A travelling wave solution of a PDE or ODE is a solution that depends on the single variable $\xi=x-ct$.
For example consider the PDE
$$
u_t=u_{xx}+f(u)-w,~~~w_t=\epsilon (u-\gamma w).~~~~~(1)
$$
Then, a travelling wave $(u(\xi), w(\xi)$ satisfies
$$
-cu_{\xi}=u_{\xi\xi}+f(u)-w,~~~~~-cw_{\xi}=\...
I have completed the questions below but am not sure if they are correct. If anyone could help me confirm them it would be much appreciated.
3)
This took me a little while but it seems to hold up. Im not sure if just writing (n+m) = odd number is ok but they use something similar in the fourth q...
If $[x]^2-5[x]+6=0$,where $[x]$ denotes the greatest integer less than or equal to $x$,then total set of values of $x$ is
$(A)x\in[3,4)$$(B)x\in[2,3]$$(C)x\in\left\{2,3\right\}$$(D)x\in[2,4)$
My attempt:
$[x]^2-5[x]+6=0$
$[x]=2,[x]=3$
$2\leq x<3,3\leq x<4$
But i cant figure out what is the ans...
My proof :
Let $x \in S'$
Suppose $x \notin S$.
Therefore $B(x,r) \cap S =\phi$ for all $r>0.$
This a contradiction as $x \in S' \Rightarrow\exists r>0 $ s.t. $B(x,r)/\{x\}\cap S \neq\phi$
So $x \in S$
$\therefore S'\subseteq S $
So $S=\bar S=S \cup S'$.
Thus $S$ is closed.
What are the definitions on Big O and little o for when $x \in R^m$ approaches $s\in R^m$ And not $x$ going to infinity?
Context
In topological groups it is more convenient to work with neighborhoods instead of opens.
In this respect one may characterize the topology by neighborhoods of the origin.
Moreover local compactness and other local concepts become straightforward this way.
For a comparison see the wikiped...
Show that $x^3 + 10x^2 + 6x + 2 = 0$ has no solutions in $\Bbb Z$.
This seems rather trivial to do but I don't know how to rigorously show this is true. Having graphed this and attempted to factor,I see that it is indeed true. Could someone please explain how I would go about showing this rigoro...
The formula would have been useful but I am not really good at logical reasoning especially in permutations so I need help from you guys to identify errors in my answer (as well as give hints for part b and e)
(a) $n_r=(n-1)_r+r(n-1)_{r-1}$
$n_r$ is the number of ways to choose $r$ objects...
Hi I am prerparing for exam and am doing old exams from other schools and places online , in particular questions that to me cover the same stuff we have. However usually I don't find any solutions. So I thought I will try them and post and see if anyone can please tell me if I am wrong or not et...
I've tried to measure something that I have in mind.
My problem is as following:
Let's assume that there is a group with 8 members.
There are two cases:
First, A group consists of 4 subgroups each with 1,1,2, and 4 members.(1+1+2+4=8)
Second, A group consists of 4 subgroups each with 2 members...
I just had to review this test in the LQ queue, which was a spam answer.
However, my thought was that spam should never had appeared in the LQ queue and therefore I was a bit confused about this. I recommended to delete and passed the test, of course, but I thought that maybe this could be an un...
I recently tried to contribute to SO by answering a question regarding what are the components of Rails. I noticed a lot of people gave very complicated answers and received lots of points for it. This is the link to the question asked by the candidate:
What exactly are the "components" of Rails...
Have a look at this question
Moreover, I can't delete my comment because the delete button overlaps with the sidebar...
Also, if I try to add another comment, the line break is still not working well.
Let $(V,\|\cdot\|)$ be a normed vector space. Let $x,y,x',y' \in V$. Say I want to estimate
$$\left| \|x\|-\|x'\|-(\|y\| - \|y'\|) \right|.$$
Does the following chain of inequalities hold?:
\begin{eqnarray*}
\left| \|x\|-\|x'\|-(\|y\| - \|y'\|) \right| &\leq& \left| \|x-x'\|-(\|y\| - \|y'...
I am not sure of my answer. In the figure, r=10 sin(theta) is a circle that doesn't look like a circle.
The area of r=5 is pi r^2 = 25 pi
You remove the area from -pi/3 to pi/3 of 10 cos(theta) from 25 pi
That is remove (1/2) ∫ (10 cos(theta))^2 dtheta = 74.0105
Required area = 25 pi - 74.0...
Let $\xi=x-ct$. Moreover, let $U(\xi)$ be a travelling wave solution of a PDE. Suppose that $U(\xi,t)$ is a solution of a PDE.
The travelling wave $U(\xi)$ is called stable (with respect to the PDE) if there is a neighborhood $N$ of it, such that for a solution $U(\xi,t)$ whose initial value $U...
I am looking for examples of three dimensional constructible proofs. By this I mean activities such as steps in proving $1^2+2^2+\cdots+n^2=n(n+1)(2n+1)/6$. In this construction the identity is proven by assembling 6 special pyramids that interlock to make a box.
