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Given the binary alphabet {a,b}, I'm trying to find the generating function that distinguishes, for all words of fixed length $n$, the count of blocks of a's and the number of a's. For example if $n=3$ there are eight words and the term associated with each of them is:
bbb = 1
bba = xy
bab = xy
b... |
okay ive figured out the first part, now ive been told the chinese remainder theorem for the second part but i dont see how it will give me the extra 2 answers since it only allows the set 1-1000
I assume the first 6 answers are x ≡ +-3(mod y) where y=7,11,13 yet what about the other 2 answers? |
I need to write a piece of software that analyzes packet switched computer networks and calculates certain characteristics based on packet loss (the application is Voice over IP quality monitoring). One approach is to use the following 4-state Markov model (as described [here][1]):
![4-state markov model][2]
[... |
Given the binary alphabet {a,b}, I'm trying to find the generating function that distinguishes, for all words of fixed length $n$, the count of blocks of a's and the number of a's. Let $x^p$ count the number of blocks of size $p$ and $y^q$ count the number of a's in a word. As a first example, take the word:
abb... |
I'm studiying for an exam I have on combinatorics next week and I'm stuck with the solution to this question:
Imagine you have a pentagon and you want to color the corners of the pentagon so that no two adjacent corners have the same color. If you have 'q' colors, how many ways of coloring the pentagon are possible.... |
Let $A$ and $B$ be compact subsets of a metric space. Denote by $\mathcal{P}(A)$ the set of (Borel) probability measures in $A$, and similarly define $\mathcal{P}(A \cup B)$. They are compact metric. Define $C$ as the set of all elements of $\mathcal{P}(A \cup B)$ which assign probability 1 to $A$.
**Question**: Is ... |
I'm studiying for an exam I have on combinatorics next week and I'm stuck with the solution to this question:
Imagine you have a pentagon and you want to color the corners of the pentagon so that no two adjacent corners have the same color. If you have 'q' colors, how many ways of coloring the pentagon are possible.... |
The biggest problem here is that you seem to be confusing the chain rule with the power rule.
The power rule is as follows: Suppose you have some real number $n$. Then the function $f(x) =x^n$ has derivative $f'(x)=n\cdot x^{n-1}$. Notice that $n$ is fixed, but $x$ is variable.
The chain rule is as follows: Give... |
You need to specify the problem better. Do you count rotations and reflections as different? For example, imagine a regular pentagon drawn on a sheet of paper with a corner up. Starting from the top corner and going clockwise, maybe we have 0,1,2,3,4 (using numbers instead of colors). Is this different from 1,2,3,4... |
In physics there are lots of identities like:
$$\nabla \wedge (\nabla \wedge A) = \nabla (\nabla \cdot A) - (\nabla \cdot \nabla) A$$
I'm wondering if there is a fast algebraic method to prove and/or derive these identities (something like using $e^{i\theta}$ to prove trigonometric identities)?
|
Let $T_f g = f \cdot g$ where $f, g, f \cdot g$ are in $H^2(\mathbb{D})$ (where $H^2$ is the Hardy space on the open unit disk). Now $T_f$ is a bounded operator.
I want to show this by showing that $f \in H^\infty$. So I try to write $f = G_1 h_1$ and $g = G_2 h_2$ where $G_i$ are outer functions and $h_i$ inner fun... |
In physics there are lots of identities like:
$$\nabla \times (\nabla \times A) = \nabla (\nabla \cdot A) - (\nabla \cdot \nabla) A$$
I'm wondering if there is a fast algebraic method to prove and/or derive these identities (something like using $e^{i\theta}$ to prove trigonometric identities)?
|
You need to specify the problem better. Do you count rotations and reflections as different? For example, imagine a regular pentagon drawn on a sheet of paper with a corner up. Starting from the top corner and going clockwise, maybe we have 0,1,2,3,4 (using numbers instead of colors). Is this different from 1,2,3,4... |
In physics there are lots of identities like:
$$\nabla \times (\nabla \times A) = \nabla (\nabla \cdot A) - (\nabla \cdot \nabla) A$$
I'm wondering if there is an algorithmic algebraic method to prove and/or derive these identities (something like using $e^{i\theta}$ to prove trigonometric identities)?
|
Let $G$ be the fundamental group of the Klein bottle,
$G = \langle x,y \ ; \ yxy^{-1}=x^{-1} \rangle = {\mathbb Z} \rtimes {\mathbb Z} \ .$
What are the nilpotent subgroups of $G$?
