## How to get a four letter Username

Hello there!
I found a nice four-letter Username on Twitter which is still available and which wasn't used before. I would really like to change my current Username to this 4-letter one. But on the Settings Page it shows "Username must be at least 5 characters". But I have seen people with less than 5 letters in there Username.
I tried contacting Twitter via Email () but I got a standart reply with "please use the Support Forms…

How to get a four letter Username

## (DnD5e) Feedback on homebrew: Monk – Way of the Four Elements

I don’t have too many friends in the RPG community that could give me some valid balance/playability etc feedback on such a thing, and was hoping the community here could. I’ve created a new version of the Monk-Way of the Four Elements, which gives a little more freedom and versatility to the class. That being said, I’m not certain how overpowered (if at all) I’ve made this. If your only feedback is to rewrite it so it sounds more fantastical, that’s cool too.

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## Nikon F mount for micro four thirds

I just bought a MFT Panasonic lumix gh3 and I have no lens for it. I found that I can put an adapter in order to use my Nikon lens.On the adapter it says : Nikon(G) to micro for thirds. I’m a little bit confused: I have two Nikons a FF an APS-C. I also use on the full frame a 50 mm D and on the APS-C a 35 mm G. But both of the bodyes has Nikon F mount. So in this case, can I use the adapter for my MFT lumix gh3 in ordr to use my Nikon lenses described earlier?

## Find four sets where each element from those four appears in at least two of those four sets

I have a list of sorted arrays (“sets”) of integers $$A_1..A_n$$ where each element is unique w.r.t. the other elements in the same array:

• $$A_i = \{x_{i,1}..x_{i,c_i}\}$$
• $$x_{i,p} < x_{i,p+1}$$

$$A_i$$ has length $$c_i$$ and the average of $$c_i << n$$. For example in one of the runs, the average $$c_i$$ ranged from $$10$$ to $$15$$ and $$n$$ from $$2000$$ to $$15000$$.

I want to find all combinations of four different arrays $$M=\{A_r,A_s,A_t,A_u\}$$, where each element that appears in any of the $$A$$‘s, appears in at least one of the other $$A$$‘s:

$$\forall A_i \in M: \forall x \in A_i: \exists A_{j \ne i} \in M: x \in A_j$$

Assuming that only a small number of the combinations $$\epsilon << n (<< O(n^4))$$ satisifies these requirements, is there a way to do this more efficiently than the obvious $$O(n^4f(c))$$? Here $$f(c)$$ is some reasonably small function in the average $$c_i$$.

It’s probably viable for me if it can be done in $$O(n^2c)$$ but not if it’s $$O(n^3c)$$.

If we consider the problem described so far to be the case with $$|M|=4$$, is there also an efficient algorithm for the case with $$|M|=3$$?

For the case with $$|M|=2$$, I can simply add each $$A_i$$ to a hash set after checking if another $$A_j$$ with the same values is already in the hash set, with expected time about $$O(nc)$$.

I’m also very interested in the cases where there’s up to $$y$$ cases of $$x_i$$ that appear in only one of the sets of $$M$$, where $$y = y’-|M|$$ and $$y’$$ is $$4$$ or $$5$$

## Four, go biking outfits. Wearing colorful outfits

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## Intersection Solutions of four nonlinear equations

I have four nonlinear equations I want to find the points of intersection of these equations, and I used the software Mathematica, unfortunately after many hours of waiting it does not give me any result Do you have an idea how to solve this kind of problem?.

My equations are the following

1) $$(52 \alpha ^2+\alpha (104 \beta +440 \sqrt{3}-1071)+\beta (65 \beta +110 \sqrt{3}-752)-2 (52 \gamma +55 \sqrt{3}-376) \delta +(-52 \gamma -440 \sqrt{3}+1071) \gamma -65 \delta ^2)=0$$

2) $$52 \alpha ^2+\alpha (-52 \beta +80 \sqrt{3}-450)+2 \beta (13 \beta +10 \sqrt{3}+38)-52 \gamma ^2+\gamma (52 \delta -80 \sqrt{3}+450)-2 \delta (13 \delta +10 \sqrt{3}+38)=0$$

3) $$\beta ^2-\alpha ^3=0$$

4) $$\delta ^2-\gamma ^3=0$$

## Elliptic curve over projective line with four points of multiplicative reduction

Consider the elliptic surface $$E$$ with affine equation

$$y^2 = x(x-1)(x-t^2)$$

over the base $$\mathbf{P}^1$$ with parameter $$t$$ (with complex scalar field). Then $$E$$ has four points of bad reduction, namely $$0$$, $$1$$, $$-1$$, and $$\infty$$. One can check that the reduction type is multiplicative at each bad place. Is this the only elliptic surface with multiplicative reduction at those four places? I understand that the condition of multiplicative reduction means that the corresponding local system has unipotent monodromy around each of the four bad points, but I don’t know how to use this to classify such elliptic surfaces.

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