# All Questions

1,108,547 questions
70 views

### Proof wanted that there is no positive integer matrix with positive integer eigenvalues u,v,w, if $0<u<v$ and $1\le w-v\le 2$

I have the following conjecture : If u,v,w are integers with $0<u<v<w$, then there is a POSITIVE INTEGER 3x3 - matrix A with eigenvalues u,v,w if and only if $w-v\ge 3$. I approved the ...
95 views

### Question regarding permutations and combinations?

Hi, I was just wondering on how you are supposed to approach this question. I keep getting 114 as an answer, but the answers say it is 174. How would anyone do this question, because I feel like I'm ...
352 views

### How to solve a non-homogeneous second-order linear difference equation with both a forward and a backward difference?

Quite a long title for this: I'm looking for the general solution of the following difference equation: $$ax_{t+1} -bx_t + x_{t-1} = c + u_t$$ where $a,b,c$ are real constants and $u_t$ is a bounded ...
516 views

357 views

### Homotopy limits

Let $\mathfrak C$ be a Grothendieck category and let ${\bf D}=\mathrm{D}(\frak C)$ be its derived category, that is, consider the injective model structure on the category $\mathrm{Ch}(\frak C)$ of ...
260 views

### Newton's method for the brachistochrone

Consider the potential $V(x,y)=-y$ and a particle at rest in the beginning of the coordinate system. We are going to examine the brachistochrone - the smooth curve of fastest descent. Assume we are ...
741 views

### distance from a point to line segment not it 's perpendicular line's distance

how to find distance between line and point in the picture ? what is the shortest distancing point in the line ? Note: distance between line and point means line segment,(the intersecting point must ...
179 views

### Why does the Fund. Theorem of Contour Integrals Need Continuity?

Why does the Fundamental Theorem of Contour Integrals need continuity? When defining the integral in real analysis we don't require continuity of the function we are integrating, is it necessary to ...
42 views

### A question about Lang's explanation of ordered fields on pg 449

Let $K$ be a field, and $P$ the set of positive elements. We know that $P$ is closed under addition and multiplication. It is also easily seen that $1\in P$. Assume that $x\in P$. Then $xx^{-1}=1$. ...
Can you help me show that $\lim_{(x,y)\to (0,0)}x\log\sqrt{x^2+y^2}=0$ I have shown that $\lim_{x\to 0}x\log x=0$. I tried to use that $\log x\leq x-1, x>0$ or that $x\leq\sqrt{x^2+y^2}$ but I'm ...