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?

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 $x_n to 0$.

Maximize AND on a sequence of XORs

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)

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

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 $0<u_1<1$ 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 $0<u_n<1$ by induction.
Base case: $n=1$, $0<u_1<1$ holds true.
Assume $0<u_n<1$.
By manipulating a bit I got $0<1-sqrt{1-u_n}<1$ that is $0<u_{n+1}<1$
Thus by induction $0<u_n<1$ holds true.(*)

Now

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

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

$0<u_{n+1}<u_n<u_{n-1}……<u_1<1$
Thus by monotone convergence theorem the sequence converges to 0.
Is this correct?

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 $(T)in H_1(M,partial M;mathbb{Z})cong H^2(M;mathbb{Z})$.

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