and galaxy structure with time-delay lenses

By: Alessandro Sonnenfeld

Context. Time-delay lensing is a powerful tool for measuring the Hubble constant H0. However, in order to obtain an accurate estimate of H0 from a sample of time-delay lenses, very good knowledge of the mass structure of the lens galaxies is needed. Strong lensing data on their own are not sufficient to break the degeneracy between H0 and the lens model parameters on a single object basis. Aims: The goal of this study is to determine whether ... more


text:
# If x + 1/x = 3, calculate x2

Question:

If $x+1 / x=3$, calculate $x^{2}+1 / x^{2}, x^{3}+1 / x^{3}, x^{4}+1 / x^{4}$

Solution:

Given, $x+1 / x=3$

We know that $(x+y)^{2}=x^{2}+y^{2}+2 x y$

$(x+1 / x)^{2}=x^{2}+1 / x^{2}+(2 * x * 1 / x)$

$3^{2}=x^{2}+1 / x^{2}+2$

$9-2=x^{2}+1 / x^{2}$

$x^{2}+1 / x^{2}=7$

Squaring on both sides

$\left(x^{2}+1 / x^{2}\right)^{2}=7^{2}$

$x^{4}+1 / x^{4}+2^{*} x^{2} * 1 / x^{2}=49$

$x^{4}+1 / x^{4}+2=49$

$x^{4}+1 / x^{4}=49-2$

$x^{4}+1 / x^{4}=47$

Again, cubing on both sides

$(x+1 / x)^{3}=3^{3}$

$x^{3}+1 / x^{3}+3 x^{*} 1 / x(x+1 / x)=27$

$x^{3}+1 / x^{3}+\left(3^{*} 3\right)=27$

$x^{3}+1 / x^{3}+9=27$

$x^{3}+1 / x^{3}=27-9$

$x^{3}+1 / x^{3}=18$

Hence, the values are $x^{2}+1 / x^{2}=7, x^{4}+1 / x^{4}=47, x^{3}+1 / x^{3}=18$


text:
# Stabilizer of a 4 by 4 skew symmetric matrix by orthogonal matrix

Matrices are over the field of complex numbers, and $X^t$ means transpose of a matrix $X$.

Consider the group action of $O(4)=\{P\mid PP^t=I\}$ on $SK(4)=\{M\mid M^t=-M\}$ by $(P,M) \rightarrow PMP^t$. Does anyone know what is the stabilizer of a general $M$?

Thank you!

-

This is only a paritial answer. The major difficulty of this question is that for every eigenvector $v$ corresponding to a nonzero eigenvalue of $M$, we have $v^Tv=0$. This directly conflicts with the conjugation of the form $PMP^T$, where $PP^T=I$. In other words, unlike the real case or the unitary equivalence case, we cannot directly use the eigenvectors of $M$ as columns of $P$ to simplify the structure of $M$.

Yet, when $M$ is diagonalizable and has nonzero distinct eigenvalues, the problem is easily solvable. As $M$ is skew symmetric, all its nonzero eigenvalues must have their negative counterparts. So, suppose the eigenvalues of $M$ are $\lambda,-\lambda,\mu,-\mu$, where $\lambda,\mu\not=0$ and $\lambda\not=\mu$. Let $v_1, v_2, v_3, v_4$ be the four corresponding unit eigenvectors. Note that when $x,y$ are eigenvectors of $M$ that correspond to some two eigenvalues $p,q$ with $p\not=-q$ and $p,q\not=0$, we have $$px^Ty = (y^Tpx)^T = (y^TMx)^T = -x^TMy = -qx^Ty$$ and hence $x^Ty=0$. Therefore, in our case, for $k\le j$, we have $v_k^Tv_j=0$ whenever $(k,j)\not=(1,2),(3,4)$.