I was only able to find a normal series of abelian subgroups with cyclic quotients in $G$, namely
$1\leq \langle y^2 \ ; \... |
Given representations $\rho_1 : G \to \mathrm{GL}(V)$ and $\rho_2 : G \to \mathrm{GL}(W)$, how can we define explicitly the representation of $G$ over $\mathrm{Hom}(V, W) \cong V^* \otimes W$? |
I need to write a piece of software that analyzes packet switched computer networks and calculates certain characteristics based on packet loss (the application is Voice over IP quality monitoring). One approach is to use the following 4-state Markov model (as described [here][1]):
![4-state markov model][2]
[... |
I'm studiying for an exam I have on combinatorics next week and I'm stuck with the solution to this question:
Imagine you have a pentagon and you want to color the corners of the pentagon so that no two adjacent corners have the same color. If you have 'q' colors, how many ways of coloring the pentagon are possible.... |
I wish to prove the following inequality. I have done a plot and it looks ok. $\mu \geq 1$ is an integer and so is $h$, where $0 \leq h \leq \mu-1$.
I started like this:
$\frac{e^{-\mu}\mu^{(\mu+h)}}{(\mu+h)!} \geq \frac{e^{-\mu}\mu^{(\mu-h-1)}}{(\mu-h-1)!}$.
I have rewritten this to
$(\mu-h-1)!\mu^{(\mu+h)... |
I'm studiying for an exam I have on combinatorics next week and I'm stuck with the solution to this question:
Imagine you have a pentagon and you want to color the corners of the pentagon so that no two adjacent corners have the same color. If you have 'q' colors, how many ways of coloring the pentagon are possible.... |
Every cyclic subgroup is abelian, hence nilpotent. Every such element is generated by an element of the form $x^ay^b$ with $a$ and $b$ integers.
In addition, $y^2$ commutes with $x$. Since $y^2$ is central, to determine the commutator of two elements we only need to consider the parity of the exponents of $b$ in the... |
Every cyclic subgroup is abelian, hence nilpotent. Every such element is generated by an element of the form $x^ay^b$ with $a$ and $b$ integers.
In addition, $y^2$ commutes with $x$. Since $y^2$ is central, to determine the commutator of two elements we only need to consider the parity of the exponents of $b$ in the... |
Every cyclic subgroup is abelian, hence nilpotent. Every such subgroup is generated by an element of the form $x^ay^b$ with $a$ and $b$ integers.
In addition, $y^2$ commutes with $x$. Since $y^2$ is central, to determine the commutator of two elements we only need to consider the parity of the exponents of $b$ in th... |
How would I start proving
$$
\lim_{x\to a}\left(\lim_{y\to b} f(x,y)\right) = \lim_{y\to b}\left(\lim_{x\to a} f(x,y)\right) = L$$
if both the $x$ and $y$ limits exist, and that
$$\lim_{(x,y)\to(a,b)} f(x,y) = L$$
in that case? |
why in homological mirror symmetry, we restrict us to a projective variety (calabi-yau)? Because in physics we don't need this condition. What's the general picture for general calabi-yau? |
does Slater condition holds trivially (because there are no inequality constraints) for the problem:
\min_{x,y} c*x+d*y
s.t.
exp(x) + exp(y) = 1
can I conclude there is a zero duality gap here? |
does Slater's condition hold for the following problem? |
As I'm sure many of you do, I read the [XKCD][1] webcomic regularly. The [most recent one][2] involves a joke about the Axiom of Choice, which I didn't get.
![alt text][3]
I went to Wikipedia to see what the Axiom of Choice is, but as often happens with things like this, the Wikipedia entry is not in plain, simp... |
Can you explain the "Axiom of choice" in simple terms? |
Reffered here by http://mathoverflow.net/questions/41750/determining-n-in-sigma-x0n
I'm not entirely sure if this question falls under MathOverflow but neither of my Calculus AP teachers in high school could help me with this:
Given $\Sigma_{x=0}^n {f(x)\over2}$ and the output of the summation, how would you fin... |
Every cyclic subgroup is abelian, hence nilpotent. Every such subgroup is generated by an element of the form $x^ay^b$ with $a$ and $b$ integers.
In addition, $y^2$ commutes with $x$. Since $y^2$ is central, to determine the commutator of two elements we only need to consider the parity of the exponents of $b$ in th... |
As I'm sure many of you do, I read the [XKCD][1] webcomic regularly. The [most recent one][2] involves a joke about the Axiom of Choice, which I didn't get.
