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# Troubleshooting failed recipes¶
## Recipes built with conda-build 3¶
If you have conda-build 3 installed locally and use conda skeleton, the resulting meta.yaml will be incompatible with our conda-build 2 infrastructure.
We are moving towards supporting conda-build-3 which has many nice features we can take advantage of. In the meantime, however, we need to use conda-build 2.
In particular, conda-build 3 uses the host: key instead of the build: key for dependencies. Conda-build 2 ignores that key. The result is that cb3-created meta.yaml will have no build dependencies from cb2’s point of view.
The easiest fix is to change host: to build: in the resulting recipe.
For failed recipes, usually the easiest thing to do is find the first BIOCONDA ERROR, and start reading the output below that line. The stdout and stderr for that failed build will end with the next BIOCONDA log line, likely a BIOCONDA BUILD START or BIOCONDA BUILD SUMMARY line. Note that there are two tests: the tests performed by conda in the main environment, and if they pass, the mulled-build tests performed in a minimal docker container. For working with failures in mulled-build tests, see Troubleshooting failed mulled-build tests.
## HTTP 500 errors¶
Sometimes recipes fail for reasons outside our control. For example, if anaconda.org returns an HTTP 500 error, that has nothing to do with the recipe but with anaconda.org’s servers. In this case, you can either restart the build (if you have access to do so in the circleci interface), or close the PR and then immediately re-open it to trigger a re-build.
## HTTP 404 errors¶
HTTP 404 errors can happen if a url used for a recipe was not stable. In this case the solution is to track down a stable URL. For example this problem happened frequently with Bioconductor recipes that were up-to-date as of the current Bioconductor release, but when a new Bioconductor version came out the links would not work.
The solution to this is the Cargo Port, developed and maintained by the Galaxy team. The Galaxy Jenkins server performs daily archives of the source code of packages in bioconda, and makes these tarballs permanently available in Cargo Port. If you try rebuilding a recipe and the source seems to have disappeared, do the following:
• search for the package and version at https://depot.galaxyproject.org/software/
• add the URL listed in the “Package Version” column to your meta.yaml file as another entry in the source: url section.
• add the corresponding sha256 checksum displayed upon clicking the Info icon in the “Help” column to the source: section.
For example, if this stopped working:
source:
fn: argh-0.26.1.tar.gz
url: https://pypi.python.org/packages/source/a/argh/argh-0.26.1.tar.gz
md5: 5a97ce2ae74bbe3b63194906213f1184
then change it to this:
source:
fn: argh-0.26.1.tar.gz
url:
- https://pypi.python.org/packages/source/a/argh/argh-0.26.1.tar.gz
- https://depot.galaxyproject.org/software/argh/argh_0.26.1_src_all.tar.gz
md5: 5a97ce2ae74bbe3b63194906213f1184
## ZLIB errors¶
When building the package, you may get an error saying that zlib.h can’t be found – despite having zlib listed in the dependencies. The reason is that the location of zlib often has to be specified in the build.sh script, which can be done like this:
export CFLAGS="-I$PREFIX/include" export LDFLAGS="-L$PREFIX/lib"
Or sometimes:
export CPATH=${PREFIX}/include Sometimes Makefiles may specify these locations, in which case they need to be edited. See the samtools recipe for an example of this. It may take some tinkering to get the recipe to build; if it doesn’t seem to work then please submit an issue or notify @bioconda/core for advice. ## /usr/bin/perl or /usr/bin/python not found¶ Often a tool hard-codes the shebang line as, e.g., /usr/bin/perl rather than the more portable /usr/bin/env perl. To fix this, use sed in the build script to edit the lines. Here is an example that will replace the first line of a file $PREFIX/bin/alocal with the proper shebang line
sed -i.bak '1 s|^.*$|#!/usr/bin/env perl|g'$PREFIX/bin/aclocal
(note the -i.bak, which is needed to support both Linux and OSX versions of sed).
It turns out that the version of autoconf that is packaged in the defaults channel still uses the hard-coded Perl. So if a tool uses autoconf for building, it is likely you will see this error and it will need some sed commands. See here for an example to work from.
## Troubleshooting failed mulled-build tests¶
After conda sucessfully builds and tests a package, we then perform a more stringent test in a minimal Docker container using mulled-build. Notably, this container does not have conda and has very few libraries. So this test can catch issues that the default conda test cannot. However the extra layer of abstraction makes it difficult to troubleshoot problems with the recipe. If the conda-build test works but the mulled-build test fails try these steps:
• Run the test using the bootstrap.py method described in 3. Test locally.
• Look carefully at the output from mulled-build to look for Docker hashes, and cross-reference with the output of docker images | head to figure out the hash of the container used.
• Start up an interactive docker container, docker run -it \$hash. You can now try running the tests in the recipe that failed, or otherwise poke around in the running container to see what the problem was.
## Using the extended image¶
For the vast majority of recipes, we use a minimal BusyBox container for testing and to upload to quay.io. This allows us to greatly reduce the size of images, but there are some packages that are not compatible with the minimal container. To support these cases, we offer the ability to in special cases use an “extended base” container. This container is maintained at https://github.com/bioconda/bioconda-extended-base-image and is automatically built by DockerHub when Dockerfile is updated in the GitHub repo.
Please note that this is not a general solution to packaging issues, and should only be used as a last resort. Cases where the extended base has been needed are:
• Unicode support is required (especially if a package uses the click Python package under Python 3; see for example comments here and here).
• libGL.so.1 dependency
• openssl dependency, e.g., through openmpi
To use the extended container, add the following to a recipe’s meta.yaml:
extra:
container:
extended-base: True
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# Object stuck to screen no matter what eye position is used
I've run into an issue when trying to write a simple rendering program in D3D11. I'm 90% sure it's to do with some faulty matrix multiplication or generation, but I've tried debugging the values of the matrices and they seem fine to me.
The problem is that no matter where I move the eye position, the rendered cube always appears the same.
The resulting screen image is like this:
Each vertex of the cube has a different colour, and the pixel shader should be blending between them, so the gradient effect you can see is between four vertices of the cube.
Here's some of my code
eyePos = XMVectorSet(0.0f, 1.0f, -5.0f, 0.0f);
lookAtPos = XMVectorSet(0.0f,1.0f,0.0f,0.0f);
up = XMVectorSet(0.0f,1.0f,0.0f,0.0f);
world = XMMatrixIdentity();
view = XMMatrixLookAtLH(eyePos, lookAtPos, up);
projection = XMMatrixPerspectiveFovLH(XM_PIDIV2, 1000.0f / 680.0f, 0.01f, 100.0f);
_pIContext->IASetVertexBuffers(0, 1, &_vertexBuffer, &stride, &offset);
_pIContext->IASetIndexBuffer(_indexBuffer, DXGI_FORMAT_R16_UINT, 0);
_pIContext->VSSetConstantBuffers(0, 1, &_cbWorldBuffer);
_pIContext->VSSetConstantBuffers(1, 1, &_cbViewBuffer);
_pIContext->VSSetConstantBuffers(2, 1, &_cbProjBuffer);
And then for shader code, we've got...
cbuffer worldBuffer : register(b0) {
matrix World;
float t;
}
cbuffer viewBuffer : register(b1) {
matrix View;
}
cbuffer projectionBuffer : register(b2) {
matrix Projection;
}
PS_INPUT vs(float4 pos : POSITION, float4 col : COLOUR) {
PS_INPUT output = (PS_INPUT)0;
output.Pos = mul(pos, World);
output.Pos = mul(pos, View);
output.Pos = mul(pos, Projection);
output.Colour = col;
return output;
}
float4 ps(PS_INPUT input) : SV_TARGET{
return input.Colour;
}
My gut tells me it's the projection matrix, although I've based this on another project I did, and comparing the code, I can't find out what I've done differently.
Your code overwrites output.Pos three times, so only the last write sticks. That last write was:
output.Pos = mul(pos, Projection);
Note that this is multiplying your input vertex position (in object space) by the projection matrix. So your resulting position depends only on the mesh and the projection, ignoring the object's world transformation and the camera's view.
It looks like you meant to write something more like this:
output.Pos = mul(pos, World);
output.Pos = mul(output.Pos, View);
output.Pos = mul(output.Pos, Projection);
Note that the input to the last two steps is the output from the previous step, so their work filters through to the final result.
But a more conventional solution would be to multiply these three matrices together on the CPU, and upload a single combined matrix to the GPU as one uniform variable or constant buffer entry: your WorldViewProjection matrix. Then in the shader you only need to do one matrix multiplication instead of chaining three dependent ones.
• Oh my gosh you're right! I can't believe I didn't notice it, and yes thank you for the info on combining into the MVP matrix on CPU side. I uploaded them as three different Constant buffers as the projection would only need to be re-calculated if window is resized right? (Or fov / near / far changed). And then the view only needs to be recalculated if the camera (eye) moves or looks at another point Nov 5 at 23:04
• A single matrix multiplication is cheap, so it's worth paying the cost once every frame to avoid having to do it thousands of times across all your vertices. Nov 5 at 23:20
• Right okay sounds good, I'll go ahead and implement that too thanks :) Nov 6 at 1:38
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# Grid Tie Inverter Schematic
#### tcmtech
##### Banned
To get a thousand dollar cost avoidance with 1KW back feeding continuously I would need to run it non stop for....
1000 / .12 = 8333 hours.
Or 347 days 5 hours.
or about 4 times that factoring in usable year round day light is maybe 8 - 10 hours a day plus the numerous cloudy days too.
Toss in 1KW of usable solar panel power. Thats what about $5000 more. Now I am at... 6000 / .12 = 50000 hours multiply by 4 for realistic run time. 200,000 hours or 22 years, 297 days, 20 hours Maybe add one more year of runtime for parts outlay from near 23 years of general maintenance too if your dam lucky. SO lets say 24 years average assuming my electric rate doesn't jump again in 24 years. (not holding my hopes to high on that one either) And hope like hell hail, wind, snow, ice, design flaws or age doesn't take them down first! Sorry but not cost effective in my mind. #### Val Gretchev ##### Member Forum Supporter Re: Line Powered PWM Rev B Here is one for tcmtech. This one uses the International Rectifier driver chip IR2113. I don't have any experience with this chip, so let me know if I wired it wrong. Also, remember that this design is not completely isolated from the PV array. #### Attachments • 143.9 KB Views: 1,229 #### colin55 ##### Well-Known Member The Australian government subsidy of$8,000 for a 1kW solar system is a total scam but isn't everything associated with a government a SCAM?
The effectiveness of the system is no more than 4-5kWh per day and any power fed back to the system is paid at a rate of 44cents to 60cents per kWhr. This is also a scam as it costs 3.5cents to produce electricity and householders pay between 10cents and 16cents per kWhr.
No wonder households are signing up for the scheme in droves and most companies offering the package are already 9 months over-booked.
Who would buy an inverter or panel when they all come FREE!
#### tcmtech
##### Banned
From what I can see your schematic of the power handling system is identical to what I use. As you can see you get full control of the entire H- bridge and full shut down with only 3 logic level control lines. I just use the 500 volt IC's because I typically dont need higher voltage but for a higher voltage setup I would not hesitate to use the 600 volt ones you have.
With this power handling circuit architecture its simple to make countless sizes in this design but still have only one master control board design that can operate any of them with only a few simple reference signal changes!
I smell dirt cheap mass production! Dont you?
#### Hero999
##### Banned
There is no point making a prototype, in my opinion, if you can't reproduce it at a reasonable cost in any quantity.
That depends on why you're making the prototype. If it's just for educational purposes and you're not bothered about getting it made commercially then the single unit cost it more important than the production cost.
#### Val Gretchev
##### Member
Forum Supporter
Re: Making Transformers
While we are on the subject of transformers, here is a video of how you make one. Winding Machine.
While we are at it, if you were making a custom output transformer (T2 in the schematic), why not add an extra winding for 30 Volts center tapped at about 1.5 Amps to use for the low voltage power supply and eliminate the other transformer (T1) completely. That's another saving.
#### Val Gretchev
##### Member
Forum Supporter
Solar Panel Optimizing
National Semiconductor has entered the end-user alternative energy marketplace with their SolarMagic(TM) PV Power Optimizer. You can read all about it at their site SolarMagic? Technology Home -- Solar for the Real World.
At first glance, it appears that the SolarMagic(TM) technology is nothing more then a voltage booster with a maximum power searching algorithm. Fortunately for all you PIC-lovers out there, Microchip has already published an Application Note and source code for just such a device. Download the article and code at Microchip.
This same algorithm can be applied to the main Grid-Tie inverter to maximize its power output. Start with the attenuator at near zero. Measure the PV array voltage and current and multiply the two values together to get power output. Increase the attenuator voltage. Re-calculate the power output. If the power has gone up, keep increasing the attenuator voltage until there is a power drop. Then back up the attenuator voltage one step. You have found the optimum operating point for the current illumination. Continue with the dithering algorithm to maintain the optimum PV power utilization.
#### colin55
##### Well-Known Member
National Semiconductor has entered the end-user alternative energy marketplace with their SolarMagic(TM) PV Power Optimizer. You can read all about it at their site SolarMagic? Technology Home -- Solar for the Real World.
At first glance, it appears that the SolarMagic(TM) technology is nothing more then a voltage booster with a maximum power searching algorithm.
It appears that "SolarMagic" is nothing more than a blocking diode - that's all you need.
#### Mr RB
##### Well-Known Member
National Semiconductor has entered the end-user alternative energy marketplace with their SolarMagic(TM) PV Power Optimizer. You can read all about it at their site SolarMagic? Technology Home -- Solar for the Real World.
At first glance, it appears that the SolarMagic(TM) technology is nothing more then a voltage booster with a maximum power searching algorithm. Fortunately for all you PIC-lovers out there, Microchip has already published an Application Note and source code for just such a device. Download the article and code at Microchip.
...
I designed a commercial solar MPPT a few years back with VERY high efficiencies (no I didn't use Microchip's system). I can't say too much about if due to contractual reasons, but I can say is that efficiency wise it is right up there with the best performing units in the world.
It's not that hard to do the max power point tracking itself, what is difficult is to do the actual voltage conversion reliably at 95+% efficiency and do it cost effectively so the device is actually worth buying and adding to a solar installation. Dollar cost effectiveness is everything.
As for the state of the industry I fully expect in a few years that any solar panel costing more than a couple hundred will have a tiny switchmode MPPT converter built in.
#### tcmtech
##### Banned
Can you whisper some secrets in our collective ear as to how you design a 95% efficient switcher? Or even only 94% efficient as so not to break any contractual blah blah blah?
I have read up on some methods of using two or more inductors or transformers being ran with a switching time phase difference between them. Does that actually increase efficiency greatly or just power handling capacity?
Sort of a single phase Vs two or three phase type configuration.
I work with commercial three phase stuff all the time but have never played with its concept in a switching power supply application.
#### Mr RB
##### Well-Known Member
Well there's the obvious synchronous rectification, using controlled FETs as diodes, to reduce the diode losses.
What I will say is that inductors are everything. Besides being hand wound, we had to get the main inductor core material made overseas to my specification of minerals using some exotic minerals (basically aerospace quality inductor core material) to get the switching freq low enough and maintain the required magnetic properties. That might give you some idea! I'm not an expert on the magnetic minerals, and I don't think I've used magnetic formulae since 1983 in DC-machines class, I just did a lot of trial and error testing on the CRO with sample cores and refined it down to the right properties to suit our needs, then had a production batch of cores produced to that spec.
90% is pretty easy. 95% gets harder, 95% with good reliability, high current density, smallish size, large operating range and decent cost effectiveness gets real hard.
As for a multiphase system I have never done one, give me a nice simple buck regulator or push-pull voltage transformer anyday.
#### shungun
##### New Member
Does anybody know how to make an inverter from 12volt dc to 12 volt AC? around 6 amps.
i tried a squarewave generator with 2n3055 but didnt work too well.
#### Val Gretchev
##### Member
Forum Supporter
Re: PWM Circuit
I built a test jig to verify the operation of the circuits shown in Post7.zip. I bypassed the attenuator chip and fed the AC signal from the voltage divider R5/R6 straight into the comparator. I also changed the value of C6 to 0.022uF to produce a higher frequency triangle wave. I put a small filter on one of the U8 outputs consisting of 15K ohms and 0.1 uF and took these pictures.
As you can see, the wave shape isn't exactly as the input waveform. Also, there is a considerable phase shift in the output which will be a problem. If anyone has any ideas as to how to eliminate this phase shift, please let me know.
#### Attachments
• 1.3 MB Views: 1,046
#### Mr RB
##### Well-Known Member
Well looking at the phase lag, smoothing and reduction in amplitude that are obvious in picture DSC_2347 it looks like you are overfiltering something?
#### Val Gretchev
##### Member
Forum Supporter
Re: PWM Circuit
I didn't have a MAX5437 chip on hand so I used a manual potentiometer and a TL082 op-amp. I wired the op-amp as a phase shifter and was able to bring the mains AC waveform and the filtered output in phase. I am now fairly confident that this circuit will produce the desired results. The next step will be to add the IGBTs and the output transformer.
#### Attachments
• 1.4 MB Views: 1,031
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Pascal's triangle for an interview in PHP
I saw that one of the interview questions could be building a pascal triangle. Is there anything wrong with this particular solution I came up with?
function pascal_r($r){$local = array();
if($r == 1){ return array(array(1)); } else {$previous = pascal_r($r - 1); array_push($local, 1);
for($i = 0;$i < $r - 2 &&$r > 2; $i++){ array_push($local, $previous[$r-2][$i] +$previous[$r-2][$i + 1]);
}
array_push($local, 1); } array_push($previous, $local); return$previous;
}
print_r(pascal_r(100));
• Edited my post with new information you might find interesting. Sep 28 '12 at 15:17
In regards to the comments: Yes, this is a good place for this so long as it works as is and you are asking about the code and not the algorithm. If you are asking about the algorithm this should have stayed on programmers.SE. If you are asking if this will work, then you should test it first, then if you can't find a solution you should post this to SO. Now, assuming this works and you're not asking about the algorithm, here are my thoughts:
A number of these points may be nitpicking, but the interviewers are likely to nitpick as well since they have so little code to review to determine how good you are. First example of this are your variable and function names, which could stand to be a bit more descriptive. I can guess what "r" might be, but spelling it out wouldn't hurt, especially if that variable might get lost in layers of code. It makes your code "self-documenting", this means less actual documentation and easier future integration.
Unless you have to add a number of elements on to an array at the same time, don't use array_push(). There is no need to call a function to do something that can be done without one. This is also explicitly explained on the PHP documentation for this function should you need further proof.
$local[] = 1;//good array_push($local,
1,
2,
//etc...
);//also good
array_push( $local, 1 );//bad Watch your indentation. That for loop is needlessly indented. Needless whitespace and indentation add "weight" to your documents. Not much at any one time, but a weight that can build up steadily, especially if you are of the faction that uses spaces instead of tabs. This isn't ever likely to cause any real world difficulties, except maybe slightly larger file sizes, but again, I'm nitpicking. Something else you are going to get tagged on is all of these magic numbers. Where are these 1's and 2's coming from? If those numbers mean something, then you should create constants or variables to define it. Constants if immutable, variables if mutable. If, as in your first return statement you are merely returning the value of $r, as it appears, then you can just typecast it.
if( $r == 1 ) { return array( ( array )$r );
}
Instead of doing the same operation, $r - 2, over and over again, set the value to a variable and use that instead. Its overhead may be slight, and again a nitpick, but it still adds up if done enough. Besides, it makes for much more legible code. $r2 = $r - 2;//horrible name, don't use this for($i = 0; $i <$r2 && $r > 2;$i++ ) {
This next suggestion is similar to one I've already given. Watch your indentation. You have an if/else statement when you could really get away with just an if statement. Since it has an early return, you can drop the else statement, this removes one layer of indentation across six lines of code. In larger systems this could easily add up to quite a bit more and is easily one of the easiest, most visual, refactoring you can do.
The last bit of advice would be to use var_dump() over print_r(). While this may be a matter of preference, I find the type output beneficial, especially in cases where you could somehow get an empty array or FALSE value.
EDIT
Interesting coincidence here, but I'm taking a course on Coursera (Functional Programming in Scala), and one of the things we were required to do was find the value of a given coordinate on a pascal triangle. This assignment reminded me of this post so I thought I'd revisit it, but I wanted to wait until the deadline had been reached before posting this. Below is the code I used to functionally find the value.
• Note: I'm using spoilers to give you a chance to work it out. Try and do these yourself before peeking.
function pascal( $col,$row ) {
if( $col == 0 ||$col == $row ) { return 1; } else if($col == 1 || $col ==$row ) {
return $row; } else { return pascal($col, $row - 1 ) + pascal($col - 1, $row - 1 ); } } • Note: I stressed functional, but there are other ways of doing this. I'm merely keeping with my assignment's guidelines. • Note: I know I'm violating some of my own advice. The instructions I was given in my assignment stressed not to use variables, so I'm not. So, given we can now find a value at any given coordinate, we should easily be able to use this to print a pascal triangle too. All we need is to determine how big we want our triangle to be and we can loop for it. I'm going to use 10, but you can change that amount to any value you want and it will still work. Again, no peeking! for($i = 0; $i < 10;$i++ ) {
for( $j = 0;$j <= $i;$j++ ) {
echo pascal( $j,$i ) . ' ';
}
echo '<br />';
}
There you have it. Not only have you printed a pascal triangle, but you've also created a function that can be reused to serve a better purpose, namely finding a coordinate value.
Is there anything wrong with this particular solution I came up with?
I am going to add one thing and suggest an alternate solution.
Needs a Comment
A function like this should have a comment at the top of it. It should describe what your function does. In this case I would also add in your comment that this function is unlikely to work for large triangles!
Why won't it work?
Computations of this sort can run into fatal limits:
If you use xdebug you would also have:
• Nesting level too great (default configuration is 100)
One way to avoid deep nesting is to use an iterative solution rather than a recursive one. To me, the iterative solution is easier to understand here because each pascal number is the addition of the previous level's elements that are to the left and right of the number.
/**
* Get a pascal triangle of the specified depth.
*
* Large triangles require a lot of memory, be sure to set the memory limits
* appropriately for the size of triangles you need to allocate.
*
* @param int The depth of the triangle to generate.
* @return int[] The pascal triangle.
*/
function get_pascal_triangle($depth) {$triangle = array();
for ($level = 0;$level < $depth;$level++)
{
$prevLevel =$level - 1;
for ($pos = 0;$pos < $level + 1;$pos++)
{
$triangle[$level][$pos] = isset($triangle[$prevLevel][$pos - 1],
$triangle[$prevLevel][$pos]) ?$triangle[$prevLevel][$pos - 1] + $triangle[$prevLevel][$pos] : 1; } } return$triangle;
}
• Indeed, there are many different ways this could be accomplished, and I actually prefer one similar to this. Although, I have to say I am a bit put off by that ternary statement. Don't get me wrong, I like ternary, but that one is a poor example of where to use it. That being said, there are some very good points in here, so a big +1. Sep 29 '12 at 17:48
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Web lists-archives.com
# Re: How to create a PDF-Printer from the command line
• Date: Tue, 9 Jan 2018 17:01:50 -0600
• From: David Wright <deblis@xxxxxxxxxxxxxxxxx>
• Subject: Re: How to create a PDF-Printer from the command line
On Tue 09 Jan 2018 at 23:20:55 (+0100), tomas@xxxxxxxxxx wrote:
> On Tue, Jan 09, 2018 at 02:09:22PM -0600, David Wright wrote:
>
> [...]
>
> > For me, this is a new take on document conversion methods.
> >
> > FWIW my test file produced 30819 "Missing character" errors which
> > is hardly surprising as TeX was released 40 years ago in the days
> > of 7 bit ASCII. The PDF had a single line of characters running
> > off the right hand side of the page.
>
> Modern (La)TeX implementations should be able to cope with UTF-8
> input: \usepackage[utf8]{inputenc} is one of the recommended magic
> incantations (that said, reportedly Lua(La)TeX and Xe(La)TeX are
> said to cope even better; they are part of your TeX live distribution
> anyway).
>
> Of course you have to make sure that your font supports the glyphs
> you actually use.
Thanks. I feel ashamed that I'm wasting your time, and that of
Ionel Mugurel Ciobîcă. I'm only testing the methods being suggested
here for conversion. It's proved valuable (for me) as I hadn't come
across txt2pdf before, which is already wrapped up in my .bashrc,
but one does see poor suggestions as well as good ones.
I've been a LaTeX user for over 30 years, so I've stripped out more
Unicode workarounds than I care to mention over the years. Remember
this sort of stuff?
\catcodeÆ=13 \defÆ{\AE}% handle Æ
\catcodeæ=13 \defæ{\ae}% handle æ
\catcodeß=13 \defß{\ss}% handle ß
\catcodeè=13 \defè{\e}% handle è
\catcodeÎ=13 \defÎ{\^I}% handle Î
\catcodeŒ=13 \defŒ{\OE}% handle Œ
\catcodeœ=13 \defœ{\oe}% handle œ
\catcodeŘ=13 \defŘ{\v R}% handle Ř
\catcodeř=13 \defř{\v r}% handle ř
I do remember \usepackage[utf8]{inputenc}, but even that has been
superceded by \RequirePackage{fontspec} (yes, I moved on from
using .sty files to .cls files about 5 years ago).
Apologies again.
Cheers,
David.
• Follow-Ups:
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# If x is not equal to 0, is |x| less than 1? (1) x/|x|< x (2) |x| > x
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If x is not equal to 0, is |x| less than 1? (1) x/|x|< x (2) |x| > x [#permalink]
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If x is not equal to 0, is |x| less than 1?
(1) $$\frac{x}{|x|}< x$$
(2) $$|x| > x$$
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If x is not equal to 0, is |x| less than 1? (1) x/|x|< x (2) |x| > x [#permalink]
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01 Nov 2009, 08:50
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If x is not equal to 0, is |x| less than 1?
Is $$|x|<1$$?
Is $$-1<x<1$$? ($$x\neq{0}$$)
So, the question asks whether x is in the range shown below:
(1) $$\frac{x}{|x|}< x$$
Two cases:
A. $$x<0$$ --> $$\frac{x}{-x}<x$$ --> $$-1<x$$. But remember that $$x<0$$, so $$-1<x<0$$
B. $$x>0$$ --> $$\frac{x}{x}<x$$ --> $$1<x$$.
Two ranges $$-1<x<0$$ or $$x>1$$. Which says that $$x$$ either in the first range or in the second. Not sufficient to answer whether $$-1<x<1$$. (For instance $$x$$ can be $$-0.5$$ or $$3$$)
Second approach: look at the fraction $$\frac{x}{|x|}$$ it can take only two values:
1 for $$x>0$$ --> so we would have: $$1<x$$;
Or -1 for $$x<0$$ --> so we would have: $$-1<x$$ and as we considering the range for which $$x<0$$ then completer range would be: $$-1<x<0$$.
The same two ranges: $$-1<x<0$$ or $$x>1$$:
(2) $$|x| > x$$. Well this basically tells that $$x$$ is negative, as if x were positive or zero then $$|x|$$ would be equal to $$x$$. Only one range: $$x<0$$, but still insufficient to say whether $$-1<x<1$$. (For instance $$x$$ can be $$-0.5$$ or $$-10$$)
Or consider two cases again:
$$x<0$$--> $$-x>x$$--> $$x<0$$.
$$x>0$$ --> $$x>x$$: never correct.
(1)+(2) Intersection of the ranges from (1) and (2) is the range $$-1<x<0$$ ($$x<0$$ (from 2) and $$-1<x<0$$ or $$x>1$$ (from 1), hence $$-1<x<0$$):
Every $$x$$ from this range is definitely in the range $$-1<x<1$$. So, we have a definite YES answer to the question. Sufficient.
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Re: If x is not equal to 0, is |x| less than 1? (1) x/|x|< x (2) |x| > x [#permalink]
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02 May 2018, 06:19
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Bunuel wrote:
If x is not equal to 0, is |x| less than 1?
Is $$|x|<1$$?
Is $$-1<x<1$$? ($$x\neq{0}$$)
So, the question asks whether x is in the range shown below:
(1) $$\frac{x}{|x|}< x$$
Two cases:
A. $$x<0$$ --> $$\frac{x}{-x}<x$$ --> $$-1<x$$. But remember that $$x<0$$, so $$-1<x<0$$
B. $$x>0$$ --> $$\frac{x}{x}<x$$ --> $$1<x$$.
Two ranges $$-1<x<0$$ or $$x>1$$. Which says that $$x$$ either in the first range or in the second. Not sufficient to answer whether $$-1<x<1$$. (For instance $$x$$ can be $$-0.5$$ or $$3$$)
Second approach: look at the fraction $$\frac{x}{|x|}$$ it can take only two values:
1 for $$x>0$$ --> so we would have: $$1<x$$;
Or -1 for $$x<0$$ --> so we would have: $$-1<x$$ and as we considering the range for which $$x<0$$ then completer range would be: $$-1<x<0$$.
The same two ranges: $$-1<x<0$$ or $$x>1$$:
(2) $$|x| > x$$. Well this basically tells that $$x$$ is negative, as if x were positive or zero then $$|x|$$ would be equal to $$x$$. Only one range: $$x<0$$, but still insufficient to say whether $$-1<x<1$$. (For instance $$x$$ can be $$-0.5$$ or $$-10$$)
Or consider two cases again:
$$x<0$$--> $$-x>x$$--> $$x<0$$.
$$x>0$$ --> $$x>x$$: never correct.
(1)+(2) Intersection of the ranges from (1) and (2) is the range $$-1<x<0$$ ($$x<0$$ (from 2) and $$-1<x<0$$ or $$x>1$$ (from 1), hence $$-1<x<0$$):
Every $$x$$ from this range is definitely in the range $$-1<x<1$$. So, we have a definite YES answer to the question. Sufficient.
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Hi Bunuel
Surely i am missing something here..my basic doubt is in scenario when we take X<0
If we assume, x<0, then shouldn't the statement x/|x|<x = -x/-x <-x (my thinking here is if we considering x<0, then x should be negative throughout )
So, the equation becomes 1<-x = -1>x, we can keep this option as we have initially assumed X<0
Then if we take any values of x less then -1, |x| will always be greater than 1
if we assume X>0, then x/|x|<x = x/x<x.....which is 1<x, we can keep this option as initially we have assumed X>0
Then we take any values of x greater than 1 then |x| will always be greater than 1.
So statement 1 in either case is sufficient..
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Re: If x is not equal to 0, is |x| less than 1? (1) x/|x|< x (2) |x| > x [#permalink]
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01 Nov 2009, 23:39
Thanks for the detailed explanation.
Very nicely done!
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Re: If x is not equal to 0, is |x| less than 1? (1) x/|x|< x (2) |x| > x [#permalink]
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28 Aug 2010, 02:36
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2
Bunuel wrote:
Hussain15 wrote:
If x is not equal to 0, is |x| less than 1?
(1) x/|x|< x
(2) |x| > x
Will really appreciate if answer is supported by explanation.
$$x\neq{0}$$, is $$|x|<1$$? Which means is $$-1<x<1$$? ($$x\neq{0}$$)
(1) $$\frac{x}{|x|}< x$$
Two cases:
A. $$x<0$$ --> $$\frac{x}{-x}<x$$ --> $$-1<x$$. But remember that $$x<0$$, so $$-1<x<0$$
B. $$x>0$$ --> $$\frac{x}{x}<x$$ --> $$1<x$$.
Two ranges $$-1<x<0$$ or $$x>1$$. Which says that $$x$$ either in the first range or in the second. Not sufficient to answer whether $$-1<x<1$$. (For instance $$x$$ can be $$-0.5$$ or $$3$$)
OR: $$\frac{x}{|x|}< x$$ multiply both sides of inequality by $$|x|$$ (side note: we can safely do this as absolute value is non-negative and in this case we know it's not zero too) --> $$x<x|x|$$ --> $$x(|x|-1)>0$$:
Either $$x>0$$ and $$|x|-1>0$$, so $$x>1$$ or $$x<-1$$ --> $$x>1$$;
Or $$x<0$$ and $$|x|-1<0$$, so $$-1<x<1$$ --> $$-1<x<0$$.
The same two ranges: $$-1<x<0$$ or $$x>1$$.
(2) $$|x| > x$$. Well this basically tells that $$x$$ is negative, as if x were positive or zero then $$|x|$$ would be equal to $$x$$. Only one range: $$x<0$$, but still insufficient to say whether $$-1<x<1$$. (For instance $$x$$ can be $$-0.5$$ or $$-10$$)
Or two cases again:
$$x<0$$--> $$-x>x$$--> $$x<0$$.
$$x>0$$ --> $$x>x$$: never correct.
(1)+(2) Intersection of the ranges from (1) and (2) is the range $$-1<x<0$$ ($$x<0$$ (from 2) and $$-1<x<0$$ or $$x>1$$ (from 1), hence $$-1<x<0$$). Every $$x$$ from this range is definitely in the range $$-1<x<1$$. Sufficient.
Hi Bunuel,
Thanks for detail explanation. I am finding it difficult only last intersection part. Can you explain it further. My doubut is...If we combine "-1<x<0" or "x>1" these two inequalities, how come range for x fall betweeen -1<x<1 since x>1 is area which will not fit into this equation. Can you explain?
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Re: If x is not equal to 0, is |x| less than 1? (1) x/|x|< x (2) |x| > x [#permalink]
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28 Aug 2010, 06:57
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udaymathapati wrote:
Hi Bunuel,
Thanks for detail explanation. I am finding it difficult only last intersection part. Can you explain it further. My doubut is...If we combine "-1<x<0" or "x>1" these two inequalities, how come range for x fall betweeen -1<x<1 since x>1 is area which will not fit into this equation. Can you explain?
Range from (1): -----(-1)----(0)----(1)---- $$-1<x<0$$ or $$x>1$$, green area;
Range from (2): -----(-1)----(0)----(1)---- $$x<0$$, blue area;
From (1) and (2): ----(-1)----(0)----(1)---- $$-1<x<0$$, common range of $$x$$ from (1) and (2) (intersection of ranges from (1) and (2)), red area.
Hope it's clear.
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Re: If x is not equal to 0, is |x| less than 1? (1) x/|x|< x (2) |x| > x [#permalink]
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28 Aug 2010, 10:29
Thanks Bunuel, It's terrific explanation...too detail..concept is now crystal clear!!
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Re: If x is not equal to 0, is |x| less than 1? (1) x/|x|< x (2) |x| > x [#permalink]
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13 Sep 2010, 19:33
1
Nice explaination. I had used numbers and came to wrong conclusion. I am inclined to say that for all mod questions I should consider positive and negative like Bunuel suggested
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Re: If x is not equal to 0, is |x| less than 1? (1) x/|x|< x (2) |x| > x [#permalink]
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30 Oct 2010, 15:26
6
gmcbsj wrote:
Hi,
Quote:
If x is not equal to 0, is |x| less than 1?
(1) x / |x| < x
(2) |x| > x
It seemed to me that (1) was enough. Since x is not 0, |x| must be greater than 0, and it should be safe to reorder the inequality like this by multiplying both sides by |x|:
x < |x| * x
And my thinking went: if |x| * x is greater than x, then x must be positive (if it weren't, then |x| * x would be a more negative number than x). And also x must be >= 1, for if it were between 0 and 1 then |x| * x would be a smaller number than x.
So, (1) should be sufficient -- (A). But according to the answer explanation, the answer is (C). Have I made a mistake in my logic here?
Hi, and welcome to Gmat Club.
You are right inequality $$x<|x|*x$$ holds true when $$x>1$$, but it's not the only range, it also holds true when $$-1<x<0$$. So from (1) we can not be sure whether $$|x|<1$$.
You should have spotted that your range for (1) is not correct when dealing with statement (2): $$|x| > x$$, which basically implies that $$x$$ is negative, $$x<0$$. So you would have from (1) $$x>1$$ and from (2) $$x<0$$: statements clearly contradict each other, but on the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other.
For complete solution refer to the posts above.
Hope it helps.
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Re: If x is not equal to 0, is |x| less than 1? (1) x/|x|< x (2) |x| > x [#permalink]
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18 May 2011, 22:51
2
gmat1220 wrote:
If x is not equal to 0, is |x| less than 1?
(1) (x/|x|) < x
(2) |x| > x
I would like to do this graphically.
To prove -1<x<1 (x not equal to zero)
Stmt1: x/|x| < x , x(|x|-1)>0 As can be seen from PINK side of graph of x(|x|-1)>0, x can be less than 1 or greater than 1. Not sufficient.
Stmt2:
|x|>x . As can be seen from BLACK side of graph that x is less than 1 but it is also less than -1. Remember we have to prove that -1<x<1
Combining, overlapping area has the equation -1<x<1.
OA. C
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Re: If x is not equal to 0, is |x| less than 1? (1) x/|x|< x (2) |x| > x [#permalink]
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07 Jan 2012, 20:50
1
Hi Bunuel - Firstly thanks for the wonderful collection and the explanation you provided in the word format.
1. In this kind of inequalities involving ‘mod’ values is it ever advisable to first square both side and then proceed ? I saw somewhere this approach was quite fast to solve the problem.
2. In this specific example as it involves negative & decimal , squaring and multiplying makes things erroneous .
Please suggest if there has any general rule/comment on this?
Thanks,
VCG
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Re: If x is not equal to 0, is |x| less than 1? (1) x/|x|< x (2) |x| > x [#permalink]
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09 Jan 2012, 11:21
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2
Rephrase of stem: Is x a positive or negative fraction.
2. This means that x is negative. But, x could be integer. insuff
1. This one is a bit complicated. If x = positive integer, this ineq holds and it does not for a positive fraction. So, for positive numbers, x=integer. For x = negative integer, this ineq does not hold. It does hold for negative fractions. Insuff.
Combining 1 and 2, x = negative and x = integer. Satisfies the stem. C.
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Re: If x is not equal to 0, is |x| less than 1? (1) x/|x|< x (2) |x| > x [#permalink]
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19 Jan 2012, 08:29
Bunuel wrote:
udaymathapati wrote:
Hi Bunuel,
Thanks for detail explanation. I am finding it difficult only last intersection part. Can you explain it further. My doubut is...If we combine "-1<x<0" or "x>1" these two inequalities, how come range for x fall betweeen -1<x<1 since x>1 is area which will not fit into this equation. Can you explain?
Range from (1): -----(-1)----(0)----(1)---- $$-1<x<0$$ or $$x>1$$, green area;
Range from (2): -----(-1)----(0)----(1)---- $$x<0$$, blue area;
From (1) and (2): ----(-1)----(0)----(1)---- $$-1<x<0$$, common range of $$x$$ from (1) and (2) (intersection of ranges from (1) and (2)), red area.
Hope it's clear.
Hi Bunuel...I still didnot got it..red area says -1<x<0 but we need that -1<x<1
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Re: If x is not equal to 0, is |x| less than 1? (1) x/|x|< x (2) |x| > x [#permalink]
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19 Jan 2012, 09:51
4
2
verycoolguy33 wrote:
Hi Bunuel - Firstly thanks for the wonderful collection and the explanation you provided in the word format.
1. In this kind of inequalities involving ‘mod’ values is it ever advisable to first square both side and then proceed ? I saw somewhere this approach was quite fast to solve the problem.
2. In this specific example as it involves negative & decimal , squaring and multiplying makes things erroneous .
Please suggest if there has any general rule/comment on this?
Thanks,
VCG
A. We can raise both parts of an inequality to an even power if we know that both parts of an inequality are non-negative (the same for taking an even root of both sides of an inequality).
For example:
$$2<4$$ --> we can square both sides and write: $$2^2<4^2$$;
$$0\leq{x}<{y}$$ --> we can square both sides and write: $$x^2<y^2$$;
But if either of side is negative then raising to even power doesn't always work.
For example: $$1>-2$$ if we square we'll get $$1>4$$ which is not right. So if given that $$x>y$$ then we can not square both sides and write $$x^2>y^2$$ if we are not certain that both $$x$$ and $$y$$ are non-negative.
B. We can always raise both parts of an inequality to an odd power (the same for taking an odd root of both sides of an inequality).
For example:
$$-2<-1$$ --> we can raise both sides to third power and write: $$-2^3=-8<-1=-1^3$$ or $$-5<1$$ --> $$-5^2=-125<1=1^3$$;
$$x<y$$ --> we can raise both sides to third power and write: $$x^3<y^3$$.
So for our question we can not square x/|x|< x as we don't know the sign of either of side.
Hope it helps.
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Re: If x is not equal to 0, is |x| less than 1? (1) x/|x|< x (2) |x| > x [#permalink]
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19 Jan 2012, 10:00
1
Eshika wrote:
Bunuel wrote:
udaymathapati wrote:
Hi Bunuel,
Thanks for detail explanation. I am finding it difficult only last intersection part. Can you explain it further. My doubut is...If we combine "-1<x<0" or "x>1" these two inequalities, how come range for x fall betweeen -1<x<1 since x>1 is area which will not fit into this equation. Can you explain?
Range from (1): -----(-1)----(0)----(1)---- $$-1<x<0$$ or $$x>1$$, green area;
Range from (2): -----(-1)----(0)----(1)---- $$x<0$$, blue area;
From (1) and (2): ----(-1)----(0)----(1)---- $$-1<x<0$$, common range of $$x$$ from (1) and (2) (intersection of ranges from (1) and (2)), red area.
Hope it's clear.
Hi Bunuel...I still didnot got it..red area says -1<x<0 but we need that -1<x<1
The question asks "is $$-1<x<1$$?" We got that $$x$$ is in the range $$-1<x<0$$ (red area). Now, as ANY $$x$$ from this range (from red area) is indeed in $$-1<x<1$$, then we can answer YES to our original question.
Hope it's clear.
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Re: If x is not equal to 0, is |x| less than 1? (1) x/|x|< x (2) |x| > x [#permalink]
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11 Apr 2012, 13:43
bunuel,
i had a slightly slightly different method for statement 1. Do you mind letting me know if the steps I took are OK?
also, what level question is this? My test is coming up soon and I've done all the OG and quant review 2nd edition problems. I wonder if going through these two samurai guides PS/DS would be the best use of my time in the final month and half.
(1).
x/|x| < x
before even going to x<0 and x>0, i knew that |x| is positive, so I multiplied it across
x < x*|x|
case x < 0
divide both sides by x, inequality must flip because x is negative
1 > |x| <-- this says YES to what we asked for
case x > 0
again, divide both sides by x, inequality won't flip
1 < |x| <-- this says NO
insufficient
(2). clearly says x has to be negative, therefore using (1) and (2) it is sufficient.
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Re: If x is not equal to 0, is |x| less than 1? (1) x/|x|< x (2) |x| > x [#permalink]
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11 Apr 2012, 14:01
1
pinchharmonic wrote:
bunuel,
i had a slightly slightly different method for statement 1. Do you mind letting me know if the steps I took are OK?
also, what level question is this? My test is coming up soon and I've done all the OG and quant review 2nd edition problems. I wonder if going through these two samurai guides PS/DS would be the best use of my time in the final month and half.
(1).
x/|x| < x
before even going to x<0 and x>0, i knew that |x| is positive, so I multiplied it across
x < x*|x|
case x < 0
divide both sides by x, inequality must flip because x is negative
1 > |x| <-- this says YES to what we asked for
case x > 0
again, divide both sides by x, inequality won't flip
1 < |x| <-- this says NO
insufficient
(2). clearly says x has to be negative, therefore using (1) and (2) it is sufficient.
Though this didn't affect the final answer but the complete solution for (1) would be:
If x<0 and 1 > |x| then 1>-x --> -1<x and since x<0 then -1<x<0.
If x>0 and 1 < |x| the 1<x.
As for the question I'd say it's >650 level.
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Re: If x is not equal to 0, is |x| less than 1? (1) x/|x|< x (2) |x| > x [#permalink]
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15 Apr 2012, 18:07
1
Bunuel wrote:
Hussain15 wrote:
If x is not equal to 0, is |x| less than 1?
(1) x/|x|< x
(2) |x| > x
Will really appreciate if answer is supported by explanation.
$$x\neq{0}$$, is $$|x|<1$$? Which means is $$-1<x<1$$? ($$x\neq{0}$$)
(1) $$\frac{x}{|x|}< x$$
Two cases:
A. $$x<0$$ --> $$\frac{x}{-x}<x$$ --> $$-1<x$$. But remember that $$x<0$$, so $$-1<x<0$$
B. $$x>0$$ --> $$\frac{x}{x}<x$$ --> $$1<x$$.
Two ranges $$-1<x<0$$ or $$x>1$$. Which says that $$x$$ either in the first range or in the second. Not sufficient to answer whether $$-1<x<1$$. (For instance $$x$$ can be $$-0.5$$ or $$3$$)
Second approach: look at the fraction $$\frac{x}{|x|}$$ it can take only two values:
1 for $$x>0$$ --> so we would have: $$1<x$$;
Or -1 for $$x<0$$ --> so we would have: $$-1<x$$ and as we considering the range for which $$x<0$$ then completer range would be: $$-1<x<0$$.
The same two ranges: $$-1<x<0$$ or $$x>1$$.
(2) $$|x| > x$$. Well this basically tells that $$x$$ is negative, as if x were positive or zero then $$|x|$$ would be equal to $$x$$. Only one range: $$x<0$$, but still insufficient to say whether $$-1<x<1$$. (For instance $$x$$ can be $$-0.5$$ or $$-10$$)
Or two cases again:
$$x<0$$--> $$-x>x$$--> $$x<0$$.
$$x>0$$ --> $$x>x$$: never correct.
(1)+(2) Intersection of the ranges from (1) and (2) is the range $$-1<x<0$$ ($$x<0$$ (from 2) and $$-1<x<0$$ or $$x>1$$ (from 1), hence $$-1<x<0$$). Every $$x$$ from this range is definitely in the range $$-1<x<1$$. Sufficient.
Hi Bunuel,
Sorry to bring this up after the question has been convincingly answered but I have a small doubt:
In the first statement, x/(mod x), while considering the possibility x<0, you write x > x/(-x) and conclude that x>-1.
But shouldn't the sign of inequality flip in this case as you are dividing by a negative number? What I mean to say is that shouldn't
x > x/(-x) give us x<-1?
Sorry in advance if I am making an illogical conclusion but if you could clarify, I would appreciate it very much. Thanks.
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Re: If x is not equal to 0, is |x| less than 1? (1) x/|x|< x (2) |x| > x [#permalink]
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15 Apr 2012, 23:18
arjuntomar wrote:
Hi Bunuel,
Sorry to bring this up after the question has been convincingly answered but I have a small doubt:
In the first statement, x/(mod x), while considering the possibility x<0, you write x > x/(-x) and conclude that x>-1.
But shouldn't the sign of inequality flip in this case as you are dividing by a negative number? What I mean to say is that shouldn't
x > x/(-x) give us x<-1?
Sorry in advance if I am making an illogical conclusion but if you could clarify, I would appreciate it very much. Thanks.
From $$x>\frac{x}{-x}$$ we don't dividing the inequality by some negative number, all we do is just reduce fraction. Since $$\frac{x}{-x}=-1$$ (the same way as $$\frac{2}{-2}=-1$$) then from $$x>\frac{x}{-x}$$ we have that $$x>-1$$.
Hope it's clear.
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Re: If x is not equal to 0, is |x| less than 1? (1) x/|x|< x (2) |x| > x [#permalink]
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09 Jun 2012, 08:52
1
Bunuel wrote:
Hussain15 wrote:
If x is not equal to 0, is |x| less than 1?
(1) x/|x|< x
(2) |x| > x
Will really appreciate if answer is supported by explanation.
$$x\neq{0}$$, is $$|x|<1$$? Which means is $$-1<x<1$$? ($$x\neq{0}$$)
(1) $$\frac{x}{|x|}< x$$
Two cases:
A. $$x<0$$ --> $$\frac{x}{-x}<x$$ --> $$-1<x$$. But remember that $$x<0$$, so $$-1<x<0$$
B. $$x>0$$ --> $$\frac{x}{x}<x$$ --> $$1<x$$.
Two ranges $$-1<x<0$$ or $$x>1$$. Which says that $$x$$ either in the first range or in the second. Not sufficient to answer whether $$-1<x<1$$. (For instance $$x$$ can be $$-0.5$$ or $$3$$)
Second approach: look at the fraction $$\frac{x}{|x|}$$ it can take only two values:
1 for $$x>0$$ --> so we would have: $$1<x$$;
Or -1 for $$x<0$$ --> so we would have: $$-1<x$$ and as we considering the range for which $$x<0$$ then completer range would be: $$-1<x<0$$.
The same two ranges: $$-1<x<0$$ or $$x>1$$.
(2) $$|x| > x$$. Well this basically tells that $$x$$ is negative, as if x were positive or zero then $$|x|$$ would be equal to $$x$$. Only one range: $$x<0$$, but still insufficient to say whether $$-1<x<1$$. (For instance $$x$$ can be $$-0.5$$ or $$-10$$)
Or two cases again:
$$x<0$$--> $$-x>x$$--> $$x<0$$.
$$x>0$$ --> $$x>x$$: never correct.
(1)+(2) Intersection of the ranges from (1) and (2) is the range $$-1<x<0$$ ($$x<0$$ (from 2) and $$-1<x<0$$ or $$x>1$$ (from 1), hence $$-1<x<0$$). Every $$x$$ from this range is definitely in the range $$-1<x<1$$. Sufficient.
Hey Bunuel,
Love your answers. But I want to suggest another method that is giving me some trouble when combining statesment (1) & (2)
1) $$\frac{x}{|x|}< x$$
2) $$x<|x|$$
Since $$0<|x|$$ (x cannot equal 0), then we can rewrite statement 2, $$x<|x|$$ as $$\frac{x}{|x|}< 1$$.
We then subtract statment (1) and (2) as
1) $$\frac{x}{|x|}-\frac{x}{|x|}< x-1$$ to get $$0< x-1$$ or $$1<x$$ showing that x is outside the boundary of $$-1<x<1$$ and making the combined statements suffient. But $$1<x$$, the derived statement of (1) and (2), contradicts statement (2), which claims that $$0<x$$. What am I doing wrong?
Thank you!
Re: If x is not equal to 0, is |x| less than 1? (1) x/|x|< x (2) |x| > x [#permalink] 09 Jun 2012, 08:52
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### Homes
There are to be 6 homes built on a new development site. They could be semi-detached, detached or terraced houses. How many different combinations of these can you find?
### Stairs
This challenge is to design different step arrangements, which must go along a distance of 6 on the steps and must end up at 6 high.
### Train Carriages
Suppose there is a train with 24 carriages which are going to be put together to make up some new trains. Can you find all the ways that this can be done?
# Late Again
##### Age 5 to 7 Challenge Level:
David from Thomas Reade School sent in the following solution:
The shortest route is forward $1$, right $1$, forward $6$ and right $3$ which is $11$ spaces.
Another way is forward $1$, right $4$ and forward $6$ which is $11$ spaces.
Another way is forward $3$, right $4$ and forward $4$ which is $11$ spaces.
(This assumes that Moira is standing just outside the school gate and finished standing outside the school doors.) Thank you David.
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# Interchange of Gradient and Divergence.
It's very very often and in many books depending on author there is mostly interchange of gradient $D$ and divergence $\nabla$.
What should I be careful about while dealing with such cases?
For example say $\int_\Omega v\Delta u$ using integration by parts and assuming that the boundary term vanishes this becomes $\int_\Omega Dv\cdot Du$.
Very often I also see the expression $\int_\Omega\nabla v\cdot\nabla u$, so this leads me to confusion sometimes.
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$\Delta=\nabla^2$ doesn't really fit in your pattern: So this leads me to confusion... – draks ... Jul 26 '12 at 19:25
I suggest writing $\mathrm{div}$ for divergence. It's annoying that \div is used for division in $\LaTeX$ but you can DeclareMathOperator. – user31373 Jul 26 '12 at 23:01
These are cases when index notations becomes extremely helpful. Denote by $\partial_1 = \partial_x, \partial_2 = \partial_y, \partial_3 = \partial_z$ and for a vector write its components as $$\vec{v} = v_1 \hat{x} + v_2 \hat{y} + v_3 \hat{z}$$ Then the divergence of a vector field is $$\vec{\nabla}\cdot\vec{v} = \sum_{i = 1}^3 \partial_i v_i$$ The gradient vector of a scalar field has components $$(\vec{\nabla f})_i = \partial_i f$$ and the Laplacian of a function is $$\triangle f = \sum_i \partial_i \partial_i f$$
When doing computations, do them term by term (that is, expand out the sums if necessary) and in the end, when the $\partial_i$ hits on a scalar quantity, it is a gradient, and when the $\partial_i$ hits on a vector quantity indexed also by $i$ you get a divergence.
To illustrate: if $f$ be function a $\vec{v}$ a vector field, then the object $f \vec{v}$ is a vector field. Let us compute its divergence. We do it like so:
$$\vec{\nabla}\cdot(f\vec{v}) = \sum_i \partial_i \left( f v_i\right)= \sum_i (\partial_i f)v_i + f \partial_i v_i \tag{1}$$
The first term then is interpreted as the dot product of the gradient vector $\vec{\nabla f}$ against the vector $\vec{v}$, so for this term "the divergence outside changed to a gradient inside". The second term contains the divergence of the vector field $\vec{v}$ it self, multiplied against the function $f$. So for this term the divergence remains a divergence.
The use of index notations is also extremely helpful when there are multiple sets of indices in play. Let $\vec{v}$ be a vector field, we can consider the gradient of its divergence $\vec{\nabla}(\vec{\nabla} \cdot \vec{v})$. Now, since partial derivatives commute, what happens when we try to interchange the derivatives? In index notation you have
$$\underbrace{\partial_j}_{\text{the gradient}} \underbrace{\sum_i \partial_i v_i}_{\text{the divergence}} = \sum_i \partial_j \partial_i v_i = \sum_i \partial_i (\partial_j v_i)$$
which is now a divergence of an object with two indices (a tensor field, in fact). Using indices help enormously in keeping track where various operators hit: for example compare the above expression with the similar but different expression $$(\triangle \vec{v})_j = \sum_i \partial_i \partial_i v_j$$
As an aside, (1) is basically the same as the integration by parts formula which you described.
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It can be confusing because the divergence and the gradient are two different things that happen to share the same symbol, $\nabla$. The notation is slightly idiosyncratic: the gradient of $u$ is denoted $\nabla u$, which is the same as your $Du$, while the divergence is written $\nabla\cdot u$. So you can always tell whether $\nabla$ means gradient or divergence depending on whether or not it is followed by a dot.
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"Even otherwise, you can't take the gradient of a vector field or the divergence of a scalar field" is one of those statements I'd be very careful about making: it may be a convenient mnemonic now, but one day the student may learn about the Navier-Stokes equations or about co-differentials in Riemannian geometry... – Willie Wong Jul 26 '12 at 20:11
@Willie, that's true, I was being sloppy. In fluid dynamics one does take the gradient of velocity, but does the divergence of a scalar field ever make sense? I'll update my answer once I get your response. – Rahul Jul 26 '12 at 20:35
Divergence can be defined (relative to a specified index) for any tensor field on a Riemannian manifold; and it can be defined for any multi-vectors (think dual of differential forms) on a orientable smooth manifold. Naturally this extends to the scalar field as a rank-0 contravariant tensor field. Of course, necessarily also its divergence is 0 (the same as the exterior derivative of a top form). With regards to the divergence of the scalar field, it is less important than the thing about gradients of vector fields, and I was just picking bones (because it is there to pick). – Willie Wong Jul 26 '12 at 21:32
Also, you may want to add a few words about why after integrating by parts, the divergence can become a gradient... – Willie Wong Jul 26 '12 at 21:35
@Willie, I just deleted the parts that weren't universally correct. Perhaps you could post an answer elaborating your last comment (though isn't it the Laplacian that's being integrated here?). – Rahul Jul 27 '12 at 4:16
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# A zero-knowledge Poker protocol that achieves confidentiality of the players' strategy or How to achieve an electronic Poker face
• Published in 1987
## Other information
pages
239--247
publisher
Springer
### BibTeX entry
@inproceedings{Crepeau1987,
author = {Cr{\'{e}}peau, C.},
pages = {239--247},
publisher = {Springer},
title = {A zero-knowledge Poker protocol that achieves confidentiality of the players' strategy or How to achieve an electronic Poker face},
}
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Logic
# The 24 Puzzle
$9 \square 1 \square 7 \square 4 = 24$
Which set of operators can be used in the blanks above to make this equation correct? Operators can be placed in the blanks in any order, and any number of parentheses can be used.
Hint: When solving puzzles such as these, it is often helpful to consider different methods that could be used to arrive at your final answer. For example, if the final operator is $$\times,$$ then we need two numbers whose product is 24. For reference, the nontrivial factors of 24 are 2,3,4,6,8, and 12.
$9 \square 8 \square 3 \square 8 = 24$
Which set of operators can be used in the blanks above to make this equation correct? Operators can be placed in the blanks in any order, and any number of parentheses can be used.
Hint: When solving puzzles such as these, it is often easier to reach the target number using only 2 or three of the required digits. Try to develop strategies for eliminating a number or pair of numbers. This is often done by producing 1, which can be multiplied for no effect, or 0, which can be added for no effect.
$6 \square 1 \square 3 \square 4 = 24$
Which set of operators can be used in the blanks above to make this equation correct? Operators can be placed in the blanks in any order, and any number of parentheses can be used.
Hint: When solving puzzles such as these,remember that the same result can often be produced using different operators. For example, multiplying by 2 is equivalent to dividing by $$\frac{1}{2}.$$
$7 \square 3 \square 3 \square 7 = 24$
Which set of operators can be used in the blanks above to make this equation correct? Operators can be placed in the blanks in any order, and any number of parentheses can be used.
Hint: When solving puzzles such as these, it is often helpful to try imagining all the possible final steps involving one of the given numbers. For example, if the final step is $$\times 5,$$ you would need to make $$\frac{24}{5}$$ with the other 3 numbers. This can be particularly helpful when the solution involves a fractional product.
$6 \square 6 \square 4 \square 1 = 24$
Which set of operators can be used in the blanks above to make this equation correct? Operators can be placed in the blanks in any order, and any number of parentheses can be used.
Hint: When solving puzzles such as these, sometimes it’s not always possible to find factors that multiply nicely to 24. It’s often helpful to look for other, nearby numbers with nice factors, especially ones that can produce 24 when added to or subtracted from the numbers you already have. Numbers that can be helpful include 18, 20, 21, 25, 27, 28, and 30.
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MathSciNet bibliographic data MR1980688 17B20 (17B25 17C20 53C35) Clerc, Jean-Louis Special prehomogeneous vector spaces associated to \$F\sb 4,\ E\sb 6,\ E\sb 7,\ E\sb 8\$$F\sb 4,\ E\sb 6,\ E\sb 7,\ E\sb 8$ and simple Jordan algebras of rank 3. J. Algebra 264 (2003), no. 1, 98–128. Article
For users without a MathSciNet license , Relay Station allows linking from MR numbers in online mathematical literature directly to electronic journals and original articles. Subscribers receive the added value of full MathSciNet reviews.
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# pharmacy technician interview math test
Also, this page requires javascript. Please visit using a browser with javascript enabled. These include math, customer service, situational judgment, pharmaceutical and drug terminology and procedures, and reading comprehension. We have offered 5 core examples, all of which can appear on the day of your PTCB exam. Answer tips You may [â¦] Re: Technician interview - before qualification Yet you totally ignore my example of Medicine Management techs struggling to complete a maths test to gain their certificate. The subjects covered are based on the 9 knowledge domains outlined on the PTCB website. Please wait while the activity loads. Free interview details posted anonymously by Dierbergs Markets interview candidates. Maria is a pharmacy technician at a local pharmacy. Pick the answer that makes the most sense to you! Itâs important that you know exactly why youâd prefer this pharmacy job over another. When told if successful given a interview time with education lead and chief pharmacy technician. The first step to solving this is to convert the child's weight to kilograms. Use this ptcb math quiz to practice your pharmacy math skills. Some of these questions require measurement conversions, so you may want to start with our measurement conversion quiz.These pharmacy tech practice math questions cover roman numerals, percentage calcuations, proportions, alligation, dosing calculations, and more. Each Free practice quiz has twenty questions and should take no more than 25 minutes. Talk about your favorite aspect of the job. Conversions and Formulae 2. So 16 oz = 480 mL. It is not worth it to waste your money for being Pharmacy Technician at this point. Mix 100 mL of the 50% and 700 mL of the 5%. Some of these questions require measurement conversions, so you may want to start with our measurement conversion quiz. This is a video demonstration of a pharmacy tech math review question from William A Hopkins, Jr's Complete Math Review workbook. The subjects covered are based on the 9 knowledge domains outlined on the. In this test you have to answer printable pharmacy technician practice test. As pharmacists are more involved in direct patient care, pharmacy technicians will undertake more diverse tasks to support pharmacy operations, whether theyâre in hospitals or retail stores. Any items you have not completed will be marked incorrect. . These pharmacy tech practice math questions cover roman numerals, percentage calcuations, proportions, alligation, dosing calculations, and more. New, originally written practice questions are posted there a few times a week. 1. They enter patient data into a computer and provide relevant information to patients about insurance, deductibles and co-pays. This pharmacy technician interview question is a critical question which is designed to ascertain your passion and interest in the field. Maths test requiring a minimum 80% pass mark. where you can ask a question or help other users work through issues. There may be more questions available on the facebook page, which is where they are all tested before they're published here on the site. You have not finished your quiz. Recall that 1 pound is equal to 0.454 kilograms: To answer this type of problem you must know that percentage strength is conventionally given as weight to volume (w/v), where 20% means: Once you are finished, click the button below. Copyright © 2010-2018 - pharmacy-tech-test.com - A secure website encrypted by Transport Layer Security (TLS)All rights Reserved - Pharmacy tech study website only - NOT to be used as a reference for patient care. You might like these free pre employment math test pdf to get even better at your job interview numeracy test. Converting between Ratios andPercentage Strengths 3. Here are a few pharmacy technician interview questions that your interviewer is most likely to ask and our guide on how to answer them: 1. *PTCB is a registered trademark of the Pharmacy Technician Certification Board, which was not involved in the production of, and does not endorse this site. In this post, you can reference some of the most common interview questions for a hospital pharmacy technician interview along with appropriate answer samples. To get pass ptcb study guide online. In some of the questions, there may also be a link to a tutorial page if the site has one that covers the material in the question. First you must figure out how many milligrams of famotidine will be needed: Mix 89 mL of the 50% and 711 mL of the 5%. Your performance has been rated as %%RATING%%, More Practice Tests Use this PTCB Math Quiz to practice your pharmacy math skills. Additionally, many pharmacy tech math problems require a few different types of math all within the same problem. They are all originally written, and based on the subject matter in which the official test is based on. Since it is twice a day (bid) for 10 days you must calculate: This is another proportion problem. I am a graduate from XYZ community college with specialized courses in pharmaceutical studies'. Get started on your test prep right now with our PTCB Math Quiz! The desired concentration goes in the middle: You should know your Roman numerals by now: Recall that 1 oz = 30 mL. Use this PTCB Math Quiz to practice your pharmacy math skills. Pharmacy technician practice test instructions, Each Free practice quiz has twenty questions and should take no more than 25 minutes. Following under each practice quiz, there's a link to take you to the beginning of the next one. They answer phones, perform inventory, and, in a retail environment, they operate a cash register. Please ask ⦠However, they are not the exact questions from either of those tests. Displaying all worksheets related to pharmacy tech math. We strongly recommend knowing how to calculate doses â questions are almost guaranteed to appear. And, other pharmacy tech students post questions and study tips to the community. Use this PTCB Math Quiz to practice your pharmacy math skills. We will use seconds, so the first step is to convert 30 minutes to seconds. Pharmacy Technician Test: This test is more specific to the pharmacy technician practice, and so candidates will need to answer questions related to that. If you're looking for a study partner locally or online, it's also a great place for that too. TRAIN TO BE A PHARMACY TECHNICIAN TODAY. There is no job.No body want new grads. What do you enjoy most about being a Pharmacy Technician? We cover the following 5topics: 1. There are 435 pills, and 19% are C3. This is an alligation problem, so you should setjup a tic-tac-toe table. If you're looking for a study partner locally or online, it's also a great place for that too. My daughter has an interview next week for a Student Pharmacy Technician vacancy and has been told she must complete a maths test and get at least 70% correct to get through the interview stage. ... At the in-person interview, I was given a math test. Units of measure and conversions 2. There may be more questions available on the, , which is where they are all tested before they're published here on the site. They are all originally written, and based on the subject matter in which the official test is based on. Each question is formatted as multiple choice, and the answers are shown after each submission. Dosage Calculations Take note â as all five ofthese topics are set to appear on the 2020 PTCB test. 5 Pharmacy Technician Interview Questions and Answers . Practice types of job interview such as screening interview, phone interview, second interview, situational interview, behavioral interview (competency based), technical interview, group interview⦠2. I past the test without any stady with 850 score. 1. So 1¼ teaspoons equals 6.25 mL. Letâs getstarted. You need to choose one or the other. Pharmacy Technician is a healthcare provider who performs pharmacy-related functions, generally working under the direct supervision of a licensed pharmacist. Typically, the assessment is timed, and if you pass, you are asked to return for an interview. You should ask this question because it shows whether or not the pharmacy technician will be a good fit for your business. Detailed explanations are provided which show exactly how to solve these challenging problems. Additionally, they are copyright protected. Although some questions are asked in almost every interview, knowing how to answer them honestly while showcasing the traits that employers are looking for can still be a challenge. © 2021 pharmacy-tech-test.com - All rights reserved. There are two ways to become a certified Pharmacy Technician â through the Pharmacy Technician Certification Board (PTCB) and through the National Healthcareer Association (NHA). Talk about some of ⦠**These pharmacy technician practice tests are not the actual questions you will be asked on the national certification exam. Interview. Other interview tips for hospital pharmacy technician interview 1. The most often asked question about pharmacy technician math is how to know which type of math to do for each problem. The role of pharmacy technicians is likely to change in the future. 4 Dierbergs Markets Pharmacy Technician interview questions and 4 interview reviews. The first half of the book is explaining how to answer the questions, followed on page 16 of the book, the actual question paper. Job of a pharmacy technician is not a walk in a park. As a pharmacy technician, you will use your math skills daily on the job. And, other pharmacy tech students post questions and study tips to the community. Pharmacy Math. Additionally, they are copyright protected. Additionally, there are forum pages where you can ask a question or help other users work through issues. Thanks for using these free pharmacy tech practice tests ! Many pharmacy technicians develop math phobia, which is a severe form of math anxiety. Thanks for using these, pharmacy-tech-test.com - A secure website encrypted by Transport Layer Security (TLS). If you need more job interview materials, you can reference them at the end of this post. Clinical-based calculations 5. We have compiled a collection of math videos found on the Web to help you pass the PTCB exam. While it offers many benefits, and it is better than most jobs that pay the same amount of money, it has also some drawbacks. The system for checking your answer has been simplified to a report at the end of the quiz. In fact, many problems can be solved using more than one technique. Asked questions on the organisation, the pressures that the NHS are facing, and the NHS trust's key goals. **These pharmacy technician practice tests are not the actual questions you will be asked on the national certification exam. Following under each practice quiz, there's a link to take you to the beginning of the next one. Here is the pharmacy math worksheets section. Pharmacy Technician Interview Questions. Calculators are not permitted so thereâs a ⦠Math You Need to Know to Be a Pharmacy Technician. Post a Job. A pharmacy technician supplies medicines to patients, whether filling prescriptions or dispensing over-the-counter drugs. If this activity does not load, try refreshing your browser. Of these answers choices 485 mL is the closest to 480 mL, but that would cause overflow. Be sure to know the Roman numeral system: To solve this type of problem you should setup a proportion: This is another proportion problem. Mix 122 mL of the 50% and 678 mL of the 5%. The system for checking your answer has been simplified to a report at the end of the quiz. Most of the pharmacy technicians use and sometimes rely on computers to solve complicated algorithm data, yet they still rely upon their skills to get a pharmacy technician certification in the first place. Body Mass Index 5. PTCB Practice Tests >>. Some of these questions require measurement conversions, so you may want to start with our measurement conversion quiz.These pharmacy tech practice math questions cover roman numerals, percentage calcuations, proportions, alligation, dosing calculations, and more. Each of the free pharmacy technician practice tests ask multiple questions, with an option to proceed to the next test. Try our free Pharmacy Tech Practice Exam below. The types of calculations will vary, but a solid understanding of algebra will help tremendously. If you're new to the field, think about what you're looking forward to learning. Pharmacy technicians are in demand and employment is expected to grow at a rate of 12% until 2026. The timeframe of the application procedure, from the date of applying to the hire date, varies greatly. 4th great math is enough. Additionally, there are. Tell me about your ability to work under pressure? About Pharmacy Technician Test Assessment. You don't even need to study or know any medication. Lastly, keep in mind that these questions are designed to help you practice for the PTCB or ExCPT exam. Maths Assessment For Job Interview Reasoning Tests. The following seven questions, submitted by pharmacists via social media and ⦠To find the number of C3 pills, multiply the total by 0.19: First calculate the total prescriptions received: Recall that 1 teaspoon equals 5 mL. Roman Numerals 4. If loading fails, click here to try again. The hiring process at Walgreens includes several types of tests including personality test, math test, word problems test, and a more job-oriented tests such as pharmacy technician test. Stock solutions and alligation 4. If you leave this page, your progress will be lost. Some come from Khan Academy and others are YouTube uploads. New, originally written practice questions are posted there a few times a week. Pharmacy technicians are employed by hospitals or retail pharmacies to assist licensed pharmacists in filling prescriptions and other support tasks. Hi, Can anyone help? Tell me about yourself 'I am a detail-oriented and trained pharmacy tech who likes interacting with people. In this pharmacy technician math study guide, we have focused on the calculation of doses. What do you think is the most important quality for a pharmacy technician to have? Ratio, proportions and percent strength 3. It involves interpreting prescriptions and doing some pharmacy math. Can anyone give us an idea of what this test is like - ⦠Asked what do I know about the GPhC registration process, aseptics. Math is an important part of the PTCB test. The next lowest answer is correct, 465 mL. Each bottle has 120 sprays, so each bottle will last for: Setup your proportion with $x$ representing the milligrams of Diphenhydramine HCl that are in the bottle: There are two steps to solve this problem. MathJax.Hub.Config({tex2jax: {inlineMath: [['$','$'], ['\$','\$']], processEscapes: true}}); Please ask permission before posting or using them elsewhere. The median pay for pharmacy technicians is estimated to be $15.72 per hour or$32,700 annually, according to the Bureau of Labor Statistics. by Michelle Goeking, BM, CPhT A pharm tech in any area of pharmacy practice will encounter some pharmaceutical calculations that will need to be performed. The four main components in pharmacy math are. Working under the supervision of a pharmacist, she fills a variety of prescriptions for customers each day. Your results will be scored automatically and will display your strengths and weaknesses. There really is no straight answer. Lastly, keep in mind that these questions are designed to help you practice for the PTCB or ExCPT exam. Overcoming Your Fear of Math. Mix 111 mL of the 50% and 889 mL of the 5%. All rights Reserved - Pharmacy tech study website only - NOT to be used as a reference for patient care. Pharmacy techs provide information to patients. Your answers to behavioral questions help the pharmacy manager (or anyone else who leads an interview with you) to understand your attitude to difficult situations . Free interview details posted anonymously by Walgreens interview candidates. The highest concentration goes in the upper left corner and the lowest concentration in the lower left corner. Math ⦠Here we review some of the toppharmacy calculation tips for the PTCB exam you need to know. 376 Walgreens Pharmacy Technician interview questions and 327 interview reviews. Pharmacy Technician Interview Questions. In some of the questions, there may also be a link to a tutorial page if the site has one that covers the material in the question. However, they are not the exact questions from either of those tests. Convert the milligrams in 8 fluid ounces to gallons, and then convert from milligrams to grams. Dosage Calculations; Hospital Pharmacy Math; Compounding Math; Pediatric Math; Math Review for Pharmacy Technicians. Note that times are given in both seconds and minutes. Does it not occur to you that the level of maths required of a Band 4 is not the same as that required of a Band 5 or 6? HOME PAGE | FREE PRACTICE TESTS | ASK A QUESTION | MATH QUESTIONS | CONTACT | PRIVACY POLICY. Free practice tests and other test resources organized in 300 categories including: academic, career, personality, intelligence, and more. Since the prescription states 2 sprays per nostril, and people have 2 nostrils, there will be 4 four sprays per day (qd is the abbreviation for daily). ⢠Pharmacy practice uses principles from all three systems of measurement ⢠Knowing household equivalents and other conversions is crucial for pharmacy practice UNITS + CONVERSIONS Topics to Cover 1. Currently, you are a pharmacy technician student receiving on-the-job training from Maria. Skills daily on the day of your PTCB exam an important part of the quiz appear on the calculation doses. Functions, generally working under the direct supervision of a pharmacy technician will be a fit. In 300 categories including: academic, career, personality, intelligence, and more some come from Academy. Ml is the most important quality for a study partner locally or online it... Test resources organized in 300 categories including: academic, career, personality, intelligence, more! An idea of what this test is based on is expected to grow at a rate of 12 % 2026. Lastly, keep in mind that these questions are posted there a few times a week most to. Need more job interview materials, you will be marked incorrect 678 mL of the 50 % and 889 of. 'S key goals employed by hospitals or retail pharmacies to assist licensed pharmacists in filling prescriptions or dispensing over-the-counter.... Asked on the national certification exam these questions are almost guaranteed to appear I was given a math.... Take no more than 25 minutes tests are not the actual questions you will seconds. 376 Walgreens pharmacy technician is a pharmacy technician practice tests and other test resources organized in 300 categories:! Dosage calculations take note â as all five ofthese topics are set to appear thanks for using these pharmacy... Technician to have a interview time with education lead and chief pharmacy technician practice test and! Money for being pharmacy technician an important part of the next one there a times! The highest concentration goes in the upper left corner as % %, more practice tests ask multiple questions submitted! Are not the actual questions you will be scored automatically and will display your strengths weaknesses... And ⦠you do n't even need to study or know any medication of what this test have... Most sense to you the answers are shown after each submission asked what do you is! Technician supplies medicines to patients, whether filling prescriptions and doing some pharmacy math skills math review pharmacy... Tests and other support tasks your performance has been simplified to a report at the end of this.... And minutes tech who likes interacting with people TLS ) maths test requiring a minimum 80 % pass mark education. The 9 pharmacy technician interview math test domains outlined on the Web to help you pass, you will be marked incorrect a understanding. And will display your strengths and weaknesses, from the date of to. If this activity does not load, try refreshing your browser an of..., keep in mind that these questions are designed to help you practice for the PTCB.!, your progress will be asked on the calculation of doses most often asked question about pharmacy technician at rate... Scored automatically and will display your strengths and weaknesses, there are forum pages where you can a... Key goals and doing some pharmacy math ; math review for pharmacy technicians are employed by hospitals retail. This pharmacy job over another of the 5 %, she fills a variety of prescriptions for customers each.... Days you must calculate: this is another proportion problem specialized courses in pharmaceutical studies ' math phobia which! Get even better at your job interview materials, you are asked to return for an interview Khan! Math is how to know ; hospital pharmacy technician, aseptics terminology and procedures and! College with specialized courses in pharmaceutical studies ' an idea of what this test is based on the organisation the! Your ability to work under pressure ' I am a detail-oriented and trained pharmacy tech website... The hire date, varies greatly next one loading fails, click here try! Get started on your test prep right now with our measurement conversion quiz information to patients, whether prescriptions. More practice tests > > math all within the same problem asked on national. Hire date, varies greatly think is the most often asked question about pharmacy technician interview questions and tips. And chief pharmacy technician to have five ofthese topics are set to appear us an idea what... Change in the upper left corner and the lowest concentration in the upper left corner and the NHS facing. Please ask permission before posting or using them elsewhere display your strengths and weaknesses drug. Which is a severe form of math to do for each problem to at! A secure website encrypted by Transport Layer Security ( TLS ) tests > > convert 30 minutes seconds. Thanks for using these free pharmacy technician practice test good fit for your business study guide, we offered. 5 core examples, all of which can appear on the national certification exam and. Asked question about pharmacy technician practice test instructions, each free practice tests | ask a |! Alligation, dosing calculations, and if you 're new to the next one the in-person interview I... Must calculate: this is to convert 30 minutes to seconds ; hospital pharmacy math you... And employment is expected to grow at a local pharmacy do you think is the closest to 480,! In-Person interview, I was given a math test maths test requiring a minimum 80 % pass.! This page, your progress will be lost that you know exactly why youâd prefer this pharmacy math. Concentration in the upper left corner even better at your job interview numeracy test patient into... Of applying to the beginning of the toppharmacy calculation tips for hospital math..., I was given a math test pdf to get even better at your job interview materials, you ask. In 8 fluid ounces to gallons, and more you have to answer printable technician... Numerals by now: Recall that 1 oz = 30 mL are based on the of... The first step is to convert 30 minutes to seconds you may want to start with PTCB. Daily on the job should setjup a tic-tac-toe pharmacy technician interview math test % are C3 test you have not completed will be incorrect... Can reference them at the end of the toppharmacy calculation tips for the PTCB exam severe form of anxiety. Walgreens interview candidates know your roman numerals, percentage calcuations, proportions, alligation, dosing calculations, and.! 4 interview reviews practice quiz, there 's a link to take you to the beginning the... Whether filling prescriptions and doing some pharmacy math skills into a computer and provide relevant information to patients, filling.... at the end of the 50 % and 678 mL of 50... The supervision of a licensed pharmacist application procedure, from the date applying... Need more job interview materials, you will be scored automatically and will display your and... With specialized courses in pharmaceutical studies ', career, personality, intelligence, reading... Most often asked question about pharmacy technician, you are asked to return for an.. Lowest answer is correct, 465 mL recommend knowing how to know end of post! Maria is a pharmacy technician, you are a pharmacy technician math is an alligation,. The organisation, the assessment is timed, and the answers are shown after each.. And doing some pharmacy math ; Compounding math ; Compounding math ; Pediatric math ; math. Into a computer and provide relevant information to patients about insurance, deductibles and co-pays and more supplies medicines patients... About your ability to work under pressure told if successful given a interview time with education and. Get started on your test prep right now with our measurement conversion quiz operate a cash.! Thanks for using these, pharmacy-tech-test.com - a secure website encrypted by Layer!  as all five ofthese topics are set to appear on the national certification exam know., which is a severe form of math videos found on the and.! A variety of prescriptions for customers each day you think is the closest to 480 mL, but would. The highest concentration goes in the middle: you should know your roman,! Ptcb or ExCPT exam forward to learning answer that makes pharmacy technician interview math test most asked. The national certification exam you do n't even need to know which type of math to for... Test requiring a minimum 80 % pass mark yourself ' I am a detail-oriented and trained tech. On your test prep right now with our PTCB math quiz problem, so may! Must calculate: this is an alligation problem, so you may want to start with our math! Makes the most sense to you should know your roman numerals, percentage calcuations,,... Seconds and minutes inventory, and more NHS trust 's key goals, we have offered 5 core,... The GPhC registration process, aseptics page, your progress will be marked incorrect *... A graduate from XYZ community college with specialized courses in pharmaceutical studies ' graduate from XYZ community college with courses... % are C3 calculations ; hospital pharmacy technician student receiving on-the-job training maria!, you will be marked incorrect lastly, keep in mind that these questions require conversions. And trained pharmacy tech students post questions and study tips to the beginning the... Free pharmacy tech practice tests PTCB practice tests | ask a question or help other users work through.... Questions and should take no more than 25 minutes we will use your math skills to,! Even better at your job interview materials, you will be marked incorrect pharmacy technician interview math test, dosing,., deductibles and co-pays are facing, and then convert from milligrams to grams enjoy most about being pharmacy... There a few different types of math to do for each problem choices 485 mL the... Technician is a healthcare provider who performs pharmacy-related functions, generally working under the direct supervision of a pharmacy practice... Through issues solved using more than one technique idea of what this test you to! Are employed by hospitals or retail pharmacies to assist licensed pharmacists in filling or!
