real analysis – Area of a decreasing positive function

Suppose we have a decreasing positive function from 0 to infinity. Now suppose that it starts from somewhere on the y axis, something like f(0)=a, where a is a positive real. Can we say that the area of the function (its integral from 0 to infinity) will be finite and not diverge to infinity if it does not drecrease “fast enought”. Trying to use series convergence theorems to infer an answer based on the discrete domain but can’t find anything there that would give a clear answer.

dnd 5e – DoIP Dragon Barrow Area D5 – how is this not a likely TPK?

I’m running Dragon of Icespire Peak, and my players have encountered the Dragon Barrow.

This question relates to the mechanics of a specific part of the quest, so I’ve liberally used spoiler blocks to avoid spoiling this for any players of the campaign who might find this question.

If you’re playing DoIP in any group (not just my players), don’t read this question or the answers.

Section D5 is described as (emphasis mine):

This tunnel is only 2 feet wide. At the halfway point, a 5-foot-long pressure plate is hidden under a 2-inch-thick layer of earth. A character prodding ahead with a pole or similar tool can detect the plate with a successful DC 10 Wisdom (Perception) check. The first character to step on the plate causes the walls of the tunnel to collapse inward, burying all creatures in the tunnel. A buried creature is blinded and restrained, has total cover against attacks, and begins to suffocate when it runs out of breath (see “Suffocation” in the rulebook). Only a creature that is not trapped in the tunnel can clear away the collapse, using an action to open up the 5-foot-deep section of tunnel closest to it. A creature in that space is no longer buried.

Given that

the tunnel is 50′, this means that the trap is 25′ down the tunnel. The trap buries all creatures in the tunnel, so given it seems normal to assume that the PCs follow fairly close behind each other, this would mean all the PCs are caught, unless they explicitly say only one or two characters go down the tunnel and the rest stay in the room.


Only a creature that is not trapped in the tunnel can clear away the collapse, therefore if the party are all in the tunnel (which seems likely), there will be a TPK because no-one is left to dig them out

Am I missing something, or is this likely to lead to a TPK, with no particular warning for the players?

Obviously as DM I can overrule and say that

the PCs left an unusually large gap between each other and so only some of the PCs are in the tunnel if/when it collapses
or say the last player jumps out of the tunnel (I could ask for a DEX save, but at that point they can’t afford to fail it, so I’d probably rule they get free even on a 1, and just take damage)

but nothing in the module as written suggests this. I suspect I’m missing something?

visas – What countries in the Schengen area accept US travel document (form I-571)

I’m planning a trip to Europe this summer (Italy, Spain and Portugal) and will be using my travel document (Form I-571) that I have based on asylum from Syria. I had a visa appointment at the Spanish consulate today and was not able to submit the application as the officer mentioned that Spain does not recognize refugee/asylee travel documents.

This wikipedia page mentions that Spain accepts U.S. travel documents, however, I’ve read other sources that site the opposite such as this thread. Do you know which countries accept a travel document (with a Schengen visa) in 2019? I’d appreciate if you can include an official website, I’m having a hard time finding any.

What’s the best plugin for a members area with a membership

What’s the best plugin to create a membership for each user and then that member can view/edit and add their own information, maybe different pages for each category. Obviously each member when logged in can only see their own information.

Then as a bonus that member can add a nominee to sign up and view their information as well.

dnd 5e – Does Dim Light created by an effect override Bright Light in an area?

Unless the spell, item, ability, etc mentions it specifically changing the level of light in a area/radius, then I would say no, it does not change it. Just think about turning on a dim flashlight outside during the day. It is still emitting light, but it doesn’t make a difference. Now take that same light and go into a tunnel or cave and the dim light matters.

Here is an example of an ability changing the level of light:

The Oathbreaker paladin’s 20th-level Dread Lord feature:

At 20th level, the paladin can, as an action, surround himself or
herself with an aura of gloom that lasts for 1 minute. The aura
reduces any bright light in a 30-foot radius around the paladin to dim

And a spell:

Shadow of Moil:

The shadows turn dim light within 10 feet of you into darkness, and
bright light in the same area to dim light.

To clarify, though: For some spells or effects, such as the Twilight Domain’s Channel Divinity, it is possible to be in the area of dim light from a spell/effect and be affected by it even if you are in an area with bright light… Because magic in D&D does not follow our world’s physics to a T.

legal – Can holders of Israeli residence visas enter area A in the West Bank?

There is a great post about this exact issue on Quora. To answer your questions…

Since October 2000, a military warrant of a major general in the IDF central region command (Maj. Gen. Itzhak Eitan at the time) forbids Israelis from entering into the Palestinian Authority A areas (as designated in the Oslo accords).

