0
votes
0answers
33 views

Probability for slot overlapping for 4 employees

There are 4-shifts in a 24-hour day distributed by 4 employees. If the slot of an employee crosses the 24 hour mark it extends into the next day. What is the probability that all the four employees ...
0
votes
3answers
91 views

Group of order $1 5$ is cyclic.

Prove that any group of order $1 5$ is cyclic. I am looking at a solution here and I am confused why "there must be one orbit with five elements and three orbits with three elements" and "fixed ...
0
votes
1answer
136 views

Basic Vector magnitudes and Quadrants Question

Express in unit vector notation each has magnitude of 17.0cm A) Vector E is directed 27 deg counterclockwise from positive x-axis B) Vector F is directed 27 deg counterclockwise from positive y-axis ...
1
vote
1answer
58 views

The determinant of a linear transformation on a finite vector space

Given a finite vector space $V$ and a linear transformation $f : V \rightarrow V,$ is it true that for any two ordered bases of $V$, call them $a$ and $b$, the determinant of the matrix of $f$ with ...
0
votes
1answer
122 views

exponential generating function of $\frac{1}{(1-x)^2}$

Hey just had a quick question related to coming up with an explicit formula for $a_n$ with relation to $F(x)=\frac{1}{(1-x)^2}$. I know to compute such a function I have to use the derivative of ...
-1
votes
1answer
60 views

Prove by induction $n^3 < 3^n$. What is the value of $n_0$? [closed]

Prove by induction for $n \geq n_0$, $n^3 < 3^n$. What is the value of $n_0$?
4
votes
1answer
192 views

Can we determine $A= 1!+2!+3!+…$'s digits starting from last?

After reading a bit about p-adic numbers, I came up with an idea. We know that for every natural number $k$, there exists a natural number $n$ so that for every $m>n$, there are at least $k$ zero ...
0
votes
1answer
89 views

Solving ODE by contraction mapping

Let a and c be real numbers. Solve the initial value problem y'(x) = ay(x), y(0) = c on the interval [0, 1/2a] with the help of the contraction mapping theorem. I understand that solving this ODE is ...
1
vote
1answer
59 views

Subgroup of a nilpotent group

Let $G$ be nilpotent and $H \le G$. Let $P_1,P_2,\ldots,P_k$ be the Sylow subgroups of $H$. Is it true that $H = P_1 P_2 \cdots P_k$? I know that when $G$ is nilpotent, it is the direct product of ...
-3
votes
1answer
73 views

Prove if the groups are isomorphic

Prove if the groups are isomorphic. The multiplicative group of all 2x2 matrices with determinant $1$ and $\operatorname{Sym}(\mathbb{Z})$ I have done questions similar to this, but struggle with ...
0
votes
2answers
47 views

Initial value problem $x'=e^{-|x|}$, $x(0)=0$

Consider $x=x(t)$ and $\frac{dx}{dt}=e^{-|x|}$, $x(0)=0$. Now I want to find the solution of this initial value problem. I want to solve it for $t\geq0$ and $t\leq0$. If $t\geq0$: ...
1
vote
1answer
404 views

The limit of sequence $(\frac{n \sin(2n)}{n^2 + \cos(n) + 4})$

I have trouble evaluating the limit of the sequence $(\frac{n \sin(2n)}{n^2 + \cos(n) + 4})$. Could anyone help me? Thank you!
1
vote
1answer
233 views

Local minima of a trivial sin(x) function

The paper on which it came had $4$ choices of answer, out of which $2$ options are creating confusion. For the function $f(x) = sin(x)$ in the interval $x\in[\frac{\pi}{4},\frac{7\pi}{4}]$, the ...
2
votes
1answer
319 views

a function is continuous iff the graph is pathwise connected

Let f : [a, b] → R. By the graph of f we mean the set F = {(x, f(x)) : a ≤ x ≤ b} ⊆ R Prove that f is continuous if and only if the graph of f is a pathwise connected subset of the plane. I ...
0
votes
1answer
57 views

Simple question about complex $e^{i}$ and angles

I'm working with angles. I have a hard time figuring something. In electric physics, I have an equation describing an AC voltage function, this way $V_{x} = 0.0469 \cdot e^{-j \cdot 1.083}\cdot ...
0
votes
1answer
62 views

A physics related question about an infinitely long pipe.

This is a really nice question I found some days ago, so I translated it into English to share. Suppose we have a water pipe which is infinitely long, with water flowing in it. We know that if a ...
0
votes
1answer
38 views

Equality question

Hi I'm a bit confused with this? $\frac{1}{x} < 0 \iff x\frac{1}{x} < x\times 0 =0 \iff 1 < 0$ This was another question that I saw which was $\frac{1}{x} < 0$ but when I multiplied by ...
2
votes
2answers
194 views

Zero, the Additive Identity, as the Multiplicative Annihilator

In the structures I have encountered so far, I have always seen a zero, which is usually defined as the additive identity. For example: $\exists 0 \in \mathbb{Z}$ s.t. $\forall a \in \mathbb{Z}, a ...
2
votes
1answer
1k views

How to determine the equivalence classes of a relation?