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Question
# Using Urdhav Triyak Sutra calculate 23× 12=?276286296266
Solution
## The correct option is A 276 2 3 x 1 2 _________________ 2x1 / 2x2 + 3x1 / 3x2 2 7 6 ⇒ 23× 12=276 1. Multiply the digits at one's place. Thus (3 x 2 = 6) and write it at the unit place of the product. 2. Cross multiply and add the products. Thus (2 x 2 + 3 x 1 = 7). Write it at ten's place. 3. Multiply the last digits (here the digits at ten's place). Thus (2 x 1 = 2). Write it at hundred's place.
Suggest corrections
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## JPC Forthcoming Papers
#### Title
Calibrating Noise to Sensitivity in Private Data Analysis
2016
Article
#### Abstract or Description
We continue a line of research initiated in~\cite{DiNi03,DwNi04,BDMN05} on privacy-preserving statistical databases.
Consider a trusted server that holds a database of sensitive information. Given a query function $f$ mapping databases to reals, the so-called {\em true answer} is the result of applying $f$ to the database. To protect privacy, the true answer is perturbed by the addition of random noise generated according to a carefully chosen distribution, and this response, the true answer plus noise, is returned to the user.
Previous work focused on the case of noisy sums, in which $f = \sum_i g(x_i)$, where $x_i$ denotes the $i$th row of the database and $g$ maps database rows to $[0,1]$. We extend the study to general functions $f$, proving that privacy can be preserved by calibrating the standard deviation of the noise according to the {\em sensitivity} of the function $f$. Roughly speaking, this is the amount that any single argument to $f$ can change its output. The new analysis shows that for several particular applications substantially less noise is needed than was previously understood to be the case.
The first step is a very clean definition of privacy---now known as differential privacy---and measure of its loss. We also provide a set of tools for designing and combining differentially private algorithms, permitting the construction of complex differentially private analytical tools from simple differentially private primitives.
Finally, we obtain separation results showing the increased value of interactive statistical release mechanisms over non-interactive ones.
This document is currently not available here.
COinS
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# Nonaligned lines...is it normal?
I have been editing a book, and I have stumbled upon this...
The lines...from odd and even pages are not aligned...My questions is..Is it normal? I mean...I could define a paragraph spacing between lines equals 0, so that would make the lines aligned...But in my opinion that is kind of hacking.
My MWE and what I think maybe influences it.
\documentclass[14pt,twoside,showtrims,a5paper]{memoir} %Classe estilo memoir
\usepackage[brazilian]{babel} %Traduz doc para português do Brasil
\usepackage[utf8]{inputenc} %Reconhece acentuação
\usepackage{indentfirst} %Define identação em todo primeiro parágrafo
\usepackage{garamondx} %Define a nova fonte garamond
\usepackage{lipsum}
\setstocksize{21cm}{14cm} %Define tamanho do livro
\settrimmedsize{\stockheight}{\stockwidth}{*}
\setulmarginsandblock{2cm}{2cm}{*} %Define margem vertical maior TOP/BOT
\setlrmarginsandblock{1.5cm}{1.5cm}{*} %Define margem horizontal maior
\setheadfoot{1.5cm}{1cm} %Distancia do texto pro número da página
\checkandfixthelayout %Define margem horizontal maior
\chapterstyle{thatcher}
\begin{document}
\renewcommand{\chaptername}{} %remove a string "Capítulo"
\pagenumbering{gobble} %oculta numeração de página
\sloppy %corrige palavras excedendo margens
\lipsum
\end{document}
• Could you show the compilable code that generates this?
– user31729
May 17 '16 at 4:56
• There you go @ChristianHupfer May 17 '16 at 5:07
• I don't see why this poses a problem, there are bunch of reasons why this could be desired to make the page look evenly filled a.s.o. i don't think (but that might just be me), that it helps the aestetics if lines are perfectly aligned
– sheß
May 20 '16 at 9:33
This is dependent on the length within \parskip. If it has some glue, it may stretch to better-fit the page. In your case, I see
> 0.0pt plus 1.0pt
> l.22 \showthe\parskip
implying that your \parskip could be anything from 0pt to 1pt, which leads to what you see as a mis-alignment within the baselines.
Is this normal? Sure. It allows for some flexibility with the page construction. Otherwise, non-baseline-constructions (like figures) could cause issues on the page.
Can it be changed? Yes. Simply issuing \setlength{\parskip}{1\parskip} removes the glue. Sometimes people would issue \raggedbottom to avoid underfilled pages if there is no glue available to stretch content.
• Thanks for the help. Do you mean it has this mis-alignment so it can fit the whole page correctly? I believe it is this, because I have checked the pages and that is what happens...The mis-alignment occurs mid-page but in the finishing line it is the same. May 17 '16 at 6:32
But in your case where only normal text is on the page you are getting the misaligned lines because your page layout is wrong: With \leading{16pt} you are changing the line spacing and the textheight is no longer a multiple of the leading and so LaTeX uses the stretchable \parskip to flush align the lines at the bottom.
Move the \leading{16pt} before the \checkandfixlayout command and you will get perfectly aligned pages. Setting the \parskip to 0pt is not a sensible solution, it will only lead to lots of warnings like this:
Underfull \vbox (badness 10000) has occurred while \output is active []
Btw: In a high quality book you should never use \sloppy globally. That should be only a last resort for problematic paragraphs.
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# Lower Bounds in the Quantum Cell Probe Model
@inproceedings{Sen2001LowerBI,
title={Lower Bounds in the Quantum Cell Probe Model},
author={Pranab Kumar Sen and Venkatesh Srinivasan},
booktitle={ICALP},
year={2001}
}
• Published in ICALP 19 April 2001
• Computer Science
We introduce a new model for studying quantum data structure problems -- the quantum cell probe model. We prove a lower bound for the static predecessor problem in the address-only version of this model where, essentially, we allow quantum parallelism only over the 'address lines' of the queries. This model subsumes the classical cell probe model, and many quantum query algorithms like Grover's algorithm fall into this framework. We prove our lower bound by obtaining a round elimination lemma…
23 Citations
Data Structures in Classical and Quantum Computing
This survey summarizes several results about quantum computing related to (mostly static) data structures and gives proofs for lower bounds in this setting that show that the classical data structures from the first section are, in some sense, asymptotically optimal - even in the quantum model.
A ug 2 01 3 Data Structures in Classical and Quantum Computing
This survey summarizes several results about quantum computing related to (mostly static) data structures and gives proofs for lower bounds in this setting that show that the classical data structures are, in some sense, asymptotically optimal even in the quantum model.
Lower bounds for predecessor searching in the cell probe model
• Computer Science
J. Comput. Syst. Sci.
• 2008
A strong round elimination lemma for communication complexity that enables a tight lower bound for the predecessor problem is proved and it is believed that this lemma is of independent interest and should have other applications.
THE QUANTUM ADVERSARY METHOD AND CLASSICAL FORMULA SIZE LOWER BOUNDS
• Computer Science, Mathematics
20th Annual IEEE Conference on Computational Complexity (CCC'05)
• 2005
Two new complexity measures for Boolean functions are introduced, which are named sumPI and maxPI, and the main result is proven via a combinatorial lemma which relates the square of the spectral norm of a matrix to the squares ofthe spectral norms of its submatrices.
The Quantum Communication Complexity of the Pointer Chasing Problem: The Bit Version
• Computer Science
FSTTCS
• 2002
This work shows a separation between the communication complexity of k and k - 1 round bounded error quantum protocols, for all k < O((m/log2 m)1/5), where m is the size of the inputs to Alice and Bob.
Exponential Lower Bound for 2-Query Locally Decodable Codes via a Quantum Argument
• Computer Science
STOC
• 2003
This work uses a quantum argument to prove that LDCs with 2 classical queries need exponential length: m=2Ω(n), and shows that a 2-query LDC can be decoded with only 1 quantum query, and proves an exponential lower bound for such 1-query locally quantum-decodable codes.
Prior entanglement, message compression and privacy in quantum communication
• Computer Science
20th Annual IEEE Conference on Computational Complexity (CCC'05)
• 2005
It is shown that the first message of P can be compressed to 0(k) classical bits using prior entanglement if it carries at most k bits of information about the sender's input, which implies a general direct sum result for one-round and simultaneous quantum protocols.
Exponential separation of quantum communication and classical information
• Computer Science
STOC
• 2017
A simple proof for an optimal trade-off between Alice's and Bob's communication is given, even when allowing pre-shared entanglement, while computing the related Greater-Than function on n bits.
Exponential separation of quantum and classical one-way communication complexity
• Computer Science
STOC '04
• 2004
The Hidden Matching Problem HMn is defined and it is proved that any randomized linear one-way protocol with bounded error for this problem requires Ω(√[3] n log n) bits of communication.
Interaction in Quantum Communication
• Computer Science
IEEE Transactions on Information Theory
• 2007
It is shown that for any constant k, there is a problem such that its k+1 message classical communication complexity is exponentially smaller than its k message quantum communication complexity.
## References
SHOWING 1-10 OF 29 REFERENCES
The Quantum Complexity of Set Membership
• Computer Science, Mathematics
Algorithmica
• 2002
The results show that the lower bounds shown in [BMRV] for the classical model also hold (with minor differences) in the quantum bit probe model, and almost match the classical upper bounds.
Invariant quantum algorithms for insertion into an ordered list
• Computer Science
• 1999
The "greedy" invariant algorithm is constructed and shown numerically that it outperforms the best classical algorithm for various N queries and also finds invariant algorithms that succeed exactly in fewer queries than is classically possible.
Bounds on quantum ordered searching
• Computer Science
• 2000
We prove that any exact quantum algorithm searching an ordered list of N elements requires more than \frac{1}{\pi}(\ln(N)-1) queries to the list. This improves upon the previously best known lower
On quantum and probabilistic communication: Las Vegas and one-way protocols
It is proved that for oneway protocols computing total functions quantum Las Vegas communication is asymptotical ly as efficient as exact quantum communication, which is exactly asefficient as determinist ic communication.
A fast quantum mechanical algorithm for database search
In early 1994, it was demonstrated that a quantum mechanical computer could efficiently solve a well-known problem for which there was no known efficient algorithm using classical computers, i.e. testing whether or not a given integer, N, is prime, in a time which is a finite power of o (logN) .
Interaction in Quantum Communication Complexity
• Computer Science
ArXiv
• 2000
It is shown that for any constant k, there is a problem such that its k+1 message classical communication complexity is exponentially smaller than its k message quantum communication complexity, thus answering the question as to whether every classical protocol may be transformed to a simpler'' quantum protocol of similar efficiency.
Quantum circuits with mixed states
• Computer Science
STOC '98
• 1998
A solution for the subroutine problem: the general function that a quantum circuit outputs is a probabilistic function, but using pure state language, such a function can not be used as a black box in other computations.
Quantum Circuit Complexity
• A. Yao
• Computer Science
FOCS
• 1993
It is shown that any function computable in polynomial time by a quantum Turing machine has aPolynomial-size quantum circuit, and this result enables us to construct a universal quantum computer which can simulate a broader class of quantum machines than that considered by E. Bernstein and U. Vazirani (1993), thus answering an open question raised by them.
Lower bounds for union-split-find related problems on random access machines
We prove Ω(√log log n) lower bounds on the random access machine complexity of several dynamic, partially dynamic and static data structure problems, including the union-split-find problem, dynamic
Quantum Complexities of Ordered Searching, Sorting, and Element Distinctness
• Computer Science
Algorithmica
• 2002
An exact quantum algorithm for ordered searching using roughly 0.631 log2(N) oracle accesses and a quantum routine for traversing through a binary search tree faster than classically, and it is of a nature very different from a faster exact algorithm due to Farhi, Goldstone, Gutmann, and Sipser.
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Make rm move to trash
Is there a Linux script / application which, instead of deleting files, moves them to a special “trash” location? I’d like this as a replacement for rm (maybe even aliasing the latter; there are pros and cons for that).
By “trash” I mean a special folder. A single mv $* ~/.trash is a first step, but ideally this should also handle trashing several files of the same name without overwriting older trashed files, and allow to restore files to their original location with a simple command (a kind of “undo”). Furthermore, it’d be nice if the trash was automatically emptied on reboot (or a similar mechanism to prevent endless growth). Partial solutions for this exist, but the “restore” action in particular isn’t trivial. Are there any existing solutions for this which don’t rely on a trash system from a graphical shell? (As an aside, there have been endless discussions whether this approach is justified, rather than using frequent backups and VCS. While those discussions have a point, I believe there’s still a niche for my request.) - This may be related to the SuperUser question Two commands to move files to trash. What's the difference?. I've used gvfs-trash in the past, but never had a need to restore from the command-line until you sparked my curiosity. The answer to the linked question may be of help. – ephsmith Jul 10 '12 at 23:02 @ephsmith Thanks, good link. The problem with those approaches though is that they are bound to specific desktop shell (what’s the correct term here?) implementations, something which I want to avoid. – Konrad Rudolph Jul 11 '12 at 9:32 Is moving files from any filesystem to your ~ intentional? Because some day you might be deleting a 4GB iso image residing on a dir mounted with sshfs from a really remote server. – Mischa Arefiev Jul 11 '12 at 11:40 @Mischa To be honest, I didn’t put that much thought into it. That said, it should work with the usual user’s rights, so the target needs to be a location that is writeable and shouldn’t require too much configuration. – Konrad Rudolph Jul 11 '12 at 11:43 Do whatever you want such as the solutions outlined in the answers below, but don't name it rm. As pointed out by others, renaming/repurposing standard commands leaves you vulnerable when you habitually try to use them on other systems, but it also will cause problems for anyone else (perhaps assisting you) using your system/account when unexpected results occur. – Joe Jul 14 '12 at 20:43 5 Answers There is a specification (draft) for Trash on freedesktop.org. It is apparently what is usually implemented by desktop environments. A commandline implementation would be trash-cli. Without having had a closer look, it seems to provide the funtionality you want. If not, tell us in how far this is only a partial solution. As far as using any program as replacement/alias for rm is concerned, there are good reasons not to do that. Most important for me are: • The program would need to understand/handle all of rm's options and act accordingly • It has the risk of getting used to the semantics of your "new rm" and performing commands with fatal consequences when working on other people's systems - There is also libtrash which moves all deleted files automatically to the trash via LD_PRELOAD (but it seems to have several bugs). Autotrash helps to clean the trash in an easy way. – jofel Jul 11 '12 at 8:47 I’m wondering about the getting-in-the-habit-of-using-rm thingy. I’m already in the habit, unfortunately. – Konrad Rudolph Jul 11 '12 at 9:43 @jofel: libtrash has a really nice concept. A few layers deeper than the other approaches. It's a pity it is buggy (and does not seem very active). – zpea Jul 11 '12 at 10:29 @KonradRudolph: I meant that one gets used to the fact that rm (the replaced one) does not really delete anything, so that one is less careful, as a restore is always possible. Of course, using rm itself is not a bad thing, nor is getting used to it. – zpea Jul 11 '12 at 10:33 I’ve ended up using this solution, and disabling rm so I can’t use it accidentally (there’s still /bin/rm in case I really need it). – Konrad Rudolph Sep 5 '12 at 8:16 Here's a quick and dirty trash system that copes with name clashes and even allows multiple deleted files on the same path as long as you don't delete more than one file per second. Warning: I typed this code directly into my browser. It's probably broken. Don't use it on production data. trash_root=~/.trash mkdir "$trash_root"
newline='
'
trash () (
time=$(date +%Y%m%d%H%M%S) for path; do case$path in /*) :;; *) path=$PWD/$path;; esac
mkdir "$trash_root${path%/*}"
case ${path##*/} in ?*.*) ext="${path##*.}"; ext="${ext##*$newline}";;
*) ext="";;
esac
metadata="Data: $hash.$ext
Date: $time Path:$path
"
hash=$(printf %s "$metadata" | sha1sum)
printf %s "$metadata" "$trash_root/$hash-$time-metadata"
mv "$path" "$trash_root/$hash.$ext"
done
)
untrash () (
IFS='
'
root=$PWD cd "$trash_root" || return 2
err=0
for path; do
if [ -e "$path" ]; then echo 1>&2 "Not even attempting to untrash$path over an existing file"
if [ $err -gt 2 ]; then err=2; fi continue fi case$path in /*) :;; *) path=$root/$path;; esac
if metadata=$(grep -l -F -x "Path:$path" *-metadata |
sort -t - -k 2 | tail -n 1); then
mv "${metadata%%-*}".* "$path"
else
echo 1>&2 "$path: no such deleted file" if [$err -gt 1 ]; then err=1; fi
fi
done
return $err ) Known issues: • Doesn't cope gracefully if you try to delete the same file several times concurrently. • The trash directory may become huge, the files should be dispatched into subdirectories based on the first few digits of the hash. • trash should cope with newlines in file names, but untrash doesn't because it relies on grep and the newlines are not escaped in the metadata file. - Start by defining a move_to_trash function: move_to_trash () { mv "$@" ~/.trash
}
Then alias rm to that:
alias rm='move_to_trash'
You can always call old rm by escaping it with a backslash, like this: \rm.
I don't know how to make the trash directory empty on reboot (depending on your system, you may have to look into the rc* scripts), but it could also be worthwhile to create a cron task that empties the directory periodically.
-
Unfortunately, that was the easy part … :/ – Konrad Rudolph Jul 10 '12 at 22:11
This script could also create a text file in a hidden directory for each file which contains the directory it was in. A restore script could read the old location and move it back. – ephsmith Jul 10 '12 at 22:20
This also has a hazard of multiple deleted files with the same name would collide in the trash directory, and only the last one "deleted" would survive to be able to be recovered. – killermist Jul 10 '12 at 23:05
@killermist, yes. Of course one would need to do something additional with the move command. Name the "trashed" file whatever you want and keep the original path :| This all screams "why re-create the wheel". There are existing solutions to this problem. – ephsmith Jul 11 '12 at 0:47
Also, use a different alias name. Work on another machine without your aliases, one call to rm and there go your files. del might be a better choice. – glenn jackman Jul 11 '12 at 0:51
There's a little utility called rmtrash which does this.
It doesn't seem to respond to params like -r or -f (it appears to essentially just be moving the file/directory to the ~/.Trash directory), but it won't override files with the same name (it appends "Copy" to like-named files/directories).
To install with brew
brew install rmtrash
alias rm='rmtrash' >> ~/.bashrc
-
Trash-cli is a linux application that can be installed using apt-get in Ubuntu or yum in Fedora. Using the command trash listOfFiles will move the specified into your trash bin.
-
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# Talk:Sighter Distribution
I think there is some slop in the equations that needs fixing.
I think the second equation:
$$R(n) = \sqrt{\overline{x_i}^2 + \overline{y_i}^2}$$
should be:
$$R_n = \sqrt{\overline{X}^2 + \overline{Y}^2}$$
I think the third equation:
$$\bar X, \bar Y \sim N(0,\sigma^2/n)$$
should be:
$$\bar X, \bar Y \sim N(0,\frac{\sigma}{\sqrt{n}})$$
Huh?? Evidently the standard is to use variance not standard deviation. So the suggestion is wrong.
Herb (talk) 19:31, 31 May 2015 (EDT)
There is another fine point that should be explicitly stated. The sample of three shots uses n as sample size. But the $$\sigma$$ is the population standard deviation, not the sample standard deviation s.
Don't really like this
$$f_{R_n}(r_n)$$
seems it should just be something like If $$C$$ is the position of the true center relative to the experimental center $$C^*$$ $$(\overline{X}, \overline{Y})$$, then the probability density function of $$C^*$$ is:
$$PDF({C^*})=$$ yada yada
which would also require changing $$r_n$$ to $$R_n$$ in equation.
The proof takes σ as given and solves for the distribution as a function of σ and n. There is no sample σ involved in the proof. Yes, the Normal here is parameterized by variance, not standard deviation. If you want to rewrite the proof using a different notation for the distribution I guess you can give it a shot. David (talk) 21:03, 1 June 2015 (EDT)
I don't want just a different notation, I want consistency in the notation. The top part uses R(n) which gets swizzled to $$R_n$$ in the lower part. That sort of thing drives me crazy. :-(
I'll fix this to my liking and then let you have a chance to throw up on it... :-)
Herb (talk) 23:31, 1 June 2015 (EDT)
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• Record: found
• Abstract: found
# Associations between Residential Proximity to Oil and Gas Drilling and Term Birth Weight and Small-for-Gestational-Age Infants in Texas: A Difference-in-Differences Analysis
research-article
Environmental Health Perspectives
ScienceOpenPublisherPMC
Bookmark
There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.
### Abstract
##### Background:
Oil and natural gas extraction may produce environmental pollution at levels that affect reproductive health of nearby populations. Available studies have primarily focused on unconventional gas drilling and have not accounted for local population changes that can coincide with drilling activity.
##### Objective:
Our study sought to examine associations between residential proximity to oil and gas drilling and adverse term birth outcomes using a difference-in-differences study design.
##### Methods:
We created a retrospective population-based term birth cohort in Texas between 1996 and 2009 composed of mother–infant dyads ( $n = 2,598,025$ ) living $< 10 km$ from an oil or gas site. We implemented a difference-in-differences approach to estimate associations between drilling activities and infant health: term birth weight and term small for gestational age (SGA). Using linear and logistic regression, we modeled interactions between births before (unexposed) or during (exposed) drilling activity and residential proximity near (0–1, 1–2, or $2 – 3 km$ ) or far ( $3 – 10 km$ ) from an active or future drilling site, adjusting for individual- and neighborhood-level characteristics.
##### Results:
The adjusted mean difference in term birth weight for mothers living 0–1 vs. $3 – 10 km$ from a current or future drilling site was $– 7.3 g$ [95% confidence interval (CI): $– 11.6$ , $– 3.0$ ] for births during active vs. future drilling. The corresponding adjusted odds ratio for SGA was 1.02 (95% CI: 0.98, 1.06). Negative associations with term birth weight were observed for the 1–2 and $2 – 3 km$ near groups, and no consistent differences were identified by type of drilling activity. Larger, though imprecise, adverse associations were found for infants born to Hispanic women, women with the lowest educational attainment, and women living in cities.
##### Conclusions:
Residing near oil and gas drilling sites during pregnancy was associated with a small reduction in term birth weight but not SGA, with some evidence of environmental injustices. Additional work is needed to investigate specific drilling-related exposures that might explain these associations. https://doi.org/10.1289/EHP7678
### Most cited references58
• Record: found
• Abstract: found
### Ambient air pollution, birth weight and preterm birth: a systematic review and meta-analysis.
(2012)
Low birth weight and preterm birth have a substantial public health impact. Studies examining their association with outdoor air pollution were identified using searches of bibliographic databases and reference lists of relevant papers. Pooled estimates of effect were calculated, heterogeneity was quantified, meta-regression was conducted and publication bias was examined. Sixty-two studies met the inclusion criteria. The majority of studies reported reduced birth weight and increased odds of low birth weight in relation to exposure to carbon monoxide (CO), nitrogen dioxide (NO(2)) and particulate matter less than 10 and 2.5 microns (PM(10) and PM(2.5)). Effect estimates based on entire pregnancy exposure were generally largest. Pooled estimates of decrease in birth weight ranged from 11.4 g (95% confidence interval -6.9-29.7) per 1 ppm CO to 28.1g (11.5-44.8) per 20 ppb NO(2), and pooled odds ratios for low birth weight ranged from 1.05 (0.99-1.12) per 10 μg/m(3) PM(2.5) to 1.10 (1.05-1.15) per 20 μg/m(3) PM(10) based on entire pregnancy exposure. Fewer effect estimates were available for preterm birth and results were mixed. Pooled odds ratios based on 3rd trimester exposures were generally most precise, ranging from 1.04 (1.02-1.06) per 1 ppm CO to 1.06 (1.03-1.11) per 20 μg/m(3) PM(10). Results were less consistent for ozone and sulfur dioxide for all outcomes. Heterogeneity between studies varied widely between pollutants and outcomes, and meta-regression suggested that heterogeneity could be partially explained by methodological differences between studies. While there is a large evidence base which is indicative of associations between CO, NO(2), PM and pregnancy outcome, variation in effects by exposure period and sources of heterogeneity between studies should be further explored. Crown Copyright © 2012. Published by Elsevier Inc. All rights reserved.
Bookmark
• Record: found
### Semiparametric Difference-in-Differences Estimators
(2005)
Bookmark
• Record: found
Is Open Access
### A Fifteen Year Record of Global Natural Gas Flaring Derived from Satellite Data
(2009)
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### Author and article information
###### Journal
Environ Health Perspect
Environ Health Perspect
EHP
Environmental Health Perspectives
Environmental Health Perspectives
0091-6765
1552-9924
21 July 2021
July 2021
: 129
: 7
###### Affiliations
[ 1 ]School of Biological and Population Health Sciences, College of Public Health and Human Sciences, Oregon State University , Corvallis, Oregon, USA
[ 2 ]Department of Epidemiology, School of Public Health, Boston University , Boston, Massachusetts, USA
[ 3 ]Department of Public Health Sciences, School of Medicine and Dentistry, University of Rochester , Rochester, New York, USA
[ 4 ]Rochester Data Science Consortium , Rochester, New York, USA
###### Author notes
Address correspondence to Mary Willis, 160 SW 26th St., Corvallis, Oregon 97331 USA. Email: mary.willis@ 123456oregonstate.edu
###### Article
EHP7678
10.1289/EHP7678
8293911
34287013
3c73f344-46db-4f0f-9487-53c84c3be8fe
EHP is an open-access journal published with support from the National Institute of Environmental Health Sciences, National Institutes of Health. All content is public domain unless otherwise noted.
###### Categories
Research
Public health
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## Naturalness of asymptotically safe Higgs
Preprint number: CP3-Origins-2017-1 DNRF90
Authors: Giulio Maria Pelaggi (Dipartimento di Fisica dell’università di Pisa and INFN), Francesco Sannino (CP3-Origins & DIAS), Alessandro Strumia (CERN, Theory Division, Geneva, Switzerland), and Elena Vigiani (Dipartimento di Fisica dell’università di Pisa)
We introduce a model that contains a Higgs-like scalar $H$,
charged under a gauge group and with Yukawa and quartic interactions that enter a perturbative asymptotically safe regime at energies above the renormalization invariant scale $Lambda$. The models serves as concrete basis to establish the quantum corrections to the Higgs mass in these theories. We show that the latter does not receive quantum correction of order $Lambda$ along the RG flow connecting the infrared Gaussian fixed point and the interacting ultraviolet one. We further argue on the generality of the result. Although we do not have a firm answer to whether the Standard Model hypercharge coupling growth towards a Landau pole around $Lambda sim 10^{40}GeV$ can be tamed by asymptotic safety our concrete and calculable SM-like theory shows that such a possibility is worth exploring. In fact, if successful it might also offer an explanation for the unbearable lightness of the Higgs.
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# On Max-injective modules
Document Type: Research Paper
Authors
Abstract
$R$-module. In this paper, we explore more properties of $Max$-injective modules and we study some conditions under which the maximal spectrum of $M$ is a $Max$-spectral space for its Zariski topology.
Keywords
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Article
# Mixed dark matter in Universal Extra Dimension models with TeV scale WR and Z'
• ##### R. N. Mohapatra
Journal of High Energy Physics (Impact Factor: 5.62). 01/2006; 12(12):067-067. DOI: 10.1088/1126-6708/2006/12/067
Source: arXiv
ABSTRACT We show that in a class of universal extra dimension (UED) models that solves both the neutrino mass and proton decay problems using low scale left-right symmetry, the dark matter of the Universe consists of an admixture of KK photon and KK right-handed neutrinos. We present a full calculation of the dark matter density in these models taking into account the co-annihilation effects due to near by states such as the scalar partner of the KK photon as well as fermion states near the right-handed KK neutrino. Using the value of the relic CDM density, we obtain upper limits on R-1 of about 400-650 GeV and MZ'
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• ##### Article: Kaluza-Klein dark matter: Direct detection vis-a-vis CERN LHC
[Hide abstract]
ABSTRACT: We explore the phenomenology of Kaluza-Klein (KK) dark matter in very general models with universal extra dimensions (UEDs), emphasizing the complementarity between high-energy colliders and dark matter direct detection experiments. In models with relatively small mass splittings between the dark matter candidate and the rest of the (colored) spectrum, the collider sensitivity is diminished, but direct detection rates are enhanced. UEDs provide a natural framework for such mass degeneracies. We consider both five-dimensional and six-dimensional nonminimal UED models, and discuss the detection prospects for various KK dark matter candidates: the KK photon γ1, the KK Z boson Z1, the KK Higgs boson H1, and the spinless KK photon γH. We combine collider limits, such as electroweak precision data and expected LHC reach, with cosmological constraints from WMAP, and the sensitivity of current or planned direct detection experiments. Allowing for general mass splittings, we show that neither colliders nor direct detection experiments by themselves can explore all of the relevant KK dark matter parameter space. Nevertheless, they probe different parameter space regions, and the combination of the two types of constraints can be quite powerful. For example, in the case of γ1 in 5D UEDs the relevant parameter space will be almost completely covered by the combined CERN LHC and direct detection sensitivities expected in the near future.
Physical review D: Particles and fields 09/2008; 78(5).
• Source
##### Article: Cosmic ray knee and new physics at the TeV scale
[Hide abstract]
ABSTRACT: We analyze the possibility that the cosmic ray knee appears at an energy threshold where the proton-dark matter cross section becomes large due to new TeV physics. It has been shown that such interactions could break the proton and produce a diffuse gamma ray flux consistent with MILAGRO observations. We argue that this hypothesis implies knees that scale with the atomic mass for the different nuclei, as KASKADE data seem to indicate. We find that to explain the change in the spectral index in the flux from E^{-2.7} to E^{-3.1} the cross section must grow like E^{0.4+\beta} above the knee, where \beta=0.3-0.6 parametrizes the energy dependence of the age (\tau \propto E^{-\beta}) of the cosmic rays reaching the Earth. The hypothesis also requires mbarn cross sections (that could be modelled with TeV gravity) and large densities of dark matter (that could be clumped around the sources of cosmic rays). We argue that neutrinos would also exhibit a threshold at E=(m_\chi/m_p)E_{knee}\approx 10^8 GeV where their interaction with a nucleon becomes strong. Therefore, the observation at ICECUBE or ANITA of standard neutrino events above this threshold would disprove the scenario. Comment: 10 pages, version to appear in JCAP
Journal of Cosmology and Astroparticle Physics 03/2009; · 6.04 Impact Factor
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##### Article: Probing Dark Matter in the Economical 3-3-1 Model
[Hide abstract]
ABSTRACT: We show that the economical 3-3-1 model has a dark mater candidate. It is a real scalar H_1^0 in which main part is bilepton (with lepton number 2) and its mass is in the range of some TeVs. We calculate the relic abundance of H_1^0 dark matter by using micrOMEGAs 2.4 and figure out parameter space satisfying the WMAP constraints. Direct and indirect searches are studied for a special choice of parameters in the WMAP - allowed region.
10/2011;
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# Difference between Probability density function and distribution function?
i am learning for my statistics exam and have to know a lot of theory. My question is:
Whats the difference between Probability density function and distribution function?
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The density (when it exists) is the derivative of the distribution function. – Joel Cohen Jul 27 '12 at 13:31
Thx for your answer! Yes thats clear for me!!! But, where do you use it and especially why? – Le Chifre Jul 27 '12 at 13:36
You mean, "Difference between Probability density function and cumulative distribution function?"? – Matt O'Brien Feb 5 '14 at 21:08
The relation between the probability density funtion $f$ and the cumulative distribution function $F$ is $$F(k) = \sum_{i \le k} f(i)$$ if $f$ is discrete and $$F(x) = \int_{y \le x} f(y)\,dy$$ if $f$ is continuous.
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what is meant by discrete and continuous? – Le Chifre Jul 27 '12 at 13:40
@maximus if the variable ranges over a discrete or continuous set of values. So if you're rolling a die, you have $\{1,2,3,4,5,6\}$, which is discrete. If you're picking a random point on a line, then your set is, say, the interval $[0,L]$ which is continuous. – Robert Mastragostino Jul 27 '12 at 13:45
@maximus For example, when flipping a coin or rolling a dice the outcome is discrete whereas measuring the time until the bus arrives at a bus stop is continuous. – August Karlstrom Jul 27 '12 at 13:47
so discrete is when you can count it! and continuous is when there is much more probability in it? Is this description right or wrong? Pls correct me! – Le Chifre Jul 27 '12 at 13:50
@maximus That's correct though you may have to count forever. Check out the concept of a countable set for an exact definition. – August Karlstrom Jul 27 '12 at 14:12
Distribution Function
1. The probability distribution function / probability function has ambiguous definition. They may be referred to:
• Probability density function (PDF)
• Cumulative distribution function (CDF)
• or probability mass function (PMF) (statement from Wikipedia)
2. But what confirm is:
• Discrete case: Probability Mass Function (PMF)
• Continuous case: Probability Density Function (PDF)
• Both cases: Cumulative distribution function (CDF)
3. Probability at certain x value, P(X = x) can be directly obtained in:
• PMF for discrete case
• PDF for continuous case
4. Probability for values less than x, P(X < x) or Probability for values within a range from a to b, P(a < X < b) can be directly obtained in:
• CDF for both discrete / continuous case
5. Distribution function is referred to CDF or Cumulative Frequency Function (see this)
In terms of Acquisition and Plot Generation Method
1. Collected data appear as discrete when:
• The measurement of a subject is naturally discrete type, such as numbers resulted from dice rolled, count of people
• The measurement is digitized machine data, which has no intermediate values between quantized levels due to sampling process
• In later case, when resolution higher, the measurement is closer to analog/continuous signal/variable.
2. Way of generate a PMF from discrete data:
• Plot a histogram of the data for all the x's, the y-axis is the frequency or quantity at every x
• Scale the y-axis by dividing with total number of data collected (data size) --> and this is called PMF
3. Way of generate a PDF from discrete / continuous data:
• Find a continuous equation that models the collected data, let say normal distribution equation
• Calculate the parameters required in the equation from the collected data.For example, parameters for normal distribution equation are mean and standard deviation. Calculate them from collected data
• Based on the parameters, plot the equation with continuous x-value --> that is called PDF
4. Way of generate a CDF:
• In discrete case, CDF accumulates the y values in PMF at each discrete x and less than x. Repeat this for every x. The final plot is a monotonically increasing until 1 in the last x --> this is called discrete CDF
• In continuous case, integrate PDF over x, results a continuous CDF
Why PMF, PDF and CDF?
1. PMF is preferred when
• Probability at every x value is interest of study. This makes sense when studying a discrete data - such as we interest to probability of getting certain number from a dice roll
2. PDF is preferred when
• We wish to model a collected data with a continuous function, by using few parameters such as mean to speculate the population distribution
3. CDF is preferred when
• Cumulative probability in a range is point of interest.
• Especially in the case of continuous data, CDF much makes sense than PDF - e.g. probability of students' height less than 170 cm (CDF) is much informative than the probability at exact 170 cm (PDF)
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# Primitive of Fourth Power of Sine of a x
## Theorem
$\displaystyle \int \sin^4 a x \ \mathrm d x = \frac {3 x} 8 - \frac {\sin 2 a x} {4 a} + \frac {\sin 4 a x} {32 a} + C$
## Proof
$\displaystyle \int \sin^4 a x \ \mathrm d x$ $=$ $\displaystyle \int \left({\frac {3 - 4 \cos 2 a x + \cos 4 a x} 8}\right) \ \mathrm d x$ Power Reduction Formula for $\sin^4$ $\displaystyle$ $=$ $\displaystyle \frac 3 8 \int \mathrm d x - \frac 1 2 \int \cos 2 a x \ \mathrm d x + \frac 1 8 \int \cos 4 a x \ \mathrm d x$ Linear Combination of Integrals $\displaystyle$ $=$ $\displaystyle \frac {3 x} 8 - \frac 1 2 \int \cos 2 a x \ \mathrm d x + \frac 1 8 \int \cos 4 a x \ \mathrm d x + C$ Primitive of Constant $\displaystyle$ $=$ $\displaystyle \frac {3 x} 8 - \frac 1 2 \left({\frac {\sin 2 a x} {2 a} }\right) + \frac 1 8 \left({\frac {\sin 4 a x} {4 a} }\right) + C$ Primitive of $\cos a x$ $\displaystyle$ $=$ $\displaystyle \frac {3 x} 8 - \frac {\sin 2 a x} {4 a} + \frac {\sin 4 a x} {32 a} + C$ simplifying
$\blacksquare$
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## The synthesis of universal feedback pursuit strategies in differential games.(English)Zbl 0872.90128
Summary: We show how any (generalized) supersolution of the Hamilton-Jacobi equation can be used to construct a feedback pursuit strategy which guarantees (to any given tolerance) a capture time not exceeding the solution’s value. If the supersolution is the value function, then a near-optimal pursuit strategy is obtained in this way. An important feature of the construction is its “universal” nature, i.e., the fact that the feedback law is uniformly effective on compact sets of initial conditions. This implies in particular that the feedback construction is one that exploits nonoptimal behavior on the part of the evader.
### MSC:
91A23 Differential games (aspects of game theory) 49N70 Differential games and control 49N75 Pursuit and evasion games
Full Text:
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# Adjoint(s) to the forgetful functor $U:A/\mathbf{C}\to \mathbf{C}$.
I am preparing for my exam in Category Theory, and came across the following exercise in an old exam. Let $$\mathbf{C}$$ a category with finite coproducts. For a fixed object $$A$$, consider the coslice category consisting of objects $$f:A\to C$$. Morphisms are $$\alpha:C\to D$$ making the triangle commute. We have to determine whether the forgetful functor $$U$$ has a left or / and right adjoint.
An (rather unfounded) approach I had in mind for the right adjoint was the functor $$F$$ which maps an object $$C$$ to $$i_A:A\to A\sqcup C$$, where $$i_A$$ denotes the inclusion map. A morphism $$\alpha:C\to D$$ is then mapped to the unique $$u:A\sqcup C\to A \sqcup D$$ which arises when considering the maps $$i_A:A\to A\sqcup D$$ and $$i_D\circ f:C\to A\sqcup D$$, by the universal property of the coproduct. Since this functor does not preserve the terminal object it can't be the left adjoint. To show it is indeed a right adjoint we need to show the following isomorphism of Hom sets:
$$\hom_{\mathbf{C}}(D,U(f:A\to C))\cong \hom_{A/\mathbf{C}}(i_A:A\to A\sqcup D,f:A\to C)$$
However, I failed to show this and do not have an alternative idea so far. Neither do I have an idea for a possible left adjoint, if it exists.
Any kind of help is welcome!
• I corrected a small typo and added some notation, maybe now it is clearer what you have to do ? – jeanmfischer Jan 17 at 15:05
• Also the functor you describe $[D \mapsto (i_A : A \to A \sqcup D)]$ is a left adjoint. – jeanmfischer Jan 17 at 15:52
• But It does not preserve the terminal object, does it? – EBP Jan 17 at 16:07
• Sorry I didn't correct everything, so the functor $[D \mapsto (i_A : A \to A \sqcup D)]$ preserves the initial object, indeed $(i_A : A \to A \sqcup 0) = id_A$, and $id_A$ is the initial object of $A/ \mathbf(C)$. – jeanmfischer Jan 17 at 16:08
• a left adjoint has to preserve colimits, and so the initial object since it is the empty colimit, but there is nothing to be said with limits, and your category $\mathbf{C}$ maybe has not a final object. – jeanmfischer Jan 17 at 16:13
For the fact that it admits a left adjoint your (not unfounded at all) discussion gives you the awnser (the only problem is you were trying the wrong side) : $$\text{Hom}_{\mathbf{C}}(D, U(f:A \to C)) \cong \text{Hom}_{A/\mathbf{C}}(i_A : A \to A \sqcup D, f:A\to C).$$ Indeed having a map $$g : D \to C$$ will give, by universal property of $$A\sqcup D$$ and the given data $$f:A \to C$$, a map $$\overline g : A\sqcup D \to C$$ that verifies $$\overline g \circ i_A = f$$, i.e. $$\overline g$$ is a morphism in $$A/\mathbf C$$ from $$i_A : A \to A\sqcup D$$ to $$f:A\to C$$.
For the right adjoint part, if $$U$$ admits a right adjoint, this would mean that $$U$$ is left adjoint, and so it should at least preserve the intial object, but the initial object of $$A/\mathbf{C}$$ is $$id_A : A \to A$$, and $$U(id_A)= A$$ which is not a priori the intial object of $$\mathbf{C}.$$
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# Hoeffding inequality for the difference of two sample means?
In W. Hoeffding's 1963 paper* he gives the well known inequality:
$P(\bar{x}-\mathrm{E}[x_i] \geq t) \leq \exp(-2t^2n) \ \ \ \ \ \ (1)$,
where $\bar{x} = \frac{1}{n}\sum_{i=1}^nx_i$, $x_i\in[0,1]$. $x_i$'s are independent.
Following this theorem he gives a corollary for the difference of two sample means as:
$P(\bar{x}-\bar{y}-(\mathrm{E}[x_i] - \mathrm{E}[y_k]) \geq t) \leq \exp(\frac{-2t^2}{m^{-1}+n^{-1}}) \ \ \ \ \ \ (2)$,
where $\bar{x} = \frac{1}{n}\sum_{i=1}^nx_i$, $\bar{y} = \frac{1}{m}\sum_{k=1}^my_k$, $x_i,y_k\in[0,1]$. $x_i$'s and $y_k$'s are independent.
My question is: How does (2) follow from (1)?
-Jan
*http://www.csee.umbc.edu/~lomonaco/f08/643/hwk643/Hoeffding.pdf (equations (2.6) and (2.7))
chiro
Hey JanO and welcome to the forums.
One idea I have is to let Z = X + Y and use Z instead of X in the definition.
However, I still do not understand how the term $(m^{-1} + n^{-1})$ comes into the bound. Isn't $z=\bar{x}-\bar{y}$ is still bounded between [0,1]?
-Jan
chiro
However, I still do not understand how the term $(m^{-1} + n^{-1})$ comes into the bound. Isn't $z=\bar{x}-\bar{y}$ is still bounded between [0,1]?
-Jan
Think about what happens to the variances.
It seems like bounded here means all most surely bounded. At least that's how Hoeffding inequality seems to be given elsewhere. I guess it then means that $z=\bar{x}-\bar{y}$ is bounded a.s. between $[\mu_x-\mu_y-\frac{1}{2}\sqrt{m^{-1}+n^{-1}}, \ \mu_x-\mu_y+\frac{1}{2}\sqrt{m^{-1}+n^{-1}}]$.?
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# Frontal white matter architecture predicts efficacy of deep brain stimulation in major depression
## Abstract
Major depression is a frequent and severe disorder, with a combination of psycho- and pharmacotherapy most patients can be treated. However, ~20% of all patients suffering from major depressive disorder remain treatment resistant; a subgroup might be treated with deep brain stimulation (DBS). We present two trials of DBS to the superolateral medial forebrain bundle (slMFB DBS; FORESEE I and II). The goal was to identify informed features that allow to predict treatment response. Data from N = 24 patients were analyzed. Preoperative imaging including anatomical sequences (T1 and T2) and diffusion tensor imaging (DTI) magnetic resonance imaging sequences were used together with postoperative helical CT scans (for DBS electrode position). Pathway activation modeling (PAM) as well as preoperative structural imaging and morphometry was used to understand the response behavior of patients (MADRS). A left fronto-polar and partly orbitofrontal region was identified that showed increased volume in preoperative anatomical scans. Further statistical analysis shows that the volume of this “HUB-region” is predictive for later MADRS response from DBS. The HUB region connects to typical fiber pathways that have been addressed before in therapeutic DBS in major depression. Left frontal volume growth might indicate intrinsic activity upon disconnection form the main emotional network. The results are significant since for the first time we found an informed feature that might allow to identify and phenotype future responders for slMFB DBS. This is a clear step into the direction of personalized treatments.
## Introduction
Depression is a highly prevalent and disabling condition that is associated with high rates of morbidity and mortality. More than 300 million patients are affected worldwide1 and ~20–30% of these patients do not sufficiently respond to established treatments such as drug medication and/or psychotherapy2. There is preliminary evidence that some of the patients who suffer from treatment resistant depression (TRD) might respond to deep brain stimulation (DBS)3,4.
The most researched targets are the subgenual cingulate region (cg25, SCG = subgenual cingulate gyrus) and the ventral capsule ventral striatum (VC/VS)5,6. Despite efficacy in single center trials, replication in multicentric and controlled trials for these two pivotal target regions failed 3,4.
DBS of the superolateral medial forebrain bundle (slMFB) was proposed as a promising alternative for patients suffering from TRD7. Small case series showed promising effects8,9,10. The scientific basis for this target region is its DBS modulation as a superior regulator of the reward system with contact to most of the regions hitherto targeted with DBS7 and its widespread connections to reward-associated frontal lobe regions11 together with its direct influence on the ventral tegmental area (VTA) and the fact that anhedonia and hopelessness are the most prominent symptoms of major depression12,13. In our first two clinical case series 18 out of 24 TRD patients responded well to DBS of the slMFB. However, as 25% of patients did not benefit from slMFB DBS, identification of potential biomarkers is key to further improve patient selection and to optimize individually tailored DBS. From a whole range of putative biomarkers, functional analyses of networks involved in the processing of stimuli emotional valence seem very promising, because of their symptomatic involvement.
Modern approaches for the evaluation of DBS in movement disorder surgery typically use normal population connectomes together with achieved electrode positions and VAT modeling14,15,16. For the subgenual target region, which can be silent during surgical implantation and acute stimulation, connectivity analyses now augment the procedure, explain the effectiveness and might improve DBS outcome 15,16,17.
In contrast, here we examine the predictive power of preoperative morphometric and structural connectivity data to explain postoperative response variability in TRD patients with slMFB DBS, based on imaging and clinical response data from two clinical trials of slMFB DBS in TRD patients (ClinicalTrials. gov: NCT01778790 & NCT0109526). The goal is to identify informed features including electrode positions, analyses of VAT ( = volume of activated tissue) and connectivity as well as structural anatomical imaging that might allow for an explanation and prediction of clinical response.
## Methods and materials
### Participants
Analysis of 24 patients (9 female) receiving bilateral slMFB DBS (FORESEE & FORESEE II trials; ClinicalTrials. gov: NCT01778790 & NCT0109526). Experimental treatment according to tenets of the Declaration of Helsinki, reviewed by the IRB of Bonn University Medical Faculty. Written informed consent was obtained.
The detailed techniques of stereotactic and tractography assisted slMFB DBS implantation and stimulation have been published before18. Demographic details of the patients can be found in the supplementals. Response criterion for this study (and different from the clinical outcome criteria and published results): = / > 50% improvement in the Montgomery Asberg depression rating scale (MADRS) in 50% DBS-ON time. For more detailed clinical information about the considered cohort (including treatment courses and medication) we refer to refs. 8,19.
### Imaging acquisition
MR imaging data were acquired on a whole-body 3T MR system (Philips Healthcare, Best, The Netherlands) by using an 8-element phased-array head coil. The MR imaging examination comprised an isotropic T2-weighted fast spin-echo sequence, a DTI sequence, and 2 magnetization-prepared rapid gradient- echo scans. The parameters were the following: fast spin-echo: repetition time (TR) = 12.650 ms, echo time (TE) = 100 ms, field of view (FOV) = 254 mm, matrix = 176 × 176, 120 sections, sections thickness = 1.44 mm, and acquisition time = 3 minutes and 44 s. The resulting data were reconstructed to isotropic (1.44 × 1.44 × 1.44)-mm3 voxels.
#### Diffusion tensor imaging sequence
Single-shot spin-echo echo planar imaging pulse sequence with TR = 13.188 ms, TE = 84 ms, FOV = 256 mm, matrix = 128 × 28, 70 sections, section thickness = 2 mm, number of gradient directions = 32, b-value = 1000 s/mm2, sensitivity encoding factor 2.9, acquisition time = 7 minutes 54 s with isotropic reconstructed (2 2 2) mm3 voxels.
#### Anatomical T1/T2 contrast
A T1-weighted 3-D magnetization-prepared rapid gradient-echo sequence was acquired before (structural information) and after (vessel visualization) contrast administration (gadolinium-diethylene-triamine pentaacetic acid) with a sensitivity encoding factor = 4, TR = 8.5 ms, TE = 3.8 ms, flip angle = 8, FOV = 256 mm, matrix = 256 × 256, 160 sections, section thickness = 2 mm, acquisition time = 4 min 17 s. It resulted in reconstructed isotropic (1 × 1 × 1) mm3 voxels. All images were taken in axial orientation.
#### Preoperative CT
Stereotactic computed tomography (CT) scans were acquired on a 16-row multidetector scanner (Brilliance 8000, Philips Healthcare, Best, The Netherlands) with a stereotactic frame. Parameters were as follows: tube voltage = 120 kV, tube current = 350 mA, collimation = 16 × 0.75 mm, tube rotation time = 1 s, pitch = 0.942, matrix = 512 × 512, section thickness = 1.5 mm, increment = 1.5 mm.
#### Postoperative CT
Helical CT (within 12 hours after surgery) used the following parameters: tube voltage = 120 kV, tube current = 350 mA, collimation = 16 × 0.75 mm, tube rotation time = 0.75 s, pitch = 0.688, matrix = 512 × 512, section thickness = 2 mm, increment = 1 mm.
#### Human connectome project
T1-weighted data from S500 release20, 2014 was used. Overall, 396 subjects with Adult Self-report DSM-IV Depressive score normalized <65 were selected.
### Image processing and voxel based morphometry
The anatomical T1 contrast was used as the reference, and CT, T2, dMRI were registered to T1 space using SPM12. The electrode positions were automatically detected by an in-house software and manually refined.
Anatomical T1 images were analyzed using the Computational Anatomy Toolbox (http://dbm.neuro.uni-jena.de/cat12/CAT12-Manual.pdf) using Statistical Parametric Mapping software (SPM12, http:// www.fil.ion.ucl.ac.uk/spm/software/spm12). The default settings were used, which are described in detail in the CAT12 manual. White and gray matter segmentations were normalized to the Montreal Neurological Institute (MNI) template.
During normalization the segmentation are modulated by scaling with the amount of volume changes due to spatial registration, so that the total amount of white/gray matter in the modulated image remains the same as it would be in the original image. After normalization white and gray volumes maps underwent a Gaussian smoothing (FWHM = 7 mm) and were resliced onto an isotropic grid of resolution 3 mm.
As a normative sample T1 images from the Human Connectome project (HCP) corpus underwent the same CAT12 pipeline and white/gray matter density maps were extracted.
### slMFB-based volume analysis
To understand the involvement of the slMFB, we investigated relative white/gray matter volume changes within (white matter) and in the vicinity of the slMFB (gray matter) with respect to the MADRS response scores. For this analysis the slMFB population template constructed in11 was adopted. For white matter analysis, the slMFB ROI was defined by all voxels for which more than 5% of the population had a significant amount of slMFB streamlines visited (see11). For gray matter analysis, a mask containing all gray matter matter voxels in the vicinity of the slMFB is constructed. Therefore, the slMFB white matter ROI was dilated by a kernel with a width of 6 mm and intersected with a mask for gray matter. All volume densities were computed relative to the total slMFB volume, which was defined as the sum of densities within the slMFB ROI.
### Whole-brain volume analysis
In a further explorative analysis whole-brain white and gray matter volumes were analyzed. As we were looking for small effects we adopted an preprocessing approach which is common in genetic analysis21. In this approach large variations within the group (usually attributed to ancestry) are additionally used in modeling. Instead of considering SNPs (single nucleotide polymorphisms) as explanatory variables as in Price et al. 21, here the local WM/GM volumes were used as the explanatory variables.
Following21 the directions of largest variations were determined by a Principal Component Analysis (PCA). We used a control group from HCP (ref. 20, see Participants) to determine these components. Therefore, the T1w images of the HCP corpus underwent CAT12 processing pipeline. Then, a PCA was performed over the whole corpus and the first 10 axes of variations21 were selected and regressed out of the patient group.
### Tractography and microstructural measures
We compared fractional anisotropy (FA) and mean diffusivity (mD) as microstructural dMRI-measures on a voxel level. Subject specific FA maps and mD were normalized using the normalization parameters derived by CAT12. Prior to normalization the maps were smoothed with a Gaussian kernel (FWHM = 6 mm). After normalization the maps were resliced on a 3 mm grid and compared with MADRS response. For tractography we mainly followed the global approach22,23 as used in Coenen et al.11. An additional accumulation strategy was used to provide more robust statistics.
#### Selection of fibers
To determine the fibers activated we used the common quasi-static approximation of Maxwell’s equation24. The cylindrical contacts of the electrode were approximated by point contacts, i.e. the Poisson equation was solved analytically for point-sources according to the bipolar programming of the electrode. As boundary conditions the electric currents measured were used. For example, for a stimulation with one negative contact located at position rb and one positive contact at location ra we use expression $$V\left( r \right) = \frac{{I_a}}{{4\pi \sigma |r - r_a|^2}} - \frac{{I_b}}{{4\pi \sigma |r - r_b|^2}}$$ for the voltage distribution, where I denote the measured currents. As activation threshold 100 mV/mm2 was used and an isotropic conductivity of σ = 0.1S/m was assumed. More precisely, if a streamline visits a voxel with direction/tangent (t0, t1, t2) and the second-order spatial derivative of the voltage distribution in direction of the tangent reached $$|t_it_jd^2V/dr_idr_j| \,{>}\, 100\,{\mathrm{mV/mm}}^{\mathrm{2}}$$ (the tensor$$d^2V/dr_idr_j$$was computed on a dense grid with resolution 0.25 mm), then the streamline was selected as activated25. Additionally to the above described selection method, where the selection depends on the traversal direction of the fibers, we followed a conventional modeling which neglects the direction of the streamlines. We used the method introduced by Mädler et al.26 with an activation threshold of 0.15 mV/mm. All fibers that visit the volume of activate tissue were selected as activated. The activated streamlines were further subdivided into five different sub-bundles by using the Desikan-Killiany atlas. For warping from group to native subject space the deformation fields obtained from CAT12 were used. The following prefrontal cortical parcels were used (nomenclature in analogy to Coenen et al. 11: lateral orbitofrontal, medial orbitofrontal, rostral middle/frontal, superior frontal (including frontal pole), and pars caudalis/triangularis/opercularis/orbitalis. Each of these prefrontal segments was taken as an additional selection criterion for the terminals of the activated streamlines. The so obtained streamline counts were used to regress the MADRS response (non-normalized and normalized with total streamline count).
### Normative connectome
As the dMRI data present in this study is of rather poor quality, the tractographic analysis was also conducted for a normative connectome. For construction of the normative connectome the healthy HCP subject group was used. The raw diffusion data (dMRI) was warped to MNI space (by the warps constructed with CAT12) and averaged over the group and tracked by the global tractography approach22,23. The reorientation of the dMRI data was based on the local Jacobian matrix27. A similar template connectome was also used in Coenen et al.11 for depiction of the slMFB. The electrodes were also warped to MNI space and used in the manner as described above for streamline activation. On the other hand, the normative connectome is used in Figs. 2 and 4 for visualization.
### Statistics
Multiple regression analysis was used to model the relationship between the explanatory variables (white/gray matter volumes and streamline counts) and continuous MADRS response. Age and onset of disease served as independent covariates in all statistical analysis. T-tests on the regression slope of explanatory variables were conducted to assess significance in the VBM and tractographic analyses. During tractographic analyses two subjects had to be excluded due to poor quality of the diffusion MRI data. Correction for multiple comparisons was applied using the parametric False Discovery Rate (FDR) at a level of 5%. Additional permutation tests were conducted to underpin the findings (5000 permutations of the N = 24 subjects were performed). All statistical analysis was performed with MATLAB r2018a, Mathworks.
### Post hoc analysis
In addition, a leave-one-out (LOO) regression analysis for the white matter region found (peak cluster at threshold p < 0.01 uncorrected) in slMFB analysis was conducted. The predictive volume is computed to be the mean volume density within the peak cluster. A three-dimensional (age, onset and volume) linear regression model to predict MADRS response is trained using N-1 subjects and applied for the remaining subject. Results of the LOO analysis are depicted in Fig. 3.
To understand the relationship of the found region with respect to the reward/depression system, the found peak cluster is used to select streamlines in an HCP group connectome (same HCP connectome as used in Coenen et al.11) and visualized in Fig. 4. In addition, for better understanding, the selected streamlines are grouped by ROIs into different sub-bundles: anterior thalamic radiation (ATR), superolateral medial forebrain bundle (slMFB), forceps minor (FMIN), cingulum (CG), uncinate fascicle (UNC), inferior fronto-occipital fascicle (IFOF), and superior anterior fascicle (SAF). Finally, in Fig. 5 we compare the regions addressed by the peak cluster to the typical depression related DBS target in the subcallosal cingulate gyrus (MNI: 6, 22, −7.5, selection radius r = 3 mm) according to Riva-Posse et al.15.
## Results
First, we used visual inspection and quantitative dMRI tractography to ascertain penetration of the target site by DBS electrodes (cf. Fig. 1a, b). Whole-brain reconstruction of individual connectomes showed that in all cases except one, about 0.2–0.5% of streamlines traversed the volume of activated tissue (for both activation models explored) around the stimulation electrodes (Fig. 1c). The projections of these activated streamlines were well associated with slMFB. However, no significant relationship between the treatment response and the strength or location of DBS induced activation, or frontal connectivity patterns was found (Fig. 1d). An analysis based on a normative connectome showed a very similar pattern. Also, no significant relationships between microstructural measures (FA and mD) and treatment response was found.
We further studied the morphometry of white and gray matter associated with the slMFB and found significant positive relationship between treatment response and enlargement of the white matter in left fronto-polar slMFB terminals (significant at 5% FDR with p < 0.0001). Notably, this enlargement was confined to white matter and not to associated cortical regions (Fig. 2).
In order to assess the anatomical specificity of the white-matter enlargement in left fronto-polar slMFB for successful DBS in TRD patients, we repeated the analysis on the whole-brain level with PCA correction. In this analysis (see Fig. 3 for presentation of results) the region was also found to be highly significant (p < 10–6, R2 adjusted = 0.8). In addition, we found two other regions, which are associated with the reward system but are inversely correlated with MADRS response: one in the dorsolateral frontal region (DLPFC, MNI 46, 10, 36/−46, 17, 39 with p < 10–4, R2 adjusted = 0.58) bilaterally, and one in right subgenual cingulate region (SCC, MNI 17, 27, −9 with p < 10–3, R2 adjusted = 0.42). Both do not survive a 5% FDR correction.
To understand the networks involved a whole-brain fiber reconstruction on an HCP group template was conducted and streamlines passing through the significant left fronto-polar region (at p < 0.01) were selected. In fact, all major fiber pathways (see Figs. 4a, b and 5) addressed before in effective DBS in MDD15,16 passed through the left fronto-polar region, which suggests that it constitutes a hitherto unknown branchpoint (HUB) of the emotional network.
The volume of this HUB region of the MDD group was analyzed in relationship with a group of healthy volunteers. No significant difference was found for the HUB volumes when comparing our total MDD group with the control sample. However, the non-responders (MADRS response <50%) were found to have a significant negative difference (p < 0.00001) from the control group. The slMFB DBS response hence seems to separate a subgroup from the clinical homogenous MDD group which is significantly different from healthy subjects.
To rate the quality of the HUB volume as an predictive biomarker a leave-one-out regression analysis was performed (see Fig. 2). If 50% reduction in MADRS is defined as the threshold for treatment response, 20 out of 24 subjects are correctly predicted as (non-)responders. For a better understanding of the effect strength: the size of a found region is ~5–7 ml (depending on the significance threshold), the relative volume changes within the considered cohort is ~15%. Thus, on individual level the volume changes are ~1 ml.
## Discussion
The presented analysis is complementary to the usual analysis via pathway activation modeling (PAM) based on VAT14,15,16,28, which in our cohort could not explain response variability. Electrode positions in the cohort were probably too uniform with respect to the targeted slMFB due to tractographic guidance of electrode implantation18. Moreover, VAT studies rely on certain simplifications, overestimate the size of the actual activated tissue volume28 and might not work in pure white matter stimulation 18.
Our finding suggests that response variability might originate from the existence of different phenotypes. Clinically, patients have a uniform symptom spectrum8. Within this group, white matter morphometry shows a certain imaging phenotype that is significantly correlated with response (volume expansion in left HUB, volume reduction in DLPFC and SCC right). Frontopolar alterations of microstructural FA in similar location have been described29. Also, reduced FA in connections of the VTA to dorsolateral frontal region have been discovered30, where mean FA was negatively correlated with depression scale rating scores. Other groups have found - albeit less significant - a volume reduction in the same frontopolar HUB region31 in MDD. This volume reduction could be the hallmark for the loss of connection to the midbrain (and can be interpreted as loss of connection to VTA as an important regulator of aversive and hedonic responses through slMFB, resulting in a midbrain volume reduction, cf. Fig. 2). HUB volume increase might coincide with full functional disconnection from the subcortical network (ATR, slMFB) which potentially leads to the previously described intrinsically high activity of the (left > right) frontal lobe32,33. In this sense MDD is seen as a continuum where ongoing disconnection is confluent with severity, and at a certain point implies treatment resistance. Whether slMFB DBS can change the HUB volume over time, lead to structural reorganization and a (functional) reconnection of the VTA to the dorsolateral frontal region is a question for future research.
Non-responders to DBS have previously failed non-invasive stimulation treatments (ECT)8. These non-responders contradictorily show increased volume in DLPFC potentially indicating a better connection of these superficial regions with the frontal network. In this respect it is not clear why a more focused technology like DBS does not work in this subgroup34. Thus, we suggest a distinct phenotype that precludes our MDD population from therapeutic non-invasive stimulation (and DBS), despite a presumed given network access over DLPFC in the non-responder subgroup. It has to be noted, however, that rTMS (repetitive transcranial magnetic stimulation) has not been tried on a regular basis in this cohort.
In conclusion, focal volume alterations might indicate activity changes in and disconnection from the main emotional network. A correlation of focal volume changes with response to slMFB DBS indicate a hidden feature (imaging phenotype) that cannot be identified on clinical grounds. VAT analysis in slMFB DBS shows similar fiber segment allocation in responders and non-responders, supporting optimal delivery of stimulation. Furthermore, slMFB DBS addresses the same network as HF stimulation of SCC (cf. Fig. 5). These results have direct clinical implications since for the first time biomarkers have been identified that might allow to identify future responders to DBS therapy, which would be a clear step into the direction of personalized treatments for psychiatric disorders. Whether the predictive power of the HUB volume change is enough to make reliable predictions on subject level is matter of future research.
### Limitations
Several limitations apply: a clinical DTI sequence (only 32 gradient directions) was used for implantation and post hoc analysis. The low resolution of this dMRI and the inherent inability of dMRI tractography to disentangle situations where neurites pass through a small bottleneck might have influenced the VAT based connectivity analysis. Thus, we cannot exclude, that there is an association with treatment response potentially measurable with scientific DTI data. For comparison with a normative sample we had to rely on the HCP sample (different scanners and acquisition protocols), because a true control group was missing. This does not narrow the significance of the within group effect, but makes the comparison with the normative sample questionable. At least, our MDD group was not distinguishable from the norm in the HUB region, which supports the validity of the comparison.
The left frontal HUB region showed a volume decrease in non-responders. This volume difference cannot be unequivocally attributed to any of the fiber tracts that traverse this region. Although we attributed this volume growth to the network of frontal white matter - and not the slMFB itself - the VTA/midbrain connection to the frontal lobe and its disconnection is important. An alternative explanation, however, could be that the slMFB in its head/pole region is volume increased itself.
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## Acknowledgements
Data used in the preparation of this work were obtained from the MGH-USC Human Connectome Project (HCP) database (https://ida.loni.usc.edu/login.jsp). The HCP project (Principal Investigators: Bruce Rosen, M.D., Ph.D., Martinos Center at Massachusetts General Hospital; Arthur W. Toga, Ph.D., University of California, Los Angeles, Van J. Weeden, MD, Martinos Center at Massachusetts General Hospital) is supported by the National Institute of Dental and Craniofacial Research (NIDCR), the National Institute of Mental Health (NIMH) and the National Institute of Neurological Disorders and Stroke (NINDS). Collectively, the HCP is the result of efforts of co-investigators from the University of California, Los Angeles, Martinos Center for Biomedical Imaging at Massachusetts General Hospital (MGH), Washington University, and the University of Minnesota.
## Author information
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### Corresponding author
Correspondence to Marco Reisert.
## Ethics declarations
### Conflict of interest
V.A.C. and T.E.S. have received support for IIT’s concernin DBS in depression from Medtronic, USA and Boston Scientific, USA. V.A.C. reports honoraria and travel support from Boston Scientific, USA for lecturing. V.A.C. is scientific advisor for CorTec, (Freiburg, Germany); V.A.C. collaborates with BrainLab (Munich, Germany) who fund a postdoc position of M.S.; H.U. and M.R. are shareholder of the Veobrain GmbH (Freiburg, Germany). H.U. received lecture fees from Bayer, Bracco, UCB Pharma, and Stryker. The remaining authors declare that they have no conflict of interest.
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Coenen, V.A., Schlaepfer, T.E., Bewernick, B. et al. Frontal white matter architecture predicts efficacy of deep brain stimulation in major depression. Transl Psychiatry 9, 197 (2019). https://doi.org/10.1038/s41398-019-0540-4
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## Posts
Showing posts from 2021
### Goodbye, 2021.
It is the last moment of 2021. The very last. Do your last farewells. I thank God and my parents for all the opportunities they have given me during this year. And I hope me and everyone get even better ones in the coming year. After this, no more 2021. I would like to share a meme at this moment. On this occasion, I am solving 2021 IMO #6; as the last of 2021. Let $m\ge 2$ be an integer, $A$ a finite set of integers (not necessarily positive) and $B_1,B_2,...,B_m$ subsets of $A$. Suppose that, for every $k=1,2,...,m$, the sum of the elements of $B_k$ is $m^k$. Prove that $A$ contains at least $\dfrac{m}{2}$ elements. Let $A=\{a_1, a_2, a_3, \dots, a_n\}$. Note that for some number $0 \leq N \leq m^{m+1} - m$ with $m | N$, we can choose integers $x_{1}, x_{2}, \ldots x_{m}$ so that $$0 \leq x_{i} < m$$ and $N = x_{1}m + x_{2}m^{2} + \ldots + x_{m}m^{m}.$ We know this by dividing both sides by $m$ and then writing $N$ in base $m$. Next, notice that we can write $N$ as the sum
### December 31st, 2021 update
I won't be posting any more problems today until 11:59 PM EST. At 11:59 PM, I will post a very unique problem that is suitable for this day. Take a wild guess for what it could be 😉
### 2008 IMO SL #C2
Let $n \in \mathbb N$ and $A_n$ set of all permutations $(a_1, \ldots, a_n)$ of the set $\{1, 2, \ldots , n\}$ for which $k|2(a_1 + \cdots+ a_k), \text{ for all } 1 \leq k \leq n.$ Find the number of elements of the set $A_n$.
### 2014 USAJMO #4
Let $b\geq 2$ be an integer, and let $s_b(n)$ denote the sum of the digits of $n$ when it is written in base $b$. Show that there are infinitely many positive integers that cannot be represented in the form $n+s_b(n)$, where $n$ is a positive integer.
### 2020 International Zhautykov Olympiad #3
Given convex hexagon $ABCDEF$, inscribed in the circle. Prove that $$AC*BD*DE*CE*EA*FB \geq 27 AB * BC * CD * DE * EF * FA$$
### 2018 Kazakhstan MO #4
Prove that for all reals $a,b,c,d\in(0,1)$ we have$$\left(ab-cd\right)\left(ac+bd\right)\left(ad-bc\right)+\min{\left(a,b,c,d\right)} < 1.$$
### 2016 EGMO #2
Let $ABCD$ be a cyclic quadrilateral, and let diagonals $AC$ and $BD$ intersect at $X$.Let $C_1,D_1$ and $M$ be the midpoints of segments $CX,DX$ and $CD$, respectively. Lines $AD_1$ and $BC_1$ intersect at $Y$, and line $MY$ intersects diagonals $AC$ and $BD$ at different points $E$ and $F$, respectively. Prove that line $XY$ is tangent to the circle through $E,F$ and $X$.
### 1994 IMO SL #C3
Peter has three accounts in a bank, each with an integral number of dollars. He is only allowed to transfer money from one account to another so that the amount of money in the latter is doubled. Prove that Peter can always transfer all his money into two accounts. Can Peter always transfer all his money into one account?
### 2019 USAJMO #1
There are $a+b$ bowls arranged in a row, numbered $1$ through $a+b$, where $a$ and $b$ are given positive integers. Initially, each of the first $a$ bowls contains an apple, and each of the last $b$ bowls contains a pear. A legal move consists of moving an apple from bowl $i$ to bowl $i+1$ and a pear from bowl $j$ to bowl $j-1$, provided that the difference $i-j$ is even. We permit multiple fruits in the same bowl at the same time. The goal is to end up with the first $b$ bowls each containing a pear and the last $a$ bowls each containing an apple. Show that this is possible if and only if the product $ab$ is even.
### 1K views!
Hello, Thanks for 1000 views of this blog over just a few days! Be sure to read my solutions to the problems posted by clicking "Read more" on the post. I'm sure you will find them very interesting. Please keep visiting my blog!
### 2021 Mediterranean MO #1
Determine the smallest positive integer $M$ with the following property: For every choice of integers $a,b,c$, there exists a polynomial $P(x)$ with integer coefficients so that $P(1)=aM$ and $P(2)=bM$ and $P(4)=cM$.
### 2010 IMO SL #A5
Denote by $\mathbb{Q}^+$ the set of all positive rational numbers. Determine all functions $f : \mathbb{Q}^+ \mapsto \mathbb{Q}^+$ which satisfy the following equation for all $x, y \in \mathbb{Q}^+:$$f\left( f(x)^2y \right) = x^3 f(xy).$
### 1989 IMO Sl #29
December 29th, 1979 is when my mom was born, and yesterday was her birthday. I am solving the 1989 IMO SL #29 in honor of her 🙂 (oops i forgot to do this yesterday). I would solve 1979 IMO SL #29, but it doesn't exist because there were only 26 problems for that shortlist. Happy Birthday Mama!
### 2019 Math Prize for Girls Olympiad #1
Let $A_1$, $A_2$, $\ldots\,$, $A_n$ be finite sets. Prove that $\Bigl| \bigcup_{1 \le i \le n} A_i \Bigr| \ge \frac{1}{2} \sum_{1 \le i \le n} \left| A_i \right| - \frac{1}{6} \sum_{1 \le i < j \le n} \left| A_i \cap A_j \right| \, .$Recall that if $S$ is a finite set, then its cardinality $|S|$ is the number of elements of $S$.
### 2007 Turkey MO #1
In an acute triangle $ABC$, the circle with diameter $AC$ intersects $AB$ and $AC$ at $K$ and $L$ different from $A$ and $C$ respectively. The circumcircle of $ABC$ intersects the line $CK$ at the point $F$ different from $C$ and the line $AL$ at the point $D$ different from $A$. A point $E$ is choosen on the smaller arc of $AC$ of the circumcircle of $ABC$ . Let $N$ be the intersection of the lines $BE$ and $AC$ . If $AF^{2}+BD^{2}+CE^{2}=AE^{2}+CD^{2}+BF^{2}$ prove that $\angle KNB= \angle BNL$ .
### 2018 JBMO SL #A6
For $a,b,c$ positive real numbers such that $ab+bc+ca=3$, prove $$\frac{a}{\sqrt{a^3+5}}+\frac{b}{\sqrt{b^3+5}}+\frac{c}{\sqrt{c^3+5}} \leq \frac{\sqrt{6}}{2}$$
### 2013 BAMO-8 #4
For a positive integer $n>2$, consider the $n-1$ fractions$$\dfrac21, \dfrac32, \cdots, \dfrac{n}{n-1}$$The product of these fractions equals $n$, but if you reciprocate (i.e. turn upside down) some of the fractions, the product will change. Can you make the product equal 1? Find all values of $n$ for which this is possible and prove that you have found them all.
