finite element method – Problem computing a cylindrical Heat equation with a parameter alpha

i have been struggling to compute a particular instance of cylindrical 3D heat equation.

Here is my code :

(Alpha) = 0.1;

eq = D(u(t, r, (Theta), z), t) == 
   D(u(t, r, (Theta), z), r, r) + 1/r D(u(t, r, (Theta), z), r) + 
    1/(Alpha).b2r.b2 D(u(t, r, (Theta), z), (Theta), (Theta)) + 
    D(u(t, r, (Theta), z), z, z);

(*initial and boundary conditions*)

ic = {u(0, r, (Theta), z) == Exp(-r)};
bc = {u(t, 10^-6, (Theta), z) == 1,
   u(t, 1, (Theta), z) == 0,
   PeriodicBoundaryCondition(u(t, r, (Theta), z), (Theta) == 0, 
    TranslationTransform({2*Pi, 0})),
   PeriodicBoundaryCondition(u(t, r, (Theta), z), (Theta) == 0, 
    TranslationTransform({2*Pi*(Alpha), 0})),
   Derivative(0, 1, 0, 0)(u)(t, 1, (Theta), z) == 1,
   Derivative(0, 1, 0, 0)(u)(t, 10^-6, (Theta), z) == 0};


sol = NDSolve({eq, ic, bc}, 
   u(t, r, (Theta), z), {t, 0, 1}, {r, 10^-6, 1}, {(Theta), 0, 
    2*Pi}, {z, 0, 1});


  Plot3D(sol, {r, 0, 1}, {(Theta), 0, 2 Pi}), {t, 0, 10}, {z, 0, 1});

The problem is, i keep getting an error like this :

NDSolve::femcnmd: The PDE coefficient {{-1,0,0},{0,-(1/(Alpha).b2r.b2),0},{0,0,-1}} does not evaluate to a numeric matrix of dimensions {3,3} at the coordinate {0.500002,3.14159,0.5}; it evaluated to {{1.,0.,0.},{0.,1/(Alpha).b2r.b2,0.},{0.,0.,1.}} instead.

I am a relatively new mathematica user, so i do not see any issue that could arise from evaluating the coefficients at the point {0.500002,3.14159,0.5}.

Can you guys help me understand ? Thank you kindly.

functional analysis – Can we use the duality notation such that the second variable is an element of the measure space?

I read article New Sequential Compactness Results for Spaces of Scalarly Integrable Functions by Erik J. Balder, on page 8 : Author defined the function $a: Ttimes Eto mathbb{R}$ by the usual duality between $E$ and $E^*=F$ $( ⟨.,.⟩)$ such that:
a(t,x)=langle x, trangle

But normally the second variable $(tin T)$ must be an element of dual of $E£, right? Why does the author make this notation?

An idea please
enter image description here

combinatorics – Prove that there is an element of S that is present in at least three of the subsets $A_1, A_2, ldots , A_7$

Suppose that $A_1, A_2, ldots , A_7$ is a collection of seven subsets of a set $S$, each of size
3, and every two subsets $A_i$ and $A_j$ $(i ne j)$ have exactly one element in common.
Prove that there is an element of S that is present in at least three of the subsets
$A_1, A_2, ldots , A_7$.

8 – Setting value of form element from $form_state not working

I need to track previous values of a few form elements on a form to detect when they change to invalidate some other options on the page. Essentially, if the value of these fields change a field that controls pagination should reset.

I’m trying to accomplish this with this:

$values = $form_state->getValues();
$form('element1') = (
      '#type' => 'radios',
      '#title' => $this->t('Element 1'),
      '#options' => (
        // Omitted for brevity
      '#weight' => '0',
      '#ajax' => (
        'callback' => ($this, 'my_callback'),
        'disable-refocus' => true

// dump($values('element1'));
$form('element1_previous') = (
      '#type' => 'value',
      '#value' => (isset($values('element1'))) ? $values('element1') : 'none',

No matter what I do the value of $values('element1_previous) is none. If I uncomment the dump() statement right before it I can see the value of $values('element1') changing each time AJAX is submitted so the value is there.