I have little task to slove. Problem is that I have 29 balls and I must distribute them into 4 boxes. An additional requirement is that each box can have max 7 balls. I think that this problem represent number of combination with repetiton, but this additional requirement makes me problem.
The function $e^{x-x^2}$ is zero if $x \to \infty$ or $x \to -\infty$ it looks like a normal-distribution-curve with the max. value at $x=0.5$. Now how can i integrate it?
Thank you.
I would be interested in knowing a little bit about the rules governing quiver conjunction. Specifically, about addition of two quivers sharing one element (say, A-B and B-C) In which way is determined the dominant element from the quiver, so to speak?
Thnaks in advance
Suppose $(a_n)$ is a sequence of real numbers such that $a_n > 0$ for all $n \in \mathbb{N}$ and that there exists $f: [0, \infty) \to \mathbb{R}$ such that $f(n) \leqslant a_n \leqslant f(n-1)$ for all $n \in \mathbb{N}$. Assume that $f$ is a continuous function and decreasing. Also $f > 0$.
I...
Today, someone asked Why do we need both Priority and Severity? (10k link) which is clearly on-topic being about software development concepts and all that, but was soon closed as primarily opinion based. That's correct, as it was not an exact duplicate of the much older How do you classify bug s...
Let $\mathcal S$ be the set of all the solutions of the equation $$z\sin z=50\space\text{with}\space z\in \mathbb C$$
Try to make a description, as complete as possible, of the set
$\mathcal S$, in particular prove that $\mathcal S \subset \mathbb R$. What are the elements of $\mathcal S$?
I was reading a book about Catalan Numbers (Thomas Koshy Catalan numbers with applications)
And I was reading through that example.
Find the number of n-element multisets $\{a_1 ,a _2 , . . . , a_n \}$
of elements $a_i \in Z_{n+1}$ such that $a_1 + a_2 + . . . + a_n = 0$,
the additive i...
The loop is generated for θ in [7π/6, 11π/6].
(this is from setting r = 0).
So, A = ∫(7π/6 to 11π/6) (1/2)(4 + 8 sin θ)^2 dθ
= ∫(7π/6 to 11π/6) (8 + 32 sin θ + 32 sin^2(θ)) dθ
= ∫(7π/6 to 11π/6) (8 + 32 sin θ + 16(1 - cos(2θ))) dθ
= ∫(7π/6 to 11π/6) (24 + 32 sin θ - 16 cos(2θ)) dθ
= (2...
I'm new to stackoverflow.
I found an error in an answer here on stackoverflow but I do not have enough reputation to post a comment under it.
Is there a way to comment it anyway or do I have to wait and maybe forget about it?
It is completely understandable that inexperienced users are not completely aware of how to handle dupes. It is also understandable that a friendly-meaning person posts an answer, (only) linking to another answer, assuming he or she is helpful. Nothing to add, nothing to elaborate, just a link.
...
I need to calculate the inverse laplace of:
$$F(s)=[\frac{1}{\sqrt{s+a}+\sqrt{s+b}}] \qquad \qquad (s>-a\quad ;\quad s>-b;\quad a\neq b) $$
I was just browsing the newly created tags when I noticed the svgz tag.
Which is created and currently being added to "a lot" of questions by a specific user.
My spidey sense tells me this is not a very useful tag, because it is simply a gzipped svg file. But I want to double check with people ...
How do I show separation of points for
(1) $\|f\|_\infty +\|f\|_1$
My answer: $\|f\|_\infty = 0 \implies f=0$ and $\|f\|_1 \implies f=0$ so $\|f\|_\infty +\|f\|_1=0 \implies f=0+0=0$ because I know $\|f\|_\infty $ and $\|f\|_1$ are norms.
And $f=0 \implies \|f\|_\infty=0 $ and $f=0 \implies \|...
Exercise from Artin's Algebra.
Describe the centralizer $Z (\sigma) $ of the permutation $\sigma = (153)(246)$ in the symmetric group $S_{7} $, and compute the orders of $Z (\sigma) $ and of $Z (\sigma)$.
My progress:
Since $P= 1/\sqrt {2} \begin {pmatrix} 1 & i \\ 1 & -I \end {pmatrix}$
has...
x and y are positive integers,
43! = 3^x.y
What is the greatest value that x can take?
Given three side lengths, how many triangles can be formed.
A. 1
B. 2
C. 3
D. infinitely many
Hi, please evaluate the limit of the function depicted in the image.
How\ Can\ I\ prove\ that :
P_{n}(1)=\frac{\left ( \frac{1}{2} \right ){n}2^{n}}{n!} {2}F{1}(\frac{1}{2}-\frac{n}{2},\frac{-n}{2};\frac{1}{2}-n;1)=1 \
using \ gauss\ '\ theorem : \ \
2F_{1}(\alpha ,\beta ;\gamma ;1)=\frac{\Gamma (\gamma )\Gamma (\gamma -\alpha -\beta )}{\Gamma (\gamma -\alpha...
Last night my reputation was $5199$, and this morning it became $5164$, without any notification under the reputation tag.
This question was asked before. But I just want to make sure where can I view how reputation changes (clearly, the usual reputation tag doesn't help). Earlier I got notific...