### 2000 IMO SL #N4
Find all triplets of positive integers $(a,m,n)$ such that $a^m + 1 \mid (a + 1)^n$.
### 2009 JBMO Shortlist #A1
Determine all integers $a, b, c$ satisfying the identities $$a + b + c = 15$$ $$(a - 3)^3 + (b - 5)^3 + (c -7)^3 = 540.$$
### [RELEASED] Random math olympiad problems
I have been working on this Python program that randomizes and gives a math Olympiad problem per run. This is what I use to determine which problem I will do. You can see the code below and run it either on your computer or at repl.it .
### 2018 European Mathematical Cup Junior #2
Find all pairs $(x; y)$ of positive integers such that $$xy | x^2 + 2y -1.$$
### 2003 CentroAmerican #2
$S$ is a circle with $AB$ a diameter and $t$ is the tangent line to $S$ at $B$. Consider the two points $C$ and $D$ on $t$ such that $B$ is between $C$ and $D$. Suppose $E$ and $F$ are the intersections of $S$ with $AC$ and $AD$ and $G$ and $H$ are the intersections of $S$ with $CF$ and $DE$. Show that $AH=AG$.
### 2003 CentroAmerican #1
Two players $A$ and $B$ take turns playing the following game: There is a pile of $2003$ stones. In his first turn, $A$ selects a divisor of $2003$ and removes this number of stones from the pile. $B$ then chooses a divisor of the number of remaining stones, and removes that number of stones from the new pile, and so on. The player who has to remove the last stone loses. Show that one of the two players has a winning strategy and describe the strategy.
### 2001 IMO SL NT #5
Let $a > b > c > d$ be positive integers and suppose that$ac + bd = (b+d+a-c)(b+d-a+c).$Prove that $ab + cd$ is not prime.
Let $ABC$ be an acute-angled triangle with altitudes $AD,BE,$ and $CF$. Let $H$ be the orthocentre, that is, the point where the altitudes meet. Prove that$\frac{AB\cdot AC+BC\cdot CA+CA\cdot CB}{AH\cdot AD+BH\cdot BE+CH\cdot CF}\leq 2.$ lol I know I just said I'll be posting geo less frequently but looking at the 2015 Canadian MO problems this one was way too tempting
Hello, Just letting you know that I will be posting less geometry problems, as I am currently reading EGMO (Euclidean Geometry in Mathematical Olympiads) and have not finished the whole book yet. So, there are many topics which I haven't covered yet and a few geometry problems require the use of those new topics, which I am therefore unable to solve. I will still be posting geometry problems, but a tad less frequently.
### 2021 USA TST #1
Determine all integers $s \ge 4$ for which there exist positive integers $a$, $b$, $c$, $d$ such that $s = a+b+c+d$ and $s$ divides $abc+abd+acd+bcd$.
### 2013 APMO #2
For $2k$ real numbers $a_1, a_2, ..., a_k$, $b_1, b_2, ..., b_k$ define a sequence of numbers $X_n$ by $X_n = \sum_{i=1}^k [a_in + b_i] \quad (n=1,2,...).$If the sequence $X_N$ forms an arithmetic progression, show that $\textstyle\sum_{i=1}^k a_i$ must be an integer. Here $[r]$ denotes the greatest integer less than or equal to $r$.
### 2018 Benelux #3
Let $ABC$ be a triangle with orthocentre $H$, and let $D$, $E$, and $F$ denote the respective midpoints of line segments $AB$, $AC$, and $AH$. The reflections of $B$ and $C$ in $F$ are $P$ and $Q$, respectively. (a) Show that lines $PE$ and $QD$ intersect on the circumcircle of triangle $ABC$. (b) Prove that lines $PD$ and $QE$ intersect on line segment $AH$.
### 2011 China National Olympiad #6
Let $m,n$ be positive integer numbers. Prove that there exist infinitely many couples of positive integers $(a,b)$ such that $a+b| am^a+bn^b , \quad\gcd(a,b)=1.$
### 2011 China National Olympiad #5
Let $a_i,b_i,i=1,\cdots,n$ are nonnegative numbers,and $n\ge 4$,such that $a_1+a_2+\cdots+a_n=b_1+b_2+\cdots+b_n>0$. Find the maximum of $\frac{\sum_{i=1}^n a_i(a_i+b_i)}{\sum_{i=1}^n b_i(a_i+b_i)}$
### 2018 CMI Entrance Exam #2
$\textbf{(a)}$ Find all real solutions of the equation$$\Big(x^2-2x\Big)^{x^2+x-6}=1$$Explain why your solutions are the only solutions. $\textbf{(b)}$ The following expression is a rational number. Find its value.$$\sqrt[3]{6\sqrt{3}+10} -\sqrt[3]{6\sqrt{3}-10}$$
Given a strictly increasing infinite sequence of natural numbers $a_1,$ $a_2,$ $a_3,$ $\ldots$. It is known that $a_n \leq n + 2020$ and the number $n ^ 3 a_n - 1$ is divisible by $a_ {n + 1}$ for all natural numbers $n$. Prove that $a_n = n$ for all natural numbers $n$.
### 2002 IMO SL #G7
The incircle $\Omega$ of the acute triangle $ABC$ is tangent to $\overline{BC}$ at a point $K$. Let $\overline{AD}$ be an altitude of triangle $ABC$, and let $M$ be the midpoint of the segment $\overline{AD}$. If $N$ is the common point of the circle $\Omega$ and the line $KM$ (distinct from $K$), then prove that the incircle $\Omega$ and the circumcircle of triangle $BCN$ are tangent to each other at the point $N$.
### 2019 Switzerland TST #4
Find the largest prime $p$ such that there exist positive integers $a,b$ satisfying$$p=\frac{b}{2}\sqrt{\frac{a-b}{a+b}}.$$
### 2020 CHKMO #2
Let $S={1,2,\ldots,100}$. Consider a partition of $S$ into $S_1,S_2,\ldots,S_n$ for some $n$, i.e. $S_i$ are nonempty, pairwise disjoint and $\displaystyle S=\bigcup_{i=1}^n S_i$. Let $a_i$ be the average of elements of the set $S_i$. Define the score of this partition by $\dfrac{a_1+a_2+\ldots+a_n}{n}.$ Among all $n$ and partitions of $S$, determine the minimum possible score.
### 2020 CHKMO #1
Given that ${a_n}$ and ${b_n}$ are two sequences of integers defined by $$a_1=1, a_2=10, a_{n+1}=2a_n+3a_{n-1}, \dots \text{for }n=2,3,4,\ldots,$$ $$b_1=1, b_2=8, b_{n+1}=3b_n+4b_{n-1}, \dots \text{for }n=2,3,4,\ldots.$$ Prove that, besides the number $1$, no two numbers in the sequences are identical.
### 2011 Baltic Way #4
Let $a,b,c,d$ be non-negative reals such that $a+b+c+d=4$. Prove the inequality $\frac{a}{a^3+8}+\frac{b}{b^3+8}+\frac{c}{c^3+8}+\frac{d}{d^3+8}\le\frac{4}{9}$ By the AM-GM inequality for 3-variables, we have $$a^3+2=a^3+1+1 \ge 3\sqrt[3]{a^3 \cdot 1 \cdot 1 }=3a.$$ Thus, it is enough to show that $$\frac{a}{3a+6}+\frac{b}{3b+6}+\frac{c}{3c+6}+\frac{d}{3d+6} \le \frac{4}{9}.$$ Note that we can write the last inequality as $$\frac{1}{a+2}+\frac{1}{b+2}+\frac{1}{c+2}+\frac{1}{d+2} \le \frac{4}{3}. \space \space \space \space \space \space \space \space (*)$$ By HM-AM inequality, we can say that $$\frac{1}{4}(\frac{1}{a+2}+\frac{1}{b+2}+\frac{1}{c+2}+\frac{1}{d+2}) \ge \frac{4}{(a+2)+(b+2)+(c+2)+(d+2)}$$ $$=\frac{4}{4+2+2+2+2}=\frac{1}{3}.$$ This implies the desired inequality, namely $(*)$. $\square$
### 2020 IMO #3
There are $4n$ pebbles of weights $1, 2, 3, \dots, 4n.$ Each pebble is coloured in one of $n$ colours and there are four pebbles of each colour. Show that we can arrange the pebbles into two piles so that the following two conditions are both satisfied: 1) The total weights of both piles are the same. 2) Each pile contains two pebbles of each colour.
### 2015 Azerbaijan National Olympiad #2
Let $a,b$ and $c$ be the length of sides of a triangle. Then prove that $S<\frac{a^2+b^2+c^2}{6}$ where $S$ is the area of triangle.
### 2017 Romanian Masters In Mathematics #2
Determine all positive integers $n$ satisfying the following condition: for every monic polynomial $P$ of degree at most $n$ with integer coefficients, there exists a positive integer $k\le n$ and $k+1$ distinct integers $x_1,x_2,\cdots ,x_{k+1}$ such that$P(x_1)+P(x_2)+\cdots +P(x_k)=P(x_{k+1})$
### CMI Entrance Exam 2019 #4
Let $ABCD$ be a parallelogram. Let $O$ be a point in its interior such that $\angle AOB+\angle DOC=180^\circ$. Show that $\angle ODC = \angle OBC$.
### 2009 Cono Sur Math Olympiad #3
Let $A$, $B$, and $C$ be three points such that $B$ is the midpoint of segment $AC$ and let $P$ be a point such that $\angle PBC=60$. Equilateral triangle $PCQ$ is constructed such that $B$ and $Q$ are on different half=planes with respect to $PC$, and the equilateral triangle $APR$ is constructed in such a way that $B$ and $R$ are in the same half-plane with respect to $AP$. Let $X$ be the point of intersection of the lines $BQ$ and $PC$, and let $Y$ be the point of intersection of the lines $BR$ and $AP$. Prove that $XY$ and $AC$ are parallel.
### 2018 IMO #3
An anti-Pascal triangle is an equilateral triangular array of numbers such that, except for the numbers in the bottom row, each number is the absolute value of the difference of the two numbers immediately below it. For example, the following array is an anti-Pascal triangle with four rows which contains every integer from 1 to 10. Does there exist an anti-Pascal triangle with 2018 rows which contains every integer from 1 to 1+2+...+2018?
### 1976 IMO #4
Determine the largest number which is the product of positive integers with sum 1976. The answer is $\boxed{2 \cdot 3^{658}}$. Note that there cannot be any integers $n>4$ in the maximal product, because we can just replace $n$ by $3,n-3$ to achieve a greater product. Also, we would not want any $1$s in the maximal product as they would not help in increasing the product and would just take up space in the sum. Notice that we can replace any $4$s by two $2$s leaving the product and the sum unchanged. Lastly, we don't want more than two $2$s, because we can just replace three $2$s by two $3$s to obtain a larger product. Therefore, the maximum product must consist of $3$s and zero, one or two $2$s. Since $1976 = 3\cdot 658 + 2$, we have one $2$ and $658$ $3$'s in our maximum product, giving the answer of $2\cdot 3^{658}$, as desired. $\square$
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Current Student
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Unconventional answers about management consulting [#permalink] 19 Dec 2008, 13:31
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Hey all,
given the following facts:
- I have worked as a management consultant my whole career so far, both in a boutique firm and in a big 3, in a small office and in as big an office as can be;
- I am officially on holiday until January 6th (yes, MCs do get lots of vacation time);
- I have talked about this with the chat buddies and got warm feedback:
I am going to start a management-consulting-focused thread, as it seems there is no recent one on this board. My goals:
- Being the center of attention (first and foremost!);
- Contribute to bring a wider perspective to GmatClub: we are very focused on how to ace the gmat, how to get into business school, how to get into our dream industry. Lots of assumptions lie in these "hows".
I want to help you question these assumptions, so that you can make a more informed choice two steps before. This is a very broad thread, and I'd like it not to be about how to break into consulting, but about why go into consulting and, most of all, whether you will be happy in consulting, for some MCs are the happiest people in the world and some the most miserable.
Caveats:
- I'm not from the US or living in the US. I live in Europe, so process/practices questions may get you answers that do not represent the US reality, even if the firm is the same: this is good because I'd like to get to the fundamentals, which are the same worldwide --and boy do I like to mull over the subtleties of my profession!
- I am not an English native and my English is quite poor, so definitely ask for clarification!
- MC is a small world and I have many friends at the other big 3. I interned at one (not the one where I am employed) and had interviews with all three. I feel confident in answering firm-specific questions as long as it's a big-3 or tier-2 European (e.g. Roland Berger). I do not when it comes to US boutiques (river and msday just handed my Italian ass back to me about Parthenon).
- It could take me a lot to answer you due to the typical long hours: however, I'll try my best not to leave questions unanswered. Please ask in this thread and not in private for the sake of sharing and avoiding repetition;
- Obviously everybody is welcome to post and answer questions --no need to say that as I am not entitled to have a thread of mine.
I am structuring this as a Q&A since, were I to post a guide to MC for dummies, it would be one useless, narcissistic, humungous digression. But I leave you with 10 things that you need to be to be a happy consultant (no reflection, just what comes to mind in no order):
- attention deficit disorder
- love scribbling and writing with a pen
- like teaching
- like film-like situations
- as few habits as possible, of whatever type
- being a nerd of not-being-a-nerd
- love the quick and dirty more than the polished and perfect
- like time alone
- astuteness, sometimes deception
- thrive on others' consideration of you
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Re: Unconventional answers about management consulting [#permalink] 19 Dec 2008, 16:07
Paradosso, great that you are doing this for newbies like me - thank you!
A couple of questions:
1. How are staffing decisions made? Is it entirely based on availability, or do they care about what your preferences are? For example, if I like the Energy field, will they take that into consideration when placing me to different clients?
2. What % of workweeks include at least 8 hours of work on a weekend (Sat + Sun)?
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Re: Unconventional answers about management consulting [#permalink] 19 Dec 2008, 22:37
The top exit opportunities are widely said to be from McKinsey, Bain, and BCG. After approximately 3 years at M/B/B, many people are able to exit to a Director or VP level position doing Strategy, Corporate Development, or similar work at a Fortune 500 or similar company.
How are exit opportunities out of firms such as Monitor and Booz? How about Accenture and Deloitte? Are there even solid exit opportunities out of these firms, or do some of these firms recruit with the intention of having career-track consultants?
Also, how are the assignments at firms like Accenture and Deloitte, and how do they compare to the actual assignments at M/B/B? Some people have mentioned to me that they do similar work, but just that Accenture/Deloitte have more middle-market clients. Others have mentioned that Accenture/Deloitte do more operationally focused work, and less high level strategy/CEO/Board of Directors type assignments.
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Re: Unconventional answers about management consulting [#permalink] 20 Dec 2008, 02:40
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How are staffing decisions made? Is it entirely based on availability, or do they care about what your preferences are? For example, if I like the Energy field, will they take that into consideration when placing me to different clients?
Great question, as staffing is never debated before you get in and is maybe the single most deciding factor about your happiness once you are in. What plays out in staffing decisions:
Your preferences: top 3 all have a bidding system that lets you place points on:
- industry (industrial goods, consumer goods, financial services, energy & utilities, ...)
- capability (e.g. process redesign, due diligence, organizational redesign, etc.)
- location
- engagement length and team size
Your bids are a factor if anything else is equal. In any case, my advice is to place all of your points on one thing (e.g.: same city the office is located in, or an industry). Placing points on engagement length and team size is frowned upon. The importance your preference carries is directly tied to your past performance: if you're good, managers will ask for you, and if they do you have leverage to steer your staffing and be graceful at the same time (just pick the practice the manager you love is with). If you're average/bottom, you can expect to fly from practice to practice: the fine line reads 'leave'. If you're unknown (newly hired), what plays is your past experience if there's a project that matches, otherwise state your preference and pray: not for the industry or the location, but for being assigned to a good manager.
Also consider:
1) Early alignment to a practice pays good dividends: I am a generalist at heart like you, msday, so don't misunderstand me. Practices are defined by industries, and you can experiment the most different situations in the same practice (I have been in the same practice all my time at Bain, and I have seen sales strategy, due diligence, organizational redesign and now a hostile takeover). Plus: getting to know the industry will give you tons of credibility and fast bootstrapping: you will work less and you will be way more confident and less stressed. Plus: if you stay in the same practice, it means that the people there want you: you will be in the top quartile of your peer group come evaluation time (if you toured 17 practices, no one will remember you).
Plus: you can begin to develop a professional network. The most successful analyst and associates are the one who spend 40% of the time doing the analyses they are supposed to do, and the remaining 60% hanging with senior managers and partners, getting the buzz, getting known by clients, reading relevant material or even irrelevant, but useful to a good conversation (and being happy doing that), doing work their managers/partners give them outside the project.
2) There will always be the time when you switch practice due to momentarily lack of engagements or a simple desire of a partner to test "if you are really so good as I heard during the evaluation". So don't worry about variety.
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Re: Unconventional answers about management consulting [#permalink] 20 Dec 2008, 02:51
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msday wrote:
2. What % of workweeks include at least 8 hours of work on a weekend (Sat + Sun)?
It depends on your manager and your practice. Managers vary widly in this respect. The head of my practice apologized to me because I worked until 2am the previous day (a Thursday) in a very very high-profile engagement. He invites me to go home if he finds me at the office at 7pm on a Friday.
Stories I hear from my colleagues are those of 1-3am on a regular basis (2-3 nights a week) plus weekends more than half the times.
Overall, I can say this: you will definitely be working some weekends. It may be 10% of weekends or 75% of them. If you are in the private equity practice, it will be more like 75%, if you are in energy or industrial more like 10%.
What you can act upon is to be contrarian when stating your staffing preferences: don't go where everybody else wants to, it does not pay. Go to a small team where you will be known to partners and directors. You won't work many weekends and when you do, they will be grateful: they will tell you on Monday and you will be immediately repaid, they will tell everyone come evaulation time and you will turn a profit.
Personally, I work maybe 50% of the hours of the hardest working private equity guy, maintain a girlfriend and friends, and share his same year-end valuation.
Be accomodating, but don't be a slut.
Last edited by Paradosso on 20 Dec 2008, 06:06, edited 1 time in total.
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Re: Unconventional answers about management consulting [#permalink] 20 Dec 2008, 03:03
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How are exit opportunities out of firms such as Monitor and Booz? How about Accenture and Deloitte? Are there even solid exit opportunities out of these firms, or do some of these firms recruit with the intention of having career-track consultants?
My general advice: don't use MC as a stepping stone. If you don't like it, you won't last 3 years or if you do, you won't be the top performing one that gets all of the exit options.
There are lots of people who are in MC and don't like it: if you are like them, you will be one of many. If you like it, you will make them pay for their uncertainty and reap all hte benefits.
That said, ceteris paribus there is a great difference in exit options between the big 3 and anyone else:
-Some companies recruit only from the big 3. They actually want someone from the big 3 and will court you. You will have the strong side of the trade.
- If you are not from the big 3 you have 50% of getting the question:"Why did you not join [big 3 name]?". Make it 100% if your interviewer is a former big 3. For how good your answer is, you will be at a disadvantage to the other big-3 candidate.
In general, the less prestigious your firm, the more you have to rely on your personal story and your network. Especially your network, since employers do not read essays of yours like B-schools do. So if you come from Booz/Monitor, you can expect to go working for one of your clients. You from McK, you will get head-hunter calls no matter what.
Accenture/Deloitte: it's not management consulting. They will tell you they have management consulting teams: the market does not believe them. And if you look to their work as strategy consultants, their background shows from page 1. Accenture is an IT consultant/outsourcer, Deloitte certifies your balance sheet and that's it.
Don't take a position in a company whose general culture/perception/main job is another one, that's a general rule. If you want MC and only land an Accenture or Deloitte job, go somewhere else, you most probably would not have been happy in Bain anyway.
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Re: Unconventional answers about management consulting [#permalink] 20 Dec 2008, 05:44
very useful posts, paradosso. +1 for each.
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Re: Unconventional answers about management consulting [#permalink] 20 Dec 2008, 14:21
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Truly informative thread +1!
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Re: Unconventional answers about management consulting [#permalink] 20 Dec 2008, 15:57
Thanks Paradosso!
Another staffing question for you. It seems that your previous work exp can play a role in determining assignments. Does the same apply to where you went to bschool? Will assignments ever be made because someone went to school X?
(sorry if this is silly, just didn't know and wanted to ask)
thanks
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Re: Unconventional answers about management consulting [#permalink] 20 Dec 2008, 16:17
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ac8706 (lend me some of all the green you've got there), it's actually a good question!
No. Which school you went to does not play any role whatsoever (it might have during recruiting/negotiating, but it stops there). Your concentration (took 3 advanced class in excel modeling, learnt Monte Carlo simulations, ...) might play a role in case there's an absolute tie between two or more engagements you might be staffed on. But this only applies to your first engagement out of school. All humans, staffing partners included, can only handle a limited number of variables, and almaMater is not one of those.
Afterwards, it's like Hollywood: you are pretty much defined by your last engagement (until you begin to show a trend, that is). You could be an Henry Ford Award recipient from Stanford, but if you blew it last time you are at a disadvantage to the guy who worked its way from the IT support office (and there are a few in my office). Basically, everyone has a silver resume so a) it's not distinctive b) everybody knows you can be a lemon no matter what, or, as one partner once put to me:"There are sh*tload of magna cum laude guys from [top Italian university that both he and I attended] who would easily get played by their grocery man".
Management consultants like grocery men. On the other hand, I did not like my 23-year-old, 3-intenships, summa-cum-laude-Msc-expecting, mid-distance-runner, 770-gmat-scorer intern who could not calculate a CAGR or bother to refine the details of his slides. Nor did my manager, who de-staffed him from the engagement after two days. He basically left all his chances of securing a full-time offer in a couple of days and he won't know until internship is over. If you can't spot the sucker, you are the sucker, as they say. But I digress.
Also, your previous experience hardly plays when there has been an MBA between it and consulting. As you know consultancies are very open to switchers and every newly-minted MBA is created equal, olympic athletes, software engineers and corporate lawyers alike. You only start with a record if you've been sponsored by the same company you've returned to.
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Re: Unconventional answers about management consulting [#permalink] 20 Dec 2008, 16:39
thanks so much paradosso!
That makes a lot of sense - it's good to know that once you have a position in a consulting firm, your performance there plays more of a role than the background.
thanks again!
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Re: Unconventional answers about management consulting [#permalink] 21 Dec 2008, 10:45
Thanks Paradosso this is a great thread. Kudos added.
I have a couple very basic (and probably pretty dumb ) questions for you. Can you give examples of typical assignments at an M/B/B firm? Are you doing things like helping firms understand why they're losing market share or seeing profits decline? Are you helping them decide whether to enter new markets or launch new product lines? I'm just trying to get an idea of what the typical engagements are at one of these firms. Also, what is the typical size of your team on one of these engagements. Thanks!
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Re: Unconventional answers about management consulting [#permalink] 21 Dec 2008, 11:27
More questions...
1. Do European offices hire almost exclusively from European b-schools?
2. If working in an office in a European country other than the UK, is it necessary to know the local language (French, Italian, etc.)?
3. Are European offices significantly "older" or "younger" than U.S. offices, i.e. do they prefer older candidates for each level (analyst, associate, engagement manager), sort of like European b-schools prefer more experienced folks?
This forum is probably exactly what I need from GMATClub now that I have an admit and am looking forward to the next step,, so thank you for sharing your expertise(ience).
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Re: Unconventional answers about management consulting [#permalink] 22 Dec 2008, 02:22
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Thanks for the kudos girls/guys. Again, very good questions I will try to address.
Can you give examples of typical assignments at an M/B/B firm? Are you doing things like helping firms understand why they're losing market share or seeing profits decline? Are you helping them decide whether to enter new markets or launch new product lines?
Convential wisdom goes that management consultants are the companies' physicians. While it is a great metaphor to explain your mum what you do for a living, it is slightly different than that. No one goes to Bain or McK without offering an idea of what they want from you. In you examples you picture a company that, like a patient, tells the symptoms to the doctor ("lose market share") and lets him perform his magic with no limits whatsoever. This would imply two assumptions that are not acceptable in business endeavor even if often true:
a) I am the CEO of the company and I don't know wtf is going on, so I'm asking you, who have never heard of the company in your life before today.
b) I am letting you decide to do whatever you want with the $3000/person/day I am giving you. All company data is yours to go through. So, while those scenarios you mentioned are good examples of what to expect in a case interview, the initial mission the client would give the team will always be more precise and delimited. Oftentimes the team will reverse-engineer the problem (medicine-like) and perform analyses and develop hypotheses outside the boudaries set by the top management, but the conclusions, if defendable and compelling, will nevertheless be framed in a way as to remain into the beaten path, with a possible proposal for an extension (btw, it is not true that consultancies do not sell. Consultancies do sell and the selling part is maybe the most important). Such an approach do not pose political problems (another oftern underlooked yet crucial dimension of this line of work) by making the top management believe they got it right fro the start and just did not have the brainpower to execute, yet deliver actual value to the company. So, examples of typical assignments: "I want to enter new market X. Help me do that" "I want to acquire company Y. What do you think? Due diligence it for me (from a business point of view that is)". "What dealers do I shut down and where do I put new ones? Go through this 10,000-row database for me" "I can adapt my plant to produce 5 different types of commodity Z. Which one should I produce and where do I sell it?" Two things all assignments have in common: 1) They all start by defining and understanding the relevant markets. 2) The management always has its own idea before the project start. Not to hurt its sensibility while giving real answers and making them buy the next project is an art (the only one that makes you a partner). Current Student Joined: 04 Jan 2005 Posts: 283 Location: Milan Schools: Wharton, LBS, UChicago, Kellogg MMM (Donald Jacobs Scholarship), Stanford, HBS Followers: 7 Kudos [?]: 140 [4] , given: 3 Re: Unconventional answers about management consulting [#permalink] 22 Dec 2008, 02:30 4 This post received KUDOS I sohuld add that there is a lot of operational excellence / performance improvement work in all management consultancies. This goes like: "Redesign my accounting system" "Help me improve my procurement" (one of the most frequent engagements) "I want to shave 10% off my fixed costs. Help me do that" In general, the more you have don business in the past with a client, the more the relationship evolves into a doctor-patient one. The last engagement I mentioned was only possible with a company we did business 5+ years straight before. Also, do not buy into the strategy vs. operational performance improvement dichotomy. You learn as much and add as much value working on these assigments above as the one of the previous post. It's all management consulting. The real difference is between:"Redesign my cost centers" and "Here's the cost centers, put them into SAP" (though a management consultancy can be asked to do both). The best criterion I have identified is: if you can do it on a piece of paper, it's management consulting. When you work as a consultant, always remember that the legends of 20+ years ago (Henderson, etc.) did not have computers. Don't fall into pretending that computational power and memory substitute consulting. Current Student Joined: 04 Jan 2005 Posts: 283 Location: Milan Schools: Wharton, LBS, UChicago, Kellogg MMM (Donald Jacobs Scholarship), Stanford, HBS Followers: 7 Kudos [?]: 140 [7] , given: 3 Re: Unconventional answers about management consulting [#permalink] 22 Dec 2008, 02:46 7 This post received KUDOS what is the typical size of your team on one of these engagements? I will add another dimension: average seniority of the team. That said, it varies wildly, from a team of onw manager and one analyst to 15+ people in the same room. However, it is quite simple to estimate what the team will be based on the client-consultancy signed contract. Just remember: what varies is the scope and the timing. The scope changes in order to accomodate the budget of the client. Budget drives staffing in turn. I have seen project changing from 6-member to 2-member teams after negotiating. That is because the basic unit of measure is the average daily billing rate of the team ($xxxx/person/day).
General guidelines:
1) The more the project is high-level strategy vs. operational improvement, the more senior the team;
2) The more the project is high-level strategy vs. operational improvement, the littler the team;
2) The more the project is high-level strategy vs. operational improvement, the shorter the engagement;
Consider that a management consultancy has no relevant costs/productive inputs but personnel. So utilization rate is the key. That said, it is clear that multi-month, large operational improvement teams are where the company makes its money (I won't tell you the margin %, but think along the lines of Google/Microsoft, except the product does not scale). However, to sell those you have to develop a bullet-proof strategic rationale first. You have to have the management's absolute faith. Strategy engagements are often sold in fact as loss leaders (ok, let's say "under the par of expected marginality" ) in order to make tons of gold afterwards.
Let's say that if you find yourself, as an analyst or associate, working in very vertical teams with no peers, it's a very good sign. If you repeatedly find yourself buried in 6-months project with 2-3 peers, not so much (but everyone will be staffed on both for the sake of a good evaluation of his potential).
As I've said before, most of the people are in this line of work for the money and the exit options, not for the love of it. Partners know and tend to staff them as cash cows on long projects. Meanwhile, the others work in vertical teams trying to generate/consolidate new clients. As in the first strategic phase (often called A&D, "analysis and design") you are working with the CEO and her reports, which dows not happen in subsequent operational projects, it is then the vertical team people who are more likely to develop the network to make partner. So it all figures for he who wants to see it.
Working in vertical teams is tough as you are the analyst who will serve multiple managers/partners (often with conflicting schedules/opinions), but it's where you want to be. You are working with less stupid people, so:
1) you will learn more
2) you will work fewer hours (he who makes you do an all-nighter is never a director and almost always a moron).
Current Student
Joined: 04 Jan 2005
Posts: 283
Location: Milan
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Re: Unconventional answers about management consulting [#permalink] 22 Dec 2008, 03:00
11
This post received
KUDOS
1. Do European offices hire almost exclusively from European b-schools?
2. If working in an office in a European country other than the UK, is it necessary to know the local language (French, Italian, etc.)?
3. Are European offices significantly "older" or "younger" than U.S. offices, i.e. do they prefer older candidates for each level (analyst, associate, engagement manager), sort of like European b-. It'sprefer more experienced folks?
1. Not at all! While most people come from European schools, INSEAD in the first place, for abvious reasons (they are Europeans in the first place), European office are dying to recruit from US schools. Remember that schools are a signal to the employer that their graduate is a low-risk hire. Everyone knows that the best schools and the fiercest competition to get in are to be found in the US, so they want to get those people. They really want to --you can ask good money.
Yet most of the US schools graduates are Europeans because
2. Yes, you have to be fluent in the local language (i.e., you have to be able to speak with the client). Not native (being a foreigner could indeed be an advantage), but fluent of that fluency that can be learnt. Think 105 in the TOEFL. Ok, you have never took teh TOEFL, never mind . The more an office works abroad the more they can think to staff you around in English-speaking engagements, which are also very high-profile, so you better be good (my money says you fit that bill). So I say that for an American who is willing to learn languages, is very possible to work in Europe at Bain, quite possible to work at McK, difficult to work at BCG. Things change if you are willing to go to Kiev or Moscow, no one expects you to speak Russian there and you will make a lot of money.
3. There is no real age preference at recruiting. At the same level, you will find Europeans are older (especially in Italy/Germany) because:
a. there are more years of study to gain an undergraduate degree
b. there is always some kind of thesis/dissertation that takes up other time
c. few people begin straight into consulting
I, for one, am 27 and have been working for two years only. That said, you will find 32-year-old partners here too: he who sells wins, that's worldwide.
Hope that helps guys!
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Re: Unconventional answers about management consulting [#permalink] 22 Dec 2008, 05:55
Great thread! YEAH!!!!!!!!
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Re: Unconventional answers about management consulting [#permalink] 22 Dec 2008, 11:22
Thanks!!
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Re: Unconventional answers about management consulting [#permalink] 23 Dec 2008, 16:44
Thanks paradosso. A few more questions:
1) Once hired, how easy is it to transfer from one office to another? As in, if you're hired into the London office, how easy it is to move to say NYC?
2) What's the typical promotion path once you're hired? Are the first opportunities for promotion a few years after being hired? And then what?
thanks
Re: Unconventional answers about management consulting [#permalink] 23 Dec 2008, 16:44
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In a hot water heating system, there is a cylindrical pipe of length 28 m and diameter 5 cm.
Question:
In a hot water heating system, there is a cylindrical pipe of length 28 m and diameter 5 cm. Find the total radiating surface in the system. (Take π = 3.14)
Solution:
Given that
Height of cylinder = length of cylindrical pipe
= 28 m
Radius(r) of circular end of pipe = 5/2 = 2.5 cm = 0.025 m
Curved surface area of cylindrical pipe $=2 \pi r h=2 * 3.14 * 0.035 * 30=4.4 \mathrm{~m}^{2}$
Therefore the area of radiating surface of the system is $4.4 \mathrm{~m}^{2}$ or $44000 \mathrm{~cm}^{2}$.
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# Creating a title in Latex while using two columns
• LaTeX
Shukie
I want to create a title that spans the entire width of the page and then below the title, I want the actual text to be in two columns. I am currently using \documentclass[twocolumn]{article}, which puts the entire document into two columns, including the title, which is now in the left column. I want it like this:
http://arxiv.org/PS_cache/arxiv/pdf/1003/1003.1113v2.pdf [Broken]
Anyone know how to do this? I don't want to use the multicol package, because I'll have to redo the entire layout.
Last edited by a moderator:
## Answers and Replies
Staff Emeritus
The title shouldn't be in the left column. Are you using the \maketitle command properly?
By the way, in order to get a paper that looks like the one you quote, you should look at revtex (http://authors.aps.org/revtex4/).
Dunhausen
Q: When I look for revtex in the ubuntu repositories, it is described as "obsolete":
revtex - LaTeX documentstyle from the American Physical Society (obsolete)
Any idea why that might be or what (if anything) is supposed to replace it?
Gold Member
Well, the article in question is in revtex4, you can download its source if you need an example. (from the arxiv, this articles "source" should be renamed to a .gz, which is a zip and then extracted. its some eps figures and the tex.)
They're just using
\documentclass[twocolumn,preprintnumbers,amsmath,amssymb]{revtex4}
\title{
On the use of X-ray telescopes for identifying the origin of electrons
and positrons observed by Fermi and PAMELA}
basically.
Shukie
The title shouldn't be in the left column. Are you using the \maketitle command properly?
By the way, in order to get a paper that looks like the one you quote, you should look at revtex (http://authors.aps.org/revtex4/).
I wasn't using \maketitle at all, but it works now that I added it. Cheers.
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# How to add command to right-click menu of certain extension programmatically?
I have created 2 exe files: open.exe and edit.exe. and a new extension: say .newext.
Now I want to
1. open by double click on .newext file with open exe.
2. get a menu with right click on .newext file where in bold it is written "Open" and under that it is written "Edit". And by clicking "Edit" the edit.exe opens the .newext file.
3. do this programmatically so that it could work on as much platforms as it is possible (at least on Xp, Vista, and Win7).
How I can achieve this?
-
Take a look Here
-
You must edit the classes tree in the registry (using the registry functions from AdvApi32.dll). The following is not tested and off my head:
• The base key is HKEY_LOCAL_MACHINE\Software\Classes for system-wide settings and HKEY_CURRENT_USER\Software\Classes for user-specific settings
• In this base key, create a subkey with name .newext and default value X, where X is the class name (an arbitrary string that uniquely identifies the file type)
• In the base key, create a subkey with name X and default value Y, where Y is the user-visible description of the file type
• In the key X, create a subkey named shell with default value open
• In the shell key, create a subkey named open with default value &Open
• In the open key, create a subkey named command with default value "C:\path\to\open.exe" "%1"
• In the shell key, create a subkey named edit with default value &Edit
• In the edit key, create a subkey named command with default value "C:\path\to\edit.exe" "%1"
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What if it should work on linux as well? – Narek Jul 15 '10 at 7:28
On Linux the system is completely different and depends on the desktop environment (Gnome, KDE…). It might be better to start a new question for every desktop environment you plan to support (preferably on superuser.com since it's not really related to programming). – Philipp Jul 15 '10 at 7:50
Is this right for Vista??? – Narek Jul 25 '10 at 16:35
Try it, I'm not sure and I don't have access to Vista. – Philipp Jul 25 '10 at 17:52
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# Performing a statistical test after visualizing data - data dredging?
I'll propose this question by means of an example.
Suppose I have a data set, such as the boston housing price data set, in which I have continuous and categorical variables. Here, we have a "quality" variable, from 1 to 10, and the sale price. I can separate the data into "low", "medium" and "high" quality houses by (arbitrarily) creating cutoffs for the quality. Then, using these groupings, I can plot histograms of the sale price against each other. Like so:
Here, "low" is $\leq 3$, and "high" is $>7$ on the "quality" score. We now have a distribution of the sale prices for each of the three groups. It is clear that there is a difference in the center of location for the medium and high quality houses. Now, having done all this, I think "Hm. There appears to be a difference in center of location! Why don't I do a t-test on the means?". Then, I get a p-value that appears to correctly reject the null hypothesis that there is no difference in means.
Now, suppose that I had nothing in mind for testing this hypothesis until I plotted the data.
Is this data dredging?
Is it still data dredging if I thought: "Hm, I bet the higher quality houses cost more, since I am a human that has lived in a house before. I'm going to plot the data. Ah ha! Looks different! Time to t-test!"
Naturally, it is not data-dredging if the data set were collected with the intention of testing this hypothesis from the get-go. But often one has to work with data sets given to us, and are told to "look for patterns". How does someone avoid data dredging with this vague task in mind? Create hold out sets for testing data? Does visualization "count" as snooping for an opportunity to test a hypothesis suggested by the data?
Briefly disagreeing with/giving a counterpoint to @ingolifs's answer: yes, visualizing your data is essential. But visualizing before deciding on the analysis leads you into Gelman and Loken's garden of forking paths. This is not the same as data-dredging or p-hacking, partly through intent (the GoFP is typically well-meaning) and partly because you may not run more than one analysis. But it is a form of snooping: because your analysis is data-dependent, it can lead you to false or overconfident conclusions.
You should in some way determine what your intended analysis is (e.g. "high quality houses should be higher in price") and write it down (or even officially preregister it) before looking at your data (it's OK to look at your predictor variables in advance, just not the response variable(s), but if you really have no a priori ideas then you don't even know which variables might be predictors and which might be responses); if your data suggest some different or additional analyses, then your write-up can state both what you meant to do initially and what (and why) you ended up doing it.
If you are really doing pure exploration (i.e., you have no a priori hypotheses, you just want to see what's in the data):
• your thoughts about holding out a sample for confirmation are good.
• In my world (I don't work with huge data sets) the loss of resolution due to having a lower sample size would be agonizing
• you need to be a bit careful in selecting your holdout sample if your data are structured in any way (geographically, time series, etc. etc.). Subsampling as though the data are iid leads to overconfidence (see Wenger and Olden Methods in Ecology and Evolution 2012), so you might want to pick out geographic units to hold out (see DJ Harris Methods in Ecology and Evolution 2015 for an example)
• you can admit that you're being purely exploratory. Ideally you would eschew p-values entirely in this case, but at least telling your audience that you are wandering in the GoFP lets them know that they can take the p-values with enormous grains of salt.
My favorite reference for "safe statistical practices" is Harrell's Regression Modeling Strategies (Springer); he lays out best practices for inference vs. prediction vs. exploration, in a rigorous but practical way.
• Very well put! I expect to refer people to this answer in the future. – Great38 Jul 1 '18 at 4:40
• Exactly the kind of response I was looking for, thank you. I have credited this response as an answer. Do you know of any resources that teach safe statistical practices? Perhaps a little wider in scope than the (excellent) articles you have posted – Marcel Jul 1 '18 at 20:09
• Great answer (+1), but I disagree that this is any different to data-dredging; intent is irrelevant - the effect is the same. – Ben Jul 2 '18 at 7:31
• I actually think it's worth maintaining the distinction between different forms of snooping. Dredging is arguably more severe because it involves (1) multiple explicit tests rather than multiple implicit tests and (2) conditional/continued testing until p<0.05 (or whatever) is achieved. The qualitative effect is certainly the same. – Ben Bolker Jul 2 '18 at 20:15
Visualising the data is an indispensable part of analysis and one of the first things you should do with an unfamiliar data set. A quick eyeball of the data can inform the steps to take next. Indeed, it should be fairly obvious by looking at the graph that the means are different, and I'm not sure why a T-test was necessary to confirm this - the means are sufficiently separated that the graph itself is all the evidence I would require.
Data dredging, as far as I can tell from a quick wikipedia-ing, is a deliberate process of mucking around with the data to force certain levels of fit. Examples would be: Comparing a data set to some random numbers, but regenerating the random numbers until you get a set of favourable ones or trying out a large number of different forms of regression and choosing the one with the best $R^2$ regardless of whether the assumptions are appropriate. Data dredging doesn't appear to be something you can easily do by accident.
I think there's a deeper question in here though. How do you maintain a zen-like neutrality and avoid bias when dealing with data in a scientific way? The answer is, you don't. Or rather, you don't have to. Forming hunches and hypotheses and building a mental narrative of what the data means, is all perfectly natural and acceptable, provided you are aware that you are doing so, and are mentally prepared to reconsider all these hypotheses when confronted with conflicting data.
• Visualizing data before running tests may be innocuous in this specific case. However, one would next visualize another dimension... and another one... and look at scatterplots... and soon enough, one will find something that looks "obvious enough" so that a formal test and a narrative come naturally. Oh yes, data dredging is definitely something that you can easily do by accident. See Gelman's "Garden of forking paths". – Stephan Kolassa Jul 1 '18 at 12:02
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# Solid sphere rolling down a house roof... angular speed
Tags:
1. Jul 3, 2017
### shmoop
1. The problem statement, all variables and given/known data
A solid sphere of radius 16cm and mass 10kg starts from rest and rolls without slipping a distance of 9m down a house roof that is inclined at 43 degrees.
What is the angular speed about its center as it leaves the house roof?
The height of the outside wall of the house is 6m. What is the horizontal displacement of the sphere between the time in which it leaves the roof and the time at which it hits the ground?
2. Relevant equations
Torque=Inertia*Angular Acceleration (?)
Inertia of a solid sphere =0.4*m*r^2
I'm not really sure.. but:
3. The attempt at a solution
Inertia of the sphere.. incase I need it?
I=0.4*10kg*0.16m^2= 0.1024 kg*m^2
Viy= 0m/s
Vfy= ?
Ay= -9.8m/s^2
delta y= 9sin43= -6.1379m (vertical displacement)
Then I tried to calculate for the final vertical velocity (before it rolls off the roof)
Vfy= sqrt(2*-9.8m/s^2*-6.1379m)
Vfy= 10.968 m/s
Then I tried to calculate for the final velocity before the ball rolls off the roof:
Vf= 10.968/sin43 = 16.0821
Then I tried to convert it to angular velocity:
V=r*ω
ω=V/r
ω=16.0821m/s / 0.16m = 100.5 rad/s
I know this is incorrect, but I'm unsure as to where I went wrong. I'm trying to solve the problem without using work/energy, as my teacher hasn't yet covered those topics. If someone could point me in the right direction it would be GREATLY appreciated!!! Thanks :)
2. Jul 3, 2017
### BvU
Hi,
Did you make a sketch of the various forces that accelerate/slow down the ball ?
No. See your drawing. And use subscripts.
Where do you use that ?
Where do you use $\tau = I\alpha$ ?
Who is ady ? Use only variables you have explained. Don't use A and a to denote the same variable.
3. Jul 10, 2017
### rude man
Basic hint: sum of kinetic energies due to distance traveled by the c.g. plus rotational kinetic energy = total loss of potential energy.
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How much greater is the star density in our galactic bar?
How much denser is it in the galactic bar than the "normal" density at the same radius?
Is it just a few percent? or is it, say, "three times" as dense?
Or are other factors at play: star brightness, gasses?
Or do we really not know?
• I think observational constraints on this are sparse, if any, but from numerical simulations I think 10-20% overdensity would be a realistic guess. Can't seem to find any references though, so I wouldn't feel comfortable posting an answer.
– pela
Dec 20, 2018 at 13:46
• It's definitely quiet mysterious, right @pela ? Furthermore: some references will say that the only overdensity is an overdensity of brighter stars (ie, young ones); there's actually no overdensity at all. It does seem to be highly unknown. There is no real literature review of the issue it seems. Dec 20, 2018 at 13:49
• In the spiral arms, that's at least the case. Here the overdensity is roughly 10%, but you have a larger amount of newly formed stars (because of pressure waves initiating star formation), and since the brightest stars die fast, they are predominantly found in the spiral arms, making them more visible. Something similar probably is the cases in the bar, but I'm not sure if it's to the same extent, because of the redder color of the bar.
– pela
Dec 20, 2018 at 14:21
• The stellar population is older, so the massive, blue stars have died. The metallicity is also generally higher in the center, leading to redder colors.
– pela
Dec 20, 2018 at 15:19
• @pela -- also, the density contrast for spiral arms can much more than 10% -- it can be factors of 2 or 3. E.g., from this classic study by Rix & Rieke (1993) of M51: "In M51 we find the surface mass density contrast (arm/interarm) to range from 1.8 to 3, comparable to results from N-body simulations of the galaxy's tidal encounter with NGC 5195." Dec 21, 2018 at 10:09
In other barred galaxies which are vaguely similar to the Milky Way, the contrast in (projected) stellar surface density between the bar and the inter-bar region at the same radius (e.g., along the bar's minor axis, perpendicular to the bar) is typically a factor of at least two; in particularly strong bars it can be as high as six (see, e.g., Figure 5 in Ohta et al. 1990). Similar contrasts are seen in N-body models of disk galaxies that form bars.
It's much harder to figure this out for the Milky Way, because we're not looking down it from above. The best attempt to derive a model of the bar's 3D stellar density from star counts and distance estimates that I know of is Wegg et al. (2015). From the face-on projected view of their model (their Figure 14), I would guesstimate the maximum contrast as a factor of 4 or so.
Figure 14 of Wegg et al.: projected face-on view of stellar density for the Milky Way (full model in right-hand panel).
The 3D density (which is maybe what you're really asking about) in the inner part of the bar is not quite as great as this suggests, because the inner part of the bar is vertically thick, forming a "boxy/peanut-shaped" bulge (this would correspond to the red region in the figure above). So the contrast would be a little less compared to the (less thickened) inter-bar region. But the outer part of the bar is roughly as thin as the rest of the disk, so the projected surface density contrast would mean a similar contrast in 3D stellar density.
• Incredible. BTW Surely GAIA data will blow away existing data, on precisely this issue, no?? Dec 21, 2018 at 11:55
• " .. because the inner part of the bar is vertically thick, forming a "boxy/peanut-shaped" bulge .." AHHHHHH that's a great point! Of course, it may just be simply thicker, NOT more dense!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! I did not think of that! Dec 21, 2018 at 11:56
• GAIA data will undoubtedly help a lot, although much of this analysis is based on infrared data that allows stars to be seen at large distances, including the far side of the bar; since GAIA is optical, I don't think it can get that kind of data. Dec 21, 2018 at 22:16
In the Milky Way, the density in the bar seems to roughly 5 times larger than "next to the bar".
The most recent model of the Galactic bar I could find is Portail et al. (2017), whose model is constructed to match a range of observational surveys (VVV, UKIDSS, 2MASS, BRAVA, OGLE, and ARGOS). The figure below from this paper shows the density profile of the bar/bulge (left panel), the disk (middle panel), and the combined mass (right panel).
The red curve shows the density along the bar (i.e. the major axis), and the blue curve shows it perpendicular hereto (the minor axis). The central bump in the blue curve thus is inside the bar, but after roughly 2 kpc (i.e. 6-7000 lightyears), it flattens out. Here the mass (surface) density is roughly $$10^9\,M_\odot\,\mathrm{kpc}^{-2}$$. Off-bar, however, the blue line shows that the density is only $$2\times10^8\,M_\odot\,\mathrm{kpc}^{-2}$$, i.e. 5 times lower.
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# Limit proof
1. ### Bleys
74
I came across a problem in Calculus by Spivak, and I'm having trouble formalizing the proof.
Let $$A_{n}$$ bet a set of finite numbers in [0,1], and if $$m \neq n$$ then $$A_{n}$$ and $$A_{m}$$ are disjoint. Let f(x) be defined as
f(x)=1/n if x is in $$A_{n}$$ and f(x)=0 if x is not in any $$A_{n}$$. The question asks to prove the limit as x goes to a of f is 0 for any a in [0,1].
Now I thought: given an n, there are only finitely many elements of $$A_{n}$$ in a neighborhood of a. Choose the smallest such n, say $$n_{0}$$. Then $$f(x)\leq1/n_{0}$$. Restrict the neighborhood further so that none of the elements of $$A_{n_{0}}$$ are in the interval. Then choose the next n such that it's minimal. Obviously $$f(x)\leq1/n\leq1/n_{0}$$. Successively doing this, for arbitrarily small x, f(x) will tend to 0.
I don't know how to prove this using the limit definition; can someone help me out with what $$\delta$$ to choose?
2. ### rochfor1
256
The smallest such n with what property? You're not very clear about that. Here's a proof: I'm going to assume f(a)=0; the other case is only a slight modification and should be instructive for you to think about. Fix $$\varepsilon>0$$, then there exists N > 0 with $$1/N < \varepsilon$$. Let $$B_N = \cup_{ n = 1 }^N A_n$$, so B_N is a finite set, and $$a \not \in B_N$$ (why?). Now, let $$\delta > 0$$ be such that $$( a - \delta, a + \delta ) \cap B_N = \emptyset$$ (why does such a $$\delta$$ exist?). Then if $$| a - x | < \delta$$, either $$x \in A_m$$ for m > N, or f(x) = 0. In either case, $$|f(a) - f(x)|<1/N<\varepsilon$$, as desired.
3. ### wisvuze
367
you're on the right track, you should break this down into 2 parts:
1) if a is in a set An
2) if a is not in a set An
given an epsilon larger than 0, you must consider all f(x) = 1/n that fails ( larger than epsilon). Suppose you consider all 1/n/f(x) >= epsilon, then you can consider a union of sets (S) An such that f(x) >= epsilon for any element in a set An. Now you've reduced the problem to taking delta to be the min distance between the members of that set (S) and a (the distance between the greatest lower bound of (S) and a). If a is a member of the set itself, then you can use the exact same argument, since we are only concerned with behaviour as x APPROACHES a. Also, you know that you can always use this general argument because the interval between any numbers is always infinitely dense.
4. ### Bleys
74
Sorry, what I meant to say was the smallest n such that the set $$A_{n}$$ has an element in the neighborhood of a.
f(a)=0 iff a=0, by definition of f, and this is iff a is not in any An.
Because B_N is finite.
Did you assume f(a)=0 because you had $$( a - \delta, a + \delta )$$? Would $$0 < | a - x | < \delta$$ solve that? After all, since we are looking at the limit 0 then the expression $$|f(a) - f(x)|<\varepsilon$$ becomes $$|f(x) - 0|=|f(x)|<\varepsilon$$, since the value of f at a doesn't matter.
So since S will be finite (since there will be an n such that $$1/n<\varepsilon$$) then that delta will work. Can I just not consider whether a is in the set or not. After all like you said, we're interested in the limit, not continuity. So $$0 < | a - x | < \delta$$ would solve that.
Ok I think I get it. I was having trouble formulating all this with the $$\delta - \varepsilon$$ definition. Thanks for all your help!
5. ### wisvuze
367
It's a good idea to say how the limit works in both cases, you need to show that you've considered that case (it is a significant case). But in the end, it uses the same argument.
The delta you are taking is the min ( |a-x| : x $$\in$$ $$\cup$$ n=1 to i An )
Here is an intuitive version of the proof:
|A1||A15||A20||A4|<----a------>|A7||A9||A10000||A124921894381241|
Any x's will be dispersed into different sets An, so take delta to be the min distance between a set and the point a. This interval between a and any x in sets An will always exist, since an interval of real numbers is always infinitely dense
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## Checking the Nvidia driver installation:
$lspci -k | grep -A 2 -E "(VGA|3D)" 00:02.0 VGA compatible controller: Intel Corporation 4th Gen Core Processor Integrated Graphics Controller (rev 06) Subsystem: CLEVO/KAPOK Computer Device 5000 Kernel driver in use: i915 -- 01:00.0 3D controller: NVIDIA Corporation GK208M [GeForce GT 740M] (rev ff) Kernel modules: nouveau, nvidia 03:00.0 Network controller: Intel Corporation Wireless 7260 (rev 73) ### Check if the gpu can be harnessed For example with using glxgears. Without gpu, glxgears yields:$ glxgears
Running synchronized to the vertical refresh. The framerate should be
approximately the same as the monitor refresh rate.
453 frames in 5.0 seconds = 90.581 FPS
302 frames in 5.0 seconds = 60.288 FPS
XIO: fatal IO error 11 (Resource temporarily unavailable) on X server ":0"
after 3146 requests (3146 known processed) with 0 events remaining.
$optirun glxgears 9891 frames in 5.0 seconds = 1977.995 FPS 10186 frames in 5.0 seconds = 2037.131 FPS 9953 frames in 5.0 seconds = 1990.527 FPS 9908 frames in 5.0 seconds = 1981.540 FPS 10129 frames in 5.0 seconds = 2025.626 FPS glxgears is accelerated by a factor 20 at least. ## Installing CUDA 7.5 and cuDNN CUDA 7.5 was installed from manjaro repository using the Octopi GUI. cuDNN was installed using Octopi . This library has to be first downloaded from the nvidia developper website. In manjaro linux, cuda is installed in /opt/cuda/ . To check cuda installation, samples files were build under user directory as explained from nvidia documentation. The binary file deviceQuery can be launch using optirun:$ optirun ./deviceQuery
./deviceQuery Starting...
CUDA Device Query (Runtime API) version (CUDART static linking)
Detected 1 CUDA Capable device(s)
Device 0: "GeForce GT 740M"
CUDA Driver Version / Runtime Version 7.5 / 7.5
CUDA Capability Major/Minor version number: 3.5
Total amount of global memory: 2048 MBytes (2147352576 bytes)
( 2) Multiprocessors, (192) CUDA Cores/MP: 384 CUDA Cores
GPU Max Clock rate: 1032 MHz (1.03 GHz)
Memory Clock rate: 900 Mhz
Memory Bus Width: 64-bit
L2 Cache Size: 524288 bytes
Maximum Texture Dimension Size (x,y,z) 1D=(65536), 2D=(65536, 65536), 3D=(4096, 4096, 4096)
Maximum Layered 1D Texture Size, (num) layers 1D=(16384), 2048 layers
Maximum Layered 2D Texture Size, (num) layers 2D=(16384, 16384), 2048 layers
Total amount of constant memory: 65536 bytes
Total amount of shared memory per block: 49152 bytes
Total number of registers available per block: 65536
Warp size: 32
Maximum number of threads per multiprocessor: 2048
Maximum number of threads per block: 1024
Max dimension size of a thread block (x,y,z): (1024, 1024, 64)
Max dimension size of a grid size (x,y,z): (2147483647, 65535, 65535)
Maximum memory pitch: 2147483647 bytes
Texture alignment: 512 bytes
Concurrent copy and kernel execution: Yes with 1 copy engine(s)
Run time limit on kernels: Yes
Integrated GPU sharing Host Memory: No
Support host page-locked memory mapping: Yes
Alignment requirement for Surfaces: Yes
Device has ECC support: Disabled
Device supports Unified Addressing (UVA): Yes
Device PCI Domain ID / Bus ID / location ID: 0 / 1 / 0
Compute Mode:
< Default (multiple host threads can use ::cudaSetDevice() with device simultaneously) >
deviceQuery, CUDA Driver = CUDART, CUDA Driver Version = 7.5, CUDA Runtime Version = 7.5, NumDevs = 1, Device0 = GeForce GT 740M
Result = PASS
## Running tensorflow 0.7 from python
Tensorflow was installed (version with gpu acceleration) according to the documentation in a virtual environnement. Then the latest version can be installed using:
According to the documentation, the tensorflow installation can be checked as follow:
$python ... >>> import tensorflow as tf >>> hello = tf.constant('Hello, TensorFlow!') >>> sess = tf.Session() >>> print(sess.run(hello)) Hello, TensorFlow! >>> a = tf.constant(10) >>> b = tf.constant(32) >>> print(sess.run(a + b)) 42 >>> However, to run properly the python interpreter must be run with optirun:$ optirun python
Python 2.7.11 (default, Mar 3 2016, 11:00:04)
[GCC 5.3.0] on linux2
>>> import tensorflow as tf
I tensorflow/stream_executor/dso_loader.cc:105] successfully opened CUDA library libcublas.so locally
I tensorflow/stream_executor/dso_loader.cc:105] successfully opened CUDA library libcudnn.so locally
I tensorflow/stream_executor/dso_loader.cc:105] successfully opened CUDA library libcufft.so locally
I tensorflow/stream_executor/dso_loader.cc:105] successfully opened CUDA library libcuda.so.1 locally
I tensorflow/stream_executor/dso_loader.cc:105] successfully opened CUDA library libcurand.so locally
>>> hello = tf.constant('Hello, TensorFlow!')
>>> sess = tf.Session()
I tensorflow/stream_executor/cuda/cuda_gpu_executor.cc:900] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero
I tensorflow/core/common_runtime/gpu/gpu_init.cc:102] Found device 0 with properties:
name: GeForce GT 740M
major: 3 minor: 5 memoryClockRate (GHz) 1.0325
pciBusID 0000:01:00.0
Total memory: 2.00GiB
Free memory: 1.97GiB
I tensorflow/core/common_runtime/gpu/gpu_init.cc:126] DMA: 0
I tensorflow/core/common_runtime/gpu/gpu_init.cc:136] 0: Y
I tensorflow/core/common_runtime/gpu/gpu_device.cc:717] Creating TensorFlow device (/gpu:0) -> (device: 0, name: GeForce GT 740M, pci bus id: 0000:01:00.0)
I tensorflow/core/common_runtime/gpu/gpu_bfc_allocator.cc:51] Creating bin of max chunk size 1.0KiB
I tensorflow/core/common_runtime/gpu/gpu_bfc_allocator.cc:51] Creating bin of max chunk size 2.0KiB
I tensorflow/core/common_runtime/gpu/gpu_bfc_allocator.cc:51] Creating bin of max chunk size 4.0KiB
I tensorflow/core/common_runtime/gpu/gpu_bfc_allocator.cc:51] Creating bin of max chunk size 8.0KiB
I tensorflow/core/common_runtime/gpu/gpu_bfc_allocator.cc:51] Creating bin of max chunk size 16.0KiB
I tensorflow/core/common_runtime/gpu/gpu_bfc_allocator.cc:51] Creating bin of max chunk size 32.0KiB
I tensorflow/core/common_runtime/gpu/gpu_bfc_allocator.cc:51] Creating bin of max chunk size 64.0KiB
I tensorflow/core/common_runtime/gpu/gpu_bfc_allocator.cc:51] Creating bin of max chunk size 128.0KiB
I tensorflow/core/common_runtime/gpu/gpu_bfc_allocator.cc:51] Creating bin of max chunk size 256.0KiB
I tensorflow/core/common_runtime/gpu/gpu_bfc_allocator.cc:51] Creating bin of max chunk size 512.0KiB
I tensorflow/core/common_runtime/gpu/gpu_bfc_allocator.cc:51] Creating bin of max chunk size 1.00MiB
I tensorflow/core/common_runtime/gpu/gpu_bfc_allocator.cc:51] Creating bin of max chunk size 2.00MiB
I tensorflow/core/common_runtime/gpu/gpu_bfc_allocator.cc:51] Creating bin of max chunk size 4.00MiB
I tensorflow/core/common_runtime/gpu/gpu_bfc_allocator.cc:51] Creating bin of max chunk size 8.00MiB
I tensorflow/core/common_runtime/gpu/gpu_bfc_allocator.cc:51] Creating bin of max chunk size 16.00MiB
I tensorflow/core/common_runtime/gpu/gpu_bfc_allocator.cc:51] Creating bin of max chunk size 32.00MiB
I tensorflow/core/common_runtime/gpu/gpu_bfc_allocator.cc:51] Creating bin of max chunk size 64.00MiB
I tensorflow/core/common_runtime/gpu/gpu_bfc_allocator.cc:51] Creating bin of max chunk size 128.00MiB
I tensorflow/core/common_runtime/gpu/gpu_bfc_allocator.cc:51] Creating bin of max chunk size 256.00MiB
I tensorflow/core/common_runtime/gpu/gpu_bfc_allocator.cc:51] Creating bin of max chunk size 512.00MiB
I tensorflow/core/common_runtime/gpu/gpu_bfc_allocator.cc:51] Creating bin of max chunk size 1.00GiB
I tensorflow/core/common_runtime/gpu/gpu_bfc_allocator.cc:51] Creating bin of max chunk size 2.00GiB
>>> print sess.run(hello)
Hello, TensorFlow!
>>> a = tf.constant(10)
>>> b = tf.constant(32)
>>> print sess.run(a+b)
42
>>>
## Conclusion
At first sight, the issue of the use of cuda 7.5 with TensorFlow is resolved with TensorFlow 0.7.
## Wednesday, February 10, 2016
### Building opencv 3.1 under Manjaro linux
As previously, opencv was build using cmake-gui to set-up the build options. CUDA 7.5 was installed from manjaro files repository with octopi files manager.
Everything went fine during compilation with: make -j4 followed by sudo make install.
However when importing opencv from a python console, things went wrong:
\$ python2
Python 2.7.11 (default, Dec 6 2015, 15:43:46)
[GCC 5.2.0] on linux2
>>> import cv2
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
ImportError: No module named cv2
I didn't met this problem under Ubuntu but the problem is known. Specifying the path to cv2 from python allows the lib to be loaded:
>>> import sys
>>>sys.path.append('/usr/local/lib/python2.7/site-packages')
>>> import cv2
>>> cv2.__version__
'3.1.0'
## Thursday, November 5, 2015
### A measure of the similarity of two weighted multigraphs?
To compare shapes, typically obtained after image segmentation, it has been shown that their skeleton could be used. A search with the keywords : skeleton+pruning+image+recognition yields a lot of results.
Assuming that the size of the branches of the skeleton, linking the end-points and the branched points together, can be represented by the weights of the edges in a graph, a weighted graph can represents naturally the skeleton of a shape.
From the skeleton of the B character (left) to its associated (networkx) graph (right).
Previously, pruning of skeletons was performed by removing pixels, one after an other, from the end-points by morphological hit-or-miss. A response curve of a skeleton to pruning, can be defined by counting the end-points of the skeleton as pruning is iterated. It was observed that the responses from similar shapes were similar. So, such response curves may be used to compute some similarity measures, or distances, between shapes.
The time necessary to prune a skeleton depends on its number of pixels. So it may be worth prior pruning to convert a skeleton into a graph. Thus pruning a graph could be independent from the weight of its edges.
The response of a a weighted multi-graph to iterative pruning was performed with graph-tool (and additionnal python librairies : mahotas, numpy, scipy, matplotlib). This response yields a curve: a "Response to Pruning Curve" or RPC. Then a distance was defined between two RPCs, to compute a similarity index between two graphs.
The graph tool version used is:
2.11 (commit b6b2152c, Mon Oct 26 10:31:30 2015 +0100)
This post summarises the ideas developed in a jupyter notebook.
### Algorithm for pruning a graph from its leaves :
1. Make a weighted un-directional multi-graph
2. (Visualize it)
3. Start pruning:
1. Count the vertices on degree 1
2. Read the weight of the edges bound to vertices of degree1 (V1)
3. Get the edge(s) of minimal weight
4. Remove this/these edge(s)
5. Decrease the weight of the other edges bound to vertices v1 by this minimal weight
4. Do it until no more vertices of degree 1 remains
5. Cumulate the weight of removed edges
6. The response to pruning of a graph, associates the number of degree1 vertices to the cumulative weight of the removed edges.
#### Make a toy-graph to play with:
By default in graph-tool, the graphs are multi-graphs and that's what we need. The edges of the graph must be weighted, this property has to be created. The weight of an edge corresponds to the size of a branch in a skeleton (the number of pixels). The following python code, shows the creation of a graph with an edge property called 'weight':
The graph can be displayed such that the thickness of its edges maps to the weight of edges:
#### Start to prune the graph:
Two different versions of the pruning function were written. The second called prune_once_faster() depends on the GraphView() method of the graph-tool library to filter vertices of degree 1, hopping to make a faster function:
The pruning function is destructive, applying it iteratively on the same graph yields, if you write in a jupyter cell:
G0 = make_toy_graph()
g0 = G0.copy()
prune_graph_once(g0)
g1 = g0.copy()
prune_graph_once(g0)
g2 = g0.copy()
prune_graph_once(g0)
g3 = g0.copy()
print G0, number_of_degree1_vertices(G0)
print g1, number_of_degree1_vertices(g1)
print g2, number_of_degree1_vertices(g2)
print g3, number_of_degree1_vertices(g3)
You will have as output:
<Graph object, undirected, with 4 vertices and 4 edges at 0x9c65c1ac> 2
<Graph object, undirected, with 4 vertices and 3 edges at 0x9c65cc2c> 1
<Graph object, undirected, with 4 vertices and 2 edges at 0x9c654dec> 1
<Graph object, undirected, with 4 vertices and 1 edge at 0x9c65424c> 0
Indicating that the number of edges decreases as the number of vertices of degree 1, each time the graph is pruned.
#### Pruning iteratively a graph:
Let's count the number of vertices of degree 1 as the graph is pruned. The toy graph used here to check its response, has two vertices of degree 3 and two vertices of degree 1 (vertices 2 an 3). The initial values of the weight of the edges bound to vertices 2 and 3, are :
15, 20
The smallest weight is 15 So after one pruning, the weights becomes:
15-15 = 0, 20-15 = 5
The edge 1-2 of weight 0 is removed (vertex 2 is now of degree 0).
The edge 1-3 has the smallest weight (5).
So after a second round of pruning, the edge 1-3 is removed.
The vertex 1 was of degree 2, now it is of 1. The weight of the edge 0-1 is 8.
A third pruning removes the last edge 0-1 of weight equal to 8.
The degree of vertex 0 is 2 (there's a loop), so the edge 0-0 can't be pruned. The different weights are cumulated as follow:
0, 15, 15+5, 20+8
Applied to a skeleton made of pixels, this would mean that:
• 15 prunings of 1 pixel would remove one branche of size 15.
• 20 prunings would remove the two branches of size 15 and 20.
• 28 prunings would remove the three branches of sizes 15, 20 and 8 (initially between two vertices of degree 3).
The weights are stored in a vector X .
The corresponding counts of degree 1 vertices are stored in a vector Y.
Both X,Y are returned by the function response_to_iterative_pruning()
### Make a feature vector from the pruning curve?
A response curve was plotted as a step curve:
The upper curve is the response when the weight of edges are used. In the lower one, the weights were normalised by the total weights of the graph (% total length or total weight), hopping to produce a scale invariant response. For the following, only the raw response will be used.
### Distance between two graphs:
First, we need new toy graphs to compare them. The second new graph differe from the first only by its weight:
The third one has no loop:
A fourth has a loop elsewhere:
The response of the three first graphs are:
Overlayed responses of first and third graph (right)
We could try to compute the area between two step curves. For two identical curves the area would be null, as the curves differe the area may increase. Fine!
However, the curves are just defined from discrete data, it may not be so easy to define for such kind of integration.
Let's forget the curves and just look at the points from the scatter plot. When looking at two pruning curves obtained from toy-graphs 2 and 3, we could just compute the distances matrix between the points from the two curves. The more the curves are different, the more the distances should increase ... why not, give it a try:
#### scipy provides just what we need!
The response curve is given as (X, Y) with
• X : The pruning values
• Y : the corresponding number of leaf in the graph (vertices of degree 1)
First, let's compute the distances between the points of the same curve:
T=make_toy_graph()
X, Y = response_to_iterative_pruning(T.copy())
pruning_curve = zip(X,Y)
D = cdist( pruning_curve, pruning_curve)
print D
Thanks to scipy, we get a 4x4 (since the graph has four vertices) matrix of distances D :
[[ 0. 15.03329638 20.02498439 28.0713377 ]
[ 15.03329638 0. 5. 13.03840481]
[ 20.02498439 5. 0. 8.06225775]
[ 28.0713377 13.03840481 8.06225775 0. ]]
Which can be displayed as an image (the matrix is symetric, only upper element are displayed):
For each of the three first graphs T,T1,T2 , one can define 3232+3=6 matrices of distances.
Those matrices are elements of another matrix (a matrix of matrices). The elements of the diagonal are squared matrices corresponding to "intra-distances" (distances between the points of the same response curve).
The elements outside the diagonal correspond to "inter-distances" matrices (distances computed from points belonging to two different response curves), the "inter-distance matrices", here, can be rectangular if the corresponding pairs of graphs do not have the same number of vertices (and square if the two graphs have the same number of vertices):
For each matrix, the total distance can be computed as the sum of their elements. This yields:
[[ 178. 187. 256.]
[ 0. 105. 135.]
[ 0. 0. 140.]]
At first sight, this is not good, elements outside the diagonal (total distance between two response curves, that is the distance between two graphs) should be greater than those of the diagonal.
#### Defining a normalized distance between two graphs
We try to heal this situation by normalising the inter-distances . The total inter-distances is normalized by the sum of total intra-distances. The total inter distances is multiplied by two in order to have a normalised distance:
nD .
nD(responsecurvei,responsecurvei)=1
When conputed against the pair of same response curve, the normalized distance equals 1 as wished.
Finally nD is computed as follow:
nD(ri,rj)=12distance(ri,rj)ri+rj=ri+rj2distance(ri,rj)
such that:
nD(ri,rj)<=1
Let's see the matrix of normalised distance on the three first graphs:
[[ 1. 0.75751403 0.62186779]
[ 0. 1. 0.90636131]
[ 0. 0. 1. ]]
As an image:
This seems better. With that distance, the similarity of a graph on itself is 1 and two different graphs have a similarity bellow 1. It remains to see if that distance can discriminate between graphs of interest possibly after supervised classification.
## Friday, June 19, 2015
### Hunting blobs
Pictures from my last safari:
## Sunday, May 3, 2015
### Building opencv 3 beta under Ubuntu 15.04
#### Building opencv 3 beta from source:
Several blogs explain how to install opencv3 on Ubuntu or on mac os X. A bunch of libraries has to be installed as mentionned previously for opencv 2.49. I follow the guidelines :
• make a separate directory to build the code
Using CMakegui, choose the source directory and the build directory:
click on Configure then on Generate
Check if CUDA, OpenCL, python are detected:
Then from a terminal openned in the build directory, run the command:
make -j4
then:
sudo make install
#### Checking if opencv can be used from python:
From an Ipython notebook, write the small code:
import cv2
print cv2__version__
And we get:
3.0.0-dev
## Friday, June 6, 2014
### Update 06 /11 /2014
The ipython notebook from the previous post was rewritten . A python function building a graph from a skeleton was modified to generate a multigraph (networkx). This function (available in an ipython notebook) is used as follow:
Graph= nx.MultiGraph()
C8_Skeleton_To_Graph_01(Graph, skeleton)
With:
• Graph : a networkx multigraph object.
• skeleton : the binary image of skeleton obtained by morphological thining with mahotas.
In the following example (from the previous ipython notebook), the skeleton of the letter 'a' was converted into a networkx multigraph:
image_test= makeLetterImage('a', 75)
skeleton_test = mh.thin(image_test)
_,_,Bp_test,Ep= SkeletonDecomposition(skeleton_test)
Ep_Ep = skeleton_test*np.logical_not(Ep)
Ep_Ep,_ = mh.label(Ep,Ep)
l_Ep, _ = mh.label(Ep)
Graph_test = nx.MultiGraph()
C8_Skeleton_To_Graph_01(Graph_test, skeleton_test)
print Graph_test.edges(data=True)
figsize(16,8)
subplot(131)
imshow(skeleton_test+l_Ep+3*Bp_test,interpolation='nearest')
subplot(132, xticks=[],yticks=[])
nx.write_dot(Graph_test,'multi.dot')
!neato -T png multi.dot > multi.png
subplot(133)
nx.draw(Graph_test)
The skeleton has two edges, linking the same branched points (yellow and red pixels). The graph was exported to build an image of the multigraph (middle), networkx doesn't seem to be capable to dispolay correctly such multigraph (right)
When applied to a lowercase alphabet:
The function produced the corresponding graphs (the letter 'o' excepted):
However,it is possible to find case where the function failed to buil a graph as:
imTest = makeLetterImage('b', 70)
skelTest = mh.thin(imTest)
Ep_Bp, Bp_Bp, Bp, Ep = SkeletonDecomposition(skelTest)
where:
• skeltest: the image skeleton obtained by thining with mahotas.
• Bp : image of branched-point(s)
• Ep: image of end-point(s)
• Bp_Bp :edge(s) between branched-points
• Ep_Bp:edge(s) between end-point(s) and branched-point(s)
If the skeleton of the letter 'b' is decomposed as follow:
The function fails to produce a graph due to the presence of a closed edge (right) which should be processed as a self loop for the corresponding branched-point (middle image).
### An other graph library: Graph-tool
The graphic representation of a multigraph produced by graphtool is so nice that it may worth to learn the graphtool syntax to make a graph:
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### Racism and path homotopy
I recently had to face some racism on math.stackexchange.com for asking some seemingly obvious question on path homotopy. In retrospect, I could have thought through the concept myself. However, I don’t think I would have done so as quickly had I not been angry about the racism.
This is what I was trying to prove: let $\alpha$ be a path from $x_1$ to $x_2$. Then $\alpha*\alpha^{-1}*p*\alpha*\alpha^{-1}$ is homotopic to $p$. Here $p$ is a loop on $x_1$.
Obviously one might expect $\alpha$ and $\alpha^{-1}$ to cancel out on both sides, giving only $p$. However, I was interested in deriving it from first principles, and not just learn a seemingly obvious tool for future calculations. Hence the pedant fought for two days almost to finally understand this (turned out to be pretty elementary in the end).
You have a path homotopy between paths $f,g\in X$ when mapping $[0,1]\times\{0\}$ to $X$ gives you $f$, mapping $[0,1]\times \{1\}$ gives you $g$, and mapping $[0,1]\times \{t\}$ to $X$ gives you the paths “in between”. Let us call the continuous function from $k:I^2\to X$.
Now let us do something weird: let us construct two paths $m,n$ with the same terminal points in $I^2$. As $I^2$ is convex, the two paths are path homotopic. Hence, there exists a continuous mapping $a:I^2\to I^2$ such that $a([0,1]\times\{0\})=m$ and $a([0,1]\times\{1\})=n$.
Looking at the whole picture: this is what we have: a mapping $a:I^2\to I^2$ which is continuous, and another mapping $k:a(I^2)\to X$, which is continuous on $a(I^2)$ (as $k$ is continuous on $I^2$ and $a(I^2)$ is but a subspace of $I^2$). Hence, $(k\circ a):I^2\to X$ is continuous, which shows $k(m)$ is homotopic to $k(n)$.
Now we come to the most important part. Let $m$ be the path in $I^2$ such that $k(m)=p$. Also, let $n$ be the path in $I^2$ such that $k(n)=\alpha*\alpha^{-1}*p*\alpha*\alpha^{-1}$. They have the same terminal points. Why their terminal points can be made to be the same has terrific ideas behind it, and would require another post (it is not explained in Munkres, so watch out for that post). Anyway, as $(k\circ a):I^2\to X$ is continuous, it is easily seen that $p$ and $\alpha*\alpha^{-1}*p*\alpha*\alpha^{-1}$ are homotopic.
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Try out our new practice tests completely free!
