# All Questions

13 views

15 views

### How to find expected number of games between two players?

I couldn't understand an answer to this question, so I'm asking it again. Can someone explain the answer or solve it by another method? The one think I didn't understood in answer is why ...
14 views

### Missing something about second derivative tests

I'm studying second derivative tests, concavity and inflection points in khan academy ...
20 views

### Checking continuity looking whether image set is interval or not

Let $A(\neq \phi)\subseteq\mathbb{R}$. Suppose $f : A \to \mathbb{R}$ is a monotone function such that the image $f (A)$ is an interval. Then prove that $f$ is a continuous function. And if $f(A)$ is ...
15 views

### A basic analysis/O.D.E/perturbation theory question

Consider a system of equations $$x'=f(x,y,\epsilon)$$ $$y'=\epsilon g(x,y,\epsilon)$$ I have seen in the book to claim the following: As $\epsilon -> 0$ the limit is $$x'=f(x,y,0)$$ $$y'=0$$ I ...
65 views

### What is the distribution of Z=min(X,Y) [on hold]

Let X and Y be independent geometric random variables. What is the distribution of Z=min(X,Y)?
32 views

### Which math class next

I just finished and Algebra for Calculus class this semester. I'm trying to work up to taking calculus (have to do up through calc 3). One person told me I should take trig next, and another calculus. ...
49 views

20 views

### Derivation of Simple Projectile Motion with Drag

Given the initial velocity $v_0$ and angle $\theta$ of a projectile on the ground, using Newton's second law and the acceleration due to gravity $\mathbf g=\left\langle0,-g\right\rangle$, I was able ...
20 views

### Visualizing Balls in Ultrametric Spaces

I've been reading about ultrametric spaces, and I find that a lot of the results about balls in ultrametric spaces are very counter-intuitive. For example: if two balls share a common point, then one ...
10 views

### Adapted but not progressively measurable?

Let $X(t,\omega)$ be a stochastic process: $$X: \mathbb{R}^+ \times \Omega \rightarrow \mathbb{R},$$ where $(\Omega, \mathcal{F}_t, \mathcal{F}, \mu)$ is a stochastic basis. Some definitions: ...
19 views

### Graph Theory into

Let M and N be matchings in a graph G with (cardinality of M) > (cardinality of N). Prove that there exists matchings M' and N' such that (Cardinality of M') = ((cardinality of M)-1), and (Cardinality ...
5 views

### Use copula to find the joint distribution of two random variables

Assuming that there are two random variables $x$, $y$ both having an Arcsine marginal distribution $F$, i.e. $F(x)=\frac{2}{\pi}\arcsin{\sqrt{x}}$ The density of their Gaussian copula can thus be ...
21 views

### Finding range for h(x)

What is the range of $\frac{1}{e^{x^2}+3}$? I know that the answer is $\frac{1}{4}$>=h(x)>0, but how do I show it
347 views

### Interesting piece of math for high school students?

I'm giving an hour long lecture to high school math students with a fairly high aptitude in math. I want to present something a little advanced for them (undergrad level) that they have to struggle ...
9 views

### extension of trigonometric functions as basis functions to higher dimensions

Trigonometric functions forms an orthonormal basis functions for $L^2[a,b]$, with corresponding normalization coefficients. I want to know if this result can be extended to higher dimensions. For ...
11 views

20 views

### Pointwise convergence and Sobolev bounded

If $\{f_n\}$ is a sequence of function on $\Omega$, and $\lim_{n\to\infty}f_n=f$ on $\Omega$. $\|f_n\|_{W^{k,p}(\Omega)}$ is bounded (or uniformly bounded), then whether $f$ is in $W^{k,p}(\Omega)$. ...
34 views

### let $D_n$ be the number of permutations of $\{1,2,3,…n\}$ which leave no element fixed.

Let $n\geq2$ and let $D_n$ be the number of permutations of $\{1,2,3,\dots,n\}$ which leave no element fixed. How to write an expression for $D_n$ in terms of $D_k$? I don't know how to start. Please ...
Let $G$ be a maximal planar graph of order at least $6$. Let $x$, $y$ be two non-adjacent vertices in $G$. Then $G + xy$ contains both $K_5$ and $K_{3, 3}$ as a topological minor. I am lost on this ...
Questions: [See below] $\rm\color{#c00}{(1)}$ What structure has $R/I$ when $I$ is a maximal left ideal? I know that if $I$ is a bilateral ideal then $R/I$ is a ring and, moreover, if $I$ is ...