## sharepoint online – Why user who is defined inside the Access Request can not approve pending access requests

We have a modern team site and inside the access request we define a user, as follow:-

now this users is defined inside the related office 365 group members, and he have a Member role, as follow:-

Now the user will receive access requests, but when the user try to approve/reject the requests the user will get Access Denied Error? any advice ?

Thanks

## magento2.3.4 – The PayPal gateway rejected the request. User authentication failed

We recently have signed up with PayPal PayFlow Pro to accept recurring payments. When we were connected to PayPal (just plain simple) , things were working fine. Since we have migrated to Payflow Pro, we are unable to connect to it. Error is “The PayPal gateway rejected the request. User authentication failed”. I can see correct API username and password being passed to PayPal. In the log files I see
‘response’ =>
array (
‘RESULT’ => ‘1’,
‘RESPMSG’ => ‘User authentication failed’,
),

and
main.CRITICAL: PayPal gateway errors: User authentication failed. {“exception”:”(object) (Exception(code: 0): PayPal gateway errors: User authentication failed. at /home/amibook/public_html/vendor/magento/module-paypal/Model/Api/PayflowNvp.php:650)”} ()

and
Trace: #1 MagentoPaypalModelApiNvp->call(‘SetExpressChecko…’, array(‘TENDER’ => ‘P’, ………… ‘BUTTONSOURCE’ => ‘Magento_Cart_Com…’)) called at (vendor/magento/module-paypal/Model/Api/Nvp.php:833)

We are using Magento CE 2.3.4. Any help will be really appreciated.

## reference request – Graph theory from a category theory perspective

Are there any textbooks on graph theory written for a category theorist?

It would probably have to be on directed graph theory, but if there’s some trick we can use to talk about undirected graphs as well that would be interesting.

A little more specifically, I’m looking for a text that begins by defining directed graphs and paths, then defines the obvious category out of a given directed graph with paths as arrows, then proceeds to derive results about directed graphs using these categories.

Most connections I see made between category theory and graph theory are in the other direction, taking the underlying graph of a category and saying something about it to derive a result about the category, but as someone comfortable with categories and not comfortable with graphs this approach isn’t particularly illuminating.

Further, unless I’m mistaken, these constructions amount to an equivalence (maybe even an isomorphism?) between the category of directed graphs and the category of categories, so it feels like we should be able to say something about directed graphs from this perspective.

Any references are appreciated.

## reference request – Optimization approaches to solving PDEs

In modern numerical methods, a PDE is often recast into the form of a variational problem, which is sometimes equivalent to a minimization problem.
However in my courses on numerical analysis (say, finite element methods) the focus is not (apparently) on developing optimization techniques to minimize the arosen energy functional, but rather on approximating the variational problem on a smaller subspace.

Are there interesting approaches that focus on the minimization of the energy directly? Is research being done in this field, and could you maybe provide some reference?

## reference request – Product of Besov and Lorentz functions

Let us fix $$ninmathbb{N}^+$$ and $$p,qin (1,infty)$$. Given $$r_1,r_2,r_3in(1,infty)$$, I would like to understand whether we have the bound
$$|fg|_{L^{q,r_3}(mathbb{R}^n)}lesssim |f|_{B^{n/p}_{p,r_1}(mathbb{R}^n)}|g|_{L^{q,r_2}(mathbb{R}^n)}quad(*),$$
where $$B$$ and $$L$$ denote respectively Besov and Lorentz spaces.

For example, $$(*)$$ holds when $$r_1=1$$ and $$r_2leq r_3$$, due to the embeddings $$B^{n/p}_{p,1}(mathbb{R}^n)hookrightarrow L^{infty}(mathbb{R}^n)$$ and $$L^{q,r_2}(mathbb{R}^n)hookrightarrow L^{q,r_3}(mathbb{R}^n)$$. When $$r_1>1$$, $$B^{n/p}_{p,r_1}(mathbb{R}^n)$$ fails to embed in $$L^{infty}(mathbb{R}^n)$$, but it is conceivable that (*) holds for suitable choices of $$r_2. This may follow by some (generalized) Moser-Trudinger inequality for $$B^{n/p}_{p,r_1}$$ combined with product estimates in Orlicz/Lorentz spaces, but I have been unable neither to come up with a proof nor to find a reference.

