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I greatly enjoyed the Lights Out game described [here][1] (I am sorry I had to link to an older page because some wikidiot keeps deleting most of the page).
Its mathematical analysis is [here][2] (it's just linear algebra)
Now I just discovered a hexagonal version:
>http://cwynn.com/games/lightsoutmobile.htm ... |
I greatly enjoyed the Lights Out game described [here][1] (I am sorry I had to link to an older page because some wikidiot keeps deleting most of the page).
Its mathematical analysis is [here][2] (it's just linear algebra)
Now I just discovered a hexagonal version:
>http://cwynn.com/games/lightsoutmobile.htm ... |
I have two random variables $X$ and $Y$, both receiving values between 0 and 1.
I know that $E[X - Y] \ge 0$.
Can I get any inequality of the form:
$P(X - Y \ge \delta) \le F(\delta,X,Y)$
where $F(\delta,X,Y)$ is a (reasonable) function of $\delta$ and $E[X-Y]$?
Markov inequality would be good here, for ... |
can I get a bound on the probability of deviation, similar to Markov inequality? |
I've read about many attempts to find patterns in prime numbers. First, is there a mathematical way to prove there is not a pattern to prime numbers? Since there are ways to check if a number is prime or not, can these methods be combined into some large function that produces prime numbers? And in case it isn't obv... |
**Part1(Solved)**
Is it possible to create a function that maps x to y as follows:
x 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 ...
y 0 1 2 3 4 5 4 3 2 1 0 1 2 3 4 5 ...
So far, this is what I have been able to come up with:
|5 sin ((1/10)*pi*x)|
Which will give the following y's ... |
You can also use trig based on the dihedral angle between two faces of the tetrahedron.
Writing $ABC$ for the base triangle, $O$ for the apex, $K$ for the center of $ABC$ (the foot of the perpendicular dropped from $O$), and $M$ for the midpoint of (for instance) side $BC$, we have a right triangle $OKM$ with right ... |
Is $L^2(\mathbb{R})$ a Banach algebra, with convolution?
I am pretty sure the answer is no, because I think that
$f,g \in L^2(\mathbb{R})$ does not imply that $f*g \in L^2(\mathbb{R})$. However, I can't seem to find a counterexample, or a proof that this is not the case, using Fourier Transform for example.
Can ... |
Is $L^2(\mathbb{R})$ with convolution a Banach Algebra? |
Suppose $R=k[[x_1,...,x_n]]$ is a formal power series ring over the field $k$, what can we say about the structure of $R/p$ if $p$ is a prime ideal of $R$ such that dim$(R/p)=1$. In particular, are these subrings of power series rings in one variable? |
It took me quite a while to understand what exactly is meant by *Fourier transform* since it can refer to various algorithms, operations and results. Though I'm quite new in this topic, I'll try to give a short but hopefully intuitive overview on what I came up with (feel free to correct me):
Let's say you have a fu... |
I have a probability space
omega = 2^{1,...,n}
sigma-algebra 2^omega
and P({s})=(p^|s|)*(1-p)^(n-|s|)
I assume that n=2k,k natural number
I need to find a random variable that will distribute like Bin(k,p^2)
can you help me with this please?
thanks.
benny |
(a)Is there a linear mapping $f : \mathbb{R}^{3} \rightarrow \mathbb{R}^3$ with
$ f(1,1,1)=(3,2,7), f(0,2,1)=(2,1,-1), f(2,0,1)=(1,0,0)$?
(b)Is there a linear mapping $f :\mathbb{R}^{3} \rightarrow \mathbb{R}^3$ with
$ f(0,2,-1)=(3,-1,3), f(1,0,2)=(0,-2,1), f(-2,2,-5)=(3,3,1)$?
