galois theory – Can elements of automorphism groups be expressed as some form of matrix?

I was reading on automorphism groups and Galois theory and this idea came to mind:

Since by definition, automorphisms are isomorphisms, we have $phi(a*b)=phi(a)cdotphi(b)$ where $phi$ is an element of the automorphism group $H$. The definition of $phi$ reminds me of the definition of linear maps.

In the context of Galois extensions, if $H= Aut(F/mathbb{Q})$(where $F/mathbb{Q}$ is a Galois extension), does this mean that $phi$ can be expressed as a matrix that transforms $F$ while fixing $mathbb{Q}$ like its the “origin”?

If this is true, does this apply to any field extensions?

8 – Error Passing Extra Parameter to Custom Form

I have a simple custom form that works until I try to add a custom parameter for my module called “forms_admin”.

These are the contents of my forms_admin.routing.yml

  path: 'admin/config/system/forms/{arg1}'
    _form: 'Drupalforms_adminFormFormSettings'
    _title: 'Forms Settings'
    _permission: 'access content'

This is a relevant part of my FormSettings.php file (Currently do not have any custom Validation or Submit actions)

public function buildForm(array $form, FormStateInterface $form_state, $arg1 = NULL) {
    $form('title') = array(
      '#type' => 'textfield',
      '#title' => t('Title'),
      '#required' => TRUE,

    $form('submit') = array(
      '#type' => 'submit',
      '#value' => t('Submit'),

return $form;

And my third file is:

  title: Forms
  route_name: forms_admin.settings
  parent: system.admin_config_system
  description: 'Forms settings'
  weight: 0

The moment that I add {arg1} to my forms_admin.routing.yml and , $arg1 = NULL to my FormSettings.php file, I am unable to acces the website.

I receive a white page with the error that states:

The website encountered an unexpected error. Please try again later.

After removing arg1 from my two files and going to the Recent Log messages, this is the error I receive:

SymfonyComponentRoutingExceptionMissingMandatoryParametersException: Some mandatory parameters are missing (“arg1”) to generate a URL for route “forms_admin.settings”. in DrupalCoreRoutingUrlGenerator->doGenerate() (line 182 of /var/www/test_site/docroot/core/lib/Drupal/Core/Routing/UrlGenerator.php).

I have tried changing arg1 to other names, not making $arg1 = NULL, etc. and I receive an error every time.

What am I missing?

When new address is selected billing address form is not showing in checkout magento 2.3.2

enter image description here

When unchecking checkbox My billing and shipping address are the same, if new address is selected the billing address form to add new billing address is not showing up. Anybody know its reason? Attaching image.

gmail – How can I show random IDs to a Google form respondents?

I want to collect contact details for invitees using a Google form created for this purpose. I want the respondents who give me their contact details to also input an appointment entry in a public calendar.

To maintain their privacy, I should not ask their names in the public calendar. I need them to input their unique ID so I can link their calendar’s entry with their form contact details. I need a public calendar so they do not pick a conflicting data taken by another respondent.

Is there any way to show a random ID for a Google form respondents? If not, are there any suggestions to link public calendar entries with contact details to contact the person?

magento2.3.2 – Frontend Checkout: Billing Address Form Fields Do Not Appear

enter image description here

When I check out on the front end and untick the “Billing and shipping address is the same” box, no new fields pop up to insert a billing address. This problem persists on all themes including Magento Luma/Default theme. I am unsure how to begin troubleshooting this to determine the cause, I hope so

enter image description here

oc.optimization and control – When does the metric projection operator have a closed form?

I have a simple question. Often times in optimization, the following function is used:

Let $H$ be a real Hilbert space and $C$ a nonempty closed convex subset of $H$, then the metric projection is defined as the function,

$$P_C(x) = text{argmin}_{y in C} ||x – y||$$

Sometimes (not always), this function will have a closed form. For example, if $C$ is the interval $(-1,1)$ in $mathbb{R}$, then $P_C(x) = min(max(x,-1),1)$.

Is there a pattern to when $P_C$ has a closed form versus when you have to solve it numerically?

I will create any kind of google form for $1

I will create any kind of google form

Hi all,

I will convert any file of DOCX, XLSX, PDF, JPG, other documents, etc to Google docs for $1 within just one day!

My service will include;

  1. Unlimited Revisions
  2. Free After Delivery Support

What I require to get started?

  1. Questionnaire or form field details
  2. Google E-mail address

Feel free to message me anytime with your queries.

Best regards.


rigid analytic geometry – Why do Coleman functions form a sheaf?

In section 4 of Ammon Besser’s 2002 ‘Coleman Integration Using the Tannakian Formalism,’ he defines abstract Coleman functions, which we can describe roughly as those functions which arise by iterated integrals along the canonical path, or more in the spirit of the paper, as matrix elements of parallel transport in unipotent fancy local systems (overconvergent isocrystals). The datum definining an abstract Coleman function on X is if you’d like, a unipotent isocrystal V, a point $x in X$, an element of the fiber: $v in V_x$, and a global section of the dual: $s in mathop{Hom}(V, mathcal{O}_X)$ and we think of the resulting function $f_{x,V,e,s}(y)$ as the formal evaluation of $y mapsto s(mathop{ParallelTransport}^V_{x to y} (v_x))$.

Details I am leaving to the paper:

  • the flavour of rigid analytic space
  • the flavour of isocrystals

But there is one subtlety which I want to bring out: the unipotence of $V.$ This is what connects these expressions to iterated integrals of finite length.

Proposition 4.21 seems to prove that these Coleman functions form a sheaf, which it does by introducing at 4.16-19 the notion of a minimal abstract Coleman function (the local system is as small as possible), and the uniqueness of these. We then show that we can glue abstract Coleman functions by appealing to this uniqueness, which also glues the isocrystals.

But wait! Unipotence isn’t a local property. If it were, every local system would be (locally trivial => locally unipotent, surely).

So I have a few questions:

  • Do Coleman functions form a sheaf after all? Does 4.21 go through as written?
  • Is there a pleasant Tannakian description of the class of Coleman functions (i.e. as functions on some unipotent fundamental group)

Apologies if the question is nonsense, feel free to tell me so.

refs (both versions have identical numbering in this section):

database theory – Is this relation in Boyce-Codd’s Normal Form?

Assuming that each book has a different title, you are correct in thinking that the relation is not in BCNF.

In fact, the (only) candidate key of the relation is Book_title, so the functional dependency User_id -> User_name violates the definition of BCNF. Assuming that a cover of the dependencies are:

User_id -> User_name    (each user_id identifies a user with a certain name)
Book_title -> User_id   (each book can be borrowed only by a certain user)

a decomposition of the original relation in BCNF is:

R1(User_id, User_name)  with candidate key User_id
R2(Book_title, User_id) with candidate key Book_title

Can we create a Modern webpart to use as a List or Library form for all the lists/Libraries in SharePoint?(SPFX or Powerapp)

Can we create solution to use a web part as list form for all Lists and Libraries?

We should have select the List/Library name accordingly the fields should be loaded to submit.