functions – Path described by a body under action of a force


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sharepoint online – Restrict user to take action on flow approval

I am working on a solution where I am using Start approval and wait for the response action in my flow so with this user gets an email on outlook as well as a teams notification seeking approval.

Apart from this I have developed spfx webpart and user can approve the request from there as well and handled those scenarios in my flow.

But the only scenario I am not able to handle is, If user has approved it from the webpart then the action buttons on outlook and teams should give user an error.

Is there anyway to handle that?

applications – How can I select multiple recycler view items and delete them with the help of action mode, simple toolbar, I mean I can delete multiple items by this

applications – How can I select multiple recycler view items and delete them with the help of action mode, simple toolbar, I mean I can delete multiple items by this – Android Enthusiasts Stack Exchange

sharepoint online – Restric user to take action on flow approval

I am working on a solution where I am using Start approval and wait for the response action in my flow so with this user gets an email on outlook as well as a teams notification seeking approval.

Apart from this I have developed spfx webpart and user can approve the request from there as well and handled those scenarios in my flow.

But the only scenario I am not able to handle is, If user has approved it from the webpart then the action buttons on outlook and teams should give user an error.

Is there anyway to handle that?

fa.functional analysis – How to think action of orthogonal projection operator on Heaviside function of some operator?

Let $mathbb P_l$ stands for the orthogonal projection in $L^{2}(S^{n-1})$ on the space of $mathcal H_{n,l}$ of harmonic homogenous polynomial with degree $l$ in $n$ variable.
By spectral decomposition theorem of Laplacian on sphere we have
$$mathrm{Id}_{L^{2}left(mathbb{S}^{n-1}right)}=sum_{l geq 0} mathbb{P}_{l}, quad-Delta_{mathbb{S}^{n-1}}=sum_{l geq 0} l(l+n-2) mathbb{P}_{l}.$$

By writing Laplacian in polar coordinate we get
$$ r^{2} Delta_{mathbb{R}^{n}}=left(r partial_{r}right)^{2}+(n-2)left(r partial_{r}right)+Delta_{mathbb{S}^{n-1}}$$

Define $Lambda=sum_{k geq 1} k mathbb{P}_{k} $. By orthogonality we have
$$|x|^{2} Delta_{mathbb{R}^{n}}=left(r partial_{r}right)^{2}+(n-2)left(r partial_{r}right)-Lambda(Lambda+n-2).$$

Now take $r=e^t$ we get
$$|x|^{2} Delta_{mathbb{R}^{n}}=partial_{t}^{2}+(n-2) partial_{t}-Lambda(Lambda+n-2)=left(partial_{t}+Lambda+n-2right)left(partial_{t}-Lambdaright)=mathcal{L}$$
We note that for $lambda geq 1$
begin{equation}
mathcal{L}=|x|^{2} Delta_{mathbb{R}^{n}}, quad mathcal{L}_{lambda}=e^{-lambda t} mathcal{L} e^{lambda t}=mathcal{L}_{-, lambda} mathcal{L}_{+, lambda}=mathcal{L}_{+, lambda} mathcal{L}_{-, lambda}
end{equation}

Where begin{equation}
mathcal{L}_{+, lambda}=partial_{t}+lambda+Lambda+n-2, quad mathcal{L}_{-, lambda}=partial_{t}+lambda-Lambda.
end{equation}

Fundamental solution of differential operator $mathcal{L}_{+, lambda} mathcal{L}_{-, lambda}$ is given by
begin{align}
E=& H(lambda-Lambda)(2 Lambda+n-2)^{-1}left(e^{-(lambda-Lambda) t}-e^{-(Lambda+lambda+n-2) t}right) H(t)notag \ &-H(Lambda-lambda)(2 Lambda+n-2)^{-1}left(e^{-(lambda-Lambda) t} H(-t)+e^{-(Lambda+lambda+n-2) t} H(t)right)
end{align}

where $H$ is Heaviside function. i.e. begin{equation}
v=E *left(mathcal{L}_{+, lambda} mathcal{L}_{-, lambda} vright)
end{equation}

Now we wanted to estimate $left|mathbb{P}_{k} v(t)right|_{L^{p^{prime}}left(mathbb{S}^{n-1}right)}$.

For that purpose we write $F=mathcal{L}_{+, lambda} mathcal{L}_{-, lambda} v$.

By property of fundamental solution we have
begin{align*}
v(t)&=frac{H(lambda-Lambda)}{2 Lambda+n-2} int_{-infty}^{t}left(e^{-(lambda-Lambda)(t-s)}-e^{-(lambda+Lambda+n-2)(t-s)}right) F(s) d s\
&quad-frac{H(Lambda-lambda)}{2 Lambda+n-2}left(int_{t}^{+infty} e^{-(Lambda-lambda)(s-t)} F(s) d sright.\
&quadleft.quad+int_{-infty}^{t} e^{-(lambda+Lambda+n-2)(t-s)} F(s) d sright)
end{align*}

Now we apply $mathbb P_k$ to both side.

I can think that
$e^{-(lambda-Lambda)(t-s)}$ can be think as series of exponential in $Lambda$. so after applying $P_k$ to that we get
$e^{-(lambda-k)(t-s)}mathbb P_k$ because of orthogonality.