Substantiate your statements and... |
Are there linear mappings for the following vectors, if so, what are they? |
Suppose $R=k[[x_1,...,x_n]]$ is a formal power series ring over the field $k$, what can we say about the structure of $R/p$ if $p$ is a prime ideal of $R$ such that dim$(R/p)=1$. In particular, are these subrings of power series rings in one variable?
Motivation: Given a subring of a power series ring in one variabl... |
Let $a$ and $b$ be real numbers and $p>0$. What is the best way to prove that $|a+b|^p<2^p(|a|^p+|b|^p)$? |
Let $\{f_n\}$ be a sequence of smooth functions which converges to a function $f$. If the convergence is not uniform at a point $a$ the $f$ is discontinuous at $a$.
Is there any different type of convergence where if it happens at $a$ then $f$ is continuous at $a$ but is not differentiable.
**EDIT**
Let $\{f_... |
If you divide $2^p$ on both sides, then you get $(|a+b|/2)^p < |a|^p + |b|^p$. Can you see why that would be true? |
I have a probability space
omega = $2^{\{1,\ldots,n\}}$
$\sigma$-algebra $2^\omega$
and $P(\{s\})=(p^{|s|})*(1-p)^{(n-|s|)}$
I assume that $n=2k$,$k$ natural number
I need to find a random variable that will distribute like $\mathrm{Bin}(k,p^2)$
can you help me with this please?
thanks.
benny |
The task:
$\lim_{x\to\infty} \sqrt{x^2+1} -x $
I've multiplied with the conjugate expression ($\sqrt{x^2+1} +x$), then I get this
$\lim_{x\to\infty} \frac{x^2+2}{\sqrt{x^2+1} +x} $
Is this correct so far? And what would be the next step? |
Another limit task, I've multiplied by the conjugate, now what? |
The task:
$\lim_{x\to\infty} \sqrt{x^2+1} -x $
I've multiplied with the conjugate expression ($\sqrt{x^2+1} +x$), then I get this
$\lim_{x\to\infty} \frac{1}{\sqrt{x^2+1} +x} $
Is this correct so far? And what would be the next step? |
>
I would like the bound to go to 0 as E[X-Y] goes to 0 as well, and it won't happen with this bound. I should have specified it explicitly when I wrote "reasonable", perhaps it was not clear. Any ideas about that?
I don't think such a bound is possible. Consider $X,Y$ i.i.d uniform. $E[X-Y] = 0$ yet $P(X-Y \geq \... |
I have a question about solving a system of geometric equations. I really hope someone on MO can help me, it's been several months since I try to solve the problem but without success. As I am not an expert in maths, I count on your help. Thank you in advance.
**Problem:**
I have 3 cercles C1, C2, C3. For exampl... |
I have a question about solving a system of geometric equations. I really hope someone on MO can help me, it's been several months since I try to solve the problem but without success. As I am not an expert in maths, I count on your help. Thank you in advance.
**Problem:**
I have 3 cercles C1, C2, C3. For exampl... |
To operate or not to operate? |
I have a question about solving a system of geometric equations. I really hope someone here can help me, it's been several months since I try to solve the problem but without success. As I am not an expert in maths, I count on your help. Thank you in advance.
**Problem:**
I have 3 cercles C1, C2, C3. For example... |
(i) You are sort of on the right track, but you are trying to (1) prove too much; and (2) drawing the wrong conclusion.
If you have a bunch of linearly independent vectors, then you can *always* find (at least one) linear transformation that maps them to whatever you want. This because we can always do it with a bas... |
As seen in the other answers $L^2(\mathbb{R})$ is not a Banach algebra. Instead we may consider a *weighted* $L^2$-space, let $w$ be a positive continuous function defined on $\mathbb{R}$ and $L^2_w= L^2_w(\mathbb{R})$ be the space of all measurable functions $f$ such that
$fw\in L^2(\mathbb{R})$ - the norm is defined... |
I have a question about solving a system of geometric equations. I really hope someone here can help me, it's been several months since I try to solve the problem but without success. As I am not an expert in maths, I count on your help. Thank you in advance.
