# All Questions

55 views

### introduction books for Dynamic systems of discrete Schrodinger operator for beginner

In this semester, I study in a class of dynamic system. recently the French professor turn to the dynamic system of discrete operator. I find it is difficult to find a book in English. (I have found ...
74 views

### Motivation for the Preprojective Algebra

Let $Q=(Q_0,Q_1)$ be a quiver and $k$ a field. We construct a new quiver $\bar{Q}$ in the following way. Let the vertices of $\bar{Q}$ be the same as the vertices of $Q$, and let the arrows of ...
42 views

### Boolean function resulting in ith bit value? [on hold]

Let's say f:{0,1}^n -> {0,1} is a boolean function. And let's say this function depends only on the ith bit. Namely, it results exactly as the ith bit value of the given input. Is this a valid boolean ...
129 views

### Properties of the time integral of Wiener process

Let $W_t$ be a Wiener process and consider the time integral $$X_T:= \int_0^T W_t dt$$ It is often mentionend in literature that $X_T$ is a Gaussian with mean 0 and variance $T^3/6$. I am ...
40 views

### Need a Proof -Unbounded function on any open set [on hold]

Lets define f(x)= {if x=m/n then f(x)=n,if x=irrational then f(x)=0}. Such f(x) is unbounded on any (a,b) . Can't understand the proof.Can somebody write detailed proof? Thanks.
57 views

### The Jordan-Brouwer Separation Theorem for Manifold

I have read the paper The Jordan-Brouwer Seperation Theorem written by Wolfgang Schmaltz. The main result in paper is below Any compact, connected hypersurface $X$ in $\mathbb R^n$ will divide ...
747 views

132 views

### Intersection theory on M_{g,n}

Is there a paper\book that lists the top intersections of Hodge classes and tautological classes on $\overline{\mathcal{M}}_{g,n}$ for small $g$ and $k$, e.g. $g=2,3$ and $k=0,1,2$ ?
82 views

### Could one recover the relative K-theory from the quotient derived category?

Let $A\to B$ be a full embedding of exact categories that induces an embedding $D^b(A)\to D^b(B)$. My question is: what can one say about the relation of the homotopy cofibre $K(A)\to K(B)$ (the ...
84 views

### Veronese surface [on hold]

I have a question(Hartshorne ,page 13,exercise 13): If Y be the image of the 2-uple embedding(described in exercise 12) of P^2 in P^5. and if Z(a subset of Y) is a closed curve(variety of dim 1) show ...
186 views

210 views

### Circle method on things other than the integers

The circle method is often used to estimate the number of solutions to the equation $$x_1 + x_2 + ... x_k = N$$ if for all $i$ $x_i\in A\subseteq\mathbb{N}_0$ and some subset of the nonnegative ...