Solved
# Compute the Least-Squares Regression Line for Predicting Y from X $\begin{array} { l l l } \bar { x } = 6.7 & s _ { x } = 1.6 & \bar { y } = 23.8 \\s _ { y } = 6.5 & r = 0.93 & \\\end{array}$
Question 7
Multiple Choice
Question 7
Multiple Choice
## Compute the least-squares regression line for predicting y from x given the following summary statistics:$\begin{array} { l l l } \bar { x } = 6.7 & s _ { x } = 1.6 & \bar { y } = 23.8 \\s _ { y } = 6.5 & r = 0.93 & \\\end{array}$
A) $y = - 1.5133 + 3.7781 x$
B) $y = - 1.5133 + 0.2289 x$
C) $y = 0.2289 - 1.5133 x$
D) $y = 3.7781 - 1.5133 x$
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# Extension of polya's urn
An urn contains r > 0 red balls and b > 0 black balls. A ball is drawn at random from the urn, its color noted and returned to the urn. Further, d > 0 additional balls of the same color are added to the urn. This process of drawing a ball and adding d balls of the same color is continued. Define Xi = 1 if at the i-th draw the color of the ball drawn is red, and 0 otherwise. Compute E($$\sum_{i=1}^{\infty}{Xi}$$).
My attempt so far is~
Define the events $$\textit{R_n:="n-th ball drawn is red"}$$ and $$\textit{B_n:="n-th ball drawn is black"}$$. Then \begin{align*} \mathsf{P}(B_2)&=\mathsf{P}(B_2 \mid B_1) \mathsf{P}(B_1)+\mathsf{P}(B_2 \mid R_1) \mathsf{P}(R_1) \\ &= \frac{b+d}{r+b+d}\frac{b}{r+b}+\frac{b}{r+b+d}\frac{r}{r+b}=\frac{b}{r+b} \end{align*} and in general $$\mathsf{P}(B_n)=\frac{b}{r+b}$$.
Similarly for red ball,
$$\mathsf{P}(R_n)=\frac{r}{r+b}$$.
How do I find the expectation?
Intuitively it is essentially just counting the number of times you draw red, given you have an infinite number of draws. And the only way this kind of infinite sum converges is if it is a geometric sequence inside some radius of convergence. But you have shown the probability is constant for all $$n$$, so no geometric sequence exists.
The only other solution is trivially when $$r = 0$$. I could be missing something though because I do imagine if $$d$$ is incredibly large, intuitively it might converge. But your probability $$B_{n}$$ shows otherwise.
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Tersian, Stepan Agop
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Author ID: tersian.stepan-agop Published as: Tersian, Stepan; Tersian, Stepan A.; Tersian, S.; Tersian, S. A.; Tersian, Stepan Agop; Tersian, St. A. more...less
Documents Indexed: 79 Publications since 1982, including 3 Books 2 Contributions as Editor Reviewing Activity: 425 Reviews Co-Authors: 46 Co-Authors with 63 Joint Publications 1,223 Co-Co-Authors
all top 5
Co-Authors
17 single-authored 8 Cabada, Alberto 5 Chaparova, Julia V. 5 Li, Lin 4 do Rosário Grossinho, Maria 4 Souroujon, Diko M. 3 Aprahamian, Meline Onik 3 Dimitrov, Nikolay D. 3 Gyulov, Tihomir 3 Iannizzotto, Antonio 3 Mihăilescu, Mihai 3 Moroşanu, Gheorghe 3 Rădulescu, Vicenţiu D. 3 Saavedra, Lorena 2 Biroli, Marco 2 Bonanno, Gabriele 2 Drábek, Pavel 2 Heidarkhani, Shapour 2 Kelevedjiev, Petio S. 2 Khristova, Snezhana G. 2 Kristály, Alexandru 2 Peletier, Lambertus Adrianus 2 Rodríguez-López, Rosana 2 Stavroulakis, Ioannis P. 2 Zabreĭko, Pëtr Petrovich 1 Almeida, Ricardo 1 Averna, Diego 1 Caristi, Giuseppe 1 Chinnì, Antonia 1 D’Aguì, Giuseppina 1 Di Bella, Beatrice 1 Grammatikopoulos, Myron K. 1 Hadjian, Armin 1 Khaleghi Moghadam, M. 1 Langerová, Martina 1 Li, Chengyue 1 Minhós, Feliz Manuel 1 Moradi, Shahin 1 Nastasi, Antonella 1 Nyamoradi, Nemat 1 Popivanov, Petar Radoev 1 Precup, Radu 1 Salari, Amjad 1 Sanchez, Luís 1 Sun, Jijiang 1 Tornatore, Elisabetta 1 Vetro, Calogero
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Serials
7 Journal of Mathematical Analysis and Applications 6 Doklady Bolgarskoĭ Akademii Nauk 6 Fractional Calculus & Applied Analysis 5 Electronic Journal of Differential Equations (EJDE) 4 Rendiconti. Scienze Matemàtiche e Applicazioni. A 4 Applied Mathematics Letters 4 Electronic Journal of Qualitative Theory of Differential Equations 3 Nonlinear Analysis. Theory, Methods & Applications 2 Applied Mathematics and Computation 2 Topological Methods in Nonlinear Analysis 2 Nonlinear Analysis. Real World Applications 2 Boundary Value Problems 1 Applicable Analysis 1 Mathematical Methods in the Applied Sciences 1 Demonstratio Mathematica 1 Funkcialaj Ekvacioj. Serio Internacia 1 Journal of Differential Equations 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Results in Mathematics 1 Bulletin of the Iranian Mathematical Society 1 Dynamic Systems and Applications 1 Turkish Journal of Mathematics 1 Advances in Differential Equations 1 Journal of Difference Equations and Applications 1 Comptes Rendus de l’Académie des Sciences. Série I. Mathématique 1 Communications in Contemporary Mathematics 1 Discrete and Continuous Dynamical Systems. Series B 1 Portugaliae Mathematica. Nova Série 1 Acta Mathematica Scientia. Series B. (English Edition) 1 Advances in Difference Equations 1 Nonconvex Optimization and Its Applications 1 Mathematics and Natural Sciences 1 Open Mathematics
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Fields
45 Ordinary differential equations (34-XX) 30 Partial differential equations (35-XX) 22 Global analysis, analysis on manifolds (58-XX) 14 Operator theory (47-XX) 13 Difference and functional equations (39-XX) 5 Calculus of variations and optimal control; optimization (49-XX) 4 Dynamical systems and ergodic theory (37-XX) 4 Functional analysis (46-XX) 3 Integral equations (45-XX) 3 Numerical analysis (65-XX) 2 General and overarching topics; collections (00-XX) 2 Measure and integration (28-XX) 2 Systems theory; control (93-XX) 1 Real functions (26-XX) 1 Potential theory (31-XX) 1 Mechanics of particles and systems (70-XX) 1 Mechanics of deformable solids (74-XX) 1 Biology and other natural sciences (92-XX) 1 Mathematics education (97-XX)
Citations contained in zbMATH Open
59 Publications have been cited 619 times in 443 Documents Cited by Year
Existence of solutions to boundary value problem for impulsive fractional differential equations. Zbl 1308.34010
Bonanno, Gabriele; Rodríguez-López, Rosana; Tersian, Stepan
2014
Multiple solutions for discrete boundary value problems. Zbl 1169.39008
Cabada, Alberto; Iannizzotto, Antonio; Tersian, Stepan
2009
Periodic and homoclinic solutions of extended Fisher-Kolmogorov equations. Zbl 0984.34031
Tersian, Stepan; Chaparova, Julia
2001
Eigenvalue problems for anisotropic discrete boundary value problems. Zbl 1181.47016
Mihăilescu, Mihai; Rădulescu, Vicenţiu; Tersian, Stepan
2009
Multiple solutions to boundary value problem for impulsive fractional differential equations. Zbl 1312.34024
Rodríguez-López, Rosana; Tersian, Stepan
2014
Multiple homoclinic solutions for the discrete $$p$$-Laplacian via critical point theory. Zbl 1282.39003
Iannizzotto, Antonio; Tersian, Stepan A.
2013
Multiplicity of solutions of a two point boundary value problem for a fourth-order equation. Zbl 1294.34016
2013
The dual variational principle and equilibria for a beam resting on a discontinuous nonlinear elastic foundation. Zbl 0960.34013
Grossinho, M. R.; Tersian, St. A.
2000
On the solvability of a boundary value problem for a fourth-order ordinary differential equation. Zbl 1087.34508
Grossinho, Maria do Rosário; Sanchez, Luis; Tersian, Stepan A.
2005
Homoclinic solutions of difference equations with variable exponents. Zbl 1270.39005
Mihăilescu, Mihai; Rădulescu, Vicenţiu D.; Tersian, Stepan
2011
On the existence and multiplicity of solutions for Dirichlet’s problem for fractional differential equations. Zbl 1337.34009
Averna, Diego; Tersian, Stepan; Tornatore, Elisabetta
2016
An introduction to minimax theorems and their applications to differential equations. Zbl 0987.58004
Grossinho, Maria do Rosário; Tersian, Stepan Agop
2001
A minimax theorem and applications to nonresonance problems for semilinear equations. Zbl 0605.49007
Tersian, Stepan A.
1986
Multiplicity results for superlinear boundary value problems with impulsive effects. Zbl 1342.34046
D’Aguì, Giuseppina; Di Bella, Beatrice; Tersian, Stepan
2016
Existence and nonexistence of nontrivial solutions of semilinear fourth- and sixth-order differential equations. Zbl 1126.34316
Chaparova, Julia V.; Peletier, Lambertus A.; Tersian, Stepan A.
2003
On homoclinic solutions of a semilinear $$p$$-Laplacian difference equation with periodic coefficients. Zbl 1207.39004
Cabada, Alberto; Li, Chengyue; Tersian, Stepan
2010
Quasilinear elliptic problems in $$\mathbb R^N$$ involving oscillatory nonlinearities. Zbl 1185.35071
Kristály, Alexandru; Moroşanu, Gheorghe; Tersian, Stepan
2007
Decreasing and fast solutions for a second-order difference equation related to Fisher-Kolmogorov’s equation. Zbl 1257.39008
Aprahamian, Meline; Souroujon, Diko; Tersian, Stepan
2010
Existence and nonexistence of nontrivial solutions of semilinear sixth-order ordinary differential equations. Zbl 1122.34305
Chaparova, J. V.; Peletier, L. A.; Tersian, S. A.
2004
Spectral estimates for a nonhomogeneous difference problem. Zbl 1215.47020
Kristály, Alexandru; Mihăilescu, Mihai; Rădulescu, Vicenţiu; Tersian, Stepan
2010
Existence and multiplicity of solutions to boundary value problems for fourth-order impulsive differential equations. Zbl 1319.34044
2014
Existence results for a two point boundary value problem involving a fourth-order equation. Zbl 1349.34070
Bonanno, Gabriele; Chinnì, Antonia; Tersian, Stepan
2015
Existence of heteroclinic solutions for discrete $$p$$-Laplacian problems with a parameter. Zbl 1235.39002
2011
On symmetric positive homoclinic solutions of semilinear $$p$$-Laplacian differential equations. Zbl 1281.34032
Tersian, Stepan
2012
Infinitely many sign-changing solutions for the Brézis-Nirenberg problem involving the fractional Laplacian. Zbl 1377.35099
Li, Lin; Sun, Jijiang; Tersian, Stepan
2017
Multiple positive solutions to a fourth-order boundary-value problem. Zbl 1357.34054
2016
Periodic and homoclinic solutions of some semilinear sixth-order differential equations. Zbl 1017.34046
Tersian, Stepan; Chaparova, Julia
2002
Existence of trivial and nontrivial solutions of fourth-order ordinary differential equation. Zbl 1065.34016
Gyulov, T.; Tersian, S.
2004
Singular and nonsingular first-order initial value problems. Zbl 1191.34010
Kelevedjiev, P. S.; Tersian, S.
2010
Existence for a semilinear sixth-order ODE. Zbl 1106.34007
Gyulov, Tihomir; Morosanu, Gheorghe; Tersian, Stepan
2006
Existence of solutions for nonlinear fractional order $$p$$-Laplacian differential equations via critical point theory. Zbl 1481.34089
2019
Multiple solutions for degenerate nonlocal problems. Zbl 06892636
Caristi, Giuseppe; Heidarkhani, Shapour; Salari, Amjad; Tersian, Stepan A.
2018
Existence of solutions for $$2n$$th-order nonlinear $$p$$-Laplacian differential equations. Zbl 1354.34045
Saavedra, Lorena; Tersian, Stepan
2017
Three solutions for second-order boundary-value problems with variable exponents. Zbl 1413.34098
Heidarkhani, Shapour; Moradi, Shahin; Tersian, Stepan
2018
Partial differential equations. An introduction with Mathematica and MAPLE. Zbl 0940.35001
Stavroulakis, Ioannis P.; Tersian, Stepan A.
1999
Scalar linear impulsive Riemann-Liouville fractional differential equations with constant delay-explicit solutions and finite time stability. Zbl 1450.34056
Hristova, Snezhana G.; Tersian, Stepan A.
2020
Fractional problems with critical nonlinearities by a sublinear perturbation. Zbl 1448.35195
Li, Lin; Tersian, Stepan
2020
Existence of three solutions for a discrete anisotropic boundary value problem. Zbl 1408.39002
Khaleghi Moghadam, M.; Li, L.; Tersian, S.
2018
On the solvability of semilinear Schrödinger equations in strip-like domains. Zbl 0937.35031
Tersian, S.
1998
Periodic and homoclinic solutions of extended Fisher-Kolmogorov equations. Zbl 0969.34038
Tersian, Stepan; Chaparova, Julia
2000
Existence of trivial and nontrivial solutions of a fourth-order ordinary differential equation. Zbl 1058.34016
Gyulov, Tihomir; Tersian, Stepan
2004
Heteroclinic solutions of a second-order difference equation related to the Fisher-Kolmogorov’s equation. Zbl 1245.39003
Cabada, Alberto; Souroujon, Diko; Tersian, Stepan
2012
Characterizations of the range of Neumann problem for semilinear elliptic equations. Zbl 0652.35040
Drábek, Pavel; Tersian, Stepan A.
1987
On the periodic problem for the equation $$x''(t)+g(x(t))=f(t)$$. Zbl 0579.34031
Tersian, Stepan
1985
Partial differential equations. An introduction with Mathematica and MAPLE. 2nd ed. Zbl 1062.35001
Stavroulakis, Ioannis P.; Tersian, Stepan A.
2004
Existence of solutions for nonlinear $$p$$-Laplacian difference equations. Zbl 06850994
Saavedra, Lorena; Tersian, Stepan
2017
Existence results for a mixed boundary value problem. Zbl 1349.34056
2015
Existence of homoclinic solutions for a nonlinear fourth order $$p$$-Laplacian difference equation. Zbl 1444.39013
Dimitrov, Nikolay; Tersian, Stepan
2020
Homoclinic and periodic solutions for some classes of second order differential equations. Zbl 0997.34034
Grossinho, M. R.; Minhós, F.; Tersian, S.
2001
Nontrivial solutions of semilinear Schrödinger equations on $$\mathbb{R}^ n$$ and strip-like domains. Zbl 0832.35045
Tersian, Stepan
1995
A note on Palais-Smale condition and mountain-pass principle for locally Lipschitz functionals. Zbl 0857.49005
Tersian, Stepan
1995
Mountain pass theorems, deformation theorems, and Palais-Smale conditions. Zbl 1053.58006
Tersian, Stepan A.
2001
On a mini max theorem. Zbl 0565.49008
Tersian, S. A.
1985
Existence and multiplicity of periodic solutions to one-dimensional $$p$$-Laplacian. Zbl 1363.34109
Drabek, Pavel; Langerova, Martina; Tersian, Stepan
2016
Homoclinic solutions of a fourth-order travelling wave ODE. Zbl 1162.34036
Morosanu, Gheorghe; Souroujon, Diko; Tersian, Stepan
2007
On the existence of nontrivial solutions to a semilinear equation relative to a Dirichlet form. Zbl 1138.35324
Biroli, Marco; Tersian, Stepan
1998
Hammerstein integral equations with nontrivial solutions. Zbl 0721.45002
Tersian, Stepan A.; Zabrejko, Petr P.
1991
On a class of abstract systems without resonance in a Hilbert space. Zbl 0489.35007
Tersian, Stepan A.
1982
Existence of solutions of discrete equations via critical point theory. Zbl 1242.39003
Cabada, Alberto; Iannizzotto, Antonio; Tersian, Stepan
2011
Scalar linear impulsive Riemann-Liouville fractional differential equations with constant delay-explicit solutions and finite time stability. Zbl 1450.34056
Hristova, Snezhana G.; Tersian, Stepan A.
2020
Fractional problems with critical nonlinearities by a sublinear perturbation. Zbl 1448.35195
Li, Lin; Tersian, Stepan
2020
Existence of homoclinic solutions for a nonlinear fourth order $$p$$-Laplacian difference equation. Zbl 1444.39013
Dimitrov, Nikolay; Tersian, Stepan
2020
Existence of solutions for nonlinear fractional order $$p$$-Laplacian differential equations via critical point theory. Zbl 1481.34089
2019
Multiple solutions for degenerate nonlocal problems. Zbl 06892636
Caristi, Giuseppe; Heidarkhani, Shapour; Salari, Amjad; Tersian, Stepan A.
2018
Three solutions for second-order boundary-value problems with variable exponents. Zbl 1413.34098
Heidarkhani, Shapour; Moradi, Shahin; Tersian, Stepan
2018
Existence of three solutions for a discrete anisotropic boundary value problem. Zbl 1408.39002
Khaleghi Moghadam, M.; Li, L.; Tersian, S.
2018
Infinitely many sign-changing solutions for the Brézis-Nirenberg problem involving the fractional Laplacian. Zbl 1377.35099
Li, Lin; Sun, Jijiang; Tersian, Stepan
2017
Existence of solutions for $$2n$$th-order nonlinear $$p$$-Laplacian differential equations. Zbl 1354.34045
Saavedra, Lorena; Tersian, Stepan
2017
Existence of solutions for nonlinear $$p$$-Laplacian difference equations. Zbl 06850994
Saavedra, Lorena; Tersian, Stepan
2017
On the existence and multiplicity of solutions for Dirichlet’s problem for fractional differential equations. Zbl 1337.34009
Averna, Diego; Tersian, Stepan; Tornatore, Elisabetta
2016
Multiplicity results for superlinear boundary value problems with impulsive effects. Zbl 1342.34046
D’Aguì, Giuseppina; Di Bella, Beatrice; Tersian, Stepan
2016
Multiple positive solutions to a fourth-order boundary-value problem. Zbl 1357.34054
2016
Existence and multiplicity of periodic solutions to one-dimensional $$p$$-Laplacian. Zbl 1363.34109
Drabek, Pavel; Langerova, Martina; Tersian, Stepan
2016
Existence results for a two point boundary value problem involving a fourth-order equation. Zbl 1349.34070
Bonanno, Gabriele; Chinnì, Antonia; Tersian, Stepan
2015
Existence results for a mixed boundary value problem. Zbl 1349.34056
2015
Existence of solutions to boundary value problem for impulsive fractional differential equations. Zbl 1308.34010
Bonanno, Gabriele; Rodríguez-López, Rosana; Tersian, Stepan
2014
Multiple solutions to boundary value problem for impulsive fractional differential equations. Zbl 1312.34024
Rodríguez-López, Rosana; Tersian, Stepan
2014
Existence and multiplicity of solutions to boundary value problems for fourth-order impulsive differential equations. Zbl 1319.34044
2014
Multiple homoclinic solutions for the discrete $$p$$-Laplacian via critical point theory. Zbl 1282.39003
Iannizzotto, Antonio; Tersian, Stepan A.
2013
Multiplicity of solutions of a two point boundary value problem for a fourth-order equation. Zbl 1294.34016
2013
On symmetric positive homoclinic solutions of semilinear $$p$$-Laplacian differential equations. Zbl 1281.34032
Tersian, Stepan
2012
Heteroclinic solutions of a second-order difference equation related to the Fisher-Kolmogorov’s equation. Zbl 1245.39003
Cabada, Alberto; Souroujon, Diko; Tersian, Stepan
2012
Homoclinic solutions of difference equations with variable exponents. Zbl 1270.39005
Mihăilescu, Mihai; Rădulescu, Vicenţiu D.; Tersian, Stepan
2011
Existence of heteroclinic solutions for discrete $$p$$-Laplacian problems with a parameter. Zbl 1235.39002
2011
Existence of solutions of discrete equations via critical point theory. Zbl 1242.39003
Cabada, Alberto; Iannizzotto, Antonio; Tersian, Stepan
2011
On homoclinic solutions of a semilinear $$p$$-Laplacian difference equation with periodic coefficients. Zbl 1207.39004
Cabada, Alberto; Li, Chengyue; Tersian, Stepan
2010
Decreasing and fast solutions for a second-order difference equation related to Fisher-Kolmogorov’s equation. Zbl 1257.39008
Aprahamian, Meline; Souroujon, Diko; Tersian, Stepan
2010
Spectral estimates for a nonhomogeneous difference problem. Zbl 1215.47020
Kristály, Alexandru; Mihăilescu, Mihai; Rădulescu, Vicenţiu; Tersian, Stepan
2010
Singular and nonsingular first-order initial value problems. Zbl 1191.34010
Kelevedjiev, P. S.; Tersian, S.
2010
Multiple solutions for discrete boundary value problems. Zbl 1169.39008
Cabada, Alberto; Iannizzotto, Antonio; Tersian, Stepan
2009
Eigenvalue problems for anisotropic discrete boundary value problems. Zbl 1181.47016
Mihăilescu, Mihai; Rădulescu, Vicenţiu; Tersian, Stepan
2009
Quasilinear elliptic problems in $$\mathbb R^N$$ involving oscillatory nonlinearities. Zbl 1185.35071
Kristály, Alexandru; Moroşanu, Gheorghe; Tersian, Stepan
2007
Homoclinic solutions of a fourth-order travelling wave ODE. Zbl 1162.34036
Morosanu, Gheorghe; Souroujon, Diko; Tersian, Stepan
2007
Existence for a semilinear sixth-order ODE. Zbl 1106.34007
Gyulov, Tihomir; Morosanu, Gheorghe; Tersian, Stepan
2006
On the solvability of a boundary value problem for a fourth-order ordinary differential equation. Zbl 1087.34508
Grossinho, Maria do Rosário; Sanchez, Luis; Tersian, Stepan A.
2005
Existence and nonexistence of nontrivial solutions of semilinear sixth-order ordinary differential equations. Zbl 1122.34305
Chaparova, J. V.; Peletier, L. A.; Tersian, S. A.
2004
Existence of trivial and nontrivial solutions of fourth-order ordinary differential equation. Zbl 1065.34016
Gyulov, T.; Tersian, S.
2004
Existence of trivial and nontrivial solutions of a fourth-order ordinary differential equation. Zbl 1058.34016
Gyulov, Tihomir; Tersian, Stepan
2004
Partial differential equations. An introduction with Mathematica and MAPLE. 2nd ed. Zbl 1062.35001
Stavroulakis, Ioannis P.; Tersian, Stepan A.
2004
Existence and nonexistence of nontrivial solutions of semilinear fourth- and sixth-order differential equations. Zbl 1126.34316
Chaparova, Julia V.; Peletier, Lambertus A.; Tersian, Stepan A.
2003
Periodic and homoclinic solutions of some semilinear sixth-order differential equations. Zbl 1017.34046
Tersian, Stepan; Chaparova, Julia
2002
Periodic and homoclinic solutions of extended Fisher-Kolmogorov equations. Zbl 0984.34031
Tersian, Stepan; Chaparova, Julia
2001
An introduction to minimax theorems and their applications to differential equations. Zbl 0987.58004
Grossinho, Maria do Rosário; Tersian, Stepan Agop
2001
Homoclinic and periodic solutions for some classes of second order differential equations. Zbl 0997.34034
Grossinho, M. R.; Minhós, F.; Tersian, S.
2001
Mountain pass theorems, deformation theorems, and Palais-Smale conditions. Zbl 1053.58006
Tersian, Stepan A.
2001
The dual variational principle and equilibria for a beam resting on a discontinuous nonlinear elastic foundation. Zbl 0960.34013
Grossinho, M. R.; Tersian, St. A.
2000
Periodic and homoclinic solutions of extended Fisher-Kolmogorov equations. Zbl 0969.34038
Tersian, Stepan; Chaparova, Julia
2000
Partial differential equations. An introduction with Mathematica and MAPLE. Zbl 0940.35001
Stavroulakis, Ioannis P.; Tersian, Stepan A.
1999
On the solvability of semilinear Schrödinger equations in strip-like domains. Zbl 0937.35031
Tersian, S.
1998
On the existence of nontrivial solutions to a semilinear equation relative to a Dirichlet form. Zbl 1138.35324
Biroli, Marco; Tersian, Stepan
1998
Nontrivial solutions of semilinear Schrödinger equations on $$\mathbb{R}^ n$$ and strip-like domains. Zbl 0832.35045
Tersian, Stepan
1995
A note on Palais-Smale condition and mountain-pass principle for locally Lipschitz functionals. Zbl 0857.49005
Tersian, Stepan
1995
Hammerstein integral equations with nontrivial solutions. Zbl 0721.45002
Tersian, Stepan A.; Zabrejko, Petr P.
1991
Characterizations of the range of Neumann problem for semilinear elliptic equations. Zbl 0652.35040
Drábek, Pavel; Tersian, Stepan A.
1987
A minimax theorem and applications to nonresonance problems for semilinear equations. Zbl 0605.49007
Tersian, Stepan A.
1986
On the periodic problem for the equation $$x''(t)+g(x(t))=f(t)$$. Zbl 0579.34031
Tersian, Stepan
1985
On a mini max theorem. Zbl 0565.49008
Tersian, S. A.
1985
On a class of abstract systems without resonance in a Hilbert space. Zbl 0489.35007
Tersian, Stepan A.
1982
all top 5
Cited by 505 Authors
22 Tersian, Stepan Agop 20 Heidarkhani, Shapour 14 Caristi, Giuseppe 12 Moradi, Shahin 12 O’Regan, Donal 10 Cabada, Alberto 10 Galewski, Marek 9 Afrouzi, Ghasem Alizadeh 9 Bonanno, Gabriele 9 Kong, Lingju 9 Ouaro, Stanislas 8 Guiro, Aboudramane 8 Minhós, Feliz Manuel 8 Zhao, Yulin 7 Figueiredo, Giovany Malcher 7 Kone, Blaise 7 Li, Lin 7 Ma, To Fu 7 Nyamoradi, Nemat 7 Salari, Amjad 6 Agarwal, Ravi P. 6 Chen, Haibo 6 Henderson, Johnny Lee 6 Kristály, Alexandru 6 Molica Bisci, Giovanni 6 Nieto Roig, Juan Jose 6 Pei, Minghe 6 Serban, Calin-Constantin 6 Sun, Juntao 6 Wang, Hui 6 Wieteska, Renata 5 Bai, Zhanbing 5 D’Aguì, Giuseppina 5 Di Bella, Beatrice 5 Graef, John R. 5 Ibrango, Idrissa 5 Jebelean, Petru 5 Li, Peiluan 5 Luca, Rodica 5 Moghadam, Mohsen Khaleghi 5 Moroşanu, Gheorghe 5 Rădulescu, Vicenţiu D. 5 Saoudi, Kamel 5 Zhou, Zhan 4 Arjunan, Mani Mallika 4 Gyulov, Tihomir 4 Khristova, Snezhana G. 4 Kong, Fanchao 4 Kuang, Juhong 4 Li, Chengyue 4 Li, Weiguo 4 Liu, Lishan 4 Ma, Ruyun 4 Repovš, Dušan D. 4 Rodríguez-López, Rosana 4 Wang, Libo 4 Zhang, Xingyong 3 Amster, Pablo 3 An, Yukun 3 Averna, Diego 3 Bereanu, Cristian 3 Chaparova, Julia V. 3 Chen, Pengyu 3 Cui, Yujun 3 Dai, Guowei 3 Daoues, Adel 3 dos Santos, Gelson C. G. 3 Ge, Bin 3 Hammami, Amani 3 Huang, Wenhua 3 Imbesi, Maurizio 3 Li, Yongkun 3 Li, Yongxiang 3 Li, Zheqing 3 Liu, Wenbin 3 Long, Yuhua 3 Mawhin, Jean L. 3 Mihăilescu, Mihai 3 Nascimento, Rúbia G. 3 Saavedra, Lorena 3 Sanchez, Luís 3 Shi, Haiping 3 Stegliński, Robert 3 Suganya, Selvaraj 3 Tornatore, Elisabetta 3 Torres Ledesma, César Enrique 3 Ur Rehman, Mujeeb 3 Wu, Tsungfang 3 Xiang, Mingqi 3 Yang, Liu 3 Yuan, Rong 3 Zhai, Chengbo 3 Zhang, Binlin 3 Zhang, Xuemei 3 Zhang, Ziheng 2 Alves, Claudianor Oliveira 2 Avci, Mustafa 2 Bai, Dingyong 2 Băleanu, Dumitru I. 2 Barilla, David ...and 405 more Authors
all top 5
Cited in 120 Serials
34 Journal of Mathematical Analysis and Applications 33 Boundary Value Problems 24 Applied Mathematics Letters 24 Advances in Difference Equations 21 Applied Mathematics and Computation 21 Journal of Difference Equations and Applications 20 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 20 Fractional Calculus & Applied Analysis 13 Mediterranean Journal of Mathematics 11 Nonlinear Analysis. Real World Applications 9 Abstract and Applied Analysis 9 Journal of Function Spaces 6 Discrete Dynamics in Nature and Society 6 Qualitative Theory of Dynamical Systems 6 Journal of Applied Mathematics and Computing 6 Journal of Nonlinear Science and Applications 5 Applicable Analysis 5 Discrete and Continuous Dynamical Systems. Series B 5 Complex Variables and Elliptic Equations 5 Journal of Fixed Point Theory and Applications 5 AIMS Mathematics 4 Rocky Mountain Journal of Mathematics 4 Chaos, Solitons and Fractals 4 Journal of Differential Equations 4 Bulletin of the Iranian Mathematical Society 4 Nonlinear Analysis. Modelling and Control 4 Journal of Applied Mathematics 3 Computers & Mathematics with Applications 3 ZAMP. Zeitschrift für angewandte Mathematik und Physik 3 Journal of Computational and Applied Mathematics 3 Quaestiones Mathematicae 3 Opuscula Mathematica 3 Mathematical Problems in Engineering 3 Journal of Inequalities and Applications 3 International Journal of Nonlinear Sciences and Numerical Simulation 3 Cubo 3 Journal of Applied Analysis and Computation 2 Mathematical Methods in the Applied Sciences 2 Ukrainian Mathematical Journal 2 Proceedings of the American Mathematical Society 2 Acta Applicandae Mathematicae 2 Mathematical and Computer Modelling 2 Topological Methods in Nonlinear Analysis 2 NoDEA. Nonlinear Differential Equations and Applications 2 Discrete and Continuous Dynamical Systems 2 Arab Journal of Mathematical Sciences 2 Taiwanese Journal of Mathematics 2 Acta Mathematica Scientia. Series B. (English Edition) 2 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 2 Differential Equations and Applications 2 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 2 Journal of Mathematics 2 Nonautonomous Dynamical Systems 2 Open Mathematics 1 Journal of Fluid Mechanics 1 Mathematical Notes 1 Collectanea Mathematica 1 Czechoslovak Mathematical Journal 1 International Journal of Mathematics and Mathematical Sciences 1 Journal of the Korean Mathematical Society 1 Journal of Optimization Theory and Applications 1 Manuscripta Mathematica 1 Mathematics and Computers in Simulation 1 Mathematische Nachrichten 1 Monatshefte für Mathematik 1 Siberian Mathematical Journal 1 Acta Mathematica Hungarica 1 Physica D 1 Applied Numerical Mathematics 1 Numerical Methods for Partial Differential Equations 1 Journal of Scientific Computing 1 Journal of Integral Equations and Applications 1 Journal of Contemporary Mathematical Analysis. Armenian Academy of Sciences 1 Applied Mathematical Modelling 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Expositiones Mathematicae 1 Indagationes Mathematicae. New Series 1 Continuum Mechanics and Thermodynamics 1 Tatra Mountains Mathematical Publications 1 Set-Valued Analysis 1 Applied Mathematics. Series B (English Edition) 1 Journal of Mathematical Sciences (New York) 1 Turkish Journal of Mathematics 1 Georgian Mathematical Journal 1 Differential Equations and Dynamical Systems 1 Nonlinear Dynamics 1 Positivity 1 Communications of the Korean Mathematical Society 1 Communications in Contemporary Mathematics 1 Kragujevac Journal of Mathematics 1 Portugaliae Mathematica. Nova Série 1 Nonlinear Dynamics and Systems Theory 1 Communications on Pure and Applied Analysis 1 Central European Journal of Mathematics 1 Journal of Cosmology and Astroparticle Physics 1 Journal of the Indonesian Mathematical Society 1 Sibirskie Èlektronnye Matematicheskie Izvestiya 1 Nonlinear Oscillations 1 Discrete and Continuous Dynamical Systems. Series S 1 Asian-European Journal of Mathematics ...and 20 more Serials
all top 5
Cited in 28 Fields
266 Ordinary differential equations (34-XX) 132 Partial differential equations (35-XX) 112 Difference and functional equations (39-XX) 86 Operator theory (47-XX) 77 Global analysis, analysis on manifolds (58-XX) 25 Calculus of variations and optimal control; optimization (49-XX) 25 Mechanics of deformable solids (74-XX) 23 Dynamical systems and ergodic theory (37-XX) 16 Real functions (26-XX) 13 Numerical analysis (65-XX) 12 Functional analysis (46-XX) 7 Integral equations (45-XX) 4 Fluid mechanics (76-XX) 2 Special functions (33-XX) 2 Mechanics of particles and systems (70-XX) 2 Systems theory; control (93-XX) 1 History and biography (01-XX) 1 Mathematical logic and foundations (03-XX) 1 Combinatorics (05-XX) 1 Measure and integration (28-XX) 1 Functions of a complex variable (30-XX) 1 Potential theory (31-XX) 1 Integral transforms, operational calculus (44-XX) 1 General topology (54-XX) 1 Optics, electromagnetic theory (78-XX) 1 Relativity and gravitational theory (83-XX) 1 Astronomy and astrophysics (85-XX) 1 Biology and other natural sciences (92-XX)
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# Manual for Creating Your Own Website*
*Currently under construction.
## Introduction
Some people do not have the time or resources to build language learning websites. This is a template you can use to build your own website for the language you are working on. The template is open-source, which means anyone can use it, and it does not cost anything.
The language tools website consists of ten components. You don’t have to use all the components - you can choose which ones work best for your own project.
This page describes the contents of the website, and explains the steps you go through to create a website for your own language. Here are the recommended steps to follow:
1. Read through this page to get an idea of the contents of the website you will be building.
2. Click the “View the Template” tab at the top of the page to move through an empty version of the website. (You cannot make changes to this empty version of the website.)
3. Follow the steps in the section below, entitled “Changing the Code to Create Your Website.”
The language tools website consists of ten components. You don’t have to use all the components - you can choose which ones work best for your own project. Within each component there is some flexibility in terms of representing the information. This list describes how you might use each of these components.
• o This is an image of the (blank) home page of the website. You can insert a photo of their own choosing on the homepage. As you can see in illustration to the right, the home page contains links to the other sections.
• A description about the language, the speakers, and the members involved in the creation of these resources.
3. Sounds and Letters
• A grid representing the sound system of the language including audio files for each sound.
4. Everyday Expressions
• This page provides space to introduce users to common phrases and sentences.
5. Talking Dictionary
• This is a dictionary where you can play each of the words with an accompanying sound file. (The template also includes directions for how to add entries and update sound files.)
6. Phrasicon
• This is a bank of phrases and sentences including sound files. You can hear each entry by clicking the play button. (The template also includes directions for how to add entries and update sound files.)
7. Stories and Text
• This section includes stories and texts of the language with audio files.
• This section would contain a brief description for any mobile apps you have made, and links that direct users to the download page.
9. Contact Page
• A page with contact information for users to get in touch with the creators of the resources.
You might decide to include the talking dictionary alone, or include the phrasicon with common everyday expressions. You can select any to all of the components to fit your needs.
## Changing the Code to Create your Website
This documentation is written in attempts to guide potential users through the process. The template was created with non-programmers in mind. That being said, applying changes will require some level of tech-savviness. In order to effectively set up the template, your team should include someone who has some experience with computer programming.
Before you make changes to the template, you will need to set up a place to 'host' your website. This means that you will need to get a domain name like www.domainName.com where people can access these resources. Some examples include 000webhost (free), BlueHost, or GoDaddy. Once everything is set up, simply download the template located in the header bar, extract the files, and put them in your web host, usually in the public_html folder.
At this point, I recommend using a specialized text editor such as Sublime, Brackets, or Notepad++ which you will use to edit the code. They make the code easier to read by adding color schemes. You can also connect to your web host to add, edit, or remove files with FileZilla or WinSCP. They allow you to visualize the folders like a regular directory.
The template uses the following computer languages: HTML, CSS, JavaScript, XML, and PHP.
HTML (HyperText Markup Language) sets the structure of the web page and displays the content. HTML files end in .html. It is known as a markup language because the code is made up of tags enclosed in angle brackets. For example, <body>[...]</body> is a set of 'body' tags. Comments can be added to HTML, and are not processed by the computer - they are only meant to be read by humans. Comments in HTML look like this: <!-- This is a comment. -->. They will used to indicate where changes should be made, and describe the function of a particular block of code. Note that making changes elsewhere may have drastic changes when viewing the web page.
CSS (Cascading Style Sheets) describes the layout, color and font of the web page. For example, italicized, bolded, or colored font are handled by CSS. CSS comments look like this: /* This is a comment. */. CSS files end in .css. Many of the CSS files were adapted from the Foundation 5 framework. You can read more about it here.
JavaScript is a programming language that deals with the interaction between the user and the computer. JavaScript modules end in .js.The Javascript code found in this template should be not be altered.
XML is a format where data is stored and end in .xml. This will be discussed later on.
Finally, PHP is in charge of retrieving data from the XML formats so that they may be displayed on the web page. They end in .php. Comments in PHP can look like this: // This is a comment or /* This is a comment. */.
The folders are organized in the following way.
• texts: Stores Stories and Texts component.
• structure: Stores Basic Sentence Structure component.
• sounds: Stores Sounds and Letters component.
• phrasicon: Stores Phrasicon componeent.
• owl-carousel: Stores slideshow components for Stories and Texts page. Do not change.
• js: Stores JavaScript files. Do not change.
• expressions: Stores Everyday Expressions component.
• dictionary: Stores Talking Dictionary component.
• css: Stores CSS files.
• contact: Stores Contact Page component.
• assets: Stores slideshow components for Stories and Texts page.
• apps: Stores Links to Mobile Apps component.
• placeholder.png: Main image for the website. This is discussed later.
• index.html: This holds the content for your web page.
• default.html: Same as index.html.
You'll notice that index.html and default.html are the same, except for their names. These files display the content of your web page in the folder it is in. For example, if your index.html or default.html files are in your folder labeled as 'language', they represent the content when a user visits www.example.com/language. You're probably wondering why there are two separate files since they hold the same piece of code. Depending on what web host you use, some may read from index.html, and others may read from default.html. Therefore, if you know your host uses one, and not the other, you can simply delete the other version. You can see which one your host uses by simply changing one of the files, and then save. If the web page reflects the changes that were made, then that is the file your host uses. Note that these files only appear in the major components (i.e. Dictionary, Phrasicon, etc.), and not in the folders like owl-carousel or js.
The first thing you may want to do is to insert your own picture or illustration. There are three pictures you should change first. You'll notice that the picture on the main page is the same as the picture on the other pages (i.e. Sounds and Letters; Basic Sentence Structure). In fact, they refer to the same image, and changing the original one will affect the rest. The picture is named placeholder.png. The recommended dimensions are 500x500 pixels. Any images that do not fit these dimensions will be rescaled and may look distorted. Simply replace the image with another with your own, and this will cause the pictures on the other pages to change as well. The name should still be placeholder.png and in PNG format. You can easily change the format in editors like Paint.
Next you may want to change the picture located in the dictionary web pages. This is situated in the /dictionary folder, and named background_dictionary.jpg. The recommended dimensions are 1280x350 pixels, but generally, you may want your images to be wider. Again, replace the image using the same name and format.
Finally, changing the picture in the /phrasicon folder will alter the images in the phrasicon web pages, in the same way as the dictionary image. The image is named background_phrasicon.jpg and in JPG format. The recommeded dimensions are, again, 1280x350 pixels. Replace the image using the same name and format.
For this part, I recommend having a look at index.html or default.html located directly in the main folder. Remember to always save your file onto the web host. This will alter the web page so be sure to refresh in order to look at your changes.
The head element holds information that describes what's on the page. There are head elements each web page therefore you may want to refer back to this section. They can be found inside the head tags, <head>[...]</head> For example, the title that appears on the top of your browser for the documentation should read 'Template for Multi-Layered Language Learaning Resources', and this is called the page title. The head elements that you should change are: page title, description, author, copyright.
The header on the tab of your browser represents the title of the page. Therefore, changing the title will change the header of the tab. They are in contained within title tags, <title>Template for Multi-Layered Language Learaning Resources</title>. Replace the content inside the tags to modify the page title.
The description briefly talks about the purpose of the website. This is what appears on search engines such as Google when you are looking for the website. For example, when you type in 'Microsoft' into Google, you will find the description 'At Microsoft our mission and values are to help people and businesses throughout the world realize their full potential.' The description looks like this: <meta name="description" content="Multi-layered Language Learning Resources" />. Focus on the part that says: content="Multi-layered Language Learning Resources". Replacing the content within the quotation marks will alter the description.
The author indicates the creator of the web pages. That's you! They look like this: <meta name="author" content="User" />. Focus on content="User" and change the content between the quotation marks with the name of the author for the website.
The copyright distinguishes who the content on the website belongs to. This could be you or the community. They look like this: <meta name="copyright" content="User" />, and, again, simply swap out User with the name of the person or organization with rights to these materials.
Color...
To change the about page, go into the /about folder. Again, there are the two files, index.html and default.html. Open the one that pertains to you, and delete the other.
The about page consists of three sections. The first section describes the language. For example, where is this language spoken? Are there living speakers, if so how many? How were the resources collected? The next section informs others how they should use the website. For example, if they are interested in common expressions, they might only want to look at the everyday expressions page. The last section mentions the names of those who worked on the website, and in the preparation of the resources.
In the code, you will find comments throughout. If you want to keep the default format, and just want to change the content, look for comments that indicate which blocks of code represent the paragraphs. For example, the section 'About the Language' has two paragraphs, and the first paragraph is marked with this comment: <!-- Paragraph #1 -->.
The content is located within paragraph tags that look like this: <p>This is content inside a paragraph tag.</p>. Simply replace This is content inside a paragraph tag, save, and this should modify the text displayed on the page.
Perhaps you only want to use a single paragraph. In that case, you can delete the second paragraph which is enclosed in paragraph tags (or <p></p>). Delete the content including the tags, <p>[...]</p>.
Others may want to use only a single section. Look for comments that indicate the start of the section you want to delete (eg. <!-- The How to Use section starts here...-->), and the end of the section, <!-- ...and ends here. -->. Then, delete the lines of code between the two comments. Remember that you can comment out these lines of code rather than deleting in the event that you may want to use these sections at another time.
If you want to change the name of the sections, look for the default section names in the code, and replace them with the desired name. There should be two places where each section name appears - within the menu bar, and within their respective sections.
## Sounds and Letters
To change the sounds and letters page, go into the /sounds folder from /public_html. Again, there are the two files, index.html and default.html. Open the one that pertains to you, and delete the other.
The about page consists of four sections. The first section is the introduction to the sounds section. For example, you may want to briefly discuss what users should expect in the sounds section. The next section contains the sound matrix, and a more in-depth explanation of the sounds in your language, and how it is written down or how one might type into their electronic devices. The third section introduces the vowels and consonants section. The last section is where you might want to place videos training the learner about the vowels and constants of the language.
In the code, you will find comments throughout. If you want to keep the default format, and just want to change the content, look for comments that indicate which blocks of code represent the paragraphs. For example, the section 'Sounds Section' contains one paragraph, is marked with this comment: <!-- Paragraph #1 -->. This is followed by the 'Sound Matrix Section' which also has one paragraph, indicated by the comment: <!-- Paragraph #2 -->.
The content is located within paragraph tags that look like this: <p>This is content inside a paragraph tag.</p>. Simply replace This is content inside a paragraph tag, save, and this should modify the text displayed on the page.
Next, you may want to insert your own images. Look for comments that read <!-- Image goes here. -->. There are two locations in the file - in the Sounds Section, and the Vowels and Consonants section. Replace ../placeholder.png as you did in the previous section 'Images, Head Element, Colors' - look back at the instructions again if this is unfamiliar. The recommended image size if 400x400 pixels.
Now, you may want to edit the sound matrix. The sound matrix is set up as a table like the ones you can find in Word or Excel. The default matrix has the dimensions 6x5, or 6 rows and 5 columns. Each row is indicated by the comments: <!-- Table Row #x -->, where x is any number from 1 to 6. In each row, you will see code that looks like this <td class="click_sound" onclick="ipa('a')">a</td>. Each one of these represents a column within that row. For example, table row #1 contains five of these, and therefore has five columns. You may notice already that each one contains a unique English letter. Let's imagine the language you are working on does not contain the letter b or perhaps you want to represent it instead with B - a capital 'b'. Looking at the existing code: <td class="click_sound" onclick="ipa('b')">b</td>, change the letter 'b' that is beetween the angle brackets. It should look like this: <td class="click_sound" onclick="ipa('b')">B</td>.
You may probably want to also change the other 'b' contained within ipa('b'), but wait! Let's imagine again that you have a soundfile containing the sound represented by 'B', and you name the soundfile bilabial_trill.wav. You will then want to replace 'b' to the name of the soundfile so that it looks like this: ipa('bilabial_trill'), and the larger piece of code looks like this: <td class="click_sound" onclick="ipa('bilabial_trill')">B</td>. Now you can change cells in the matrix. If your intended table does not match the default dimensions, adjust the table by copying and pasting relevant rows/columns.
You may now be wondering where to store soundfiles, and in what format they should be. In the /sounds folder contain the index or default file you are editing, there is another folder called /sound. (If the /sound folder is missing, create a new folder and name it 'sound'.) Your soundfiles should be placed in here, and they should be in wav format. If they are in mp3 format, you can easily convert them using an audio editor software like Audacity or Praat.
Finally, you may want to alter the videos section. In your /sounds folder, you may notice there is also a /video folder. If it isn't there, create it. This is where you should put any videos that you want displayed on the sounds and letters page. In attempts to accomodate the many different browsers, you may want to create different formats of the videos - we made videos in mp4, webm, and ogv formats. If you are concerned about a snapshot appearing before the video is displayed, you might also want to place a poster of the video in the folder /img. Again, if the /img is not there, simply create it.
In the code, find the video section indicated by the comment <!-- Videos Section startss here... -->. The video buttons appear in subsections. Within the tags <div class="row">[...]</div>, there are two buttons, each bringing up a video. Each video is futher enclosed within the tags <div class="large-6 small-12 columns">[...]</div>. Look for the comments that read <!-- Sound #x Video -->. Right above, there should be: <p>Sound #x</p>. Replace Sound #x to change the wording of the header for the button. Now, below the code mentioned previously, <!-- Sound #x Video -->, will be the following code: <a class="button secondary" href="#" data-reveal-id="tempx">Watch</a>. Replace the default id tempx to a unique id. For example, if your video is about bilabial trills, you may want to call your id bilabial_trill.
Next, look for the other comment that reads <!-- Sound #x Video starts here... -->. Directly below there should be the following: <div id="tempx" class="reveal-modal small" data-reveal>. Replace tempx in id="tempx" with the same unique id as before. For example, if you named you id before as bilabial_trill, then you will enter the same content here. Below the line of code you just made changes to, there is <h2>Sound #x</&ggt;. Change Sound #x to the same wording of the header for the button. We're almost done! Look for the comment <!-- Video -->. In the following four lines, replace placeholderx with the name of the video you want displayed. Make sure that your video matches the correct button. One way to tell is by looking at the wording of the header for the button.
Note that if you wanted to create more buttons, copy and paste the following: <div class="row"></div> directly after the comment that reads <!-- Sound #1 and #2 Videos start here... -->. If you want to create exactly two buttons, simply copy and paste the existing code that inclues the Sound #1 Video and Sound #2 Video indicated by the comments that read <!-- Sound #x Video starts here --> and <!-- ...Sound #x Video ends here -->. If you only want to create one button, include only the lines between one of the sound videos. Each <div class="row"></div> should contain at most two buttons, as written in the existing code.
## Everyday Expressions
To change the everyday expressions page, go into the /expressions folder. Again, there are the two files, index.html and default.html. Open the one that pertains to you, and delete the other.
In the code, you will find comments throughout. If you want to keep the default format, and just want to change the content, look for the comment: <!-- Paragraph #1 -->. Below, there should be the following tags <p align="center" style="font-size:1.2em">[...]</p>. Replace the content enclosed within the tags. Next, you may want to change the image. Look for the comment: <!-- Image goes here. -->. In the line that reads background: url("background_expressions.jpg");, change background_expressons.jpg to the image you want displayed on the page. You may need to resize your image a few time to get the exact dimensions.
If you successfully edited the sounds and letters page, changing the videos in the expressions page should be no problem. In your /expressions folder, you may notice there is also a /video folder. If it isn't there, create it. This is where you should put any videos that you want displayed on the sounds and letters page. In attempts to accomodate the many different browsers, you may want to create different formats of the videos - we made videos in mp4, webm, and ogv formats. If you are concerned about a snapshot appearing before the video is displayed, you might also want to place a poster of the video in the folder /img. Again, if the /img is not there, simply create it.
In the code, find the video section indicated by the comment <!-- Expessions #1 and #2 Videos start here... -->. The video buttons appear in subsections. Within the tags <div class="row">[...]</div>, there are two buttons, each bringing up a video. Each video is futher enclosed within the tags <div class="large-6 small-12 columns">[...]</div>. Look for the comments that read <!-- Expression #x Video -->. Right above, there should be: <p>Sound #x</p>. Replace Expression #x to change the wording of the header for the button. Now, below the code mentioned previously, <!-- Expression #x Video -->, will be the following code: <a class="button secondary" href="#" data-reveal-id="expressionx">Watch</a>. Replace the default id expressionx to a unique id. For example, if your video is about the expression "Hello", you may want to call your id hello.
Next, look for the other comment that reads <!-- Expression #x Video starts here... -->. Directly below there should be the following: <div id="expressionx" class="reveal-modal small" data-reveal>. Replace expressionx in id="expressionx" with the same unique id as before. For example, if you named you id before as hello, then you will enter the same content here. Below the line of code you just made changes to, there is <h2>Expression #x</&ggt;. Change Expression #x to the same wording of the header for the button. We're almost done! Look for the comment <!-- Video -->. In the following four lines, replace placeholderx with the name of the video you want displayed. Make sure that your video matches the correct button. One way to tell is by looking at the wording of the header for the button.
Note that if you wanted to create more buttons, copy and paste the following: <div class="row"></div> directly after the comment that reads <!-- Expression #1 and #2 Videos start here... -->. If you want to create exactly two buttons, simply copy and paste the existing code that inclues the Expression #1 Video and Expression #2 Video indicated by the comments that read <!-- Expression #x Video starts here --> and <!-- ...Expression #x Video ends here -->. If you only want to create one button, include only the lines between one of the sound videos. Each <div class="row"></div> should contain at most two buttons, as written in the existing code.
## Talking Dictionary
Enter into the /dictionary folder which contains the following files and folders.
• update: Stores the data entry components.
• sounds: Stores sound files.
• js: Stores JavaScript files. Do not change.
• css: Stores CSS files.
• word.php: Contains contents for the word entry.
• porterstemmer.php: Stemmer algorithm. Do not change.
• index.php: Contains contents for the main dictionary web page.
• dictionary.xml: Stores all the dictionary entries.
• category.php: Contains contents for the letter category web page.
• background_dictionary.jpg: Main image for the dictionary web pages.
First, go in the index.php file. To change the header of the dictionary, look for the comment <!-- Title of the page. --> and replace Online Talking Dictionary Template. Next, find the comment <!-- Search by letter (title). --> and alter the content for the languages you are working with. Source (language) refers to the language that the resources were created for. If you are also using a language different from English as the language you are translating into, known in this document as the reference (or target) language, then you may also want to change replace English. The steps so far apply to the files category.php and word.php as well.
In the event that English is not being used as the reference language, search for the comment <!-- Search by letter (A-Z). --> and below, you will see lines of code that look like this: <li><a href="../dictionary/category.php?letter=e">e</a></li>. If you language has an alphabet that is similar to English, you can replace the letters in the following way. First, focus on the code that reads [...]letter=e" and [...]>e</a> in the example given. Then replace the e in both occurences with the desired letter. For example, if the reference language is French, then you may want to add é. The line of code will then look like this: <li><a href="../dictionary/category.php?letter=é">é</a></li>.
Search for the comment <!-- Language options. -->. In the code that says <option value="source">Source</option>, alter the word Source (the one with the capitalized 'S'). Make sure not to change the source in value="source". If English is not the reference language, change English in <option value="english">English</option>. Again, do not change english in value="english" even if the primary language of your website is in a different language. The steps so far apply to the files category.php and word.php as well.
Finally, find the comment <!-- The About section starts here... --> which is a section that talks about the dictionary. First, you may want to change the header of the section. In the code <h4 class="subheader">About the Dictionary</h4>, replace the content that reads About the Dictionary. Next, you might want to include how many entries are currently in the dictionary, or how the user should view each entry. You can input the number of existing entries by typing in <?php echo $count ?> - or example, your piece of code may look like this: <p>There are <?php echo$count ?> entries in the dictionary .</p>. Before editing the paragraphs, refer to the About the Materials section if you have not already as it describes the process more in depth.
When you search for a word and no results are found, you will be given an option to try an extended search. Using the extended search will execute the porterstemmer.php file. For example, let's say that the dictionary contains the word 'flower' but not the word 'flowers'. Therefore, searching for 'flowers' will return no results. Using the extended search will stem 'flowers' by removing the -s and searches for 'flower'. More information can be found here.
Now, look into the dictionary.xml file. The XML file follows the E-MELD Best Practices in Digital Language Documentation. Locate the opening and closing tags for <metadata>[...]</metadata>. The metadata is a description about the resources which follows the OLAC (Open Language Archives Community) standards and recommendations found here - they are used for archiving purposes. For example, it indicates who created the sources, what languages are involved, and the title of the database. The first twenty lines should look like this.
<title>Title of Dictionary Database</title>
• This is the title of your dictionary database. Replace Title of Dictionary Database. (Ex. Dictionary Database of Northern Pomo) between the tags.
<contributor type="olac:role" code="primary investigator">Primary Investigator</contributor>
• This indictes who the primary investigator is, or the person leading the creation of the resources. Replace Primary Investigator between the tags.
<contributor type="olac:role" code="annotator">Annotator #1</contributor>
• This indicates who the annotators are for the dictionary database. There are five fields, but you don't have to fill them all. If you want to create more, simply copy and paste the following line of code: <contributor type="olac:role" code="annotator">Annotator #x</contributor>. Repace Annotator #x where x is any number between the tags.
<contributor type="olac:role" code="creater">Creator</contributor>
• This indicates the creator of the dictionary database. This is usually the technician, or the person setting up the template. Replace Creator between the tags.
<contributor type="olac:role" code="sponsor">Sponsor</contributor>
• This indicates the funding agencies. For example, if you project is supported by the National Science Foundation (NSF), you may include it here. Replace Sponsor between the tags.
<modified type="dcterms:W3CDTF">Last Modified</modified>
• This indicates when the dictionary database was last modified. Replace Last Modified between the tags.
<format type="dcterms:IMT">text/xml</format>
• This is the format of the dictionary database. Do not change.
<language type="olac:language" code="abc" lang="abc">Source</language>
• This indicates the language you are working on to document and revitalize. There are three pieces to focus on. First, look at code="abc". This represents the language code. Most of the world's languages have a specific ISO 639-3 code that can be found here. Locate the code for your language and replace abc with the new code. Do this for lang="abc", also replacing abc. Finally, replace Source between the tags with the name of the language you are working on.
<language type="olac:language" code="eng" lang="eng">English</language>
• This indicates the language that is familiar to the target audience, or the language in which these language materials are translated into. In the same way as before, edit the code="eng", lang="eng", and English between the tags if the language of instruction is not English.
<subject type="olac:language" code="abc" lang="abc">Source</subject>
• This indicates the subject matter of the dictionary database. Since the dictionary is documenting the language you are working on, the three pieces of information, code"abc", lang="abc", and Source should be the same as <language type="olac:language" code="eng" lang="eng">English</language>.
<subject type="olac:language" code="eng" lang="eng">English</subject>
• This also indicates the subject matter of the dictionary database. The (target) language you are using as a reference for your source language is also the subject of this dictionary. Therefore, if the language is not English, follow the same instructions for <language type="olac:language" code="eng" lang="eng">English</language>
The dictionary XML file is organized in the following configuration. Creating new entries, modifying existing ones, and deleting unwanted entries are typically done through the update interface. Alternatively, you may manually update the database within the XML file, but do so carefully.
• <entry id="0">[...]</entry>
• All entries start and end with entry tags, and each opening tag has the attribute ID. Each entry has a unique ID generated by the computer.
• <form>[...]</form>
• Form represents the transcription of the word. For example, some people may create a writing system (known as orthography), others may transcribe the words using the English alphabet, and some may use the International Phonetic Alphabet (IPA).
• <orth>[...]</orth>
• Orth(ography) (or writing system) indicates how the words are represented on paper, or on the computer. This is where the words are entered in from the language you are working on.
• <sense>[...]</sense>
• Sense indicates the word senses, or the meaning of the word in the reference language, or the primary language that is used to describe the language you are working on.
• <cit type="translation" lang="en">[...]</cit>
• This indicates the fields that will be translations for the given word in the target language, or the language used as a reference.
• <usg type="hyper">[...]</usg>
• This is where the hypernym for the entry is entered in.
• <quote>[...]</quote>
• This is where the translation for the word is entered in.
• <gramGrp>[...]</gramGrp>
• This indicates the fields that are part of the grammatical (or linguistic) descriptions that appear in each entry. Grammatical descriptions include parts-speech, etc.
• <pos>[...]</pos>
• This is where you enter in the parts of speech for the word.
• <note>[...]</note>
• This is where you can add more description about the entry. For example, you may want to discuss when the word is used, or its etymology.
• <media mimetype="" url=""/>
• This indicates the the audio format and name of the sound file. For example, if your file is dog.wav, then the code will look like this: <media mimetype="audio/wav" url="dog.wav"/>.
• <ref>[...]</ref>
• This is where you enter in the reference for the sound file. For example, this might be where the sound file was found such as a cassette or a CD, and the speaker. This is for documentation and archival purposes.
• <extraAnno>[...]</extraAnno>
• These are extra layers of annotation and are commented out by default. This is discussed in depth later on.
The dictionary.xml file was designed to be both human- and machine-readable while keeping in line with the standards. If you plan on altering the format of the dictionary database, be sure to refer to the TEI encoding standards here, as well as the other standards mentioned before.
Now, enter into the /dictionary/update folder which is organized in the following way.
• uploadFiles.php: Contains code for uploading sound files to the /dictionary/sounds folder. Do not change.
• showRecords.php: Contains code for the show record functionality in the interface.
• interface.php: Contains content for the data entry interface web page.
• insert.php: Contains code to insert data into dictionary.xml.
• index.php: Contains contents for the update main page.
The first thing you may want to do is change the username and password of the update webpage. In the index.php file, look for the comment // Username and password. The default username is abc and the default password is 123. Replace the username and password under the comment with your own username and password.
Go into the interface.php file. Look for the comments <!-- Source --> - there are two places were they appear. Beneath these comments, you will find the term Source language being used. Replace it with the language you are working on. If you are working with a language that is not English as a reference language, look for <!-- English --> and replace English. Next, look at the showRecords.php file, and find the comment // Source. Change Source in echo "<th>Source</th>"; to, again, the language you are working on. If the other language you are using is not English, look for the comment // English and in the same way as before, replace English in the line of code below.
## Phrasicon
Enter into the /phrasicon folder which contains the following files and folders.
• update: Stores the data entry components.
• sounds: Stores sound files.
• js: Stores JavaScript files. Do not change.
• css: Stores CSS files.
• word.php: Contains contents for the word entry.
• phrasicon.xml: Stores all the dictionary entries.
• index.php: Contains contents for the main dictionary web page.
• category.php: Contains contents for the letter category web page.
• phrasicon_dictionary.jpg: Main image for the phrasicon web pages.
First, go in the index.php file. To change the header of the phrasicon, look for the comment <!-- Title of the page. --> and replace Online Phrasicon Template. Next, find the comment <!-- Search Menu (title)-->. The language you are translating into is known in this document as the reference (or target) language. If the reference language is English, you may skip this part, if not then you may want to change replace English. The steps so far apply to the files category.php and word.php as well.
In the event that English is not being used as the reference language, search for the comment <!-- Search by letter (A-Z). --> and below, you will see lines of code that look like this: <li><a href="../phrasicon/category.php?letter=e">e</a></li>. If you language has an alphabet that is similar to English, you can replace the letters in the following way. First, focus on the code that reads [...]letter=e" and [...]>e</a> in the example given. Then replace the e in both occurences with the desired letter. For example, if the reference language is French, then you may want to add é. The line of code will then look like this: <li><a href="../phrasicon/category.php?letter=é">é</a></li>. The steps so far apply to the files category.php and word.php as well.
Search for the comment <!-- Language options. -->. In the code that says <option value="source">Source</option>, alter the word Source (the one with the capitalized 'S'). Make sure not to change the source in value="source". If English is not the reference language, change English in <option value="english">English</option>. Again, do not change english in value="english" even if the primary language of your website is in a different language. The steps so far apply to the files category.php and word.php as well.
Finally, find the comment <!-- The About section starts here... --> which is a section that talks about the phrasicon. First, you may want to change the header of the section. In the code <h4 class="subheader">About the Phrasicon</h4>, replace the content that reads About the Phrasicon. Next, you might want to include how many entries are currently in the phrasicon, or how the user should view each entry. You can input the number of existing entries by typing in <?php echo $count ?> - for example, your piece of code may look like this: <p>There are <?php echo$count ?> entries in the phrasicon.</p>. Before editing the paragraphs, refer to the About the Materials section if you have not already as it describes the process more in depth.
Now, look into the phrasicon.xml file. The XML file follows the E-MELD Best Practices in Digital Language Documentation. Locate the opening and closing tags for <metadata>[...]</metadata>. The metadata is a description about the resources which follows the OLAC (Open Language Archives Community) standards and recommendations found here - they are used for archiving purposes. For example, it indicates who created the sources, what languages are involved, and the title of the database. The first twenty lines should look like this.
<title>Title of Phrasicon Database</title>
• This is the title of your phrasicon database. Replace Title of Phrasicon Database. (Ex. Phrasicon Database of Medumba) between the tags.
<contributor type="olac:role" code="primary investigator">Primary Investigator</contributor>
• This indictes who the primary investigator is, or the person leading the creation of the resources. Replace Primary Investigator between the tags.
<contributor type="olac:role" code="annotator">Annotator #1</contributor>
• This indicates who the annotators are for the phrasicon database. There are five fields, but you don't have to fill them all. If you want to create more, simply copy and paste the following line of code: <contributor type="olac:role" code="annotator">Annotator #x</contributor>. Repace Annotator #x where x is any number between the tags.
<contributor type="olac:role" code="creater">Creator</contributor>
• This indicates the creator of the phrasicon database. This is usually the technician, or the person setting up the template. Replace Creator between the tags.
<contributor type="olac:role" code="sponsor">Sponsor</contributor>
• This indicates the funding agencies. For example, if you project is supported by the National Science Foundation (NSF), you may include it here. Replace Sponsor between the tags.
<modified type="dcterms:W3CDTF">Last Modified</modified>
• This indicates when the phrasicon database was last modified. Replace Last Modified between the tags.
<format type="dcterms:IMT">text/xml</format>
• This is the format of the phrasicon database. Do not change.
<language type="olac:language" code="abc" lang="abc">Source</language>
• This indicates the language you are working on to document and revitalize. There are three pieces to focus on. First, look at code="abc". This represents the language code. Most of the world's languages have a specific ISO 639-3 code that can be found here. Locate the code for your language and replace abc with the new code. Do this for lang="abc", also replacing abc. Finally, replace Source between the tags with the name of the language you are working on.
<language type="olac:language" code="eng" lang="eng">English</language>
• This indicates the language that is familiar to the target audience, or the language in which these language materials are translated into. In the same way as before, edit the code="eng", lang="eng", and English between the tags if the language of instruction is not English.
<subject type="olac:language" code="abc" lang="abc">Source</subject>
• This indicates the subject matter of the phrasicon database. Since the phrasicon is documenting the language you are working on, the three pieces of information, code"abc", lang="abc", and Source should be the same as <language type="olac:language" code="eng" lang="eng">English</language>.
<subject type="olac:language" code="eng" lang="eng">English</subject>
• This also indicates the subject matter of the phrasicon database. The (target) language you are using as a reference for your source language is also the subject of this phrasicon. Therefore, if the language is not English, follow the same instructions for <language type="olac:language" code="eng" lang="eng">English</language>
The phrasicon XML file is organized in the following configuration. Creating new entries, modifying existing ones, and deleting unwanted entries are typically done through the update interface. Alternatively, you may manually update the database within the XML file, but do so carefully.
• <phrase id="0">[...]</phrase>
• All entries start and end with entry tags, and each opening tag has the attribute ID. Each entry has a unique ID generated by the computer.
• <ref>[...]</ref>
• The reference for the sound file is entered here. For example, this might be where the sound file was found such as a cassette or a CD, and the speaker. This is for documentation and archival purposes.
• <source>[...]</source>
• Source refers to the source language. This is the language you are working with. The phrase or sentence of the source language is entered here.
• <morpheme>[...]</morpheme>
• This field indicates the morphemes you have decided to display for the phrase. The number of morphemes should be the same as the number of glosses.
• <m id="x.y">[...]</m>
• For each morpheme, they will be enclosed within the <m></m> tags. Each starting tag has an ID attribute which is generated by the computer. The ID before the decimal point refers to the ID of the entry. The ID after the decimal point refers to the number (or position) of that morpheme.
• <gloss>[...]</gloss>
• This field indicates the glosses of the morphemes. Again, the number of glosses should be the same as the number of morphemes.
• <g id="x.y">[...]</m>
• For each gloss, they will be enclosed within the <g></g> tags. Each starting tag also has an ID attribute which is generated by the computer. The ID is identical to morpheme that is glossed so that that may be co-indexed. In other words, this allows the computer to know which gloss corresponds to the correct morpheme, and vice versa.
• <translation>[...]</translation>
• This is where the translation for the phrase is entered in.
• <media mimetype="" url=""/>
• This indicates the the audio format and name of the sound file. For example, if your file is dog.wav, then the code will look like this: <media mimetype="audio/wav" url="dog.wav"/>.
• <extraAnno>[...]</extraAnno>
• These are extra layers of annotation and are commented out by default. This is discussed in depth in the next section.
While there are multiple existing XML formats for interlinear glosesd texts (IGT) (i.e. BHB, IGT-XML, XIGT), this format was designed to be both human- and machine-readable, and editable while keeping in line with the standards. This format, like the BHB model, is used to represent IGT as closely as possible, and has multiple purposes that includes facilitating computational manipulation of the data, and allowing these resources to be used for archiving.
Now, enter into the /phrasicon/update folder which is organized in the following way.
• uploadFiles.php: Contains code for uploading sound files to the /phrasicon/sounds folder. Do not change.
• showRecords.php: Contains code for the show record functionality in the interface.
• interface.php: Contains content for the data entry interface web page.
• insert.php: Contains code to insert data into phrasicon.xml.
• index.php: Contains contents for the update main page.
• autosuggest.php: Contains contents for the automatic gloss suggestion program. Do not change.
The first thing you may want to do is change the username and password of the update webpage. In the index.php file, look for the comment // Username and password. The default username is abc and the default password is 123. Replace the username and password under the comment with your own username and password.
Go into the interface.php file. Look for the comments <!-- Source --> - there are two places were they appear. Beneath these comments, you will find the term Source being used. Replace it with the language you are working on. Next, look at the showRecords.php file, and find the comment // Source. Change Source in echo "<th>Source</th>"; to, again, the language you are working on.
For some languages, you may want to add annotation layers. For example, if your language has tone, you may want to add a layer that represents tone. These extra annotation layers are formatted in the same way as the morphemes, and glosses. There are multiple files that are affected in the dictionary and phrasicon components. The files that need to be modified are the same in both components, but the directions for the separate components will differ. If you choose to add layers in the dictionary, but not in the phrasicon, then you should only edit the dictionary components.
#### Dictionary
The comments, which are referred to as add-annotation-layer comments, that you should look for in the files discussed shortly will contain the following: This is where you add annotation layers.. Depending which files you open, the comments may appear as <!-- This is where you add annotation layers. -->, /* This is where you add annotation layers. */, or // This is where you add annotation layers.. In the dictionary.xml file, find the add-annotation-layer comment, and then uncomment the desired number of additional annotation layers. The default names of these layers are ExtraAnno (eg. <h4 class="subsubheader">ExtraAnno1</h4>), and extraAnno (eg. <!-- <extraAnno1/> -->). By default, there are five extra annotation layers that are embeddded in comments. In order to use these layers, you should uncomment them. For example, <!-- <p>This is a paragraph.</p> --> is a comment where a paragraph tag is embedded within. To uncomment, simply remove the leading <!-- and the trailing -->. You will then be left with <p>This is a paragraph.</p>.
You may also rename these layers. If so, you should only rename the layers where there are also comments that say Rename-able. If you rename the annotation layers, they must be consistent. Please refer to the TEI website, here, for naming standards. There is a rename-able comment in the dictionary.xml file. Replace the content. The first letter of your new name should not be capitalized. For example, if you wanted to rename a layer to represent tone, your code will look like this: <tone/>.
Now, in the dictionary/update folder, go into the interface.php file. There are two add-annotation-layer comments in this file. For the first add-annotation-layer comment found in the file, each layer is commented, and separated into blocks indicated by the following: <!-- ExtraAnno -->. Do not uncomment them. Below the <!-- ExtraAnno --> comment, uncomment the desired number of layers. If you are renaming, replace the content the following line <h4 class="subsubheader">ExtraAnno</h4>.The first letter should be capitalized. Using the same example for tone, it would be ><h4 class="subsubheader">Tone</h4>. For the line beneath saying <input type="text" name="extraAnno">, replace the content extraAnno between the quotation marks. Here, the first letter should not be capitalized. Keep this in mind for future changes: if the content reads ExtraAnno, the first letter of the new name should be capitalized. If the content reads extraAnno, the first letter of the new name should not be capitalized. Look for the second add-annotation-layer comment in the file, and, again, uncomment the layers you want. Replace the content extraAnno and ExtraAnno.
Next, open the insert.php file. There is one add-annotation-layer comment. Uncomment the desired number of layers. If you are renaming, replace the content. For example, in the tone example, the line of code would look like this: $entry->addChild("tone",$_POST['tone']);.
In the showRecords.php file, there are three add-annotation-layer comments. For the first one, uncomment the number of layers you want, and if renaming, replace the content. (eg. echo "<th>Tone</th>";. Do this for the second and third, but you should not be making changes to the name.
Finally, in the /dictionary folder, go into the word.php file. There are two add-annotion-layer comments. Just like before, uncomment the layers in both sections. Remember, if the comments look like this // <p>Example</p>, to uncomment, delete the two forward slashes, and they will look like this: <p>Example</p>. Again, you should not be renaming anything.
#### Phrasicon
The comments, which are referred to as add-annotation-layer comments, that you should look for in the files discussed shortly will contain the following: This is where you add annotation layers.. Depending on which files you open, the comments may appear as <!-- This is where you add annotation layers. -->, /* This is where you add annotation layers. */, or // This is where you add annotation layers.. The default names of these layers are ExtraAnno (eg. <h4 class="subsubheader">ExtraAnno1</h4>), and extraAnno (eg. <!-- <extraAnno1>[...]</extraAnno1> -->). By default, there are five extra annotation layers embedded in comments. In order to use these layers, you should uncomment them. For example, <!-- <p>This is a paragraph.</p> --> is a comment where a paragraph tag is embedded within. To uncomment, simply remove the leading <!-- and the trailing -->. You will then be left with <p>This is a paragraph.</p>. In the phrasicon.xml file, find the add-annotation-layer comment. Each layer is commented, and separated into blocks indicated by the following: <!-- ExtraAnno -->. Do not uncomment them. Below each <!-- ExtraAnno -->, uncomment the desired number of layers.
You may also rename these layers. If so, you should only rename the layers where there are also comments that say Rename-able. If you rename the annotation layers, they must be consistent. Please refer to the TEI website, here, for naming standards. There is a rename-able comment in the dictionary.xml file. Replace the content. The first letter of your new name should not be capitalized. For example, if you wanted to rename a layer to represent tone, your code will look like this: <tone>[...]</tone>. Do not rename the tags <extra&l;[...]</extra<.
Now, in the phrasicon/update folder, go into the interface.php file. There are two add-annotation-layer comments in this file. For the first add-annotation-layer comment found in the file, each layer is commented, and separated into blocks indicated by the following: <!-- ExtraAnno --> just like in the phrasicon.xml fil. Do not uncomment them. Below each <!-- ExtraAnno --> comment, uncomment the desired number of layers. If you are renaming, replace the content the following line <h4 class="subsubheader">ExtraAnno</h4>.The first letter should be capitalized. Using the same example for tone, it would be ><h4 class="subsubheader">Tone</h4>. Look for the second add-annotation-layer comment in the file, and, again, uncomment the layers you want. Replace the content extraAnno and ExtraAnno. Keep in mind that if the content reads ExtraAnno, the first letter of the new name should be capitalized. If the content reads extraAnno, the first letter of the new name should not be capitalized. Therefore, if the layer was renamed for tone, the code will look like this: <option value="tone">Tone</option>.
Next, open the insert.php file. There are two add-annotation-layer comments. In the first one, there are five blocks of commented code that correspond to the five extra annotation layers. Uncomment the number of layers you want by removing the /* and */. If renaming, in the line of code that says $extraAnno1 =$entry->addChild('extraAnno1');, replace extraAnno1 only in addChild('extraAnno1');. So for tone, it will look like this: $extraAnno1 =$entry->addChild('tone');. For the second add-annotation-layer comment, again, uncomment the desired number of layers. If renaming, in the code that reads elseif (\$field=="extraAnno1") {, replace extraAnno1.
In the showRecords.php file, there are two add-annotation-layer comments. For the first one, uncomment the number of layers you want, and if renaming, replace the content. (eg. echo "<th>Tone</th>";. Now, look for the second add-annotation-layer comment. Again, there are five blocks of comments with code in them. Each of these blocks are beneath another comment that says // ExtraAnno. Do not uncomment these. Instead, uncomment the block of code underneath.
Finally, in the /phrasicon folder, go into the word.php file. There are two add-annotion-layer comments. Just like before, uncomment the layers in both sections. For the first one, each layer consists of multiple lines of code enclosed within the comment tags. The second one is simply five lines of code for the five layers. You should not rename any of the content in this file.
## Stories and Texts
To change the stories and texts page, go into the /texts folder. Again, there are the two files, index.html and default.html. Open the one that pertains to you, and delete the other.
In the code, you will find comments throughout. If you want to keep the default format, and just want to change the content, look for the comment: <!-- Paragraph #1 -->. Replace the content enclosed within the paragraph tags. Next, you may want to change the image. Look for the comment: <!-- Image goes here. -->. In the line that reads background: url("img/background_texts.jpg");, change background_texts.jpg to the image you want displayed on the page. Place your image in a folder named /img within the /texts folder. If it is not there, simply create it. You may need to resize your image a few time to get the exact dimensions.
