## Brief Summary

1. A reaction can precede (and even erase) its trigger, (as in the Shield spell)
2. A plain reading of Absorb Elements, shows it in effect when the triggering damage is received
3. Both effects of Shocking Grasp occur at the same time
4. The Absorb Elements reaction is in effect, before the target loses its ability to take reactions

## Full Explanation

### A Reaction can Precede its own Trigger

…as it does in the Shield spell:

CASTING TIME: 1 Reaction* | *- which you take when you are hit by an
attack…

… Until the start of your next turn, you have a +5 bonus to AC, including against the triggering attack

From the Casting Time, Shield can only be cast once the triggering event has already happened; yet the spell’s effect ends up preceding the (hit) trigger and can even prevent the trigger from existing, (the hit was actually a miss!)

Moving past Shield to a general analysis of reactions, you notice the Casting Time on reaction spells (e.g. Feather Fall, Counter Spell, Hellish Rebuke,) all read as if the spell is cast after the trigger. But since we know reaction effects can occur before the trigger, we must look at the spell text for reaction timing.

### When does Absorb Elements take effect

CASTING TIME: 1 Reaction* | * – which you take when you take acid, cold, fire, lightning, or thunder damage

The spell captures some of the incoming energy, lessening its effect
on you and storing it for your next melee attack. You have resistance
to the triggering damage type until the start of your next turn.

As expected, the Casting Time reads as if casting occurs after the trigger is done, but the spell text in bold explicitly narrates the damage resistance (effects) of Absorb Elements, as already in place when the damage is received.

Another Q&A and a Crawford tweet confirm that Absorb Elements is intended to effect the triggering damage.

### Shocking Grasp

… On a hit, the target takes 1d8 lightning damage, and it can’t take
reactions until the start of its next turn.

With no text or rule to separate them, both of Shocking Grasp’s effects occur at the same time. As such, any effect that occurs before the lightning damage (e.g. Absorb Elements), also occurs before the reaction debuff.

Absorb Elements is a defensive reaction spell that exists to trigger and reduce incoming elemental damage, before it is actually received. Since its effect precedes the damage from Shocking Grasp, it also precedes Shocking Grasp’s reaction debuff.

## set theory – Obtaining Elements of a Generic Extension from a Boolean-Valued Model of ZFC

Let $$mathcal{M}$$ be a countable transitive standard-model of ZFC.
Let $$B in mathcal{M}$$ be a boolean algebra that is complete in $$mathcal{M}$$.
Further, let $$mathcal{M}^{(B)}$$ be the corresponding boolean model of ZFC.

Now we consider an $$mathcal{M}$$-generic ultrafilter $$U$$ on $$B$$.
According to Jech (Set Theory, p.216), the elements of the generic extension $$mathcal{M}(U)$$ can be obtained via the map $$cdot^U: x mapsto x^U := lbrace{y^U mid x(y) in U rbrace}$$ where $$x in mathcal{M}^{(B)}$$. But when reading Bell (Set Theory Boolean-Valued models and Independence Proofs, p.91) the following map is given: $$i(x) = lbrace i(y) mid Vert y in xVert in U rbrace$$ where $$x in mathcal{M}^{(B)}$$. I assume that the following holds:
$$forall x in mathcal{M}^{(B)}: x^U = i(x). (*)$$

But at the same time I am not yet fully convinced as $$u(x) leq Vert x in u Vert$$ for $$x in text{dom}(u)$$.

Can anyone verify that $$(*)$$ (or a variant of that statement) holds (and give a short reason why)?

## expression manipulation – How to drop/extract elements of a list which starts with Plus

I have the following list :

``````list={a^2, b^2, a^-1, a^2+b^2, (a+b+c)^-1, (a+b-c)^-2}
Do(Print(list((i))//FullForm),{i,1,Length(list)})
``````

I want to break this list into two lists: one containing elements starting with `Power` and another starting with `Plus`. In this case it will be

``````list1 = {a^2, b^2, a^-1, (a+b+c)^-1, (a+b-c)^-2}
list2 = {a^2+b^2}
``````

A priori the position of elements starting with `Power` or `Plus` is not fixed and also the elements could be complicated. Is it possible to do this?