![The Banach-Tarski theorem was actually first developed by King Solomon, but his gruesome attempts to apply it set back set theory for centuries.][3]
I wen... |
Can we have a measurable function $f$, whose inverse is not measurable? |
Think of $t$ and $r$ as two independent variables.
- Suppose $E$ be a function of $r$ and $V$ be a function of $(t,r)$ such that both go to $0$ at $r=0$.
- There exists positive definite function $M(r)$ such that $M(0)=0$ and $V(t,r) = -\frac{M(r)}{R(t,r)}$ where $R$ is another positive definite function such... |
It might be a good idea to say something about the connection between the axiom of choice and the Banach-Tarski paradox. The reason the Banach-Tarski paradox is counterintuitive is that we expect that if you split up a sphere into finitely many pieces, the total "mass" of all the pieces is still the same - so you shou... |
So, from what I understand, the axiom of choice is equivalent to the claim that every set can be [well ordered][1]. A set is well ordered by a relation, $R$ , if every subset has a least element. My question is: as anyone constructed a well ordering on the reals?
First, I was going to ask this question about the rat... |
Is there a known well ordering of the reals? |
One of the definitions of stochastic continuity is: $\forall a > 0$ and $\forall s \geq 0$ $$\lim_{t\rightarrow s}\;P(|X(t)-X(s)|>a) = 0.$$ What does it mean intuitively? I know that it implies the jumps but am not sure how and why. |
Online, I have read contradicting opinions on whether `intersect` should take precedence over `union` (by analogy to logical `and` and `or`), or whether all set operators should have equal precedence.
Which way makes more sense and why?
And where does `difference` fit in? (I'd say it should be equal precedence t... |
Precedence of set union, intersect, and difference? |
I am of, and I would like to retain a, mindset that mathematics does not have to have numbers as the central object of interest. With that in mind, I have done a fair amount of self-study on topics in undergrad modern algebra, looking for examples to show this is the case.
For objects like groups, it is often stated... |
Are there broad or powerful theorems of rings that do not involve numbers? |
Reffered here by http://mathoverflow.net/questions/41750/determining-n-in-sigma-x0n
I'm not entirely sure if this question falls under MathOverflow but neither of my Calculus AP teachers in high school could help me with this:
Given $\Sigma_{x=0}^n {f(x)\over2}$ and the output of the summation, how would you fin... |
Let $M$ be an $n \times n$ matrix whose elements are random reals in [0,1].
Two questions.
<ol>
<li> What is the growth rate of the magnitude of the elements of $M^k$ as a function of $k$? It is definitely
exponential, but maybe the exponent is known?</li>
<li> Is it the case that eventually one element of $M^k$ ... |
Given an $n >0$ is it possible to partition the set $\mathcal{P} = \\{1,2, \cdots, 2n\\}$ into $n$ pairs $(a_{i},b_{i})$ such that $a_{i} + b_{i}$ is a prime? |
Let $k$ be a field, $V$ a finite-dimensional $k$-vectorspace and $M \in End(V)$. How can I determine $Z$, the centralizer of $M \otimes M$ in $End(V) \otimes End(V)$?
For example, if
$$M=[[1,0],[0,2]],$$ then $M$ is 6-dimensional, consisting of block matrices of shape 1,2,1.
I was confused at first, because t... |
So i am reading up on some interesting network topologies for a CS course and what i am reading is $r$-dimensional meshes of tree's.
An $r$-dimensional mesh of trees is formed by adding complete binary tree's to an $N$-sided $r$-dimensional grid where the grid vertices act as the leafs of each binary tree.
This ... |
So i am reading up on some interesting network topologies for a CS course and what i am reading is $r$-dimensional meshes of tree's.
An $r$-dimensional mesh of trees is formed by adding complete binary tree's to an $N$-sided $r$-dimensional grid where the grid vertices act as the leafs of each binary tree.
This ... |
I need help understanding how to derivate this function:
f(x) = x^(arctan x)
f'(x) = ???
