Christian Chapman

general recent conversations

MathOverflow

General discussion for mathoverflow.net

Christian Chapman

Jun 30, 2024 23:26

Does anyone know what happened to Gerhard Paseman? I haven't seen a recent comment of his in a while.

$Mathematics$ Mathematics

Associated with Math.SE; for both general discussion & math qu...

enthdegree

Oct 17, 2016 10:01

(in ref to my last post)

enthdegree

Oct 17, 2016 10:01

the sign error was at the very end, from line 24 to line 25

enthdegree

Oct 17, 2016 08:50

I have picked up or lost a factor of -i somewhere in the (short) analysis but I can't figure out where

enthdegree

Oct 17, 2016 08:49

Hey can anyone spot the constant error here? dropbox.com/s/hsouvysj0gybi6h/…

enthdegree

Oct 13, 2016 04:23

wait, maybe not.

enthdegree

Oct 13, 2016 04:21

*rotation

enthdegree

Oct 13, 2016 04:21

But it sounds like rotation is defined in terms of Euler's notation theorem: "When a sphere is moved around its centre it is always possible to find a diameter whose direction in the displaced position is the same as in the initial position."

enthdegree

Oct 13, 2016 04:18

@keshav, this is a totally intuitionist answer, but my gut feel is that the reason a fixed point implies well-defined-ness of an axis of rotation is tautological

enthdegree

Oct 13, 2016 04:16

smart people answered though

enthdegree

Oct 13, 2016 04:16

Q: Where are the other solutions to this ODE disappearing in this analysis?

I am asked to solve the following ODE involving constants $\alpha, L, V_0 > 0$ and $E < 0$: $$-\psi'' - \alpha V_0\psi\cdot [\delta(x)+\delta(x-L)] = \alpha E\psi.$$ In particular, we want solutions $\psi:\mathbb{R}\to \mathbb{C}$ that are: Continuous $L^2$ We are given that the solutions l...

enthdegree

Oct 13, 2016 04:16

once i asked a physics question on MSE and they caught on

enthdegree

Oct 13, 2016 03:36

what is a banach lattice? is that just a banach algebra with more structure

enthdegree

Oct 13, 2016 03:35

are open

enthdegree

Oct 13, 2016 03:35

with the weak topology we assert that sets of the form {x: |phi(x-z)|<\varepsilon, z in X} (for phi in the dual, varepsilon positive)

enthdegree

Oct 13, 2016 03:34

alright i cant believe i was being this dense before, i was basically not interpreting my definition of the weak* topology

enthdegree

Oct 13, 2016 03:13

does anyone online right now know functional analysis?

enthdegree

Oct 13, 2016 03:13

alright, it looks like i have some fundamental misunderstanding of what the weak* topology is

enthdegree

Oct 13, 2016 02:56

I guess i should add, I^{-w} denotes the closure of I in the weak topology

enthdegree

Oct 13, 2016 02:55

I can't figure out how to show that the epsilon ball intersects \mathfrak{I}, even given the hint!

enthdegree

Oct 13, 2016 02:54

Does anyone have any idea how to complete this? imgur.com/Zpxdwjo.png

enthdegree

Oct 13, 2016 02:15

I have a normed vector space X and its dual X*, and X* induces a 'weak topology' on X (the weakest topology where all the functionals in the dual are continuous, i.e. a sequence (xn) --> x weakly in X iff (psi(xn))--> psi(x) for any psi in X*)

enthdegree

Oct 13, 2016 02:13

Can anyone explain how on earth you get your hands on the weak closure of a subset of a space?

enthdegree

Oct 13, 2016 02:06

This can't be right

enthdegree

Oct 13, 2016 01:37

Hello I have a small question, the weak open unit ball in a hilbert space $\mathfrak{H}$ looks like: $B_\varepsilon(0) = \{x\in\mathfrak{H}|\,|(x|y)|<\varepsilon \forall y \in \mathfrak{H}\},$ right?

