dnd 5e – Can a gargantuan creature be shoved into a demiplane using polymorph and released into a different plane of existence

For context, my party is going to face a gargantuan (20 by 20 ft. or larger) creature with obscene levels of health, so would it be possible to make a demiplane and polymorph the gargantuan creature down to size and then shove it into the demiplane, trapping it there.

This spell transforms a creature that you can see within range into a new form. An unwilling creature must make a Wisdom saving throw to avoid the effect. The spell has no effect on a shapechanger or a creature with 0 hit points.
The transformation lasts for the duration, or until the target drops to 0 hit points or dies. The new form can be any beast whose challenge rating is equal to or less than the target’s (or the target’s level, if it doesn’t have a challenge rating).

After trapping it there, would it be possible to release it in, let’s say, Hell or just a ‘void’?
This is saying that the creature has utilised everything it can to resist magic and it is shoved into the demiplane.

This is saying that the creature has utilised everything it can to resist magic and it is shoved into the demiplane.

logic – Does the existence of Gödel universal functions make the S-m-n theorem unnecessary?

The problem of deciding, for any $x$, whether $phi_x$ is a constant function, is undecidable. I came across the following proof of this fact in Rogers’ book:

enter image description here

To me, it looks too bulky and unnecessarily complicated (things like the unnecessary (I think) use of the S-m-n theorem, the introduction of this weird function $gh_1$…). I think if one uses the existence of a Gödel universal function, it makes the proof much more clear (and shorter). Namely, define the partial function $V:Ntimes Nto N$
by (see the definition of $K$ below) $$(q,x)mapsto 1 text{ if $qin K$} \ (q,x) text{ is undefined if $qnotin K$}$$ This is a computable function by the Church-Turing thesis (a program that computes it would accept a pair $(q,x)$ (if this pair is coded as one number, it would decode it), run $phi_q(q)$; if it stops, the output would be one; if not, then it would run forever). Now let $U$ be a Gödel universal function. Then there exists a total computable $s:Nto N$ such that for all $q,tin N$, $$V(q,t)=U(s(q),t).$$ Now $K={q:phi_q(q)text{ halts}}$ is $m$-reduced to ${x:phi_xtext{ is constant}}$ via $s$. Thus the latter set is unsolvable.

If this proof is correct (is it?), it makes me wonder if one can forget about the S-m-n theorem and only remember the existence of Gödel universal functions. Is it some kind of archaic result? Another thing that make me think this way is that there exist textbooks in computation theory (more modern than Rogers’ book) which do not make any explicit mention of this S-m-n theorem, but they use these Gödel universal functions quite a bit.

co.combinatorics – Powerful existence theorems with mild conditions: more recent examples

I would like to write an article about powerful existence theorems that assert, under mild and simple conditions, that a minimum regular pattern always exists. By mild conditions I mean short, easy, broad conditions. By simple conditions I mean not requiring advanced mathematical education. The conditions and the statement should be accessible to undergraduate mathematics/science students.

I am interested mostly in low-dimensional examples which allow an easy graphical representation.

I have some obvious examples in mind (given below), but they are rather classical results that were established between 1900 and 1950, roughly speaking.
I would be interested to see examples that are more recent.

Classical examples I have in mind

(1) Lemma of Sperner and Brouwer Fixed Point Theorem (for $n=2$)

(2) Lemma of Tucker and Borsuk-Ulam Theorem (for $n=2$)

(3) Ramsey’s Theorem (for the simplest case of 6 edges)

(4) Wagner’s Theorem about Planar Graphs

I would be grateful if you could point me to more recent examples.

reference request – Existence of Analytic Continuation of Dirichlet Series Corresponding to the Indicator Sequence of a Complement of a Special Multiplicative Set

Let $K/ mathbb Q $ be a finite Galois extension and let $X$ be a proper non-empty subset of the Galois group $G=Gal(K/ mathbb Q)$ that is closed under conjugation. Consider a set of integer primes $P$ such that for all sufficiently large primes $p$, the following equivalence holds
$$p in P iff text{ the conjugacy class of the Frobenius element }sigma_p text{ is contained in }X$$