**Problem:**
I have 3 cercles C1, C2, C3. For example... |
I have a question about solving a system of geometric equations. I really hope someone here can help me, it's been several months since I try to solve the problem but without success. As I am not an expert in maths, I count on your help. Thank you in advance.
**Problem:**
I have 3 cercles C1, C2, C3. For example... |
Let $\ell^n_p$ denote $\mathbb{R}^n$ with the $p$-norm; assume $n>1$. Now it's well-known that for $p\ne q$, $\ell^n_p$ and $\ell^n_q$ are never isometric unless $n=2$ and $\{p,q\}=\{1,\infty\}$, but I realized recently I didn't actually know how to prove this.
I can prove most of it - the only case I still need to... |
How to show $\ell^2_p$ not isometric to $\ell^2_{p'}$ unless $p\in\{1,2,\infty\}$? |
Does every Latin square contain a diagonal in which no symbol appears thrice? |
(i) You are sort of on the right track, but you are trying to (1) prove too much; and (2) drawing the wrong conclusion.
If you have a bunch of linearly independent vectors, then you can *always* find (at least one) linear transformation that maps them to whatever you want. This because we can always do it with a bas... |
I greatly enjoyed the Lights Out game described [here][1] (I am sorry I had to link to an older page because some wikidiot keeps deleting most of the page).
Its mathematical analysis is [here][2] (it's just linear algebra)
Now I just discovered a hexagonal version:
>http://cwynn.com/games/lightsoutmobile.htm ... |
(i) You are sort of on the right track, but you are trying to (1) prove too much; and (2) drawing the wrong conclusion.
If you have a bunch of linearly independent vectors, then you can *always* find (at least one) linear transformation that maps them to whatever you want. This because we can always do it with a bas... |
Suppose $R=k[[x_1,...,x_n]]$ is a formal power series ring over the field $k$, what can we say about the structure of $R/p$ if $p$ is a prime ideal of $R$ such that dim$(R/p)=1$. In particular, are these subrings of power series rings in one variable?
Motivation: Given a subring of a power series ring in one variabl... |
Could someone provide me with good explanation of why $0^0 = 1$?
My train of thought:
$x > 0$
$0^x = 0^{x-0} = 0^x/0^0$, so
$0^0 = 0^x/0^x = ?$
Possible answers:
1. $0^0 * 0^x = 1 * 0^x$, so $0^0 = 1$
2. $0^0 = 0^x/0^x = 0/0 = undefined$
Thank you
PS. I've read the explanation on mathforum... |
In fact, there is no agreement on what $0^0$ "should" be, so it is usually left undefined.
Basically, if you consider $x^y$ as a function of two variables, then there is no limit as $(x,y)\to(0,0)$ (with $x\geq 0$): if you approach along the line $y=0$, then you get $\lim\limits_{x\to 0^+} x^0 = \lim\limits_{x\to 0^... |
A different proof of the insolubility of the quintic? |
In fact, there is no agreement on what $0^0$ "should" be, so it is usually left undefined.
Basically, if you consider $x^y$ as a function of two variables, then there is no limit as $(x,y)\to(0,0)$ (with $x\geq 0$): if you approach along the line $y=0$, then you get $\lim\limits_{x\to 0^+} x^0 = \lim\limits_{x\to 0^... |
In fact, there is no agreement on what $0^0$ "should" be, so it is usually left undefined.
Basically, if you consider $x^y$ as a function of two variables, then there is no limit as $(x,y)\to(0,0)$ (with $x\geq 0$): if you approach along the line $y=0$, then you get $\lim\limits_{x\to 0^+} x^0 = \lim\limits_{x\to 0^... |
Why does X divided by zero not equal X? After all, X is not being divided by anything. |
Why does X divided by zero not equal X? |
Here's an approach that leverages the geometry of the situation.
