8 – How do I create custom webform reference settings?

I have a Content type, in which there is a field of type Webform Reference.

I want to have a custom setting (a checkbox) in Webform (Webform Add Page), which should also appear in Content type under Webform Reference settings.

Also how can I get that setting value in Node context?

enter image description here

reference request – Spectral sequences in algebraic topology

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How to create custom Webform Reference settings in D8?

I have a Content type, in which there is a field of type Webform Reference.

I want to have a custom setting (a checkbox) in Webform (Webform Add Page), which should also appear in Content type under Webform Reference settings.

Also how can I get that setting value in Node context?

enter image description here

reference request – A simple form of choice

While reviewing some categorical versions of the axiom of choice, it occurred to me that none of the formulations I’m aware of actually reflect how I use choice in practice: pronounce that we ‘choose an element $x$ of $X$‘ or something like this.

That is, while I understand that ‘every surjection in ${bf Set}$ splits’ and ‘every collection of nonempty sets has a choice function’ etc. are ways to formalize choice that can be mildly contorted to give the way I used it above (surject onto a singleton and split, consider a collection containing one set, etc.), none of them straight up axiomatize my intuitive usage of choice. To this end:

Define simple choice (SC) to be the axiom asserting that every nonempty set $X$ comes equipped with a simple choice function $$f_X:1to X,$$ where $1$ is the ordinal (and not some random singleton, to make things more concrete).

Using SC, when we say ‘choose an element $x$ of $X$‘ we really mean ‘look at $f_X(0)$‘, instead of the above more involved interpretations. For any nonempty collection of sets $Y$, I believe we can define a choice function $c_Y:Ytobigcup Y$ in the classical sense with $c_Y(X)in X$ for all $Xin Y$ by defining $$c_Y(X)=f_X(0).$$

Further, while the classical versions introduce auxiliary contortions that are relatively harmless when working with sets, we suddenly have to use things like Scott’s trick to get good behavior when working with the globalized versions of choice and proper classes — the globalized version of SC seems to work in a more straightforward manner with proper classes.

Let’s call global simple choice (GSC) the axiom asserting that every nonempty class $X$ comes equipped with a simple choice function $f_X:1to X$. I believe this implies global choice in the same manner that it implies regular choice above, but if we have a proper class and want to select an element of it we don’t need Scott’s trick to intersect with some stage of the cumulative hierarchy anymore.

I’m certain that I’m not the first one to cook up something like this, so my questions are

What is wrong with this version of choice? Is it actually equivalent to the standard formulation? If it is equivalent, is this version of it less appealing for some reason that isn’t occurring to me? Are there existing references to it somewhere?

Any assistance is appreciated.

theming – How to get theme suggestions for a custom block type attached via a Drupal 8 core entity reference field?

I have created a custom block type with the machine name “score_card”. I am displaying it on a node page via a paragraph with an entity reference field that references blocks. I would like to get a template suggestion for it along the lines of “block–block_content–score_card.html.twig”.

I have template suggestions turned on and I do see suggestions in the HTML output for the paragraph, the reference field and the individual custom block type fields. There are no suggestions shown for blocks at all, not even block.html.twig. Attempting to just place ‘block–block_content–score_card.html.twig’ or ‘block–score_card.html.twig’ in my theme has no effect.

I also attempted to generate the theme suggestion using the suggested fix in this thread of adding hook_theme_suggestions_block_alter to no effect. Running this code through the debugger shows that the hook is not called for the block referenced via a field.

Using Drupal 8.9 latest how can I implement a custom theme for a custom block type referenced via a an entity reference field?

Entity reference additional field

In D7 I have two new node type defined e.g. branch and leaf. The branch is a collection of leaves that I’m referring to using the entity_reference module. In the picture below the leaves are the nodes representing the colors. The leaves could be re-used in several branches.

Here is a picture of my collection enter image description here

I would like to add for each of the referenced leaves, two checkboxes to add some information about that leaf that is referenced in that branch. I have added on the picture manually the checkboxes. This is what I would like to achieve. Then, programmatically when I read the branch and all its leaves, I want to be able to retrieve the checkboxes value as well. Everything is working far, I just need to know how to add the leaves, so that at edit time when I edit a branch I can tick the checkboxes as needed.

How could I do that? If there is no module that exists, which hooks should I use for adding this fields to the referred leaf node in the branch?
I do not want to add new fields for the leaf node type, I need the new fields/chekboxes to be added to a branch for each leaf thus at the moment of referring to the leaf and for each leaf.

8 – How to get a multilevel taxonomy reference field to output as nested UL in node tpl?

I have a simple 2 level taxonomy vocabulary field but I can’t seem to find a way to output the terms (labels) in a nested UL in my node TPL. There are no display formatter options at all and I can’t find any info on this?

{{ content.field_my_terms }} just gives me field__items with flattened field__item.

reference request – Schrodinger equations on foliated spaces

Schroedinger type equations have been constantly explored in mathematics. I would like to know if is it possible to make sense of physical interpretation in the following setting:

One has a closed manifold $M$ (I mean, it is compact and has no boundary (such as a sphere)) with a group action by a Lie group $G$. Then, state a Schroedinger type equation on this manifold. On could possible ask to: are there $G$-invariant solutions for this equation?

More generally, assume that $M$ is foliated by sub manifolds and analogously pose a Schroedinger equation on it. One could ask: are there solutions that are constant along the leaves?

Are there people studying physics problems on these settings?

I do appreciate comments/references, etc.

reference request – Sources for multiple Stieltjes integral

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  • Please be sure to answer the question. Provide details and share your research!

But avoid

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  • Making statements based on opinion; back them up with references or personal experience.

Use MathJax to format equations. MathJax reference.

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ra.rings and algebras – Reference for a certain derivation on the ring of ordered series over a free monoid

Let $R$ be a (commutative or non-commutative) unital ring, $X$ be a non-empty set, and $R langle! langle X rangle! rangle$ be the ordered series ring (in fact, a ring of formal power series over $R$ in $|X|$ non-commuting variables) obtained by endowing the set of all functions $mathscr F(X) to R$ with the usual operations of pointwise addition and Cauchy product. Here, $mathscr F(X)$ is the free monoid on $X$, whose operation (that is, word concatenation) I’ll denote by $ast$.

While looking for a counterexample to a certain property in the class of local rings, I happened to note that, for each $z in X$, the mapping $partial_z$ that sends an ordered series $f in R langle! langle X rangle! rangle$ to the function
$$
mathscr F(X) to R colon mathfrak z mapsto sum_{(mathfrak u, mathfrak v) in mathscr F(X) times mathscr F(X): mathfrak u ast z ast mathfrak v = mathfrak z} f(mathfrak u ast mathfrak v),
$$

is a well-defined derivation of $R langle! langle X rangle! rangle$. In particular, the Leibniz identity follows from the fact that $mathscr F(X)$ is a cancellative monoid with trivial group of units and every $X$-word factors uniquely in $mathscr F(X)$ as a product of elements of $X$ (that is, $X$-words of length one).

My question is whether anyone here can offer a reference where $partial_z$ is being introduced: I thought I would have found $partial_z$ defined in Cohn’s book on FIRs (where ordered series rings are discussed in Sect. 1.5), but it’s not there (as far as I can see).