Note that $v_1^Tv_2\not=0$ (and similarly $v_3^Tv_4\not=0$), otherwise we would have $\langle v_j,\bar{v}_1\rangle=0$ for $j=1,\ldots,4$, which is impossible. Therefore, if we define $c^2=1/(2v_1^Tv_2),\,w_1=c(v_1+v_2)$ and $w_2=ic(v_1-v_2)$ (here $i=\sqrt{-1}$) and define $w_3,w_4$ with $v_3,v_4$ analogously, it can be verified that $w_k^Tw_j=\delta_{kj}$, i.e. the matrix $W$ containing the $w_i$s as columns is complex orthogonal ($W^TW=I_4$). Hence $$W^TMW = \begin{pmatrix}i\lambda J_2\\&i\mu J_2\end{pmatrix}; \ J_2 = \begin{pmatrix}0&1\\-1&0\end{pmatrix}.$$ The stabilizers of $J_2$ are "rotation matrices" of the form $R(z)=\begin{pmatrix}\cos z&\sin z\\ -\sin z&\cos z\end{pmatrix}$, where $z\in\mathbb{C}$. Therefore the stabilizers of $M$ are given by $P=W\left(R(z_1)\oplus R(z_2)\right)W^T$.

The other cases, such as $M$ has zero eigenvalues, or some eigenvalues of $M$ have geometric multiplicity $>1$, etc., are more difficult to handle. I will try to cook up something if I can and if I have time.

-
Thank you! That is very helpful! –  Danny Jan 31 '13 at 5:45
The Jordan canonical form of M can only be diag{\lambda_1, -\lambda_1, \lambda_2, -lambda_2} or diag{M_1, M_2} where M_i's are 2 by 2 Jordan blocks with two \lambda's on the diagonal of M_1 and two -\lambda's on the diagonal of M_2. I found this by googling "The Jordan Canonical Forms of complex orthogonal and skew-symmetric matrices", one of the top 5 entries with this website: citeseerx.ist.psu.edu –  Danny Jan 31 '13 at 6:02
Actually I have some doubts on your result. So you mean there are only finitely many (16 as you mentioned) stabilizers for a general M, right? What I think so far is there may be a two-dimensional family of such stabilizers for a general M. –  Danny Jan 31 '13 at 6:10
@Danny And I had read the thesis you mentioned before I answered the question. According to thm 1.2.5, it is also possible that the Jordan form of $M$ is $J_3(0)\oplus J_1(0)$. What it says is that except for odd-order Jordan blocks that correspond to the zero eigenvalue, all other Jordan blocks of $M$ (of odd or even orders) must occur in $(\lambda,-\lambda)$ pairs (and $\lambda$ can be zero). –  user1551 Jan 31 '13 at 7:36
So, when $n=4$, there are three possibilities: (i) $\operatorname{diag}(a, -a, b, -b)$, (ii) $J_2(a)\oplus J_2(-a)$ or (iii) $J_3(0)\oplus J_1(0)$, where $a,b$ may be zero and are not necessarily distinct. –  user1551 Jan 31 '13 at 7:40


text:
# Is the square root of 14 rational?

Sep 30, 2015

No, $\sqrt{14} = \sqrt{2 \cdot 7}$ is irrational for the same reasons that $\sqrt{15}$ is irrational.
See my proof for $\sqrt{15}$.


text:
• Create Account

Programming

Term Name Description

3D Engine

A set of code that creates graphics that looks 3D. An engine would have all the necessary components from loading the models and data to drawing them on the screen.

A*

A algorithm for searching through data using heuristics, most usually used for path finding.

Abstract Data Type

A mathematically specified collection of data-storing entities with operations to create, access, change, etc. instances.

ActionScript

ActionScript: A ECMAScript-based programming language used for controlling Macromedia Flash movies and applications. More

An artificial intelligence system that can re-program itself based on environmental factors and influences.

Algorithm

A series of instructions for performing a task. This is the backbone of all programming.

Allegro

A game programming library which has been ported to a number of operating systems. (WWW)

Alpha Testing

The first phase of testing, where the software is tested in-house. The code is normally mostly functional, but some minor design decisions may still be tested.

ANN

Artificial Neural Net: A structure based on several weighted nodes used to process inputs. Particularly useful to Artificial Intelligence, because they aren't perfectly precise, and can be "trained" in a more realistic fashion.

API

Application Program Interface. A set of routines which acts as a go-between for the operating system and a program. For instance, DirectX is a Windows API.

