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In other words, can we find, for each $B$, a rational number $P/Q$ such that whenever $P/Q = p_1/q_1 + p_2/q_2$ then $q_1 + q_2 \geq B$?
Can you see any relation between the denominators $Q,q_1,q_2$? |
I posted this on [gamedev.stackexchange.com][1] earlier, but I didn't get any answers... and only a few views.
How can I find out the distance traveled by a Bezier Curve?
For example, the distance traveled by a Linear Bezier Curve is:
$distance = \sqrt{(x_1 - x_0)^2 + (y_1 - y_0)^2}$
But what of a Quadratic, ... |
Was trying to calculate $$\int_{0}^{\infty}e^{-x}\ln x dx=-\gamma$$ and I found this question:
I want to analyze $$\int\frac{e^{-x}}{x}dx$$
With $u=\displaystyle\frac{1}{x} \Rightarrow du = \displaystyle\frac{-1}{x^{2}} dx $, and $dv=e^{-x} \Rightarrow v=-e^{-x}$
Then
$$\int\frac{e^{-x}}{x}dx = \displays... |
These calculations are correct ? About $\int\frac{e^{-x}}{x}dx$ $ \bf{[EDITED]}$: |
A function $f(x)$ is defined $\forall x \in \mathbb{Q}$ and $ x \in (0,1)$ as $f(x) = q $ where $x = (p/q)$ in simplest form. Find $\sup_{\tau} \quad \min_{a} \quad f(a) + f(\tau-a)$ where $ a \in \mathbb{Q}$ and $ a \in (0,1)$ and $ \tau \in (\alpha,\beta)$ where $ 0< \alpha < \beta <2 $ and $ \alpha,\beta \in \m... |
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 $y$ in th... |
As a homework assignment, I've been given a particular subring of $M_2(Q)$, and asked to list all the ideals... For reference, $S$ = { set of matrices in $M_2(Q)$ with bottom left entry $0$ } is the subring in question.
I don't really see how to get a handle on this. Is there any sort of algorithmic way of doing thi... |
For a common basis, I'll state basic definitions of a category and the relation type I'm thinking of. They're here for quick clarity, not precision, so feel free to revise for an answer.
Category:
A collection of objects, a collection of arrows each with a source and target among said objects, identity arrows, an... |
I would appreciate some help with factoring a trivariate polynomial.
The polynomial in question is
$p(x,y,z)=a_1 x^7+a_2 x^5*y+a_3 x^3*y^2+a_4 x*y^3+a_5 x^4*z+a_6 x^2*y*z+a_7 y^2*z+a_8 x*z^2$, where the coefficients are integers. I would like to assign values to these coefficients such that $p$ can be factored.
Fo... |
I posted this on [gamedev.stackexchange.com][1] earlier, but I didn't get any answers... and only a few views.
How can I find out the distance traveled by a Bezier Curve?
For example, the distance traveled by a Linear Bezier Curve is:
$distance = \sqrt{(x_1 - x_0)^2 + (y_1 - y_0)^2}$
But what of a Quadratic, ... |
This is a follow-up to the question
Field reductions
http://math.stackexchange.com/questions/12082/field-reductions
There isn't a unique largest subfield not containing a,
so let {R(\a)} denote the set of maximal subfields of R not containing a,
What is the cardinality of {R(\a)} ?
From the previous questio... |
For a common basis, I'll state basic definitions of a category and the relation type I'm thinking of. They're here for quick clarity, not precision, so feel free to revise for an answer.
Category:
A collection of objects, a collection of arrows each with a source and target among said objects, identity arrows, an... |
I know that "x exp(x) = e" means x = 1, but how do you solve for it? |
I [tried to improve][1] the Wikipedia article but the edits were promptly reverted as if well-known solutions of Lights Out are "original research", despite providing several citations.
If any Stack Exchange members are Wikipedians who can assist in restoring the article, it would be greatly appreciated. Also, I wou... |
My friend claims that one could reduce the number of states of a given turning machine by somehow blowing up the tape alphabet. He does not have any algorithm though. He only has the intuition.
