Solving integral involving absolute value of a vector

I am trying to integrate the following in mathematica:
$ \int_0^r \frac{exp(-k_d(|\vec{r}-\vec{r_j}|+|\vec{r}-\vec{r_i}|)}{|\vec{r}-\vec{r_j}|\times|\vec{r}-\vec{r_i}|}r^2dr$ .
I have first defined, the following functions,
$ \vec p(x,y,z)= (x-x_j)\hat i + (y-y_j)\hat j+(z-z_j)\hat k$
$ \vec q(x,y,z)= (x-x_i)\hat i + (y-y_i)\hat j+(z-z_i)\hat k$ .
$ \vec r(x,y,z)=x\hat i + y\hat j+z\hat k $
Then I clicked the integration symbol in the classroom assistant panel and typed the integrand in the $ expr$ portion. While typing this, I have used $ Abs$ to take modulus of the functions $ \vec p(x,y,z)$ and $ \vec q(x,y,z)$ . I have included the limits as $ 0$ to $ Abs(r)$ and the $ var$ as $ r$ in the integration symbol. But when I press( Shift + Enter ) no output value is shown . Can anyone tell me where I have made mistake ?

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Partition into pairs with minimum absolute difference, NP-hard?

I have a set $ S$ of an even number of positive elements $ 2m$ and $ m$ values $ t_1,t_2,\ldots,t_m$ where each $ t_i\leq1$ for all $ i$ .

The question is: can you select $ m$ pairs $ (a_i,b_i)$ from $ S$ such that $ |a_i-b_i|\geq t_i$ ?

I was trying to prove that this problem is NP-hard by a reduction from 3-Partition Problem. I failed because if I choose the numbers as in 3-partition I cannot guarantee that their absolute difference is at least $ t_i$ .

Do you have any hints?

Absolute URL for (MultiSite) link images

How I can I get WordPress to stop making link-image URLs relative?

I’m trying to add logos to the blog-roll widget, but WordPress makes the URLs of the images relative to the current blog.

For example, if the site is, the images in the blog-roll widget at the main blog work correctly, but the ones at are broken because instead of using something like /common/bloglogos/main.png (or even, it uses

I’ve tried various combinations of URLs and formats, but it always makes the images’ URLs relative to the current blog which is annoying because it would require uploading the images for all of the blogs to each of them instead of having them all in a central location which can be updated as necessary with just one change.

The URLs of the links themselves are fine, it’s just the URLs of the images of the links that are the problem.

LibreOffice linked images: why relative paths looks like absolute

Does anybody know, for what reason relative paths of the linked images looks like the absolute ones?

Here is quick test:

  1. Open Writer.

  2. Ensure your LibreOffice options are correct:

    • Menu > Tools > Options > Load/Save > General
    • Save URLs relative to file system = True
  3. Then, insert some linked image (don’t simply paste it). Before inserting, the image should be in the same directory with the document.

  4. Close Writer.

  5. Move the document with the image to some another directory.

  6. Open Writer again. Ensure the image is visible.

  7. Close Writer again. Move the image outside this directory. The image should not be visible anymore.

In case all these steps works correctly for you, you know that the image is really the linked one, and is linked via relative path.

But now, look at this relative path:

Open image properties window > Open Image tab > See that the path in the File Name field looks as the absolute one.


getCanonicalPath() does not return absolute path on Ubuntu Server 18.04

I’m having an issue fetching the complete path of using getCanonicalPath() inside a spring boot app that I deployed in ec2 .

String absolute_path = new File("../datalake").getCanonicalPath()+"/"+files_path; absolute_path = absolute_path.replaceAll("\\", "/"); System.out.println(absolute_path); 

Expected Output :


Current Output :


More Detail

I have deployed a spring boot web application inside an ec2 instance under and I’m trying the fetch the path of ” data lake ” folder in the location


from a war, I deployed under /opt/apache-8/webapps/

I’ve tried all internet answers I could find, not sure how to approach this, is it a permission issue, I was hoping if someone encountered similar issue

FYI Right now the permission distribution is as follows

Jenkins User/group: Jenkins/Jenkins

Tomcat, Apache2, SFTP Server User/group: ubuntu/ubuntu

I’ve spent like 2 days on this alone

How to get an absolute value of Around?

Around is a useful feature of Mathematica 12 to work with uncertain data.

x = Around[-1, {0.5, 1.5}] 

$ -1.0^{+1.5}_{-0.5}$

I’m curious how to get an absolute value of such uncertain data. When I use Abs directly I get an unexpected result:


$ 1.0^{+1.5}_{-0.5}$

I have expected: $ 1.0^{+0.5}_{-1.0}$ , because


Interval[{0, 1.5}]

In total there are two issues:

  1. Upper and lower uncertainties are not interchanged when taking Abs.

  2. Crossing of zero is ignored.

Is this intended behaviour of Around or some sort of a bug?

How should I calculate absolute values of uncertain data points? For example, when I want to plot Abs of uncertain of data?