Array

A set of characters and/or numbers defined within a variable. Used in programming to store data, create matrices, and other. C++ Example: char array[11]="Hello world"; ^ ^ ^ ^ | | | | | | | contents | | | | | number of characters | | | variable name type

Artificial Intelligence

Intelligence that mimics human intelligence. The main types of Artificial Intelligence used in games currently are State Machines, Expert Systems, Fuzzy Logic, Genetic Algorithms and Neural Networks.

Assembler

An assembler is basically a low level compiler which translates assembly instructions into object code, which can be read by the processor. See also: Assembly language.

Assembly Language

A low level programming language that uses hexadecimal values in the form of mnemonics. Each mnemonic corresponds to one or a set of instructions which is specific to the processor that the code is being written for. This means that assembly language is not very portable but is extremely powerful for optimizations. In fact many C/C++ compilers today come with inline assemblers for optimization. However unlike C/C++ and other higher level languages, which shields the programmer from a lot of what's going on, in assembly language the programmer must enter every instruction that the computer is to do. That also means that to write anything useful takes many more lines of code.

Asset

A generic term for graphics, sounds, maps, levels, models, and any other resources. Generally assets are compiled into large files. The file formats may be designed for fast loading by matching in-memory formats, or tight compressions for handheld games, or designed to otherwise help in-game use. It is often useful to have an asset tool chain. The original models may be high-density models with R8G8B8A8 images. You may have a model striper and image compresser that reduces the model for LOD, and compresses the texture to a DXT compressed image. These assets may then go through further transformations, and end up in the large resource file.

Bank

A 64K segment of video memory commonly found in older video cards which were made during the times of 16-bit compilers which had a maximum word size of 2 bytes, allowing a programmer to linearly address only 65K of screen space at any time.

BASIC

Beginners All-Purpose Symbolic Instruction Code. Originally created to teach the basics of programming, it uses a loose type casting system and has been brought back into the mainstream by Microsoft's Visual Basic.

Beta Testing

The second stage of testing where software is given to a group of users to test it in a real world environment. Software is usually functionally complete by this point and the goal is to work out the glitches.

Big-O Notation

A theoretical measure of the execution of an algorithm, usually the time or memory needed, given the problem size n, which is usually the number of items.

Informally saying some equation f(n) = O(g(n)) means it is less than some constant multiple of g(n). More formally it means there are positive constants c and k, such that 0 f(n) cg(n) for all n k. The values of c and k must be fixed for the function f and must not depend on n.

Binary Operator

An operator(like +, -, *, or /) that take two operands.

Bitwise Operators

Operators (such as And, Or, Not, and Xor) that do operations on the bits of an integeral type.

Modification by Michael Tanczos

Operations:
A AND B
C/C++ : A & B

Truth Table
-----------
0  1
/-----
0 | 0  0
1 | 0  1

Translation: Yields true if A and B are true

--------------------

A OR B
C/C++ : A | B

Truth Table
-----------
0  1
/-----
0 | 0  1
1 | 1  1

Translation: Yields true if either A or
B is true

--------------------

NOT B
C/C++ : ~B
NOT is an operator which negates a bit value

--------------------

A XOR B
C/C++ : A ^ B

Truth Table
-----------
0  1
/-----
0 | 0  1
1 | 1  0

Translation: Yields true if A and B are different

bloatware

Software that is needlessly large in size, that is, requiring a noticable amount of hard drive space (for installation) and RAM (while running). Bloatware is created by the inclusion of more than the necessary features for a particular program.

Boolean

An expression resulting in a value of either true or false. In general, zero is considered false while any other value is true. Also used as a variable type in some languages for storing boolean results.

BSOD

Acronym short for "Blue Screen Of Death", commonly displayed after a major system error under numerous versions of Microsoft Windows. Seeing a BSOD generally means a reboot is soon to follow.

C++

A programming language derived from C, based on Object Oriented Programming (OOP) using classes. The programming model for OOP focuses on the data being used instead of procedures.


text:
Equivalent Fractions – Explanation & Examples

In mathematics, equivalent fractions are simply fractions with different numerators and denominators but represent the same proportion of a whole. Equivalent fractions seem to be different at a look, but they have similar or equal value.

For example, the equivalent fractions for 1/4 are:

2/8, 3/12, 4/16, etc.