The warrant is very short (1 page, Hebrew) and states that the area is “closed”: Israeli citizens as recognised by Israeli law, are forbidden from entering, and required to immediately leave if they are in that area. People who are “not citizens of the area, who have a standing visa to be in Israel” are not allowed to enter area A as well. (“מי שאינו תושב האיזור ובידו אשרת כניסה בתוקף לישראל” which may refer to foreign nationals, the language is vague)

So legally speaking the situation is not entirely clear. The military order itself is on shaky legal grounds and it’s not being systematically enforced:

The warrant was tested in Israeli courts and ruled to be one that can
be enforced (i.e soldiers may prohibit entry for an Israeli citizen),
though in April 2013 a civil court ruled that civilians failing to
comply with it are not to be arrested (after the fact).

On the ground, de facto, Israeli Arabs are not stopped at the
checkpoints and generally speaking, usually allowed to enter area A
without hindrance. Also tourists / foreign nationals are usually
allowed in. So, almost always, only Israeli Jews are turned back.

This means you should be okay, regardless of your current visa in Israel. If stopped by Israeli military personnel apologize and try again at another time. Also see our related question on visiting Palestine as an Israeli citizen.

P.S. A rough Google Translate of the linked military order from October 2000 can be found here.

cruising – Cruise ship in the Schengen area: How would the following add up

Given the following cruise scenario, how many days would be counted again a Schengen 90 day count?
DAY 1 Southampton UK
DAY 2 At Sea
DAY 3 Kirkwall, Orkney Islands (UK)
DAY 4 Tórshavn Faroe Islands (Denmark protectorate)
DAY 5 At Sea
DAY 6 Akureyri (Iceland)
DAY 7 Isafjörður (Iceland)
DAY 8-9 Reykjavik (Iceland) overnight
DAY 10-12 At Sea
DAY 13 Honningsvåg, Norway
DAY 14 Tromsø, Norway
DAY 15 Leknes, Lofoten Island (Norway)
DAY 16 Narvik (Norway)
DAY 17 At Sea
DAY 18 Trondheim (Norway)
DAY 19 Kristiansund (Norway)
DAY 20 Alesund (Norway)
DAY 21 Skjolden (Norway)
DAY 22-23 At Sea
DAY 24 Southampton (UK)

I am expecting every day from day 4 through day 21, i.e. first Schengen port to last, but if this can be confirmed I’d be most appreicative as we try to count the days for multiple vacations.

how can I make this metabox area

how can I make this metabox area

enter image description here

function bolumler_metabox()
    $screens = ('post', 'page');
    foreach ($screens as $screen) {
            'episodes',   // Benzersiz ID
            'Bölümler',       // Meta Box adı
            'bolumler_callback',       // Meta Box içeriğini bize gösterecek callback fonksiyonumuzun adı
            $screen                   // Yazı türü
add_action('add_meta_boxes', 'bolumler_metabox');

function bolumler_callback()

    global $post;
    $post_id = $post->ID;
    $meta_value = get_post_meta($post_id, 'episodes', true);
    Bölüm Sayısı Örnek 1.Bölüm:
        " id="episodes" />

    if (isset($_POST('episodes')) && !empty($_POST('episodes'))) {
        update_post_meta($post_id, 'episodes', $_POST('episodes'));
    } else {
        delete_post_meta($post_id, 'episodes');
add_action('save_post', 'bolumler_save');

linear algebra – Determinant: signed area of parallelogram question from Wiki

Wiki defines the determinant as follows and my question is if this definition is correct:

Signed Area = $|u||v| sin theta = |u^Gamma||v| cos theta’ = begin{bmatrix} -b \ a end{bmatrix} cdot begin{bmatrix} c \ d end{bmatrix} = ad – bc$, where $u = (a, b)$ and $u^Gamma = (-b, a)$ is of the complementary angle to a perpendicular vector.

Is this definition true? I use an example vector and the result differs in sign for the $sin$ equation between $-1$ and $1$. For instance:

$u = (0, 1), v = (1, 0), u^Gamma = (-1, 0)$

$|u||v| sin theta = 1*1*sin(frac pi 2) = 1$

$|u^Gamma||v| cos theta’ = |-1| * |1| cos(pi) = -1$

$begin{bmatrix} -b \ a end{bmatrix} cdot begin{bmatrix} c \ d end{bmatrix} = begin{bmatrix} -1 \ 0 end{bmatrix} cdot begin{bmatrix} 1 \ 0 end{bmatrix} = -1*1 + 0*0 = -1$

$ad – bc = 0*0 – 1*1 = -1$