Let $K_i$ be the center of circle $C_i$.
Points $N_2$ and $N_3$ on $C_1$ can be considered "known". Hence, the measure of the central angle $N_2 K_1 N_3$ (corresponding to the "top" arc $N_2 N_3$ in your diagram) is also known, and easily computable... |
A homework problem states:
An aquarium 5 ft long, 2ft wide, and 3ft deep is full of water. Part C: find the hydrostatic force on one end of the aquarium.
Questions (I've completed part a and b. B asked for the force on the bottom which was 1875 lbs.:
1. What exactly does one end of the aquarium mean?
2. Is ... |
Just today I had a bet with my friend over the following problem:
How many winning configurations can you have in a nxn Tic-Tac-Toe game where players win if a they get n/2 in either a row or column, consecutively.
n is even.
For example, in a 4x4 game, players win if a they get 2 of their symbols in either a ... |
In fact, there is no agreement on what $0^0$ "should" be, so it is usually left undefined.
Basically, if you consider $x^y$ as a function of two variables, then there is no limit as $(x,y)\to(0,0)$ (with $x\geq 0$): if you approach along the line $y=0$, then you get $\lim\limits_{x\to 0^+} x^0 = \lim\limits_{x\to 0^... |
Just today I had a bet with my friend over the following problem:
How many winning configurations can you have in a nxn Tic-Tac-Toe game where players win if a they get n/2 in either a row or column, consecutively.
n is even.
For example, in a 4x4 game, players win if a they get 2 of their symbols in either a ... |
Could someone provide me with good explanation of why $0^0 = 1$?
My train of thought:
$x > 0$
$0^x = 0^{x-0} = 0^x/0^0$, so
$0^0 = 0^x/0^x = ?$
Possible answers:
1. $0^0 * 0^x = 1 * 0^x$, so $0^0 = 1$
2. $0^0 = 0^x/0^x = 0/0 = \text{undefined}$
Thank you
PS. I've read the explanation on ma... |
Let $F \to E \to B$ be a fibration with $B$ simply connected (more generally, such that $\pi_1(B)$ acts trivially on the homology of $F$). Then there is a Serre spectral sequence $H_p(B, H_q(F)) \to H_{p+q}(E)$. One can do the same for singular cohomology. However, for reasonable spaces (specifically, locally contract... |
Is the Serre spectral sequence a special case of the Leray spectral sequence? |
I am looking to expand my knowledge on set theory (which is pretty poor right now -- basic understanding of sets, power sets, and different (infinite) cardinalities). Are there any books that come to your mind that would be useful for an undergrad math student who hasn't taken a set theory course yet?
Thanks a lot ... |
What are good books/other readings for intro set theory? |
What are good books/other readings for elementary set theory? |
Let $\ell^n_p$ denote $\mathbb{R}^n$ with the $p$-norm; assume $n>1$. Now it's well-known that for $p\ne q$, $\ell^n_p$ and $\ell^n_q$ are never isometric unless $n=2$ and $\{p,q\}=\{1,\infty\}$, but I realized recently I didn't actually know how to prove this.
I can prove most of it - the only case I still need to... |
I recommend Naive Set Theory by Halmos. It's a friendly, thin and fun to read introduction to set theory.
http://books.google.com/books?id=x6cZBQ9qtgoC&printsec=frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false |
I recently bought the book [Basic Set Theory](http://www.amazon.com/Basic-Theory-Student-Mathematical-Library/dp/0821827316/ref=sr_1_1?ie=UTF8&qid=1290317475&sr=8-1) by A. Shen and N.K. Vereshchagin and it has been a really nice read. It is very accessible and has a lot of exercises. It covers the basics and is very sh... |
In Calculus and Analysis, there is no good answer as to what $0^0$ "should" be, so it is usually left undefined.