If I do something like:

$form('element1_previous') = (
          '#type' => 'value',
          '#value' => rand()

I can see $values('element1_previous') being set to a different integer each AJAX submission. I just can’t assign the value of $form('element1') to that field.

What am I doing wrong? Is there a better way I could handle this?

html – Localization of multi style text element in Vue

After following up this question, I’m thinking if there’s a better/shorter way to write this text element that has part with different style, while allowing localizations:

    <span class="has-text-grey">{{ $store.releaseList != null ? $store.releaseList.length : 0 }}</span>
    <span> versions released</span>

With vue-i18n:

<p v-html="$t('downloads.releases.table.versions-total')
    .replace('{0}', '<span class=has-text-grey>{1}</span>')
    .replace('{1}', $store.releaseList != null ? $store.releaseList.length : 0)">

The localizable text would be {0} versions released.

I could set the localizable text to <span class=has-text-grey>{0}</span> versions released, but that would make the life of the translators (usually people without knowledge about HTML) a bit more difficult.

Is there any better built in way to add support for localizations in a multi-styled text?

USB Flash Disk with Security Element

I am thinking of buying USB flash disk with Security Element(stores Private-Key/Secret-Key/X.509-Certificates) and some encrypted data(8 Megabyte). The disk has to be protected against cloning and possibly maintains logs of insert history with UNIX timestamp & USB Host ID when inserted.

I found YubiKey & NitroKey, but they do not have additional storage. Is there a USB Device like that satisfy above requirements.

(Or) Is there any cost effective SoC+Security Element Over USB with flash storage available to implement my requirement using Opensource?


javascript – jQuery get index of .active element, but with reference to its original siblings

I am toggling an active class to an object in jquery in a grid like so :

$(".cinema-seats .seat").on("click", function () {

Basically, if I have a 3×3 grid of boxes, and click on 2 boxes randomly, they will be assigned active classes. Now, I want to get the index of the active boxes, but with respect to the original 3×3 grid.

For example,

   box 1(active)       box2             box3
   box 4               box5(active)     box6
   box 4               box5             box6

Now, as output, I am expecting to get 1,5 as they are the indexes of the active classes with respect to the boxes.

This is a small example, I want to do this with a 7×14 grid, arranged into columns and rows and have only one class => “.seats” in common. Again, I want to get the index (n-th child) of the active boxes with respect to all the seats.

Codepen –

javascript – How to toggle selected or clicked element not all

Am trying to toggle only clicked element and adding some class to it but it’s applying to all.
How can i do that?.any suggestion would be helpful.thank you

    <label class="checkbox">
        <input type="checkbox" />
        <span class="secondary"></span>
    <label class="checkbox">
        <input type="checkbox" />
        <span class="secondary"></span>

   $(".checkbox span").toggleClass("checked");

list manipulation – Enumerating over matrix element values in Table

I have a $N$ dimensional array $M$, and a function $f({M_{i}})$ in terms of the array elements, where each matrix element $M_{i}$ can be 0 or 1. I’d like to construct a table

Table(f({M_{ij}}), {M_{1},0,1},{M_{2},0,1},...,{M_{N},0,1})

For a given N, I can write down the code to construct the table, but for general N, it there a convenient way to write the above code? Namely, I’d like to keep N as an input variable.

As an example, let us use


and define f as the sum of all the elements in Mat. so the table I want to construct is

Table(Sum(M(i),{i,1,n}), {M(1),0,1},{M(2),0,1}, {M(3),0,1})

The outcome is

{{{0, 1}, {1, 2}}, {{1, 2}, {2, 3}}}

Of course, when I change n to other values, I need to rewrite the code for the table. So there should be a way for us to construct the table without modifying the code.