But I say it's not possible. Else one could arbitrarily keep decreasing the states via the same algorithm and arrive at so... |
Can we reduce the number of states of a Turing Machine? |
This is a follow-up to the question
Field reductions
http://math.stackexchange.com/questions/12082/field-reductions
There isn't a unique largest subfield of $\mathbb{R}$ not containing $a$,
so let $\{\mathbb{R}(\setminus a)\}$ denote the set of maximal subfields of $\mathbb{R}$ not containing $a$,
What is the ... |
Define $A \neq \emptyset, \mathcal{B}:=\{f: A \rightarrow \mathbb{R}: f(A) \text{is bounded} \} ,d_\infty:=\text{sup}\{|f(x)-g(x)|:x \in A\}$.
For which $A$ is $\overline {B_1(0)} \subset \mathcal{B}$ compact?
Notes: ${B_1(0)}$ is the unit sphere. I already proved that $(\mathcal{B},d_\infty)$ is a metric space.... |
As a homework assignment, I've been given a particular subring of $M_2(\mathbb{Q})$, and asked to list all the ideals... For reference, $S$ = { set of matrices in $M_2(\mathbb{Q})$ with bottom left entry $0$ } is the subring in question.
I don't really see how to get a handle on this. Is there any sort of algorithmi... |
This is a follow-up to the question
[on field reductions][1].
There isn't a unique largest subfield of $\mathbb{R}$ not containing $a$,
so let $\{\mathbb{R}(\setminus a)\}$ denote the set of maximal subfields of $\mathbb{R}$ not containing $a$,
What is the cardinality of $\{\mathbb{R}(\setminus a)\}$ ?
From... |
A function $f(x)$ is defined $\forall x \in \mathbb{Q}$ and $ x \in (0,1)$ as $f(x) = q $ where $x = (p/q)$ in simplest form. Find $\sup_{\tau} \quad \min_{a} \quad f(a) + f(\tau-a)$ where $ a \in \mathbb{Q}$ and $ a \in (0,1)$ and $ \tau \in (\alpha,\beta)$ where $ 0< \alpha < \beta <2 $ and $ \alpha,\beta \in \m... |
I want to ask, how can I simplify this formula ?
e^(i*-0.5*t)+e^(i*0.5*t)
I know that it can be simplify to cos(0.5*t), but I don't know how :/ |
I wonder if someone could shed some light in the following question
Let $(x,y)$ denote the greatest common divisor of $x$ and $y$, and let $x_1,y_1,x_2,y_2$ be integers.
Is the following statement true?
If $(x_1,y_1)=(x_2,y_2)=(x_1^2+y_1^2,x_2^2+y_2^2)=1$, then $$(x_1x_2\pm y_1y_2, x_1y_2\mp x_2y_1)=1$$
If... |
I want to ask, how can I simplify this formula ?
e^{ia} = \cos a + i\sin a
I know that it can be simplify to cos(0.5*t), but I don't know how :/ |
I want to ask, how can I simplify this formula ?
$ e^{-i*0.5t}+e^{i0.5t} $
I know that it can be simplify to cos(0.5*t), but I don't know how :/ |
I want to ask, how can I simplify this formula ?
$ e^{-i0.5t}+e^{i0.5t} $
I know that it can be simplify to $\cos(0.5t)$, but I don't know how :/ |
Define $A$ as a nonempty set, $\mathcal{B}:=\{f: A \rightarrow \mathbb{R}: f(A) \text{is bounded} \} ,d_\infty:=\text{sup}\{|f(x)-g(x)|:x \in A\}$.
For which $A$ is $\overline {B_1(0)} \subset \mathcal{B}$ compact?
Notes: ${B_1(0)}$ is the unit sphere. I already proved that $(\mathcal{B},d_\infty)$ is a metric s... |
I'll answer question 1 only for now, but I might edit this to address the others later.
One should note that corresponding to any set of orthogonal polynomials, there exists a symmetric tridiagonal matrix, called a **Jacobi matrix**, whose characteristic polynomial is the monic (leading coefficient is 1) version of ... |
Let $G$ be a group. The *canonical residually finite quotient* of $G$ is $R(G)=G/K$ where $K$ is the intersection of all the finite-index subgroups of $G$.