Basically, if you consider $x^y$ as a function of two variables, then there is no limit as $(x,y)\to(0,0)$ (with $x\geq 0$): if you approach along the line $y=0$, then you get $\lim\limits_{x\to 0^+} x^0 ... |
In Calculus and Analysis, there is no good answer as to what $0^0$ "should" be, so it is usually left undefined.
Basically, if you consider $x^y$ as a function of two variables, then there is no limit as $(x,y)\to(0,0)$ (with $x\geq 0$): if you approach along the line $y=0$, then you get $\lim\limits_{x\to 0^+} x^0 ... |
Let ( L, ≤ ) be a lattice, x, y, z ∈ L. Prove that : $x ∧ y ≤ x$ and $x ∧ y ≤ y$
Here is how I proceeded to solve it:
*Approach 1 : Proceeding by definition*:
$x ∧ y ∈$ { x, y }
Therefore, x ∧ y either x or y
If $x ∧ y = x, x ≤ x$ is true by reflexive property and $x ≤ y$ as L is a poset
If $x ∧ y = y... |
I do not see why you assert that $x\wedge y$ must be either $x$ or $y$. This is not true in an arbitrary lattice: for instance, in the lattice of subsets of a given set $X$ (with $\wedge$ corresponding to intersection and $\vee$ to union) it is false that $x\cap y$ must be either $x$ or $y$.
As to your "proof by co... |
I do not see why you assert that $x\wedge y$ must be either $x$ or $y$. This is not true in an arbitrary lattice: for instance, in the lattice of subsets of a given set $X$ (with $\wedge$ corresponding to intersection and $\vee$ to union) it is false that $x\cap y$ must be either $x$ or $y$. So you should really be fee... |
I do not see why you assert that $x\wedge y$ must be either $x$ or $y$. This is not true in an arbitrary lattice: for instance, in the lattice of subsets of a given set $X$ (with $\wedge$ corresponding to intersection and $\vee$ to union) it is false that $x\cap y$ must be either $x$ or $y$. So you should really be fee... |
I do not see why you assert that $x\wedge y$ must be either $x$ or $y$. This is not true in an arbitrary lattice: for instance, in the lattice of subsets of a given set $X$ (with $\leq$ corresponding to inclusin, $\wedge$ corresponding to intersection, and $\vee$ corresponding to union) it is false that $x\cap y$ must ... |
I read that one can prove by AM-GM-inequality that for all $a,b,c\in\mathbb{R}_+$ we have that
$$11(a^6 + b^6 + c^6) + 40abc(ab^2 + bc^2 + ca^2) \ge 51abc(a^2b + b^2c + c^2a)$$
How this can be done? Is it possible to prove stronger inequalities like
$$10(a^6 + b^6 + c^6) + 41abc(ab^2 + bc^2 + ca^2) \ge 51abc(a^2b + ... |
Let $r \in \mathbb{N}$. Observe the equivalence relation $\sim \subseteq \mathbb{Z} \times \mathbb{Z}$ defined as $x \sim y :\Leftrightarrow (\exists k \in \mathbb{Z})(y=x+kr)$. Show that an operation $'+'$ on $\mathbb{Z}/\sim$ given by $[x]_\sim + [y]_\sim := [x+y]_\sim$ is well-defined.
My attempt at a proof:
... |
Could someone provide me with good explanation of why $0^0 = 1$?
My train of thought:
$x > 0$
$0^x = 0^{x-0} = 0^x/0^0$, so
$0^0 = 0^x/0^x = ?$
Possible answers:
1. $0^0 * 0^x = 1 * 0^x$, so $0^0 = 1$
2. $0^0 = 0^x/0^x = 0/0 = \text{undefined}$
Thank you
PS. I've read the [explanation][1] ... |
What is the :
1. most useful
2. prettiest
way to visualise extra dimensions in shapes and charts?