Now let $E$ be a multiplicative set of natural numbers (that is, for all coprime $m, n in mathbb N$, we have the equivalence $mn in E iff m in E$ or $n in E$) such that the set of prime numbers in $E$ is exactly the set $P$ above and let $E’ := mathbb N setminus E$ denote the complement of $E$. Consider the indicator sequence $(a_n)_{n geq 1}$ of $E’$ (so that $a_n := 1 iff n in E’$ and $a_n=0$ otherwise) and let $F(s) := sum_{n geq 1} a_n n^{-s}$ be the Dirichlet Series corresponding to the sequence $(a_n)_{n geq 1}$.

I want to show that the function $F$ analytically continues to a region of the form given in the image The Mentioned Region has been Coloured in Yellow. where $delta>0$ is fixed, the circle around the point $1$ is of radius $epsilon < delta$ and the infinite branches $C$ and $D$ are defined by
$$Re(s) = 1 – frac{a}{(log (2+|Im(s)|))^A}$$
(where $a$ and $A$ are fixed positive numbers, note that the interior of the circle has been excluded from the aforementioned region) such that in this region we have
$$F(s) = O((log |Im(s)|)^A) text{ as } |Im(s)| rightarrow infty$$

The only results of this kind I am somewhat familiar with are those on the analytic continuation of the usual Riemann Zeta Function (which I read in Apostol’s “Introduction to Analytic Number Theory”). Although I have obtained some other immediate observations (for instance: the natural and Dirichlet density of $P$ must both be $|X|/|G| in (0,1)$ by the Chebotarev Density Theorem and that the sequence $(a_n)$ should be multiplicative hence we can get something akin to an `Euler-Product’ representation of the Dirichlet Series $F(s)$), I have no general idea on how to get started on this problem and I would really a proof or a reference containing a complete (and preferably not too inaccessaible) proof of the same. Thank you.

P.S.: It says here (Continuation up to zero of a Dirichlet series with bounded coefficients) that a Dirichlet series with bounded coefficients need not be meromorphically continuable to the right of zero, but I haven’t found any positive results on M.O. in this direction.

real analysis – existence of a non-trivial zero curve

Look at the ring-shaped area $ mathcal {A}: = {(r, theta) in mathbb {R} ^ 2: 1 leq r leq 2 } $. Suppose that $ f: mathcal {A} rightarrow mathbb {R} $ is a smooth function satisfying $ f | _ {r = 1} <0 $ and $ f | _ {r = 2}> 0 $. Also assume that the zero amount of $ f $ is a collection of smooth curves. Is it true that there is a component of? $ {f = 0 } $ What winds around the origin?

comment: Continuity of $ f $ implies that on every curve that connects the outer boundary of $ mathcal {A} $ at its inner limit there is a zero of $ f $. However, only this observation does not imply the existence of a zero curve that winds around the origin.

Thank you so much!

alternative proof – Prove the existence of the nth roots for non-negative real numbers

I would like to prove the following result: "Let $ x, y geq 0 $ don't be negative real and let $ n, may 1 $ be positive integers. If $ y = x ^ { frac {1} {n}} $, then $ y ^ {n} = x $"This is Lemma 5.6.6 (a) from the Analysis 1 book by Terence Tao.

The nth root is defined as follows. $ x ^ { frac {1} {n}}: = $sup$ {y in mathbb {R}: y geq 0 $ and $ y ^ {n} leq x } $.