Any suggestions? |
I need help understanding how to derivate this function:
$$f(x) = x^{\arctan(x)}$$
Any suggestions? |
It is clear that a finte group of order 105 is not simple since it contains a normal Sylow 7-subgroup or a normal Sylow 5-subgroup. I wonder if it is possible that there exists a Sylow 7-subgroup and a Sylow 5-subgroup ? |
It can be shown that
$$ n \int_{0}^{1} \frac{x^n - (1-x)^n}{2x-1} \\ dx = \sum_{k=0}^{n-1} {n-1 \choose k}^{-1}$$
(For instance see my answer here: http://math.stackexchange.com/questions/4783/finding-displaystyle-lim-n-to-infty-sum-limits-k0n-n-choose-k/6533#6533)
It can also be shown that $$\lim_{n \rightarr... |
So i am reading up on some interesting network topologies for a CS course and what i am reading is $r$-dimensional meshes of tree's.
An $r$-dimensional mesh of trees is formed by adding complete binary tree's to an $N$-sided $r$-dimensional grid where the grid vertices act as the leafs of each binary tree.
This ... |
My previous answer is wrong.
Take $f(x) = x$ ($f: \mathbb{R} \to \mathbb{R}$) where the domain has the Borel $\sigma$-algebra and the range the trivial $\sigma$-algebra. Then $f$ is clearly measurable but $f$ maps for example $[0,1]$ to $[0,1]$ which is not measurable.
Or do you want both $\sigma$-algebra's to be... |
Of *course* there exist Sylow $7$-subgroups and Sylow $5$-subgroups: Sylow's Theorems tell you that the group has Sylow $p$-subgroups for every $p$ (with the Sylow $p$-subgroup being trivial if $p$ does not divide $105$).
If you meant to ask "Can the group have *normal* Sylow $5$- *and* Sylow $7$ subgroup?" then th... |
My previous answer is wrong.
Take $f(x) = x$ ($f: \mathbb{R} \to \mathbb{R}$) where the domain has the Borel $\sigma$-algebra and the range the trivial $\sigma$-algebra. Then $f$ is clearly measurable but $f$ maps for example $[0,1]$ to $[0,1]$ which is not measurable.
Or do you want both $\sigma$-algebra's to be... |
I have multiple objects in my lab which are fully described in two coordinate systems. Both systems are Cartesian and in meters. If they had a common origin but were rotated relative to each other I could easily reconcile the two. Additionally, if it was just a displacement it would be even easier. However the two are ... |
I'm looking to brush up on SAT math. Anyone know of good resources? (That's basic algebra and probability. Basic trig is good too.) |
SAT math resources? |
I've been trying to find a way to do this: given a point $P(\alpha,\beta)$, a function $f(x)$, and an angle $\theta$, find the area of the sector determined by extending a horizontal line from $P$ to $f$, and then another one from $P$ to $f$ at the angle $\theta$ from the first line. If you look at this picture:
![d... |
Good SAT math resources? |
Maybe you're going to tell me that if all you've got is a hammer, all problems look like nails, but here goes my proposal -following the same strategy as in my answers to [this question][1].
First of all, take as a model for the projective plane the disk
$$
D^2 = \left\\{ (x,y) \in \mathbb{R}^2\ \vert \ x^2 + y^... |
Maybe you're going to tell me that if all you've got is a hammer, all problems look like nails, but here goes my proposal -following the same strategy as in my answers to [this question][1].
First of all, take as a model for the projective plane the disk
$$
D^2 = \left\\{ (x,y) \in \mathbb{R}^2\ \vert \ x^2 + y^... |
Consider I have two sets that neither one is a subset of the other (for example, the set of prime numbers and the set of odd integers). Is there a specific notation that combines the meanings of both ⊄ and ⊅ ?
Also, is there a notation to mean that two sets are completely distinct and share no elements in common (fo... |
Good SAT learning resources? |
If you want to complement Bill Dubuque's answer with trying to figure out *how* you might have come up with the formula, think about what $g(x)=f(x)-2$ is telling you to do: in order to compute $g(x)$, you first compute $f(x)$, and then you subtract $2$. The inverse of this should be something that "unravels" the proce... |
Yes, it is easier using polar coordinates. If you have a region in the plane determined by two straight lines $OA$ and $OB$ starting in a point $O$ -like those in your picture- and forming angles $\theta_1$ and $\theta_2$ with respect the $x$-axis ($OB$ doesn't need to be horizontal) and you close your region with a cu... |
I've been trying to find a way to do this: given a point $P(\alpha,\beta)$, a function $f(x)$, and an angle $\theta$, find the area of the sector determined by extending a horizontal line from $P$ to $f$, and then another one from $P$ to $f$ at the angle $\theta$ from the first line. If you look at this picture:
![d... |
Maybe you're going to tell me that if all you've got is a hammer, all problems look like nails, but here goes my proposal -following the same strategy as in my answers to [this question][1].
