# All Questions

0answers
71 views

### Probability of differently loaded dice summing to a value

I have a real world problem that boils down to the following: I'm playing dice. I have $n \approx o(10)$ differently biased die. The probability of the $i^{th}$ die showing $x_i$ is given by ...
0answers
43 views

### How to find the inverse function of a function like f: N x N -> N [on hold]

I need help on how to find the inverse of a function N x N -> N For example, if anybody could give me a step by step explanation how to find the inverse function of f(x,y)=3x-2y I would be very ...
2answers
346 views

### Is it meaningful to work on convergencies, integration, etc. on the Zariski topology? [on hold]

Since I have studied analysis as well as algebra recently, I am familiar to work on integrablities, and such concepts when I look at topologies. Currently, I am studying algebraic geometry, and I want ...
0answers
28 views

### Depth of multigraded modules

Can any one please give me some references on depth of multigraded module over a standard multigraded ring.
0answers
90 views

### Besides F_q, for which rings R is K_i(R) completely known?

With the exception of finite fields and "trivial examples", which rings $R$ are such that Quillen's algebraic $K$ groups $K_i(R)$ are completely known for all $i\geq 0$? Here, by "trivial examples" ...
0answers
28 views

0answers
106 views

### Rational Hodge Theory

I am currently learning about the formality result for Kaehler manifolds proved in DGMS. Their result uses some basic Hodge theory, and so only gives formality over $\mathbf{R}$. Later, however, ...
1answer
138 views

### What is the Essential Reason that allows a PTAS for the EUCLIDEAN TSP?

Questions: Is there some understanding of the reason, why the euclidean TSP allows a PTAS, whereas the metric TSP in general does not and, is the PTAS stable under sufficiently small perturbation ...
1answer
149 views

### Generalization of notion of convexity

I am searching for the correct term for the following, if it exists. A set $X\subset \mathbb{R}^2$ is called $r$-convex if for any two points $x_1, x_2\in X$ such that there exists an arc of radius ...
1answer
64 views

### Clique factorization

I'm reading about Clique factorization in wikipedia: http://en.wikipedia.org/wiki/Gibbs_random_field#Clique_factorization but I'm unable to understand this: What is $X_C$ here? Ok I understood ...
1answer
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 ...
1answer
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 ...
0answers
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 ...
1answer
126 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 ...
0answers
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.
0answers
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 ...

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