# All Questions

9 views

### Any variety contain reals

What types of projective varieties over $\mathbb{R}$ contain a real point?
10 views

### Two notions of total derivative.

Let $f:\mathbb R^n\rightarrow \mathbb R^m$ be a function. By definition, $f$ is differentiable at $a$ if there exists a linear map $D_af:\mathbb R^n\rightarrow\mathbb R^m$ such that ...
5 views

### Minimise quadratic total cost function that has summation notation

The context: minimise a quadratic objective function that has summation notation. There are two groups of countries: Annex B and non-Annex I (this comes from international climate change mitigation ...
10 views

### differentiability in metric spaces

I have a question in mind . Why cann't we define differentiability in arbitrary metric spaces? Or can we define REALLY? Please discuss. I only have studied the notion of Differentiability in ...
34 views

### Questions about Divisibility of $2^n$ by $3$

Why is it that $\forall n \in N$, $2^n$ is not divisible by $3$? I can prove it easily by induction, but I don't understand the intuition of why this is true. Could anyone please supply the ...
4 views

### Fubini-Study metric makes a quadric into a symmetric space.

I tried to show that the quadric $$Q_{n-1} = \{[z_{0},...,z_{n}]|\sum_{j=0}^{n}z_{j}^{2} = 0\} \in \mathbb{CP}^{n}$$ is a symmetric space under the Fubini-Study metric. I expand the formula using ...
17 views

### Help with Proof of the Chain Rule

I'm trying to prove the chain rule. I started out using the standard Frechet Derivative definition. After getting stuck (and generally disliking the heavy use of inequalities), I adopted an approach a ...
7 views

### An action of an automorphism of a field $C$ on a variety $X$ over $C$

My question comes from the reading of the first two pages of the article "Bernhard Köck - Belyi's Theorem Revisited". Consider a field $C$ and a variety $X$ over $C$. In particular $X$ is a ...
10 views

16 views

### Help Reducing simple fraction

This has got to be easy, but for some reason I just don't see it, probably because it's late. Solution key to a quiz we took online says that: $\frac{A^2 + A + AB}{(A + B)(A + B + 1)}$ can get ...
21 views

### Prove every isometry of the plane is expressible as product of reflections, translations, rotations

Prove every isometry of the plane is expressible as product of reflections, translations, rotations I know that the distance preserving isometries are a group but I have no idea how to use this ...
11 views

### Linear Regression complexity simplest form

Dear all I have solve the complexity of linear regression by the help of Chris document. Please check and let me know is it correct or not. Specially if Chris do it I will be very thankful to him. N: ...
35 views

### Simplify this complex algebraic fraction

I'm stumped on this problem, I need to know how this answer was arrived at but my text book doesn't show this. $$\frac{\frac{1}{x+y}}{\frac{x}{y}}$$ The text book says the answer is this: ...
14 views

33 views

### Laurent series expansion of $z^4/(z-2)^2$ about $z=2$ [on hold]

Please help me expand $\frac{z^4}{(z-2)^2}$ into the Laurent series about $z=2$. Many thanks.
37 views

### Chance of adjacent lockers with the same combination

One weird thing that happened to me in high school was that the combination lock on my locker had the exact same combination as the locker next to it. It always struck me that the odds were crazy on ...
60 views

### random thought: are some infinite sets larger than other [duplicate]

I was in the shower today and I just thought of this so I'm asking it. I'm sure this has been thought of before. Let's say we have two sets, the set of all even numbers and the set of all natural ...
16 views

### If every finite subcomplex is nullhomotopic, is a simplicial complex contractible?

Suppose $X$ is a CW-complex such that for every finite subcomplex $Y$, $Y$ can be contracted in $X$, that is, the inclusion map $i \colon Y \to X$ is nullhomotopic. Is it then true that $X$ is ...
28 views

### Is the ordinal $\omega \uparrow^\omega \omega$ still recursive?

In this question, a very large countable ordinal $\omega \uparrow^\omega \omega$ is defined. Is this ordinal still recursive?
2 views

### “Optimal Disjoint Decomposition” of a Boolean Lattice Subset?

I am looking for the name (and, possibly, an efficient solution) of the following problem: Given a Boolean lattice $(L, \sqcap, \sqcup)$ with least element $0$, and a finite subset $X \subseteq L$, ...
### Find $\alpha,\beta,K$ $\frac{a_{n+1}+\alpha}{a_{n+1}+\beta}=K \left(\frac{a_{n}+\alpha}{a_{n}+\beta}\right)$
I would appreciate if somebody could help me with the following problem Q: Find $\alpha,\beta,K(\alpha,\beta,K\in\mathbb{R})$ such that if $a_{n+1}=\frac{4a_n+8}{a_n+6}, a_1=4(n=1,2,\cdots)$ then ...