(Possibly should be a community wiki, but I can't make these) |
<br> T(n) = 2 * ∑i=1 to n-1 T(i) + 1 for n>1<br><br>
T(1) = 1
any hint or how to solve? |
$$T(n)=2\sum_{i=1}^{n-1}T(i)+1 , \quad n > 1$$
$$T(1)=1$$
any hint or how to solve? |
While experimenting with certain sums, I came to the following sum:
$$S_n = \sum_{k=0}^n \frac{n-k+1}{(n+1) (n+2) (n-k+2)}.$$
After rewriting the summand as
$$\frac{n-k+1}{(n+1) (n+2) (n-k+2)} = \frac{n^{\underline{k}}}{(n+2)^{\underline{k}}(n-k+2)^2}$$
and then feeding the sum to Mathematica, i obtained
$$S_n... |
$$T(n)=1+2\sum_{i=1}^{n-1}T(i) , \quad n > 1$$
$$T(1)=1$$
any hint or how to solve? |
I should prove or give a counterexample for:
$\partial (\bigcup_{i \in \mathbb{N}} U_i) \subset \bigcup_{i \in \mathbb{N}} (\partial U_i)$
Where $\partial$ is the boundary and (X,d) is a metric space with $A_{i} \subset X $ for each $i \in \mathbb{N}$
I cannot make up a counterexample for finite sets $A_{i}$... |
I should prove or give a counterexample for:
$\partial (\bigcup_{i \in \mathbb{N}} A_i) \subset \bigcup_{i \in \mathbb{N}} (\partial A_i)$
Where $\partial$ is the boundary and (X,d) is a metric space with $A_{i} \subset X $ for each $i \in \mathbb{N}$
I cannot make up a counterexample for finite sets $A_{i}$... |
Let $\Omega \subset R^n$ be open, and let us equip $\mathcal E = C^\infty$ with the locally convex topology induced by the following family of semi-norms:
For $K \subset \Omega$ and $\alpha, \beta \in \mathbb N _ 0 ^n$, let $|f|_{K,\alpha,\beta} = sup_{x \in K} | \partial_x^{\alpha} f(x) |$.
It is easy to see tha... |
Why is $\mathcal E$ a Montel-space? |
How to find center of ellipse from two points, and two radiuses(rx and ry) of that ellipse? (there will be two centers, I assume) |
I don't have enough karma to comment, so I'll just drop this here:
http://www.artofproblemsolving.com/Forum/viewtopic.php?t=154225
discusses the problem. |
How can I show the sequence $a_{n+1}=\frac{4a_{n}+2}{a_{n}+3}$ is bounded for every $a_{1}\in \mathbb{R}$? |
Recommended books/links for Fourier Transform beginners? |
My consideration might be total nonsense (as a high school student, I lack the mathematical knowledge to really check my idea), but I was just wondering whether one could find a continuous generalization of the Taylor series comparable to the continous Fourier transform.
Just like the Fourier transform decomposes a ... |
Is there a continuous Taylor/MacLaurin transform (like the Fourier transform)? |
What about $a_1 = -3$? The function don't even exists there.
Anyway, your argument is valid: if $a_n = f(n)$ and $\lim_{x\to \infty} f(x) = L$ then $\lim_{n\to \infty} a_n = L$.