**Lemma:** *If $G$ is finitely generated (update)* then $G$ has at most one subgroup of each index if and only if $R(G)$ is cyclic.
*Proof:* First, note th... |
Lets imagine that we have some experiments. Each experiment may result in one of the outcomes: A, B, C. So we have probability distributions for each experiment $P_A, P_B, P_C$ which is context-dependent, e.g.:
1. $Context_1 \Rightarrow \{P_A^1, P_B^1, P_C^1\},$ experimental outcome is A
2. $Context_2 \Rightarrow... |
For a given $\tau=\frac{1}{q}$, it seems that $a$ should be (perhaps among other choices) $\frac{\tau}{2}$ with $\sup_{\tau} \quad \min_{a} \quad f(a) + f(\tau-a)=2q$. Can you prove this? If so, then the sup over $\tau$ is infinity as you can find $\tau$ with arbitrarily large denominator. |
We have (using ab for those who favor I and II, n for those who favor none, etc)
a+b+c+2ab+2ac+2bc+3abc=?
a+b+c+2ab+2ab+2ac=?
a+b+c+ab+ac+bc+abc=?
a+b+c+ab+ac+bc=?
and so? |
For a given $\tau=\frac{1}{q}, q$ prime it seems that $a$ should be (perhaps among other choices) $\frac{\tau}{2}$ with $\sup_{\tau} \quad \min_{a} \quad f(a) + f(\tau-a)=2q$. Can you prove this? If so, then the sup over $\tau$ is infinity as you can find $\tau$ with arbitrarily large denominator. |
Let C be a collection of subsets of $\mathbb{N}$ such that $A,B\in C \Rightarrow A \not\subseteq B$. Can C be uncountable? |
Can a collection of subsets of N such that no one set contains another be uncountable? |
Let $T$ be a bounded linear operator on $L^2(\mathbb R)$. So, let us now assume that $T$ commutes with the translations $\tau_x$. How do I now show that $T$ is given by a convolution with respect to a distribution?
By the way, I know I can probably find the proof somewhere in one of Stein's books, but I would like t... |
Let $T$ be a bounded linear operator on $L^2(\mathbb R)$. So, let us now assume that $T$ commutes with the translations $\tau_x$. How do I now show that $T$ is given by a convolution with respect to a distribution?
By the way, I know I can probably find the proof somewhere in one of Stein's books, but I would like t... |
I have the following situation:
I have a hermitian Matrix $A$ that satisfies some symmetries which I can express via
$AS = SA$ for a unitary matrix $S$. Now I am interested in the eigenvectors of $A$, but I want that these eigenvectors also respect my symmetries ( compare to Bloch waves in physics where the eigenvec... |
Your function is really
$$F: Context \mapsto \mathbb{P}(X|Context)$$
or in other words you just want to determine the probability of a particular outcome, conditional on a certain context. The question is, what are your data? Do you know about the different contexts? Or do you only dispose of the outcomes?
A... |
I have the following situation:
I have a hermitian Matrix $A$ that satisfies some symmetries which I can express via
$AS = SA$ for a unitary matrix $S$. Now I am interested in the eigenvectors of $A$, but I want that these eigenvectors also respect my symmetries ( compare to Bloch waves in physics where the eigenvec... |
According to precedence of logical connectives ([link text][2]), operator => gets higher precedence than <=> operator. But what about associativity of => operator?
I couldnot locate any book/webpage that mentions about associativity of logical operators in discrete mathematics.
Please also cite the reference (book... |
A function $f(x)$ is defined $\forall x \in \mathbb{Q}$ and $ x \in (0,1)$ as $f(x) = q $ where $x = (p/q)$ in simplest form. Find $\sup_{\tau} \quad \min_{a} \quad f(a) + f(\tau-a)$ where $ a \in \mathbb{Q}$ and $ a \in (0,1)$ and $ \tau \in (\alpha,\beta)$ where $ 0< \alpha < \beta <2 $ and $ \alpha,\beta \in \m... |
For a given matrix $A$ the question "is there a vector (or are there vectors)
whose direction remain the same when it is multiplied with the matrix"
leads to the well-known eigenvalue problem $A\mathbf{v}=\lambda\mathbf{v}$,
where $\mathbf{v}$ is an eigenvector of the matrix. Since a vector is fully
described by it... |
Yes it is possible to reduce the number of states a Turing machine uses to decide a problem $X$ by increasing the number of symbols.