I don't fully understand how to find the equivalence classes of a relation. Over $\mathcal P(E)$, where $E = \{1,2,3,4,5,6\}$, $ARB \iff |A\cap\{1,2\}| = |B\cap\{1,2\}|$ From what I've seen, ...
0
votes
1answer
138 views

Proof for hamiltonian cycle in grids having even no. of nodes

How can I go about proving that an undirected graph having even no. of nodes (at least one of the rows or columns are even - excluding line graphs of course) have a hamiltonian cycle? I have managed ...
1
vote
1answer
100 views

Radon measure not locally integrable

I need some help with this exercise: If we have $N=2$, $\Omega=\mathbb{R}^2$ and $T:\cal{D}(\Omega)\to\mathbb{C}$, with $$\langle T,\phi\rangle=\phi(0,1)-\phi(1,0)$$ I have to show that it is a ...
1
vote
2answers
113 views

Metric space question

Let (M,p) be a metric space and suppose that ${x_n}$ is a sequence in (M,p) so that $x_n -> x$ and $x_n->y$. prove x=y Let $E>0$. then, $p(x_n,x)->0$ $lim$ $n->inf$ ...
0
votes
1answer
39 views

Definition of an active hyperplane

We are learning about the Geometry of Duality in Linear Programming, and my prof uses the terminology active hyperplane. I'm wondering what the formal definition of this is. I can't seem to find any ...
-4
votes
2answers
60 views

How to find this Linear Transformation

Q. Find the Linear Transformation $T:V_3\rightarrow V_3$ , such that $T(0,1,2)=(3,1,2)$ $T(1,1,1)=(2,2,2)$ I tried considering $(0,1,2),(1,1,1)$ as basis, it doesnt seem to work that way. Just need ...
-4
votes
1answer
82 views

Proving various properties of metric spaces

Suppose that $p_1$ and $p_2$ are metrics on $M$. Prove that the following are also metrics: (a) $p = p_1 + p_2$ define $p_1(x,y) = |x-y|$ define $p_2(a,b) = |a-b|. p = p_1+p_2 = |x-y|+|a-b|$. But I ...
0
votes
1answer
85 views

Convergence to Gaussian with infinitesimal condition with relation to Levy Triple.

I have posted this question before under the title "Uniform infinitesimality Condition and convergence in distribution to Gaussian distribution". I managed to find something related to this question ...
1
vote
1answer
58 views

Almost sure convergence of sample mean

I have a sequence of events $(A_n : n \in \mathbb{N})$ with $\mathbb{P} (A_n) = 1/n^2$ for all $n$. We have $X_n = n^2 1_{A_n} - 1$, and $m_n = (X_1 + ... + X_n )/n$ is the sample mean. I would like ...
2
votes
1answer
263 views

$L^p$ Spaces, Young's Theorem, Convolutions, and Minkowski's Inequality

I need to show \begin{align} \|f*g\|_p \le \|f\|_p\|g\|_1 \end{align} By using the generalized Minkowski inequality instead of just Young's Theorem. I have spent a lot of time, but I keep hitting a ...
3
votes
1answer
2k views

Find all real zeros of $f(x)=2x^3+10x^2+5x-12$

Hey guys I'm having a little trouble with one problem: Find all real zeros of $$f(x)=2x^3+10x^2+5x-12.$$ I got $x=-4,(2x^2+2x-3)$. I'm just having trouble using the quadratic formula to get ...
1
vote
1answer
108 views

Dirac Delta — Symmetry

I had a curiosity question rise up in the middle of the night regarding the behavior of the Dirac Delta. Because it's not a function per-se, I am not sure how a concept like "integration" symmetry ...
-1
votes
2answers
73 views

If $f$ is continuous, so is $f(x^3)$

Suppose $f:R\rightarrow R$ is differentiable and define $g(x)=x^2 f(x^3)$. Show $g$ is differentiable and compute $g'$. So I know how to do the proof, I just want to know that even though $f$ is ...
1
vote
0answers
301 views

Successive parabolic interpolator for sub pixel interpolation

Is it possible to use successive parabolic interpolator for doing sub pixel interpolation. In the case of non sub pixel interpolation it is very easy to apply successive parabolic interpolation as ...
0
votes
0answers
373 views

linearization topological sorting which repeatedly removes source nodes from the graph

The chapter suggests an alternative algorithm for linearization (topological sorting), which repeatedly removes source nodes from the graph (page 101). Show that this algorithm can be implemented in ...
4
votes
1answer
156 views

Initial Segments of Modular Arithmetic

Modular arithmetic (MA) has the same axioms as first order Peano arithmetic (PA) except $\forall x(Sx \neq 0)$ is replaced with $\exists x(Sx=0)$. MA is $\omega$-inconsistent and all infinite models ...
1
vote
1answer
54 views

Any predetermined sequence in the decimal expansion of an irrational number

I came up with this question in a random math discussion with my friend. I am wondering if one can always find a predetermined sequence of numbers, such as 123456, 33333, in the decimal expansion of a ...
1
vote
2answers
105 views

What are the steps to take the derivative of this function?