Can anyone help to tell me if this is how you would do the following;
I calculated that $k=6$, for b I got $0.7407$, and for c I got $E[Y]=0.5$ while for d I got $V[Y]=0.05$
But I dont know if I am did the question correct or completely wrong. Would anyone mind please letting me know?
Just now I tried to edit this question to remove the urgent begging, so I took out this line:
Urgently waiting for a solution, thanks in advance.
When I did so, even prior to submitting the edit, a pop-up complained about the first line, saying:
Body cannot contain "I encounte"
Hmm, I...
This is my first question posted here.
I apologize if this post is misformatted or inappropriate in any way.
I have a relatively simple fitting function f(m):
$$f(m) = {1\over\sqrt{{A\over M_1} + {BV_1\over m}}} + C$$
where $A, B, C, M_1$ and $ V_1 $ are known fitting parameters for a particul...
Each time I open a profile with an empty description, I read:
Apparently, this user prefers to keep an air of mystery about them.
The correct would not be
Apparently, this user prefers to keep an air of mystery about him/her.
?
Why them if it's not plural?
This annoys me each time, ...
This is an exercise of Bredon (pg. 190) which I tried to do but got stuck at one part. He asks the following:
Let $X$ be a Hausdorff space and let $x_0 \in X$ be a point having a closed neighbourhood $N$ in $X$, of which $\{x_0\}$ is a strong deformation retract. Let $Y$ be a Hausdorff space ...
Let $A_{1}=A_{2}$ and $BM=MC$. Then prove that $AB=AC$.
Thank you
how to show that map σ((a,1),(1,b)) = ((a^3,1),(a^2,b)) is an automorphism?
Thank You.
When I go to the flag any question, I get two options for flagging as duplicate.
One is a duplicate...:
the other is duplicate of...:
There even no difference in there short description.
From intuition, as far I understand that the first one means "This question is a duplicate question of...
Let $X$ bea proper closed subset of $[0,1]$ .which of following statements is always true?
$A)$the set $X$ is countable
$B)$the set $X$
contain an open interval
$C)$ the exist $x$ $\in$$X$ such that $X$/{x} is closed
$D)$none of above
This user has a page or more of approved edits - that carry on in the proposed edit review queue-, as you may see here, which involve fixing always the same "noisy" issue: thanks found in the questions.
It seems very suspicious to me: what's going on?
Any help with Q2)b,c and Q3 appreciated
What are the most notable open problems in the field of noncommutative algebraic geometry?
If $\lim a_n = L$, then $\lim s_n = L$, where $s_n = \frac{ a_1 + \dots + a_n}{n}$
I was wondered how to find the function in this equality:
f(x^2)=1/2x
find f(x)
please help me
Just a very small premise: this meta-question is about a specific question, but the take-home lesson can concern many more questions (both from my past and my future behavior as a user).
Recently I asked a question concerning a passage from a book, and after some time I put a 150 Bounty (still ...
Given $p\in \mathbb{R}$ and $p\geq 2$ .
prone that:
$$|x+y|^p+|x-y|^p\geq 2(|x|^p+|y|^p)$$
Let $A \in \mathbb{R}^{n \times n}$ such that $$ \sum_{k=1}^n |a_{ik}| \leq 1$$ and $$ \sum_{k=1}^n |a_{kj}| \leq 1 $$ for every $1 \leq i, j \leq n.$
As far as I know then there exist scalars $\lambda_i$ such that $\sum_i |\lambda_i| \leq 1 $ such that
$$ A = \sum_{i} \lambda_i P_i,$$ whe...
The problem: Let $a$ and $b$ be commuting elements of a group $G$. Let ord($a$) $=m$ and ord($b$) $= n$; let lcm($m,n$) denote the least common multiple of $m$ and $n$.
Prove that there is an element $c$ in $G$ whose order is lcm($m,n$).
(HINT: Use the facts that (1) If $m$ and $n$ are relative...
Let $A : l_p \to l_p, 1 \le p \le \infty$ be an operator defined by $A\left ( x_n \right ) = \left ( a_n x_n \right )$ where $\left \{ a_n \right \}$ is a bounded real sequence. Prove that $A$ is compact if and only if $\lim_{n \to \infty} a_n =0$.
$A$-compact if and only if $A(B)$ is relative...
I think yes, just wanted to be sure!
http://stackoverflow.com/review/reopen/10406756
Yeah I passed the audit. It's hard to fail an audit when you know you're looking at it. But I shouldn't know it's audit before I'm done reading the first paragraph of the question. I did. I don't know how I did.
I should mark this question CW but ...
A lot of the locked questions in SO that I have seen have been really cool to explore and have a great time laughing and having fun. Apparently, I can't find a way to search for a list of all the locked questions.
Is there anyway to search for only locked questions?
prove a1,a2,a3, ...,an are distinct prime numbers where a1=2 and n>1 then a1a2a3...an+1 can be written in the form 4k+3
I have no ideas how to approach this question. Any hints?
I recently ran into this answer in the First Posts review queue.
Please clean your application and build it again.
To me, this should be a comment, not an answer, as it is not a concrete answer to the question and more of a suggestion, possibly even asking for clarification from the author....