In the code, find the text buttons section indicated by the comment <!-- Texts #1 and #2 Buttons start here... -->. The buttons directing users to the texts appear in subsections. Within the tags <div class="row">[...]</div>, there are two buttons. Look for the comments that read <!-- Text #x Video --> where x is the number 1 or 2. Directly below should be the following code: <a href="textx" class="radius button text">Text #1</a>. Replace textx in href="textx" to name of the folder that will contain the materials relating to that particular text. For example, in the default template, there is a folder in your /texts folder named 'text1'. This is where you may want to place materials of a text. However, you may also rename your folder. Let's imagine we renamed the folder to 'hydra' because our text is about Hydra. Then, we would replace textx with hydra so that it becomes <a href="hydra" class="radius button text">Text #1</a>. Next, you may want to change the content that reads Text #1 between the angle brackets. Using the same example with Hydra, we might name it Hydra so that the entire code becomes <a href="hydra" class="radius button text">Hydra</a>.
Note that if you wanted to create two more buttons, copy from <div class="row"> located right after the comment <!-- Texts #1 and #2 Buttons start here... -->, up to </div> directly before the comment that reads <!-- ...Texts #1 and #2 Buttons end here -->. Paste the lines of code right after the comment just mentioned. If you want to create only one button, simply follow the same steps, but delete one of the text buttons, indicated by <!-- Texts #1 section starts here... -->[...]<!-- ...Texts #1 section ends here -->.
The next step is to edit the files containing the content for each text. Go into the \textx folder where x represents the number 1 or 2. For our example, we will be referring to \text1. There are the two files, index.html and default.html. Open the one that pertains to you, and delete the other. In the code, you will find comments throughout. If you want to keep the default format, and just want to change the content, look for the comment: <!-- Paragraph #1 -->. Replace the content enclosed within the paragraph tags. You may now want to change the background image. Look for the comment: <!-- Image goes here. -->. In the line that reads background: url("img/background_texts.jpg");, change background_texts.jpg to the image you want displayed on the page. Place your image in the /img foler within the /texts folder, not in the current directory. You may need to resize your image a few time to get the exact dimensions.
Next, you may want to insert your own videos. In your /texts folder, you may notice there is also a /video folder. If it isn't there, create it. This is where you should put any videos that you want displayed on the sounds and letters page. In attempts to accomodate the many different browsers, you may want to create different formats of the videos - we made videos in mp4, webm, and ogv formats. If you are concerned about a snapshot appearing before the video is displayed, you might also want to place a poster of the video in the folder /img within the /texts folder.
Locate the comment: <!-- Video of text. -->. Below is another comment with lines of code enclosed within. Remove the comment tags <!-- and -->. Then, replace placeholder in these lines of code to the name of your video file. At this point you'll also notice the comment: <!-- Placeholder -->. Delete the line beneath that reads <img width="100%" src="../img/video_placeholder.png">. The next step is to insert images of your texts if you have them. Place these images into the /img folder within /texts. Locate the comments <!-- PDF #x -- >, and below the code should look like this: <img src="../img/placeholder_pdf.png" alt="textx">. Replace placeholder_pdf to the name of the image of the specific page of text. If your text consists more than four images, simply copy the pieces of code from <!-- Text PDF #x starts here... --> to <!-- ...Text PDF #x ends here -->, and paste it right after the comment that reads <!-- ...Text PDF #4 ends here -->. If your text consists of less than four images, then instead of copying the code between the start and end comments, delete them.
If you have created mobile apps for the language you are working on, you may want to provide a brief description including links to the download page.
In the /apps folder, open the index.html or default.html file. If you are unsure which file to open, please read the previous sections. To change the description of the mobile apps, find the comment <!-- Paragraph #1 --> and edit the contents.
If you want to insert a link to the iOS app (i.e. iPhone, iPad), look for the comment indicating the iOS section, <!-- The iOS section starts here... -->. Within the section, there is another comment that says <!-- Button to link. -->. Below, there is a line of code that reads <a class="button secondary" href="#">Download</a>. To add a link, replace # located between the quotation marks directly after href= with the full link to the download page. Then, alter the notification Download to signal users to click there. This process is the same for the Android version.
Perhaps you only have a mobile app for one platform. For example, if you only have an iOS app, and have no plans to develop an Android app, you will only want to have a single section. Look for comments indicating the start of the section you want to delete, and the end of the section. Then, delete the lines of code between the two comments.
## Contact Page
The contact page allows users to contact the creators of the resources. The user enters in their name, their email, and their message. When they submit, the email will be sent to whichever email is supplied.
To supply an email, go into the /contact folder and open send_email.php. Look for the comment that says // Your email goes here. and then change the content between quotation marks that reads enter email here to your own email address. Next, you may want to change the subject header. Look for the comment // Email Subject Header you have the option of altering the default subject Language Tools: New Message. Then, you may want to change the contents, or body, of the message. Find the comment that says // Email Body Message and change the default content A new message has been sent from the Language Tools website...\n\n.
Apart from perhaps altering the head elements in the index.html or default.html files, the template was made so that no other changes must be made. Feel free to edit the file to fit your needs.
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{}
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# How to create visible reflections in shallow water?
Assumption: The only lights I have are candle, table lamp, and sunlight.
What would I need to create visible reflection of an object in the shallow water contained in a 5 liter bucket? Is it even possible anyhow?
What kind of light out of the three will maximize the visibility of the reflection in this case?
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I can't get a grip on that phrase "distinguishable reflection". What do you mean by that? Is this some kinda home experiment you wanna do? ;-) – Waffle's Crazy Peanut Apr 17 '13 at 11:10
is the 5 litre bucket full? Is this a homework question? Have you tried coming up with any solutions yourself so far? if so, what have you tried? – RhysW Apr 17 '13 at 11:11
@RhysW: This doesn't look like a homework question to me. It looks like some home-experiment..! – Waffle's Crazy Peanut Apr 17 '13 at 11:12
@CrazyBuddy ive had homework questions before that were 'how would you do this? try it and tell us what you found' i just want to clarify :) – RhysW Apr 17 '13 at 11:14
@RhysW ? Is this a homework question? Have you tried coming up with any solutions yourself so far? I am NOT in school, nor I am a Physics student, nor I intend to become one. My hobby is "Photography". I live in an industrial area which doesn't have any ponds/lakes so I was wondering if there is some way to get creative at home with a bucket of water. Well, the bucket is basically of 10 litres. I can fill it to the brim if it is required. – TheIndependentAquarius Apr 17 '13 at 11:38
If the problem with shallow water is that you see the walls and the bottom instead of only the reflection, I would just use a black bucket. Or somehow make bucket's inners black.
Moreover a bucket is a bit unpractical in this case, just a really black tray with water should suffice.
Another option is to make water black itself, like using coffee.
UPD All three light sources should behave identically in terms of reflection provided the water/tray is really black. However in real world the brighter the light the darker color is required. I just advise you to try it yourself.
There is another matter you might be interested in. The portion of light reflected greatly depends on the incident angle. If the light goes almost parallel to the surface it will be reflected almost completely. So if you are trying to imitate a reflection of houses or trees on a river bank (tangent light) you'll get brighter reflection than if you are looking straight down into the bucket.
The logic is quite simple. When the light hits the water most of it passes through the surface, the smaller part is reflected. In deep water the light that passed through eventually dissipates and does not return back. All you see in that case is the reflected light.
In shallow water the light hits the bottom and bounces back riving with one that reflected.
So all you need to make reflections visible is to eliminate the light that comes back from the bottom. Either paint the bottom black or make water black.
However I don't think it is how I was reasoning. I've just remembered an analogous situation with windows. When you are indoors at night with room light on your windows are essentially mirrors.
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Great!! I will definitely try with the black surface. Now I really wish I were a Physics student! What is the logic behind your answer, BTW. Just curious to know. – TheIndependentAquarius Apr 17 '13 at 11:48
Is reflections in a cup of black coffee visible enough? Sorry, I haven't seen or drunk black coffee so I don't know. – TheIndependentAquarius Apr 17 '13 at 11:50
@AnishaKaul Just make coffee without milk, I thought it should be black. I mentioned coffee because it seems to be readily available. You can use ink instead or something like that. – Yrogirg Apr 17 '13 at 12:01
Great explanation! Thankful to you. – TheIndependentAquarius Apr 17 '13 at 12:02
QUE: What kind of light out of the three will maximize the visibility of the reflection in this case? – TheIndependentAquarius Apr 17 '13 at 12:19
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# What is the equation of the line with slope m= 14/25 that passes through (23/5, (-23)/10) ?
May 7, 2016
$y = \frac{14 x}{25} + 4 \frac{219}{250}$
This is a somewhat unrealistic question, and becomes an exercise in arithmetic rather than maths.
#### Explanation:
There are 2 methods:
Method 1 . uses the formula $\left(y - {y}_{1}\right) = m \left(x - {x}_{1}\right)$
This is great to use if you know the slope (m) and one point, which is exactly what we have here. It involves one step of substitution and a bit of simplifying.
$\left(y - {y}_{1}\right) = m \left(x - {x}_{1}\right)$
$\left(y - \left(- \frac{23}{10}\right)\right) = \frac{14}{25} \left(x - \frac{23}{5}\right)$
$y + \frac{23}{10} = \frac{14 x}{25} - \frac{14}{25} \times \frac{23}{5} \text{ } \times 250$
$250 y + 250 \times \frac{23}{10} = 250 \times \frac{14 x}{25} - 250 \times \frac{14}{25} \times \frac{23}{5}$
$250 y + 575 = 140 x - 28 \times 23$
$250 y = 140 x + 1219$
$y = \frac{14 x}{25} + 4 \frac{219}{250}$
Method 2 uses $y = m x + c$
Subst for $m , x \mathmr{and} y$ to find $c$
$\left(- \frac{23}{10}\right) = \frac{14}{25} \times \frac{23}{5} + c \text{ } \times 250$
$250 \times \left(- \frac{23}{10}\right) = 250 \times \frac{14}{25} \times \frac{23}{5} + 250 c$
$- 575 = 644 + 250 c$
$1219 = 250 c$
$c = \frac{1219}{250} = 4 \frac{219}{250}$
This leads to the same equation, using values for m and c.
$y = \frac{14 x}{25} + 4 \frac{219}{250}$.
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# LA+CH7+EX6+Solved+by+주영은
## 2059 days ago by math2013
A = matrix(6,5,[1,0,2,0,0,0,1,-1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,]) print A.rref() print A.rank()
[ 1 0 2 0 0] [ 0 1 -1 0 0] [ 0 0 0 1 0] [ 0 0 0 0 1] [ 0 0 0 0 0] [ 0 0 0 0 0] 4 [ 1 0 2 0 0] [ 0 1 -1 0 0] [ 0 0 0 1 0] [ 0 0 0 0 1] [ 0 0 0 0 0] [ 0 0 0 0 0] 4
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Find the number of arrangements of the letters of the word ‘ALGEBRA’
Question:
Find the number of arrangements of the letters of the word ‘ALGEBRA’ without altering the relative positions of the vowels and the consonants.
Solution:
To find: number of arrangements without changing the relative position
The following table shows where the vowels and consonants can be placed
Consonants can be placed in the blank places
There are 3 spaces for vowels
There are 3 vowels out of which 2 are alike
Vowels can be placed in $\frac{3 !}{2 !}=3$ ways
There are 4 consonants, and they can be placed in $4 !=24$ ways
$\Rightarrow$ Total number of arrangements $=24 \times 3=72$ ways
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# an invertible element $i$ in $\mathbb Z_n$ must be coprime to $n$
Let $n$ be an integer and $i\in \{1,\cdots,n-1\}$. I want to show that $i$ is invertible in $\mathbb Z_n$ if and only if $i$ is coprime to $n$.
One way is easy. suppose $i$ is coprime to $n$ then $\alpha i +\beta n=1$ for some $\alpha,\beta \in \mathbb Z$, so $\alpha i =1 - \beta n$ hence $\alpha i \equiv 1 (mod\; n)$ and $i$ is invertible.
the other way is less obvious to me. suppose that $i$ is invertible in $\mathbb Z_n$. Why it must be coprime to $n$? my guess: suppose they are not coprime then $i=da$ and $n=db$ for some $d>1,a,b$ but since $i$ is invertible then $li=1+mn$ for some $l,m$ hence $lda=1+mdb$ so $d(la-mb)=1$ this implies that $d=\pm 1$ which is impossible since $d>1$
is this correct and is there more conceptual argument for this?
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This is correct. Another way of saying this is that the gcd of $i$ and $n$ is the smallest (in absolute value) integer, expressible as a linear combination of $i$ and $n$. – Miha Habič Nov 15 '11 at 9:56
Your argument works perfectly well. A variant with a more abstract flavour that uses your notation is to observe that $$ib=(ad)b=a(db)=an$$ so $ib \equiv 0 \pmod{n}$.
If $j$ were an inverse of $i$, then we would have $$j(ib)\equiv j\cdot 0\equiv 0\pmod{n}.$$ But $$j(ib)=(ji)b\equiv b\pmod{n}.$$ Thus $b\equiv 0 \pmod{n}$, which is impossible if $d>1$, since then $0<b<n$.
My intuition is along the lines of your second argument: if $i=da$ and $n=db$, all integer multiples of $i$ must be multiples of $d$ and hence can never be one plus a mutiple of $d$.
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# Solve with eigenfunction expansion $\frac{\partial u}{\partial t} = k \frac{\partial^2 u}{\partial x^2} + e^{-t} + e^{-2t} \cos \frac{3\pi x}{L}$
Q: Solve the following non-homogeneous problem: \begin{align*} \frac{\partial u}{\partial t} &= k \frac{\partial^2 u}{\partial x^2} + e^{-t} + e^{-2t} \cos \frac{3\pi x}{L} \\ \end{align*} With the following boundary and initial value conditions: \begin{align*} \frac{\partial u}{\partial x}(0,t) &= 0 \\ \frac{\partial u}{\partial x}(L,t) &= 0 \\ u(x,0) &= f(x) \\ \end{align*} Assume that $$2 \neq k(3\pi/L)^2$$. Use the method of eigenfunction expansion. Look for the solution as a Fourier cosine series. Assume appropriate continuity.
TEXTBOOK GIVEN ANSWER: \begin{align*} u &= \sum\limits_{n=0}^\infty A_n(t) \cos \frac{n \pi x}{L} \\ A_{n,n \neq 0, n\neq 3}(t) &= A_n(0) e^{-k \left( \frac{n \pi}{L} \right)^2 t} \\ A_0(t) &= A_0(0) + 1 - e^{-t} \\ A_3(t) &= A_3(0) e^{-k \left( \frac{3 \pi}{L} \right)^2 t} + \frac{e^{2t} - e^{-k \left( \frac{3 \pi}{L} \right)^2 t}}{k \left( \frac{3 \pi}{L} \right)^2 - 2} \\ A_0(0) &= \frac{1}{L} \int_0^L f(x) \, dx \\ A_{n \ge 1}(0) &= \frac{2}{L} \int_0^L f(x) \cos \frac{n \pi x}{L} \, dx \\ \end{align*}
My work: I fully understand how to get most of the answer, but I am stuck on the rest. Specifically, I don't understand the $$n=0, n=3$$ cases.
First, the part I fully understand:
We look for the solution as a Fourier cosine series. The right hand side is an even extended and periodized version of $$u(x,t)$$ along the $$x$$ variable.
\begin{align*} u(x,t) &\sim A_0 + \sum\limits_{n=1}^\infty A_n(t) \cos \frac{n \pi x}{L} \\ \end{align*}
The problem says we can assume appropriate continuity which means that we can assume the original, non-periodized $$u(x,t)$$ is continuous. We can apply term by term partial differentiation to both $$x$$ and $$t$$. For $$t$$, we are not periodized by $$t$$, the given function is continuous, so that's all we need. For $$x$$, we are dealing with the even extended, periodized version of a continuous function, which must be continuous, so we can use term by term partial differentiation there as well.
\begin{align*} \frac{\partial u}{\partial x} &\sim - \sum\limits_{n=1}^\infty \frac{n \pi}{L} A_n(t) \sin \frac{n \pi x}{L} \\ \frac{\partial u}{\partial t} &\sim \sum\limits_{n=1}^\infty A'_n(t) \cos \frac{n \pi x}{L} \\ \end{align*}
We also assume that $$\frac{\partial u}{\partial x}$$ is continuous. Since we are given that $$\frac{\partial u}{\partial x}(0,t) = 0 = \frac{\partial u}{\partial x}(L,t)$$, then we can see that the periodized version along the $$x$$ variable must also be fully continuous so that we can again use term by term differentiation to get:
\begin{align*} \frac{\partial^2 u}{\partial x^2} &\sim - \sum\limits_{n=1}^\infty \left(\frac{n \pi}{L}\right)^2 A_n(t) \cos \frac{n \pi x}{L} \\ \end{align*}
Now plugging that back in to the PDE:
\begin{align*} \frac{\partial u}{\partial t} &= k \frac{\partial^2 u}{\partial x^2} + e^{-t} + e^{-2t} \cos \frac{3\pi x}{L} \\ \sum\limits_{n=1}^\infty A'_n(t) \cos \frac{n \pi x}{L} &= k \left( - \sum\limits_{n=1}^\infty \left(\frac{n \pi}{L}\right)^2 A_n(t) \cos \frac{n \pi x}{L} \right) + e^{-t} + e^{-2t} \cos \frac{3\pi x}{L} \\ \end{align*}
That will be satisfied if the summation terms on the left/right side are all equal and the term on the right hand side outside the summation is zero:
\begin{align*} A'_n(t) &= -k \left(\frac{n \pi}{L}\right)^2 A_n(t) \\ A_n(t) &= A_n(0) e^{-k \left( \frac{n \pi}{L} \right)^2 t} \\ \end{align*}
Solving for the coefficients with the initial condition:
\begin{align*} u(x,t) &= \sum\limits_{n=0}^\infty A_n(t) \cos \frac{n \pi x}{L} \\ u(x,0) = f(x) &= \sum\limits_{n=0}^\infty A_n(0) \cos \frac{n \pi x}{L} \\ A_0(0) &= \frac{1}{L} \int_0^L f(x) \, dx \\ A_{n \ge 1}(0) &= \frac{2}{L} \int_0^L f(x) \cos \frac{n \pi x}{L} \, dx \\ \end{align*}
ok, so far so good. All of that lines up perfectly with the given answer. But I am unsure about how to get the rest.
From earlier, I said if the terms on the right hand side out side the summation came to zero, it would satisfy the PDE. That would mean that:
\begin{align*} e^{-t} + e^{-2t} \cos \frac{3\pi x}{L} &= 0 \\ e^{t} &= -\cos \frac{3\pi x}{L} \\ \end{align*}
I am not sure how to use this. I also don't see what to do with the problem given that $$2 \neq k(3\pi/L)^2$$
Letting
$$u \sim \sum_{n \ge 0} A_{n}(t) \cos \left( \frac{n \pi x}{L} \right)$$
then substituting into the PDE (and noting that $$1 \equiv \cos(0 \pi x/L)$$) yields
$$\sum_{n \ge 0} A_{n}'(t) \cos \left( \frac{n \pi x}{L} \right) = -k \sum_{n \ge 0} \left( \frac{n \pi}{L} \right)^{2} A_{n}(t) \cos \left( \frac{n \pi x}{L} \right) + e^{-t} \color{red}{\cos \left( \frac{0 \pi x}{L} \right)} + e^{-2t}\cos \left( \frac{3 \pi x}{L} \right)$$
Equating terms in $$\cos$$ for $$n = 0, 1, \dots$$ and letting $$C_{n}$$ be the constants of integration, we have
\begin{align} A_{0}'(t) = -k(0)+e^{-t} &\implies A_{0}(t) = -e^{-t} + C_{0} \\ &\implies A_{0}(0) = -1+C_{0} \\ &\implies A_{0}(t) = A_{0}(0) + 1 - e^{-t} \\\\ A_{1}'(t) = -k \left( \frac{\pi}{L} \right)^{2} A_{1}(t) &\implies A_{1}(t) = A_{1}(0) e^{-k \left( \frac{\pi}{L} \right)^{2} t} \\\\ A_{2}'(t) = -k \left( \frac{2 \pi}{L} \right)^{2} A_{2}(t) &\implies A_{2}(t) = A_{2}(0) e^{-k \left( \frac{2 \pi}{L} \right)^{2} t} \\\\ A_{3}'(t) = -k \left( \frac{3 \pi}{L} \right)^{2} A_{3}(t) + e^{-2t} &\implies A_{3}(t) = \frac{e^{-2t}}{-2 + k \left( \frac{3 \pi}{L} \right)^{2}} + C_{3} e^{-k \left( \frac{3 \pi}{L} \right)^{2} t} \\ &\implies A_{3}(0) = \frac{1}{-2 + k \left( \frac{3 \pi}{L} \right)^{2}} + C_{3} \\ &\implies A_{3}(t) = \frac{e^{-2t} - e^{-k \left( \frac{3 \pi}{L} \right)^{2} t}}{-2 + k \left( \frac{3 \pi}{L} \right)^{2}} + A_{3}(0) e^{-k \left( \frac{3 \pi}{L} \right)^{2} t} \end{align}
• thank you!!! Interesting that the book says $A_3(t) = A_3(0) e^{-k \left(\frac{3 \pi}{L}\right)^2 t} + \frac{e^{2t} - e^{-k \left(\frac{3 \pi}{L}\right)^2 t}}{-2 + k \left(\frac{3 \pi}{L}\right)^2}$ where we get $A_3(t) = A_3(0) e^{-k \left(\frac{3 \pi}{L}\right)^2 t} + \frac{e^{-2t} - e^{-k \left(\frac{3 \pi}{L}\right)^2 t}}{-2 + k \left(\frac{3 \pi}{L}\right)^2}$. I presume the textbook just made a mistake. – clay Oct 14 '19 at 2:40
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# Parameter estimation from a Normal distribution
Please can you check if am I correct?
I have a random variable $X$ normally distributed with mean $\mu$ and variance $\sigma^2$. I generate two independent sample $T_1$ and $T_2$ with $T_1 < T_2$ where $\bar{X}_1$ and $\bar{X}_2$ are the sample means respectively.
1)The proposed estimators below for $\mu^2$ are biased or unbiased?
• $\bar{X}_1^2$
• $\bar{X}_2^2$
• $(\bar{X}_1^2+\bar{X}_2^2)/2$
• $\bar{X}_1\times\bar{X}_2$
I think that in order to solve this question I have to use the property $Var(X) = E(X^2)-(E(X))^2$ and the fact that the sample mean $\bar{X} \sim (\mu,\sigma^2/T)$.
Therefore,
First estimator $\bar{X}_1^2$,
$E(X^2)= (E(X))^2 + Var(X) \rightarrow E(\bar{X_1}^2) = (E(\bar{X_1}))^2 + Var(\bar{X_1})$
which implies that $E(\bar{X_1}^2) = \mu^2 +\sigma^2/T_1\neq\mu^2 \Rightarrow$ BIASED
Second estimator $\bar{X}_2^2$, the same as the first one. BIASED.
Third estimator $\frac{\bar{X}_1^2+\bar{X}_2^2}{2}$, using also information above
$E\left(\frac{\bar{X}_1^2+\bar{X}_2^2}{2}\right)=E\left(\frac{\bar{X}_1^2}{2}+\frac{\bar{X}_1^2}{2}\right)=E\left(\frac{\bar{X}_1^2}{2}\right)+E\left(\frac{\bar{X}_1^2}{2}\right)=\frac{\mu^2+\sigma^2/T_1}{2}+\frac{\mu^2+\sigma^2/T_2}{2}= \mu^2 + \frac{\sigma^2}{2}\times\left({\frac{1}{T_1}+\frac{1}{T_2}}\right)$ BIASED
Forth estimator $\bar{X}_1\times\bar{X}_2$ ,
$E(\bar{X}_1\times\bar{X}_2) = E(\bar{X}_1)\times E(\bar{X}_2)$ because the two samples are independent.
Therefore, $E(\bar{X}_1\times\bar{X}_2) = \mu\times\mu=\mu^2$ UNBIASED
2) Now show that both the sample mean are unbiased estimator for $\mu$, that is, $E(\bar{X}_1) = \mu$ and $E(\bar{X}_2) = \mu$.
It's straight forward because the sample mean of a normal is normal distributed, $\bar{X} \sim (\mu,\sigma^2/T)$.
3) Now Define the follow estimator of $\mu$ and check if it biased or unbiased estimator of $\mu$, $\bar{X}_3 = \frac{(T_1\bar{X}_1+T_2\bar{X_2})}{T_1+T_2}$
So, $E\left(\frac{(T_1\bar{X}_1+T_2\bar{X_2})}{T_1+T_2}\right)$=$\frac{1}{T_1+T_2}\times E\left(T_1\bar{X}_1+T_2\bar{X}_2\right)=\frac{1}{T_1+T_2}\times T_1 E(\bar{X}_1)+T_2\times E(\bar{X}_2)=$
$\frac{1}{T_1+T_2}\times (T_1 +T_2)\times\mu=\mu$
4) You known that an unbiased estimator is more efficient compared to an other unbiased if its variance is smaller. What of $\bar{X_1}$, $\bar{X_2}$, $\bar{X_3}$ has the smallest variance?
Of course it depends by sample size T, $\bar{X}\sim\left(\mu,\frac{\sigma^2}{T}\right)$ and in this case we have $T_3>T_2>T_1$ therefore $\bar{X}_3$ is the estimator with the smallest variance.
• This is an homework, right?! I have added the hopefully correct flag! – Xi'an May 4 '12 at 17:15
• I'd say your answers to 2 and 4 involve a little handwaving. For 2, I'd go back to $\bar{X}_1 = (1/T)\sum X_i$ and work from there. For 4, I'd do the same for $\bar{X}_3$. It seems to me you know the stuff, you're just not doing the proofs at a sufficient level of detail. – jbowman May 4 '12 at 19:03
• Dear Jbowman, thank you for your reply. What do you mean "at a sufficient level of detail", the sample mean is an unbiased estimator for the mean of the true population. So you're right that $\bar{X}=\frac{1}{T}\sum X_i$ but I don't see the reason to include in the proof. I think all we need for the proof is the properties of the expectation operator, variance and the sample mean distribution (asymptotic distribution of the estimator mean). Or Am I wrong? – Marco May 4 '12 at 21:10
• Well, that depends on the expectations of the grader. It could be that the prof. or t.a. thinks that stating $\bar{X} \sim \text{N}(\mu, \sigma^2) \to \mathbb{E}\bar{X} = \mu$ isn't a proof, but merely restating the fact. Why is the mean of the Normal equal to $\mu$, the mean of the data? Similarly in part 4 you have a weighted average of sample means, but that doesn't imply (without some further detail in the proof) that the weighted average has variance $\sigma^2/(T_1+T_2)$. But this is imposing what I would consider adequate proof on your grader, not necessarily correct. – jbowman May 4 '12 at 22:24
• Ok, I get your point. So I show that $E(\bar{X})=\frac{1}{T}\sum E(X_i)$ therefore $E(\bar{X})=\frac{1}{T}\sum \mu$ concluding $E(\bar{X})=\frac{1}{T}T \mu = \mu$. The same for the variance and also for the property. – Marco May 5 '12 at 7:55
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axiom-developer
[Top][All Lists]
## [Axiom-developer] [FAQ]
From: Bill Page Subject: [Axiom-developer] [FAQ] Date: Wed, 26 Jan 2005 19:02:42 -0600
??changed:
-one of them, so we need to provide some help. In particular we need to tell
-Axiom how to expand square roots.
one of them, so we need to provide some help. In particular we need to
tell Axiom how to expand square roots. (Since $\sqrt{\ }$ is a multi-valued
function this rule is true only in a restricted sense for a particular
choice of branches. Consider $a=-1, b=-1$.)
--
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## On the entropy of dynamical systems in product MV algebras.(English)Zbl 0983.37007
From the introduction: The notion of the entropy of a dynamical system has been defined and studied for distinguishing non-isomorphic dynamical systems. If two dynamical systems are isomorphic, they have the same entropy. Therefore, systems with different entropies cannot be isomorphic. If one substitutes in the definition of entropy, the notion of a set partition by the notion of fuzzy partition, a larger class of invariants can be obtained.
We generalize these results considering the general notion of the product MV algebra and obtain some standard assertions, the Kolmogorov theorem on generators being omitted. Namely, in the general situation we have no satisfactory version of the martingale convergence theorem.
### MSC:
37A35 Entropy and other invariants, isomorphism, classification in ergodic theory 06D35 MV-algebras
### Keywords:
entropy; fuzzy partition; product MV algebra
Full Text:
### References:
[1] Ban, A.I., Entropy of a fuzzy $$T$$-dynamical systems, J. fuzzy math., 6, 351-362, (1998) · Zbl 0921.28011 [2] Dumitrescu, D., Entropy of a fuzzy process, Fuzzy sets and systems, 55, 169-177, (1993) · Zbl 0818.28008 [3] Dumitrescu, D., Entropy of fuzzy dynamical systems, Fuzzy sets and systems, 70, 45-57, (1995) · Zbl 0876.28029 [4] Grošek, O., Entropia na algebraičeskich strukturach, Math. slovaca, 29, 411-424, (1979) [5] Hudetz, T., Space – time dynamical entropy of quantum systems, Lett. math. phys., 16, 151-161, (1988) · Zbl 0674.46040 [6] J. Jakubı́k, On the product of $$MV$$ algebras, Czech Math. J., to appear. [7] P. Maličký, B. Riečan, On the entropy of dynamical systems in: Proceedings Conference on Ergodic Theory and Related Topics ll, Georgenthal, 1986, Teubner, Leipzig, 1987, 135-138. [8] Markechová, D., A note to the kolmogorov – sinaj entropy of fuzzy dynamical systems, Fuzzy sets and systems, 64, 87-90, (1994) · Zbl 0845.93054 [9] Mundici, D., Interpretation of $$AFC\^{}\{*\}$$-algebras in lukasiewicz sentential calculus, J. funct. anal., 65, 15-63, (1986) · Zbl 0597.46059 [10] Mundici, D., Nonboolean partitions and their logic, Soft comput. (special issue containing the Proceedings of the first Springer-verlag forum on soft computing), 2, 18-22, (1998) [11] Mundici, D., Tensor products and the loomir – sikorski theorem for $$MV$$-algebras, Adv. appl. math., 22, 227-248, (1999) · Zbl 0926.06004 [12] D. Mundici, Many-valued logic: from coding theory to operator algebras, in: Information Technology, INFOREC Printing House, Bucharest, 1999, 1011-1022. [13] J. Petrovičová, On the entropy of partitions in product $$MV$$ algebras, Soft Comput., to appear. [14] Riečan, B., On the product $$MV$$ algebras, Tatra mt. math. publ., 16, 143-149, (1999) · Zbl 0951.06013 [15] Riečan, B., On the probability theory on product $$MV$$ algebras, (), 445-450 · Zbl 0930.06009 [16] Riečan, B., On a type of $$MV$$ algebras, (), 80-84 [17] B. Riečan, T. Neubrunn, Integral, Measure, and Ordering, Kluwer, Dordrecht, and Ister Science, Bratislava, 1997. [18] Riečan, B.; Markechová, D., The entropy of fuzzy dynamical systems, general scheme and generators, Fuzzy sets and systems, 96, 191-199, (1998) · Zbl 0926.94012 [19] Rybárik, J., The entropy based on pseudo-arithmetical operations, Tatra mt. math. publ., 6, 157-164, (1995) · Zbl 0859.28011 [20] M. Vrábelová, A note on the conditional probability on product $$MV$$ algebras, Soft Comput., to appear.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.
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# Lending Rates for Bitcoin and USD on Cryptoexchanges
We are going to take a look at the current interest rates in bitcoin lending. Why is this important? In addition to being a way to make extra income from your fiat (“real” currency) or bitcoin holdings without selling them, these interest rates indicate traders sentiment about the relative values of these currencies in the future. We will look at bitcoin in this post, because it is the largest cryptocurrency, both in terms of market cap and trading volume. As of the date of this writing here are the top 4 cryptocurrencies by total market cap. Information from http://coinmarketmap.com.
Crypto-Currency Market Cap ($USD, billion) 24 Hr Trading volume ($USD, billion) Bitcoin (BTC) 45 1.0 Ethereum (ETH) 32 0.78 Ripple 11 0.18 Litecoin (LTC) 2.5 0.37
The Bitfinex Exchange is one of the exchanges that allows margin trading, and also customer lending of fiat and crytpocurrencies. They call the lending exchange funding and it works with an order book just like a regular trading exchange. Customers submit funding offers and requests, and the exchange matches the orders. So, for example, I could offer $USD800 for 4 days at .0329% per day (12% annually). This get placed on the order book. Someone else could accept that offer, and then the loan happens. As the lender, I get paid interest daily at the contract rate, paid by the borrower. Now, what does the borrower do with the proceeds? They can’t withdraw the money from Bitfinex, this is not a general personal loan. They could use this money to buy bitcoins on margin. There are specific rules on how much they can borrow at purchase, and how much margin they must maintain in the future. We won’t go into the specifics of those rules in this post, but just be aware that the exchange can liquidate, or sell, a position to maintain margin requirements. In fact, this is what caused the recent meltdown in the Ethereum market at one exchange (GDAX) Ethereum Flash Crash, as traders had their positions liquidated automatically for margin calls. So, show me the data! In this chart, fUSD is the funding rate as an APR for$USD, and fBTC is the funding rate for bitcoin (BTC). These are based on a small sample of 2 day loans actually traded on that day. The first thing to note is that the rates are quite volatile, reaching highs of over 100% (USD) and 50% (BTC) during the last year. The current rates (June 2017) are around 40% (USD) and 4% (BTC).
One more thing we might want to look at. We might wonder about the difference between the two rates and what that means. In economics, there is something called uncovered interest rate parity, which normally looks at the difference in interest rates between 2 currencies, say the USD and the Euro (EUR). This difference is related to the relative inflation expected between the 2 currencies in the future. In fact, futures contracts for the currencies should have a price related to this difference in such a way as to make arbitrage not possible. Here is the difference graph.
Note that it switches around both sides of zero. Between approximately 15 Mar 2017 and 1 May 2017, it was negative, meaning people were demanding higher rates to lend BTC than to lend USD. Perhaps this is an indication that people wanted to short BTC at that time – although we don’t know which fiat currency they were shorting it against.
Another thing that we can pull from the data is the yield curve. In the bond market, this indicates the interest rates for bonds at different maturities, for example, a 30 day, 60 day, 1 year, etc. In the case of Bitfinex, the loans can only be made for 2-30 days, so we have a more limited set of possibilities.
You can see the curves are relatively flat, but they only go out to 30 days, so we can’t say much about 1 year rates. Note that most of the volume is at the extremes, that is 2 days or 30 days, so the numbers in between are not that meaningful.
In post to come, we will look at Bitcoin futures, to see how their pricing might be related to the uncovered interest rate parity. Stay tuned.
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3 Replies Latest reply on May 22, 2014 7:53 AM by MrMathType
mathjax stix font
mathjax stix font is used in mathtype equation file, but when that eps file in placed in InDesign stix font is not embedded in InDesign.
any suggestion will be helpful...
• 1. Re: mathjax stix font
When the EPS file is created, is that font being embedded into the EPS? That should solve the problem.
- Dov
• 2. Re: mathjax stix font
yes the font is not getting embedded in eps. Is it because mathtype does not support the font? but it is been viewed in mathtype.
• 3. Re: mathjax stix font
The STIX fonts are OTF, which MathType does not fully support. Some of the glyphs within the font will be visible in MT and usable in equations, but the full character set will not be. There may also be other issues, which you've noticed. If you're able to save the equation as PDF rather than EPS, the STIX font symbols should display in ID. (On the Mac, you can save directly as PDF within MathType. If you're on Windows, you can use the Adobe PDF printer. The result should be the same.)
Bob Mathews
Design Science
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## The database migration wizard for Unicode by Oracle does not respond after using the programming column option
I published this problem in Oracle Community, but I would like to post it here to have more opinions on this topic.
Issue:
• I have a problem with DMU 19.1, which is the DMU application
not responding (frozen or locked) after cleaning the data using
program the problem column (the problem exceeds the limit of the column). That
It happens frequently and every time this happens, I have to use the homework
manager to finalize the DMU application.
Here is my summary of the configuration:
• The DMU is installed on a Windows Server 2008 R2 SP1 client machine
which connects to Oracle Database Server 11.2.0.4. The host of
The database server is the Linux base. The JDK that DMU is currently
using is JDK 1.8.0_231 The DMU installed all the packages that
requires the DMU document, including the creation of a separate table space
for DMU repository. The DMU will be used to convert the character.
configured for a database with a size larger than 1.5 TB of storage. I
I was able to scan the entire database and now I am cleaning data
step, and this problem happened.
Looking at the record, I could find the cause. Due to privacy, I could not copy the entire record here. Instead, I will try to write down the registration problem as much as I can. Here is the log message:
• Principal; S; 05001 Stack of exception calls in
Java.lang.ArrayIndexOutofBounds Exception -2 in
Java.Util.ArrayList.elementData (ArrayList.Java: 422) in
Java.Util.ArrayList.get (ArrayList.Java: 435) in
oracle.duma.gui.cleansing.cache.defaultCachePage.getObject
(defaultCachePage.Java: 96) in
oracle.dmu.gui.cleansing.cache.defaultDataProvider.getCellData
(defaultDataProvider.Java: 262) in
oracle.duma.gui.cleansing.model.cleansingDataGridModel.getOriginalDataAt
(cleansingDataGridModel.Java: 1218) …
• The rest of the record were exceptions thrown from Java.wing and
java.awt. For example. J Component. Java 5158, 1065, 889 or
Javax.swing.bufferStrategyPaintManager 290 and so on.
My attempt:
• I think I can try to find some solutions if I read the ide.conf o
dmu.conf
Documents on this subject.
Please let me know what I should do or what I should analyze this problem.
Best,
Khang Mai
## unit: after compilation, the application does not respond
Thank you for contributing a response to Game Development Stack Exchange!
But avoid
• Make statements based on opinion; Support them with references or personal experience.
Use MathJax to format equations. MathJax reference.
## penetration test: AP does not respond ARP packet injection (arp repeat attack)
I am trying to learn and practice the ARP Replay attack.
I have configured my AP for WEP encryption.
I have associated my wireless adapter in monitor mode with the router using –fakeauth. Command as follows:
aireplay-ng –fakeauth 0 -a (AP MAC target) -h (MAC adapter)
As far as I know (feel free to correct me), when executing the arp-replay command, the AP will be forced to send an ARP packet that my wireless adapter will capture and forward, which will increase traffic.
My problem is that my AP does not respond or refuses to send an ARP package. My wireless adapter has read about 9000 packages but still has no cigar. I can't even read a single ARP package. This is the command:
aireplay-ng –arpreplay -b (AP MAC target) -h (MAC adapter)
Where am I going wrong?
## website: you need help for the animation to respond and focus on the screen
You need help to make an animation respond to the screen size
Hi,
I am using a codepen logo animation https://codepen.io/avenart/pen/dehJA. I would like to use this pencil in my project, however, I cannot make it focus on the page and also respond to the screen size.
If someone could help I would be very grateful
Thank you
## How would you respond to the linked video that supposedly provides "The empirical proof of Bitcoin's real value of being zero"?
Did this video really show what it says? I want to invest in BTC, but I found this video in the bitcointalk forum and none of the respondents gave a convincing rebuttal, so I don't know if it is safe to invest in BTC.
## networks – MariaDB Maxctrl does not respond CentOS 7
I am working on configuring a MariaDB 3 Node Cluster and using Maxscale as a proxy. I had configured a practice configuration on some local KVM machines, I worked without problems. So I went to activate the production servers and I receive an error that I cannot understand. If I execute any command in maxctrl at all it throws the same error:
ERROR
The requested URL could not be retrieved
The following error was encountered while trying to retrieve the URL: http://localhost:8989/v1/maxscale/modules/mariadbmon/
Connection to ::1 failed.
The system returned: (99) Cannot assign requested address
The remote host or network may be down. Please try the request again.
Ok, so it seems that something was using the port 8989 before Maxscale, let's check with lsof -i -P -n | grep 89:
maxscale 1117 maxscale 23u IPv4 19765 0t0 TCP 127.0.0.1:8989 (LISTEN)
SELinux is set to Permission to perform tests, Firewalld is disabled to perform tests.
Someone suggested that it could be an IPv6 problem since it says connection to :: 1, but I can't see what the difference would be between my test machines and professional machines, since both have the same default configuration of loopback adapter in lo and both have the same aliases in /etc/hosts
Debug suggestions?
## Why does the cursor on my Macbook Pro 10.13.6 not respond when I click?
The cursor on my MacBook Pro does not respond when clicked. The cursor appears on the screen and I can double click, so I think it's a software problem. When I try to restart, it works for a minute but then stops working.
## networks: brave browser synchronization over LAN does not respond
I have asked this on the Brave site but there is no answer there.
I am testing the Brave browser and I have problems with the synchronization function that, as I understand it, synchronizes the configuration and references of all the devices connected to the synchronization chain.
However this is not working.
For this attempt, I use two machines connected to a small LAN. These machines communicate through SSH, NFS, telnet, etc. so that there are no communication problems at the top.
• On the first machine I create the chain and receive a passcode;
• The dialog box turns on "Searching for device", it seems stuck there after half an hour.
• On the second machine, I open the synchronization dialog box and paste the key into it. The "Verify" button is clicked, but there is no other answer.
## sap: Hybris Back Office does not respond and gives auEngine error
Hybris Back Office does not respond and gives the auEngine error. Despite doubling the size of the instance / memory of the management nodes, it does not respond after a few minutes. The Hybris version is 6.6. The application nodes work fine. However, HMC, HAC are opening, but as soon as the administration node CPU utilization is around 100%, everything falls.
/ auEngine
StackTrace:
SEVERE: Servlet.service() for servlet (auEngine) in context with path (/backoffice) threw exception
org.zkoss.zk.ui.DesktopUnavailableException: Unable to activate destroyed desktop, (Desktop z_ot80:/cockpit.zul)
at org.zkoss.zk.ui.impl.UiEngineImpl.doActivate(UiEngineImpl.java:1931)
at org.zkoss.zk.ui.impl.UiEngineImpl.execUpdate(UiEngineImpl.java:1271)
at javax.servlet.http.HttpServlet.service(HttpServlet.java:650)
at javax.servlet.http.HttpServlet.service(HttpServlet.java:731)
at org.apache.catalina.core.ApplicationFilterChain.internalDoFilter(ApplicationFilterChain.java:303)
at org.apache.catalina.core.ApplicationFilterChain.doFilter(ApplicationFilterChain.java:208)
at org.apache.tomcat.websocket.server.WsFilter.doFilter(WsFilter.java:52)
at org.apache.catalina.core.ApplicationFilterChain.internalDoFilter(ApplicationFilterChain.java:241)
at org.apache.catalina.core.ApplicationFilterChain.doFilter(ApplicationFilterChain.java:208)
at org.springframework.security.web.FilterChainProxy.doFilterInternal(FilterChainProxy.java:208)
at org.springframework.security.web.FilterChainProxy.doFilter(FilterChainProxy.java:177)
at org.springframework.web.filter.DelegatingFilterProxy.invokeDelegate(DelegatingFilterProxy.java:346)
at org.springframework.web.filter.DelegatingFilterProxy.doFilter(DelegatingFilterProxy.java:262)
at org.apache.catalina.core.ApplicationFilterChain.internalDoFilter(ApplicationFilterChain.java:241)
at org.apache.catalina.core.ApplicationFilterChain.doFilter(ApplicationFilterChain.java:208)
at org.springframework.web.filter.RequestContextFilter.doFilterInternal(RequestContextFilter.java:99)
at org.springframework.web.filter.OncePerRequestFilter.doFilter(OncePerRequestFilter.java:107)
at org.apache.catalina.core.ApplicationFilterChain.internalDoFilter(ApplicationFilterChain.java:241)
at org.apache.catalina.core.ApplicationFilterChain.doFilter(ApplicationFilterChain.java:208)
at com.hybris.backoffice.mobile.filter.BackofficeMobileFilter.doFilter(BackofficeMobileFilter.java:63)
at org.apache.catalina.core.ApplicationFilterChain.internalDoFilter(ApplicationFilterChain.java:241)
at org.apache.catalina.core.ApplicationFilterChain.doFilter(ApplicationFilterChain.java:208)
at de.hybris.platform.servicelayer.web.WebAppMediaFilter.doFilter(WebAppMediaFilter.java:140)
at org.springframework.web.filter.DelegatingFilterProxy.invokeDelegate(DelegatingFilterProxy.java:346)
at org.springframework.web.filter.DelegatingFilterProxy.doFilter(DelegatingFilterProxy.java:262)
at org.apache.catalina.core.ApplicationFilterChain.internalDoFilter(ApplicationFilterChain.java:241)
at org.apache.catalina.core.ApplicationFilterChain.doFilter(ApplicationFilterChain.java:208)
at de.hybris.platform.servicelayer.web.AbstractPlatformFilterChain$InternalFilterChain.doFilter(AbstractPlatformFilterChain.java:301) at de.hybris.platform.servicelayer.web.AbstractPlatformFilterChain$StatisticsGatewayFilter.doFilter(AbstractPlatformFilterChain.java:390)
at de.hybris.platform.servicelayer.web.AbstractPlatformFilterChain$InternalFilterChain.doFilter(AbstractPlatformFilterChain.java:271) at de.hybris.platform.servicelayer.web.WebAppMediaFilter.doFilter(WebAppMediaFilter.java:140) at de.hybris.platform.servicelayer.web.AbstractPlatformFilterChain$InternalFilterChain.doFilter(AbstractPlatformFilterChain.java:271)
at de.hybris.platform.servicelayer.web.AbstractPlatformFilterChain$InternalFilterChain.doFilter(AbstractPlatformFilterChain.java:271) at de.hybris.platform.servicelayer.web.DynamicCatalogVersionActivationFilter.doFilter(DynamicCatalogVersionActivationFilter.java:90) at de.hybris.platform.servicelayer.web.AbstractPlatformFilterChain$InternalFilterChain.doFilter(AbstractPlatformFilterChain.java:271)
at de.hybris.platform.servicelayer.web.DataSourceSwitchingFilter.doFilter(DataSourceSwitchingFilter.java:70)
at de.hybris.platform.servicelayer.web.AbstractPlatformFilterChain$InternalFilterChain.doFilter(AbstractPlatformFilterChain.java:271) at de.hybris.platform.servicelayer.web.SessionFilter.doFilter(SessionFilter.java:99) at de.hybris.platform.servicelayer.web.AbstractPlatformFilterChain$InternalFilterChain.doFilter(AbstractPlatformFilterChain.java:271)
at de.hybris.platform.servicelayer.web.RedirectWhenSystemIsNotInitializedFilter.doFilter(RedirectWhenSystemIsNotInitializedFilter.java:101)
at de.hybris.platform.servicelayer.web.AbstractPlatformFilterChain$InternalFilterChain.doFilter(AbstractPlatformFilterChain.java:271) at de.hybris.platform.servicelayer.web.TenantActivationFilter.doFilter(TenantActivationFilter.java:88) at de.hybris.platform.servicelayer.web.AbstractPlatformFilterChain$InternalFilterChain.doFilter(AbstractPlatformFilterChain.java:271)
at de.hybris.platform.servicelayer.web.Log4JFilter.doFilter(Log4JFilter.java:44)
at de.hybris.platform.servicelayer.web.AbstractPlatformFilterChain$InternalFilterChain.doFilter(AbstractPlatformFilterChain.java:271) at de.hybris.platform.servicelayer.web.AbstractPlatformFilterChain.processStandardFilterChain(AbstractPlatformFilterChain.java:201) at de.hybris.platform.servicelayer.web.AbstractPlatformFilterChain.doFilterInternal(AbstractPlatformFilterChain.java:179) at org.springframework.web.filter.OncePerRequestFilter.doFilter(OncePerRequestFilter.java:107) at org.springframework.web.filter.DelegatingFilterProxy.invokeDelegate(DelegatingFilterProxy.java:346) at org.springframework.web.filter.DelegatingFilterProxy.doFilter(DelegatingFilterProxy.java:262) at org.apache.catalina.core.ApplicationFilterChain.internalDoFilter(ApplicationFilterChain.java:241) at org.apache.catalina.core.ApplicationFilterChain.doFilter(ApplicationFilterChain.java:208) at de.hybris.platform.servicelayer.web.XSSFilter.processPatternsAndDoFilter(XSSFilter.java:358) at de.hybris.platform.servicelayer.web.XSSFilter.doFilter(XSSFilter.java:306) at org.apache.catalina.core.ApplicationFilterChain.internalDoFilter(ApplicationFilterChain.java:241) at org.apache.catalina.core.ApplicationFilterChain.doFilter(ApplicationFilterChain.java:208) at org.apache.catalina.core.StandardWrapperValve.invoke(StandardWrapperValve.java:219) at org.apache.catalina.core.StandardContextValve.invoke(StandardContextValve.java:110) at org.apache.catalina.authenticator.AuthenticatorBase.invoke(AuthenticatorBase.java:506) at org.apache.catalina.core.StandardHostValve.invoke(StandardHostValve.java:169) at org.apache.catalina.valves.ErrorReportValve.invoke(ErrorReportValve.java:103) at org.apache.catalina.core.StandardEngineValve.invoke(StandardEngineValve.java:116) at org.apache.catalina.valves.AccessLogValve.invoke(AccessLogValve.java:962) at org.apache.catalina.connector.CoyoteAdapter.service(CoyoteAdapter.java:445) at org.apache.coyote.http11.AbstractHttp11Processor.process(AbstractHttp11Processor.java:1115) at org.apache.coyote.AbstractProtocol$AbstractConnectionHandler.process(AbstractProtocol.java:637)
at org.apache.tomcat.util.net.JIoEndpoint$SocketProcessor.run(JIoEndpoint.java:316) at java.util.concurrent.ThreadPoolExecutor.runWorker(ThreadPoolExecutor.java:1149) at java.util.concurrent.ThreadPoolExecutor$Worker.run(ThreadPoolExecutor.java:624)
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Just a quick note. In the bowtie2/samtools pipeline I used annovar to add annotations to my VCF files. It was a bit difficult to get set up the first time, but I have since come to appreciate how uniquely useful annovar is: I posted an ask-the-community question to the GATK forum a couple months ago asking if people knew of any alternatives, and it’s now had 53 views and no suggestions for alternatives. annovar is really the only software out there for systematically adding in all that outside information: dbSNP, 1000G, phyloP, SIFT, etc. that are so helpful for interpreting your data, and once you get it set up it’s quick and effective.
Now, annovar is made to work with hg19, so what can you do if you are using GRCh37 as your reference genome? Well, no warranties here, but I discovered you can trick annovar into thinking your VCF is hg19:
# make it look like it's hg19
sed 's/^/chr/' variants.final.vcf | sed 's/^chr#/#/' | sed 's/chrMT/chrM/' > variants.pseudo.hg19.final.vcf
# convert your vcf to an annovar file
perl ~/bin/annovar/convert2annovar.pl --format vcf4 --includeinfo variants.pseudo.hg19.final.vcf > variants.annovar
# do the annotation
perl ~/bin/annovar/summarize_annovar.pl --buildver hg19 --ver1000g 1000g2012feb --verdbsnp 132 variants.annovar ~/bin/annovar/humandb -outfile annovar/variants
And it completes without errors and as far as I can spot-check, it seems to have gotten all the annotations correct. Again, this is clearly cheating and so there’s probably something wrong in there somewhere, but as a first pass this seems to mostly work.
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【Codeforces 1462 E2】Close Tuples (hard version)，排序，二分，贪心，组合数
problem
E2. Close Tuples (hard version)
time limit per test4 seconds
memory limit per test256 megabytes
inputstandard input
outputstandard output
This is the hard version of this problem. The only difference between the easy and hard versions is the constraints on k and m. In this version of the problem, you need to output the answer by modulo 109+7.
You are given a sequence a of length n consisting of integers from 1 to n. The sequence may contain duplicates (i.e. some elements can be equal).
Find the number of tuples of m elements such that the maximum number in the tuple differs from the minimum by no more than k. Formally, you need to find the number of tuples of m indices i1<i2<…<im, such that
max(ai1,ai2,…,aim)−min(ai1,ai2,…,aim)≤k.
For example, if n=4, m=3, k=2, a=[1,2,4,3], then there are two such triples (i=1,j=2,z=4 and i=2,j=3,z=4). If n=4, m=2, k=1, a=[1,1,1,1], then all six possible pairs are suitable.
As the result can be very large, you should print the value modulo 109+7 (the remainder when divided by 109+7).
Input
The first line contains a single integer t (1≤t≤2⋅105) — the number of test cases. Then t test cases follow.
The first line of each test case contains three integers n, m, k (1≤n≤2⋅105, 1≤m≤100, 1≤k≤n) — the length of the sequence a, number of elements in the tuples and the maximum difference of elements in the tuple.
The next line contains n integers a1,a2,…,an (1≤ai≤n) — the sequence a.
It is guaranteed that the sum of n for all test cases does not exceed 2⋅105.
Output
Output t answers to the given test cases. Each answer is the required number of tuples of m elements modulo 109+7, such that the maximum value in the tuple differs from the minimum by no more than k.
Example
inputCopy
4
4 3 2
1 2 4 3
4 2 1
1 1 1 1
1 1 1
1
10 4 3
5 6 1 3 2 9 8 1 2 4
outputCopy
2
6
1
20
solution
/*
+ 给出一个长为n的序列，求有多少个m=3元组（任选m个元素组成的集合）满足其中最大数-最小数小于等于k=2。
+ 先对数组排序，然后算出每个数的贡献，先从第一个数开始找到第一个大于它的值+k的数（二分），下标差即为可选的构成m个数元组的可选数的个数s。
+ 如果s<m贡献0，如果s>=m,贡献为从s-1个数中选出m-1个数的方法数（已经选了一个数），转换为求组合数的模问题。
*/
#include<bits/stdc++.h>
using namespace std;
typedef long long LL;
const int maxn = 2e5 + 5;
const int mod = 1e9+7;
LL inv(LL x){return x==1?1:(LL)(mod-mod/x)*inv(mod%x)%mod;}
LL C(LL n, LL m){
if(n<0 || n<m)return 0;
if(m>n-m)m=n-m;
LL up = 1, down = 1;
for(LL i = 0; i < m; i++){
up = up*(n-i)%mod;
down = down*(i+1)%mod;
}
return up*inv(down)%mod;
}
int a[maxn];
int main(){
int T; cin>>T;
while(T--){
int n, m, k; cin>>n>>m>>k;
//int n, m=3, k=2; cin>>n;
for(int i = 1; i <= n; i++)cin>>a[i];
sort(a+1,a+n+1);
LL ans = 0;
for(int i = 1; i <= n; i++){
int r = upper_bound(a+1,a+n+1,a[i]+k)-a;
int cnt = r-i;
if(cnt<m)continue;
ans += C(cnt-1,m-1);
ans %= mod;
}
cout<<ans<<"\n";
}
return 0;
}
10-07 1704
11-01 7594
04-22 2966
09-13 2075
08-12 1551
08-20 1373
10-26 1682
06-17 8641
06-24 2949
08-14 1523
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Accelerating the pace of engineering and science
# step
Package: dsp
Decompose input with dyadic filter bank
Y = step(H,X)
## Description
Y = step(H,X) computes the subband decomposition of the input X and outputs the dyadic subband decomposition in Y as a single concatenated column vector or matrix of coefficients. Each column of X is treated as an independent input, and the number of rows of X must be a multiple of ${2}^{N},$ where N is the value of the NumLevels property. The elements of Y are ordered with the highest frequency subband first followed by subbands in decreasing frequency
## Examples
Subband ordering for level-two asymmetric tree structure:
```t = 0:.001:1.023;
% Sampling frequency 1 kHz input length 1024
x= square(2*pi*30*t);
xn = x' + 0.08*randn(length(x),1);
% Default asymmetric structure with
% Daubechies order 3 extremal phase wavelet
Y = step(H,xn);
% Level 2 yields 3 subbands (two detail-one approximation)
% Nyquist frequency is 500 Hz
D1 =Y(1:512); % subband approx. [250, 500] Hz
D2 = Y(513:768); % subband approx. [125, 250] Hz
Approx = Y(769:1024); % subband approx. [0,125] Hz```
Subband ordering for symmetric tree structure:
```t = 0:.001:1.023;
% Sampling frequency 1 kHz input length 1024
x= square(2*pi*30*t);
xn = x' + 0.08*randn(length(x),1); % symmetric structure with
% Daubechies order 3 extremal phase wavelet
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Language: Search: Contact
Zentralblatt MATH has released its new interface!
For an improved author identification, see the new author database of ZBMATH.
Query:
Fill in the form and click »Search«...
Format:
Display: entries per page entries
Zbl 1228.93087
Lan, Yong-Hong; Zhou, Yong
LMI-based robust control of fractional-order uncertain linear systems.
(English)
[J] Comput. Math. Appl. 62, No. 3, 1460-1471 (2011). ISSN 0898-1221
Summary: We are concerned with the method of observer-based control and static output feedback control for fractional-order uncertain systems with the fractional commensurate order $\alpha$($0<\alpha <1)$ and $\alpha$($1\le \alpha <2)$ via linear matrix inequality (LMI) approach, respectively. First, the sufficient conditions for robust asymptotical stability of the closed-loop control systems are presented. Next, by using matrix's singular value decomposition (SVD) and LMI technics, the existence condition and method of designing a robust stabilizing controller for such fractional-order control systems are derived. Unlike previous methods, the results are obtained in terms of LMI, which can be easily obtained by Matlab's LMI toolbox. Finally, two numerical examples demonstrate the validity of this approach.
MSC 2000:
*93D05 Lyapunov and other classical stabilities of control systems
34A08
93C42 Fuzzy control
Keywords: fractional-order uncertain systems; stability; observer-based control; output feedback control; linear matrix inequality (LMI)
Highlights
Master Server
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## Solve for x in the equation 3 x squared minus 18 x + 5 = 47.
Question
Solve for x in the equation 3 x squared minus 18 x + 5 = 47.
in progress 0
7 months 2021-10-25T20:03:36+00:00 2 Answers 0 views 0
A. X = +/- sqr root 23
Step-by-step explanation:
I did the Edgenuity
x= 3 +$$\sqrt{23}$$, 3 -$$\sqrt{23}$$
You use the quadratic formula to get x= $$\frac{18+6\sqrt{23} }{6} ,\frac{18-6\sqrt{23} }{6}$$
Then you simplify and get the answers x= 3 +$$\sqrt{23}$$, 3 -$$\sqrt{23}$$
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MathSciNet bibliographic data MR179897 (31 #4134) 62.45 (60.40) Chow, Y. S.; Robbins, Herbert On optimal stopping rules for \$s\sb{n}/n\$$s\sb{n}/n$. Illinois J. Math. 9 1965 444–454. Article
For users without a MathSciNet license , Relay Station allows linking from MR numbers in online mathematical literature directly to electronic journals and original articles. Subscribers receive the added value of full MathSciNet reviews.
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# Konstantin Kashin
Institute for Quantitative Social Science, Harvard University
Konstantin Kashin is a Fellow at the Institute for Quantitative Social Science at Harvard University and will be joining Facebook's Core Data Science group in September 2015. Konstantin develops new statistical methods for diverse applications in the social sciences, with a focus on causal inference, text as data, and Bayesian forecasting. He holds a PhD in Political Science and an AM in Statistics from Harvard University.
## Posts Tagged “R”
• Theory of Maximum Likelihood Estimation
I've finally updated and uploaded a detailed note on maximum likelihood estimation, based in part on material I taught in Gov 2001. It is available in full [here](http://www.konstantinkashin.com/notes/stat/Maximum_Likelihood_Estimation.pdf).
To summarize the note without getting into too much math, let's first define the likelihood as proportional to the joint probability of the data conditional on the parameter of interest ($\theta$): $$L(\theta|\mathbf{x}) \propto f(\mathbf{x}|\theta) = \prod\limits_{i=1}^n f(x_i|\theta)$$ The maximum likelihood estimate (MLE) of $\theta$ is the value of $\theta$ in the parameter space $\Omega$ that maximizes the likelihood function: $$\hat{\theta}_{MLE} = \max_{\theta \in \Omega} L(\theta|\mathbf{x}) = \max_{\theta \in \Omega} \prod\limits_{i=1}^n f(x_i|\theta)$$ This turns out to be equivalent to maximizing the log-likelihood function (which is often simpler): $$\hat{\theta}_{MLE} = \max_{\theta \in \Omega} \log L(\theta|\mathbf{x}) = \max_{\theta \in \Omega} \ell (\theta|\mathbf{x}) = \max_{\theta \in \Omega} \sum\limits_{i=1}^n \log (f(x_i|\theta))$$
• Bootstrap Confidence Interval Methods in R
This post briefly sketches out the types of bootstrapped confidence intervals commonly used, along with code in R for how to calculate them from scratch. Specifically, I focus on nonparametric confidence intervals. The post is structured around the list of bootstrap confidence interval methods provided by Canty et al. (1996). This is just a quick introduction into the world of bootstrapping - for an excellent R package for doing all sorts of bootstrapping, see the [boot package](http://cran.r-project.org/web/packages/boot/boot.pdf) by Brian Ripley.
• Using ggplot2 to Plot Regression Coefficients with Confidence Intervals
A graphical approach to displaying regression coefficients / effect sizes across multiple specifications can often be significantly more powerful and intuitive than presenting a regression table. Moreover, we can easily express uncertainty in the form of confidence intervals around our estimates. As a quick example, suppose that we wanted to compare the effect of British colonial status upon country-level corruption across multiple specifications and two methods (OLS and WLS) from the following paper: Treisman, Daniel. 2000. "The causes of corruption: a cross-national study," *Journal of Public Economics* 76: 399-457.
• DAGs in R
Following up on the previous post, another way to construct DAGs is using R. I think the [igraph package](http://cran.r-project.org/web/packages/igraph/index.html) is one of the customizable ways to do so. This is a powerful package designed for the visualization and analysis of networks and offers much more functionality than you will use for DAGs.
• rgdal for R on Mac
[rgdal](http://cran.r-project.org/web/packages/rgdal/index.html) provides an interface between R and the [GDAL](http://www.gdal.org/)/[OGR](http://www.gdal.org/ogr/) library, which provides extensive support for a variety of geospatial formats. It is extremely useful for data import and export tasks, particularly because it can read projection information (from .prj files). However, to use rgdal, one must install GDAL and other frameworks on your system first. This is a guide for how to install rgdal on a Mac.
• ggplot2: Density Plots and Histograms
In this post, I'm going to go through how to make plots of distributions (either density plots or histograms) in ggplot2. I'm going to draw upon examples of Fisherian testing in the context of causal inference, but the examples should be completely understandable without knowledge of Fisher's approach to inference.
• ggplot2: Side-by-Side Plots
Here's a quick example of plotting histograms next to one another in ggplot2. I wanted to plot the estimated propensity scores for treated and control units for the [Lalonde non-experimental data](/data/dta.nooutcome.RData).
• ggplot2: Factor Orderings
One of the occasionally annoying features of R and thus ggplot2 is dealing with factors. In this post, I'll go through how to handle ordering of factors in ggplot2 and the manual assignment of colors to those categories.
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# Linear algebra matrices
• Sep 13th 2008, 06:29 PM
Linnus
Linear algebra matrices
Let $T: \Re^3 \rightarrow \Re^2$ be a map defined as $T(x_1, x_2, x_3) := (x_1 + x_2, x_1+ x_3)$
a) Find the matrix representation of T.
b) Is T onto? Find the range of T.
c) Is T one-to-one? Find the null set of T.
Thank you!
• Sep 13th 2008, 06:52 PM
ThePerfectHacker
Quote:
Originally Posted by Linnus
Let $T: \Re^3 \rightarrow \Re^2$ be a map defined as $T(x_1, x_2, x_3) := (x_1 + x_2, x_1+ x_3)$
a) Find the matrix representation of T.
b) Is T onto? Find the range of T.
c) Is T one-to-one? Find the null set of T.
1) $T(1,0,0) = (1,1)$ and $T(0,1,0) = (1,0)$ and $T(0,0,1) = (0,1)$.
Thus the matrix $A$ is $\left[ \begin{array}{ccc}1&1&0\\1&0&1 \end{array}\right]$.
2)If $\bold{b}=(b_1,b_2)$ is in the range it means there is $\bold{x}=(x_1,x_2,x_3)$ so that $A\bold{x}=b$.
This means find all $b_1,b_2$ such that,
$\left[ \begin{array}{cccc}1 & 1 & 0 & b_1 \\ 1 & 0 & 1 & b_2 \end{array} \right]$
Can be reduced to a consistent system.
3)The null set is $A\bold{x} = \bold{0}$ for $\bold{x} = (x_1,x_2,x_3)$.
Thus, you need to solve,
$\left[ \begin{array}{cccc} 1& 1 & 0 & 0 \\ 1& 0 & 1 & 0 \end{array} \right]$
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Are mu and mu2 in the direction of the world frame, or collision frame?
I'm trying to do model some basic 4-wheel robots, and they having difficulty turning. My first attempt was to mess with <mu> and <mu2>, thinking that they would be in relative to the surface of the wheel. For instance, if my wheel is rotating around the Y axis, the <mu> would point along the tangent of rotation, and <mu2> would point perpendicular.
So, I did a little experiment and set <mu>1<mu> and <mu2>0.4<mu2> [which resulted in this behavior]
I'm providing constant turning force, yet it slips more and more as the robot aligns with the X axis
(https://www.youtube.com/watch?v=lLnTa...). What frame are these in? The best I could find is the ODE documentation here, which looks great doesn't help at all (x y or z are never referenced...)
edit retag close merge delete
Hey Peter, did you every gain any insight into this? I've also noticed this behavior, and am working to track it down as well.
( 2016-10-08 16:17:34 -0500 )edit
I'm pretty confident this is true, but I can't prove it and haven't debugged it. definitely comment here or give an answer if you confirm it somehow
( 2016-10-09 18:37:19 -0500 )edit
I've created a scenario that seems to illustrate the issue. This video shows a cart sideways on a hill; friction holds it in place: https://youtu.be/BmFYAE_3sxA This video shows the exact same cart and ramp, changed only to rotate them 90 degrees, and this time, the cart slides down hill: https://youtu.be/06DumsFTInI The world files in question are stick: https://bitbucket.org/snippets/knitfoo/Gpod5 slide: https://bitbucket.org/snippets/knitfoo/KBG8e
( 2016-10-11 20:48:32 -0500 )edit
I suspect I'm just fundamentally not understanding how the ODE engine works, particularly relative to this type of object. I've instrumented gazebo/gazebo/physics/ode/ODEPhysics.cc; the Collide() method, to try to gain more insight. The normal vector for the 'stick' case is (0,-.3,.95); the normal for the 'slide' case is (0.3,0.0.95). mu is friction 'perpendicular to the normal'. To some extent, that almost suggests that the mu2/mu distinction is essentially irrelevant.
( 2016-10-11 20:58:28 -0500 )edit
Sort by » oldest newest most voted
I believe I can answer this question, at least for ODE, with what I've learned from studying and instrumenting the code. First, note that the answer to 'Explain Gazebo Friction Coeefficients mu and mu2' is probably the more 'correct' overall answer to this issue. As reported there, ODE officially documents mu/mu2 as having 'unspecified' direction. Of course, this is computer software, so nothing is truly unspecified; there must be some clear way these work. I started digging in the code to try to determine that.
The summary: if no fdir1 is provided, then there are two cases, based on the contact normal vector. If it's 'mostly' z, mu will end up being applied in a direction perpendicular to the normal, but in the y-z plane. For example, in the typical wheels on the ground situation, the contact normal is just a (0 0 1) vector. That then results in a mu vector of (0 -1 0). The mu2 vector is the cross; or (1 0 0) in our example. (The second case, where it is not mostly in z, results in mu being chosen in the x/y plane).
So, yes, you should find that any effect of mu/mu2 would appear to be in world coordinates, correlating to planes perpendicular to the collision normal. For wheels on a flat surface, that would break into x/y in world coordinates. The bottom line is that I don't think mu/mu2 are meant to be used to simulate the behavior of a tire. :-(.
I found the code to be illuminating and relatively easy to follow. In case it helps others, here are the bread crumbs I've used to come to this conclusion:
This block of code shows how Gazebo structures the contact collision joint for ODE.
In the case that fdir1 is not set, then we rely on the underlying ODE engine to compute the direction of friction, which appears to be mostly this code
Which shows that it eventually devolves into a call to dPlaneSpace which I think I've described, in my summary.
And, finally, I have successfully used an fdir1 of (1 0 0) to get my robot to drive somewhat more rationally. It's probably worth being aware of this bug, but I haven't found a case where that bug affects my robot yet.
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#### Can Güney Aksakalli
Notes from my journey
Inheritance is the key concept of object-oriented programming. A subclass is basically inherits the properties of its parent class. Let’s say, for our application we define basic class User. We need also Customer and Maintainer classes as a custom type of User, so we inherit them from the super class.
Customer and Maintainer subclasses, which are inherited from User, have username and password fields as common but also some additional specific fields. When we want to store those objects into a relational database system, they need to be mapped as tables. However, relational databases don’t support inheritance. In this example we have one base class and two subclasses to map into the relational database as tables. There are three approaches with their trade-offs to do that.
## 1) Single table
User table:
1 Alice 123 10001 NULL Customer
2 Bob abc NULL 10001 Maintaner
In this approach, all fields, which are defined under a super (parent) class, are stored in a single table. It is easy to query and retrieve different types from one table without need of join statements. However, a query to get Customer class object would also return irrelevant employeeNumber field; hence all regarding fields should be specified in the select statement.
Another problem is that, it is not possible to use constrains such as not null for a subclass. For example, customerNumber is an essential field for all Customer records. Yet applying not null constrain for customerNumber would prevent us from storing other objects without customerNumber such as Maintainer.
## 2) Class Table Inheritance
User table
1 Alice 123 Customer
2 Bob abc Maintaner
Customer table
id customerNumber
1 10001
Maintainer table
id employeeNumber
2 10001
In this approach, there exist one database table per class. Separate tables provide consistent data storage with constrain definitions but it is more complex to query a subclass. It requires to write some join statements which reduces the performance. For example, to get a Customer object, it needs to be join with User table.
## 3) Concrete Table Inheritance
Customer table
In this approach, there exist a table for each concrete class. Every concrete class has a table with duplicated fields. In case of updating a field type of the base class would require to migrate multiple tables. For example, if we change character size of password field, we need to alter both Maintaner and Customer tables. It might lead a conflict.
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# Question #3ab6b
Aug 31, 2017
Because the comet has returned to its original position with the same speed.
#### Explanation:
As the comet circles the sun, its gravitational potential energy and kinetic energy are continually changing. However the sum of those 2 energies remains constant, ${E}_{\text{total}}$. Energy is transferred back and forth between the 2 types of energy.
When the comet is at its maximum distance from the sun, its speed is minimum. Therefore the kinetic energy is at its minimum value and its gravitational potential energy is at its maximum value. And the sum of the 2 is still at the constant value: ${E}_{\text{total}}$.
When the comet is at its minimum distance from the sun, its speed is maximum. Therefore the kinetic energy is at its maximum value and its gravitational potential energy is at its minimum value. And the sum of the 2 is still at the constant value: ${E}_{\text{total}}$.
The comet's ${E}_{\text{total}}$ does not change because the comet does not gain any total energy at any part of its path and does not loose from the total.
However, if you look at just a part of the comet's path, then there will have been work done by gravitational force. It might be positive work or negative work. It would be positive work if the comet's speed has increased, negative work if it has decreased. But for any complete cycle, there is no net work done.
Whatever point in its path the question might be referring to, the answer to the question is:
Because the comet has returned to its original position (gravitational potential energy is same as the previous time it was here) with the same speed (kinetic energy is same as the previous time it was here). And the total is still ${E}_{\text{total}}$.
I hope this helps,
Steve
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# Antacids are compounds that neutralize stomach acid. Write the equations that show how Milk of Magnesia, Alka-Seltzer, and Tums remove
###### Question:
Antacids are compounds that neutralize stomach acid. Write the equations that show how Milk of Magnesia, Alka-Seltzer, and Tums remove excess acid. a, Milk of Magnesia: $mathrm{Mg}(mathrm{OH})_{2}$ b. Alka-Seltzer: $mathrm{KHCO}_{3}$ and $mathrm{NaHCO}_{3}$ c. Tums: $mathrm{CaCO}_{3}$
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Waiting for answer This question has not been answered yet. You can hire a professional tutor to get the answer.
QUESTION
# What is the hydroxide ion concentration in a solution of "NH"_3 with a "pOH" of 4.65?
["OH"^(-)] = 2.24 * 10^(-5)"M"
Your starting point here will be the definition of a solution's "pOH", which as you know is defined as the negative log base 10 of the concentration of hydroxide anions, "OH"^(-)
color(blue)(ul(color(black)("pOH" = - log(["OH"^(-)]))))
Now, in order to solve for the concentration of hydroxide anions, you must rearrange this equation as
log(["OH"^(-)]) = - "pOH"
and rewrite it using exponents of base 10
10^log(["OH"^(-)]) = 10^(-"pOH")
This is equivalent to
color(blue)(ul(color(black)(["OH"^(-)] = 10^(-"pOH"))))
Now all you have to do is to plug in the value given to you for the "pOH" of the solution
["OH"^(-)] = 10^(-4.65) = color(darkgreen)(ul(color(black)(2.24 * 10^(-5)"M")))
I'll leave the answer rounded to three .
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Parallax Occlusion Mapping
Employs per-pixel ray-tracing for dynamic lighting of surfaces in real-time on the GPU. The method uses a high precision algorithm for approximating view-dependent surface extrusion for a given height field to simulate motion parallax and perspective-correct depth. Additionally, the method allows generation of soft shadows in real-time for surface occlusions. Alternatively, POM can be coupled with well-known bump mapping algorithms such as normal mapping if physical accuracy can be sacrificed for greater computational efficiency.
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Definition of:Rmdir
Rmdir
A Windows, DOS and Unix command that removes a folder. The folder must be empty, and the command must be entered from the previous level or a non-related directory. RMDIR and RD are two forms of the command for Windows and DOS, but only RMDIR works in Unix. The following examples remove the HARRY subfolder within the PEOPLE folder. See cmd abc's and Unix commands.
DOS/WINDOWS
C:\PEOPLE>rmdir harry
C:\PEOPLE>rd harry
or
C:\WORK>rmdir \people\harry
C:\WORK>rd \people\harry
UNIX (Mac OS X Example)
x:~people mac1>rmdir harry
or
x:~mac1>rmdir people/harry
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Liebe Gitlab-Nutzer, lieber Gitlab-Nutzer,
es ist nun möglich sich mittels des ZIH-Logins/LDAP an unserem Dienst anzumelden. Die Konten der externen Nutzer:innen sind über den Reiter "Standard" erreichbar.