The following lemma was previously proven. ""$ textbf {Lemma 5.6.5:} $ "To let $ x geq 0 $ be a non-negative real and let $ n geq 1 $ be a positive integer. Then the set $ E: = {y in mathbb {R}: y geq 0 $ and $ y ^ {n} leq x } $ is not empty and is also limited at the top. Certain, $ x ^ { frac {1} {n}} $ is a real number. "

Given Lemma 5.6.5, we just have to show that $ y ^ {n} <x $ and $ y ^ {n}> x $ lead to contradictions. For example in the case where $ n = 2 $ and $ y ^ {2} <x $ we can find one $ varepsilon> 0 $ so that $ (y + varepsilon) in E $ only by expanding $ (y + varepsilon) ^ {2} $ and choose $ varepsilon $ reasonable, which contradicts the assumption that $ y = sup E $.

I am aware of how this result can be verified based on identity $ b ^ {n} – a ^ {n} = (b-a) (b ^ {n-1} + b ^ {n-2} a + … + a ^ {n-1}) $, which is used, for example, in Rudin's real analysis book or in the binomial theorem. However, I try to prove the result with just a few pointers in the textbook. The instructions are as follows:

1) Check the evidence that $ sqrt2 $ is a real number (the proof follows the exact outline above).
2) Evidence by contradiction.
3) The trichotomy of order.
4) Theorem 5.4.12

$ textbf {Proposition 5.4.12:} $ "To let $ x $ be a positive real number. Then there is a positive rational number $ q $ so that $ q leq x $and there is a positive integer $ N $ so that $ x leq N $. "

I tried to prove the result using only the four clues given above, but was unable to achieve anything. The four clues are given for the entire lemma, which consists of more than the above statement, so it is not clear that all clues should be used for this particular statement. Exponentiation properties for real numbers and integer exponents have been proven so far, so that these can be used in the proof.

There is a similar question here. Help with a lemma of the nth root (without the binomial formula), but my question is not answered there (and was not answered in any other similar post that I read).

My experiments focused on the following idea: Suppose $ y ^ {n} <x $. Then $ x-y ^ {n}> 0 $what implies the existence of $ q in mathbb {Q} ^ {+} $ so that $ q leq x -y ^ {n} $. We could also assume that $ 0 <q <1 $ to get $ q ^ {n} leq x-y ^ {n} $, although it is not clear to me that this helps. If we accept that $ (y + varepsilon) ^ {n} geq q ^ {n} + y ^ {n} $ for all $ varepsilon> 0 $, then we could get a contradiction by taking the limit as $ varepsilon $ tends to zero. However, limits will only be developed in the next chapter. Instead I tried to find it $ varepsilon $ directly, especially by trying to use hint number four without luck (I think all the messy attempts here would make a long post unreadable).

Any help would be appreciated. Please excuse the long post. Thank you to everyone who takes the time to read this post.

real analysis – existence of an integrable Lebesgue function with a counting measure that corresponds to the measure of the domain?

Is it true if $ m $ is a Lebesgue measure on $ (0.1) $ and the $ lambda $ is the count $ (0.1) $and both defined on the Lebesgue $ sigma $-algebra, then there is $ h in L ^ 1 ( lambda) $ so that $ m (E) = int_Eh , d lambda $?

I thought about it for a while now and went back and forth to make sure that it was true and then made sure that it wasn't !!! I would be very happy if someone would solve this problem for me !! Thank you so much!

Why do feminists and other SJW deny the existence of the Frankfurt School and its cultural Marxism theories?

"Why do feminists and other SJW deny the existence of the Frankfurt School and its cultural Marxism theories?"

Cultural Marxism stands for radical social change. Feminists TODAY still want us to believe that feminism in its current form is a simple advocacy for women and NOT a cultural Marxist ideology for radical social change.

If the majority of people really investigated what feminists are pushing for by adhering to cultural Marxism, most people would not support feminism because most people actually do not support Marxist cultural goals.

I will repeat the last bit. Most people do not support Marxist cultural goals.

And that's why all cultural Marxists hide their true identity and prefer to call themselves "progressive" or "social justice" or some other nonsense that doesn't really apply to what they do.

