All Questions
1,659,243
questions
0
votes
0
answers
2
views
Prove that for all sufficiently large positive integers $n$ and a positive integer $k \leq n$?
Prove that for all sufficiently large positive integers $n$ and a positive integer $k \leq n$, there exists a positive integer $m$ having exactly $k$ divisors in the set $\{1,2, \ldots, n\}$.
here is ...
- 69
-1
votes
0
answers
9
views
Prove, without using derivatives, that xsin(1/x) is not Lipschitz in (0,1]
I know that it is not Lipschitz by using derivatives, but I can't prove it without.
0
votes
0
answers
17
views
Oven temperature
This question is a crosspost from this one on another StackExchange subsite due to the recommendation given there. The question arose in the kitchen, not while doing homework.
The motivation
Consider ...
- 717
0
votes
0
answers
6
views
Equality of two completions
I have the following question.
Suppose $R$ is Noetherian ring, $I$ is ideal in $R$ and $S$ is multiplicatively closed set. Let $(I^n\colon\langle S\rangle) = \varphi^{-1}(I^nS^{-1}R),$ where $\varphi\...
- 75
0
votes
0
answers
24
views
Why do Fibonacci sequences result from this process?
If we have two columns of numbers made by the following rule, we get two Fibonacci sequences.
Is there a straightforward way that enables us to just 'see' why this would happen. If anyone can find ...
- 611
1
vote
0
answers
10
views
Inaccurate Eigenvectors from LAPACK's ZHEEVR routine
I was trying to replace Scipy's eigh routine in my cython code with C-level LAPACK. Essentially I want to compute eigenvectors corresponding to the largest and smallest eigenvalues of a hermitian ...
- 196
-1
votes
0
answers
13
views
How much a material will be removed from 1 unit volume of sediments?
Let's consider that in 1 unit volume of sediments the removal rate if a substance is 5 gm.m-^2.yr-1 then how much amount of it will removed from this sediments. Given that porosity is 50%, density iis ...
0
votes
0
answers
6
views
Under what conditions is the matrix norm of $||(R + A^T P A)^{-1}B^T P||$ finite for all positive semi-definite matrices $P$?
Assume $R$ is a positive definite matrix, $A$ and $B$ are square matrices, and $P$ is a positive semi-definite matrix. I would like to know the conditions under which $\sup_{P \geq 0} \|(R + A^T P A)^...
0
votes
0
answers
15
views
Finding area of triangle in Argand Plane
Question says : Given |z|^2=4 , find the area of the triangle formed by the complex numbers z , wz, z+wz (w= complex cube root of unity).I understand the solution which claims that the given numbers ...
0
votes
1
answer
18
views
Kurtosis of b(n,p) - binomial distribution
So I been at this for hours. I don’t know where my simplification is going wrong but here it is:
$\frac{n[(n-1)(n-2)(n-3)p^4 + 6(n-1)(n-2)p^3 +7(n-1)p^2 + p] - 4(n[(n-1)(n-2)p^3 +3(n-1)p^2 + p + 6(np)^...
0
votes
0
answers
30
views
Double-checking my formula derivation
The formula for the surface area of a right antiprism with regular n-gonal bases B isn't on the wikipedia page for antiprisms so I derived it myself. Based on the diagram below
I got that Surface ...
- 97
2
votes
2
answers
57
views
Use $\,\varepsilon-\delta\,$ definition of limits to show that $\lim\limits_{(x,y)\to(-1,2)}\frac{x^3+y^3}{x^2+y^2}=\frac{7}{5}$
We need to show that for every $\varepsilon >0$ there exists a $\delta >0$ such that
$$\left\lvert\frac{x^3+y^3}{x^2+y^2}-\frac{7}{5}\right\rvert<\varepsilon $$
whenever
$$0<\sqrt{(x+1)^2+(...
- 117
2
votes
1
answer
25
views
Any two disjoint subsets in a family of subsets intersect, prove that any maximal such family of subsets must contain $2^{n-1}$ subsets
Here is the problem: Let $\mathcal{F}$ be a family of subsets of an $n$-element set $X$ with the property that any two members of $\mathcal{F}$ meet, i.e., $A \cap B \neq \emptyset$ for all $A, B \in \...
- 21
0
votes
0
answers
21
views
Let $f,g\in C[0,1]$ and $U= \{h\in C[0,1]:f(t)<h(t)<g (t),\forall t\in [0, 1]\}$ in $X= (C[0,1], \| .\|_{\infty} ).$ Is $U$ a ball in $X?$
Let $f,g: [0,1]\to\Bbb R$ be continuous and $f(t) < g (t)$ for all
$t\in [0,1].$ Consider the set
$$U= \{h\in C[0,1] : f (t) < h(t) < g (t) ,\text{ for } t\in [0, 1]\}$$
in the space $X= (C[0,...
- 3,065
1
vote
0
answers
23
views
multiplication in the ring of formal Laurent series
Let $F$ be a field and define the ring $F((x))$ of formal Laurent series with coefficients from $F$ by
$$
F((x))=\left.\left\{\,\sum_{n\geqslant N}^{\infty}a_nx^n\,\right|\,a_n\in F\text{ and }N\in\...
- 361