enthdegree

Mar 25, 2016 23:51

it would be nice if, given a stopping time you were interested in, there were some general way to identify a martingale in terms of how that stopping time was defined

enthdegree

Mar 25, 2016 23:50

all the exercises i am finding ask you to prove that some pie-in-the-sky transformation magically turns out to be a martingale

enthdegree

Mar 25, 2016 23:49

does anyone know of any heuristic/general procedures for identifying martingales?

enthdegree

Mar 4, 2016 23:55

Look, the guy even knew the answer before it was posted. He comments to one of the answerers: "Your answer is not useful. I think checking the eigenvalue of the Hessian matrix maybe a good approach"

enthdegree

Mar 4, 2016 23:52

Q: How to check convexity?

How can I know the function $$f(x,y)=\frac{y^2}{xy+1}$$ with $x>0$,$y>0$ is convex or not?

convex-analysis

enthdegree

Mar 4, 2016 23:52

how does this question have so much attention

enthdegree

Mar 4, 2016 23:51

wew

enthdegree

Mar 3, 2016 04:14

x \preceq y according to proper cone K if y-x is in K

enthdegree

Mar 3, 2016 04:11

But the story is not so clear for other cones!!!

enthdegree

Mar 3, 2016 04:09

It is clear what orderings some cones induce, e.g. the positive orthant of Rn creates an ordering where x<y if each component of x is less than its corresponding y component.

enthdegree

Mar 3, 2016 04:08

Everyone knows every proper cone in Rn defines a partial order on the space... but how are we to understand the partial ordering of an arbitrary proper cone K???

enthdegree

Mar 1, 2016 17:43

Where did I go wrong???

enthdegree

Mar 1, 2016 17:42

But the answers say its supposed to be x*(N-x)

enthdegree

Mar 1, 2016 17:42

I used the optional stopping theorem to say that E[X_T^2-T]=E[X_0^2-0]=x^2, so that E[T]=E[X_T^2]-x^2=x/(N+x)*(N+x)^2-x^2=Nx

enthdegree

Mar 1, 2016 17:41

Hi everyone, I'm a gambler and I start with $x$ money, i put down a dollar and get 2 dolalrs back with p=0.5, and lose my dollar with p=0.5. I am interested in how long it will take me to either A) go broke or B) reach N dollars. Take T to be this stopping time.

I showed $(X_n^2-n)$ is a martingale and that I reach N dollars with probability $x/(N+x)$, but now how do I get the EV of how long it takes to finish the game?

enthdegree

Mar 1, 2016 15:06

morning

enthdegree

Mar 1, 2016 10:36

@Agawa001 sure thing

enthdegree

Mar 1, 2016 10:34

Hi guys

enthdegree

Feb 22, 2016 03:50

I am not sure this is a question in measure theory. Maybe it would be better suited for the physics stackexchange

enthdegree

Feb 22, 2016 03:43

i am no physicist, i can't attempt to answer

enthdegree

Feb 22, 2016 03:43

skimming the wikipedia article it looks like its an open question that so far is partially resolved by just pulling it from the second law of thermodynamics

enthdegree

Feb 22, 2016 03:40

Arrow of time

This article is an overview of the subject. For a more technical discussion and for information related to current research, see Entropy (arrow of time). The Arrow of Time, or Time's Arrow, is a concept developed in 1927 by the British astronomer Arthur Eddington involving the "one-way direction" or "asymmetry" of time. This direction, according to Eddington, can be determined by studying the organization of atoms, molecules, and bodies, might be drawn upon a four-dimensional relativistic map of the world ("a solid block of paper"). Physical processes at the microscopic level are believed to be...

enthdegree

Feb 22, 2016 03:38

@VermillionAzure hmm...

enthdegree

Feb 22, 2016 03:37

i do not think it is a stretch to say that the vast majority of engineers also consider haskell a joke

$Mathematics$ Discussion on answer by Mhenni Bengho…

Imported from a comment discussion on math.stackexchange.com/q...

enthdegree

Feb 27, 2016 07:20

$e^{x} \neq 1$ for almost all $x$!!!