First of all, take as a model for the projective plane the disk
$$
D^2 = \left\\{ (x,y) \in \mathbb{R}^2\ \vert \ x^2 + y^... |
I've been trying to find a way to do this: given a point $P(\alpha,\beta)$, a function $f(x)$, and an angle $\theta$, find the area of the sector determined by extending a horizontal line from $P$ to $f$, and then another one from $P$ to $f$ at the angle $\theta$ from the first line. If you look at this picture:
![d... |
So i am reading up on some interesting network topologies for a CS course and what i am reading is $r$-dimensional meshes of tree's.
An $r$-dimensional mesh of trees is formed by adding complete binary tree's to an $N$-sided $r$-dimensional grid where the grid vertices act as the leafs of each binary tree.
Somet... |
Properties of a trisected rectangle? |
Maybe you're going to tell me that if all you've got is a hammer, all problems look like nails, but here goes my proposal -following the same strategy as in my answers to [this question][1].
First of all, take as a model for the projective plane the disk
$$
D^2 = \left\\{ (x,y) \in \mathbb{R}^2\ \vert \ x^2 + y^... |
Consider I have two sets that neither one is a subset of the other (for example, the set of prime numbers and the set of odd integers). Is there a specific notation that combines the meanings of both ⊄ and ⊅ ?
Also, is there a notation to mean that two sets are completely distinct and share no elements in common (fo... |
The answer to your question is yes. All numbers of the form $x=\sum_{n\ge0}\frac{C_k}{g^{Z(k)}}$ for Z(k) eventually dominating any polynomial are indeed transcendental. As in the question, g and C<sub>k</sub> are integers with 1 ≤ C<sub>k</sub> ≤ g-1. In fact, the methods used by the paper li... |
The other day I [came across][1] the following statement:
<blockquote> A polynomial $f(x,y)$ of degree at most $3$ that vanishes at $8$ of the $9$ points $(x,y)$ with $x, y \in \{-1,0,1\}$ must also vanish at the $9$th point. </blockquote>
I am wondering about how this statement generalizes. Specifically, I am lo... |
I was wondering about the relation between complement of a subset, different between two subsets, union and intersection of subsets. Can we reduce the set of the above operations in a minimal way so that other operations can be represented by these "independent" operations? And how many ways to do this?
For example... |
(1). According to Wikipedia, a [field of subsets][1] of X is defined to be a non-empty subset of the power set of X closed under the intersection and union of pairs of sets and under complements of individual sets. I was wondering if there is any redundancy in this definition?
Can it be defined to be closed only und... |
Since union of sets is defined to be independent of the number of sets as in [Wikipedia][1]
> If M is a set whose elements are themselves sets, then x is an element of the union of M if and only if for at least one element A of M, x is an element of A.
I was wondering why for a class of subsets of a set, it being... |
Given a certain coordinate frame, I can compute a new one by applying a set of rotations in a given order (what I call Euler Z-Y-X). So I yaw, then pitch then roll.
Now imagine that I want to do exactly the opposite: given two coordinate frames (same origin to simplify), how do I find out roll, pitch and yaw angles ... |
How to extract Euler angles from a a point in a plane? |
A field is an abelian group under addition and a group under multiplication. But for the power set of a set S, under union and intersection operations and with S and the empty set being their identities, the inverse of any set is not unique for either union or intersection. So is the power set a field of sets?
Must ... |
Hey guys, I have a couple things I want to prove. I'm pretty sure a proof by induction is the best route for these.
----------
First, I need to show that $5^n < n!$ from some $n_{0} > 0$. I'm choosing $n_{0} = 12$ since that's the smallest positive integer where $n! > 5^n$.
So: $P(k) : 5^k < k!$
1. Show... |
Your first proof is correct. (If $a\le c$ and $b\le d$ and they're all positive, then $ab\le cd$.) Your second one needs just a tiny bit more. How do we know that $n!\le (n+1)^n$? It follows from your inductive hypothesis, but it's not completely trivial.
As a general tip, try not to work your proofs backwards. ... |
I am an amateur mathematician (but I do have degree's in computer science (with mathematics)). Anyways, I have written this paper, where I have proved that for $\zeta(\rho) = 0$ if $\Im(\rho) \to \infty$ then $\Re(\rho) \leq \log_2(3) - 1$.