This calculus derivation is giving me an extremely difficult time. I am having trouble understanding how to manipulate the $e^t$. The function is $$P*{e}^t/[(1-q)*{e}^t]$$ I want to take the ...
8
votes
1answer
391 views

Finding the Integer solution to $a^3+b^2+c^2=2013$

this is my first time posting and I hope someone can help because this question has been driving me crazy... For a bit of background I am a sophomore math major in college, I have taken math up ...
0
votes
1answer
58 views

Find image under Riemann map without the explicit map

How can I find the image of the line segments $(0,1)$ and $(0,1+i)$ under the unique Riemann map $f$ from the square with vertices at $\pm1\pm i$ onto the unit disc satisfying $f(0)=0$ and ...
1
vote
0answers
144 views

Friend Group and Hater Group

Consider a set $S$ of $n$ people such that, for all distinct $x$ and $y$ in $S$, it is the case that either $x$ and $y$ like each other or $x$ and $y$ hate each other. Let us call $S' \subseteq S$ a ...
1
vote
0answers
57 views

Prove that a finite complete graph can be embedded in $\mathbb{R}^3$

I've actually found a few intuitive examples where edges are taken to a twisted cubic and and the vertices are arranged in a certain way and that's very nice, but I'm actually more interested in a ...
0
votes
2answers
909 views

Find the power series representation for arctan.

Find a power series representation for the following function and determine the interval of convergence: $f(x)=\arctan\left(\frac{3x}{2}\right)$ So I found its derivative and used U-subsitution and ...
1
vote
3answers
321 views

How prove this inequality $\frac{x}{x+yz}+\frac{y}{y+zx}+\frac{z}{z+xy}\ge \frac{3}{2}$

let $x,y,z>0$,and such $x^n+y^n+z^n=3(n\ge 1),n\in N^*$, show that: $$\dfrac{x}{x+yz}+\dfrac{y}{y+zx}+\dfrac{z}{z+xy}\ge \dfrac{3}{2}$$ My try: if $n=1$ , since $x+y+z=3$,then use Cauchy-Schwarz ...
2
votes
4answers
129 views

Group where you can see all the finite subgroups.

Is there any group $G$ for which every finite group is a subgroup ? I thing we can consider $S_\mathbb{N}$, because $S_n$ is subgroup of $S_\mathbb{N}$ for all $n$. so by Caylay's theorem we are ...
0
votes
1answer
163 views

Calculate the error given a tolerance

I have a noob statistics question. Is there a function, such that given the residuals from the line of best fit, and a probability, A, it will return B such that there is an A probability of being ...
0
votes
1answer
42 views

Greatest common denominator

My problem is figuring out how to express the GCD as a linear combination of $(9,11)$. So far, I have: $$11 = 9 + 2$$ $$9 = 4 \cdot 2 + 1$$ From here, I'm not sure if I put $2 = 2 \cdot 1$ As for ...
3
votes
1answer
3k views

Conjugate class in the dihedral group

List all the conjugate classes in the dihedral group of order $2n$ and verify the class equation. The dihedral group is generated by two elements $r$ and $s$. The order of $r$ is two since $r^2=e$ ...
1
vote
1answer
105 views

infinite limit cycles

Can we find differential equations in the real plane and class $C^{k}(\mathbb{R})\ k\geq 1 $" that have an infinity of limit cycles accumulating in the origin with the origin as singular point? I ...
0
votes
1answer
39 views

Computational complexity of Newtons Method

I'm trying to do a worst case complexity analsis of another algorithm that involves computing an nth root of a real number at each step. I have a bound B on the size of this number also n is fixed and ...
2
votes
0answers
33 views

Properties of matrix Lie groups which are not shared by general Lie groups

I am reading Brian Hall's book 'Lie groups, Lie algberas, and Representations' and on p52, corollary 2.34 reads : " Every continuous homomorphism between two matrix Lie groups is smooth." I am ...
1
vote
1answer
206 views

If $M$ is positive definite, then $\operatorname{det}{(M)}\leq \prod_i m_{ii}$

In the Wikipedia article on positive definite matrices they claim that if $M$ is positive definite, then the determinant of $M$ is bounded by the product of its diagonal entries. How might we show ...

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