## javascript – Having trouble swapping elements

I’m trying to visualize a simple Hanoi solver that uses an algorithm, and I’m swapping elements on array to visualize it.

Here’s my code:

``````        let A = ();
let B = ();
let C = ();
let moveCount = 0;
let once = true;
hanoi(3, A, C, B);
// 3, how many disk
// A C B are rods
alert(A + '.n' + B + '.n' + C + '.')

function hanoi(n, start, target, other)
{
if (once)
{
once = false;
for (var i = 1; i <= n; i--)
{
start.push(i);
}
}

if (n <= 1)
{
let temp = start(n-1);
start(n-1) = target(target.length);
start = start.filter(Boolean)
target(target.length) = temp;
target = target.filter(Boolean);
//console.log('Moving disk '+n+' from rod '+start+' to '+target+' rod');
moveCount++;
}
else
{
hanoi(n-1, start, other, target);

let temp = start(n-1);
start(n-1) = target(target.length);
start = start.filter(Boolean)
target(target.length) = temp;
target = target.filter(Boolean);
//console.log('Moving disk '+n+' from rod '+start+' to rod '+target);
moveCount++;

hanoi(n-1, other, target, start);
}
}
``````

The C value should be expected `(3, 2, 1)` but only shows 2. I also checked A and B and `1 is nowhere to be found`

How do I make this properly so the output would be `(3, 2, 1)`

Imagine 3 is the largest disk and so on…

## calculus and analysis – Picking elements from separate lists and multiplying them

So I’m doing some instruction items about surface integrals. I’ve written the following code. it calculates curl and partial derivatives of the surface. I now want to create the following function, which will be my integrand. Merely dot producting the two vectors doesn’t change the signs like I need. Is there a way to says multiply one element of a vector times its corresponding one and changing the sign, along the way?

What I want to do is change the sign of the first two elements created by the dot product, whle leaving the third alone.

Here’s my code;

``````F = {2 z, 4 x, 5 y};
Print("The curl is:")
NewF = Curl(F, {x, y, z}) (*Step 1*)

g = x + 4;(*Step 3 solving for z of the curve*)
Print("The partial derivatives of z are the following (with 1 as a placeholder for R):")
g1 = {D(g, x), D(g, y), 1}(*Step 4, the partials of z*)
Print("The new integrand is the following (don't forget to sub g for z.")
NewF . g1
``````

The curl is shown to be 5,2,4 and the partials are 1,0,1. But a correct answer for what i want to do gives 1 as the ‘new integrand’ while the code here gives ‘9.”

Any thoughts?

## nt.number theory – Products of short elements in a field

Consider a field $$F$$ of characteristic zero. Let $$L=F[alpha]$$ be an extension of degree $$d.$$ We call an element
$$x=a_0 + a_1 alpha +ldots+ a_{d-1}alpha^{d-1}in L$$
short if $$a_{d-1}=0.$$
Under which conditions on $$alpha$$ every element in $$L^times$$ is a product of short elements?

It is easy to see that every element of $$L$$ is a quotient of two short elements for $$dgeq 3$$.

## linear algebra – Quick Question about Representation of Elements in \$operatorname{Span}(S)\$

Let $$X$$ be a vector space over a field $$mathbb{F}$$ and let $$S subset X$$ be a nonempty subset of $$X$$. We know that $$operatorname{span}(S)$$ is the set of all linear combination of vectors in $$S$$.

If $$x_0 in operatorname{Span}(S)$$, then $$x_0 = c_1 s_1 + cdots + c_n s_n$$ for some scalars $$c_i in mathbb{F}$$ and vectors $$s_i in S$$.

Now suppose $$x_1 in operatorname{Span}(S)$$ and is different from $$x_0$$. My question is about the representation of $$x_1$$. In the first scenario, would the same vectors $$s_1,dotsc,s_n$$ used in the representation of $$x_0$$ be used in the linear combination of $$x_1$$ where only some of the scalars are different? That is, $$x_1 = d_1 s_1 + cdots + d_n s_n$$ for some scalars $$d_i$$?

Or would both the scalars and possibly the vectors in the linear combination of $$x_1$$ be different, say $$x_1 = d_1 s^{star}_1 + cdots + d_m s^{star}_m$$?

