# All Questions

10 views

### PDE basic traffic flow problem

I am analyzing a basic example of traffic flow presented here http://people.uncw.edu/hermanr/pde1/PDEbook/PDE_Main.pdf and have a question to the last transition in the traffic flow equation ...
24 views

### If $F ⊂ \mathbb{C}$ and $α_1,\ldots,α_n$ ∈ $\mathbb{C}$ are algebraic over $F$, prove that $F(α_1, \ldots, α_n)$ is a simple extension of $F$.

The statement is true for $n = 1$: $F(α_1)/F$ is ﬁnite (since $α_1$ is algebraic over $F$) and is simple, so we need to show that it holds for $n ≥ 2$. By induction on $n$; suppose the theorem is true ...
6 views

### Solution for the inhomogeneous 3D heat equation with initial temperature distribution

Can anyone describe the general solution for the inhomogeneous 3-dimensional heat equation: $u_t = K\nabla^2u + \frac{1}{c\rho}f$, with initial condition $u(x, 0) = g(x)$, no boundary conditions. ...
16 views

### Determine Integrability without use of Riemann Integral

Determine the function is integrable or not on its interval of definition: $f(x)=\begin{cases}0 \quad \textrm{if} \quad 0\le x\le1\\ x \quad \textrm{if} \quad 1\lt x \le2\end{cases}$ So in our class ...
37 views

16 views

### If set $A_n$ converges to $A$ in $L^1$, then is it also true for the $r$-neighborhood?

Let $A$ be a bounded simply connected set in $\mathbb{R}^2$, and $A^r$ denote the $r$-neighborhood of $A$, that is, $A^r:=\{x: d(x,A) \le r\}$. Suppose there exists $A_n \rightarrow A$ in $L^1$, that ...
66 views

### What is the derivative of $x^i$?

What would the derivative be of $x^i$? Would it simply be $ix^{(1-i)}$? I tried running the Power rule, and I got that is that right?
56 views

### Prove that all trees are bipartite

I've been trying to prove this for a while. I can think about it intuitively, but I can't come up with a formal proof. I would appreciate some help. Here's how I'm thinking about it Let T be the ...
8 views

### Is it possibile to compute the transient response from the FFT?

I'm measuring the user acceleration using the iPhone accelerometer, but I have to discard the initial data that is taken when the user is still not moving and has to put the phone in the pockets. Like ...
9 views

### Topology on function space between smooth manifolds

I'm having trouble reconciling my intuitive notion of "functions close to $f$" with the seemingly very technical definition of the weak and strong topologies on $C^r(M,N)$ in Hirsch's Differential ...
30 views

14 views

29 views

### Rearrangement of equations

Trying to find solutions to the equation of $$(1/x)+1=2\sin⁡x+3$$ and I have to rearrange it into the form of $x=f(x)$ as I am using the fixed point method and iterations. Struggling to find new ...
9 views

14 views

### Recursive formula in term of original value

$$P_1=P_0G_{0,1}A_1\\ P_m=P_{m-1}G_{m-1,m}A_m+A_0\sum_{i=0}^{m-2}P_i G_{i,m}~~\text{for}~~m\geq 2$$ Is it possible to write $P_m$ in terms of only $P_0$, i.e., without other $P_j$ terms?
39 views

### How to formally prove whether this function is onto or not?$K(x) = x^ 2$ where $x \ge 0$.

$K(x) = x^2.$ The domain and range of this function comprise of non-negative real numbers. If it were real numbers instead of "non-negative" real numbers, then it seems easy to prove it by ...
24 views

### equations, formula, or proofs that cause one to feel “sad,” or negatively in general. [on hold]

It's extremely commonplace for mathematician's to refer to work as "elegant," "beautiful," and I've seen many compare the process of doing mathematics to painting, or playing music. I think that for ...
7 views

### A matrix decomposition problem for row/column element order

Indeed, I don't know how to classify this problem, but I try to use matrix to describe it. The problem is that there exists a function $f(x, y)$ and its exact form remains unknown. But I have some ...
38 views

### I need someone to explain this shape to me.

The hexagon fits in the circle perfectly, the circle fits in the square perfectly. but the hexagon doesn't fit in the square perfectly. Doesn't this defy this formula below? a = b b = c a = c (what ...
36 views

### Why must the determinant of the hessian of a scalar function be positive for there to be a local min/max? Intuition needed

Is there any intuition behind having the determinant of the Hessian matrix being negative corresponding to a saddle point, and positive corresponding to a max/min depending on the sign of $f_{xx}$ for ...
24 views

### Adjoint of a normal operator A is a polynomial in A

Is it true that adjoint of a normal operator A can be written as a polynomial in A?
27 views

### Complementary Text to Gunning and Rossi - Analytic functions in several complex variables

I'm currently a second year student who has a background in group theory, ring theory, galois theory, metric spaces and point set topology. I'm currently taking courses in algebraic topology, advanced ...
21 views

30 views

7 views

### Applying the Hoeffding bound compenentwise to a vector

Given $v \in [0,1]^n$ and let $r$ be a random vector such that $\mathbf{E}[r_i] = v_i$ for $i$ in $\{ 1, \dots, n \}$, i.e., $r_i$ is an unbiased estimate for $v_i$. Can I now just apply a Hoeffding +...
7 views

### Of $n^2$ points of intersection, $np$ lie on curve of deg. $p < n$, then remaining $n(n - p)$ lie on a curve of deg. $n - p$

Let $C$, $C'$ be two plane curves of degree $n$. Is the following statement true or not? Suppose that of the $n^2$ points of intersection, $np$ lie on a curve of degree $p < n$, then the ...
36 views

### Loaded coin: probability I will never get two heads [on hold]

I'm currently starting to learn probability in an intro course in college and am wondering how to solve this. Given a loaded coin that gives a 60% chance of flipping heads, and 40% chance of tails, ...
### solve the initial value problem on the half line for the diffusion equation $U_x(t,0)=\sin t$ [on hold]
solve $U_t-U_{xx}=0$ for the half line with initial conditions: $$\quad Ux(t,0)=\sin t\\ U(0,x)=x$$
In Harthshorne (and pretty much everywhere else I know) a proper morphism is defined to be A morphism of schemes $f:X\to Y$ is said to be proper if it is sperated, of finite type and ...