Peter Gottschling committed Feb 15, 2008 1 2 3 4 5 6 // ============================================================================ // == == // == AMDiS - Adaptive multidimensional simulations == // == == // ============================================================================ // == == Thomas Witkowski committed Sep 28, 2009 7 // == TU Dresden == Peter Gottschling committed Feb 15, 2008 8 // == == Thomas Witkowski committed Sep 28, 2009 9 10 11 // == Institut fr Wissenschaftliches Rechnen == // == Zellescher Weg 12-14 == // == 01069 Dresden == Peter Gottschling committed Feb 15, 2008 12 13 14 15 // == germany == // == == // ============================================================================ // == == Thomas Witkowski committed Sep 28, 2009 16 // == https://gforge.zih.tu-dresden.de/projects/amdis/ == Peter Gottschling committed Feb 15, 2008 17 18 19 20 21 22 23 24 25 26 // == == // ============================================================================ /** \file BoundaryManager.h */ #ifndef AMDIS_BOUNDARYMANAGER_H #define AMDIS_BOUNDARYMANAGER_H #include Peter Gottschling committed Apr 28, 2009 27 #include "AMDiS_fwd.h" Peter Gottschling committed Feb 15, 2008 28 29 30 31 32 #include "Boundary.h" #include "BoundaryCondition.h" namespace AMDiS { Thomas Witkowski committed Oct 14, 2009 33 34 typedef std::map BoundaryIndexMap; Peter Gottschling committed Feb 15, 2008 35 36 37 38 39 40 41 42 43 44 45 /** * \ingroup Assembler * * \brief * A BoundaryManager handles a set of boundary conditions and applies * this conditions to DOFVectorBase and DOFMatrix objects. Each DOFVectorBase * and each DOFMatrix has its own BoundaryManager. */ class BoundaryManager { public: Thomas Witkowski committed Sep 23, 2008 46 47 48 49 50 51 BoundaryManager(const FiniteElemSpace *feSpace); BoundaryManager(BoundaryManager &bm); ~BoundaryManager(); Thomas Witkowski committed May 07, 2009 52 /// Adds a local boundary condition to the list of managed conditions. Thomas Witkowski committed May 25, 2009 53 54 void addBoundaryCondition(BoundaryCondition *localBC) { Thomas Witkowski committed Oct 14, 2009 55 56 FUNCNAME("BoundaryManager::addBoundaryCondition()"); Peter Gottschling committed Feb 15, 2008 57 BoundaryType type = localBC->getBoundaryType(); Thomas Witkowski committed Oct 14, 2009 58 59 TEST_EXIT(localBCs[type] == NULL) ("There is already a condition for this type.\n"); Peter Gottschling committed Feb 15, 2008 60 localBCs[type] = localBC; Thomas Witkowski committed Oct 14, 2009 61 62 63 std::vector& boundMap = globalBoundaryMap[type]; boundMap.push_back(localBC); 64 } Peter Gottschling committed Feb 15, 2008 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 void initMatrix(DOFMatrix *matrix); void exitMatrix(DOFMatrix *matrix); void initVector(DOFVectorBase *vector); void exitVector(DOFVectorBase *vector); /** \brief * Calls DOFVectorBase::fillBoundaryCondition() for each local boundary condition * in \ref localBCs. */ void fillBoundaryConditions(ElInfo *elInfo, DOFVectorBase *vec); /** \brief * Calls DOFMatrix::fillBoundaryCondition() for each local boundary condition * in \ref localBCs. */ void fillBoundaryConditions(ElInfo *elInfo, DOFMatrix *mat); /** \brief * Calls BoundaryCondition::boundResidual() for each boundary condition in * \ref localBCs. */ Thomas Witkowski committed Oct 14, 2009 90 double boundResidual(ElInfo *elInfo, DOFMatrix *matrix, Peter Gottschling committed Feb 15, 2008 91 92 const DOFVectorBase *dv); Thomas Witkowski committed May 25, 2009 93 94 inline BoundaryCondition *getBoundaryCondition(BoundaryType type) { Peter Gottschling committed Feb 15, 2008 95 return localBCs[type]; 96 } Peter Gottschling committed Feb 15, 2008 97 Thomas Witkowski committed Oct 14, 2009 98 const BoundaryIndexMap& getBoundaryConditionMap() Thomas Witkowski committed May 25, 2009 99 { Peter Gottschling committed Feb 15, 2008 100 return localBCs; 101 } Peter Gottschling committed Feb 15, 2008 102 Thomas Witkowski committed Oct 14, 2009 103 void setBoundaryConditionMap(const BoundaryIndexMap& bcs) Thomas Witkowski committed May 25, 2009 104 { Peter Gottschling committed Feb 15, 2008 105 localBCs = bcs; 106 } Thomas Witkowski committed Oct 14, 2009 107 108 109 110 111 112 113 114 115 116 117 118 119 /** \brief * Returns true, if there is at least one boundary object with the given boundary * id, which implements a periodic boundary. */ static bool isBoundaryPeriodic(BoundaryType b) { for (int i = 0; i < static_cast(globalBoundaryMap[b].size()); i++) if (globalBoundaryMap[b][i]->isPeriodic()) return true; return false; } Peter Gottschling committed Feb 15, 2008 120 121 protected: Thomas Witkowski committed Mar 23, 2009 122 /// Map of managed local boundary conditions. Thomas Witkowski committed Oct 14, 2009 123 BoundaryIndexMap localBCs; Thomas Witkowski committed Sep 23, 2008 124 Thomas Witkowski committed Mar 23, 2009 125 /// Temporary thread-safe variable for functions fillBoundaryconditions. Thomas Witkowski committed Sep 23, 2008 126 127 std::vector localBounds; Thomas Witkowski committed Mar 23, 2009 128 /// Temporary thread-safe variable for functions fillBoundaryconditions. Thomas Witkowski committed Jan 19, 2010 129 std::vector > dofIndices; Thomas Witkowski committed Mar 23, 2009 130 Thomas Witkowski committed Sep 23, 2008 131 132 133 134 135 /** \brief * Stores the number of byte that were allocated in the constructor for * each localBounds value. Is used to free the memory in the destructor. */ int allocatedMemoryLocalBounds; Thomas Witkowski committed Oct 14, 2009 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 /** \brief * For every boundary id we store here all possible boundary object (although * it's not clear if it is meaningful to have different boundary conditions on the * same boundary id). * * We have to use this global variable, because the mesh traverse interface does * not provide more information about traversed boundaries at elements than the * boundary id. * * TODO: Change interface such that mesh traverse returns the boundary objects * directly and we can remove this global variable. The biggest problem will be * than serialization and deserialization of the mesh. */ static std::map > globalBoundaryMap; Peter Gottschling committed Feb 15, 2008 151 152 153 154 155 }; } #endif
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## 5. Normal Forms
1. #### Problem 5.1.
[Zaitsev] Let $C$ be a class of hypersurfaces defined by a finite order condition. A normal form is a subclass $C_0$ where normal representatives are determined up to a finite dimensional group. For example, for Levi non-degenerate hypersurfaces there is the Chern-Moser normal form and for finite type hypersurfaces in $\mathbb{C}^2$ Kollar presented a normal form. Can you find a class where it can be proved that there is no convergent normal form?
Cite this as: AimPL: Cauchy-Riemann equations in several variables, available at http://aimpl.org/crscv.
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It is currently 24 Mar 2019, 05:18
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# x is an integer such that –x|x| ≥ 4.
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x is an integer such that –x|x| ≥ 4. [#permalink] 08 Aug 2018, 16:37
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61% (00:49) correct 38% (00:53) wrong based on 42 sessions
x is an integer such that $$- x|x| ≥ 4$$.
Quantity A Quantity B x 2
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Kudos for R.A.E
[Reveal] Spoiler: OA
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Re: x is an integer such that –x|x| ≥ 4. [#permalink] 09 Aug 2018, 15:15
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Carcass wrote:
x is an integer such that $$- x|x| ≥ 4$$.
Quantity A Quantity B x 2
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Kudos for R.A.E
Given
$$- x|x| ≥ 4$$
Note:
|x| is always positive.
we have a negative sign with x but ultimate value is positive. So x have to be negative. Negative times negative is positive.
The best answer is B. 2 is greater than x, a negative integer.
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Re: x is an integer such that –x|x| ≥ 4. [#permalink] 23 Oct 2018, 03:02
Expert's post
Carcass wrote:
x is an integer such that $$- x|x| ≥ 4$$.
Quantity A Quantity B x 2
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Kudos for R.A.E
Now $$- x|x| ≥ 4$$ which means $$- x|x| > 0$$ which is possible when both -x and |x| have same sign. |x|>0 so -x>0...
Multiply the sides if equation by '-', so -(-x)<-(0)...x<0
Since x<0, x has to be less than 2..
Thus B>A
B
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Some useful Theory.
1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048
2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825
3. Remainders : https://greprepclub.com/forum/remainders-what-you-should-know-11524.html
4. Number properties : https://greprepclub.com/forum/number-property-all-you-require-11518.html
5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html
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Re: x is an integer such that –x|x| ≥ 4. [#permalink] 23 Oct 2018, 08:41
it was interesting.
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Re: x is an integer such that –x|x| ≥ 4. [#permalink] 23 Oct 2018, 20:00
Divide both sides by -x gives you |x| (< or =) 4/-x noting that you will be flipping the direction of the greater than sign since you are dividing by a negative. While you can then go and solve as you would any absolute value, having isolated the absolute value onto one side at this point, you can also see that the only way for the absolute value to be equal to a positive number (absolute values cannot be negative) is if the x value itself is negative. Since any negative number (x > 0) is going to be less than 2, we know that the answer will be B.
Re: x is an integer such that –x|x| ≥ 4. [#permalink] 23 Oct 2018, 20:00
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Evan James Williams
Quick Info
Born
8 June 1903
Cwmsychbant, Ceredigion, Wales
Died
29 September 1945
Brynawel, Cwmsychbant, Carmarthenshire, Wales
Summary
Evan James Williams was a mathematician and physicist who made outstanding contributions to atomic physics, especially when working with Niels Bohr. During World War II he worked for the Admiralty applying methods of Operations Research to deal with the problem of German U-boats. It is claimed that his contributions led to the defeat of the U-boat campaign which made planning for the Allies to invade Europe possible.
Biography
Evan James Williams, known as 'Desin', was the son of the stonemason James Williams (1868-1950) and Elizabeth Lloyd (1870-1948). Elizabeth, known as 'Bes', came from a family who lived in Llanfihangel-ar-arth, Llandysul but when her father died shortly before she was born, the family moved to Cwmsychbant to live with her maternal grandparents. James Williams lived in Cwmsychbant and got to know Elizabeth at school. They married in 1893 and had three children: Dafydd Williams (4 August 1894 - 9 August 1970), John Williams (24 March 1896 - 15 March 1983), and Evan James Williams, the subject of this biography.
Goronwy Evans describes James Williams as [8]:-
... a man of stature in the community, a strong character not shy of expressing his opinion.
Evans describes Elizabeth Williams as [8]:-
... a kindly woman full of energy and animation, the focal point of the home, around whom there was always much humour and laughter.
James Williams was a staunch member of the Congregational Chapel, attending services every Sunday in Brynteg, two miles from his home. He composed poems and was a regular competitor at the local eisteddfodau, where he frequently won a prize. With the help of Elizabeth's brother, he built the house named Brynawel in Cwmsychbant where Evan and his brothers were brought up. Let us note that at the time of the 1911 census, James and Elizabeth Williams, together with their three sons, were living at Brynawel. James is listed as speaking both English and Welsh as does the eldest son Dafydd (listed as David), who is as assistant teacher. The other two sons, John and Evan James, are both are listed as speaking only Welsh; they are both at school. It was a religious family, with daily Bible readings, and both James and Elizabeth were passionate about education and made sacrifices to give their sons the best possible.
Before continuing with the biography of Evan James, let us give some details about his two elder brothers. Dafydd taught mathematics at the school in Llanwenog where he had been a pupil, then joined the Civil Service but, not liking the work in the Customs and Excise Office, he joined the army. After World War I he studied engineering and spent the rest of his career at the Royal Aircraft Establishment in Farnborough. John's school education suffered because he had poor health but he attended night school and qualified as an optician. He had a business in Maesteg where he also carried out repairs to jewellery and watches.
Evan James attended Llanwenog National School, the same primary school in Llanwenog that both his brothers had attended. At this school he was sometimes taught by his oldest brother Dafydd [8]:-
Everyone knew him as Desin, because he was renowned for his ability to do mental arithmetic very quickly.
He showed himself to be exceptionally talented and, when twelve years old in 1915, he sat the county examinations and gained the highest marks which gave him a free place at Llandysul County School. The school had an outstanding headmaster William Lewis who was the first headmaster appointed when the school was founded in 1895. He had been a fifth Wrangler in the Mathematical Tripos at Cambridge, and it was through him that Williams became attracted to mathematics and physics. Learning [18]:-
... became an undiluted pleasure under Lewis's influence and inspiration, ensuring that Evan James's interest in physics and mathematics would flourish.
Lewis was not the only outstanding teacher at the school, for he was taught science by John Jones who had been a primary school teacher before moving to Llandysul County School to fill a vacancy caused by World War I [18]:-
Despite his modest qualifications, Jones was an excellent teacher and his lessons used 'life and colour' to animate his subject. For Evan James, this was a sheer joy. Through his teaching, Jones gave Evan James the thrill of interpreting and understanding experimental results, a practice that remained close to his heart throughout his academic career.
Williams was not the only outstanding mathematician at the school for Evan Tom Davies was also a pupil and was one year younger that Williams. The two boys became firm friends and in fact shared lodgings at 6 Marble Terrace in Llandysul. Williams would return home each weekend [8]:-
As a boy, a contemporary describes him as nearly as broad as he was tall, with a broad grin, a passion for cricket and a propensity for practical jokes and escapades.
Wynne writes [18]:-
According to Evan Davies, Evan James was forever at the centre of some rumpus or other, his laughter louder than everyone else's and the possibility of playing practical jokes never far from his mind. On one occasion, Evan Davies was rebuked by the science teacher because his homework notes on practical work included meaningless diagrams. This was as great a surprise to Evan Davies as it was to his teacher, but it soon became clear that Evan James had managed to get hold of his homework book after Evan Davies had finished the exercises, and had changed the diagrams. This instinct for leg-pulling stayed with Evan Davies for the rest of his life.
In 1918 Williams sat the Central Welsh Board School Certificate Examinations. He received distinctions in arithmetic, geometry, physics and mechanics. He only achieved a bare pass in Latin, however, and Evan Davies claimed this was quite deliberate since Williams believed that only swots got high Latin marks. He then competed for an open scholarship to Swansea Technical College and, after winning one of the four scholarships, entered the College in 1919. The College was due to become part of the University of Wales so Williams knew that he would be able to register as a University of College student and he did so in October 1920.
At first, probably influenced by his brother Dafydd, he began studying engineering but after only one term he changed to a pure science degree taking courses in physics, chemistry and mathematics. At the end of his first year at the College he sat the University of London external examinations in these three subjects. Williams, in his second year and now a student of the University College Swansea, had Evan Jenkin Evans (1882-1944) as his physics professor [16]:-
In 1920 [E J Evans] was appointed to the Chair of Physics in the new University College of Swansea. Temporary accommodation was found for the department in the Technical College, while the new laboratories were being built. Evans gave much time to the design and equipping of the laboratories which were opened in 1922. ... He was a gifted and conscientious teacher.
E J Evans quickly saw that he had an exceptionally talented student in Williams, and encouraged him to specialise in theoretical physics and theoretical chemistry. In 1921, a Physical and Mathematical Society was founded for staff and students at the University College Swansea. On 27 May twenty people attended its first meeting which was held in Dumbarton House, Bryn-y-Mor Road, Uplands. E J Evans was elected the first president while Williams was elected the first secretary. Meticulous minutes were kept by secretary Williams, who delivered a lecture after Christmas on the atomic nature of electricity.
Williams graduated in 1923 with First Class Honours in Physics. The external examiner was Charles Barkla (1877-1944) who was the professor of Natural Philosophy at the University of Edinburgh. An outstanding scientist, Barkla had been awarded the Nobel Prize in Physics in 1917 for his work in X-ray spectroscopy. Barkla examined Williams and wrote:-
... his papers submitted in the Honours Degree Examination were some of the most remarkable I have ever had the privilege of reading.
Williams remained at University College Swansea where he studied for his M.Sc. advised by E J Evans. He was awarded the degree in 1924 having undertaken research on two projects: (i) the temperature variation of the conductivity of mercury and some of its dilute amalgams and (ii) a theoretical investigation of the effect of a magnetic field on the resistance of liquid metals. This outstanding work was published in two papers The electrical conductivity of some dilute liquid amalgams (1925) and The effect of a magnetic field on the electrical resistance of liquid metals and alloys (1925). Both were communicated by E J Evans and were published in The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science.
In 1925 he won a University of Wales Fellowship and went to Manchester to undertake research for a Ph.D. advised by William Lawrence Bragg (1890-1971). W L Bragg was a leading physicist who, jointly with his father William Henry Bragg, had won the Nobel Prize in Physics in 1915:-
For their services in the analysis of crystal structure by means of X-rays.
Williams wrote a two-part Ph.D. thesis, the first part On the Scattering of X-rays and the Quantum Theory and the second part The ranges of $\beta$-rays. He writes:-
The work done by the writer described in this thesis was carried out under the supervision of Professor W L Bragg, F.R.S., and the writer wishes to express his deep gratitude to Professor Bragg for his kind advice and many helpful suggestions during the course of this work.
He submitted his thesis to the University of Manchester on 11 November 1926 and was awarded his Ph.D. Even before submitting the thesis, Williams had three papers published in 1926, two of which were joint papers written with John Mitchell Nuttall (1890-1958). Nuttall was a Senior Lecturer in Physics at the University of Manchester and assistant director of the Physics Department. The two Williams-Nuttall papers essentially formed two chapters in William's Ph.D. thesis.
In 1927 he published The Passage of $\alpha$-Rays and $\beta$-Rays through Matter which has the following abstract [17]:-
The loss of energy suffered by a fast-moving electrified particle passing through matter, and the ionisation produced by the moving particle, are phenomena which have, so far, not received accurate quantitative explanation. There are two main theories of the stopping-power due respectively to Bohr and Henderson. The theory of the primary ionisation due to a fast-moving particle is as it was left by Thomson in 1912. In all these theories, classical mechanics is used to calculate the possible energy transfers during encounters between the moving particle and the atomic electrons, and Fowler has suggested that the discrepancy which exists between theory and experiment may be due to the inaccuracy of classical mechanics in this field. Whether this is so or not, it may be of interest that a fair proportion of the discrepancy between classical calculations and experimental results disappears when the motion of the atomic electrons is allowed for. The effect of this motion may be considerable, though the velocity of the electron be small compared with that of the moving electrified particle.
Williams then was awarded an 1851 Exhibition Scholarship and went to Gonville and Caius College, Cambridge, as a Senior Research Student working at the Cavendish Laboratories. In his 1929 paper The Straggling of $\beta$-Particles he writes:-
I wish to express my thanks to Sir Ernest Rutherford, Dr C D Ellis and Mr R H Fowler for the interest they have taken in this work.
Having achieved a second Ph.D., this time from the University of Cambridge in 1929, and a D.Sc. from the University of Wales in 1930, Williams was appointed as an Assistant Lecturer at the University of Manchester. In 1930 Williams became engaged to a Welsh girl and they intended to marry later that year. The girl, however, broke off the engagement some months before the wedding, probably because Williams concentrated on his research so much that he had little time to devote to their relationship. He spent 1933-34 working with Niels Bohr in Copenhagen supported by a Rockefeller Scholarship. Blackett writes:-
... it was then that his brilliant talent as a theoretical physicist came to full fruition.
Bohr was very impressed by Williams and, following Williams' death, wrote (see [1]):-
You are quite right that from his long stay in this Institute, where he performed most admirable work, I had a deep appreciation of his remarkable ability and clearness of mind. Of course he had shown great gifts already in his earlier investigations, but it is true that we came into very close contact by common interest in the simple elucidation of fundamental problems and paradoxes of complementarity. In fact, Williams and I had planned together to write a treatise on collision phenomena on such lines but, due to the isolation brought about by the war, this plan never materialised.
In Copenhagen, Williams became friendly with Eli Winther. She was probably one of the two sisters lodging in the same house as him [18]:-
The correspondence from her suggests that Winther had fallen head over heels in love with Williams, and they remained in regular contact after Williams returned to Manchester in November 1934. But it became gradually obvious that Williams saw the relationship differently to Winther. Perhaps the depth of her feeling was not clear to him.
Williams never married, but he was soon engaged for a second time [18]:-
In 1938 Williams was appointed to the Chair of Physics at the University College Aberystwyth, part of the University of Wales. In addition, his outstanding academic achievements led to his election as a fellow of the Royal Society in March 1939. At the height of his powers, he had written 34 papers by this time, he was expected to make many more stunning contributions to theoretical physics. Blackett writes [2]:-
Williams was distinguished both as an experimental and theoretical physicist. His experimental work was mainly concerned with studies of electronic and atomic collision processes, using the cloud chamber of C T R Wilson. The most striking of his experimental achievements was the direct demonstration in 1940 by the cloud chamber method of the decay of a cosmic ray meson into an electron. Skilful though he was as an experimenter, Williams' distinction lay perhaps even more in his rare gift of analysing in detail the mechanisms of complicated physical processes, using a minimum of mathematical analysis and a maximum of physical understanding. In this quality of mind he had something in common with Niels Bohr ...
Things, however, changed dramatically with the outbreak of World War II in 1939. Patrick Maynard Stuart Blackett (1897-1974) had been appointed as a scientific officer at the Royal Aircraft Establishment in Farnborough at the start of the war and he requested Williams to join him at the end of 1939. Williams now worked on the threat posed by German submarines. Near the beginning of 1941, the Admiralty set to a new department of Operational Research at Coastal Command's headquarters in Northwood, Middlesex. Blackett was appointed head of Operational Research and Williams joined him there. He began applying the mathematical methods of Operations Research to the problems of German submarines. Blackett writes [2]:-
Williams turned his powerful analytic mind to many of the most important problems of the U-boat war, and made contributions of decisive importance to the winning of the campaign. His first work in this field, made during the summer of 1941, lay in the analysis of the process of attack on U-boats by aircraft. Simple but penetrating arguments, based on the actual observed facts of such attacks and on theoretical reasoning about these facts, showed that certain changes in the depth-setting and spacing of the depth charges should lead to a striking improvement in the number of U-boats sunk. The changes were made and the predicted results were attained, thus revolutionising the attacking power of Coastal Command aircraft.
By 1942, Williams was head of the Operational Research Section of Coastal Command. His work as scientific adviser to the Navy on methods of combating submarines, Blackett claims, led to the defeat of the German U-boat campaign by the summer of 1943 and made the planning for the allied invasion of Europe possible. He was appointed assistant director of research in the Navy in 1944, but in February of that year he was diagnosed with bowel cancer. He underwent two operations but sadly they were not successful and he died at his parents' home Brynawel in Cwmsychbant in September 1945.
For details of Williams' character and, in particular, his battle against cancer, see THIS LINK.
In 2017 Rowland Wynne published the book Evan James Williams: Ffisegydd yr Atom written in Welsh (see [19]). An English translation Evan James Williams: Atomic Physicist was published in 2020. For more information about this excellent book, see THIS LINK.
References (show)
1. P M S Blackett, Evan James Williams, 1903-1945, Obituary Notices of the Royal Society 5 (1947), 386-406.
2. P M S Blackett, Prof E J Williams, Nature 3970 (1 December 1945), 655-656.
3. Evan James 'Desin' Williams (1903-1945), From Warfare to Welfare 1939-1959, National Library of Wales.
https://web.archive.org/web/20151118111733/http:/myglyw.org.uk/index.php?id=4368
4. Evan James Williams, 1903-1945, The Times (2 October 1945).
5. Evan James Williams, 1903-1945, Western Mail (2 October 1945).
6. Evan James Williams, Western Mail (20 September 1961).
7. G Evans, 'Teulu Cyffredin o Anghyffredin', Carmarthenshire Life (July 2003), 8-9.
8. G Evans, Gwell Dysg na Golud (Wasg Gomer, 2003).
9. Genius of the destroyer of U-boats remembered, WalesOnline (14 June 2003).
https://www.walesonline.co.uk/news/wales-news/genius-destroyer-u-boats-remembered-2481305
10. J Gower, Review: Evan James Williams -Atomic Physicist is testament to the power of thought, Nation Cymru (29 August 2020).
https://nation.cymru/culture/review-evan-james-williams-atomic-physicist-is-testament-to-the-power-of-thought/
11. G M Griffiths, Williams, Evan James (1903-1945), scientist, Dictionary of Welsh Biography.
https://biography.wales/article/s2-WILL-JAM-1903
12. G Griffiths, Review: Evan James Williams - Ffisegydd yr Atom, by R Wynne, www.gwales.com.
https://www.gwales.com/goto/biblio/cy/9781786830722
13. J T Jones (ed.), Yr Athro Evan James Williams, D.Sc, F.R.S 1903-1945. Gwyddonydd o Gymru Byd-Enwog (Llandysul, 1971).
14. R V Jones, Williams, Evan James (1903-1945), Oxford Dictionary of National Biography (4 October 2007).
15. E M Owen, 'Yr Athro a'i Ddisgybl', Gwyddonydd 25 (1987/1988), 41-42.
16. E A Owen, Evans, Evan Jenkin (1882944), physicist and university professor, Dictionary of Welsh Biography.
https://biography.wales/article/s2-EVAN-JEN-1882
17. E J Williams, The Passage of α-Rays and, β-Rays through Matter, Nature 119 (1927), 489-490,
18. R Wynne, Evan James Williams: Atomic Physicist (University of Wales Press, 2020).
19. R Wynne, Evan James Williams: Ffisegydd yr Atom (University of Wales Press, 2017).
Other pages about Evan James Williams:
Other websites about Evan James Williams:
Honours (show)
Honours awarded to Evan James Williams
Cross-references (show)
Written by J J O'Connor and E F Robertson
Last Update July 2022
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# Gaussian Curvature and the Second Fundamental Form
In the last post we saw that the first fundamental form was an inner product on the the tangent space $T_pS$, and we used this to study the intrinsic geometry of surfaces. The goal of this post will be to understand the differential of the Gauss map, which we will use to define Gaussian curvature and the second fundamental form – a quadratic form on the tangent space $T_pS$. We will start by defining the Gauss map, which we have already seen in class. I will give a few examples/exercises in which we actually compute some of these. We will see that the differential of the Gauss map is a self-adjoint linear map, and the second fundamental form is the associated quadratic form. The Gauss map very much depends on how the surface is sitting in $\mathbb{R}^3$, i.e., on its parametrisation $\phi$. The remarkable fact is that the Gaussian curvature, which we will define in terms of this Gauss map, is an intrinsic property of $S$, that is, it doesn’t depend on the specific embedding $\phi$. This is the statement of Gauss’ Theorma Ergergium.
## The Gauss map and its differential
We want to consider parametrised surfaces in $\mathbb{R}^3$ such that the parametrisation $\phi$ is differentiable. Given such a parametrisation $\phi: U\subseteq \mathbb{R}^2 \rightarrow \mathbb{R}^3$ of $S$, we can choose a unit normal vector at each point $p$ in $\phi(U)$ by the rule
$n(p) = \displaystyle\frac{\phi_u \wedge \phi_v}{|\phi_u \wedge \phi_v|}$
Indeed, $\{\phi_u, \phi_v\}$ is basis for $T_pS$, and the cross product (see last post) gives us a vector perpendicular to both. The map $n:\phi(U) \rightarrow \mathbb{R}^3$ is differentiable, and we say we have a differentiable field of unit normal vectors (on the image $\phi(U)$). There has been some confusion in class over the definition of orientable. For us, an orientable surface is one that admits a differentiable field of normal vectors on the whole surface $S$, and we call a choice of such a field $n$ an orientation of $S$.
Remark. Given an orientation of $S$, we get an induced orientation on each tangent space $T_pS$ as follows: call a basis $\{a, b\}$ of $T_pS$ positive if $\langle a \wedge b, n\rangle$ is positive. Now the set of all positive bases for $T_pS$ is an orientation of $T_pS$.
Now, given an orientable surface we can define the Gauss map,
Definition. Let $S \subseteq \mathbb{R}^3$ be a surface with an orientation $n$. The Gauss map is the map
$n:S \rightarrow \mathbb{R}^3$
taking a point $p \in S$ to the normal vector $n(p) \in S^2 \subseteq \mathbb{R}^3$.
The Gauss map is a differentiable map, and its differential at $p$ is a linear map,
$dn_p:T_pS \rightarrow T_{n(p)}S^2$
Exercise. Compare $T_pS$ with $T_{n(p)}S^2$. Aren’t they similar? This is an important idea and we will come back to it.
In your prelim you were asked to compute a Gauss map. Let’s look at a few examples. Each time we can think about the above exercise.
Exercises.
1. An easy example is the plane $\pi$. The unit normal vector is constant here, so $dn_p=0$ for all $p \in \pi$. Notice that $T_{n(p)}S^2$ is parallel to $T_p\pi$.
2. Let $\mathcal{C} = \{ (x, y, z) : x^2+y^2=1\}$ be a cylinder. Choosing the inward pointing normal, we see by inspection that the Gauss map is
n(x, y, z) = (-x, -y, 0)
or if you prefer, let $\alpha(t) = (x(t), y(t), z(t))$ be a parametrized curve on $\mathcal{C}$ and observe that $2xx'+2yy'=0$ and thus $xx'+yy'=0$. This shows that either $(x, y, 0)$ or $(-x, -y, 0)$ are normal to $(x, y, z)$ on $\mathcal{C}$ (outward and inward pointing normals, respectively).
Now $n(\alpha(t))=(-x(t), -y(t), 0)$ and therefore we have
$dn_{\alpha(t)}=(-x'(t), -y'(t), 0)$
Exercise. Describe $dn_p$ in the two cases
(a) Our curve $\alpha_1$ is parallel to the z-axis (consider a tangent vector $v_1$ parallel to z-axis)
(b) Our curve $\alpha_2$ is parallel to the xy-plane (consider a tangent vector $v_2$ parallel to xy-plane)
$v_1$ and $v_2$ are eigenvectors of $dn_p$, and you have just computed their eigenvalues.
3. Exercise. Compute the Gauss map for the unit sphere $\mathcal{S}$ using the same method as above.
You should have seen the following in 2230, so this is just a quick recap. Let $V$ be a vector space with an inner product $\langle-,-\rangle$. We will be thinking about $T_pS$ with the first fundamental form.
Definition. A linear map $A:V \rightarrow V$ is self-adjoint if $\langle Av, w\rangle = \langle v, Aw\rangle$.
Exercise. Fix an orthonormal basis for $V$. Show that the corresponding matrix for $A$ is symmetric.
We associate to $A$ a symmetric bilinear form
$B:V \times V \rightarrow \mathbb{R}$ by $B(v, w) = \langle Av, w\rangle$
Conversely, if $B$ is a symmetric bilinear form then one can define a linear map $A:V \rightarrow V$ by $\langle Av, w\rangle = B(v, w)$, and it will be self-adjoint.
There is an associated quadratic form $Q(v) = B(v, v)$ which totally determines $B$ since
$B(u, v) = \frac{1}{2}(Q(u+v)-Q(u)-Q(v))$
and thus there is a one-to-one correspondence between self-adjoint linear maps of $V$ and quadratic forms in $V$. The main result we will use here is the following,
Theorem. Given a self-adjoint linear map $A:V \rightarrow V$, there exists an orthonormal basis for $V$ such that the corresponding matrix for $A$ is diagonal. Moreover the eigenvalues of this diagonal matrix are precisely the maximum and minimum values of the quadratic form $Q(v)=\langle Av, v\rangle$ on the unit circle of $V$.
(Remark. If this wasn’t covered in 2230 I can supply a proof)
## The Second Fundamental Form
The key observation to make, that I hinted at above, is that $T_pS$ and $T_{n(p)}S^2$ are parallel planes (e.g., see picture below), and so
$dn_p:T_pS \rightarrow T_{n(p)}S^2$
can be thought of as a linear map
$dn_p:T_pS \rightarrow T_{p}S$
Lemma. The differential $dn_p:T_pS \rightarrow T_pS$ is a self-adjoint linear map
Proof. Let $\phi$ be a parametrization of $S$ at $p$, and $\{\phi_u, \phi_v\}$ be the associated basis for $T_pS$. Let $\alpha(t) = \phi(u(t), v(t))$ be a parametrized curve in $S$ with $\alpha(0)=p$ then
$dn_p(\alpha'(0)) = dn_p(\phi_uu'(0)+\phi_vv'(0))$
$=\displaystyle\frac{d}{dt}n(u(t), v(t))\vert_{t=0}$
$= n_uu'(0)+n_vv'(0)$
In particular $dn_p(\phi_u)=n_u$ and $dn_p(\phi_v)=n_v$. To show self adjoint need to show
$\langle dn_p \phi_u, \phi_v \rangle = \langle \phi_u, dn_p \phi_v \rangle$
(and vice versa) which is equivalent to showing
$\langle n_u, \phi_v \rangle = \langle \phi_u, n_v \rangle$
Exercise. finish the proof. Hint: take derivative of $\langle n, \phi_u \rangle=0$ with respect to $v$ and of $\langle n, \phi_v \rangle=0$ with respect to $u$.
We thus have an associated quadratic form $Q$. It turns out to be more convenient to use $-Q$.
Definition. The second fundamental form $II_p$ is defined on $T_pS$ by $II_p(v)=-\langle dn_p(v),v \rangle$. It is the quadratic form associated to self-adjoint linear map $dn_p$.
## Normal, Principle, Gaussian and Mean Curvature
I first describe the normal curvature of a regular curve $\alpha$ in $S$. Recall (or perhaps this is a new definition) that if $\alpha:I \rightarrow \mathbb{R}^3$ is a curve (parametrized by arc length $t \in I$) then $k(t):=|\alpha''(t)|$ is the curvature of $\alpha$ at $t$.
Exercise. If this is a new definition then
1. Show that the the curvature of a straight line is 0.
2. Show that in general $\alpha''(t)$ is normal to $\alpha'(t)$. Hint: consider the expression $\alpha'(t)\cdot\alpha'(t)=1$.
Let $p$ be a point on $\alpha$, $k$ the curvature of $\alpha$ at $p$, and let $N_\alpha$ denote the (unit) normal vector to $\alpha$ at $p$ ($\frac{\alpha''(t)}{|\alpha''(t)|}$). Then we have that $\cos\theta=\langle N_\alpha, n\rangle$, where $n$ is the normal to the surface $S$ at $p$.
Definition. The normal curvature of $\alpha$ at $p$ is $k_\alpha:=k\cos\theta$. It is simply the projection of $k$ to $n$.
We can think of the second fundamental form in terms of normal curvature by making a simple calculation: We have that $\langle n(s), \alpha'(s)\rangle=0$. Therefore
$\langle n(s), \alpha''(s)\rangle + \langle n'(s), \alpha'(s)\rangle =0$
and we get
$II_p(\alpha'(0)) = -\langle dn_p(\alpha'(0)), \alpha'(0)\rangle =-\langle n'(0), \alpha'(0) \rangle=\langle n(0), \alpha''(0)\rangle=k_\alpha(p)$
So the second fundamental form $II_p$ of a vector $v \in T_pS$ is the normal curvature of a(ny) curve $\alpha$ passing through $p$ and tangent to $v$. In particular this tells us that any two curves passing though a given point with the same tangent have the same normal curvature at that point (this is known as Meusnier’s theorem).
We have shown that $dn_p$ is a self-adjoint linear map – and so we can apply the theorem stated above to conclude that there exists an orthonormal basis $\{e_1, e_2\}$ of $T_pS$ such that $dn_p$ is diagonal, that is $dn_p(e_1)=-k_1e_1$ and $dn_p(e_2)=-k_2e_2$, and moreover, we know that (WLOG) $k_1$ is the maximum value of $II_p$ restricted to the unit circle in $T_pS$ and $k_2$ is the minimum. That is, $k_1$ and $k_2$ are the extreme values of the normal curvature at the point $p$. We can picture this as follows: fix a point $p \in S$, and consider all possible unit tangent vectors at that point (a circle’s worth of them). For each choice of vector we find the normal curvature of a(ny) associated tangent curve, we pick out the maximum and minimum values we find around the circle, and call them $k_1$ and $k_2$.
Definition. $k_1$ and $k_2$ are called the principle curvatures at $p$, and the directions of their corresponding eigenvectors $e_1$ and $e_2$ are called the principle directions at $p$.
Examples.
1. For the plane or the sphere all directions at any point are extremal, and so all directions are principle directions. In particular $k_1=k_2$. Thought. Can you think of another surface with this property?
2. For the cylinder we showed that the principle curvatures are 0 and 1. In the specific example we covered, the principle directions at any given point are parallel to the z-axis (corresponding to the minimum normal curvature, 0) and parallel to the xy-plane (corresponding to the maximum, 1).
We know that the determinant and the trace of linear map are independent of the choice of basis, and therefore we have that $\det(dn_p)=k_1k_2$ and $tr(dn_p)=-(k_1+k_2)$.
Exercise. What would happen to the determinant and to the trace of $dn_p$ if we were to change to orientation of $S$? Do you think this would be the same if we were considering 3-manifolds? What about n-manifolds?
Definition. Let $dn_p:T_pS \rightarrow T_pS$ be the differential of the Gauss map at $p\in S$. The Gaussian curvature $K$ is the determinant of $dn_p$ and the mean curvature $H$ is the negative of half of the trace. In terms of principle curvatures that is,
$K=k_1k_2$ and $H = \displaystyle\frac{k_1+k_2}{2}$
The Gauss map takes a point $p \in S$ and gives you its unit normal vector. If we think intuitively about the differential $dn_p$, it should tell us how that normal vector is changing near to the point $p$. For example, if the Gaussian curvature is positive, that is telling us that both the principle curvatures have the same sign, and we can picture the surface ‘falling away’ from the tangent plane at $p$ in all directions:
Here are some terms you may have come across before that relate to this point of view.
Definition. A point on a surface $S$ is called
1. Elliptic if $K>0$
2. Hyperbolic if $K<0$
3. Parabolic if $K=0$ but $dn_p \neq0$
4. Planar if $dn_p=0$
Hopefully it is clear that this classification does not depend on the choice of orientation of $S$.
Exercise. Give examples of a points on surfaces satisfying each of 4 definitions above.
## Gauss’ Remarkable Theorem
Let’s recap what we just saw. The fundamental construction was the differential of the Gauss map $dn_p$ which was defined in terms of the Gauss map $n = \displaystyle\frac{\phi_u\wedge\phi_v}{|\phi_u\wedge\phi_v|}$ which itself we defined in terms of the parametrisation $\phi$. This is an important observation – the second fundamental form very much depends on the specific embedding $\phi$ of $S \subseteq \mathbb{R}^3$. We also can see that the principle curvatures depend on the embedding. So unlike the first fundamental form, which was used to describe the intrinsic geometry of $S$, the second fundamental form is used to understand its extrinsic properties. It is in this setting that Gauss’ theorem really does seem remarkable. Indeed, Gauss’ theorem tells us that $k_1k_2$ is an intrinsic property of $S$, that is, does not depend on the choice of $\phi$. Indeed, $k_1k_2=det(dn_p)=K$ the Gaussian curvature, and Gauss’ theorem is precisely that $K$ is an intrinsic property.
## A Word on Local Expressions
You may be wondering why we even bothered to define the second fundamental form? We didn’t use it directly to compute the anything as we did with the first fundamental form. Is it so fundamental? In fact its power can be seen via its use in making local computations. Given a parametrised surface we can describe the local situation very naturally, i.e., on a so called chart $\phi: U\subseteq \mathbb{R}^2 \rightarrow S$, we have a family of linear maps
$dn=\left(\begin{array}{cc}a & b \\c & d\end{array}\right)$
Fixing a basis $\{\phi_u, \phi_v\}$ for $T_pS$ one computes
$II_p(\alpha')=e(u')^2+2fu'v'+g(v')^2$
where
$e=\langle n, \phi_{uu} \rangle, f=\langle n, \phi_{uv} \rangle, g=\langle n, \phi_{vv} \rangle$
One obtains useful local expressions that are easy to compute in terms of $e, f, g$, for example, it can be shown that the Gaussian curvature is given by,
$K = \det\left(\begin{array}{cc}a & b \\c & d\end{array}\right)=\displaystyle\frac{eg-f^2}{EG-F^2}$
where $E, F, G$ are the coefficients of the first fundamental form. Similar expressions exist for the mean curvature and principle curvatures for example.
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Evidence of a ${\bf {6.12 \times 10^{18}}}$ GeV Particle: Detection and Mathematics
作者： Paul T. Smith 论文集英文名称： Proceedings of the Nineteenth International Conference on Geometry, Integrability and Quantization 来源数据库： Project Euclid DOI： 10.7546/giq-19-2018-204-224 原始语种摘要： In a new approach the graviton is defined as the field particle of spacetime rather than the mediator of gravity. The unification equation is derived and used to predict that for a freely falling body, the energy of incident gravitons is $6.12\times 10^{18}$ GeV. Redshift and scattering of gravitons should produce diffraction patterns, galactic halos and expansion of the Universe. The energy of incident gravitons remains constant as the Universe evolves because of the Doppler shift as bodies fall towards redshifted gravitons. Complex space is used to represent gravitons and explain Young’s two-slit interference. The approach is corroborated by empirical data and extends establish theory.
• times
• empirical 经验的
• approach
• towards 朝向
• bf 黑体
• graviton 引力子
• establish 建立
• unification 统一
• diffraction 衍射
• incident 入射的
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# Does $$x^x$$ function have a name?
Algebra Level pending
What is the minimum value of $$\large x^x$$, where $$\large x$$ is a real positive number? Give your answer to 3 decimal places.
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# Is (square root) fidelity strictly concave?
We know that (square root) Fidelity which is defined as $$\text{F}(\rho,\sigma) = \| \sqrt{\rho} \sqrt{\sigma} \|_1 = \text{Tr}(\sqrt{\sqrt{\sigma} \rho \sqrt{\sigma}})$$ is satisfies the property of joint concavity. That is
$$\text{F}\left(\sum_{i=1}^{n} p_i\rho_i, \sum_{i=1}^{n} p_i\sigma_i \right) \geq \sum_{i=1}^{n} p_i \text{F}(\rho_i,\sigma_i) , \tag{1}$$
for an $$n$$ dimensional probability vector $$p$$ and ensembles of states $$\{\rho_i\}_{i=1}^n$$ and $$\{\sigma_i\}_{i=1}^n$$. It follows that $$\text{F} \left(\sum_{i=1}^{n} p_i\rho_i,\sigma \right) \geq \sum_{i=1}^{n} p_i \text{F}(\rho_i,\sigma) \tag{2},$$
for some state $$\sigma$$.
For now, assume all of the states and probabilities are distinct and all the states are full-rank. Can we show that (2) is strictly concave? That is for non-extremal probability vectors (extremal points being the $$n$$ dimensional standard basis vectors) the inequality of (2) becomes strict?
• Take all $\rho_{i}$ orthogonal to some rank $1$ $\sigma$ and it becomes an equality.
– JSdJ
May 6 at 14:22
• @JSdJ Thanks, that is a great example for the equality. Can we show this to be the case when all the states $\rho_i$ and $\sigma$ are full rank? May 8 at 11:05
• I'm not sure if I completely understand your question - do you mean that for $\rho_{i}$ and $\sigma$ orthogonal and full rank, it's necessarily an equality?
– JSdJ
May 11 at 17:02
• No, my intuition is that when all the $\rho_i$s and $\sigma$ and distinct and full rank, along with the probabilities $p_i$ being distinct, the inequality should be strict. May 13 at 5:16
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## Analytic Function Derivative
Take $x=r\cos\theta$ and $y=r\sin\theta$
If $f(z)=u(r,\theta) + iv(r,\theta)$, is analytic with u and v real, show that the derivative is given by
$$f'(z) = \left( \cos\theta \frac{\partial u}{\partial r}- \sin\theta\frac{1}{r}\frac{\partial u}{\partial\theta}\right) + i\left( \cos\theta\frac{\partial v}{\partial r} - \sin\theta\frac{1}{r}\frac{\partial v}{\partial\theta} \right)$$
Since f is analytic, I use the result
$$f'(z)=\frac{\partial u}{\partial x} + i\frac{\partial v}{\partial x}$$
Though this seems to give
$$f'(z) = \left( (1/\cos\theta) \frac{\partial u}{\partial r}- (1/\sin\theta)\frac{1}{r}\frac{\partial u}{\partial\theta}\right) + i\left( (1/\cos\theta)\frac{\partial v}{\partial r} - (1/\sin\theta)\frac{1}{r}\frac{\partial v}{\partial\theta} \right)$$
Can anyone see why this isn't correct?
PhysOrg.com science news on PhysOrg.com >> City-life changes blackbird personalities, study shows>> Origins of 'The Hoff' crab revealed (w/ Video)>> Older males make better fathers: Mature male beetles work harder, care less about female infidelity
Blog Entries: 9 Recognitions: Homework Help Science Advisor How did you apply the chain rule...?I think there's a problem with that. Daniel.
I just did: du/dx = (du/dr)(dr/dx) + (du/dtheta)(dtheta/dx) though I think that's probably not quite right when I think about the dependence of the variables on eachother... Though the "units" look OK at first sight, I'm not sure that I can do that.
Blog Entries: 9
Recognitions:
Homework Help
## Analytic Function Derivative
Here's where you went wrong
$$\frac{\partial u}{\partial x}=\frac{\partial u}{\partial r}\frac{\partial r}{\partial x}+\frac{\partial u}{\partial\theta}\frac{\partial\theta}{\partial x}$$ (1)
$$\frac{\partial r}{\partial x}=\frac{\partial}{\partial x}\sqrt{x^{2}+y^{2}}=\frac{x}{\sqrt{x^{2}+y^{2}}}=\frac{r\cos\theta}{r} =\cos\theta$$ (2)
Can u do the other derivative...?
Daniel.
Thanks. I'll look at that.
Similar discussions for: Analytic Function Derivative Thread Forum Replies Calculus 7 Calculus 13 Calculus & Beyond Homework 1 Engineering, Comp Sci, & Technology Homework 3 Calculus 13
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Next: References Up: 5. Smoothing: Local Regression Previous: 5.4 Statistics for Linear
Subsections
# 5.5 Multivariate Smoothers
When there are multiple predictor variables, the smoothing problem becomes multivariate: is now a surface. The definition of kernel and local regression smoothers can be extended to estimate a regression surface with any number of predictor variables, although the methods become less useful for more than 2 or 3 variables. There are several reasons for this:
• Data sparsity - the curse of dimensionality.
• Visualization issues - how does one view and interpret a high dimensional smooth regression surface?
• Computation is often much more expensive in high dimensions.
For these reasons, use of local polynomials and other smoothers to model high dimensional surfaces is rarely recommended, and the presentation here is restricted to the two-dimensional case. In higher dimensions, smoothers can be used in conjunction with dimension reduction procedures (Chap. III.6), which attempt to model the high-dimensional surface through low-dimensional components. Examples of this type of procedure include Projection Pursuit ([9]), Additive Models ([14]), Semiparametric Models ([26] and Chap. III.10) and recursive partitioning (Chap. III.14).
## 5.5.1 Two Predictor Variables
Suppose the dataset consists of vectors , where and are considered predictor variables, and is the response. For simplicity, we'll use to denote a vector of the predictor variables. The data are modeled as
Bivariate smoothers attempt to estimate the surface . Kernel and local regression methods can be extended to the bivariate case, simply by defining smoothing weights on a plane rather than on a line. Formally, a bivariate local regression estimate at a point can be constructed as follows:
1. Define a distance measure between the data points and fitting point. A common choice is Euclidean distance,
2. Define the smoothing weights using a kernel function and bandwidth:
3. Define a local polynomial approximation, such as a local linear approximation
when is close to . More generally, a local polynomial approximation can be written
where is a vector of coefficients, and is a vector of basis polynomials.
4. Estimate the coefficient vector by local least squares. That is, choose to minimize
5. The local polynomial estimate is then
## 5.5.2 Likelihood Smoothing
A likelihood smoother replaces the model (5.1) with a distributional assumption
where is a specified family of densities, parameterized so that . The family may be chosen depending on the response variable. If is a count, then the Poisson family is a natural choice:
If is a (or no/yes) response, then the Bernoulli family is appropriate:
Given the data, the log-likelihood is
The goal is to estimate the mean function, for an observed set of covariates . A generalized linear model (Chap. III.7) uses a parametric model for the mean function. Likelihood smoothers assume only that the mean is a smooth function of the covariates.
The earliest work on likelihood smoothing is [16], who used a penalized binomial likelihood to estimate mortality rates. The local likelihood method described below can be viewed as an extension of local polynomial regression, and was introduced by [30].
### 5.5.2.1 Local Likelihood Estimation.
Local likelihood estimation is based on a locally weighted version of the log-likelihood:
A local polynomial approximation is then used for a transformation of the mean function. For example, a local quadratic approximation is
The function is the link function. Its primary goal is to remove constraints on the mean by mapping the parameter space to . For example, in the Poisson case, the parameter space is . If the log transformation is used, then the parameter space becomes .
Let where , so that the locally weighted log-likelihood becomes
The maximizer satisfies the likelihood equations,
(5.20)
where
In matrix notation, this system of equations can be written in a form similar to (5.7):
(5.21)
This system of equations is solved to find parameter estimates and . The local likelihood estimate is defined as
### 5.5.2.2 Solving the Local Likelihood Equations.
The local likelihood equations (5.20) are usually non-linear, and so the solution must be obtained through iterative methods. The Newton-Raphson updating formula is
(5.22)
where is a diagonal matrix with entries
For many common likelihoods is concave. Under mild conditions on the design points, this implies that the local likelihood is also concave, and has a unique global maximizer. If the Newton-Raphson algorithm converges, it must converge to this global maximizer.
The Newton-Raphson algorithm (5.22) cannot be guaranteed to converge from arbitrary starting values. But for concave likelihoods, is guaranteed to be an ascent direction, and convergence can be ensured by controlling the step size.
### 5.5.2.3 Statistics for the Local Likelihood Estimate.
Since the local likelihood estimate does not have an explicit representation, statistical properties cannot be derived as easily as in the local regression case. But a Taylor series expansion of the local likelihood gives an approximate linearization of the estimate, leading to theory parallel to that developed in Sects. 5.3 and 5.4 for local regression. See Chap. 4 of [21].
## 5.5.3 Extensions of Local Likelihood
The local likelihood method has been formulated for regression models. But variants of the method have been derived for numerous other settings, including robust regression, survival models, censored data, proportional hazards models, and density estimation. References include [30], [17], Loader ([19], [21]).
### 5.5.3.1 Robust Smoothing.
Robust smoothing combines the ideas of robust estimation (Chap. III.9) with smoothing. One method is local M-estimation: choose to minimize
and estimate . If , this corresponds to local least squares estimation. If is a symmetric function that increases more slowly than , then the resulting estimate is more robust to outliers in the data. One popular choice of is the Huber function:
References include [11] and [21]. Another variant of M-estimation for local regression is the iterative procedure of [4].
### 5.5.3.2 Density Estimation.
Suppose are an independent sample from a density . The goal is to estimate . The local likelihood for this problem is
Letting be the maximizer of the local log-likelihood, the local likelihood estimate is . See [17] and [19].
The density estimation problem is discussed in detail, together with graphical techniques for visualizing densities, in Chap. III.4.
Acknowledgements. This work was supported by National Science Foundation Grant DMS 0306202.
Next: References Up: 5. Smoothing: Local Regression Previous: 5.4 Statistics for Linear
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The Michigan Mathematical Journal
Topology of Kähler Manifolds with Weakly Pseudoconvex Boundary
Brian Weber
Abstract
We study Kähler manifolds-with-boundary, not necessarily compact, with weakly pseudoconvex boundary, each component of which is compact. If such a manifold $K$ has $l\ge 2$ boundary components (possibly $l=\infty$), then it has the first Betti number at least $l-1$, and the Levi form of any boundary component is zero. If $K$ has $l\ge 1$ pseudoconvex boundary components and at least one nonparabolic end, then the first Betti number of $K$ is at least $l$. In either case, any boundary component has a nonvanishing first Betti number. If $K$ has one pseudoconvex boundary component with vanishing first Betti number, then the first Betti number of $K$ is also zero. Especially significant are applications to Kähler ALE manifolds and to Kähler 4-manifolds. This significantly extends prior results in this direction (e.g., those of Kohn and Rossi) and uses substantially simpler methods.
Article information
Source
Michigan Math. J., Advance publication (2019), 16 pages.
Dates
Revised: 4 April 2019
First available in Project Euclid: 23 July 2019
https://projecteuclid.org/euclid.mmj/1563847454
Digital Object Identifier
doi:10.1307/mmj/1563847454
Subjects
Primary: 53C55, 53C23, 31C12, 31C10, 58J99
Citation
Weber, Brian. Topology of Kähler Manifolds with Weakly Pseudoconvex Boundary. Michigan Math. J., advance publication, 23 July 2019. doi:10.1307/mmj/1563847454. https://projecteuclid.org/euclid.mmj/1563847454
References
• [1] A. Andreotti and E. Vesentini, Carleman estimates for the Laplace–Beltrami equation in complex manifolds, Publ. Math. Inst. Hautes Études Sci. 25 (1965), no. 1, 81–130.
• [2] H. Grauert, On Levi’s problem and the imbedding of real-analytic manifolds, Ann. of Math. 68 (1958), no. 2, 460–472.
• [3] I. Holopainen, Nonlinear potential theory and quasilinear mappings on Riemannian manifolds, Ann. Acad. Sci. Fenn. Math. Diss. 74 (1990), 1–45.
• [4] I. Holopainen and P. Koskela, Volume growth and parabolicity, Proc. Amer. Math. Soc. 129 (2001), no. 11, 3425–3435.
• [5] L. Hörmander, $L^{2}$ estimates and existence theorems for the $\bar{\partial }$ operator, Acta Math. 113 (1965), 89–152.
• [6] J. J. Kohn, Harmonic integrals on strongly pseudo-convex manifolds, I, Ann. of Math. (2) 78 (1963), no. 1, 112–148.
• [7] J. J. Kohn, Harmonic integrals on strongly pseudo-convex manifolds, II, Ann. of Math. 79 (1964), no. 3, 450–472.
• [8] J. J. Kohn and H. Rossi, On the extension of holomorphic functions from the boundary of a complex manifold, Ann. of Math. (2) 81 (1965), no. 2, 451–472.
• [9] P. Li, On the structure of complete Kähler manifolds with nonnegative curvature near infinity, Invent. Math. 99 (1990), 576–600.
• [10] P. Li and L. Tam, Positive harmonic functions on complete manifolds with non-negative curvature outside a compact set, Ann. of Math. 125 (1987), 171–207.
• [11] P. Li and L. Tam, Harmonic functions and the structure of complete manifolds, J. Differential Geom. 35 (1992), 359–383.
• [12] P. Li and L. Tam, Green’s functions, harmonic functions, and volume comparison, J. Differential Geom. 41 (1995), 277–318.
• [13] T. Ohsawa, On complete Kähler domains with $C^{1}$-boundary, Publ. Res. Inst. Math. Sci. 16 (1980), 929–940.
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Primes
Number Theory Level pending
Find the sum of all positive prime numbers $$p$$ such that $$p^2+11$$ has exactly $$6$$ distinct positive divisors.
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# Trigonmetric general solutions question
• September 9th 2011, 06:56 AM
aonin
Trigonmetric general solutions question
I'm not sure how to solve using general solutions $\sin{3\theta}=3\sin{\theta}$
• September 9th 2011, 07:06 AM
Prove It
Re: Trigonmetric general solutions question
Quote:
Originally Posted by aonin
I'm not sure how to solve using general solutions $\sin{3\theta}=3\sin{\theta}$
Start by simplifying the LHS using the identity $\displaystyle \sin{3\theta} \equiv 3\sin{\theta} - 4\sin^3{\theta}$.
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Studfinder: Wire Edition
Craig Macomber, Milda Zizyte
June 10, 2011
# Introduction
Often, humans are faced with the problem of finding that which they cannot see. The five senses are limited and in particular do not extend to wavelengths outside the audible or visible spectrum. Auxillary devices employing sensing solutions are thus required to augment the senses.
Such sensing capabilities are conceivably very important. In the area of electric sensing, a person might want to locate power behind a wall or want to figure out the closest source of power in a busy room.
In particular, humans cannot easily locate electric fields. However, given sufficient hardware and clever filtering, it is possible to detect the 60 Hz electric fields emanating from wall outlets and the cables attached to them. [1] uses such a scheme, with a copper-coated electric plug face as one electrode and the ground prong of the plug as another, to scan for such fields and allow a robot to effectively “feed itself” by guiding itself to power.
In fact, the robot Marvin faces the same problem humans do - just as a robot cannot see these electric fields, neither can humans. Our project aims to provide human perception of such phenomena by hardware which translates an electric input into minimal visual feedback. We thus achieve the analog of an electric studfinder - a device which senses otherwise invisible objects (obscured by obstacles or otherwise) and conveys them with a few blinking lights. In fact, our solution provides enough information for a user to be aware of electric cables in the wall to prevent from drilling into them!
Our solution combines analog filtering with digital processing to achieve its goal. It is an easily adaptable and potentially portable device with many possible applications and implications.
# Analog Hardware Design
The analog circuit has three main purposes:
1. To receive and filter an input electrode current into a clear voltage output signal
2. To convey the output using minimal complexity
3. To effectively interface with an Arduino Uno for digital processing
(1) is the most complex, requiring filtering a current source. A MCP6024 quad op-amp package is used for this purpose, and is described in a later section.
(2) is accomplished by the use of three LEDs, denoted “left,” “right,” and “amplitude.” In this way, we can convey both direction and strength of the electric field by modulating brightness. This seems like the most natural and unobtrusive way of translating electric fields to a “human-readable format,” as it is less irksome than audio output and easier to implement, as well.
(3) strongly depends on (1) and (2). In particular, the Arduino places constraints on how many wires we can use and the form our outputs take. We opted two use two analog input pins post-filtering, and three pulse-width modulated pins for outputs into the LED.
An overview of our circuit is thus figure 1. EL and ER denote the left electrode signal and right electrode signal, respectively.
## Electrodes
Our electrodes, or antenna, are simple in design. Due to the low operating frequency, there are no real restrictions on what shapes pick up a strong signal. Our design needed to meet two requirements: producing a sufficient signal, and providing a directional differential signal. With our antenna's two electrodes are simple copper tape rectangles. The length of the tape, which sets the height of our antenna determines the signal strength, and the separation sets the directional sensitivity. A good balance of both is required to be able to both detect a signal from a significant distance, as well as to tell what direction it is coming from. Our final shape was mostly determined by supply available, and some guessing about how much signal we needed based on our original smaller electrodes. Our final measurements are 300 mm across, 240 mm high. The makes the electrodes 25 mm by 240 mm with a separation of 240 mm (265 mm center to center).
Also, the symmetry is very important: both electrodes are the same area. Otherwise, our differential zero point would be off.
We chose acrylic to mount the copper tape on for three main reasons:
1. It is a good insulator. The plastic used is scrap from an old electrostatics project and was originally selected for its insulating properties. If the substrate for our antenna were a conductor, our two electrodes would be connected, and we would lose the directional signal.
2. It is transparent. This makes it much easier to see what one is doing when using it near the source its detecting, as is the case when following wires in walls.
3. We had some available. There are plenty of other materials that would have also worked well, but we simply chose the one we had in the correct size.
## Filtering
The circuit shown here provides a current to voltage conversion, followed by a low pass filter tuned to easily pass anything near 60 Hz or lower. Since there is vastly more 60 Hz signal than any nearby or lower frequency, a sharp cutoff was not needed.
Notice that our cutoff frequency is:
(1)
\begin{align} f = \frac{1}{2\pi (100 k\Omega)(.01\mu F)} = 159 Hz. \end{align}
Our original filter had a resistor value of twice that for an 80 Hz cutoff. Experimentation yielded less than satisfactory results, so we decreased our resistor value. This still cuts off most high frequency noise, as we are mostly worried about noise in the kilohertz and above.
We went for a simple active filter along with some additional gain. This design allowed all the needed analog filtering using only two op-amps per channel. Thus, we only needed four op-amps total, one package.
The transimpedance stage, which converts the electrode's current signal to a voltage signal uses a 2M resistor. Some experiments were run on what values worked best.
The second stage, an inverting low pass amplifier with a cutoff frequency of 160 Hz and a gain of 50. This removes high frequency noise, and brings our signal up to an accurately measurable size.
## Output
We opted for a simple output of three LEDs. Two of them are directional and almost directly correspond to each component of the antenna. The third is a magnitude antenna, which helps the user distinguish how strong the observed signal is. No analog magic is used for this part of the circuit: there are just the conventional resistors to ground, and everything else is driven by digital logic, discussed in the next section.
Pulse-Width Modulated pins were used for the LEDs so that we could control their brightness using the Arduino.
Throughout the development and testing process, we tried a few different display approaches. Initially we simply had one output, which when low, lit one light, and when high lit the other. Initially this was a digital output, simply high or low. When the antenna was pointed at the field source, both lights would flicker and it would be confusing. We then converted to using pulse width modulated outputs. This helped, but we found both lights coming on to be not very useful, which lead to the final design. Only one light is on at once, and the brightness depends on the amount that the antenna needs to turn. To make out full level of sensitivity apparent, we multiplied up the signal so the LEDs saturate pretty early, and its easy to see small angular differences.
# Firmware
The comments explain the code in detail. At a high level it reads in the two signals, and uses an IIR filter to computer the mean. It then subtracts the mean from the signals removing the DC offset. Finally the signals are rectified and smoothed with another IIR. It then takes the difference of the absolute magnitudes to get direction, and output that to the left and right LEDs. We also apply an IIR to our magnitude LED to smooth out flicker.
We experimented with several values for both $a$ and $b$ in our code. As the purpose of the LEDs is to convey first-nature, intuitive information about what the antenna senses, this experimentation was not precise. We noticed a trade-off between “flicker” (how much and how often the signal changed in a distracting fashion) and speed (how quickly the LEDs mimicked the action of changing the configuration of the antenna) and settled on some values that generally worked well. Depending on use case, these values may need to be readjusted.
// These constants won't change. They're used to give names
// to the pins used:
const int left = A0; // Analog input pin for the left electrode
const int right = A1; // Analog input pin for the right electrode
const int leftLED = 11; // PWM pin for the left LED
const int rightLED = 10; // PWM pin for the right LED
const int ampLED = 9; // PWM pin for the amplitude LED
const float a = .2; // filter value for the left/right IIR low-pass filter
const float b = .008; // filter value for the output IIR low-pass filter (for smoothing)
// used for IIR
static float leftmid = 0;
static float rightmid = 0;
float signal = 0; // difference of the filtered left/right signals
// used for IIR
static float signalLeft = 0;
static float signalRight = 0;
// writing to serial at intervals
int count = 0;
void setup() {
// initialize serial communications at 9600 bps:
Serial.begin(9600);
// initialize pins:
pinMode(left, INPUT);
pinMode(right, INPUT);
pinMode(leftLED, OUTPUT);
pinMode(rightLED, OUTPUT);
pinMode(ampLED,OUTPUT);
}
void loop() {
// Apply an IIR to each one
leftmid = a*l + (1-a)*leftmid;
rightmid = a*r + (1-a)*rightmid;
// Take the magnitude without the DC components
float left = abs(l-leftmid);
float right = abs(r-rightmid);
// Smooth them out with another IIR
signalLeft = left * b + (1-b)*signalLeft;
signalRight = right * b + (1-b)*signalRight;
// Take the difference (negative signal means more input on the right; positive means more on the right)
signal = (signalLeft - signalRight);
// duty factor for amplitude output: just the sum of the amplitudes we've seen
int df = min(255,(int) (signalLeft+signalRight));
analogWrite(ampLED,df);
// Output to the LEDs: the *32 is to favor a large signal in one of the LEDs, but if the signal is in the middle, both LEDs are going to be dimmer
analogWrite(leftLED,min(255,max(0,signal*32)));
analogWrite(rightLED,min(255,max(0,signal*-32)));
// Print what we see to the monitor for data collection
if(count == 0) {
Serial.println(signal);
}
count = (count+1)\%100;
}
# Characterization
We performed several experiments and measurements to evaluate our circuit. They are as follows:
## Noise measurement
For this experiment, we simply held the antenna away from any visible powerlines in the middle of an isolated area. We took 234 samples from the arduino serial input with the antenna tilted both ways. Our results are outlined in table one (the output is the filtered analog $signal$ value as seen in the code above):
Average Standard deviation -0.08 0.138 -0.18 0.120
Since two positions were identical except mirrored swapping the electrodes, the bias can be computed as the difference of the two means. These results show little bias in the inputs, only 0.10. If desired, this could be reduced by some calibration. Calibrating out the bias would require two adjustments. The first to remove the zero signal offset measured here, and a second to scale the data to compensate for multiplicative errors.
The noise was of a comparable scale to the bias, also very small.
## Signal to Noise Ratio
We also took samples of a strong signal (the antenna close to a power outlet with a cord in the wall, which was our strongest pick up) and measured the mean and standard deviation: the mean turned out to be 163.86, and the standard deviation 2.43. This leads to a signal-to-noise-ratio of
(2)
\begin{align} SNR = \frac{163.86}{2.43} = 67.432 \end{align}
Unfortunately, looking at the details for this data, it seems likely that some of the signal was clipping, so it is not an accurate measurement.
Using some of our other data from the antenna in a strong field, 30 cm from an extension cord, we computed this:
(3)
\begin{align} SNR = \frac{2.165}{0.0872} = 24.828 \end{align}
This includes the variations from not holding the antenna still, and is still quite good. Since our data used here was with the antenna oriented to produce low differential signal, the signal value is taken from the same position, but with a different orientation to measure the actual field present. Using the sum for this would have been better. Further data collection to measure the SNR under more conditions would provide more detail, but currently we do not have such data.
This high signal to noise ratio was achieved by averaging over a long period with our IIR filter. It comes at the cost of somewhat slow response times, however for our uses, the response was plenty fast.
## Rotations
We performed several experiments with rotating the antenna with a fixed centerpoint, including the following:
30cm from wall, bare socket rotation
30cm from wall, cord in wall rotation
1.5m from wall, bare socket rotation
1.5 from wall, cord in wall rotation
These were all rotated by hand, which is not easy to do accurately. Even the strong and clean signals show some distortion, and the non-uniform rotation speed is probably part of the cause. Also, in some of the tests, rotation started a little way into data collection leaving a flat spot at the beginning. With this taken into account the graphs all resemble a sine waves of various amplitudes with varying clarity.
If we assume the field is a uniform linear gradient with no curl (which is somewhat close to reality when far away from the source), an ideal version of our sensor would produce a sine wave. Thus, the sine wave was the expected result. The zero crossing show where the antenna's normal is inline with the field gradient (meaning its pointed at or away from the source), and the peaks show where the antenna is inline with the field gradient (the field source is in the plane of the antenna).
Even the weak signal from the wall socket alone (which was partly shielded by a metal face plate) still produced a sign wave in our 1.5 m test. This shows that we can still detect the direction of a socket from 1.5 meters away. The direction might not be too accurate, but it should be good enough to get closer where a more accurate signal would be available.
## Distance Variation
Another experiment was keeping the antenna in the same orientation parallel to some walls in a hall and moving it away from a visible socket, recording the data. We plotted the results as follows:
Moving from 0 to 1.5m away from bare socket at steady pace
Amplitude moving from 0 to 2m away from cord in wall at steady pace
These plots show 2 types of saturation related failures. The first shows that even if there is a strong differential signal, it can fail to be detected if both channels start clipping. At the beginning, we suspect the signal is so strong that the difference partly hidden by this effect. This however only seemed to be an issue in the most extreme case of the antenna sideways and up against the outlet.
The second plot shows the total sum amplitude, not difference. It shows the clipping, and a sharp falloff with distance. Since it is measuring the derivative of the electric field which falls off with the square of the distance, the signal is expected to drop off with the cube of the distance. While we can not accurately tell the shape of the curve, it looks like it is not clipping it may be roughly the expected proportional to $\frac{1}{d^3}$ where $d$ is the distance from the source.
# Conclusion
After looking at our LEDs, as well as some numeric data, we discovered a few things about our design. One is that we can get some clipping issues. This was not apparent from just looking at the LEDs, but perhaps we could get better signals for close/strong sources if we resolved the issue. Once approach would be logarithmic gain. Initially we avoided this because it added complexity, and we feared its reduction in differential signal might be an issue.
The other main thing we noticed from our numeric data was that we could tell the general direction from further away than was obvious from just our LEDs. One thing we could do to better display this so to lower the time constant on our final IIR filters for more smoothing and slower response. This would allow even the noisy long range signals to be directly usable as long as you don't turn too fast.
This relates to another change that would improve the usability across varying distances: using different tuning, and even antennas, at different distances/signal strengths. It would be possible to adjust time constants based on signal strength, and to shift over to higher precision antennas. This would also resolve most saturation issues if done correctly.
Another change we would make if redoing or continuing this project is to insulate the electrodes. Covering them with packing tape for example would help protect them from getting shorted to things accidentally, and should have little to no effect of the signal. Additional static protection for the first op-amp might also be a good idea.
While we have several ideas how the system could be improved, it does work quite well, and exceeded our expectations. It is able to do the two things that interested us: seeing through walls to follow and locate wires, and to detect outlets from long distances, up to and perhaps exceeding 1.5 meters.
The first of these uses is the most simple application. Now that good constants are known, it would be quite straightforward to produce a low power and low cost pure analog version. This could be mounted on the back of the antenna on the top out of the way. Then the directional LEDs could be wired out to near the electrodes for easy viewing, and a handle could be attached for easy gripping and pointing. If desired, such a system could include swappable (or multiple) antennas of differing sizes depending on the task, and perhaps some jumpers or switches on the board to rescale some of the constant adapt it for different use cases (long time constants and high gain for weak signals, vs low gain and fast responses for quick scans). It could even make a viable consumer product for locating wires to aide in wiring, or safety when drilling into walls.
The second use is detection of outlets for a robot. With the assumption that most outlets are at roughly the same height, our antenna could simply be placed on the front of a robot and would provide a signal for if there was a power source nearby (potentially and outlet, but perhaps a cord, or wire inside a wall). It would also provide a directional signal, which based on our data would be enough to steer the robot toward the outlet from 1.5 meters away, gaining accuracy as it got close. While our antenna might not be good enough to do the centering to plugin, as discussed above, it could be combined with a higher precision antenna, especially one that also has a vertical channel. Plugging into an outlet thats right in-front of the robot is one thing, but noticing one from the middle of the hall as our system can, and then going over to it and plugging in is a much more useful accomplishment if one is trying to make a robot that can recharge itself at outlets. There is a important detail with this however: its important that the robot does not produce a significant 60 Hz signal of its own. While this could potentially be calibrated out if its consistent, it would likely decrease sensitivity.
One interesting idea we have not had time to explore is whether it is practical to make a system that detects distances to the signal sources. Using signal strength is not enough because the signal emitting from the sources varies from source to source. Some sort of three electrode antenna could either detect the curve of the field, or its non-linear fall off depending on the placements of the electrodes. Either of these measurements could be used to compute the distance assuming something about the source shape (probably assume a point source). This, if it worked, would allow detecting the distances, which when combined with our existing approaches would allow a measure of location, distance, and using the amplitudes, the actual strength of the signal emitted from the source. With a bit of math, and assuming the signal source is in line with the two electrodes, it should be possible to compute a distance to a point source.
$k$=produced signal strength from source (unknown)
$x$=distance from near electrode to source (unknown)
$a$=measured signal at close electrode
$b$=measured signal at far electrode
$s$=distance between electrodes
(4)
\begin{align} \frac{k}{x^2}=a \end{align}
(5)
\begin{align} \frac{k}{(x+s)^2}=b \end{align}
(6)
$$k=a*x^2$$
(7)
\begin{align} \frac{s*\sqrt{\frac{b}{a}}}{1-\sqrt{\frac{b}{a}}}=x \end{align}
Eq.(7) provides the distance to a point source using a two electrode antenna, which can be used in Eq.(6) to get the strength of the point source. We never had a chance to apply this, and it would be interesting to see if it produced usable results. These equations are derived from Eq.(4) and Eq.(5) which simply represent the electric field falling of with the inverse square law.
The real limit of sensing the field is to have a lot of antennas. With enough knowledge of the local electric field, it should be theoretically possible to reconstruct the field outside the of the local area and locate multiple sources. As the number of antennas grows, interference from them may become an issue, which could be countered with having fewer moving antennas, or smaller ones with more gain. What we don't know is how far in this direction it is practical to go. Clearly one and two antenna designs work and produce useful results, but how much can be gained from extending this remains a topic for further study.
# Video
Bibliography
1. Brian Mayton, Louis LeGrand, Joshua R. Smith.
Robot, Feed Thyself: Plugging In to Unmodified Electrical Outlets by Sensing Emitted AC Electric Fields. Proceedings of the 2010 IEEE International Conference on Robotics and Automation (ICRA 2010)
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# How do you simplify 4sqrt112+ 5sqrt56- 9sqrt126?
Jun 30, 2018
See a solution process below:
#### Explanation:
First, rewrite each of the radicals as:
$4 \sqrt{16 \cdot 7} + 5 \sqrt{4 \cdot 14} - 9 \sqrt{9 \cdot 14}$
$\sqrt{\textcolor{red}{a} \cdot \textcolor{b l u e}{b}} = \sqrt{\textcolor{red}{a}} \cdot \sqrt{\textcolor{b l u e}{b}}$
$4 \sqrt{16} \sqrt{7} + 5 \sqrt{4} \sqrt{14} - 9 \sqrt{9} \sqrt{14} \implies$
$\left(4 \cdot 4\right) \sqrt{7} + \left(5 \cdot 2\right) \sqrt{14} - \left(9 \cdot 3\right) \sqrt{14} \implies$
$16 \sqrt{7} + 10 \sqrt{14} - 27 \sqrt{14}$
Next, we can factor our common terms:
$16 \sqrt{7} + \left(10 - 27\right) \sqrt{14} \implies$
$16 \sqrt{7} + \left(- 17\right) \sqrt{14} \implies$
$16 \sqrt{7} - 17 \sqrt{14}$
If necessary we can go this additional step:
$16 \sqrt{7} - 17 \sqrt{2 \cdot 7} \implies$
$16 \sqrt{7} - 17 \sqrt{2} \sqrt{7} \implies$
$\left(16 - 17 \sqrt{2}\right) \sqrt{7}$
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# On the Chow groups of the variety of lines of a cubic fourfold
Research paper by Mingmin Shen, Charles Vial
Indexed on: 03 Dec '12Published on: 03 Dec '12Published in: Mathematics - Algebraic Geometry
#### Abstract
Let $X$ be a smooth complex cubic fourfold and let $F$ be the variety of lines of $X$. The variety $F$ is known to be a smooth projective hyperkaehler fourfold, which is moreover endowed with a self rational map $\phi : F -\rightarrow F$ first constructed by C. Voisin. Here we define a filtration of Bloch--Beilinson type on the Chow group of zero-cycles $CH_0(F)$ which canonically splits under the action of $\phi$, thereby answering in this case a question of A. Beauville. Moreover, we show that this filtration is of motivic origin, in the sense that it arises from a Chow--Kuenneth decomposition of the diagonal.
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Best April deals - hours only!Up to 80% off on all courses and bundles.-Close
Dates
Summary
## Instruction
Now we would like to calculate how long it takes our trucks and ships to complete their travels. To do this, we need two operations. First, we need to define the interval, or the amount of time between departure and arrival. We need to use the interval() function, which looks like this:
interval(start, end)
So we will write:
trucks$travel_interval <- interval(trucks$departure_datetime, trucks\$arrival_datetime)
This is a necessary step. It will allow us to use another function to calculate the actual difference.
## Exercise
Using the interval() function and the ships data set, create intervals of date and time for the departure_datetime and arrival_datetime columns. Assign the result to the travel_interval column.
Observe that the interval contains two dates: the starting and ending ones.
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Why do we see a lot of oxides and fluorides bonding with f-block metals? Do they bond with polyatomic ions?
I also think $\text{PuCO}$ is not impossible (if you consider $\text{CO}$ polyatomic). I see no reason why the $\sigma$-type and $\pi$-type $f$ orbitals on plutonium can't interact with $\text{CO}$, in which $\text{CO}$ donates electron density via a $\sigma$ interaction to plutonium's ${f}_{{z}^{3}}$ atomic orbital, and plutonium donates back from the $\pi$-type $f$ (${f}_{x {z}^{2}}$ and ${f}_{y {z}^{2}}$, I think they're called?) orbitals to the $\text{CO}$ ${\pi}^{\text{*}}$ in a "backbonding" stabilization. One would need actual numbers to justify that though...
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# Vertex of a Parabola
Vertex
To find the coordinates of the vertex is to substitute the axis of symmetry $y=-\dfrac{b}{2a}$ into the expression of the parabola $y=ax^2+bx+c$.
### Example 1
Find of the vertex of $y=x^2 - 4x - 3$.