The equivalent fractions have an equal amount or value after simplification of both their numerator and denominators. The fractions will generate the same value if cancellation by a common factor is made on both the numerator and denominator.

What are Equivalent Fractions?

Equivalent fractions are two or more fractions that result in the same value after simplification. Suppose a/b and c/d are two fractions, then the fractions are equivalent only if the simplification of each fraction results in e/f.

In other words,

a/b = c/d = e/f.

For example, a fraction 1/3 has an equivalent of 5/15 because of simplification of 5/15 results in the same value as 1/3.

Now the question arises for why these fractions are equal despite having different numbers. The answer to this query is that the fractions contain numerators and denominators that are not co-prime numbers. Therefore they have a common multiple which on division produces the same value.

Let’s take an example:

1/2 = 2/4 = 4/8

You can notice that yet the above two factions have different integers, but after dividing both the numerator and denominator by a common factor, the result is:

(4 ÷ 4)/(8 ÷ 4)

=1/2

In this case, if we simplify 2/4, the result 1/2 again.

(2 ÷ 2)/(4 ÷ 2)

= 1/2

It has been shown that either dividing the denominator or multiplying the numerator with the same factor does not alter the value of the fraction. And therefore, equivalent fractions have an equal value when simplified.

How do you find equivalent fractions?

Consider a case with the fraction 1/5.

Multiplying both the numerator and denominator with 2, 3 and 4 gives:

1/5 x 2/2 = 2/10

1/5 x 3/3 = 3/15

1/5 x 4/4 = 4/20

Therefore, it can be concluded that:

1/5 = 2/10 = 3/15 = 4/20

The equivalent fraction can only be generated by multiplication or division by a common factor. Carrying out addition or subtraction on the fraction only changes the value of a fraction.

Example 1:

Given that the fractions 5/16 and x/12 are equivalent calculate the value of x.

Solution

Given that:

5/16 = x/12

x = (5 x 12)/16

x = 60/16

x =15/4

And thus, the value of x is 15/4.

Example 2:

Find the value of x if the fractions 3/5 and 4/x are equivalent.

Solution

Given that,

3/5 = 4/x

x = (4 x 5)/3

x = 20/3

Practice Questions

1. Which of the following is not equivalent to $\dfrac{3}{4}$?

2. Which of the following is not equivalent to $\dfrac{4}{5}$?

3. Which of the following is not equivalent to $\dfrac{6}{7}$?

4. Which of the following is not equivalent to $\dfrac{2}{9}$?

5. What is the equivalent fraction of $\dfrac{1}{2}$ so that it has a denominator of $12$?

6. What is the equivalent fraction of $\dfrac{1}{3}$ so that it has a denominator of $18$?

7. What is the equivalent fraction of $\dfrac{3}{4}$ so that it has a denominator of $20$?

8. What is the equivalent fraction of $\dfrac{5}{6}$ so that it has a denominator of $30$?

9. What is the equivalent fraction of $\dfrac{6}{12}$ so that it has a numerator of $24$?

10. What is the equivalent fraction of $\dfrac{3}{8}$ so that it has a numerator of $24$?

11. What is the equivalent fraction of $\dfrac{2}{6}$ so that it has a numerator of $48$?

12. What is the equivalent fraction of $\dfrac{4}{6}$ so that it has a numerator of $12$?

13. Which of the following pairs of fractions are not equivalent fractions?

14. I’m thinking of an equivalent fraction to $\dfrac{10}{15}$ with $2$ as the numerator. What fraction am I thinking of?

15. Erick notices that either $\dfrac{3}{5}$ or $\dfrac{3}{4}$ is equal to the fraction $\dfrac{12}{20}$. Which fraction is equal to $\dfrac{12}{20}$?

16. Peter gave $\dfrac{1}{4}$ and $\dfrac{3}{12}$ of orange to Donald and Pedro, respectively. Did he give out an equivalent fraction of an orange?


text:
Find the sign of $\int_{0}^{2 \pi}\frac{\sin x}{x} dx$

I'd love your help with finding the sign of the following integral: $\int_{0}^{2 \pi}\frac{\sin x}{x} dx$,I know that computing it is impossible. I tried to use integration by parts and maybe to learn about the sign of each part and conclude something but It didn't work for me.