However it gets very tricky when you are close to the *minimum number* of states/symbols needed to solve $X$
Here is a nice survey paper about the efforts to find the minimum number ... |
A function $f(x)$ is defined $\forall x \in \mathbb{Q}$ and $ x \in (0,1)$ as $f(x) = q $ where $x = (p/q)$ in simplest form. Find $\sup_{\tau} \quad \min_{a} \quad f(a) + f(\tau-a)$ where $ a \in \mathbb{Q}$ and $ a \in (0,1)$ and $ \tau \in (\alpha,\beta)$ where $ 0< \alpha < \beta <2 $ and $ \alpha,\beta \in \m... |
I'm trying to wrap my head around this:
$a \equiv b^{-1} (\mod y)$
$x \equiv c^{-1} (\mod y)$
I know all values but $x$ and $y$. Is it possible to solve this problem for $x$?
Can anyone point out a good ressource on this kind of problems?
|
In other words, can we find, for each $B$, a rational number $P/Q$ such that whenever $P/Q = p_1/q_1 + p_2/q_2$ then $q_1 + q_2 \geq B$?
Can you see any relation between the denominators $Q,q_1,q_2$?
EDIT: Taking a common denominator, we see that $Q | q_1 q_2$ and in particular, $Q \leq q_1 q_2$. Thus, if $Q \geq... |
Some suggestions:
Even though the delta function is not in $L^2$, heuristically what does your condition on $T$ say when applied to the delta function? Now, given the answer to the previous question and the fact that every function is an average of translated delta functions, what does one expect $Tf$ to be for an a... |
For a given group of data, I have both a mean and variance (already calculated). Looking over the raw spread of data, and its numerous outliers, I expect that variance will be high.
My question is -- now that I have my variance calculated, what do I need to compare it to to determine if the variance is significant (... |
How do I determine if my variance is significant? |
In other words, can we find, for each $B$, a rational number $P/Q$ such that whenever $P/Q = p_1/q_1 + p_2/q_2$ then $q_1 + q_2 \geq B$?
Can you see any relation between the denominators $Q,q_1,q_2$?
EDIT: Taking a common denominator, we see that $Q | q_1 q_2$ and in particular, $Q \leq q_1 q_2$. Thus, if $Q \geq... |
I have skimmed this video that I found on mathoverflow:
http://tube.sfu-kras.ru/video/407?playlist=397
At about 15:05 the lecturer wrote down an equality
$\sum F(m_1, \ldots, m_m)z^{m_1}\ldots z^{m_m} = \frac{1}{det(zI - A)}$, where F is given in terms of coefficients of the $m$-by-$m$ matrix $A$. The definition o... |
I know this is a trivial problem but am stuck with this thing.
We want to minimize $$x^TAx - 2x^Tb$$ subject to $$C^Tx = 0$$ $A \in \mathbb{R}^{m \times m}$ is a symmetric positive definite matrix and $C \in \mathbb{R}^{m \times p}$
Using Lagrange multipliers minimizing the above leads to the well-known KKT syste... |
Let $P$ and $Q$ be complex polynomials with $deg(P) < deg(Q)$.
Let $Q(z) = (z-z_1)^{k_1} (z-z_2)^{k_2}...(z-z_m)^{k_m}, z_i \in \mathbb{C} \text{ and } k_i \in \mathbb{N}$ be a complete decomposition. Then, I have to prove that there exists a unique exposition of the following form:
$\frac{P(z)}{Q(z)} = \sum\lim... |
I'm trying to wrap my head around this:
$a \equiv b^{-1}\pmod{y}$
$x \equiv c^{-1} \pmod{y}$
I know all values but $x$ and $y$. Is it possible to solve this problem for $x$?