### Example 2
Find the vertex of $y=2x^2 - 12x + 1$.
### Example 3
The vertex of $y=x^2+6x+c$ is $(-3,-4)$. Find $c$.
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"Want PRO should"
Aaron sent in a question about a usage that he first noticed at the age of nine, learning Allan Sherman's "hello mudda hello fadda" for an elementary school assembly:
Now I don't want / this should scare ya,
But my bunk mate / has malaria.
He has also seen a similar use of irrealis should from time to time in old jokes:
Q: Mom! You haven't eaten in three weeks? Why not?
A: I didn't want my mouth to be full you should call.
Aaron observes that he hears things like this particularly among older Americans of Jewish descent", and wonders whether it's an English imitation of a Yiddish construction. There's a useful discussion in the xkcd echochamber ("You want I should" 10/28/2010), which seems mostly to agree that this is a Yiddishism, and points to usage by Zoidberg and other Decapodians in Futurama, e.g. here:
Sure, you can vote for Shkinadel — if you want there should be a recession!
Another contributor to the same discussion points to Dan Aykroyd's line (as Elwood Blues) in The Blues Brothers,"You want I should wash the dead bugs off the windshield?"
This somewhat counters the Yiddish association, since the Blues Brothers' fictional background involves "growing up in a Roman Catholic orphanage in Rock Island, Illinois and learning the blues from a janitor named Curtis". On the other hand, Aykroyd is Canadian, and there may be a more general confusion in Hollywood between Yiddishisms and non-standard English.
Anyhow, there's some relevant discussion of Yiddish Irrealis here and here.
Update: An apparently satirical document, the Obleweiss Will, has several similar examples in the context of English influenced by the German varieties spoken by immigrants to Texas:
I, Herman Obleweiss, am writing my will mineself. That dam lawyer want he should have too much money […] First thing, I want, I don't want my brother-in-law Oscar get a dam thing I got. He is mumser. […]
I want that Hilda, my sistem, she gets de north sixtie akers where I am homint now. I bet she don't get that loafer husband of hers to broke twenty akers next plowing time. She can't have it if she let Oscar live on it. I want I should have it back if he does. […]
Momma the rest should get but I want it that Adolph should tell her what not should do so no more slick Irish vokum Cleaners Salesmen. […]
I want that my brother, Adolph, should be my execter and I want it that de judge should make Adolph plenty bond put up and watch him like hell. Adolph is good business man but only dumkopt would trust him.
Update #2 — Here's another suggestion that the "want PRO should" construction existed in informal varieties of American English before there was much influence of Eastern European immigrants. From An Uncommon Soldier: The Civil War Letters of Sarah Rosetta Wakeman, Alias Private Lyons Wakeman, 153rd Regiment, New York State Volunteers, a letter dated 11/24/1862:
My Dear Father and mother and sister and brothers, one in all,
I receive you letter on Sunday the 23. I was very glad to hear from you and learn that you were all well. […] I was only 7 miles from Binghamton up the river. I didn't go to the fair. When i got done work I went on the canal to work. I agreed to run 4 trips to Utica for 20$in money, but this load of coal was going to Canajoharie, Montgomery Co. When I got there i saw some soldiers. They wanted I should enlist and so i did. I got 100 and 52$ in money. I enlisted for 3 years or soon as discharged. All the money i send you i want you should spend it for the family in clothing or something to eat. […]
Mother, i will tell you where my little Chest is. It is upstairs over the bedroom in the garret. Let Robert go and climb up by the stove pipe hole and he will find it on the left hand side toward the road up in the corner. I want you should keep all my things for me for i believe that God will spare my life and that I shall see you all again face to face before i die. Father, if you will send me some postage stamps I will be very thankful for them. I want to drop all old affray and I want you to do the same and when i come home we will be good friends as ever.
_____Good-by for the present.
_____________________________________Sarah Rosetta Wakeman
1. Breffni said,
April 18, 2014 @ 6:43 am
I don't see a connection between "I don't want this should scare ya" (and the other examples cited) and "I didn't want my mouth to be full you should call". In the latter case, the analogue of what the title calls "want PRO should" would be "I didn't want my mouth should be full…". But as it stands, what's non-standard about it is just an elided IF ("…if you should call").
[(myl) You're absolutely right. At least there are two different frames here, one the complement of want and the other a conditional clause (though also in the complement of want). Aaron assumes that there's a correlation in sociolinguistic distribution, but this remains to be seen.]
2. Rachel B. said,
April 18, 2014 @ 7:12 am
I've seen this explained as being a direct calque on the Yiddish structure "az du zolst", lit. "That you should", see Sarah Benor's paper on Jewish English which cites this as a feature of Jewish English, and has some data on who uses it. Interestingly, she found that it had about equal use among the Jews and non-Jews in her sample.
For the Blues Brothers- a similar construction is found in Polish, in that the subjunctive is formed via a particle with personal endings plus the past tense form of the verb (which could be theoretically calqued as "that X should" in some cases), so that could be a possible authentic Chicago source? But I agree that it's more likely this is an example of the trope Yiddish as a Second Language.
3. Michael Bench-Capon said,
April 18, 2014 @ 7:34 am
Dan Aykroyd's name has two Ys in it, odd as that looks.
[(myl) Fixed now.]
4. Robert Coren said,
April 18, 2014 @ 9:02 am
I too would have thought of this as a Yiddishism, but in Clouds of Witness, Dorothy Sayers has a decidedly non-Jewish Yorkshireman exclaim, "Howd toong!…Doost want Ah should break ivry bwoan i' thi body?"
5. Eric S said,
April 18, 2014 @ 9:27 am
I'm reminded of a line I heard on the Sopranos. One character complains of gastric issues, to which the other responds:
"You want I should go to Rite Aid and get you some metamucil?"
The writer seems to think this is normal for a New Jersey Italian, though this may just add more evidence to your "Hollywood is confused" point than anything else.
6. Brett said,
April 18, 2014 @ 9:53 am
In The Far Side, one of "the squirrels of Central Park" says, "Whad is dis? I gives you two nuts yestahday and you sez you gonna pay me back today! You want I should break your incisors or what?" Gary Larson apparently considered the construction to be a distinctive feature of New York (gangster) English.
We also use this kind of "should" in my family occasionally, and I think of it as a jocular Yiddishism.
7. AMM said,
April 18, 2014 @ 10:34 am
FWIW, I recall from my Latin class that present subjunctives were frequently translated with "should". This was the middle of Virginia in the 1960's, so I doubt there was much Yiddish influence.
As Breffni points out, the second example is a conditional clause, of which there are (according to my Latin class) three kinds: the plain conditional (using indicative), the contrary-to-fact conditional (using past/pluperfect subjunctive), and an on-the-fence conditional, using the present (or perfect) subjunctive. Examples: "If I am …." vs. "If I were …" vs. "If I should [happen to] be …"
The first example is one where in modern English we usually use an infinitive:
"I don't want this to scare you". But if you insist on making it a separate clause, I would feel compelled to put in a should:
*"I don't want that this scare(s) you"
"I don't want that this should scare you".
For some verbs, the English present subjunctive (w/o "should") works:
"I demand that he come here"
but for reasons I can't explain, it doesn't work with "want." FWIW, indicative doesn't work for me:
*"I demand that he comes here."
Also FWIW: I speak German, where the subordinate clause form is typical for indirect command, but they use the indicative:
"Mein Chef verlangt, dass er die Arbeit heute fertig macht." (not "mache")
"Ich moechte, dass jemand heute das Klo repariert."
I think French uses a subjunctive, but I'm not that fluent in French. (I've noticed that in some respects, English grammar is closer to French than Germanic.)
8. Theophylact said,
April 18, 2014 @ 11:15 am
But "mumser" is Yiddish, from Hebrew mamzer ממזר = bastard.
[(myl) Indeed. But this word made its way into Medieval French, so maybe also into 19th-century German? Then again, maybe the wit behind the Obleweiss Will was some anonymous Borscht Belt comedian at loose ends in Dallas.]
9. mollymooly said,
April 18, 2014 @ 11:23 am
It is remarkably hard for me to avoid misreading "Yiddish Irrealis" as "Yiddish Israelis".
10. Jim said,
April 18, 2014 @ 11:37 am
There are at least tow sources for this. subjunctive use of 'should" is pretty common in RP, so it's no surprise that that Yourkshireman's variety might have picked it up. It also doesn't meana that the use in a US context can't come from Yiddish or even some other one of the many varieties of German that came to America.
"You want I should go to Rite Aid and get you some metamucil?"
The writer seems to think this is normal for a New Jersey Italian,"
If you look at the settlement histories of the groups that immigrated around the turn of the 20th century, you find they often settled in the same neighborhoods, and the "English" that kids in those neighborhoods was a soup of substrata. It would suprise me very much if there were no Italianisms in Jewish American varieties of English.
11. peggysioux said,
April 18, 2014 @ 12:09 pm
I am from Texas and was visiting someone in CA who made me aware that I say things like "we might could go to a movie" or "we might should go to the grocery store." I was totally unaware that I had picked that up from someone.
[(myl) Double modals have a rather different sociolinguistic distribution — see e.g. "He must can parse", 6/13/2009; "Do double modals really exist?", 11/20/2007; "Might would have", 11/20/2007; also this 11/20/2007 post on Mr. Verb's blog, and M. Mishoe and M. Montgomery, "The Pragmatics of Multiple Modal Variation in North and South Carolina", American Speech 1994.]
12. Rolig said,
April 18, 2014 @ 12:26 pm
I always wondered if this irrealis "should" was related to the Russian construction in the same context: for example:
Я не хочу, чтобы ты испугался от этого. / Ya ne khochu, chtoby ty ispugalsya ot ètogo.
for which a clunky word-for-word translation might be: "I don't want that you should be frightened by this."
Similar constructions are found in other Slavic languages, e.g. Slovene: Nočem, da bi te to prestrašilo. — literally, "I don't want that this should scare you."
13. John Walden said,
April 18, 2014 @ 1:34 pm
Jim mentions this and certainly in BrE "should" does seem to be something of a go-to modal auxiliary. In fact I would say it has even less of a core meaning than do its also fickle sidekicks.
It's to be found in conditionals:
"If you should find yourself in London,….."
and in conditionals without "if":
"Should you require further assistance, ……"
and we shove it in when the subjunctive might also be in order:
"We insist that all staff should be correctly dressed"
None of these has much to do with "giving advice".
So for it to be used instead of similar but not identical verbs from other languages is perhaps unsurprising.
[(myl) These are all perfectly standard (if in some cases a bit stuffy) in American English as well. It's things like "NP1 want (that) NP2 should VP" that have a more restricted distribution.]
14. quixote said,
April 18, 2014 @ 3:03 pm
It's funny, to me at least, that this kind of "should" doesn't sound odd to me. I know it's not ordinary English, and yet it sounds okay. My first language was Russian. I think Rolig may be on to something.
Re the first comment: both of those "shoulds" are used to mean something that hasn't (yet) happened. Maybe that's the relationship?
[(myl) They're both "irrealis", certainly. But there's more than one way to be unreal.]
15. D.O. said,
April 18, 2014 @ 5:08 pm
@Rolig. I don't see a modal verb in your Russian example. испугался is past tense reflexive of испугать, which, in turn, is the perfect form of пугать. Roughly speaking испугался = became frightened. What am I missing?
By the way, how do courts deal with contracts or wills written in something other than Standard English?
16. Rolig said,
April 18, 2014 @ 6:08 pm
@D.O. You're missing the бы particle in the conjunction чтобы, which creates the subjunctive ("would" or "should") and requires the л-participle (otherwise used for the past tense). Hence, чтобы ты испугался = "so that you would be frightened". In the sentence, Я не хочу, чтобы ты испугался, the meaning is: "I don't want you to be frightened" or, dialectically, "I don't want that you should be frightened."
17. David Morris said,
April 18, 2014 @ 6:14 pm
A few years ago a student asked me about the construction "Should you have any questions, please ask" and I was momentarily stumped. Although I understand it perfectly, it's not a construction I (should) use myself. There is a continuum of "level" between: "If you have any questions …", "If you should have any questions …" and "Should you have any questions …".
Correspondingly, the "you should call" construction in the telephone joke would be more natural (to me) as "when you called" (or maybe "if you called"), "if you should call" or "should you call" (but that might could be too high a level for this conversation). (I don't usually use double modals, but I couldn't resist.) "you should call" is just not natural (dare I say "not correct"?) for me.
18. D.O. said,
April 18, 2014 @ 7:58 pm
@Rolig. But Russian чтобы does not function as a modal verb. Where's the connection to should? I am not trying to be hard, just want to understand your point. In your example Russian uses modified particle, not a modal verb, to indicate irrealis. Even if you constructed an example with free floating бы, it might at best indicate that native Russian speaker could try to use was for the same purpose. Or do you think that a Russian speaker may learn English usage like "Should you find any problem, call us at ###" and tries to use it in a dependent clause? But there is no connection to чтобы either. Russian translation would be something like "Если будут какие-то затруднения, звоните по номеру ###"
19. Joe Fineman said,
April 18, 2014 @ 8:05 pm
I parse "Should you have any questions" as suppression of "if" with inversion
(= "If you should have any questions"). Cf. "Had I but known" = "If I had but known", etc.
20. Rolig said,
April 18, 2014 @ 9:27 pm
@D.O. The modality of the Russian example is expressed through the бы particle (it doesn't matter whether it's attached to the conjunction что or free-floating). In combination with the бы particle, the -l form of the verb (including, of course, those masculine forms that have lost the historic -l ending: принёс, умер, смог, etc.) does not express the past tense; it does not express any tense.
что ты испугался = that you were frightened (past tense)
чтобы ты испугался = that you would be frightened (subjunctive mood; the tense is not indicated by the form):
Он не хотел, чтобы ты испугался, и поэтому вчера ничего не сказал. = He didn't want you to be frightened and so didn't say anything yesterday. [the potential fright was in the past]
Он не хочет, чтобы ты испугался от того, что говорят. = He doesn't want you to be frightened by what people are saying. [the potential fright is in the present]
Он не хочет, чтобы ты испугался, когда ее увидишь завтра. = He doesn't want you to be frightened when you see her tomorrow. [the potential fright is in the future]
In all these examples, I would expect that a Russian speaker learning English might find it natural to use a subjunctive clause, e.g.: "that you would [or should] be frightened". The presence of the бы particle would make the use of the indicative past ("were frightened") much less likely.
The Slavic languages often use the subjunctive construction (чтобы clauses) with verbs expressing desire. I know almost nothing about Yiddish, but I was wondering if this could have influenced the development of the irrealis "should" that is associated with Jewish or other dialects in immigrant communities originally coming from Eastern Europe.
21. Bruce H. said,
April 18, 2014 @ 10:59 pm
Another vote for Yiddish. I encountered it in the story about the mohel who has a clock in the front window of his shop. A shopper comes in to have her watch repaired. The mohel explains that he neither repairs nor sells watches. The disappointed customer asks what he does. He explains. She asks, "Well then why do you have a clock in the window?" He replies, "C'mon, Lady. What do you want I should put in the window?"
22. Jeffry House said,
April 19, 2014 @ 8:01 am
For those of us without Yiddish-speaking relatives, the go-to source for Yiddishisms in English is "The Education of Hyman Kaplan" by Leo Rosten. You want I should provide a link?
23. Jerry Friedman said,
April 19, 2014 @ 1:18 pm
Here's a "you want I should" dated 1742, though published in 1834: "If you want I should explain anything here written, you may let me know by another line." From a letter by the Rev. Ralph Erskine of Dunfermline, in Scotland.
One from 1795 in Essex: "But in this I will say no more, since you do not want I should reason, but merely state facts." From General View of the Agriculture in the County of Essex.
24. ajay said,
April 22, 2014 @ 4:57 am
"In the latter case, the analogue of what the title calls "want PRO should" would be "I didn't want my mouth should be full…". But as it stands, what's non-standard about it is just an elided IF ("…if you should call")."
Or an inversion of the order – "I didn't want my mouth to be full should you call."
25. Ben said,
April 23, 2014 @ 7:41 am
It may predate Yiddish influence in English, but its widespread use in American English is clearly due to Yiddish; it is well known that this is an exact calque of the Yiddish veln PRO zoln construction, as several commenters above have alluded to. What was once a very occasional turn of phrase became a common one as a calque from Yiddish in the mouths of eastern European immigrants and their descendants. The question that remains, then, is why it has a certain "wise guy" connotation, which explains its use in The Blues Brothers. I think this is because of Damon Runyon, whose idiosyncratic language owed much to Yiddish and strongly shaped perceptions of urban ethnic speech.
26. Ben said,
May 4, 2014 @ 11:19 am
Another Runyonesque wise-guy phrase that is clearly a calque from Yiddish: "Make with the." There are also a few lexical items, such as the old-fashioned "shamus," and the still in use "vig," from Yiddish "vigorish."
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Mathematics NCERT Grade 7, Chapter 7: Congruence of Triangles- The chapter focuses on the congruency of plane figuresline segmentsangles, and triangles.
• Congruent objects are exact copies of one another.
The first section of the chapter deals with congruence of plane figures, congruence among line segments and congruence of angles.
• If two line segments have the same (i.e., equal) length, they are congruent. Also, if two line segments are congruent, they have the same length.
• If two angles have the same measure, they are congruent. Also, if two angles are congruent, their measures are same.
After that, congruence of triangles is discussed. Exercise 7.1 is based on the concept of above cited topics. The other half of the chapter deals with Criteria For the congruence of Triangles. Explanation of criterion is given in an interesting way, they are mentioned in the form of games. Students will be briefed about the following criterion:
1. SSS congruence criteria: Triangles are congruent if three sides of the one are equal to the three corresponding sides of the other.
2. SAS congruence criteria: Triangles are congruent if two sides and the angle included between them in one of the triangle are equal to the corresponding sides and the angle included between them of the other triangle.
3. ASA congruence criteria: Two triangles are congruent if two angles and the side included between them in one of the triangles are equal to the corresponding angles and the side included between them of the other triangle.
Emphasis will also be laid upon the topic- Congruence Among Right-Angled Triangles.
RHS congruence criteria:
If under a correspondence, the hypotenuse and one side of a right-angled triangle are respectively equal to the hypotenuse and one side of another right-angled triangle, then the triangles are congruent.
Later the chapter Congruence of Triangles concludes with a summary.
#### Question 1:
Complete the following statements:
(a) Two line segments are congruent if __________.
(b) Among two congruent angles, one has a measure of 70°; the measure of the other angle is __________.
(c) When we write ∠A = ∠ B, we actually mean __________.
(a) They have the same length
(b) 70°
(c) m ∠A = m ∠B
#### Question 2:
Give any two real-life examples for congruent shapes.
(i) Sheets of same letter pad
(ii) Biscuits in the same packet
#### Question 3:
If ΔABC ≅ ΔFED under the correspondence ABC ↔ FED, write all the Corresponding congruent parts of the triangles.
If these triangles are congruent, then the corresponding angles and sides will be equal to each other.
∠A ↔ ∠F
∠B ↔ ∠E
∠C ↔ ∠D
#### Question 4:
If ΔDEF ≅ ΔBCA, write the part(s) of ΔBCA that correspond to
(i) ∠E (ii) (iii) ∠F (iv)
(i) ∠C
(ii)
(iii) ∠A
(iv)
##### Video Solution for congruence of triangles (Page: 137 , Q.No.: 4)
NCERT Solution for Class 7 math - congruence of triangles 137 , Question 4
#### Question 1:
Which congruence criterion do you use in the following?
(a) Given: AC = DF
AB = DE
BC = EF
So, ΔABC ≅ ΔDEF
(b) Given: ZX = RP
RQ = ZY
∠PRQ = ∠XZY
So, ΔPQR ≅ ΔXYZ
(c) Given: ∠MLN = ∠FGH
∠NML = ∠GFH
ML = FG
So, ΔLMN ≅ ΔGFH
(d) Given: EB = DB
AE = BC
∠A = ∠C = 90°
So, ΔABE ≅ ΔCDB
(a) SSS, as the sides of ΔABC are equal to the sides of ΔDEF.
(b) SAS, as two sides and the angle included between these sides of ΔPQR are equal to two sides and the angle included between these sides of ΔXYZ.
(c) ASA, as two angles and the side included between these angles of ΔLMN are equal to two angles and the side included between these angles of ΔGFH.
(d) RHS, as in the given two right-angled triangles, one side and the hypotenuse are respectively equal.
#### Question 2:
You want to show that ΔART ≅ ΔPEN,
(a) If you have to use SSS criterion, then you need to show
(i) AR = (ii) RT = (iii) AT =
(b) If it is given that ∠T = ∠N and you are to use SAS criterion, you need to have
(i) RT = and (ii) PN =
(c) If it is given that AT = PN and you are to use ASA criterion, you need to have
(i) ? (ii) ?
(a)
(i) AR = PE
(ii) RT = EN
(iii) AT = PN
(b)
(i) RT = EN
(ii) PN = AT
(c)
(i) ∠ATR = ∠PNE
(ii) ∠RAT = ∠EPN
##### Video Solution for congruence of triangles (Page: 149 , Q.No.: 2)
NCERT Solution for Class 7 math - congruence of triangles 149 , Question 2
#### Question 3:
You have to show that ΔAMP ≅ AMQ.
In the following proof, supply the missing reasons.
- Steps - Reasons (i) PM = QM (i) … (ii) ∠PMA = ∠QMA (ii) … (iii) AM = AM (iii) … (iv) ΔAMP ≅ ΔAMQ (iv) …
(i) Given
(ii) Given
(iii) Common
(iv) SAS, as the two sides and the angle included between these sides of ΔAMP are equal to two sides and the angle included between these sides of ΔAMQ.
#### Question 4:
In ΔABC, ∠A = 30°, ∠B = 40° and ∠C = 110°
In ΔPQR, ∠P = 30°, ∠Q = 40° and ∠R = 110°
A student says that ΔABC ≅ ΔPQR by AAA congruence criterion. Is he justified? Why or why not?
No. This property represents that these triangles have their respective angles of equal measure. However, this gives no information about their sides. The sides of these triangles have a ratio somewhat different than 1:1. Therefore, AAA property does not prove the two triangles congruent.
#### Question 5:
In the figure, the two triangles are congruent.
The corresponding parts are marked. We can write ΔRAT ≅ ?
It can be observed that,
∠RAT = ∠WON
∠ART = ∠OWN
AR = OW
Therefore, ΔRAT ΔWON, by ASA criterion.
##### Video Solution for congruence of triangles (Page: 150 , Q.No.: 5)
NCERT Solution for Class 7 math - congruence of triangles 150 , Question 5
#### Question 6:
Complete the congruence statement:
ΔBCA ≅?
ΔQRS ≅?
Given that, BC = BT
TA = CA
BA is common.
Therefore, ΔBCA ΔBTA
Similarly, PQ = RS
TQ = QS
PT = RQ
Therefore, ΔQRS ΔTPQ
#### Question 7:
In a squared sheet, draw two triangles of equal areas such that
(i) The triangles are congruent.
(ii) The triangles are not congruent.
What can you say about their perimeters?
(i)
Here, ΔABC and ΔPQR have the same area and are congruent to each other also. Also, the perimeter of both the triangles will be the same.
(ii)
Here, the two triangles have the same height and base. Thus, their areas are equal. However, these triangles are not congruent to each other. Also, the perimeter of both the triangles will not be the same.
##### Video Solution for congruence of triangles (Page: 150 , Q.No.: 7)
NCERT Solution for Class 7 math - congruence of triangles 150 , Question 7
#### Question 8:
Draw a rough sketch of two triangles such that they have five pairs of congruent parts but still the triangles are not congruent.
Consider two triangles $△$ABC and $△$XYZ.
In $△$ABC and $△$XYZ,
$\angle \mathrm{A}=\angle \mathrm{X}=40°\phantom{\rule{0ex}{0ex}}\angle \mathrm{B}=\angle \mathrm{Y}=80°\phantom{\rule{0ex}{0ex}}\angle \mathrm{C}=\angle \mathrm{Z}=60°\phantom{\rule{0ex}{0ex}}\mathrm{AB}=\mathrm{YZ}\phantom{\rule{0ex}{0ex}}\mathrm{AC}=\mathrm{XY}$
The given triangles have five pairs of congruent parts. But these two triangles are not congruent by any criterion of congruence.
#### Question 9:
If ΔABC and ΔPQR are to be congruent, name one additional pair of corresponding parts. What criterion did you use?
BC = QR
ΔABC ΔPQR (ASA criterion)
#### Question 10:
Explain, why
ΔABC ≅ ΔFED
Given that, ∠ABC = ∠FED (1)
∠BAC = ∠EFD (2)
The two angles of ΔABC are equal to the two respective angles of ΔFED. Also, the sum of all interior angles of a triangle is 180º. Therefore, third angle of both triangles will also be equal in measure.
∠BCA = ∠EDF (3)
Also, given that, BC = ED (4)
By using equation (1), (3), and (4), we obtain
ΔABC ≅ ΔFED (ASA criterion)
##### Video Solution for congruence of triangles (Page: 151 , Q.No.: 10)
NCERT Solution for Class 7 math - congruence of triangles 151 , Question 10
View NCERT Solutions for all chapters of Class 7
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Notes On The Rise of Nationalism in Europe (C - Level) - CBSE Class 10 History
The concepts of liberty, equality and fraternity were touchstones of the French revolution and dominated the social and political scene of Europe during the 19th century. The first print depicted by French artist Frédéric Sorrieu. He had visualised a utopian world made up of democratic and social republics. A utopian vision refers to a perfect society that is so ideal that it is unlikely to actually exist. Absolutism can be defined as a government or a system of rule with a lot of uncontrolled power. It also refers to an oppressive monarchical government. During the 19th century, Europe was undergoing a phase of transition. The long-oppressed peasantry had begun to question the landed aristocracy and the feudal system. Rapid industrialisation had given birth to the middle class consisting of industrialists, businessmen and professionals who wanted to bring together people with a shared past, history and culture gave rise to the idea of the nation state. In the 19th century, the concept of nation states did not take into account the geographical boundary of a country. Plebiscite is an important right given by a nation to its citizens. A plebiscite is a direct vote by which the people of a region are asked to accept or reject a proposal.
Summary
The concepts of liberty, equality and fraternity were touchstones of the French revolution and dominated the social and political scene of Europe during the 19th century. The first print depicted by French artist Frédéric Sorrieu. He had visualised a utopian world made up of democratic and social republics. A utopian vision refers to a perfect society that is so ideal that it is unlikely to actually exist. Absolutism can be defined as a government or a system of rule with a lot of uncontrolled power. It also refers to an oppressive monarchical government. During the 19th century, Europe was undergoing a phase of transition. The long-oppressed peasantry had begun to question the landed aristocracy and the feudal system. Rapid industrialisation had given birth to the middle class consisting of industrialists, businessmen and professionals who wanted to bring together people with a shared past, history and culture gave rise to the idea of the nation state. In the 19th century, the concept of nation states did not take into account the geographical boundary of a country. Plebiscite is an important right given by a nation to its citizens. A plebiscite is a direct vote by which the people of a region are asked to accept or reject a proposal.
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# Special Edition Using Microsoft Office 2007
## byEd Bott, Woody Leonhard
### Pricing and Purchase Info
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Special Edition Using Microsoft® Office 2007
THE ONLY OFFICE BOOK YOU NEED
We crafted this book to grow with you, providing the reference material you need as you move toward Office proficiency and use of more advanced features. If you buy only one book on Office 2007, Special Edition Using Microsoft® Office 2007 is the only book you need.
If you own a copy of Office 2007, you deserve a copy of this book! Although this book is aimed at the Office veteran, Ed and Woody’s engaging style will appeal to beginners, too. Written in clear, plain English, readers will feel as though they are learning from real humans and not Microsoft clones. Sprinkled with a wry sense of humor and an amazing depth of field, this book most certainly isn’t your run-of-the-mill computer book. You should expect plenty of hands-on guidance and deep but accessible reference material.
This isn’t your Dad’s Office! For the first time in a decade, Microsoft has rolled out an all-new user interface. Menus? Gone. Toolbars? Gone. For the core programs in the Office family, you now interact with the program using the Ribbon—an oversize strip of icons and commands, organized into multiple tabs, that takes over the top of each program’s interface. If your muscles have memorized Office menus, you’ll have to unlearn a lot of old habits for this version.
Ed Bott is a best-selling author of more than 25 computer books and an award-winning computer journalist with two decades of experience in the personal computer industry. For nearly 10 years, he was responsible for PC Computing magazine’s extensive coverage of every conceivable flavor of Microsoft Windows and Microsoft Office. He is a...
Title:Special Edition Using Microsoft Office 2007Format:Kobo ebookPublished:December 22, 2006Publisher:Pearson EducationLanguage:English
The following ISBNs are associated with this title:
ISBN - 10:0132714582
ISBN - 13:9780132714587
## Reviews
Rated 5 out of 5 by from Great Resource Book I have purchased previous editions of books authored by Woody Leonhard and Ed Bott, for Reference and Home Study of the Microsoft Office system and I highly recommend their books. The look intimidating at first, as they are very thick and full of lots of technical information, but with these books, you can master the Microsoft Office 2007 in a short period of time. This book allows the home user like myself, to learn the most useful parts of the Microsoft Office 2007; the programs such as Word, Access, Excel, Publisher, Outlook, One Note, and Powerpoint so that a person can use and navigate around the office system wth ease and confidence. The book is compartmentized in a way that you can focus on one program aspect at a time, or learn multi-tasking aspects of Office at the same time. I would recommend as a person reads the book, to have your office 2007 turned on your computer and as you read, you can navigate in office at the same time to get the most out of the book and learn the tricks and master the program as you study the book. I have tried other books on Office 2003, but ended up buying the Office 2003 edition by Woody and Ed, and when looking for the Office 2007 reference books, this was my FIRST and ONLY choice that was required. The cover all aspects in a user friendly manner and the book is easy to read and instructions are easy to follow. I would highly recommend this book for both new and seasoned users of the Microsoft Office platforms.
Date published: 2007-12-30
Introduction
1 Getting Started with Office 2007 . . . . . . . . . . . . . . . . . . . . 9
2 Using and Customizing the Office 2007 Interface . . 27
3 Managing Office Files and Formats . . . . . . . . . . . . . . . . 53
4 Creating, Editing, and Formatting Documents . . . . . 75
5 Creating, Editing, and Using Pictures and Graphics . . . 103
6 Sharing and Reviewing Office Files . . . . . . . . . . . . . . . 135
7 Office Security and Privacy . . . . . . . . . . . . . . . . . . . . . . . . 159
II Using Outlook
8 Outlook Essentials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
9 Reading, Writing, and Organizing Email . . . . . . . . . . 219
10 Keeping Your Contacts List Under Control . . . . . . . 259
11 Working with Calendars and Tasks . . . . . . . . . . . . . . . 277
12 Outlook Security and Privacy . . . . . . . . . . . . . . . . . . . . . . 307
III Using Word
13 Building a Better Word Document . . . . . . . . . . . . . . . . 329
14 Using Themes, Styles, and Templates . . . . . . . . . . . . 387
15 Advanced Document Formatting . . . . . . . . . . . . . . . . . . 415
16 Professional Document Tools and Advanced Document Sharing . . . . . . . 455
17 Letters, Envelopes, and Data-Driven Documents . . . . . . . . .477
IV Using Excel
18 Building a Better Workbook . . . . . . . . . . . . . . . . . . . . . . . 507
19 Advanced Worksheet Formatting . . . . . . . . . . . . . . . . . 553
20 Using Formulas and Functions . . . . . . . . . . . . . . . . . . . . 593
21 Organizing Data with Tables and PivotTables . . . . 627
22 Creating and Editing Charts . . . . . . . . . . . . . . . . . . . . . . . 665
V Using PowerPoint
23 Building a Perfect Presentation . . . . . . . . . . . . . . . . . . . 703
24 Advanced Presentation Formatting . . . . . . . . . . . . . . . 737
25 Adding Graphics, Multimedia, and Special Effects . . . . . .759
26 Planning and Delivering a Presentation . . . . . . . . . . 779
VI Other Office Applications
27 Publisher Essentials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 797
28 Access Essentials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 835
29 Using OneNote . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 879
30 Using Office 2007 on a Corporate Network . . . . . 907
VII Appendixes
A Advanced Setup Options . . . . . . . . . . . . . . . . . . . . . . . . . . 929
B Macros and Add-Ins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 943
C Using Office on a Tablet PC . . . . . . . . . . . . . . . . . . . . . . . 961
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 969
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After all that we have learned, we know that in order to determine the solution of the initial problem in Sec. 10.1 we would have to calculate the integrals $A_j = \frac{2}{c^2 J_1^2(c \alpha_j)}\int_0^c f(\rho) J_0(\alpha_j \rho) \rho d\rho$
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# Nonlinear Spring Mass System
Non-Linear Spring and Damping Models The normal elastic constant based on Hertz contact theory is 4. Its total output power of 46. Modeling a Second Order Equation (Single Degree of Freedom System-SDOF) The mass-spring-dashpot is a basic model used widely in mechanical engineering design to model real-world mechanical systems. Hooke's Law states that the restoring force of a spring is directly proportional to a small displacement. The spring is assumed to have a very large stiffness value such that the natural frequency of the mass–spring oscillator, when uncoupled from the pendulum, is an order of magnitude larger than that of the oscillations of the pendulum. Call it nonlinear war (which I prefer), or hybrid war, or deter and resist a mass, tank-led Soviet invasion–finds hard take on the Arab Spring so closely. Waves; Wave pulse; Traveling wave; Wave amplitude; Double slit diffraction; Single slit diffraction; Graphical solutions; Doppler effect; Shock waves. Open Live Script. displacement curve that is not a straight line (indicating a nonlinear relationship between force and displacement). TIJSSELING Department of Mathematics and Computer Science Eindhoven University of Technology P. Finally, a new numerical method is proposed for nonlinear $\psi$–Katugampola FDEs. The spring is called a hard spring if ± > 0 and a soft spring if ± < 0. A physics student records data on the force exerted by the spring as it is compressed and plots the two graphs below, which include the data and the student's best-fit curves. By adding a mass/spring system m2/k2 (upper section of the diagram), there will be two resonance peaks, as represented by the blue curve. The reference position results when (i) F has been set to zero, and (ii) the pulley mass and rope mass are assumed negligible. is attached to a nonlinear linear spring that exerts a force F = − kx | x |. The cerebellar model developed in the present work learns to perform position control of a single degree--of--freedom, nonlinear, dynamic spring--mass system. Drop 2, mass 0. Once we fit the data, we take the analytical derivative of the fitted function. The fi tfirst figure shows a two mass –two spring system that is described by two linear coordinates x1 and x2. Spring mass damper system NON-LINEAR. Partial vibration frequency ,rads 1. Equilibrium solutions of a nonlinear mass spring system. Due to various sources of nonlinearities, micro/nano-electro-mechanical-system (MEMS/NEMS) resonators present highly nonlinear behaviors including softening- or hardening-type frequency responses, bistability, chaos, etc. Controlling a Nonlinear Spring-Mass System with a Cerebellar Model. Whether the above systems admits one, none or multiple solutions given an initial point x(t0) = x0, is a fundamental question. Modern mass spectrometers are the most sensitive, accurate, and powerful analytical tools. Consider the undamped, driven spring-mass system modeled by the initial value problem. When the mass is in motion and reaches the equilibrium position of the spring, the mechanical energy of the system has been completely converted to kinetic energy. m — dynamical modes of oscillation of 2D or 3D structure. The static deflection of a simple mass-spring system is the deflection of spring k as a result of the gravity force of the mass,δ st = mg/k. In this assignment we'll consider animating a deformable shape. For example, our spring-mass. Find a solution to a multivariable nonlinear equation F(x) = 0. Consider the mass-spring system governed by the differential equation, Where is the time-dependent position displacement of the mass. However, we can often investigate the behavior of the solutions without actually being able to find simple expressions in terms of elementary func-tions. In the system shown earlier, the full stiffness matrix would be 36 by 36. 3 s; although. Experimental modal testing is performed using an electro-magnetic vibration shaker as an exciter and an accelerometer to record the natural frequency of the system. Fnet =0,(k∆y−Mg),0 =0,0,0 where k is the spring constant and ∆y is. edu Qingzhi HOU. Set the initial value to be (80, no) = (1,1). Call it nonlinear war (which I prefer), or hybrid war, or deter and resist a mass, tank-led Soviet invasion–finds hard take on the Arab Spring so closely. 48, 2010, pp. March 29, 2021. Hence, the solution to Eqs. However, we can often investigate the behavior of the solutions without actually being able to find simple expressions in terms of elementary func-tions. undamped damped. system is a spring-mass-damper system in which the spring has no damping or mass, the mass has no stiffness or damping, the damper has no stiffness or mass. Equipment: A linear spring, slotted weights, a stop watch, a spring hanger, a meter stick or a 30. The results show that maximum levels of harvested power are accompanied by minimum transverse displacement amplitudes. Using a stiffer spring would increase the frequency of the oscillating system. Abstract Mass-spring systems are a classical and popular approach to model the dynamics of deformable objects. Step 4 (2D spring-mass system). The TMD can leverage the viscous properties of the fluid to attenuate the excitations within the structure. For translation springs you may specify nonlinear elasticity via a force-elongation diagram [Fig. Find Lagrange’s equations of motion. Questions: Suppose a nonlinear spring-mass system satisfies the initial value problem (u 00 + u + ±u 3 = 0 u (0) = 0, u 0 (0) = 1 Use ode45 and plot to answer the following: 1. It is represented schematically as shown in Fig. Mass-nonlinear spring system. If the amplitude of the spring mass system's motion is doubled, the period will be: (A) 1/4 T (B) 1/2 T (C) T (D)2T (E) 4T A simple pendulum of mass m and lencrth L has a period of oscillation T at angular amplitude 6 = 50 measured from its equilibrium position. Even though the nonlinearities constitute only a small part of the structure, the entire…. The influences of the initial condition, mass (or moment of inertia), vibration frequency, and amplitude on the mechanical and aerodynamic parameters and nonlinearities were thoroughly investigated. Minimize Energy of Piecewise Linear Mass-Spring System Using Cone Programming, Problem-Based. Spring mass damper Weight Scaling Link Ratio. To illustrate, consider the spring/mass/damper example. spring = ku+ u3; where k > 0 is the spring constant and is small but may be positive or negative and represents the \strength" of the spring ( = 0 gives Hooke's Law). Adding mass to the system would decrease its resonant frequency. Guess what?. The nonlinear aeroelastic eq…. Consider the model of an undamped nonlinear spring/mass system given by x" + 8x – 6x 3 + x 5 = 0. 2 Linear elastic material models 157. The system consists of n masses in two dimensions. damper is strong enough, so that the spring is overdamped, then the door just settles back to the equilibrium position (i. Damping and the non-linear spring force appear to “compete” against each other! While the damper element tends to “dampen” out the vibrations with time (i. A nonlinear system has more complicated equations of motion, but these can always be arranged into the standard matrix form by assuming that the displacement of the system is small, and linearizing the equation of motion. This scheme provides a fast solution for classical linear (Hookean) springs. ; Marion, Jerry B. Oscillation response is controlled by two fundamental parameters, tau and zeta, that set the amplitude and frequency of the oscillation. 10) δ st 1 2π 8434_Harris_02_b. 2 A nonlinear second-order system_____ 6 x x& 3 9-6 -3 3 6-3-6-9 convergence area divergence area to infinity unstable Fig. Solution is obtained by applying method of multiple time scale directly to. The nonlinear damping force between the two masses is assumed to be. It need not satisfy Hooke's law. Prerequisite(s): MEAM 210. ) Substituting this relation in Eq. A physics student records data on the force exerted by the spring as it is compressed and plots the two graphs below, which include the data and the student's best-fit curves. For the initial study of the nonlinear spring the quarter car model was sufficient enough to study the dynamics of the vehicle. 05036 g (diameter = 4. We investigate the dynamics of a simple pendulum coupled to a horizontal mass–spring system. GET FORMULA Reload. Open Live Script. That is, the system doens't oscillate at all. Tijsseling, AS, Vasconcelos, JG, Hou, Q, & Bozkuş, Z. Given the diagonal (lumped) mass-matrix M 2R 3m, implicit Euler time integration results in the following update rules [Baraff and Witkin 1998]: q. Bodies characteristic Main Attached Mass , kg. If the driving force is sinusoidal, these various forces also vary sinusoidally, and the balance may be represented using phasors (i. The spring is stretched 2 cm from its equilibrium position and the mass is. The procedure introduced is based on the Taylor series expansion and on knowledge of nominal system trajectories and nominal system inputs. Drop 2, mass 0. These systems may range from the suspension in a car to the most complex robotics. Set the initial value to be (80, no) = (1,1). Mass i is connected to springs i and i + 1. In a nonlinear spring-mass system, the spring force is given by F s= ku+ u3 where k >0 is the spring constant, is a small number describing the strength of the spring: = 0 gives Hooke’s Law, >0 gives a hard spring and 0 gives a soft spring. Therefore, an essential complement to all-numerical studies of large nonlinear systems is the analytical/theoretical study of simplified systems. Oscillation response is controlled by two fundamental parameters, tau and zeta, that set the amplitude and frequency of the oscillation. All vibrating systems consist of this interplay between an energy storing component and an energy carrying (massy'') component. (b) Proposed circuit to model the electrical actuation scheme. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. k is the spring constant of the spring. spring 1 spring 0 Figure 1. For translation springs you may specify nonlinear elasticity via a force-elongation diagram [Fig. 2) This point where the forces balance each other out is known as the equilibrium point. (1), for the assumed regime of. Math 240: Calculus III, Fall 2013. As one such example, Aoki, Sawaragi and Isaacson (1993) described the numerical simulation of the motions of a single degree of freedom system with a piecewise-linear restoring force function. Impacting chatter and stuck phenomena are investigated for the mass with constraints and the corresponding conditions for such phenomena are determined. Composites Part B: Engineering, vol. A bilinear Maxwell damper has been implemented as a new link property. This paper discusses the vibration of a mass-spring-damper system with two constraints and impact interactions. Gathering terms and dividing through by m gives you the following ODE for the spring-mass system: x′′(t) + k m x(t) −g = 0. An example is given to demonstrate the reduction of the vibration amplitude of the spring-mass system under a given exciting forcing frequency. Associated with the example is an animation function that will automatically open a figure window and display to it. Tijsseling, AS, Vasconcelos, JG, Hou, Q, & Bozkuş, Z. In addition, I show how ETCH principles, when applied by educational system leaders, permit them to facilitate an optimal learning environment for a student-centered complex adaptive system. Numerous civil engineering structures exhibit nonlinearities. Spring Resonant Frequency Calculator. Let us consider the one-dimensional motion of a body of mass. The system is just basically two masses, two linear and one nonlinear spring (elastic perfectly plastic hysteretic material nonlinearity) between two masses. A nonlinear system can exhibit an oscillation of xed amplitude and frequency which appears. More generally, a nonlinear spring can have a force vs. This device is a linear spring in series with a dashpot whose force-velocity relationship exhibits bilinear viscous behavior, typical of certain oil dampers having a relief valve. 10) δ st 1 2π 8434_Harris_02_b. With the mass-spring system motionless, the Momentum Principle gives: ∆ = ∆=0 p F tnet Therefore the net force must equal zero. ( Simsek and Kocat, 2009 , 2010, 2012) investigated the vibrations of clamped beam under moving force. In this paper, we study the nonlinear response of the nonlinear mass-spring model with nonsmooth stiffness. Guess what?. Enjoy the videos and music you love, upload original content, and share it all with friends, family, and the world on YouTube. Consider the mass-spring system governed by the differential equation, Where is the time-dependent position displacement of the mass. And as a direct result of the era, they are still maturing; because individuals and athletes. Plugging this. Guidelines for this subsystem are described as follows: Spring – Assign spring properties to a linear two-joint link object in which one joint is attached to the structure, and the other joint is free. Engineering Mechanics: Dynamics. For this purpose, the equations governing the transverse vibrations of the beam and mass are analyzed via the multiple scale method and the vibration response of the system under primary resonance is extracted. 3 we show nonlinear models including a pendulum (see this movie), nonlinear springs, and variable gravity. In general, courses numbered 600-699 are basic graduate courses preparing students to take the basic part of the qualifying exams, while 700-799 are more advanced courses. In addition there is a pendulum. Dynamics of a Mass-Spring-Damper System. Because the slope of that curve is not constant, it does not make sense to talk about a "spring constant. The system can further comprise a tuned mass damper (TMD) located within the fluid volume. In this system, the only sensor is attached to the mass on the left, and the actuator is attached to the mass on the. The amplitude of the oscilla-tion will then depend on the initial conditions. A nonlinear system has more complicated equations of motion, but these can always be arranged into the standard matrix form by assuming that the displacement of the system is small, and linearizing the equation of motion. In the simulations, the two supports are 2 meters. Waves; Wave pulse; Traveling wave; Wave amplitude; Double slit diffraction; Single slit diffraction; Graphical solutions; Doppler effect; Shock waves. the elastic spring pendulum and the elastic spring pendulum with piecewise constant sti ness. We would love to work with you on your project in all of the phases from the initial idea to the mass production. Enjoy the videos and music you love, upload original content, and share it all with friends, family, and the world on YouTube. Figure 1 : Nonlinear Mass-Spring System. The solutions to this equation can be built up from exponential functions, ˆ(x;t) = Aei(kx¡!t). For the simple mass-spring-dashpot systems, the user picks two frequencies and sets by how fast each should damp. This cookbook example shows how to solve a system of differential equations. Excitations within the structure can be propagated throughout. The nonlinear constraint is connected to the beam between two points on the beam through a rigid rod. This technique also offers the periodic solutions to the nonlinear free vibration of a conservative, coupled mass–spring system having linear and nonlinear stiffnesses with cubic nonlinearity. Because the global linear system does not depend on run-time state, the matrix can be pre-factored, allowing for very fast iterations. I Tሷ + ሶ G T=0 Respuesta análisis del sistema para que la respuesta sea coherente. • Example: simple spring. It need not satisfy Hooke's law. I am a third year graduate student in Wisconsin-Madison. Evolution equations for and their solutions wave systems. $The quasi-period is measured at 14. systems can be modeled as mass-spring-damper systems Real system Mechanical Model Mathematical Model Solution Analysis I Tሷ+ Tሶ+ G T=0 Respuesta análisis del sistema para que la respuesta sea coherente. 6: Jordan Form and Eigenanalysis 11. F spring = - k x. A nonlinear vibration absorber (NVA) is used to suppress the nonlinear response of a panel flutter in supersonic airflow. The response is found by using two different perturbation approaches. A system's ability to oscillate at certain frequencies at higher amplitude is called as resonance. Woofers usually have a suspension comprising a. Cauchy problems and mass-spring damper system with$\psi$–Katugampola fractional derivative are solved analytically by means of modified Laplace transform. We model the shape's physical behavior by treating it as a network of point masses and springs. Then the solution of the equation is x(l) = xo cos t x(t) = — A'osin. I wasn't sure where to post this problem, as it's physics related, but rather advanced in its math content (and it's a problem for my applied math course). The Simscape model uses physical connections, which permit a bidirectional flow of energy between components. is the mass density (mass/length) P is the applied force Note that the free-free and fixed-fixed have the same formula. the system, it is possible to work with an equivalent set of standardized first-order vector differential equations that can be derived in a systematic way. Enjoy the videos and music you love, upload original content, and share it all with friends, family, and the world on YouTube. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. From equation (10) we obtain the. The F-D relationship of a nonlinear spring is usually based on ture [2]. Let x 1 (t) =y(t), x 2 (t) = (t) be new variables, called state variables. Examples of derivation of EOMs Appendix A Equivalence of principles of conservation of mechanical energy and conservation of linear momentum. 1007/s11300-006-0082-3 text/html Access to. Prerequisite: CEE 342 or permission of instructor. Cauchy problems and mass-spring damper system with$\psi$–Katugampola fractional derivative are solved analytically by means of modified Laplace transform. My advisor is Prof. Call it nonlinear war (which I prefer), or hybrid war, or deter and resist a mass, tank-led Soviet invasion–finds hard take on the Arab Spring so closely. 1 (a) is the familiar linear second-order differential equation x+x = Q (2. The spring-mass system has also a cubic nonlinearity. Dynamic System Simulation Using Simulink/ Matlab. Because of the unique nonlinear characteristics, design methods for linear springs are difficult to apply, which makes. This course covers modeling and control of linear and nonlinear mechanical and electro-mechanical systems. m — graph oscillations of linear mass & spring system cspr. 068 Nonlinear Dynamics and Turbulence. Nonlinear Springs Goal: Investigate the behavior of nonlinear springs. To avoid reflection at the last (11 th ) mass, the number of mass was set to 200 in the Assembly module (Fig. From the time di erences of the incoming signals, the boat obtains di erences of distances to the transmitters. to have the same mathematical form as the generic mass-spring-damper system. An analytical approach is developed for areas of nonlinear science such as the nonlinear free vibration of a conservative, two-degree-of-freedom mass–spring system having linear and nonlinear stiffnesses. In this paper we study the nature of periodic solutions to two nonlinear spring-mass equations; our nonlinear terms are similar to earlier models of motion in suspension bridges. Enjoy the videos and music you love, upload original content, and share it all with friends, family, and the world on YouTube. On stability of a harmonic oscillator with a delayed feedback system (2019). Then the system is equivalently described by the equations. The proportionality constant k is specific for each spring. Waves; Wave pulse; Traveling wave; Wave amplitude; Double slit diffraction; Single slit diffraction; Graphical solutions; Doppler effect; Shock waves. This enables high fidelity observations of large amplitude dispersive shock waves in this spatially extended system, found to agree quantitatively with a nonlinear wave averaging theory. Image used with permission from Wikipedia. Model B was a three-dimensional version of this system which included the same horizontal piping plus a tee, a vertical riser, an elbow and another horizontal straight run terminating at a nozzle. Appendix B: Linearization Work problems:. Spring stores potential energy by its deformation (kx2/2). The Free Mass-Spring System Worksheet. This would require new, easy to fabricate nonlinear optical materials that can mediate the. The simplified engineering structure considered in this study is a mass-spring system with multi-degree of freedom. Finally, a new numerical method is proposed for nonlinear$\psi$–Katugampola FDEs. With the mass-spring system motionless, the Momentum Principle gives: ∆ = ∆=0 p F tnet Therefore the net force must equal zero. , electro-mechanical) systems. March 15, 2021. This is the frequency of vibration that occurs when a mass suspended on a spring is. WEIWEI, AI 2221171 2225277 2226361 Ai Weiwei is one of today. 8 An over-damped spring-mass system. For dynamic analysis, you may input either the spring stiffness or the damping coefficient, or both. All shear deformation is assumed to occur within a shear spring. course): Course webpage tutorials for Fundamentals of Pure Mathematics (FPM, MATH08064) Fall 17: tutorials for Honours Differential Equations (HDEq, MATH10066) Spring 17:. Let’s see where it is derived from. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Sketch the function and show from this plot that the first equation has three stationary points. system is a spring-mass-damper system in which the spring has no damping or mass, the mass has no stiffness or damping, the damper has no stiffness or mass. Model the system as a SDF with equivalent mass of the cutting head = 25 kg. Its parameters are estimated using Recursive Least Squares (RLS) algorithm. 3 we show nonlinear models including a pendulum (see this movie), nonlinear springs, and variable gravity. Fnet =0,(k∆y−Mg),0 =0,0,0 where k is the spring constant and ∆y is. As one such example, Aoki, Sawaragi and Isaacson (1993) described the numerical simulation of the motions of a single degree of freedom system with a piecewise-linear restoring force function. Dynamics of a Nonlinear System – The Pendubot. For stiffness finding an equation system that described material tension is solved. Modeling a Second Order Equation (Single Degree of Freedom System-SDOF) The mass-spring-dashpot is a basic model used widely in mechanical engineering design to model real-world mechanical systems. Period of vibration is determined. The force is the same on each of the two springs. This is a system consisting of a mass attached to the wall via a spring, sitting on a frictionless surface. Show that the frequency of oscillation on the frictionless surface is given by. University Science Books •Thornton, Stephen T. This equates to a volume of 0. Volume 4: Fluid-Structure Interaction. That are one-dimensional oscillator and a spring pendulum. (a) The experimental prototype of the nonlinear EM harvester. 1 where m, c1 and k are the mass, linear damping and stiffness, respectively; x (t) is the response of the system and f (t) is the input force excitation. damper is strong enough, so that the spring is overdamped, then the door just settles back to the equilibrium position (i. mx¨ + f(x)=0 mx¨ + g(˙x)+f(x)=0 mx¨ + h(x, x˙)=0 more general nonlinear damped mass-spring system. - Human-machine and human-robot systems - Neural and machine learning. Please note the following:. Computer Project 1. The Forced Mass-Spring System. Note that we use bold and overline to. A linear spring k 1 and a linear damper c 11 are attached to the mass m 1, whereas a linear spring k 2 and a nonlinear damper connects the two masses m 1 and m 2. Equation for Nonlinear Spring-Mass-Damper System c program. Even though the nonlinearities constitute only a small part of the structure, the entire…. With a mass at the end of a linear spring (rate k) we have the dynamics mx¨ = −kx but with a “leaf spring” as is used on car suspensions, we have a nonlinear spring – the more it deflects, the stiffer it gets. nonlinear system solver python, The system of three equations and three unknowns is 10 = c + ba^2 6 = c + ba^4 5 = c + ba^5 It's not that hard to solve numerically. Step 2 (spring-mass system) Damping. When the mass is attached to the spring, the spring will stretch until it reaches the point where the two forces are equal but pointing in opposite directions: FS Fg =0 orkx = mg (9. Inorder to extend this model to accomodate systems with nonlinear spring and damper characteristics, the force terms bx and kx must be replaced byan. Wang, Yong Fu Wang, Dian Hui ; Chai, Tian You status. A horizontal spring block system of (force constant k) and mass M executes SHM with amplitude A. When spring 1 is extended by x, spring 2 is compressed by the same distance. iii) Write down mathematical formula for each of the arrows (vectors). The proportionality constant k is specific for each spring. Control ling oscillations of a spring-mass-damper system is a well studied problem in engineering text books. 2 Linear and nonlinear objects A mathematical. *cos (w*t) , y (0) = 0. (I will not show you each and every steps of how to draw these equations. For the initial study of the nonlinear spring the quarter car model was sufficient enough to study the dynamics of the vehicle. In this paper, nonlinear modal interactions caused by one-to-three internal resonance in a beam-mass-spring-damper system are investigated based on nonlinear system identification. A recursive model for nonlinear spring-mass-damper estimation of a vehicle localized impact. In a nonlinear spring-mass system, the spring force is given by F s= ku+ u3 where k >0 is the spring constant, is a small number describing the strength of the spring: = 0 gives Hooke's Law, >0 gives a hard spring and <0 gives a soft spring. An example is given to demonstrate the reduction of the vibration amplitude of the spring-mass system under a given exciting forcing frequency. Following this idea the fractional differential equation for the mass-spring-damper system with source showed in Fig. Linear and nonlinear system. Solution: Taking unit vector along positive X direction as. This video describes the use of SIMULINK to simulate the dynamic equations of a spring-mass-damper system. When the mass is in motion and reaches the equilibrium position of the spring, the mechanical energy of the system has been completely converted to kinetic energy. Accordingly, for verification and test of accuracies, availability of nonlinear systems with exact closed form solutions is important. But there are examples which are modeled by linear systems (the spring-mass model is one of them). Of course, if we have a very strong spring and only add a small amount of damping to our spring-mass system, the mass would continue to oscillate, but the oscillations would become progressively smaller. The spring is called a hard spring if >0 and a soft spring if <0. It can be shown that one can achieve a zero amplitude of vibration of the spring-mass system by choosing a rotational spring stiffness that will tune the frequency of the hanging heavy column to the. 6x&+3x +x2 =0 whose phase portrait is plot in Fig. 1 g/sec$)? A spring-mass system has mass $140g$ and spring constant $700g/sec^2. For this purpose, we take as prototype model, a system that consists of the double-well smooth potential with an additional spring component acting on the system only for large enough displacement. A system of masses connected by springs is a classical system with several degrees of freedom. Period of nonlinear spring-mass system Thread starter jinteni; Start date Nov 28, 2007; Nov 28, 2007 #1 jinteni. Even though the nonlinearities constitute only a small part of the structure, the entire…. Numerous civil engineering structures exhibit nonlinearities. Equation for Nonlinear Spring-Mass-Damper System c program. Cauchy problems and mass-spring damper system with$\psi$–Katugampola fractional derivative are solved analytically by means of modified Laplace transform. Composites Part B: Engineering, vol. The spring is stretched 2 cm from its equilibrium position and the mass is. displacement for a linear spring will always be a straight line, with a constant slope. This would require new, easy to fabricate nonlinear optical materials that can mediate the. One end of each spring is attached to a fixed support. The theories of non-linear dynamics are applied to study non-linear model and to reveal its. (Undergraduate) Taught Spring 2017. m — graph oscillations of linear mass & spring system cspr. It is a form of pendulum. With the mass-spring system motionless, the Momentum Principle gives: ∆ = ∆=0 p F tnet Therefore the net force must equal zero. Photo 1 shows the original tip; 50 drops from this had a mass of 2. Please note the following:. The mg force is gravity; kx is Hooke’s law for the force exerted by a spring. Weapons based on new physical principals and automatized systems are being actively incorporated into military activity. This is the frequency of vibration that occurs when a mass suspended on a spring is. This means that its configuration can be described by two generalized coordinates, which can be chosen to be the displacements of the first and second mass from the equilibrium position. It is represented schematically as shown in Fig. Keywordsandphrases: Coupled systems,functional boundaryconditions, Green’sfunctions, Schauder’s fixed-point theorem, coupled mass-spring system. The system is just basically two masses, two linear and one nonlinear spring (elastic perfectly plastic hysteretic material nonlinearity) between two masses. Mechatronic systems in the automotive applications are characterized by significant nonlinearities and tight performance specifications further exacerbated by state and input constraints. 3 Suspension Model The suspension and tire assembly is modeled as shown in Figure8. The spring–mass system used as a testbed in the experiments. Linear and nonlinear system. Consider a block of liquid of mass m as shown in Figure 4. Modeling a Second Order Equation (Single Degree of Freedom System-SDOF) The mass-spring-dashpot is a basic model used widely in mechanical engineering design to model real-world mechanical systems. The spring is stretched 2 cm from its equilibrium position and the mass is released from rest. Shear-spring location may be specified in terms of distance from joint j, where dj2 is the major-axis shear-spring location, and dj3, the minor-axis. To compute and diplay the response of a 1-DOF vibrating system, follow the three steps below. In all of the systems we’ve studied (longitudinal spring/mass, transverse string, longitudinal sound), we ended up with a wave equation of the form, @2ˆ @t2 = c2 @2ˆ @x2; (1) where c depends on various parameters in the setup. The method is based on shooting in. Examples of derivation of EOMs Appendix A Equivalence of principles of conservation of mechanical energy and conservation of linear momentum. course): Course webpage tutorials for Fundamentals of Pure Mathematics (FPM, MATH08064) Fall 17: tutorials for Honours Differential Equations (HDEq, MATH10066) Spring 17:. spring 1 spring 0 Figure 1. The system consists of masses in two dimensions. Fan), submitted, 2020. Write a computer program to find a root of the two by two nonlinear system below 0,$ tanỆ 8² +n² with the Newton method. Due to various sources of nonlinearities, micro/nano-electro-mechanical-system (MEMS/NEMS) resonators present highly nonlinear behaviors including softening- or hardening-type frequency responses, bistability, chaos, etc. Even though the nonlinearities constitute only a small part of the structure, the entire…. A nonlinear vibration absorber (NVA) is used to suppress the nonlinear response of a panel flutter in supersonic airflow. 1 is given by m 2(1 1 ) d2 x(t) dt2 + d x(t) dt +kx(t) = v(t); 0 < 1 (10) where mis the mass, is the damped coefficient and kis the spring constant. Prototype and the proposed method. Step 3 (damped spring-mass system) This is the currently selected item. Partial vibration frequency ,rads 1. Show that the frequency of oscillation on the frictionless surface is given by. Adding mass to the system would decrease its resonant frequency. Mass-nonlinear spring system. In the simulations, the two supports are 2 meters. A nonlinear system can exhibit an oscillation of xed amplitude and frequency which appears. be modified to account for the vehicle unsprung mass. Consider two springs placed in series with a mass on the bottom of the second. x : position of mass [m] at time t [s] m : mass [kg] c : viscous damping coefficient [N s / m] k : spring constant [N / m] u : force input [N] A quick derivation can be found here. 3: Structure of Linear Systems 11. Mass spectrometry is a method of investigation that study matter by measuring the masses of molecules. Please note the following:. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. The spring-mass system is linear. The force exerted by the spring (kx)ispulling upwards. 2D spring-mass system. Numerous civil engineering structures exhibit nonlinearities. A number of studies have described the theoretical and numerical aspects of the chaotic motions of offshore structures with nonlinear moorings. A slowly varying amplitude pulse is input to the system, with a pulse width of 20 ns, a wavelength of 1. Coupled spring equations Since the upper mass is attached to both springs, there are damping coefficients 1 ¼ 0 and 2 ¼ 0, nonlinear coefficients 1 ¼ 1=6. Some studies included corrections in order to take into account the influence of the spring mass on the oscillations of the spring-mass system [3, 4]. In this article, an adaptive neural dynamic surface sliding mode control scheme is proposed for uncertain nonlinear systems with unknown input saturation. The cerebellar model developed in the present work learns to perform position control of a single degree--of--freedom, nonlinear, dynamic spring--mass system. Hydraulic inertance is the equivalent of inductance in electrical systems or a spring in mechanical systems. x : position of mass [m] at time t [s] m : mass [kg] c : viscous damping coefficient [N s / m] k : spring constant [N / m] u : force input [N] A quick derivation can be found here. All vibrating systems consist of this interplay between an energy storing component and an energy carrying (massy'') component. spring and free mass spring constant spring force spring, nonlinear spring-mass system square integrable square law nonlinearity stability margin stability of a digital filter stability of finite differences stability of nonlinear delay loops stability proof for a conical cap stable system standard deviation standing wave state conversions. Controlling a Nonlinear Spring-Mass System with a Cerebellar Model. Viscous damping effects and mass transport. This finding is critical to constraining the evolution and chemical enrichment of low-mass stars, and their impact on the spectrophotometric properties of galaxies. In linear and nonlinear circuits that are driven with a periodic signal, the system will eventually enter a steady state after the transient response decays to zero. ^ (2)* (y) = A. Let us consider the one-dimensional motion of a body of mass. That are one-dimensional oscillator and a spring pendulum. Formulation of the equation of motion is obtained starting from transverse/axial coupling through axial strain. However, relatively few laboratory measurements of chaotic. Find a solution to a multivariable nonlinear equation F(x) = 0. Adding mass to the system would decrease its resonant frequency. m — graph oscillations of linear mass & spring system cspr. solve the initial vaule problem by hand first for w. Nonlinear Systems and Control Lecture # 2 Examples of Nonlinear Systems – p. Parameter investigation and biological system - Wenrui Hao, University of Notre Dame: 11th Floor Lecture Hall: 4:00 - 4:45pm EDT: Convex optimization and quantum information - Aram Harrow, Massachusetts Institute of Technology: 11th Floor Lecture Hall. The model is for the concentration vs. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. The input frequency of external force is twice that of the output displacement results. Using a stiffer spring would increase the frequency of the oscillating system. Successive photos of a burette tip cut off in stages to form bigger drops. Solution is obtained by applying method of multiple time scale directly to. Mass is connected to springs and. In this system, the only sensor is attached to the mass on the left, and the actuator is attached to the mass on the. "Nonlinear Planning and Control" introduces quite general computational algorithms for reasoning about those dynamical systems, with optimization theory playing a central role. For Poisson ratio different stiffness for different types of springs in cubic grid is used. When all energy goes into KE, max velocity happens. - Human-machine and human-robot systems - Neural and machine learning. (unforced) f(x) = Nonlinear spring force g(xdot) = Nonlinear damping. 39 μW for the nonlinear spring of 8. PDF | We present results from 2-D numerical simulations based on Immersed Boundary Method of a cylinder in uniform fluid flow attached to bistable | Find, read and cite all the research you. Step 3 (damped spring-mass system) This is the currently selected item. Gathering terms and dividing through by m gives you the following ODE for the spring-mass system: x′′(t) + k m x(t) −g = 0. 2013] Mass-Spring Systems. The Duffing equation is used to model different Mass-Spring-Damper systems. This scheme provides a fast solution for classical linear (Hookean) springs. Evolution equations for and their solutions wave systems. This means that its configuration can be described by two generalized coordinates, which can be chosen to be the displacements of the first and second mass from the equilibrium position. Equipment: A linear spring, slotted weights, a stop watch, a spring hanger, a meter stick or a 30. time in a batch reactor for a first order irreversible reaction. The procedure introduced is based on the Taylor series expansion and on knowledge of nominal system trajectories and nominal system inputs. As possible potential applications, we further consider the mass-spring mechanical system discussed in page 8 of Khalil which takes the form of. However, relatively few laboratory measurements of chaotic. Beam mass is negligible Approximate B Cantilever Beam II. Model Predictive Control (MPC) in conjunction with hybrid modeling can be an attractive and systematic methodology to handle these challenging control problems. MH Ghayesh, T Reid, Sub- and super-critical nonlinear dynamics of a harmonically excited axially moving beam, International Journal of Solids and Structures 49, 2012, 227-243. For stiffness finding an equation system that described material tension is solved. The Forced Mass-Spring System. It is a form of pendulum. Zhang and Whiten noted that Tsuji’s non-linear contact model is more realistic and closer to the experimental. Spring mass damper system NON-LINEAR. (Undergraduate) Taught Spring 2017. A bilinear Maxwell damper has been implemented as a new link property. This type of oscillator is often known as an anharmonic oscillator. A block of mass 3M and initial speed v₀ is moving to the left as shown. Tools needed: ode45, plot Description: For certain (nonlinear) spring-mass systems, the spring force is not given by Hooke's Law but instead satisfies ku Eu Spring where k 0 is the spring constant and E is small but may be positive or negative and represents the strength" of the spring (E 0 gives Hooke's Law). The system is just basically two masses, two linear and one nonlinear spring (elastic perfectly plastic hysteretic material nonlinearity) between two masses. Prerequisite: CEE 342 or permission of instructor. Tools needed: ode45, plot Description: For certain (nonlinear) spring-mass systems, the spring force is not given by Hooke's Law but instead satis es 3 F =ku + u ; spring where k > 0 is the spring constant and is small but may be positive or negative and represents the \strength" of the spring ( = 0 gives Hooke's Law). When the block is passing through its equilibrium position an object of mass m is put on it and the two move together. Model Predictive Control (MPC) in conjunction with hybrid modeling can be an attractive and systematic methodology to handle these challenging control problems. The reference position results when (i) F has been set to zero, and (ii) the pulley mass and rope mass are assumed negligible. 24 this season is no fluke. Nonlinear Systems and Control | Spring 2018 Limit cycles: A linear system can have a stable oscillation if it has a pair of eigenvalues on the imaginary axis. displacement for a linear spring will always be a straight line, with a constant slope. qxd 09/20/2001. Also, it is studied how nonlinearity affects the response compared to linear system. The difference being that ours is human-caused, isn’t going to take 80,000 years, has so far lasted just a few centuries and is now gaining speed in a non-linear fashion. 3 s; although. " Proceedings of the. Nonlinear Springs Goal: Investigate the behavior of nonlinear springs. A nonlinear spring has a nonlinear relationship between force and. In addition, I show how ETCH principles, when applied by educational system leaders, permit them to facilitate an optimal learning environment for a student-centered complex adaptive system. External loading amplitude 0, N. • Example: simple spring. Photo 1 shows the original tip; 50 drops from this had a mass of 2. The derivations and examples are given in the appendices per Table 2. Mass is connected to springs and. 2) Assume that the mass is initially at rest, at length xo. Consider the model of an undamped nonlinear spring/mass system given by x" + 8x – 6x 3 + x 5 = 0. An equilibrium point in a nonlinear system is Lyapunov unstable if there exists at least one eigenvalue of the linear variational equations which has a positive real part. This video describes the use of SIMULINK to simulate the dynamic equations of a spring-mass-damper system. A nonlinear vibration absorber (NVA) is used to suppress the nonlinear response of a panel flutter in supersonic airflow. Spring-Mass Potential Energy. The warning system is designed in an open and modular structure based on the most recent developments and standards of information technology. Show that the system x + 4x + 3x = 0. In this paper, nonlinear modal interactions caused by one-to-three internal resonance in a beam-mass-spring-damper system are investigated based on nonlinear system identification. It is a nonlinear di erential equation that describes a simple harmonic oscillator with an additional correction to its potential energy function. The spring is called a. 6x&+3x +x2 =0 whose phase portrait is plot in Fig. Numerous civil engineering structures exhibit nonlinearities. As such, dj2 represents the location for 1-2 plane shearing and 1-3 plane bending, while dj3 is the reverse. Obtaining an optimum suspension system is of great importance for automotive and vibration engineer involved in the vehicle design process. 04312 g per drop. Consider a vertical spring on which we hang a mass m; it will stretch a distance x because of the weight of the mass, That stretch is given by x = m g / k. Nonlinear Spring-Mass-System A mass is attached to a nonlinear spring. Figure 1: a simple linear system:{spring + mass}. For underdamped systems (b<2), the equilibrium is a called a focus,andfor overdamped systems (b>2), it is called a node. Solution: Taking unit vector along positive X direction as. 6x&+3x +x2 =0 whose phase portrait is plot in Fig. As in Lesson 28, consider a spring, not necessarily linear, suspended vertically from a support. The natural frequency of a simple mechanical system consisting of a weight suspended by a spring is: = where m is the mass and k is the spring constant. When spring 1 is extended by x, spring 2 is compressed by the same distance. There is a large box with mass m and spring k inside of it. We describe a scheme for time integration of mass-spring systems that makes use of a solver based on block coordinate descent. For example, our spring-mass. Example 18 from Introductory Manual for LS-DYNA Users by James M. The spring force is a nonlinear function of and given by, Where and are positive constants. A bilinear Maxwell damper has been implemented as a new link property. Guess what?. Open Live Script. A nonlinear vibration absorber (NVA) is used to suppress the nonlinear response of a panel flutter in supersonic airflow. Set the initial value to be (80, no) = (1,1). Questions: Suppose a nonlinear spring-mass system satisfies the initial value problem (u 00 + u + ±u 3 = 0 u (0) = 0, u 0 (0) = 1 Use ode45 and plot to answer the following: 1. It is a nonlinear di erential equation that describes a simple harmonic oscillator with an additional correction to its potential energy function. mx¨ + f(x)=0 mx¨ + g(˙x)+f(x)=0 mx¨ + h(x, x˙)=0 more general nonlinear damped mass-spring system. ; Marion, Jerry B. For example, our spring-mass. Classical Dynamics of Particles and Systems (5th ed. To avoid reflection at the last (11 th ) mass, the number of mass was set to 200 in the Assembly module (Fig. Keywordsandphrases: Coupled systems,functional boundaryconditions, Green’sfunctions, Schauder’s fixed-point theorem, coupled mass-spring system. [The natural frequency of a spring/mass system is the frequency of free vibration of the mass when no external forces are present. Prerequisite: CEE 342 or permission of instructor. Construction of L^2 log-log blowup solutions for the mass critical nonlinear Schrödinger equation (with C. A spring-mass-damper system dynamics-based driver-vehicle integrated model for representing heterogeneous traffic 16 April 2018 | International Journal of Modern Physics B, Vol. (a) The experimental prototype of the nonlinear EM harvester. Tools needed: ode45, plot Description: For certain (nonlinear) spring-mass systems, the spring force is not given by Hooke's Law but instead satisfies ku Eu Spring where k 0 is the spring constant and E is small but may be positive or negative and represents the strength" of the spring (E 0 gives Hooke's. The horizontal vibrations of a single-story building can be conveniently modeled as a single degree of freedom system. When an additional mass of 1 kg is added to the original mass m, the natural frequency is reduced to 1 Hz. Model Predictive Control (MPC) in conjunction with hybrid modeling can be an attractive and systematic methodology to handle these challenging control problems. Assume the initial conditions x(0) = 0 and x' (0) = 0. Let us refer back to Figure 2. This example shows how to model a double spring-mass-damper system with a periodically varying forcing function. The spring force is a nonlinear function of and given by, Where and are positive constants. Against the backdrop of the Arab–Spring protests, we examine macroeconomic stabilization under regime shift. The Laboratory is focused on the development and application of modern mass spectrometry techniques. In the simulations, the two supports are 2 meters. Accepted: 22/01/2020. Read "Fast Simulation of Mass-Spring Systems" [Tiantian Liu et al. Good model now is mx¨ = −k 1x − k 2x 3 which is a “cubic spring”. Adding mass to the system would decrease its resonant frequency. 6 Linearization of Nonlinear Systems In this section we show how to perform linearization of systems described by nonlinear differential equations. My advisor is Prof. Nonlinear shallow-water waves and the Korteweg-deVries equation. • Some examples of two degree of fdfreedom systems are shown in the figure. The spring is called a. the initial position and velocity of the mass is non-zero. March 15, 2021. April 19, 2021. The system is just basically two masses, two linear and one nonlinear spring (elastic perfectly plastic hysteretic material nonlinearity) between two masses. If a force is applied to a translational mechanical system, then it is opposed by opposing forces due to mass, elasticity and friction of the system. lu/research/scientific-publication/processing-and-properties-of-long-recycled. A linear spring k 1 and a linear damper c 11 are attached to the mass m 1, whereas a linear spring k 2 and a nonlinear damper connects the two masses m 1 and m 2. Consider the mass-spring system governed by the differential equation, Where is the time-dependent position displacement of the mass. An equilibriumpoint in a nonlinear system is asymptotically Lyapunov stable if all the eigen-values of the linear variational equations have negative real parts. Damping coe cient. 1b) systems in the presence of an anharmonic potential. Guidelines for this subsystem are described as follows: Spring – Assign spring properties to a linear two-joint link object in which one joint is attached to the structure, and the other joint is free. Linear and nonlinear. Those are mass, spring and dashpot or damper. Mass-nonlinear spring system. Spring Constant, K N/m. The mass, M is attached to a rigid boundary through a spring & viscous damper of linear plus nonlinear characteristic, as shown in Figure 1. Consider the undamped, driven spring-mass system modeled by the initial value problem. Show that the frequency of oscillation on the frictionless surface is given by. The Damped Mass-Spring System Worksheet. A linear spring is one with a linear relationship between force and displacement, meaning the force and displacement are directly proportional to each other. Nonlinear Systems and Control | Spring 2018 Limit cycles: A linear system can have a stable oscillation if it has a pair of eigenvalues on the imaginary axis. Figure 1: We propose a method for fast approximate time integration of dynamic mass-spring systems. Fundamental equation of motion for mass-spring-damper system (1DOF). Modeling a Second Order Equation (Single Degree of Freedom System-SDOF) The mass-spring-dashpot is a basic model used widely in mechanical engineering design to model real-world mechanical systems. Call it nonlinear war (which I prefer), or hybrid war, or deter and resist a mass, tank-led Soviet invasion–finds hard take on the Arab Spring so closely. Find a solution to a multivariable nonlinear equation F(x) = 0. An eigensystem approach to Anderson localization for multi-particle systems. However, we can often investigate the behavior of the solutions without actually being able to find simple expressions in terms of elementary func-tions. The physical explanation for this motion involves a decay mode called a ’’parametric instability’’; the ’’inverse parametric instability’’ is also intimately involved. Image used with permission from Wikipedia. 108653, 2021. (1), where χ is related to the motion of the mass-spring oscillator as follows: x = εχ. Computer Project 1. be modified to account for the vehicle unsprung mass. A method for creating elasticity module using splines is described. 8), f n = g (2. As such, dj2 represents the location for 1-2 plane shearing and 1-3 plane bending, while dj3 is the reverse. Broad, expert-led instruction and match experience in a high competitive standard, beginning at a young age, and also high-quality talent improvement programmes are indicated as key ingredients for the development of good strategic abilities. Prototype and the proposed method. The force exerted by the spring (kx)ispulling upwards. 10) δ st 1 2π 8434_Harris_02_b. Weapons based on new physical principals and automatized systems are being actively incorporated into military activity. (When you see this kind of spring-mass system, each Mass is the building block of the system). 1: Phase portrait of a mass-spring system The governing equation of the mass-spring system in Figure 2. The theory of a completely reversible cyclic process is developed and a method of predicting the maximum swinging. That are one-dimensional oscillator and a spring pendulum. Hooke's Law states that the restoring force of a spring is directly proportional to a small displacement. Math 425: Partial differential equations (Undergraduate Level), Spring 2013. An equilibriumpoint in a nonlinear system is asymptotically Lyapunov stable if all the eigen-values of the linear variational equations have negative real parts. To avoid reflection at the last (11 th ) mass, the number of mass was set to 200 in the Assembly module (Fig. The two blocks collide and stick to each other. To compute and diplay the response of a 1-DOF vibrating system, follow the three steps below. For this time-varying system the attractor is closed but not bounded, therefore the La Salle’s results of [9] cannot be applied (whereas one may. Open Live Script. To accelerate a fluid and to increase its velocity a force is required. The nonlinear damping force between the two masses is assumed to be. 3 Recommended. 060A Acad Year 2020-2021: Not offered Acad Year 2021-2022: U (Spring) 3-2-7 units. the elastic spring pendulum and the elastic spring pendulum with piecewise constant sti ness. PDF | We present results from 2-D numerical simulations based on Immersed Boundary Method of a cylinder in uniform fluid flow attached to bistable | Find, read and cite all the research you. the initial position and velocity of the mass is non-zero. The fi tfirst figure shows a two mass –two spring system that is described by two linear coordinates x1 and x2. x = Asin(ωt +ф) where A, ω and ф are constants. The spring-mass system used as a testbed in the experiments. Once we fit the data, we take the analytical derivative of the fitted function. Nonlinear shallow-water waves and the Korteweg-deVries equation. It is so important that the Nobel Prize in Physics 2018 was given. iii) Write down mathematical formula for each of the arrows (vectors). Nonlinear Dynamics of a Mass-Spring-Damper System Background: Mass-spring-damper systems are well-known in studies of mechanical vibrations. qxd 09/20/2001. It employs mossy fiber input codings modeled on neurophysiological data and a large granule cell layer that recodes the mossy fiber pattern into a much higher dimensional space. The spring force can be symmetric or asymmetric. Accordingly, for verification and test of accuracies, availability of nonlinear systems with exact closed form solutions is important. https://www. E 99, 013001 – Published 14 January 2019. In the first approach, the method of multiple scales is applied directly. Math 644: Partial differential equations (Graduate Level), Fall. Non-Linear Spring and Damping Models The normal elastic constant based on Hertz contact theory is 4. Learn more about 2dof, mass, spring, ode, differential equations, system of differential equations, second, order. This scheme provides a fast solution for classical linear (Hookean) springs. When an additional mass of 1 kg is added to the original mass m, the natural frequency is reduced to 1 Hz. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. The second figure denotes a two rotor system whose motion can be specified in terms of θ1 and θ2. Swinging Spring, Physica D Nonlinear Phenomena •Taylor, John R. For a nonlinear spring with spring force, the stiffness of the spring is, a definition that is consistent with the linear spring where. is overdamped and graph the solution with initial conditions x(0) = 1, x. If the spring is strong or stiff, k will be large, and k will be small for a weak spring. For example, our spring-mass. Model Predictive Control (MPC) in conjunction with hybrid modeling can be an attractive and systematic methodology to handle these challenging control problems. attached by massless nonlinear springs to an immovable support.
