## custom list – Restrict numbers in sequence

I have a text box in a New Form (list) on SharePoint 2013 and I am looking for it to recognize (assuming using column validation) 8 and/or 16 digits in sequence and provide a warning that this is not allowed as either a pop up or text alert below the text box.

Essentially looking to restrict account numbers from being entered into the sharepoint with other text. Example : process reversal of fee on account 12345678 – (this should initialize a warning or restriction) and allow the submitter to change to only include the last 4 digits.

Any thoughts or way of doing this?

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## elementary set theory – When does a set sequence admit a limit?

Let $$(X,d)$$ be a metric space, let $$B_n subset X$$ be a set sequence in $$X$$, then we say that $$B_n$$ has a limit $$B$$ if
$$B=limsup_{nto infty}B_n=liminf_{nto infty} B_n$$
where $$limsup_{nto infty}B_n=cap_{k=1}^infty cup_{j=k}^infty B_n$$ and $$liminf_{nto infty}B_n=cup_{k=1}^infty cap_{j=k}^infty B_n$$.

QUESTION Are there sufficient conditions on the sets $$B_n$$ such that a limit set $$B$$ exists?

I would be tempted to say that a sufficient condition is the following: $$forall xin B$$ there exists $$n_x$$ and a sequence $$(x_n)_{ngeq x}$$ such that $$x_n in B_n$$, for $$n=n_x,n_x+1,ldots$$, and $$d(x_n,x)to 0$$. However this can be true only in the case where the set theoretical definition of limit set also admits a topological characterization, which may fail to be true.

For example, in the trivial case of $$X=mathbb{R}$$ and $$d$$ the Euclidean metric, we could choose $$B_n={1/n}$$ and have $$B_{n}cap B_{n+k}=emptyset$$, for any integer $$kgeq 1$$, thus $$liminf_{nto infty}B_n =emptyset$$; consequently, defining $$B={0}$$, we would have that $$Bneq liminf_{nto infty}B_n$$, whence we could not conclude $$B=lim_{ntoinfty}B_n$$ even if the choice $$x_n=1/n$$ satisfies $$x_nin B_n$$ and $$x_n to 0$$.

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## Problem

We are given 2 arrays `a` and `b` both of length `n`. We build a third array `c` by rearranging the values in `b`. The goal is to find the optimal `c` that maximizes

``````result = (a(0) ^ c(0)) & (a(1) ^ c(1)) & ... & (a(n - 1) ^ c(n - 1))
``````

where `^` is XOR and `&` is AND.

Is it possible to do this efficiently? It’s straightforward to iterate through all possible permutations of `b`, but this is infeasible for large `n`.

## More details

• The order of the values in `a` is fixed.
• The order of the values in `b` may be rearranged to form `c`. That is, starting with `b = (1, 2, 3)`, it may be that the maximum result is obtained when the values are rearranged to `c = (2, 1, 3)`.
• `b` may be rearranged in-place if needed.
• Since the optimal `c` is not necessarily unique, any optimal `c` may be returned.
• Assume all values are 32-bit unsigned integers.
• `1 <= n <= 10,000`.

## Test cases

``````Input:
a = (3, 4, 5)
b = (6, 7, 8)
Output:
c = (8, 7, 6) (result = 3)
``````
``````Input:
a = (1, 11, 7, 4, 10, 11)
b = (6, 20, 8, 9, 10, 7)
Output:
c = (8, 6, 10, 9, 7, 20) (result = 9)
``````
``````Input:
a = (0, 1, 2, 4, 8, 16)
b = (512, 256, 128, 64, 32, 16)
Output:
c = (16, 32, 64, 128, 256, 512) (result = 0)
``````

## Prove, that DFS produces the correct Topologically ordered sequence

I am having a hard time understanding the question itself. Should I prove the correctness of DFS?Should I use the pseudocode?