It really doesn't help that unconscious or unsuspecting self-proclaimed "feminists" come here to apologize for cultural Marxist feminists just because both share the name "feminist", but that only helps to fight for the truth.

.

stochastic processes – sufficient condition for the weak existence of a solution of an SDE

Please note that I am posting this question to each other from MSE as it is very likely to remain unresolved and I have not received an answer from my colleges / professors.

It is a known result from Skorokhod that when for the SDE:
$$ dX_t = b (t, X_t) dt + sigma (t, X_t) dW_t $$
the coefficients $ b (t, x) $ and $ sigma (t, x) $ are accepted continuously and limited then weak existence applies.

Regarding Ikeda & Watanabe's book (especially Theorem IV.2.3.), The authors state:

Given continuous coefficients $ sigma (x) $ and $ b (x) $ all the time
homogeneous) markovian type SDE

$$ dX_t = b (X_t) dt + sigma (X_t) dW_t $$ Then for every measure of probability
$ mu $ With compact support, there is a solution for the SDE, whose
The initial distribution matches $ mu $.

(Note that the resulting solution can be explosive, but this could be "solved" by assuming a quadratic integrability of the initial state and linear growth.)

I'm looking for more references to this particular result (which doesn't seem to be as well known). Neither Karatzas & Shreve nor Revuz & Yor seem to mention it. In the Cherny and Engelbert survey, they only mention the classic result of Skorokhod and the same thing happens at Strook & Varadhan.

I am therefore curious about this result, which Ikeda & Watanabe mentioned, which is less restrictive (although it only seems to apply to the homogeneous Markovian case).

Thanks in advance for any comment!

Javascript – Data existence error

Hello, when I requested to create a new instructor using the Post method to include the data in the database table, the following error occurs:

ReferenceError: date is not defined
    at post (/Users/thalesviniciusf/Desktop/launchbase/academia-bd/src/app/controllers/instructors.js:35:22)
    at Layer.handle (as handle_request) (/Users/thalesviniciusf/Desktop/launchbase/academia-bd/node_modules/express/lib/router/layer.js:95:5)
    at next (/Users/thalesviniciusf/Desktop/launchbase/academia-bd/node_modules/express/lib/router/route.js:137:13)
    at Route.dispatch (/Users/thalesviniciusf/Desktop/launchbase/academia-bd/node_modules/express/lib/router/route.js:112:3)
    at Layer.handle (as handle_request) (/Users/thalesviniciusf/Desktop/launchbase/academia-bd/node_modules/express/lib/router/layer.js:95:5)
    at /Users/thalesviniciusf/Desktop/launchbase/academia-bd/node_modules/express/lib/router/index.js:281:22
    at Function.process_params (/Users/thalesviniciusf/Desktop/launchbase/academia-bd/node_modules/express/lib/router/index.js:335:12)
    at next (/Users/thalesviniciusf/Desktop/launchbase/academia-bd/node_modules/express/lib/router/index.js:275:10)
    at Function.handle (/Users/thalesviniciusf/Desktop/launchbase/academia-bd/node_modules/express/lib/router/index.js:174:3)
    at router (/Users/thalesviniciusf/Desktop/launchbase/academia-bd/node_modules/express/lib/router/index.js:47:12)

POST method:

post(req, res) {
        var keys = Object.keys(req.body);

        for (key of keys) {
            if (req.body(key) == "") {
                return res.send("Preencha todos os campos!");
            }
        }

        var query = `
            INSERT INTO instructors (
                name,
                avatar_url,
                gender,
                services,
                birth,
                created_at
            ) VALUES ($1, $2, $3, $4, $5, $6)
            RETURNING id
        `

        var values = (
            req.body.name,
            req.body.avatar_url,
            req.body.gender,
            req.body.services,
            889326000000,
            date(Date.now()).iso
        )

        db.query(query, values, function(err, results) {
            console.log(err);
            console.log(results);
        });

    },

The numbers of the values They are a timestamp that I set up because I didn't script to convert the date placed on the form.