Can anyone point out a good resource on this kind of problems?
|
I have skimmed this video that I found on mathoverflow:
http://tube.sfu-kras.ru/video/407?playlist=397
At about 15:05 the lecturer wrote down an equality
$\sum F(m_1, \ldots, m_m)z^{m_1}\ldots z^{m_m} = \frac{1}{det(zI - A)}$, where F is given in terms of coefficients of the $m$-by-$m$ matrix $A$. The definition o... |
If a cyclic subgroup has a proper subgroup of infinite order, how many finite subgroups does it have? Explain. Any help appreciated! Thank you. |
I know this is a trivial problem but am stuck with this thing.
$A \in \mathbb{R}^{m \times m}$ is a symmetric positive definite matrix and $C \in \mathbb{R}^{m \times p}$
How do I show that the matrix $$B = \begin{bmatrix} A & C \\ C^T & 0 \end{bmatrix}$$ is indefinite?
I can show that there exists a vector $v... |
Was trying to calculate $$\int_{0}^{\infty}e^{-x}\ln x dx=-\gamma$$ and I found this question:
I want to analyze $$\int\frac{e^{-x}}{x}dx$$
With $u=\displaystyle\frac{1}{x} \Rightarrow du = \displaystyle\frac{-1}{x^{2}} dx $, and $dv=e^{-x} \Rightarrow v=-e^{-x}$
Then
$$\int\frac{e^{-x}}{x}dx = \displays... |
Taken from [this](http://forumserver.twoplustwo.com/15/poker-theory/how-does-standard-deviation-relate-poker-867847/) post of mine from a poker forum.
---
You need to somehow compute the standard deviation for your distribution, and then count how many standard deviations away from the expected value your actual ... |
Taken from [this](http://forumserver.twoplustwo.com/15/poker-theory/how-does-standard-deviation-relate-poker-867847/) post of mine from a poker forum.
---
You need to somehow compute the standard deviation for your distribution, and then count how many standard deviations away from the expected value your actual ... |
Taken from [this](http://forumserver.twoplustwo.com/15/poker-theory/how-does-standard-deviation-relate-poker-867847/) post of mine from a poker forum.
---
You need to somehow compute the standard deviation for your distribution, and then count how many standard deviations away from the expected value your actual ... |
Euler's formula for connected planar graphs (i.e. a single connected component) states that $v-e+f=2$. State the generalization of Euler's formula for planar graphs with $k$ connected components (where $k\geq1$).
The correct answer is $v-e+f=1+k$, but I'm not understanding the reasoning behind it. Anyone care to sh... |
I posted this on [gamedev.stackexchange.com][1] earlier<s>, but I didn't get any answers... and only a few views</s>.
EDIT: I've got two answers there (as of now), and I'm investigating them now.
How can I find out the distance traveled by a Bezier Curve?
For example, the distance traveled by a Linear Bezier Curve... |
According to precedence of logical connectives ([link text][2]), operator $\Rightarrow$ gets higher precedence than $\Leftrightarrow$ operator. But what about associativity of $\Rightarrow$ operator?
I could not locate any book/webpage that mentions about associativity of logical operators in discrete mathematics.
... |
I'm trying to help my son study 8th grade math (in Texas). He's having trouble with the "Nth rule". Is anyone familiar with this terminology? I think that it may be related to the Nth term in a series, but I also think that it has a more specific meaning. |
What's the largest regular tetrahedron (side length x) you can fit inside a sphere with a radius of one? |
A quick google search suggests that "the $n$th rule" means finding the formula for the $n$th term of a sequence given.
For example, given $1$, $3$, $5$, $7,\ldots$, the expected "nth rule" is probably "$2n-1$", since the 1st term is $2(1)-1$, the 2nd term is $2(2)-1$, the 3rd term is $2(3)-1$, etc.
*What follows... |
What they mean is this: Suppose I give you a sequence like
2,4,6,8,...
Then I ask you: How can I obtain the n-th term in this sequence?
And you'll say: It's just $2n$.
Now, for sequences of the form $an + b$, it is quite easy to obtain the rule: Just look how the element increases in each step, this gives y... |
A quick google search suggests that "the $n$th rule" means finding the formula for the $n$th term of a given sequence of numbers.
For example, given $1$, $3$, $5$, $7,\ldots$, the expected "nth rule" is probably "$2n-1$", since the 1st term is $2(1)-1$, the 2nd term is $2(2)-1$, the 3rd term is $2(3)-1$, etc.
