# Tag: element

## wide angle – How to use a filter on a lens with a bulbous front element? (Rokinon AF 14/2.8)

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## loops – In C++ how does “sizeof(array)/sizeof(array[0])” give the number of elements in an array? Why isn’t it affected by the length of each element?

I’m playing around with C++ and was looking at how to loop through an array of unknown length. The following code was suggested and works perfectly from the little testing I’ve done:

```
std::string words(5) = {"Lorem ipsum dolor sit amet orci aliquam.", "Hi", "Welcome", "World", "LoopyDoopyDoo"};
for (int i = 0; i < sizeof(words)/sizeof(words(0)); i++){
DO STUFF
}
```

From what I’ve read the sizeof() operator returns the size of a variable in bytes.

What I don’t understand is how this isn’t affected by the number of characters in each element of the array. I printed out the sizeof() value to check and the array size is always evaluated at 160 bytes and element 0 as 32 no matter how many characters are present. I thought that it might be allocating 32 bytes but not using them all so I stored some text that should use 40 bytes, but still no change. Am I missing something here? Is text stored differently in C++?

Any help in understanding how this actually works would be appreciated, thanks!

## satisfiability – How to represent bottom element (integer domains) in SMT formula

I’m doing some work with static analysis and need to represent local variables as SMT formulas. In general this is fairly straight forward, depending on the domain of the static analysis. However, my question lies when needing to represent impossible or infeasible values, e.g., divide by zero paths from the static analysis under an integer domain. This is often referred to as the bottom element, ⊥.

I’m struggling to develop a formula which can represent these “impossible” (integer) values. Is there a way to do this?

I’ve been thinking along the lines as an impossible inequality, but I’ve been unsuccessful thus far. Similarly, I’ve thought about attempting to represent using divide by zero within an SMT formula, such as the following Z3/SMT formula:

```
(declare-const a Int)
(assert (= (/ a 0.0) 1.0))
(assert (= (/ a 0.0) 2.0))
(check-sat)
```

However, given the application, I’m not sure this is going to be helpful.

Application: I’m using this to compare results between two different static analyses between different domains.

tl;dr:

How to represent infeasible, bottom integer elements as SMT formula?

## at.algebraic topology – $pi_{2n-1}(operatorname{SO}(2n))$ element represents the tangent bundle $TS^{2n}$, not torsion and indivisible?

Question: Is the element $alpha$ in $pi_{2n-1}(operatorname{SO}(2n))$ representing the tangent bundle $TS^{2n}$ of the sphere $S^{2n}$ indivisible and not torsion?

My understanding so far —

An $operatorname{SO}(2n)$ bundle over $S^{2n}$ corresponds to an element in $pi_{2n}operatorname{BSO}(2n) =pi_{2n-1}operatorname{SO}(2n)$.

Not torsion: There does not exist any integer $m > 0$ such that $malpha$ is a trivial element.

Indivisible: There does not exist any integer $k > 1$ and any element $beta$ in $pi_{2n-1}operatorname{SO}(2n)$ such that $alpha=kbeta$.

Ref: Mimura, Toda: Topology of Lie groups. Chapter IV Corollary 6.14.

## Null being added to every element in list list

Welcome to MMA SE! So, essentially the problem here is that line breaks don’t count for anything inside expressions—only *between* expressions. So,

```
a = 4
b = 5
```

is fine, and is interpreted as two separate inputs;

```
a = (Echo(3)
5)
```

is not interpreted as “do `Echo`

, then `5`

“. Within an expression, you need to use `;`

to separate sequentially-evaluated parts. Otherwise, line breaks, like spaces, are interpreted as `Times`

!

That’s relevant here because in the lines

```
For(i = StringLength(word), i > 0, i--,
AppendTo(wordchar, StringPart(word, i)
)
)
wordchar
```

you’re essentially multiplying the output of the `For`

loop, which is `Null`

, by the list `wordchar`

. Since multiplication is threaded over lists automatically, you get `Null`

multiplying every string in the list. Check out `butterfly("abcdef") // FullForm`

to see the `Times`

explicitly!

So, modifying it to

```
butterfly(word_) :=
Module({wordchar = {}},
For(i = StringLength(word), i > 0, i--,
AppendTo(wordchar, StringPart(word, i)
)
);
wordchar
)
```

should fix it!

Note, however, that `For`

loops are very “non-Mathematica-l”! Generally, you’ll want to use `Table`

(or maybe `Array`

, or `Sow`

and `Reap`

for “`AppendTo`

—like functionality”) to build lists, not `For`

and `AppendTo`

—and it’ll typically be easier than setting up a `For`

-loop, since the iterated-over variable already behaves the way you want.

Your code also sets the global variable `i`

; “good practice” would be to put it in the `Module`

as well (if you were going to use it)!

## finite element method – Solving sine-Gordon equation with boundary condition

There are several issues. First there need to be sufficient initial conditions for this telegraph type equation. Also you do not specify a Dirichlet type boundary condition. I have added arbitrary (wrong) information to get you started but you’d need to fix that.

Here is a tensor product version – which you should use if you are not familiar with the finite element method given below:

```
al = 0.08; ga = 0.01; h = 5; aext = 3; omegaext = 1.4;
sol1 = NDSolveValue({D(u(x, t), x, x) - D(u(x, t), t, t) -
Sin(u(x, t)) - al*D(u(x, t), t) + ga == 0,(*(D(u(x,t),
x)/. {x(Rule)0})(Equal)h,*)(D(u(x, t), x) /. {x -> 15}) ==
h + aext Sin(omegaext t)
(* fix these *)
, u(0, t) == 0
, u(x, 0) == 0
, Derivative(0, 1)(u)(x, 0) == 0
}, u, {x, 0, 15}, {t, 0, 2})
```

FEM version:

```
al = 0.08; ga = 0.01; h = 5; aext = 3; omegaext = 1.4;
sol2 = NDSolveValue({D(u(x, t), x, x) - D(u(x, t), t, t) -
Sin(u(x, t)) - al*D(u(x, t), t) + ga ==
NeumannValue(h + aext Sin(omegaext t), x == 15)
, u(x, 0) == 0
, Derivative(0, 1)(u)(x, 0) == 0
, DirichletCondition(u(x, t) == 0, x == 0)
}, u, {x, 0, 15}, {t, 0, 2})
```

For this one you probably want to think about the sign in the `NeumannValue`

```
Plot3D({sol1(x, t), sol2(x, t)}, {x, 0, 15}, {t, 0, 2},
PlotRange -> All)
```

Also note this coupled nonlinear Sine-Gordon example.

## magento2 – How to find cause of Element ‘handle’: Character content other than whitespace is not allowed because the content type is ‘element-only’

I have reviewed the other posts for this and none of them seem to apply to this situation, so I’ve been unable to find what’s causing this error in the exception.log. The error is thrown during xml validation of the merged xml file. I inserted some code to write the xml to a file so I could inspect it I didn’t find anything wrong such as having invalid characters.

We are running Magento 2.4.2 (right now in Developer mode).

How can I find the root cause of this Element ‘handle’ error?

## theming – Drupal 8 get specific element in site path in twig template

```
The current page url is http://website/p1/p2/p3/p4
In Drupal 8 twig, use function to get path p1/p2/p3/p4
{{ set site_path = path("<current>") }}
{{ site_path }}
The site_path is p1/p2/p3/p4
How to get the element in the path, for example, the second p2
```