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Let $X,Y$ be schemes of finite type over a field $k$. In particular, they are quasi-compact. Let $f: X to Y$ be a morphism of finite type...
2Mathematics Asked on 2 years ago
Prove that $$frac{pi^e}{x-e}+frac{e^pi}{x-pi}+frac{pi^pi+e^e}{x-pi-e}=0$$ has one real root in$(e,pi)$ and other in $(pi,pi+e)$.For $xin (-infty,e)$ the equation will be always be negative and for $xin (pi+e,infty)$...
1Mathematics Asked on 2 years ago
I encountered the following problem in my textbook-Let $a, b, c$ be three arbitrary real numbers. Denote $$ x = sqrt{b^2-bc+c^2}, y = sqrt{c^2-ca+a^2}, z = sqrt{a^2-ab+b^2} $$...
1Mathematics Asked on 2 years ago
I have a polynomial $P(x,y,z,...)$ which has integer coefficients and real roots. I want an efficient method that is guaranteed to find a root (I only need one), and...
0Mathematics Asked on 2 years ago
The matrix is:$$begin{bmatrix}k&1\0&k^2end{bmatrix}$$I am aware that a square matrix is diagonalizable if there exists a matrix $P$ such that $D = P^{-1 }* A * P$...
1Mathematics Asked by Math Comorbidity on 2 years ago
I have an expression of the below form: $$sum_{i=1}^k (A_i+B)^{-1}=0$$where ${A_i}_{iin {1,...k}}$ are a set of known square symmetric invertible matrices and $B$ is an unknown...
0Mathematics Asked on 2 years ago
I want to show that an algebraically closed field $F$ cannot be contained in a larger field $K$. So if $F subseteq K$ then $F =...
1Mathematics Asked on 2 years ago
I came across a strange equation in the solution to a problem. It looks like this:$$My - Mx = lambda x$$ In this problem $M$ is an ...
2Mathematics Asked on 2 years ago
My apartment has double hung windows, but they are quite narrow (~19.5 inches at the screen, 22 inches at the opening). I'm currently using a portable air conditioner, but...
1Home Improvement Asked on 2 years ago
We are installing a laminate floor in our family room and have precisely the same problem as described in this question. The brick is not even close to...
1Home Improvement Asked on 2 years ago
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