I’m leaning towards the latter, but I”m not entirely sure. The two texts that I’ve looked at both begin with a list of vectors $$v_1,dotsc,v_n$$, and then talk about the span of that list, but not an arbitrary set.

## arrays – non-zero elements C++

I would be glad, if you help me with this problem:

I have two-dimenssion array with m rows and n columns. I have to write a program with C++, which creates a new array A, whose value is equal to average of the non-zero elements in the i-th row in G.

``````#include <iostream>
#include <iomanip>
#include <cmath>

using namespace std;

const int m = 5;
const int n = 5;
int G(m)(n);
int i, j;
double sum = 0, A;

void randNum()
{
srand(89);
for (i = 0; i < m; i++)
{
cout << endl << endl;
for (j = 0; j < n; j++)
{
G(i)(j) = rand() % 10;
cout << setw(6) << G(i)(j);
}
}
cout << endl << endl;
}

void randAvg()
{
for (int i = 0; i < m;i++)
{
float sum = 0.f;
for (int j = 0; j < n; j++) {
sum += G(i)(j);

}
float A = sum / m;
cout << "Average of row " << i << ": " << A << endl;
}

float sum = 0.f;
for (int i = 0; i < m; i++)
{
for (int j = 0; j < n; j++) {
sum += G(i)(j);
}
}
float A = sum / (m * n);
cout << "Overall average: " << A << endl;
}

int main()
{
randNum();
randAvg();
}
``````

This is the code that I wrote, but these “non-zero elements” are still there.

Adobe Photoshop Elements 2020.2 (x64) Multilingual

Adobe Photoshop Elements 2020.2 (x64) Multilingual | 3.46 GB | Language: Multilanguage

Amazing photos. Fun creations. Forever memories. It’s never been easier to create incredible photos. Put your best photos forward with auto-generated creations and intelligent editing options. Easily organize your photos and share them in fun ways.

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Release Notes:

System Requirements:
– 1.6GHz or faster processor with SSE2 support
– Microsoft Windows 10 (recommended versions 1809, 1903) or Windows 8.1 (Windows 7 not supported); 64-bit versions only (32-bit not supported)
– 4GB of RAM (8GB recommended)
– 5.2GB of available hard-disk space to install applications; additional 2.4GB to download all optional content (cannot install on a volume that uses a case-sensitive file system or on removable flash storage devices)
– 1280×800 display resolution (at 100% scale factor)
– Microsoft DirectX 9 or 10 compatible display driver.

Homepage:

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x64 | Lanugages:Multilanguage | File Size: 3.56 GB

Dive right in and do something incredible with your photos and videos.​

Auto-generated photo and video slideshows and collages are made just for you and delivered upon launch. Make your photos and videos look their best with intelligent editing options, turn them into stunning creations, organize them easily, and quickly share your memories.

Beautiful photo and video slideshows and collages are created just for you and delivered upon launch. It’s all powered by Adobe Sensei AI technology. Plus, get up and running quickly with the new home screen – see what’s new since your last version, discover fun things to try, and get inspiring ideas, help, and tutorials.

Create amazing photos and videos – no experience required – with automated editing options and step-by-step guidance.

– Photo and video slideshows and collages are created for you highlighting memorable moments. Adobe Sensei AI does all the work.

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– Videos are automatically organized by date, and you can easily tag and find them by people, places, and events.

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– Share on YouTube and Vimeo.*

– Create animated bounce-back GIFs to easily share on social.*

– Share videos on DVDs (Windows only) and HDTVs.

OS:Microsoft Windows 10 (recommended versions 1809, 1903) or Windows 8.1/ Win 10 build 1809 or above,

CPU:2GHz or faster processor with SSE2 support; dual-core processor required for HDV editing

Memory:16 GB RAM recommended for 4K editing

Space:6.8 GB of available hard-disk space to install applications; additional 10GB to download all optional content (cannot install on a volume that uses a case sensitive file system or on removable flash storage devices)

– Microsoft DirectX 9 or 10 compatible sound and display driver

– Windows Media Player (required if importing/exporting Windows Media formats)

– DVD burner required to burn DVDs