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## unity png sequence animation chaning position in animation

We are making frame by frame animation and we have a canvas size for animation. Attack animation is changing position in canvas. In unity after attack animation completed it teleports back to the initial position. I tried setting animation event and updating parent position but it does not work.it teleports to nonsense locations like player is looking at +x but it teleports to -x. Anybody have solution for this ? since it is not rigged root motion is not working

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## prove that a sequence whose range is relatively compact admits a convergent partial sequence

I need help with this demo please.
prove that a sequence whose range is relatively compact admits a convergent partial sequence.
the truth is that I have looked for information but I can not

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## Sum of a sequence that has an answer, but I can’t get that answer by hand

Find n if

$$a_1 = 4$$

$$r = -4$$

$$S_n = 13108$$

Using the formula

$$S_n = frac{a_1(1 – (r)^n)}{1 – r}$$ I would have

$$13108 = frac{4(1 – (-4)^n)}{5}$$

$$65540 = 4(1 – (-4)^n)$$

$$16385 = 1 – (-4)^n$$

$$16384 = -(-4)^n$$

$$-16384 = (-4)^n$$

I can’t take the log now though because I have negatives! I know the answer is 7 because if I plug in n = 7, I do get the desired result. However, I’m not sure how to get this by hand. Can someone please clear this up?

## solution verification – Is my proof correct about the limit of this sequence?

If $$0 and $$u_{n+1}=1-sqrt{1-u_n}$$ for $$ngeq 1$$,prove that the sequence$$(u_n)$$ converges to 0.

My attempt:

First prove that $$0 by induction.
Base case: $$n=1$$, $$0 holds true.
Assume $$0.
By manipulating a bit I got $$0<1-sqrt{1-u_n}<1$$ that is $$0
Thus by induction $$0 holds true.(*)

Now

$$u_{n+2}-u_{n+1}$$=$$({1-u_{n}})^{1/2}-({1-u_{n}})^{1/4}<0$$
Thus,$$u_{n+2}
Thus, sequence is monotonic decreasing. (**)

By (*) and (**) we have,

$$0
Thus by monotone convergence theorem the sequence converges to 0.
Is this correct?

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## at.algebraic topology – Boundary map in Mayer-Vietoris sequence of cohomology

Suppose $$M$$ is a 3-manifold with connected boundary. Let $$T$$ be a tangle in $$M$$, i.e., $$T$$ is a embedded connected 1-submanifold whose boundary is on $$partial M$$. Moreover, suppose $$T$$ represents a torsion element in $$H_1(M,partial M;mathbb{Z})$$. Suppose $$M_T=M-N(T)$$ is the tangle complement. Consider the boundary map $$delta_*:H^1(M_Tcap N(T);mathbb{Z})to H^2(M;mathbb{Z})$$ from the Mayer-Vietoris sequence associated to $$(M,M_T,N(T))$$. We have $$H^1(M_Tcap N(T);mathbb{Z})cong H^1(S^1times I;mathbb{Z})congmathbb{Z}$$. What’s the image of $$delta_*$$? I guess it is generated by the Lefschetz (Poincare) duality of $$(T)in H_1(M,partial M;mathbb{Z})cong H^2(M;mathbb{Z})$$.

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## authentication – Is Windows+L a secure attention sequence?

Ctrl+Alt+Del is a secure attention sequence (Microsoft) (or secure attention key (Wikipedia), but it’s more a Linux term).

As we can read,

A key sequence that begins the process of logging on or off. The default sequence is CTRL+ALT+DEL.

it is only the default sequence, which means that other sequences might exist. In an answer to a related question, we can read that Win+Pwr is also a SAS, at least on some devices.

I’ve been using Win+L to lock my desktop, since I find it easier to use, and I even recommend that to other people. For my own research, this combination cannot be registered as a hotkey either. But: I have no official documentation on it.

So, is Win+L a secure attention sequence?

I have seen previously linked questions and

• How does CTRL-ALT-DEL to log in make Windows more secure? (ServerFault)
• some code from 2010 where it might have been possible to bypass the combination, but it does no longer work on Windows 10 20H2
• the flag LLKHF_INJECTED in KBDLLHOOKSTRUCT, which makes me believe that Windows can distinguish between physical and simulated keypresses, explaining why the code might not work any more
• I am aware of the Registry key `DisableLockWorkstation` in `HKEY_LOCAL_MACHINESoftwareMicrosoftWindowsCurrentVersionPoliciesSystem`, but that would affect Ctrl+Alt+Del as well
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