Mathematics Questions, Problems & Solutions : TransWikia.com ~ Page 97

What can be concluded about an equilibrium point that has finitely many trajectories that converge to it?

If you have a dynamical system $dot{x}=f(x)$ and $f(x)$ is smooth , given that $f(x_0)=0$ and only finitely many trajectories converge to $x_0$ . I think...

Asked on 11/06/2021 by abc1455

0 answer

Constant invariant quantities

What is the intuition behid the constant invariant quantities and why do we need it? How is this related with probability theory? I was solving some maximization problem and when...

Asked on 11/06/2021

0 answer

Convergence of martingales is a martingale

I am reading the book "Introduction to Stochastic Integration (Second Edition)" by K.L. Chung and R.J. Williams. I have a question about the proof of Proposition 1.3 (on page 13)...

Asked on 11/06/2021 by Satana

1 answer

Question on cardinality of a set

Does anyone know the size of this set or how to figure it out: $$ left{0.a_1a_2a_3dots colon sum_{i=2}^{infty}frac{1}{G_i}inmathbb{R}right},$$where $G_i=(9-a_{(sum_{j=1}^{i-1}j)+1})dots(9-a_{(sum_{j=1}^{i-1}j)+i})$ and if $G_i=0$, define $frac{1}{G_i} =...

Asked on 11/06/2021 by Rosco

0 answer

$X$ is a random variable with PDF $f$, with $f$ continuous at $x=a$. Then $lim_{varepsilonto0^-}frac{1}{varepsilon}P(Xin(a,a+varepsilon))=f(a)$

The Problem: Let $X$ be a random variable with density function $f$, and assume that $f$ is continuous at $x=a$. Prove that$$lim_{varepsilonsearrow0}frac{1}{varepsilon}P(Xin(a,a+varepsilon))=f(a).$$My Attempt:...

Asked on 11/06/2021 by Stackman

0 answer

Suppose that $N$ and $r$ are positive integers. Prove or disprove that if $N$ is an even integer and $r$ is odd, then $binom{N}{r}$ is even.

Suppose that $N$ and $r$ are positive integers. Prove or disprove that if $N$ is an even integer and $r$ is odd, then $binom{N}{r}$ is...

Asked on 11/02/2021 by s1mple

3 answer

Confusions about the proof of representations of isometries as products of reflections.

I am reading a proof of reflection representations of isometries that fix the origin in $mathbb{R}^n$. It is a simple induction on the dimension $n$. For $f(0)=0$...

Asked on 11/02/2021 by user806566

1 answer

Combinatorics doubts

Good morning folks, I'm really struggling with combinatorics which I have to use to arbitrate tag collisions in RFID exercises for my IOT exams. I'll also have a discrete math...

Asked on 11/02/2021 by Pietro Morri

1 answer

$limlimits_{n rightarrow infty} e^{-2n}sum_{k=0}^n frac{(2n)^k}{k!}$

Find the value of $limlimits_{n rightarrow infty} e^{-2n}sum_{k=0}^n frac{(2n)^k}{k!}$ A similar type of question was discussed here Evaluating $limlimits_{ntoinfty} e^{-n} sumlimits_{k=0}^{n} frac{n^k}{k!}$ I have tried and my answer...

Asked on 11/02/2021

2 answer

Why is $[1,2]$ relatively open in $[1,2] cup [3,4]$?

From Tao, Analysis II.Consider the set $X := [1,2] cup [3,4]$, with the usual metric. This set is disconnected because the sets $[1,2]$ and $[3,4]$ are open...

Asked on 11/02/2021

1 answer

Ask a Question

Get help from others!

Mathematics : Recent Questions and Answers (Page 97)

Ask a Question