Forms – Common input fields for registering and logging in with separate buttons

While working on the registration / login page for mine AppI came up with the idea of ​​combining the two into one. When you click Register, users are redirected to a new page where you can enter the rest of the details.

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I want to keep onboarding users as easy as possible. For example, using the traditional approach, users first see a login page. If you want to register, click on a Sign in instead Button that opens a new page.

By using my approach, users are saved by an additional click and a page load. But what are the advantages and disadvantages here?

Vector fields – Show that every solution $ G $ of the equation curl $ (G) = F $ has the form $ G = G_0 + nabla f $.

To let $ F $ be a magnetic field, that is, div $ F = 0 $in a simply connected domain $ D leq mathbb {R} ^ 3 $ and let $ G_0 $ to be a potential field of $ F $that is, lure $ (G_0) = F $. Show that every solution $ G $ of the equation curl $ (G) = F $ is in shape $ G = G_0 + nabla f $, where f is a scalar field.

With this div $ F = 0 $I have to share curl $ (G_0) = 0 $, but I don't know if that helps me.

Any idea?

Plotting – How do I compare and visualize two two-dimensional time-dependent vector fields?

Suppose we activated two 2D vector fields $ (x, y) $, $ boldsymbol {f} $ and $ boldsymbol {g} $that are defined by two InterpolatingFunction that received from NDSolve. I wonder what is the most efficient and sensible way to "compare" and visualize to show what effect represented by the fields is "larger" than the other in a given region $ (x, y) $ Plane?

For two scalars, the ratio of them can reveal their relative size. However, does it make sense to compare the norm of the two vector fields with a ratio of? $ || boldsymbol {f} || / || boldsymbol {g} || $, the outline should be on $ (x, y) $ Plane? Another challenge is that the fields are time-dependent, because I also want to show the change in their relative size over time.

Consider the following PDEs $ u (x, y, t) $ and $ v (x, y, t) $,

L = 4;
sol = NDSolve({D(u(t, x, y), t, t) == 
D(u(t, x, y), x, x) + D(u(t, x, y), y, y) + Sin(u(t, x, y)), 
u(t, -L, y) == u(t, L, y), u(t, x, -L) == u(t, x, L), 
u(0, x, y) == Exp(-(x^2 + y^2)), Derivative(1, 0, 0)(u)(0, x, y) == 0}, 
u, {t, 0, 4}, {x, -L, L}, {y, -L, L})

v,{t, 0, 4}, {x, -L, L}, {y, -L, L})

and these two vector fields

f = u(t, x, y)*Grad(v(t, x, y), {x, y}) + Grad(u(t, x, y), {x, y})

g = Grad(u(t, x, y), {x, y})*u(t, x, y)

Thanks in advance.

Website Design – How Many Input Fields on a Line of a Form?

If you really want columns in your forms

When designing forms with multiple columns, the following quick rule applies:

Double your font size and enter the largest realistic value that the input should accept. If it fits, your input is large enough.

The reason for this is that many people increase the font size in their browser and WCAG 1.4.4, although not entirely clear, suggests that this should allow an enlargement of up to 200%.

I'm not saying what it says as long as the page can be zoomed in, and this has always been a matter of controversy over what the rule actually means.

Even if this point is not clear, it is good practice.

Provided you use rem or em Units at 1rem / 1em, just adjust font-size: 200% In your HTML code, enter the longest realistic information you can think of (i.e., enter "" as the email address) if it suits you.

Since the font size is complex with Rems, Ems, etc., you can manually set the font size to 32 pixels with each input, as this is the equivalent. Also, don't forget to check your labels to see if they work.

If you find that there is still a lot of space left at the end, add another entry to the line if this makes sense.

A couple of additional considerations

Since this is labeled "Accessibility", make sure that the edge of your entrances has at least a 3: 1 contrast ratio to the surroundings. At first glance, it looks okay, but it is borderline.

One last thing to consider is, do items belong together? First name and last name do, but is the ID number related? I would be tempted to have the ID number on a different line.

Should you design forms with more than one column?

With all of this said, put an input on one line.

As soon as you start adding error messages, all of the above points fall apart (since error messages are usually longer).

Error messages still have to work with larger font sizes and usually become unclear if there are two or three columns.

Also, don't worry about vertical scrolling, it's common nowadays, and since a form ends with a submit button, users know when they have reached the end of their form (so you don't have to worry about people having fields miss.)

After I have created the first list of selection fields, I cannot look up these fields. How can I maintain data integrity and still link?

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8 – Check the visibility of paragraphs without fields

I am pre-processing a paragraph to add a custom form, but have visibility issues. I don't need fields in this paragraph.

If I just add the form to the paragraph, the entire paragraph is hidden from anonymous users.

function my_module_preprocess_paragraph__my_paragraph(&$variables) {
  $paragraph = $variables('paragraph');
  $form = Drupal::formBuilder()->getForm('Drupalmy_moduleFormMyCustomForm');
  $variables('content')('form') = $form;

However, if I add a title field to this paragraph, everything will be displayed well. Is there a way to view the form without having to add fields?

Intuition – topologically equivalent to conjugate fields

Two fields $ f: U subseteq mathbb {R} ^ n to mathbb {R} ^ n $, $ g: V subseteq mathbb {R} ^ n to mathbb {R} ^ n $ are continuously differentiable in their respective areas topologically conjugated if there is a homeomorphism $ h: U to V $ so for everyone $ t $ we have
$$ varphi_t = h ^ {- 1} , phi_t , h $$
Where $ varphi $ and $ phi $ are the respective streams of $ f $ and $ g $. The fields are topologically equivalent if there is a homeomorphism $ h: U to V $ that takes tracks from $ f $ in lanes of $ g $ and does not change the direction of the orbits.

My lecture notes state that the conjugation is strong and the equivalence is weaker, but 1) the only difference I see is that the conjugation may not keep the direction of the orbits and 2) the equivalence (?) Implies conjugation , so the conjugation is weaker

Can someone clarify?

Thank you so much!