How do i create request number and save in sharepoint list?

How do I create a request number and save that request number in the SharePoint list?

fa.functional analysis – Reference request: sufficiently smooth functions on the plane belong to the projective tensor square of \$L^2\$ of the line

Let $$newcommand{ptp}{widehat{otimes}}ptp$$ denote the projective tensor product of Banach spaces. Some back of the envelope calcuations, using the Fourier transform and Plancherel/Parseval, suggest to me that the following should be true:
$$newcommand{Real}{{bf R}}$$

for some $$k > 1$$, every compactly supported $$C^k$$-function $$Real^2toReal$$ belongs to $$L^2(Real)ptp L^2(Real)$$.

(Recall that in contrast, there are continuous functions on $$(0,1)^2$$ that do not belong to $$C(0,1)ptp C(0,1)$$.)

If the claim above is true, I would like to know if there are standard references, perhaps from the world of integral kernel operators or Sobolev spaces, which I could cite, rather than reinventing the wheel (and probably getting suboptimal values of $$k$$).

In a slightly different direction, I would also be interested to know of references which prove analogous resuts for $$C^k$$ functions (suitably interpreted) on compact connected Lie groups.

upload image error "An Ajax http request terminated abnormally.." on Google Chrome [closed]

My website i use Drupal 7.69

I use Google Chrome Version 83.0.4103.61 (Official Build) (64-bit)

https://ibb.co/wR0wVr0

And click “Remove”

https://ibb.co/M9rj222

But i use Safari not have error.

Request: Looking for dedicated server in USA

Hi,
I am looking for dedicated server as per below, please PM me your offers. thanks

Location: USA
8-16 Core
48 to 128GB RAM

"Are you sure?" Request for confirmation modal usability research

1. A user is about to delete a crucial object with no undo.
2. The designer puts an “Are you sure?” modal confirmation.
3. The user says “Yeah yeah yeah do it”
4. Immediately the user regrets his/her decision and panics.

Clearly Undo would be great. But sometimes that is impractical.

Question:

• What public usability studies are there on this topic?
• Do users REALLY think about the question or do they just click Yes without thinking?

Thank you.

Package Request

Site URL: https://envyforums.net/
Package: Garnet
Total posts your site: 8 posts
Packager Preference: N/A
Preferred posting location: Anywhere but I’d prefer empty categories first if possible.
Do you permit our packagers to promote Forum Promotion on your site?: Yes
Extra Notes: Member less than a month so I think the package is free

reference request – A bounded extension operator

Let $$Omegasubsetmathbb{R}^n$$ be a bounded domain with smooth boundary $$partialOmega$$. Consider the harmonic extension operator $$E :L^2(partial Omega) rightarrow H^{1/2}(Omega)$$ which assigns to a prescribed boundary value $$g$$ a function $$f$$ with $$frvert_{partialOmega}=g$$ and $$Delta_Omega f=0$$.

Can $$E$$ be bounded from $$L^2(partial Omega)$$ into $$L^2(Omega)$$ as a right inverse of the trace operator? (or possibly another modification of $$E$$ or another extension operator).

Is there any explicit characterization of the range of $$E$$: $$mathrm{ran}(E):=E,L^2(partial Omega)$$?

Finally, any reference on some properties of such operator would be helpful.

facebook – I deleted a friend request and now I need to retrieve it again

I did not except a friend request by mistake. Now when I go to his page, it does not all me to add him as a friend. When he goes to my page, he can no longer add me as a friend either. Both of our settings are set for Everyone on & off Facebook can request our friendship. When I go into “Friend suggestions” and click “All”, we can no longer find each other under Friend suggestions. My question is, how can we friend each other again? I should have excepted his friend request but I clicked the wrong button and denied his request. Now we can no longer add each other as friends on Facebook. Help. Thank you

reference request – a square root inequality for symmetric matrices?

In this post all my matrices will be $$mathbb R^{Ntimes N}$$ symmetric positive semi-definite (psd), but I am also interested in the Hermitian case. In particular the square root $$A^{frac 12}$$ of a psd matrix $$A$$ is defined unambigusouly via the spectral theorem.
Also, I use the conventional Frobenius scalar product and norm
$$:=Tr(A^tB), qquad |A|^2:=$$

Question: is the folowing inequality true
$$|A^{frac 12}-B^{frac 12}|^2leq C_N |A-B|quad ???$$
for all psd matrices $$A,B$$ and a positive constant $$C_N$$ depending on the dimension only.

For non-negative scalar number (i-e $$N=1$$) this amounts to asking whether $$|sqrt a-sqrt b|^2leq C|a-b|$$, which of course is true due to $$|sqrt a-sqrt b|^2=|sqrt a-sqrt b|times |sqrt a-sqrt b|leq |sqrt a-sqrt b| times |sqrt a+sqrt b|=|a-b|$$.

If $$A$$ and $$B$$ commute then by simultaneous diagonalisation we can assume that $$A=diag(a_i)$$ and $$B=diag(b_i)$$, hence from the scalar case
$$|A^frac 12-B^frac 12|^2 =sumlimits_{i=1}^N |sqrt a_i-sqrt b_i|^2 leq sumlimits_{i=1}^N |a_i-b_i| leq sqrt N left(sumlimits_{i=1}^N |a_i-b_i|^2right)^frac 12=sqrt N |A-B|$$

Some hidden convexity seems to be involved, but in the general (non diagonal) case I am embarrasingly not even sure that the statement holds true and I cannot even get started. Since I am pretty sure that this is either blatantly false, or otherwise well-known and referenced, I would like to avoid wasting more time reinventing the wheel than I already have.

This post and that post seem to be related but do not quite get me where I want (unless I missed something?)

Context: this question arises for technical purposes in a problem I’m currently working on, related to the Bures distance between psd matrices, defined as
$$d(A,B)=minlimits_U |A^frac 12-B^frac 12U|$$
(the infimum runs over unitary matrices $$UU^t=Id$$)