Any suggestions?

Thanks!

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Do you want an approximate? –  Pedro Tamaroff Feb 8 '12 at 16:34
Wolfram alpha will give you an approximation. (by the way it's positive) –  Bill Cook Feb 8 '12 at 16:34
No, as I said I want to find only the sign, I want to find it by a "calculus- investigation", and not by checking it on W.A :) Thanks! –  Jozef Feb 8 '12 at 16:38

\begin{align*} \int_0^{2\pi}\frac{\sin x}{x}\,dx&=\int_0^{\pi}\frac{\sin x}{x}\,dx+\int_\pi^{2\pi}\frac{\sin x}{x}\,dx\\ &=\int_0^{\pi}\frac{\sin x}{x}\,dx+\int_0^{\pi}\frac{\sin(x+\pi)}{x+\pi}\,dx\\ &=\int_0^{\pi}\Bigl(\frac{1}{x}-\frac{1}{x+\pi}\Bigr)\sin x\,dx\\ &=\pi\int_0^{\pi}\frac{\sin x}{x(x+\pi)}\,dx\\ &>0 \end{align*}

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Thanks Julian! :) very nice solution! –  Jozef Feb 8 '12 at 16:49

Regarding the sign, it is easy the check that every area in each $\pi$ interval is always smaller than the preceeding one. The sign is positive.

For the value, integrate in the same interval

$$y = \cos \frac{x}{2} \cos \frac{x}{4} \cos \frac{x}{8}$$

The difference between the sinc function and that is at most $\approx 0.015$ in that interval.

Adding $$\cos \frac{x}{16}$$ makes the error at most $\approx 0.003$

For the first one you have.

$$I = \frac{104}{105} \sqrt{2} \sim\sqrt{2}$$

For the latter:

$$I = \frac{{1568}}{{2145}}\frac{{\sqrt {2 + \sqrt 2 } }}{2} \sim \sqrt{2}$$

Maybe the area is $\sqrt{2}$ after all.

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Let $f(x)=\sin(x)/x$. So $f(x)=0$ when $\sin(x)=0$. So the only solution in the interval $(0,2\pi)$ is $x=\pi$. Plugging in test points shows that $f(x)$ is positive to the left of $x=\pi$ and negative to the right.

Next, if you accept that $1-x/3 \leq \sin(x)/x$ (make some argument using MacLaurin series), then $\int_0^{\pi} f(x)\,dx \geq \frac{1}{2}(3)(1)=3/2$. On the other hand $|\sin(x)|/x \leq |\sin(x)|/3$ for $x \geq 3$ so $\int_{\pi}^{2\pi} |f(x)|\,dx \leq \int_{\pi}^{2\pi} \frac{|\sin(x)|}{3}\,dx = 2/3$.

So $\int_0^{2\pi} f(x)\,dx \geq 3/2-2/3>0$

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text:
# Formatting “List of Algorithms”

My school requires the list of Algorithms to be formatted the same way as the list of figures. I found a similar question here. Upon trying this answer from Werner, I did get the formatting spot on as shown in image:

However, the word 'Figure' appears in place of 'Algorithm' everywhere in Table of contents and the list-of-Algorithms. How can I replace the text 'Figure' with 'Algorithm' in these places?

You may change names with the following commands

\renewcommand{\figurename}{New Figure Caption Name}
\renewcommand{\figureautorefname}{New Figure Autoref Name}
\renewcommand{\listfigurename}{List of Figures Modifyed}

However, I would suggest to use \usepackage{listings} and then rename the captions with

\renewcommand{\lstlistingname}{Algorithm}
\renewcommand{\lstlistlistingname}{List of Algorithms}

And using the command \lstlistoflistings to insert the list of all listings. This approach does not mix figures and others objects you might have in your work.

You may insert external code with

% firstline = 1, lastline = 10, firstnumber = 1, nolol,
\lstinputlisting[label = {alg:file_name}, caption = {Legenda}]
{file_name.m}

or copy and paste it internally with

\begin{lstlisting}
insert code here
\end{lstlisting}

You may find some more advice at How to put a list of code in appendix? and the links in it.