But I have doubt how to apply $mathbb P_k$ on $frac{H(lambda-Lambda)}{2 Lambda+n-2}$.

I thought about Fourier series of Heaviside function but there is problem about convergence and Heaviside on whole real line is not periodic function as such so I can not get Fourier series. Also how to apply on its denominator $2 Lambda+n-2$. Final expression is given as
begin{align*}
mathbb{P}_{k} v(t)&=frac{H(lambda-k)}{2 k+n-2} int_{-infty}^{t}left(e^{-(lambda-k)(t-s)}-e^{-(lambda+k+n-2)(t-s)}right) mathbb{P}_{k} F(s) d s\
&quad-frac{H(k-lambda)}{2 k+n-2}left(int_{t}^{+infty} e^{-(k-lambda)(s-t)} mathbb{P}_{k} F(s) d sright.\
&quadleft.quad+int_{-infty}^{t} e^{-(lambda+k+n-2)(t-s)} mathbb{P}_{k} F(s) d sright)
end{align*}

Any help or hint will be appreciated.

images – Hover action not working since adding custom CSS to make container responsive

I am making a grid where there is a background image and when the mouse hovers over the box, a solid color appears and text appears. See screenshot below.

I wanted to make the images responsive, so I added the following code:
.imageContainer {
position: relative;
padding-bottom: 25%;
width: 100%;
float: center;
height: 0;
margin-top: 10px;
margin-bottom: 10px;
margin-right: 10px;
margin-left: 10px;
}

The images are responsive now, but the hover action no longer works (no longer showing the solid color). The text is also not responsive, even if I add the CSS class imageContainer. In the image below, the box with the text should be showing the color #FF3333. I added the hover color change using Elementor.

enter image description here

dnd 5e – Is there a limit to how many allies can use the help action, to help you in combat?

With suitable timing, each help action grants advantage on one attack

As you’ve surmised, for this scheme to work all the helping creatures except the first one must ready actions with triggers of “after my ally’s first attack”, “after my ally’s 2nd attack” and so on, because if they all took the help action before your turn, then all the extra help would stack up on your first attack and be wasted, since multiple sources of advantage don’t stack. However, assuming you can organize all your helpers appropriately, there’s no reason that each help action can’t grant advantage on one attack, giving you advantage on as many attacks each round as you have helpers. Obviously at some point you could run into other limits such as the number of helpers able to get into melee range, but the vast majority of the time, the limiting factor will be the number of attacks you can make in one round.

Each help action grants advantage on the next attack

I’m claiming that each help action grants advantage on the next attack, but the wording of the help action doesn’t fully spell this out, so let’s think about it a bit. The relevant part is:

If your ally attacks the target before your next turn, the first Attack roll is made with advantage.

Which attack roll is the “first” one? It’s a bit ambiguous. Clearly it’s not the first attack roll of the campaign, and it probably doesn’t mean the first attack made by the ally during the current combat. That would make the help action mostly useless after the first round. Hence, the “first attack roll” must be implicitly referring to the first attack roll within a certain time period. The end of that period is given explicitly: it’s the start of the next turn of the creature taking the help action. But when does it start? The only start point that makes any sense is when the help action is taken. Hence, if multiple help actions are taken at different times using readied actions, they can grant advantage to different attacks made by the same creature during a single turn.

In other words, the wording above is equivalent to (addition in bold):

If your ally attacks the target before your next turn, the first Attack roll after you take the help action is made with advantage.

Presumably, the text doesn’t specify this explicitly because usually it doesn’t matter. The only time it would be ambiguous is if a creature readies a help action to be taken during another creature’s turn, which is a rare occurrence. And it is well established that 5e doesn’t try to spell out rare interactions in the rules, but instead expects the DM to handle them.

power automate – What format does the ‘Base Time’ field in the ‘Convert time zone’ action expect?

As shown in the screenshot below, the following timestamps format worked for me for onvertTimeZone(variables('TimestampYYYYMMdd'), 'Eastern Standard Time', 'UTC')

YYYY-MM-DD hh:mm:ss=> 2021-07-19 08:50:00 - Worked
MM/DD/YYYY hh:mm:ss => 07/19/2021 08:51:00 - Worked
YYYY-MM-DDThh:mm:ss.0000000Z => 2021-07-19T08:55:00.0000000Z - Worked

However, DD-MM-YYYY hh:mm:ss throws the error shown below

Unable to process template language expressions in action ‘Compose’ inputs at line ‘1’ and column ‘6070’: ‘In function ‘convertTimeZone’, the value provided for date time string ’19/07/2021 09:51:00′ was not valid. The datetime string must match ISO 8601 format.’

enter image description here

dnd 5e – Is Otto’s Irresistible Dance saving throw action compulsory?

Otto’s Irresistible Dance has following effect/end condition:

As an action, a dancing creature makes a Wisdom saving throw to regain control of itself. On a successful save, the spell ends.

I’m unsure how to interpret the indicative(?) mood “makes” here. Is this action optional, “can choose to make”, or is it compulsory, “is forced to make”, and why?

This’s QA suggests it is optional, but none of the answers explain why.

I haven’t cast the spell yet, and the DM may of course make their own ruling for this campaign, but I still want to know the correct RAW interpretation. None of us are native English speakers.

applications – “Complete action using” with duplicate app


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