Now this is a big claim, and I am a cranky fella ;) who has a number of with... |
A "field of sets" is a collection $\mathcal{F}$ of subsets of a given set $X$ which is closed under binary unions, intersections, and under complementation. Alas, it is not an "field" in the sense of abstract algebra.
It *is* a "subalgebra" of the Boolean algebra of the power set of $X$. Alas, here as well, "Boolean... |
A "field of sets" is a collection $\mathcal{F}$ of subsets of a given set $X$ which is closed under binary unions, intersections, and under complementation. Alas, it is not an "field" in the sense of abstract algebra.
It *is* a "subalgebra" of the Boolean algebra of the power set of $X$. Alas, here as well, "Boolean... |
If f is in $L^1(R)$, is it true that $lim\_{h \to 0+} 1/h \int_x^{x+h} f(t) dt$ exists and is finite for every x in R?
Would a statement like this follow from absolute continuity of the integral? |
If f is in $L^1(R)$, is it true that $lim\_{h \to 0+} 1/h \int_x^{x+h} f(t) dt$ exists and is finite for every x in R?
Would it be possible to use the following argument: The Lebesgue Differentiation Theoremsays that this integral is equal to f(x) a.e., which is finite a.e. if f is in $L^1(R)$. And since the integra... |
If f is in $L^1(R)$, is it true that $lim\_{h \to 0+} 1/h \int_x^{x+h} f(t) dt$ exists and is finite for every x in R?
Would it be possible to use something along the lines of the following argument: The Lebesgue Differentiation Theorem says that this integral is equal to f(x) a.e., which is finite a.e. if f is in $... |
No one on the internet (or elsewhere) is obliged to check your paper. So you have to catch people's interest and minimize the amount of investment they have to make.
Here are some suggestion based not on personal experience but from being an spectator round the Net:
1. Make your work easy to understand: Present ... |
There are other places to post papers, but most are either harder to get into (most online journals) or are less reputable than the arXiv (like viXra). Finding math forums and posting there may be your best bet.
* http://mymathforum.com/
* http://mersenneforum.org/
* http://physicsforums.com/
to name just a fe... |
If f is in $L^1(\mathbb{R})$, is it true that $\lim_{h \to 0^+} \frac1{h} \int_x^{x+h} f(t)\mathrm{d}t$ exists and is finite for every x in $\mathbb{R}$?
Would it be possible to use something along the lines of the following argument: The Lebesgue Differentiation Theorem says that this integral is equal to f(x) a.e.... |
If f is in $L^1(\mathbb{R})$, is it true that $\lim_{h \to 0^+} \frac1{h} \int_x^{x+h} f(t)\mathrm{d}t$ exists and is finite for every x in $\mathbb{R}$?
Would it be possible to use something along the lines of the following argument: The Lebesgue Differentiation Theorem says that this integral is equal to f(x) a.e.... |
If f is in $L^1(\mathbb{R})$, is it true that $\lim_{h \to 0^+} \frac1{h} \int_x^{x+h} f(t)\mathrm{d}t$ exists and is finite for every x in $\mathbb{R}$?
Would it be possible to use something along the lines of the following argument: The Lebesgue Differentiation Theorem says that this integral is equal to f(x) a.e.... |
$\lim_{\epsilon \rightarrow 0} \int \frac{1}{x^(1+\epsilon)} \mathrm{d}x $
How should I go about evaluating this integral?
Does this integral converge to $log_e x $ or to something else? |
How do I evaluate this integral? |
$\lim_{\epsilon \rightarrow 0} \int \frac{1}{x^{1+\epsilon}} \mathrm{d}x $
How should I go about evaluating this integral?
Does this integral converge to $log_e x $ or to something else?
NOTE/EDIT: The denominator is meant to be $x ^ {1+\epsilon} $ , it apprears I formatted it badly before. |
$\displaystyle\lim_{\epsilon \rightarrow 0} \int \frac{1}{x^{1+\epsilon}} \mathrm{d}x $
How should I go about evaluating this integral?
Does this integral converge to $log_e x $ or to something else?
NOTE/EDIT: The denominator is meant to be $x ^ {1+\epsilon} $ , it apprears I formatted it badly before. |
We know that the Mandelbrot set is derived from the iterations of z^2 + c.
Do anyone know something about magnet Mandelbrot? I found it in the software UltraFractal, and it is much more beautiful than the original Mandelbrot, in my opinion.
Do you know anything about it? What is it iterating? |
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