Does estimate $$(*)$$ actually hold for some $$(r_1,r_2,r_3)$$ with $$r_1>1$$ and $$r_2? In case, does there exist some reference for this kind of bounds?

## reference request – Finitely-generated conjugation action on a subgroup that is not normal… what is that?

If $$H lhd G$$, then $$G$$ acts on $$H$$ by conjugation. I need to talk about this action but in a situation where $$H$$ is not (necessarily) normal. When $$H leq G$$, there is a “partial action” of $$G$$ on $$H$$ by $$G$$-conjugation, and clearly it has very nice properties, for example $$h^g h^{g’} = h^{gg’}$$ and $$(hk)^g = h^g k^g$$ when these expressions are defined. To my amazement (at how bad I am at searching), I did not find a discussion of this anywhere. I’m sure it is very standard, and I’m looking for some pointers for a good formal setting.

Question. Is there a good basic reference for the “partial conjugation action” of a group on a subgroup, in some formalism? Is there a standard way to talk about this object?

I know many ways to talk about partial actions, and I can specialize them to my case, so in theory I can solve this question in many ways myself. However, it seems like such a natural example of a partial action that the fact I am not finding this discussed anywhere suggests to me that I may be missing something, so a reference or situation where this appears would be nice.

A more serious problem that tripped me up is “generation”. In many of the settings of partial actions, it is difficult to state that a partial group action is finitely-generated. If $$G = langle S rangle$$, then the partial actions given by partial conjugation by $$s in S$$ on a subgroup $$H leq G$$ obviously “generate” the partial action of $$G$$ in some sense. But I don’t really know how to say this in a good way, especially I run into issues with domains, when trying to state write down the axioms, and I don’t want to reinvent the wheel.

More specifically, it is natural enough to say that a group action $$G curvearrowright H$$ is finitely generated when $$G$$ is, so…

Question. Is there a standard way to say a “partial group action” is “finitely-generated”, so that in the case above of a finitely-generated group $$G$$ partially acting on its subgroup $$H$$ by conjugation, the partial action of $$G$$ would indeed be finitely-generated?

I tried to look at some existing formalisms for partial actions. One thing you can do is form the action groupoid of $$G$$ acting on itself by conjugation, so take the action groupoid with $$Gamma = G$$ acting group, $$Omega = G$$ the set where it acts, then take the subgroupoid for the restriction $$H subset Omega$$. Unfortunately then it is a bit awkward (I think) to discuss individual partial bijections that may or may not end up being part of such an action (they should of course be “partial automorphisms”, but the list of axioms does not seem to be suggested by the subgroupoid definition). It is also not obvious to me how to state finite generation correctly. Groupoidification drops the group, and after taking the subgroupoid corresponding to $$H$$, it might not even be determined up to isomorphism, so when you say that a groupoid of partial automorphisms on $$H$$ is finitely-generated, there is no $$G$$ this could possibly refer to. Furthermore a “finitely-generated groupoid” seems to usually have a finite number of objects, so this doesn’t look correct.

I then thought of pseudogroups, but all pseudogroup references I found deal with pseudogroups of homeomorphisms, and discuss mostly orthogonal issues. By any definition of a pseudogroup I could find, an action by partial automorphisms is not really a pseudogroup (unless I introduce some topological structure that I’m not going to use). Furthermore, I did not find a discussion of finite generation that tells me what I should do with domains.

There is also literally the notion of a partial action of a group. I thought of this last because I had never actually seen this before (people I know only talk about groupoids), but this was maybe the most promising formalism. I guess I would like to discuss the representations of groups by the “inverse semigroup of partial automorphisms of a group”, but I don’t know the jargon, and at least based on a brief look I did not find a notion of finite generation with the correct properties.

