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# SQT

what if (one of, not all) protons, neutrons or electrons stopped existing right now

How do I show that the cesaro operator is in lp space?I.e: If x=(xi)is in lp, then I want to show that (T(x))n=(x1+...+xn)/n is also in lp space.

a) binomial n=5, p=0.03 (although they don't say specify n)

b) from a)

c) exp(-5*0.03) * (5*0.03)^k / k!

All the atoms in every molecule are suddenly repulsed and everything flies everywhere, striking everything else that exists. The change in equilibrium of even the uniform and relatively sparse matter is agitated due to the force with which complex arrangements of matter are traveling, and gravity is overcome as matter dissipates into a universal soup with an unbelievably high ambient temperature

Can someone explains what happens here? How does he extract those functions and why does one equal 0 and the other 1?

Does Sphingomyelin have a built in fatty acid chain attached to the sphingosine? Like is the fatty acid chain actually part of the sphingosine instead of merely being bonded to it (like the other fatty acid chain, the kinked one that actually is)

Bitcoin was created by someone under a pseudonym right? How do we know bitcoins aren't just to trick us into giving a rogue AGI more and more processing power, and the AGI rewards us with magic internet money?

t. Schizophrenic

there isnt a reason someone would want the hashes used for cryptocurrency mining, they arent particularly meaningful beyond just being hard to calculate

How do I show that the cesaro operator is in lp space?I.e: If x=(xi)is in lp, then I want to show that (T(x))n=(x1+...+xn)/n is also in lp space.

u:=ln(x)

du=dx/x ==> dx=xdu ("u=ln(x) => x=e^u") ==> dx=e^u du

sin(ln(x)) dx ==> sin(u) e^u du

The rest you can do it yourself.

also, to be more formal and not divide by x, just do

u=ln(x) ==> x=e^u ==> dx = e^u du

I'm supposed to prove

[math] f(x) \in \mathbb{Z} [x] \land a \equiv b (mod n) \implies f(a) \equiv f(b) (mod n) [/math]

but I've never seen anything like [math] \mathbb{Z} [x] [/math]. Could anyone tell me what it means?

[math] \mathbb{Z} [x] [/math] the ring of polynomials with coefficients from [math] \mathbb{Z} [/math] .

[math] f(a)=f(b) [/math] is just trivial using the fact that multiplication and addition modn are well defined.

Im pretty new to programming (and sort of to math, but not as bad) so i may not be phrasing my question correctly but, do any programming languages implement mathematical (or algebraic) structures as their types? For instance in my programming 2 class we were asked to make a simple mxn grid in the command prompt and a player object that can traverse the grid (his position on the grid simply represented by the first letter of the players name). I wanted to make my program allow the player to loop back to the opposite side of the grid if the user tried to make him go off it (so if we say have a 5x5 grid and the player is at position (4,3) and tries to move to the right, he will be transported to position (0,3)). To implement this I tried using the mod operator in my move() functions (so if we did player.moveRight () the code set the players position in the x-direction to itself + 1 mod m, with m being how big the grid extends in the x direction) but it only loops back if the player tries to go too far forward (positive integers) - I get an error if the player attempts to go in a negative direction (so, again assuming 5x5, if we were at position (0,0) and tried player.moveLeft () the position in the x direction should be (0 - 1) % 5, which would take the player to position (4, 0)) However I would get an error here, despite -1 being in the the residue class [4] mod 5.

I am programming in java btw.

do any programming languages implement mathematical (or algebraic) structures as their types?

yes, you want computer algebra systems that implement symbolic manipulation.

see "sage", "macaulay 2", "maxima", etc.

havent read the rest of your post, but if you just need matrices and modular arithmetic with integers, you can trivially do that in any programming language.