You never care about the first terms of the sequence, because when you've convergence to the infinity, you can just pick a maximum value... |
I am trying to simplify this expression by as usual the expansion way,
$$\biggl(\frac{ 1+x^2}{1-x^2}\biggr)^2 = \frac{1}{1-y^2}$$
After some steps I am getting:
$$4x^2 - y^2 - 2x^2y^2 - x^4y^2 = 0$$
The answer suggested in my module is $x^2y = 2x - y$
For the answer to be correct I think what I should ge... |
How to prove :
$$ \ln \biggl(\frac{x+1}{x-1}\biggr) = \frac{1}{x} + \frac{1}{3x^3} + \frac{1}{5x^5} + \cdots $$ where $|x| \gt 1$
I am not able to get how to proceed on this one ? |
How to prove :
$$ \ln \biggl(\frac{x+1}{x-1}\biggr) = 2\biggl[\frac{1}{x} + \frac{1}{3x^3} + \frac{1}{5x^5} + \cdots \biggr]$$ where $|x| \gt 1$
I am not able to get how to proceed on this one ? |
I am trying to simplify this expression by as usual the expansion way,
$$\biggl(\frac{ 1+x^2}{1-x^2}\biggr)^2 = \frac{1}{1-y^2}$$
After some steps I am getting:
$$4x^2 - y^2 - 2x^2y^2 - x^4y^2 = 0$$
The answer suggested in my module is $x^2y = 2x - y$
For the answer to be correct I think what I should ge... |
Let $f_n,f \in L^p$ and $f_n \to f$ uniformly. Further let $g \in L^q$. Now, clearly $\int (f_n - f) g$ is defined. How do I show that
$$\int |f_n - f||g|$$
can be made arbitrary small if I choose $n$ large enough? If we just naively apply Hölder we will not be able to make it small but just finite. Further, we ... |
I am trying to simplify this expression by as usual the expansion way,
$$\biggl(\frac{ 1+x^2}{1-x^2}\biggr)^2 = \frac{1}{1-y^2}$$
After some steps I am getting:
$$4x^2 - y^2 - 2x^2y^2 - x^4y^2 = 0$$
The answer suggested in my module is $x^2y = 2x - y$
For the answer to be correct I think what I should ge... |
There are 1000 light bulbs and 1000 tutors. All light bulbs are off. Tutor 1 goes flipping light bulb 1,2,3,4... tutor 2 then flips 2,4,6,8...tutor 3 then 3,6,9...etc until all 1000 tutors have done this. What is the status of light bulb 25? 93? 576? Is there a general solution to find out the status of any light bul... |
Let $\mathbb{Z}_p$ be te ring of p-adic integers and let $T$,$T'$ be two free $\mathbb{Z}_p$-module with a continuous action of $G_{\mathbb{Q}_p}$ (the absolute Galois group of $\mathbb{Q}_p$).
It is not hard to see that if $T$ and $T'$ are of rank one, then there is a non zero $G_{\mathbb{Q}_p}$-equivariant map $T ... |
Let's say you have a single-lane road (single in this case meaning single lane in each direction, or what you could also call two-lane). Let's say you have a random number of vehicles on a given 10-mile stretch of road. The speed limit is 45 mph, but some people go faster and some go slower.
Is there any math that d... |
Probability in single-lane traffic flow: What are the odds of "choke points" being encountered? |
Let $f: \mathbb{R}^2 \rightarrow \mathbb{R}^2$ be bijective map with following properties:
1) $f|_{\mathbb{Q}^2}=id$;
2) Image of any line under map $f$ is again a line.
Is it right that $f=id$? |
For a 2D Gaussian distribution with
$$ \mu = \begin{pmatrix} \mu_x \\ \mu_y \end{pmatrix}, \quad \Sigma = \begin{pmatrix} \sigma_x^2 & \rho \sigma_x \sigma_y \\ \rho \sigma_x \sigma_y & \sigma_y^2 \end{pmatrix},
$$
its probability density function is
$$
f(x,y) = \frac{1}{2 \pi \sigma_x \sigma_y \sqrt{1-\rho^... |
What is the :
1. most useful
2. prettiest
way to visualise extra dimensions in shapes and charts? |
$\underset{x\rightarrow 0 }{\lim } \frac{x}{ln x}$
This was wrong, I got a big red wrong! Why doesn't L'hopital work on this one?
The problem is that ln is not defined for 0. It needs to be rewritten?
(Thanks to everyone helping me out with my homework, due anxiety I'm not able attend the class workshops.)
... |
Another limit task, x over ln x, L'Hopital won't do it? |
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