## timeout – aiohttp request times out when using a proxy, but is fine when i run without a proxy

I am attempting to scrape a site using a proxy in aiohttp with asyncio but whenever I run the code with a proxy it times out. I have removed the proxy from the code because it is a DC proxy. Does anyone know why my request would be timing out? It does work when I run without a proxy.
code:

``````import aiohttp
import asyncio
import random

async def fetch(session,):
UAList = ('Mozilla/5.0 (Macintosh; Intel Mac OS X 10_15_5) AppleWebKit/605.1.15 (KHTML, like Gecko) '
'Version/13.1.1 Safari/605.1.15',
'Mozilla/5.0 (Windows NT 10.0; Win64; x64; rv:77.0) Gecko/20100101 Firefox/77.0',
'Mozilla/5.0 (Macintosh; Intel Mac OS X 10_15_5) AppleWebKit/537.36 (KHTML, like Gecko) '
'Chrome/83.0.4103.97 '
'Safari/537.36',
'Mozilla/5.0 (Macintosh; Intel Mac OS X 10.15; rv:77.0) Gecko/20100101 Firefox/77.0',
'Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) '
'Chrome/83.0.4103.97 Safari/537.36', )
# chooses a random User Agent(From the list above) for the header
rUserAgent = random.choice(UAList)
'accept': 'text/html,application/xhtml+xml,application/xml;q=0.9,image/avif,image/webp,image/apng,*/*;q=0.8,'
'application/signed-exchange;v=b3;q=0.9',
'accept-encoding': 'gzip, deflate, br',
'accept-language': 'en-US,en;q=0.9',
'cache-control': 'max-age=0',
'sec-fetch-dest': 'document',
'sec-fetch-mode': 'navigate',
'sec-fetch-site': 'same-origin',
'sec-fetch-user': '?1',
'user-agent': rUserAgent
}

proxy = 'http://'
url = 'http://www.yeezysupply.com/product/GY7657'
assert resp.status == 200
return await resp.text()

async def main():
conn = aiohttp.TCPConnector()
async with aiohttp.ClientSession() as session:
html = await fetch(session)
print(html)

policy = asyncio.WindowsSelectorEventLoopPolicy()
asyncio.set_event_loop_policy(policy)
loop = asyncio.get_event_loop()
loop.run_until_complete(main())
``````

## How to only return last api request (ReactJS)

Alternating between the 2 buttons will display first names or last names, but pressing them together really fast will chain requests and will combine the two. How can I make create a check, and only display the names from the button that was pressed last

``````export default function App() {
const (name, setName) = useState();

return (
<div className="App">
<button onClick={() => setName("first_name")}>1</button>
<button onClick={() => setName("last_name")}>2</button>
<Users name={name} />
</div>
);
}
``````
``````export default function Users({ name }) {
const (users, setUsers) = useState(());

useEffect(() => {
setUsers(());

axios({
method: "GET",
url: `https://reqres.in/api/users?delay=1`
})
.then((res) => {
const allUsers = res.data.data.map((user) => <p>{user(name)}</p>);
setUsers((prev) => (...prev, ...allUsers));
})
.catch((e) => {
console.log(e);
});
}, (name));

return <div className="Users">{users}</div>;
}
``````

## reference request – Proof of Denjoy-Riesz Theorem and Moore’s Generalization?

The Denjoy-Riesz Theorem states that any zero-dimensional subset of the plane can be covered by an arc, i.e. an embedded image of $$[0,1]$$. Sometimes it’s stated just for covering a Cantor Set, and there’s also a generalization by Moore and Kline:

If $$M subset mathbb{R}^2$$ is compact, then it’s contained in an embedded arc if and only if each component of $$M$$ is a point or a simple arc $$A$$ such that if $$x in A$$ is a limit point of $$M setminus A$$ then $$x$$ is an endpoint of $$A$$.

Does anyone know a modern reference for the Denjoy-Riesz Theorem?

Either a book, or a paper giving some modernized proof. I don’t mind if it’s just the Cantor Set version. It’s not in Arkhangel’skii or Novikov. The only two sources I’ve ever seen this proved in are Kuratowski’s tome, where it’s derived from a mountain of other theory that’s only tangentially related, or in Moore’s paper which is nearly unreadable. It references many technical results from a previous paper, and together it’d probably be 20 pages of math just for this one theorem.

Has anyone ever encountered this theorem in a book with a proof?

## reference request – Equivariant smooth approximation

Suppose we have a compact manifold $$M$$ with the action of a compact group $$G$$. Consider the space of $$C^l$$ $$G$$-equivariant diffeomorphisms $$text{Diff}_G^{l}(M)$$ with the $$C^l$$ topology and the space of $$C^infty$$ $$G$$-equivariant diffeomorphisms $$text{Diff}_G^{infty}(M)$$ with the $$C^infty$$ topology.

Then is the inclusion $$text{Diff}_G^{infty}(M) hookrightarrow text{Diff}_G^{l}(M)$$ a homotopy equivalence? If so what is a good reference where the proof is spelt out?