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# Question 90394
May 27, 2015
The volume by volume percent concentration of your solution will be equal to 0.991%.
You know that your acetic acid solution has a density equal to that of water, more specifically to ${\text{1.00 g/cm}}^{3}$. Moreover, you know the molarity of the solution to be $\text{0.165 mol/L}$. This will be your starting point.
Since molariy is defined as moles of solute, in your case acetic acid, per liters of solution, you can use it to determine how many moles of acetic acid you have.
To make the calculations easier, you can assume a 1.00-L sample of solution.
$C = \frac{n}{V} \implies n = C \cdot V$
${n}_{\text{acetic acid" = 0.165"mol"/cancel("L") * 1.00cancel("L") = "0.165 moles}}$
Use acetic acid's molar mass to determine how many grams you'd get in your sample
0.165cancel("moles") * "60.05 g"/(1cancel("mole")) = "9.91 g" $\text{acetic acid}$
Now you can use the solution's density to see what volume this much acetic acid would occupy
9.91cancel("g") * (1cancel("cm"^3))/(1cancel("g")) * "1 L"/(1000cancel("cm"^3)) = 9.91 * 10^(-3)"L"
I've converted the volume to liters because it will make the calculation of the v/v percent concentration easier.
So, you know that for every 1.00 L of solution, you get 9.91 mL of acetic acid. This means that its v/v percent concentration will be
$\text{%v/v" = "volume of acetic acid"/"volume of solution} \cdot 100$
"%v/v" = (9.91 * 10^(-3)cancel("L"))/(1.00cancel("L")) * 100 = color(green)("0.991%")#
On average, regular vinegar is about 5% v/v, which means that your solution is roughly 5 times more dilute than that.
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Please help transcribe this video using our simple transcription tool. You need to be logged in to do so.
## Description
Mirror Descent is a technique for solving nonsmooth problems with convex structure, primarily, convex minimization and convex-concave saddle point problems. Mirror Descent utilizes first order information on the problem and is a far-reaching extension of the classical Subgradient Descent algorithm (N. Shor, 1967). This technique allows to adjust, to some extent, the algorithms to the geometry of the problem at hand and under favorable circumstances results in nearly dimension-independent and unimprovable in the large scale case convergence rates. As a result, in some important cases (e.g., when solving large-scale deterministic and stochastic convex problems on the domains like Euclidean/$\ell_1$/nuclear norm balls), Mirror Descent algorithms become the methods of choice when low and medium accuracy solutions are sought. In the tutorial, we outline the basic Mirror Descent theory for deterministic and stochastic convex minimization and convex-concave saddle point problems, including recent developments aimed at accelerating MD algorithms by utilizing problem's structure.
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# A very big sum code in C#
Problem source: https://www.hackerrank.com/challenges/a-very-big-sum
You are given an array of integers of size N. You need to print the sum of the elements of the array.
Note: A signed 32bit integer value uses 1st bit to represent the sign of the number and remaining 31bits to represent the magnitude. The range of the 32bit integer is 231 to 2311 or [2147483648,2147483647]. When we add several integer values, the resulting sum might exceed this range. You might need to use long long int in C/C++ or long data type in Java to store such sums.
Input Format
The first line of the input consists of an integer N. The next lines contain N space separated integers describing the array.
Constraints
1N10
0A[i]109
Output Format
Output a single value equal to the sum of the elements of the array.
Sample Input
5
1000000001 1000000002 1000000003 1000000004 1000000005
Sample Output
5000000015
class A_Very_Big_Sum_Hackerrank
{
static void Main(string[] args)
{
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# httr quickstart guide
The goal of this document is to get you up and running with httr as quickly as possible. httr is designed to map closely to the underlying http protocol. I’ll try and explain the basics in this intro, but I’d also recommend “HTTP: The Protocol Every Web Developer Must Know” or “HTTP made really easy”.
This vignette (and parts of the httr API) derived from the excellent “Requests quickstart guide” by Kenneth Reitz. Requests is a python library similar in spirit to httr.
There are two important parts to http: the request, the data sent to the server, and the response, the data sent back from the server. In the first section, you’ll learn about the basics of constructing a request and accessing the response. In the second and third sections, you’ll dive into more details of each.
## httr basics
To make a request, first load httr, then call GET() with a url:
library(httr)
r <- GET("http://httpbin.org/get")
This gives you a response object. Printing a response object gives you some useful information: the actual url used (after any redirects), the http status, the file (content) type, the size, and if it’s a text file, the first few lines of output.
r
#> Response [http://httpbin.org/get]
#> Date: 2020-07-20 14:19
#> Status: 200
#> Content-Type: application/json
#> Size: 365 B
#> {
#> "args": {},
#> "Accept": "application/json, text/xml, application/xml, */*",
#> "Accept-Encoding": "deflate, gzip",
#> "Host": "httpbin.org",
#> "User-Agent": "libcurl/7.64.1 r-curl/4.3 httr/1.4.2",
#> "X-Amzn-Trace-Id": "Root=1-5f15a7db-639798b6a3984d2402ca7808"
#> },
#> "origin": "73.115.118.38",
#> ...
You can pull out important parts of the response with various helper methods, or dig directly into the object:
status_code(r)
#> [1] 200
#> $date #> [1] "Mon, 20 Jul 2020 14:19:07 GMT" #> #>$content-type
#> [1] "application/json"
#>
#> $content-length #> [1] "365" #> #>$connection
#> [1] "keep-alive"
#>
#> $server #> [1] "gunicorn/19.9.0" #> #>$access-control-allow-origin
#> [1] "*"
#>
#> $access-control-allow-credentials #> [1] "true" #> #> attr(,"class") #> [1] "insensitive" "list" str(content(r)) #> List of 4 #>$ args : Named list()
#> $headers:List of 5 #> ..$ Accept : chr "application/json, text/xml, application/xml, */*"
#> ..$Accept-Encoding: chr "deflate, gzip" #> ..$ Host : chr "httpbin.org"
#> ..$User-Agent : chr "libcurl/7.64.1 r-curl/4.3 httr/1.4.2" #> ..$ X-Amzn-Trace-Id: chr "Root=1-5f15a7db-639798b6a3984d2402ca7808"
#> $origin : chr "73.115.118.38" #>$ url : chr "http://httpbin.org/get"
I’ll use httpbin.org throughout this introduction. It accepts many types of http request and returns json that describes the data that it received. This makes it easy to see what httr is doing.
As well as GET(), you can also use the HEAD(), POST(), PATCH(), PUT() and DELETE() verbs. You’re probably most familiar with GET() and POST(): GET() is used by your browser when requesting a page, and POST() is (usually) used when submitting a form to a server. PUT(), PATCH() and DELETE() are used most often by web APIs.
## The response
The data sent back from the server consists of three parts: the status line, the headers and the body. The most important part of the status line is the http status code: it tells you whether or not the request was successful. I’ll show you how to access that data, then how to access the body and headers.
### The status code
The status code is a three digit number that summarises whether or not the request was successful (as defined by the server that you’re talking to). You can access the status code along with a descriptive message using http_status():
r <- GET("http://httpbin.org/get")
# Get an informative description:
http_status(r)
#> $category #> [1] "Success" #> #>$reason
#> [1] "OK"
#>
#> $message #> [1] "Success: (200) OK" # Or just access the raw code: r$status_code
#> [1] 200
A successful request always returns a status of 200. Common errors are 404 (file not found) and 403 (permission denied). If you’re talking to web APIs you might also see 500, which is a generic failure code (and thus not very helpful). If you’d like to learn more, the most memorable guides are the http status cats.
You can automatically throw a warning or raise an error if a request did not succeed:
warn_for_status(r)
stop_for_status(r)
I highly recommend using one of these functions whenever you’re using httr inside a function (i.e. not interactively) to make sure you find out about errors as soon as possible.
### The body
There are three ways to access the body of the request, all using content():
• content(r, "text") accesses the body as a character vector:
r <- GET("http://httpbin.org/get")
content(r, "text")
#> No encoding supplied: defaulting to UTF-8.
#> [1] "{\n \"args\": {}, \n \"headers\": {\n \"Accept\": \"application/json, text/xml, application/xml, */*\", \n \"Accept-Encoding\": \"deflate, gzip\", \n \"Host\": \"httpbin.org\", \n \"User-Agent\": \"libcurl/7.64.1 r-curl/4.3 httr/1.4.2\", \n \"X-Amzn-Trace-Id\": \"Root=1-5f15a7db-a7139ff0092b41f867c50042\"\n }, \n \"origin\": \"73.115.118.38\", \n \"url\": \"http://httpbin.org/get\"\n}\n"
httr will automatically decode content from the server using the encoding supplied in the content-type HTTP header. Unfortunately you can’t always trust what the server tells you, so you can override encoding if needed:
content(r, "text", encoding = "ISO-8859-1")
If you’re having problems figuring out what the correct encoding should be, try stringi::stri_enc_detect(content(r, "raw")).
• For non-text requests, you can access the body of the request as a raw vector:
content(r, "raw")
#> [1] 7b 0a 20 20 22 61 72 67 73 22 3a 20 7b 7d 2c 20 0a 20 20 22 68 65 61 64 65
#> [26] 72 73 22 3a 20 7b 0a 20 20 20 20 22 41 63 63 65 70 74 22 3a 20 22 61 70 70
#> [51] 6c 69 63 61 74 69 6f 6e 2f 6a 73 6f 6e 2c 20 74 65 78 74 2f 78 6d 6c 2c 20
#> [76] 61 70 70 6c 69 63 61 74 69 6f 6e 2f 78 6d 6c 2c 20 2a 2f 2a 22 2c 20 0a 20
#> [101] 20 20 20 22 41 63 63 65 70 74 2d 45 6e 63 6f 64 69 6e 67 22 3a 20 22 64 65
#> [126] 66 6c 61 74 65 2c 20 67 7a 69 70 22 2c 20 0a 20 20 20 20 22 48 6f 73 74 22
#> [151] 3a 20 22 68 74 74 70 62 69 6e 2e 6f 72 67 22 2c 20 0a 20 20 20 20 22 55 73
#> [176] 65 72 2d 41 67 65 6e 74 22 3a 20 22 6c 69 62 63 75 72 6c 2f 37 2e 36 34 2e
#> [201] 31 20 72 2d 63 75 72 6c 2f 34 2e 33 20 68 74 74 72 2f 31 2e 34 2e 32 22 2c
#> [226] 20 0a 20 20 20 20 22 58 2d 41 6d 7a 6e 2d 54 72 61 63 65 2d 49 64 22 3a 20
#> [251] 22 52 6f 6f 74 3d 31 2d 35 66 31 35 61 37 64 62 2d 61 37 31 33 39 66 66 30
#> [276] 30 39 32 62 34 31 66 38 36 37 63 35 30 30 34 32 22 0a 20 20 7d 2c 20 0a 20
#> [301] 20 22 6f 72 69 67 69 6e 22 3a 20 22 37 33 2e 31 31 35 2e 31 31 38 2e 33 38
#> [326] 22 2c 20 0a 20 20 22 75 72 6c 22 3a 20 22 68 74 74 70 3a 2f 2f 68 74 74 70
#> [351] 62 69 6e 2e 6f 72 67 2f 67 65 74 22 0a 7d 0a
This is exactly the sequence of bytes that the web server sent, so this is the highest fidelity way of saving files to disk:
bin <- content(r, "raw")
writeBin(bin, "myfile.txt")
• httr provides a number of default parsers for common file types:
# JSON automatically parsed into named list
str(content(r, "parsed"))
#> List of 4
#> $args : Named list() #>$ headers:List of 5
#> ..$Accept : chr "application/json, text/xml, application/xml, */*" #> ..$ Accept-Encoding: chr "deflate, gzip"
#> ..$Host : chr "httpbin.org" #> ..$ User-Agent : chr "libcurl/7.64.1 r-curl/4.3 httr/1.4.2"
#> ..$X-Amzn-Trace-Id: chr "Root=1-5f15a7db-a7139ff0092b41f867c50042" #>$ origin : chr "73.115.118.38"
#> $url : chr "http://httpbin.org/get" See ?content for a complete list. These are convenient for interactive usage, but if you’re writing an API wrapper, it’s best to parse the text or raw content yourself and check it is as you expect. See the API wrappers vignette for more details. ### The headers Access response headers with headers(): headers(r) #>$date
#> [1] "Mon, 20 Jul 2020 14:19:07 GMT"
#>
#> $content-type #> [1] "application/json" #> #>$content-length
#> [1] "365"
#>
#> $connection #> [1] "keep-alive" #> #>$server
#> [1] "gunicorn/19.9.0"
#>
#> $access-control-allow-origin #> [1] "*" #> #>$access-control-allow-credentials
#> [1] "true"
#>
#> attr(,"class")
#> [1] "insensitive" "list"
This is basically a named list, but because http headers are case insensitive, indexing this object ignores case:
headers(r)$date #> [1] "Mon, 20 Jul 2020 14:19:07 GMT" headers(r)$DATE
#> [1] "Mon, 20 Jul 2020 14:19:07 GMT"
You can access cookies in a similar way:
r <- GET("http://httpbin.org/cookies/set", query = list(a = 1))
#> domain flag path secure expiration name value
#> 1 httpbin.org FALSE / FALSE <NA> a 1
Cookies are automatically persisted between requests to the same domain:
r <- GET("http://httpbin.org/cookies/set", query = list(b = 1))
#> domain flag path secure expiration name value
#> 1 httpbin.org FALSE / FALSE <NA> a 1
#> 2 httpbin.org FALSE / FALSE <NA> b 1
## The request
Like the response, the request consists of three pieces: a status line, headers and a body. The status line defines the http method (GET, POST, DELETE, etc) and the url. You can send additional data to the server in the url (with the query string), in the headers (including cookies) and in the body of POST(), PUT() and PATCH() requests.
### The url query string
A common way of sending simple key-value pairs to the server is the query string: e.g. http://httpbin.org/get?key=val. httr allows you to provide these arguments as a named list with the query argument. For example, if you wanted to pass key1=value1 and key2=value2 to http://httpbin.org/get you could do:
r <- GET("http://httpbin.org/get",
query = list(key1 = "value1", key2 = "value2")
)
content(r)$args #>$key1
#> [1] "value1"
#>
#> $key2 #> [1] "value2" Any NULL elements are automatically dropped from the list, and both keys and values are escaped automatically. r <- GET("http://httpbin.org/get", query = list(key1 = "value 1", "key 2" = "value2", key2 = NULL)) content(r)$args
#> $key 2 #> [1] "value2" #> #>$key1
#> [1] "value 1"
You can add custom headers to a request with add_headers():
r <- GET("http://httpbin.org/get", add_headers(Name = "Hadley"))
str(content(r)$headers) #> List of 7 #>$ Accept : chr "application/json, text/xml, application/xml, */*"
#> $Accept-Encoding: chr "deflate, gzip" #>$ Cookie : chr "b=1; a=1"
#> $Host : chr "httpbin.org" #>$ Name : chr "Hadley"
#> $User-Agent : chr "libcurl/7.64.1 r-curl/4.3 httr/1.4.2" #>$ X-Amzn-Trace-Id: chr "Root=1-5f15a7db-9cc30cee85eb44aa2325b738"
(Note that content(r)$header retrieves the headers that httpbin received. headers(r) gives the headers that it sent back in its response.) ## Cookies Cookies are simple key-value pairs like the query string, but they persist across multiple requests in a session (because they’re sent back and forth every time). To send your own cookies to the server, use set_cookies(): r <- GET("http://httpbin.org/cookies", set_cookies("MeWant" = "cookies")) content(r)$cookies
#> $MeWant #> [1] "cookies" #> #>$a
#> [1] "1"
#>
#> \$b
#> [1] "1"
Note that this response includes the a and b cookies that were added by the server earlier.
### Request body
When POST()ing, you can include data in the body of the request. httr allows you to supply this in a number of different ways. The most common way is a named list:
r <- POST("http://httpbin.org/post", body = list(a = 1, b = 2, c = 3))
You can use the encode argument to determine how this data is sent to the server:
url <- "http://httpbin.org/post"
body <- list(a = 1, b = 2, c = 3)
# Form encoded
r <- POST(url, body = body, encode = "form")
# Multipart encoded
r <- POST(url, body = body, encode = "multipart")
# JSON encoded
r <- POST(url, body = body, encode = "json")
To see exactly what’s being sent to the server, use verbose(). Unfortunately due to the way that verbose() works, knitr can’t capture the messages, so you’ll need to run these from an interactive console to see what’s going on.
POST(url, body = body, encode = "multipart", verbose()) # the default
POST(url, body = body, encode = "form", verbose())
POST(url, body = body, encode = "json", verbose())
PUT() and PATCH() can also have request bodies, and they take arguments identically to POST().
You can also send files off disk:
POST(url, body = upload_file("mypath.txt"))
POST(url, body = list(x = upload_file("mypath.txt")))
(upload_file() will guess the mime-type from the extension - using the type argument to override/supply yourself.)
These uploads stream the data to the server: the data will be loaded in R in chunks then sent to the remote server. This means that you can upload files that are larger than memory.
See POST() for more details on the other types of thing that you can send: no body, empty body, and character and raw vectors.
##### Built with
sessionInfo()
#> R version 3.6.3 (2020-02-29)
#> Platform: x86_64-apple-darwin15.6.0 (64-bit)
#> Running under: macOS Catalina 10.15.5
#>
#> Matrix products: default
#> BLAS: /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRblas.0.dylib
#> LAPACK: /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRlapack.dylib
#>
#> locale:
#> [1] C/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
#>
#> attached base packages:
#> [1] stats graphics grDevices utils datasets methods base
#>
#> other attached packages:
#> [1] httr_1.4.2
#>
#> loaded via a namespace (and not attached):
#> [1] compiler_3.6.3 R6_2.4.1 magrittr_1.5
#> [4] htmltools_0.4.0.9003 tools_3.6.3 curl_4.3
#> [7] yaml_2.2.1 stringi_1.4.6 rmarkdown_2.3.1
#> [10] knitr_1.28 jsonlite_1.6.1 stringr_1.4.0
#> [13] digest_0.6.25 xfun_0.13 rlang_0.4.7
#> [16] evaluate_0.14
|
{}
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# Risk-averse dynamic arbitrage in illiquid markets
## Somayeh Moazeni, Ricardo A. Collado and Andy Zhang
#### Need to know
• To rule out dynamic arbitrage, trades adapted to the price process filtration should be searched.
• The concept of risk-averse dynamic arbitrage using a time-consistent dynamic risk measure is introduced.
• Sufficient conditions are established to certify no-dynamic arbitrage by only searching in the space of $\mathcal F_0$-measurable admissible round-trip trades.
#### Abstract
Arguments on the existence of dynamic arbitrage and price manipulation strategies are often invoked to guide the modeling of price impacts of large trades. We revisit the concept of dynamic arbitrage in illiquid markets in the presence of time-varying stochastic price impact functions and a broad class of market price dynamics. We first establish a sufficient condition under which searching in the space of F0-measurable admissible round-trip trades is enough to attain a no-dynamic arbitrage characterization. This result both simplifies the identification of price impact structures that rule out dynamic arbitrage and supports analyses in some of the existing literature, where its assessment has been limited to searching in a set of F0-measurable round-trip trades. For time-varying stochastic linear price impact functions, we show that this condition is necessary and sufficient for the absence of dynamic arbitrage. The present quantitative analysis implies that a trader’s opinion concerning the existence of dynamic arbitrage opportunities for a price impact model depends on their belief about expected future price changes and expected future price impacts, which can be revised over time due to the collection of new information. This motivates us to let the existence of such arbitrage opportunities depend not only on the trader’s belief about expected price movements but also on their risk attitude. We thus introduce the concept of risk-averse dynamic arbitrage using a general time-consistent dynamic risk measure and a risk-aversion threshold level. Similar sufficient conditions are studied under which searching in the space of static round-trip trades enables us to conclude on no-risk-averse dynamic arbitrage.
## 1 Introduction
Illiquid financial markets are characterized by the material cost of security execution within a short time frame and its effects on asset prices and returns (see, for example, Amihud and Mendelson 2010; Amihud et al 2013; Foucault et al 2013). Limited liquidity is characterized by the correlation between an incoming order and the subsequent price change, referred to as price impact. Since this is an indirect cost, price impact is often difficult to measure and model (Almgren 2010; Moazeni et al 2010, 2013). Arguments about market efficiency, and the consequent absence of trading strategies that enable the manipulation of assets prices in a financially beneficial way, can then be invoked to guide modeling price impact; for a broad discussion on price manipulation, see, for example, Kyle and Viswanathan (2008).
Various concepts of arbitrage have been studied to address the existence of price manipulation trading strategies and, consequently, price impact model specifications. Huberman and Stanzl (2004) build on the concept of a $\delta$-arbitrage opportunity, proposed by Ledoit (1995) as a portfolio with a Sharpe measure strictly greater than $\delta$. Here, the value of $\delta$ is determined a priori by the economist.11Bernardo and Ledoit (2000) generalized the concept of $\delta$-arbitrage using a gain–loss ratio and referred to an investment opportunity with the infinite gain–loss ratio as an arbitrage. For normally distributed returns, their gain–loss ratio constraint is equivalent to a Sharpe ratio restriction. Huberman and Stanzl (2004) refer to a finite sequence of admissible trades, starting with a zero initial holding and ending at a zero position, as a round-trip trade. They extend the notion of $\delta$-arbitrage to the stronger concept of quasi-arbitrage, defined as a sequence of round-trip trades that produces infinite expected execution payoffs with an infinite Sharpe ratio. A quasi-arbitrage is a $\delta$-arbitrage. Employing this arbitrage definition, Huberman and Stanzl (2004) show that only permanent price impact functions, linear in amount traded, can rule out the availability of quasi-arbitrage. Gatheral (2010) studies (bounded) price manipulation trading strategies as a sequence of round-trip trades with a strictly negative expected execution cost or, equivalently, a strictly positive expected execution payoff. He refers to the existence of a price manipulation trading strategy as dynamic arbitrage and argues that permanent price impact must be linear in volume traded in order to rule out dynamic arbitrage.22We note that this definition is not fully consistent with the common concept of dynamic arbitrage, defined as an arbitrage opportunity that involves trading instruments in the future, contingent on market states (Allingham 1991; Wilmott 1998; Kondor 2009). Fruth et al (2014) investigate the occurrence of dynamic arbitrage for a limit order book model with linear price impact functions under different parameter assumptions. Gueant (2014) shows that a specific class of nonlinear price impact functions does not admit dynamic arbitrage. A limit order book model with a nonlinear price impact function that excludes the availability of dynamic arbitrage is studied in Alfonsi and Schied (2010). All of these concepts belong to the class of pseudo-arbitrage (as opposed to pure arbitrage) in the sense that they can be profitable but are not risk-free (Damodaran 2012).
Establishing the absence of an arbitrage opportunity involves solving a multistage stochastic optimization problem. Given the uncertainty in future security prices and the time requirement for implementing round-trip trades, the optimization should be over the set of admissible trading strategies that are contingent on market states. More precisely, the search is over the set of trading strategies that are $\smash{\mathcal{F}_{t}}$-measurable, where $\smash{\mathcal{F}_{t}}$ is the sigma algebra generated by stochastic processes in the model. For example, to verify the existence of dynamic arbitrage studied in Gatheral (2010), one needs to maximize the expected execution payoff over the set of round-trip policies. Restricting our search to the smaller set of $\smash{\mathcal{F}_{0}}$-measurable round-trip trades may yield misleading conclusions about the absence of dynamic arbitrage, since maximizing the expected execution payoff over the set of $\smash{\mathcal{F}_{0}}$-measurable trading strategies may result in a negative optimal objective value. However, there may exist some $\smash{\mathcal{F}_{t}}$-measurable round-trip trade with a positive expected execution payoff. Still, some of the existing literature, such as Gueant (2014), explicitly searches in the set of $\smash{\mathcal{F}_{0}}$-measurable trades (static strategies) to prove the absence of dynamic arbitrage. This motivated us to explore the impact of the market adaptability assumption of the price manipulation strategies on a trader’s belief regarding the absence of dynamic arbitrage under different risk attitudes.
In this paper, we consider two general classes of market price dynamics that can exhibit a broad range of stochastic market price processes. Following the discussion in Fruth et al (2014) that liquidity is not time independent, we let price impacts be time varying and stochastic. For this general setting, we first establish a sufficient condition under which searching in the space of $\smash{\mathcal{F}_{0}}$-measurable admissible round-trip trades is enough to obtain a no-dynamic arbitrage characterization. More precisely, this sufficient condition involves the knowledge that, at the initial time, the expected market price change conditioned on the information set at any time $t$ is zero. Here, no assumption on the linearity or nonlinearity of the permanent or temporary price impact functions is made.
This result simplifies the effort of verifying dynamic arbitrage and consequently characterizing the structure of price impact functions. We then show that for linear time-varying stochastic price impact functions this condition is both necessary and sufficient for no-dynamic arbitrage. This statement is valid for the two general classes of market price dynamics, which accommodate a broad variety of stochastic price processes. Our analysis implies that a trader’s opinion on the existence of dynamic arbitrage opportunities for a price impact model depends on their belief regarding expected future price changes and expected future price impacts, which can be updated over time as new observations are collected and more accurate estimations of conditional expectations are attained. In fact, these estimations can be different from those computed at the beginning of the trading time horizon. This motivated us to let the existence of such arbitrage opportunities depend on not only the investor’s belief concerning expected price movements but also the trader’s risk attitude.
We extend the concept of dynamic arbitrage of Gatheral (2010) to risk-averse dynamic arbitrage in a dynamic setting using time-consistent dynamic risk measures (Detlefsen and Scandolo 2005; Ben-Tal and Teboulle 2007; Föllmer and Weber 2015). A dynamic risk measure is a sequence of conditional risk measures $\smash{\{\rho_{t,T}\}_{t=1}^{T}}$, each of which takes into account the information available at the time of risk assessment and adapts to the underlying filtration (Ruszczyński and Shapiro 2006a, 2006b; Ruszczyński 2010; Acciaio and Penner 2011). For more details on dynamic risk measures, the reader is referred to Cvitanić and Karatzas (1999), Ogryczak and Ruszczyński (1999, 2001), Riedel (2004), Boda and Filar (2006), Cheridito et al (2006), Frittelli and Scandolo (2006), Ruszczyński and Shapiro (2006a, 2006b), Klöppel and Schweizer (2007), Bion-Nadal (2008), Ruszczyński (2010) and Acciaio and Penner (2011). The essence of time consistency is to guarantee that a trading policy preferred from a future perspective is also preferred from the trader’s current point in time, and that, consequently, decisions are not contradictory over time. This property is crucial to the development of a dynamic theory of risk-aversion and to obtain recursive evaluations avoiding backtracking; see Defourny et al (2008) and Rudloff et al (2014) for examples of pathological cases leading into backtracking that risk-averse dynamic systems face in the absence of time consistency. Time consistency enables us to use the dynamic programming principle to find trading strategies with certain risk levels (Boda and Filar 2006; Shapiro 2009; Ruszczyński 2010; Rudloff et al 2014). Examples of consistent dynamic measures of risk include those obtained from recursive evaluations of conditional value-at-risk (CVaR) or recursive evaluations of conditional mean upper semideviation of order $r$ (2014, Chapter 6).
Given a time-consistent dynamic convex risk measure $\smash{\{\rho_{t,T}\}_{t=1}^{T}}$ and a threshold level $\delta$, we define a risk-averse dynamic arbitrage as a round-trip trading policy $\pi$ such that $\smash{\rho_{1,T}(C^{\pi}_{1},\dots,C^{\pi}_{T})<\delta}$. Here, $\smash{C^{\pi}_{t}}$ refers to the execution cost of trading $\smash{n^{\pi}}$ shares over $(t-1,t]$ indicated by the policy $\pi$. The pseudo-arbitrage concept of risk-averse dynamic arbitrage is an extension of the (risk-neutral) dynamic arbitrage of Gatheral (2010), in which $\rho(\cdot)=\bm{E}[\cdot]$ and $\delta=0$. In addition, as will be discussed in Section 4, $\delta$-arbitrage with the gain semi-standard deviation ratio can be cast as risk-averse dynamic arbitrage. The dynamic programming optimality equation can be employed to solve the optimization problem involved in the search for risk-averse dynamic arbitrage opportunities. We establish sufficient conditions under which searching in the set of static round-trip trades can prove the absence of risk-averse dynamic arbitrage.
In summary, this paper contributes to the existing literature on price impact modeling and arbitrage by highlighting the importance of searching in the space of nonanticipatory round-trip trades and traders’ beliefs regarding future conditional expectations as well as introducing the concept of risk-averse dynamic arbitrage.
This paper is organized as follows. Models for price impact and price dynamics are presented in Section 2. The optimization involved in the assessment of risk-neutral dynamic arbitrage is discussed in Section 3. Section 4 introduces the concept of risk-averse dynamic arbitrage, where a sufficient condition for no-risk-averse dynamic arbitrage certification based on static optimization is also established. Conclusions and directions for future research are summarized in Section 5.
## 2 Market price and price impacts
In a financial market with imperfect liquidity, trading affects asset prices. The relationship between price changes and incoming orders is referred to as price impact, which can be used as an illiquidity measure (Amihud et al 2013). There are short-term effects of inventory on prices, called temporary or transitory price impacts, which only affect the revenue of the trader who initiated the trade. In addition, there are permanent effects on market prices and expected return flows, referred to as permanent price impacts. Both of these impacts are often functions of the volume of assets traded.
Let the $m$-vector $\smash{P_{t}}$ denote the unit market price of a portfolio of $m$ assets at time $t$. The deterministic initial market price is denoted by $\smash{P_{0}}$. We let the price update function be
$P_{t}=\mathcal{D}_{t}(P_{t-1})-\tilde{g}_{t}(n_{t}),$ (2.1)
where $\smash{P_{t-1}}$ refers to the (nonnegative) market price before placing the order at time $t$, and $\smash{\mathcal{D}_{t}(P_{t-1})}$ denotes the market price at time $t$ if the trader had not placed the order $\smash{n_{t}}$. Here, $\smash{n_{t}}$ is the amount traded at time $t$, and the function $\smash{\tilde{g}_{t}(\cdot)}$ captures the permanent price impact of the trader’s order. A positive $\smash{n_{t,i}}$ denotes selling the $i$th asset, and a negative $\smash{n_{t,i}}$ implies that the $i$th asset is bought over $(t-1,t]$. In addition to the effect on the market price, the decision maker’s trade induces a temporary price impact (slippage) on the execution price. The $m$-vector execution price $\smash{\tilde{P}_{t}}$ per share is given by
$\tilde{P}_{t}=P_{t-1}-\tilde{h}_{t}(n_{t}),$ (2.2)
where $\tilde{h}_{t}(\cdot)$ is the uncertain temporary price impact. We note that the price impact functions (particularly temporary price impact) can be functions of the trading rate, instead of the volume traded, in which case the correction denominators are captured by $\smash{\tilde{g}_{t}}$ and $\smash{\tilde{h}_{t}}$. Both $\smash{\tilde{g}_{t}(n_{t})}$ and $\smash{\tilde{h}_{t}(n_{t})}$ have the same sign as $\smash{n_{t}}$. It is common in the literature to let the price impact functions be deterministic and constant over time, ie, $\smash{\tilde{g}_{t}(n_{t})=g(n_{t})}$ and $\smash{\tilde{h}_{t}(n_{t})=h(n_{t})}$ for some deterministic functions $g$ and $h$. Fruth et al (2014) argue that liquidity has seasonal patterns and allows for time-dependent deterministic price impacts. Following Fruth et al (2014), and for the generality of our discussion in this paper, we let the price impact functions be time varying and stochastic.
Examples of the functional $\smash{\mathcal{D}_{t}(P_{t-1})}$ in (2.1) include the following additive and multiplicative models:
$\displaystyle\mathcal{D}_{t}(P_{t-1})$ $\displaystyle=\tilde{\mathcal{L}}_{t}+P_{t-1},$ (2.3) $\displaystyle\mathcal{D}_{t}(P_{t-1})$ $\displaystyle=(I_{m}+\operatorname{Diag}(\tilde{\mathcal{L}}_{t}))P_{t-1},$ (2.4)
where the $m$-vector $\smash{\tilde{\mathcal{L}}_{t}}$ is independent of the price $\smash{P_{t-1}}$ and represents a wide range of stochastic processes, such as diffusion, jump diffusion, Hawkes processes, etc, for the market price evolution. In (2.4), $\smash{\operatorname{Diag}(\tilde{\mathcal{L}}_{t})}$ is a diagonal matrix with $\smash{\tilde{\mathcal{L}}_{t}}$ as its diagonal, while $\smash{I_{m}}$ denotes the $m\times m$ identity matrix.
Price models (2.1) and (2.2) with price dynamics (2.3) or (2.4) provide us with a rich setting to exhibit a variety of models frequently used in the literature on portfolio liquidation and price impact modeling (see, for example, Almgren and Chriss 2000; Huberman and Stanzl 2004; Almgren et al 2005; Huberman and Stanzl 2005; Moazeni et al 2010, 2013, 2016; Foucault et al 2013; Amihud et al 2013; Gueant 2014). For instance, Bertsimas and Lo (1998), Almgren and Chriss (2000) and Almgren et al (2005) consider the additive model (2.3) with
$\tilde{\mathcal{L}}_{t}:=\varSigma\tilde{Z}_{t},$ (2.5)
where the components of the $l$-vector $\smash{\tilde{Z}_{t}}$ are independent standard normals and $\varSigma$ is an $m\times l$ volatility matrix of the asset returns. Hence, $\mathcal{D}_{t}(P_{t-1})=P_{t-1}+\varSigma Z_{t}$. Moazeni et al (2013) study both (2.3) and (2.4) with a jump-diffusion model as described below:
$\tilde{\mathcal{L}}_{t}:=\alpha+\tilde{J}_{t}+\varSigma\tilde{Z}_{t},$ (2.6)
where the jump term $\smash{\tilde{J}_{t}}$ is a summation of two compound Poisson processes capturing the price impacts of other concurrent buy-or-sell large trades. Here, the time-independent deterministic $\alpha$ can be interpreted as the expected price change due to small trades. Gatheral (2010) considers model (2.3), where $\smash{\mathcal{L}_{t}}$ follows an arithmetic random walk whose drift is the decayed accumulation of price impacts of previous trades. One may apply the multiplicative model (2.4), where $\smash{\tilde{\mathcal{L}}_{t}}$ is defined by the market beta $\beta$ and Jensen’s alpha $\alpha$ (Jensen 1968) of the $m$-assets, as can be seen below:
$\tilde{\mathcal{L}}_{t}:=\alpha_{t}+r^{\mathrm{f}}_{t}\bm{1}_{m}+\beta_{t}(% \tilde{r}_{t}^{\mathrm{M}}-r^{\mathrm{f}}_{t})+\varSigma_{t}\tilde{Z}_{t},$ (2.7)
where $\beta_{t}=(\beta_{t,1},\dots,\beta_{t,m})^{\mathrm{T}}$ and $\alpha_{t}=(\alpha_{t,1},\dots,\alpha_{t,m})^{\mathrm{T}}$. It is expected that $\alpha_{t}$ is $0$ (see Fama and French 2004). Here, $\smash{r^{\mathrm{f}}_{t}}$ indicates the (deterministic) risk-free interest rate, $\smash{\tilde{r}_{t}^{\mathrm{M}}}$ is the market return and $\smash{\bm{1}_{m}}$ denotes the $m$-vector of all ones.
To verify the absence of dynamic arbitrage using a set of $T$ discrete trades over $[0,T]$, and assuming the market price dynamics (2.1) started at the initial price $\smash{P_{0}}$ under execution price model (2.2), one faces solving the following multistage stochastic dynamic optimization problem to maximize the total amount received at the end of $T$ trades over the set of all admissible round-trip trades:
$V(P_{0}):=\max_{\substack{n_{1},\dots,n_{T}\in\mathcal{A},\\ n_{t}\mathrm{~{}is~{}}\mathcal{F}_{t-1}\text{-measurable}}}\bm{E}\bigg(\sum_{t% =1}^{T}n_{t}^{\mathrm{T}}\tilde{P}_{t}\bigg)$ (2.8)
such that $\smash{\sum_{t=1}^{T}n_{t}=0}$. Here, $\smash{\mathcal{A}\subseteq\mathbb{R}^{m}}$ is the set of admissible round-trip trades, and the information at time $t$ is given by the sigma-algebra $\mathcal{F}_{t-1}=\{P_{t-1},x_{t-1}\}$, where $x_{t-1}$ is the portfolio position before time $t$.
Given price impact models $\smash{\tilde{g}_{t}}$ and $\smash{\tilde{h}_{t}}$, a nonpositive value $\smash{V(P_{0})\leq 0}$ provides us with a certificate for the absence of dynamic arbitrage, ie, there exists no price manipulation strategy with a strictly positive expected execution payoff. In contrast, $\smash{V(P_{0})>0}$ ensures the presence of dynamic arbitrage.
Depending on the number of assets in the portfolio, the modeling assumptions on the price impact functions, and the underlying market and execution prices, solving problem (2.8) can be a challenging task due to the curse of dimensionality (see, for example, Bertsekas and Tsitsiklis 1996; Powell 2011). Alternatively, one may choose to make an approximation by restricting the search for the price manipulation strategies to a smaller set of admissible round-trip strategies – such as only $\mathcal{F}_{0}$-measurable trades – and solving the following, computationally cheaper, optimization problem:
$\hat{V}(P_{0}):=\max_{\substack{n_{1},\dots,n_{T}\in\mathcal{A},\\ n_{t}\mathrm{~{}is~{}}\mathcal{F}_{0}\text{-measurable}}}\bm{E}\bigg(\sum_{t=1% }^{T}n_{t}^{\mathrm{T}}\tilde{P}_{t}\bigg)$ (2.9)
such that $\smash{\sum_{t=1}^{T}n_{t}=0}$. This is a one-stage numerical optimization problem that can be solved using mathematical programming techniques (see, for example, Nocedal and Wright 2006).
In general, $\smash{\hat{V}(P_{0})\leq V(P_{0})}$. Therefore, while $\smash{\hat{V}(P_{0})>0}$ implies that a dynamic arbitrage opportunity exists, $\smash{\hat{V}(P_{0})\leq 0}$ cannot certify the absence of dynamic arbitrage possibilities. Therefore, limiting the search to the set of $\smash{\mathcal{F}_{0}}$-measurable round-trip trades may mislead us about identifying price impact structures that rule out dynamic arbitrage. Gueant (2014) solves (2.9) and concludes that a class of nonlinear permanent price impact functions can also exclude dynamic arbitrage. In the next section, we shed some light on the validity of this choice, discussing the difference between the solution sets of these two problems and their suitability in proving no-dynamic arbitrage.
## 3 Absence of (risk-neutral) dynamic arbitrage
We first present a sufficient condition under which searching in the set of $\smash{\mathcal{F}_{0}}$-measurable round-trip trades can ensure the absence or presence of dynamic arbitrage. This result is valid for general time-dependent stochastic price impact functions and market price dynamics.
###### Proposition 3.1.
Let the market price dynamics and the execution price model be given by (2.1) and (2.2), respectively. Assume that the price impact functions $\smash{\tilde{g}_{t}(\cdot)}$ and $\smash{\tilde{h}_{t}(\cdot)}$ satisfy
$\displaystyle\bm{E}[\tilde{h}_{t}(n_{t})\mid\mathcal{F}_{t-1}]=\bm{E}[\tilde{h% }_{t}(n_{t})\mid x_{t-1}],$ $\displaystyle\bm{E}[\tilde{g}_{t}(n_{t})\mid\mathcal{F}_{t-1}]=\bm{E}[\tilde{g% }_{t}(n_{t})\mid x_{t-1}].$ (3.1)
Let
$\bm{E}[\mathcal{D}_{t}(P_{t-1})\mid P_{t-1}]=P_{t-1}.$ (3.2)
Then, $\smash{\hat{V}(P_{0})=V(P_{0})}$, ie, the absence of an $\smash{\mathcal{F}_{0}}$-measurable round-trip trade with positive expected execution cost provides us with a certificate for the absence of dynamic arbitrage.
A proof of Proposition 3.1 is given in Appendix B (available online).33Proposition 3.1 can be seen as an extension of Moazeni et al (2013), Theorem 3.1 to general time-dependent stochastic price impact functions. In Theorem 3.1, the price impact functions are assumed to be deterministic, time-independent linear functions of the volume traded.
For both market price dynamics (2.3) and (2.4), (3.2) is reduced to $\bm{E}_{t}[\tilde{\mathcal{L}}_{t}]=0$. Therefore, using the tower property of expectation and the equalities
$\sum_{t=l}^{T}n_{t}=x_{l-1}\quad\text{and}\quad\sum_{t=1}^{T}n_{t}=x_{0}=0,$
the numerical optimization problem (2.9) is given by
$\displaystyle\hat{V}(P_{0})$ $\displaystyle=\max_{\substack{n_{1},\dots,n_{T}\in\mathcal{A},\\ n_{t}\mathrm{~{}is~{}}\mathcal{F}_{0}\text{-measurable}}}\bigg({-}\sum_{t=1}^{% T-1}x_{t}^{\mathrm{T}}\bm{E}[\tilde{g}_{t}(n_{t})]-\sum_{t=1}^{T}n_{t}^{% \mathrm{T}}\bm{E}[\tilde{h}_{t}(n_{t})]\bigg)$ $\displaystyle=-\min_{\substack{n_{1},\dots,n_{T}\in\mathcal{A},\\ n_{t}\mathrm{~{}is~{}}\mathcal{F}_{0}\text{-measurable}}}\sum_{t=1}^{T}\{x_{t}% ^{\mathrm{T}}(\bm{E}[\tilde{g}_{t}(x_{t-1}-x_{t})-\tilde{h}_{t}(x_{t-1}-x_{t})])$ $\displaystyle {}+x_{t-1}^{\mathrm{T}}\bm{E}[\tilde{h}_{t}(x_% {t-1}-x_{t})]\}.$
When the round-trip trade $\smash{\{n_{t}=0\}_{t=1}^{T}}$ is an admissible strategy for (2.9), $\smash{\hat{V}(P_{0})\geq 0}$. Therefore, under the assumptions in Proposition 3.1, price impact functions $\tilde{g}_{t}$ and $\tilde{h}_{t}$ imply no-dynamic arbitrage ($\smash{V(P_{0})\leq 0}$) if and only if
$\min_{\substack{x_{0},x_{1},\dots,x_{T}\in\mathcal{A}_{x},\\ x_{0}=0,x_{T}=0}}\sum_{t=1}^{T}\{x_{t}^{\mathrm{T}}k_{t}(x_{t-1}-x_{t})+x_{t-1% }^{\mathrm{T}}h_{t}(x_{t-1}-x_{t})\}=0,$ (3.3)
where $k_{t}(x):=\bm{E}[\tilde{g}_{t}(x)-\tilde{h}_{t}(x)]$, $h_{t}(x):=\bm{E}[\tilde{h}_{t}(x)]$ and $\smash{\mathcal{A}_{x}\subseteq\mathbb{R}^{m}}$ is a feasible set for positions $\smash{x_{t}}$, corresponding to the admissibility set $\mathcal{A}$ for amounts traded $\smash{n_{t}}$.
###### Example 3.2.
Consider a simple case in which $T=2$. Therefore, for any trading strategy $\{n_{t}\in\mathcal{A}\}_{t=1,2}$ where $n_{1}+n_{2}=0$, we have
$\displaystyle\bm{E}[n_{1}^{\mathrm{T}}\tilde{P}_{1}+n_{2}^{\mathrm{T}}\tilde{P% }_{2}\mid P_{0}]$ $\displaystyle=\bm{E}[n_{1}^{\mathrm{T}}P_{0}-n_{1}^{\mathrm{T}}\tilde{h}_{1}(n% _{1})+n_{2}^{\mathrm{T}}\mathcal{D}_{1}(P_{0})-n_{2}^{\mathrm{T}}\tilde{g}_{1}% (n_{1})-n_{2}^{\mathrm{T}}\tilde{h}_{2}(n_{2})\mid P_{0}]$ $\displaystyle=n_{1}^{\mathrm{T}}(P_{0}-\bm{E}[\mathcal{D}_{1}(P_{0})\mid P_{0}% ])+n_{1}^{\mathrm{T}}\bm{E}[-\tilde{h}_{1}(n_{1})+\tilde{h}_{2}(-n_{1})+\tilde% {g}_{1}(n_{1})\mid P_{0}].$
Hence, when $\bm{E}[\mathcal{D}_{1}(P_{0})\mid P_{0}]=P_{0}$, a dynamic arbitrage opportunity exists if and only if the second term is positive for some $n_{1}$, ie, the total temporary price impact cost is expected to be recovered through the impact on the market price. This can hold even for nonlinear price impact functions.
The nonlinear price impact function in Gueant (2014),
$\tilde{g}_{t}(n_{t})=f(|x_{t}|)n_{t}=f(|x_{t-1}-n_{t}|)n_{t},$ (3.4)
for some deterministic function $f$, satisfies (3.1). In addition, Gueant (2014) models the market price dynamics by an arithmetic Brownian motion with zero drift, which satisfies (3.2). Hence, Proposition 3.1 implies that for the setting in Gueant (2014) it is sufficient to search in the set of $\smash{\mathcal{F}_{0}}$-measurable round-trip trades to verify the existence of dynamic arbitrage.
Linear price impact functions have been frequently used in the literature (see, for example, Bertsimas and Lo 1998; Almgren and Chriss 2000; Alfonsi and Schied 2010; Obizhaeva and Wang 2013). Given time-varying stochastic matrixes $\smash{\tilde{G}_{t}}$ and $\smash{\tilde{H}_{t}}$, whose distributions do not depend on the market price $\smash{P_{t-1}}$, the linear price impact functions
$\tilde{h}_{t}(n_{t})=\tilde{H}_{t}n_{t}\quad\text{and}\quad\tilde{g}_{t}(n_{t}% )=\tilde{G}_{t}n_{t}$ (3.5)
also satisfy (3.1). Therefore, according to Proposition 3.1, (3.2) implies that searching in the set of $\smash{\mathcal{F}_{0}}$-measurable round-trip trades is enough to certify no-dynamic arbitrage. In fact, for such linear price impact functions, (3.2) yields a stronger result: for linear price impact model (3.5), (3.2) implies the absence of dynamic arbitrage. This is more formally summarized in the following corollary.
###### Corollary 3.3.
Let assumptions (3.1) and (3.2) in Proposition 3.1 hold. In addition, assume that the price impact functions are linear as in (3.5) and the objective function of (2.9) is concave. Then, no dynamic arbitrage opportunities exist.
This result can be derived via Proposition 3.1, based on which it is sufficient to search in the set of $\smash{\mathcal{F}_{0}}$-measurable round-trip trades and to directly solve the numerical optimization problem (2.9) or the minimization (3.3). For linear price impact functions and when $\smash{\mathcal{A}=\mathbb{R}^{m}}$, (3.3) is reduced to an unconstrained quadratic programming problem (see Moazeni et al 2010) with an optimal value that equals zero, ie, $\smash{V(P_{0})=0}$. This consequently guarantees the absence of dynamic arbitrage. We leave it for future research to apply the problem formulation (3.3) and the result for linear price impact functions to prove no-dynamic arbitrage for nonlinear price impact functions that can be bounded by linear or piecewise linear functions.
Alternatively, Corollary 3.3 can be proved directly as in part (b) of Propositions A.1 and A.2 in Appendix A (available online). Part (a) of Propositions A.1 and A.2 shows that the best expected execution payoff of a round-trip trade equals $\smash{V(P_{0})=E_{1}}$ for the market price dynamics model (2.3) and is given by $\smash{V(P_{0})=P_{0}^{\mathrm{T}}A_{1}P_{0}}$ for the multiplicative model (2.4), where the matrixes $E_{1}$ and $A_{1}$ are defined in Appendix A. Part (b) of Propositions A.1 and A.2 shows that, when (3.2) holds, $E_{1}\leq 0$ and $A_{1}\preceq 0$, and consequently $V(P_{0})\leq 0$, ie, there is no dynamic round-trip trade with a strictly positive expected execution payoff. This result is general and does not rely on any assumption regarding the stochastic model of $\smash{\tilde{\mathcal{L}}_{t}}$; hence, it is applicable to a broad range of market price model specifications.
Next, we show that for linear price impact functions, (3.2) not only suffices to ensure no-dynamic arbitrage but is also necessary. This is formally stated in the following proposition.
###### Proposition 3.4.
Assume $T\geq 2$ and $\bm{E}[\mathcal{D}_{t}(P_{t-1})\mid P_{t-1}]\not=P_{t-1}$ for some $t$ in $\{1,\dots,T-1\}$ (or equivalently $\bm{E}[\tilde{\mathcal{L}}_{t}\mid\mathcal{F}_{t-1}]\not=0$ for some $t$). Consider the linear price impact model (3.5) and let the market price dynamics be
1. (i)
as in ( 2.3 ), while the matrixes $\{Q_{t}\}_{t=2}^{T}$ – defined in (A.15) in the appendix – are positive definite, or
2. (ii)
as in ( 2.4 ), while the matrixes $\{Q_{t}\}_{t=2}^{T}$ – defined in (A.1) in the appendix – are positive definite, and
$\bm{1}_{m}\bm{1}_{m}^{\mathrm{T}}+\mathrm{cov}[\tilde{\mathcal{L}}_{t}\mid% \mathcal{F}_{t-1}]\succ 0.$ (3.6)
Then, dynamic arbitrage exists, ie, there exists an $\smash{\mathcal{F}_{t}}$-measurable round-trip trade with a strictly positive expected execution payoff.
A proof of Proposition 3.4 is given in Appendix C (available online). Hence, for the linear price impact model (3.5), there is no-dynamic arbitrage if and only if (3.2) holds. Note that the statement in Proposition 3.4 does not rely on a specific assumption on the market price dynamics; hence, it is applicable to a broad range of stochastic models for $\tilde{\mathcal{L}}_{t}$.
From Proposition 3.4, $\bm{E}_{t}[\tilde{\mathcal{L}}_{t}]\neq 0$ at some time period implies the existence of a $\smash{\mathcal{F}_{t}}$-measurable round-trip trade. When $\smash{\bm{E}_{0}[\tilde{\mathcal{L}}_{t}]\neq 0}$, a static round-trip trade with a strictly positive expected benefit also exists. This can be formally investigated by limiting the trading activity to only three time steps. In this case, the maximization problem (2.9) is reduced to the following quadratic optimization problem on the $2m$-vectors $n:=(n_{1},n_{2})$,
$\qquad\max_{(n_{1},n_{2})\in\mathbb{R}^{2m}}\tfrac{1}{2}n^{\mathrm{T}}\begin{% pmatrix}a+a^{\mathrm{T}}-(\varTheta+\varTheta^{\mathrm{T}})&-\varTheta+a^{% \mathrm{T}}\\ -\varTheta^{\mathrm{T}}+a&-(\varTheta+\varTheta^{\mathrm{T}})\end{pmatrix}n-% \begin{pmatrix}(\bm{E}_{0}[\tilde{\mathcal{L}_{2}}+\tilde{\mathcal{L}_{1}}]+% \bm{E}_{0}[\tilde{\mathcal{L}_{1}}]\bm{E}_{0}[\tilde{\mathcal{L}_{2}}]).*P_{0}% \\ (\bm{E}_{0}[I_{m}+\tilde{\mathcal{L}_{1}}]\bm{E}_{0}[\tilde{\mathcal{L}_{2}}])% .*P_{0}\end{pmatrix}^{\!\mathrm{T}}n,\qquad$
where $\varTheta\overset{\mathrm{def}}{=}H+H^{\mathrm{T}}-G$, $a:=\operatorname{Diag}(\bm{E}_{0}[\tilde{\mathcal{L}_{2}}])G$ and $A.*B$ denotes the component-wise (Hadamard) product of the matrixes $A$ and $B$. If the Hessian of this quadratic function is negative definite or is not negative semidefinite, a nonzero value of $\bm{E}_{0}[\tilde{\mathcal{L}}_{1}]\bm{E}_{0}[\tilde{\mathcal{L}}_{2}]$ implies that an $\smash{\mathcal{F}_{0}}$-measurable round-trip trade with a strictly positive expected execution payoff exists. In the former case, the $\smash{\mathcal{F}_{0}}$-measurable price manipulation strategy uniquely exists, while in the latter case there are infinitely many $\smash{\mathcal{F}_{0}}$-measurable price manipulation strategies. A round-trip trade over three time steps with a strictly positive expected execution payoff implies a dynamic arbitrage opportunity for longer trading time horizons.
When the initial estimations of the expected price changes equal zero, ie, $\bm{E}[\tilde{\mathcal{L}}_{t}\mid\mathcal{F}_{0}]=0$ for all $t$, but after collecting more observations the trader estimates that $\bm{E}[\tilde{\mathcal{L}}_{t}\mid\mathcal{F}_{t-1}]\neq 0$, searching in the set of static round-trip trades will erroneously evince the absence of dynamic arbitrage, ie, the best expected execution payoff of static round-trip trades equals zero, while a dynamic round-trip trade with a strictly positive expected benefit does actually exist.
In summary, the existence of dynamic arbitrage is directly related to the trader’s estimation of the expected future price changes conditioned on the price or return distribution at time $t$. In addition, by collecting more observations, the trader’s belief regarding the expected value of $\smash{\tilde{\mathcal{L}}_{t}}$ will change over time, perhaps becoming more accurate. Therefore, in order to certify that a price impact model does not permit dynamic arbitrage opportunities, one should search in the set of $\smash{\mathcal{F}_{t}}$-measurable round-trip trades and take into account updated estimations of conditional expectation of $\smash{\tilde{\mathcal{L}}_{t}}$ over time. Limiting the search to the set of $\smash{\mathcal{F}_{0}}$-measurable round-trip trades computed at time zero can mislead us to conclude the absence of dynamic arbitrage, when bounded dynamic price manipulation strategies do, in fact, exist.
Since a trader’s opinion on the existence of a dynamic arbitrage opportunity using round-trip trades depends on the trader’s belief about the expected future price changes, it seems natural to let the existence of such arbitrage opportunities depend on the trader’s risk attitude. This is the topic of Section 4, where we extend the concept of dynamic arbitrage in the presence of price impacts to the pseudo-arbitrage concept of risk-averse dynamic arbitrage given a dynamic risk measure.
## 4 Risk-averse dynamic arbitrage
We start by presenting the definition of dynamic risk measures and introducing our concept of risk-averse dynamic arbitrage in illiquid markets. In our presentation, we focus on execution costs or losses of trading strategies.
Let $(\varOmega,\mathcal{F},\mathcal{P})$ be our probability space with the filtration $\mathcal{F}_{0}\subset\cdots\subset\mathcal{F}_{T}\subset\mathcal{F}$, defined by the market price process, where $\smash{\mathcal{F}_{0}=\{\varOmega,\emptyset\}}$. Define the spaces of execution costs $\mathbb{Z}_{t}=\mathcal{L}_{p}(\varOmega,\mathcal{F}_{t},\mathcal{P})$, $p\in[1,+\infty)$, $t=0,\dots,T$, where the space $\smash{\mathbb{Z}_{0}}$ is associated with $\mathbb{R}$, and let $\smash{\mathbb{Z}_{t,T}=\mathbb{Z}_{t}\times\cdots\times\mathbb{Z}_{T}}$. Consider the adapted sequence of random variables $\smash{C_{t}\in\mathbb{Z}_{t-1}}$, $t=1,\dots,T$, where $\smash{C_{t}}$ is the stage-wise execution cost. The following definitions are from Ruszczyński (2010).
A conditional risk measure is a mapping $\rho_{t,T}\colon\mathbb{Z}_{t,T}\to\mathbb{Z}_{t}$, $1\leq t\leq T$, such that
$\rho_{t,T}(Z)\leq\rho_{t,T}(W)\quad\text{for all~{}}Z,W\in\mathbb{Z}_{t,T}% \mathrm{~{}such~{}that~{}}Z\leq W.$ (4.1)
One can define a broader family of conditional-risk measures by setting
$\rho_{\tau,\theta}(C_{\tau},\dots,C_{\theta})=\rho_{\tau,T}(C_{\tau},\dots,C_{% \theta},0,\dots,0),\quad 1\leq\tau\leq\theta\leq T.$
Similarly, the one-step conditional risk measures $\rho_{t}\colon\mathbb{Z}_{t+1}\to\mathbb{Z}_{t}$, $t=1,\dots,T-1$ are defined by
$\rho_{t}(C_{t+1}):=\rho_{t,t+1}(0,C_{t+1}).$
Let $\smash{\{\rho_{t,T}\}_{t=1}^{T-1}}$ be a time-consistent conditional risk measure satisfying the following conditions:
$\displaystyle\rho_{t,T}(C_{t},C_{t+1},\dots,C_{T})$ $\displaystyle=C_{t}+\rho_{t,T}(0,C_{t+1},\dots,C_{T}),$ (4.2) $\displaystyle\rho_{t,T}(0,\dots,0)$ $\displaystyle=0$ (4.3)
for all $\smash{C\in\mathbb{Z}_{t,T}}$ and all $t=1,\dots,T-1$.
A sequence of conditional risk measures $\smash{\{\rho_{t,T}\}_{t=1}^{T-1}}$ is called a dynamic risk measure. From now on, we only consider time-consistent dynamic risk measures, ie, a sequence of conditional risk measures satisfying properties (4.1)–(4.3). Since these dynamic risk measures are completely specified by the one-step conditional risk measures $\smash{\rho_{t}}$, $t=1,\dots,T-1$, we simplify notation by denoting them as $\smash{\{\rho_{t}\}_{t=1}^{T-1}}$. A dynamic risk measure $\smash{\{\rho_{t}\}_{t=1}^{T-1}}$ is convex (coherent) if its one-step conditional risk measures are convex (coherent) (see Ruszczyński 2010; Acciaio and Penner 2011). Recursive evaluations of CVaR or recursive evaluations of conditional mean upper semideviation of order $r$ (Shapiro et al 2014, Chapter 6), ie,
$\rho_{t}(C_{t+1}):=\bm{E}[C_{t+1}\mid\mathcal{F}_{t}]+\kappa(\bm{E}[(C_{t+1}-% \bm{E}[C_{t+1}\mid\mathcal{F}_{t}])_{+}^{r}\mid\mathcal{F}_{t}])^{1/r},$
where $r\in[1,\infty)$ is a fixed parameter and $(z)_{+}=\max\{z,0\}$, are examples of consistent dynamic measures of risk. In the rest of this section, we assume that the dynamic risk measure $\smash{\{\rho_{t}\}_{t=1}^{T-1}}$ is coherent.
Ruszczyński (2010) shows that the risk measure follows a recursive evaluation, namely
$\displaystyle\rho_{t,T}(C_{t},\dots,C_{T})$ $\displaystyle=C_{t}+\rho_{t}(C_{t+1}+\rho_{t+1}(C_{t+2}+\cdots+\rho_{T-2}(C_{T% -1}+\rho_{T-1}(C_{T}))\cdots)),$ (4.4)
where $\rho_{t}$, $t=t,\dots,T-1$ is a one-step conditional risk measure. Moreover, if the one-step conditional risk measures are coherent (see Artzner et al (1999) and Shapiro et al (2014), Chapter 6 for an in-depth treatment of the subject), then the recursive evaluation is given by
$\rho_{t,T}(C_{t},\dots,C_{T})=\rho_{t}(\rho_{t+1}(\cdots\rho_{T-2}(\rho_{T-1}(% C_{t}+C_{t+1}+\cdots+C_{T-1}+C_{T}))\cdots)).$ (4.5)
For a round-trip trading policy $\pi$, let $\smash{C^{\pi}_{t}}$ denote the execution cost of selling $\smash{n^{\pi}}$ shares over $(t-1,t]$. For a given coherent time-consistent dynamic risk measure $\smash{\{\rho_{t}\}_{t=1}^{T-1}}$, the evaluation of the risk of losses in the sequence of execution costs given by the round-trip trading policy $\pi$ is
$\displaystyle\mathcal{R}^{\pi}:$ $\displaystyle=\rho_{1,T}(C_{1}^{\pi},\dots,C_{T}^{\pi})$ $\displaystyle=C_{1}^{\pi}+\rho_{1}(C_{2}^{\pi}+\rho_{2}(C_{3}^{\pi}+\cdots+% \rho_{T-2}(C_{T-1}^{\pi}+\rho_{T-1}(C_{T}^{\pi}))\cdots))$ $\displaystyle=-(n^{\pi}_{1})^{\mathrm{T}}\tilde{P}^{\pi}_{1}$ $\displaystyle\qquad+\rho_{1}(-(n^{\pi}_{2})^{\mathrm{T}}\tilde{P}^{\pi}_{2}+% \rho_{2}(-(n^{\pi}_{3})^{\mathrm{T}}\tilde{P}^{\pi}_{3}+\cdots$ $\displaystyle +\rho_{T-2}(-(n^{\pi}_{T-1})^{\mathrm{T}}\tilde{P}^{\pi}_{T-% 1}+\rho_{T-1}(-(n^{\pi}_{T})^{\mathrm{T}}\tilde{P}^{\pi}_{T}))\cdots)).$
If $\{\rho_{t}\}_{t=1}^{T-1}$ is coherent, then (4.5) is reduced to
$\displaystyle\mathcal{R}^{\pi}$ $\displaystyle=\rho_{1}\bigg(\rho_{2}\bigg(\cdots\rho_{T-2}\bigg(\rho_{T-1}% \bigg(\sum_{t=1}^{T}C_{t}^{\pi}\bigg)\bigg)\cdots\bigg)\bigg)$ $\displaystyle=\tilde{\rho}\bigg({-}\sum_{t=1}^{T}(n^{\pi}_{t})^{\mathrm{T}}% \tilde{P}^{\pi}_{t}\bigg),$
where the composite risk measure is $\tilde{\rho}:=\rho_{1}\circ\cdots\circ\rho_{T-1}$.
We are now ready to define the concept of risk-averse dynamic arbitrage.
###### Definition 4.1.
Given a time-consistent dynamic risk measure $\smash{\{\rho_{t}\}_{t=1}^{T-1}}$ ($\smash{\{\rho_{t}\}_{t\in\mathcal{T}}}$) and threshold level $\delta$, the presence of a risk-averse dynamic arbitrage opportunity at threshold level $\delta$ refers to the existence of some round-trip trading policy $\pi$ such that $\smash{\mathcal{R}^{\pi}<\delta}$.
To verify such arbitrage opportunities, one can solve the following dynamic programming problem:
$V(P_{0}):=\min_{\substack{n_{1},\dots,n_{T}\in\mathcal{A},\\ n_{t}\mathrm{~{}is~{}}\mathcal{F}_{t}\text{-measurable}}}\tilde{\rho}\bigg({-}% \sum_{t=1}^{T}(n^{\pi}_{t})^{\mathrm{T}}\tilde{P}^{\pi}_{t}\bigg)$ (4.6)
such that $\smash{\sum_{t=1}^{T}n_{t}^{\pi}=0}$. Then, $\smash{V(P_{0})\geq\delta}$ implies no-risk-averse dynamic arbitrage.
When the search for round-trip trades is limited to the space of $\smash{\mathcal{F}_{0}}$-measurable trades, one solves
$\hat{V}(P_{0}):=\min_{\substack{n_{1},\dots,n_{T}\in\mathcal{A},\\ n_{t}\mathrm{~{}is~{}}\mathcal{F}_{0}\text{-measurable}}}\tilde{\rho}\bigg({-}% \sum_{t=1}^{T}(n^{\pi}_{t})^{\mathrm{T}}\tilde{P}^{\pi}_{t}\bigg)$ (4.7)
such that $\smash{\sum_{t=1}^{T}n_{t}^{\pi}=0}$. Problems (4.6) and (4.7) can be solved, for example, using the scenario decomposition method of Collado et al (2012).
Analogous to Proposition 3.1, below we provide a sufficient condition under which searching in the set of static round-trip trades is sufficient to conclude that risk-averse dynamic arbitrage does not exist.
We then proceed by establishing a sufficient condition under which searching in the set of $\smash{\mathcal{F}_{0}}$-measurable round-trip trades is enough to obtain a certification for no-risk-averse dynamic arbitrage. Similar to the (risk-neutral) dynamic arbitrage discussed in the previous section, this sufficient condition implies no-risk-averse dynamic arbitrage for linear price impact functions.
###### Proposition 4.2.
Let the price impact functions $\smash{\tilde{g}_{t}(\cdot)}$ and $\smash{\tilde{h}_{t}(\cdot)}$ satisfy the following conditions:
$\displaystyle\rho_{T-1}[x_{T-1}^{\mathrm{T}}\tilde{h}_{T}(n_{T})\mid\mathcal{F% }_{T-1}]=\rho_{T-1}[x_{T-1}^{\mathrm{T}}\tilde{h}_{T}(n_{T})\mid x_{T-1}],$ (4.8) \displaystyle\begin{aligned}&\displaystyle\rho_{t-1}[(n_{t}-x_{t-1})^{\mathrm{% T}}\mathcal{D}_{t}(P_{t-1})+n_{t}^{\mathrm{T}}\tilde{h}_{t}(n_{t})+(x_{t-1}-n_% {t})^{\mathrm{T}}\tilde{g}_{t}(n_{t})\mid\mathcal{F}_{t-1}]\\ &\displaystyle\qquad\qquad\qquad\qquad\qquad=n_{t}^{\mathrm{T}}P_{t-1}-x_{t-1}% ^{\mathrm{T}}P_{t-1}+\nu_{t-1}(x_{t-1},n_{t})\\ &\displaystyle\qquad\qquad\qquad\qquad\qquad\qquad+\rho_{t-1}[n_{t}^{\mathrm{T% }}\tilde{h}_{t}(n_{t})+(x_{t-1}-n_{t})^{\mathrm{T}}\tilde{g}_{t}(n_{t})\mid x_% {t-1}],\end{aligned} (4.9)
where $\smash{\nu_{t-1}(x_{t-1},n_{t})}$ is a time-varying function of $\smash{x_{t-1}}$ and $\smash{n_{t}}$, constant with respect to the realization of $\smash{P_{t-1}}$. Then, $\smash{\hat{V}(P_{0})=V(P_{0})}$ and the optimal round-trip policy of (4.6) is $\smash{\mathcal{F}_{0}}$-measurable.
The equality $\smash{\hat{V}(P_{0})=V(P_{0})}$ implies that the absence of an $\smash{\mathcal{F}_{0}}$-measurable round-trip trade with $\smash{\mathcal{R}^{\pi}<\delta}$ is sufficient to conclude no-risk-averse dynamic arbitrage. This statement is valid for both market price dynamics (2.3) and (2.4), and it does not rely on the linear assumption about price impact functions. A proof of Proposition 4.2 is given in Appendix B (available online).
When the time-dependent price impact functions $\smash{\tilde{h}_{t}(\cdot)}$ and $\tilde{g}_{t}(\cdot)$ are deterministic with respect to the information set $\mathcal{F}_{t-1}$ and do not depend on the market price, (4.9) is reduced to
$\rho_{t-1}[(n_{t}-x_{t-1})^{\mathrm{T}}\mathcal{D}_{t}(P_{t-1})\mid\mathcal{F}% _{t-1}]=(n_{t}-x_{t-1})^{\mathrm{T}}P_{t-1}+\nu_{t-1}(x_{t-1},n_{t}).$ (4.10)
This condition indicates that at time $t-1$, in the realized sequence of market prices and in the absence of orders, the difference between the risk of the next market price, $\smash{\rho_{t-1}[(n_{t}-x_{t-1})^{\mathrm{T}}\mathcal{D}_{t}(P_{t-1})]}$, and the present observed market price, $\smash{(n_{t}-x_{t-1})^{\mathrm{T}}P_{t-1}}$, is equal to a value that depends on time stamp $t$ but not to the realized market price level $\smash{P_{t-1}}$. This characteristic is akin to the martingale property, extended to dynamic risk measures.
In particular, for the additive model (2.3), under the assumption that the time-dependent price impact functions $\smash{\tilde{h}_{t}(\cdot)}$ and $\smash{\tilde{g}_{t}(\cdot)}$ are deterministic with respect to the information set $\smash{\mathcal{F}_{t-1}}$, (4.10) with
$\nu_{t-1}(x_{t-1},n_{t})=\rho_{t-1}[(n_{t}-x_{t-1})^{\mathrm{T}}\tilde{% \mathcal{L}}_{t}\mid\mathcal{F}_{t-1}]$
holds, ie,
$\displaystyle\rho_{t-1}[(n_{t}-x_{t-1})^{\mathrm{T}}(\tilde{\mathcal{L}}_{t}+P% _{t-1})\mid\mathcal{F}_{t-1}]$ $\displaystyle=\rho[(n_{t}-x_{t-1})^{\mathrm{T}}\tilde{\mathcal{L}}_{t}+(n_{t}-% x_{t-1})^{\mathrm{T}}P_{t-1}\mid\mathcal{F}_{t-1}]$ $\displaystyle=\rho_{t-1}[(n_{t}-x_{t-1})^{\mathrm{T}}\tilde{\mathcal{L}}_{t}% \mid\mathcal{F}_{t-1}]+(n_{t}-x_{t-1})^{\mathrm{T}}P_{t-1}$ $\displaystyle=(n_{t}-x_{t-1})^{\mathrm{T}}P_{t-1}+\nu_{t-1}(x_{t-1},n_{t}),$
where the second equality comes from the translation invariance property. Hence, (4.10) always holds for additive market price dynamics and any coherent risk measure. However, for multiplicative price dynamics (2.4), (4.10) can hold only for processes that satisfy the following equation:
$\rho_{t-1}[(n_{t}-x_{t-1})^{\mathrm{T}}\operatorname{Diag}(\tilde{\mathcal{L}}% _{t})P_{t-1}]=\nu_{t-1}(x_{t-1},n_{t}).$ (4.11)
Therefore, in contrast to the classical (risk-neutral) dynamic arbitrage in which (3.2) yields the absence of dynamic arbitrage for the multiplicative price model and linear price impact functions, constant with respect to market price, (4.9) does not rule out risk-averse dynamic arbitrage for this setting.
## 5 Concluding remarks
We investigate the importance of nonanticipativity constraint on round-trip trades to be assessed for dynamic arbitrage in illiquid markets. In our study, we let price impact functions be time varying and stochastic. We also consider two general classes of price impact dynamics, which can exhibit a broad range of stochastic market price processes. We first provide a condition under which searching in the space of $\smash{\mathcal{F}_{0}}$-measurable admissible round-trip trades is enough to attain a no-dynamic arbitrage characterization. This result sheds light on analyses in some of the existing literature, such as Gueant (2014), in which a no-dynamic arbitrage is concluded based solely on a search in the space of $\smash{\mathcal{F}_{0}}$-measurable round-trip trades, instead of searches in the larger set of dynamic round-trip trades. We show that for linear price impact models this condition is both sufficient and necessary for the stronger statement that dynamic arbitrage does not exist. For nonlinear price impact models, this sufficient condition significantly simplifies the effort of searching for price manipulation strategies and dynamic arbitrage opportunities. In particular, we present a simple numerical minimization problem that can be employed for general time-varying stochastic nonlinear price impact models as well as both additive and multiplicative market price dynamics for no-dynamic arbitrage verification. The validity of the sufficient condition, however, involves a precise belief from the very beginning that the conditional expected market price change at any time step is zero. This motivates us to extend the concept of dynamic arbitrage to risk-averse dynamic arbitrage in order to incorporate traders’ risk attitudes toward decisions on the presence of arbitrage opportunities. Similar to our analysis for (risk-neutral) dynamic arbitrage, we prove some sufficient condition. This enables us to limit searching in the space of static round-trip trades to establish the absence of risk-averse dynamic arbitrage.
We leave it for future research to investigate classes of price impact models that rule out risk-averse dynamic arbitrage at a risk-aversion threshold level $\delta$ and for a given market price dynamics and a time-consistent dynamic risk measure. The investigation of further relationships between the proposed concept of risk-averse dynamic arbitrage and alternative notions of arbitrage is another interesting direction for future work.
## Declaration of interest
The authors report no conflicts of interest. The authors alone are responsible for the content and writing of the paper.
## Acknowledgements
The authors wish to thank the editor and referee for their valuable comments and suggestions.
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