*W... |
I know this is a trivial problem but am stuck with this thing.
$A \in \mathbb{R}^{m \times m}$ is a symmetric positive definite matrix and $C \in \mathbb{R}^{m \times p}$
How do I show that the matrix $$B = \begin{bmatrix} A & C \\ C^T & 0 \end{bmatrix}$$ is indefinite?
I can show that there exists a vector $v... |
At Wikipedia's [Erlangen program][1] I read that "quite often, it appears there are two or more distinct geometries with isomorphic automorphism groups".
> What are (counter-)examples of geometries
> uniquely (up to isomorphism) defined
> by the isomorphism class of their
> automorphism group?
>
> What are exa... |
At Wikipedia's [Erlangen program][1] I read that "quite often, it appears there are two or more distinct geometries with isomorphic automorphism groups". *[Added:]* Some examples are given.
> What are examples of geometries nevertheless being
> uniquely (up to isomorphism) defined
> by the isomorphism class of the... |
I'm attempting to understand how B-Spline derivatives work.
To do this, i've generated some data in MATLAB to plot sin(x) over 0 - 2*pi. I then use the splinetool to fit an order 2 spline to the data which it fits perfectly. However, when I look at the 1st derivative of this sine wave data it's max is 0.017 and it'... |
At Wikipedia's [Erlangen program][1] I read that "quite often, it appears there are two or more distinct geometries with isomorphic automorphism groups". Some examples are given.
> But what are examples of geometries nevertheless *being*
> uniquely defined (up to isomorphism)
> by the isomorphism class of their
... |
Hecke operators are things that act on modular forms and give rise to a lot of interesting arithmetical results:
http://en.wikipedia.org/wiki/Hecke_operator
On the other hand on the wikpedia page for Hecke algebras, which should naively be an algebra of Hecke operators, the term seems to acquire very different me... |
I'll place something as an answer in the interest of not having questions with no answers.
I don't know what the cardinality of $\{\mathbb{R}(\setminus a)\}$ is, but I would be surprised if it is not uncountable. I'll see if I can think about it some in the next couple of days.
As for your final paragraph, the di... |
At Wikipedia's [Erlangen program][1] I read that "quite often, it appears there are two or more distinct geometries with isomorphic automorphism groups". Some examples are given.
> But what are examples of geometries nevertheless *being*
> uniquely defined (up to isomorphism)
> by the isomorphism class of their
... |
According to [the precedence of logical connectives][2], operator $\rightarrow$ gets higher precedence than $\leftrightarrow$ operator. But what about associativity of $\rightarrow$ operator?
I could not locate any book/webpage that mentions about associativity of logical operators in discrete mathematics.
Pleas... |
I think I got it. It seems to be problem 10360, originally published in 1994 (volume 101, issue 1, page 76), proposed by Richard Stanley. I'm looking at <a href="http://www.jstor.org/pss/2589004">the JSTOR page of the solution</a> (by <a href="http://math.stackexchange.com/users/226/robin-chapman">Robin Chapman</a>), w... |
I'll place something as an answer in the interest of not having questions with no answers.
I don't know what the cardinality of $\{\mathbb{R}(\setminus a)\}$ is, but I would be surprised if it is not uncountable. I'll see if I can think about it some in the next couple of days.
As for your final paragraph, the di... |
For a common basis, I'll state basic definitions of a category and the relation type I'm thinking of. They're here for quick clarity, not precision, so feel free to revise for an answer.
Category:
A collection of objects, a collection of arrows each with a source and target among said objects, identity arrows, an... |
Problem:
Let $\omega\in\Omega^r(M^n)$ suppose that $\int_\sum \omega = 0$ for every oriented smooth manifold $\sum \subseteq M^n$ that is diffeomorphic to $S^r$. Show that $d\omega = 0$.
Proof:
Assume $d\omega \neq 0$. Then there exists $v_1, \ldots, v_{r+1}\in T_pM$ such that $d\omega_p(v_1, \ldots, v_{r+1}) \ne... |
Recall that a **model category** is a complete and cocomplete category with classes of morphisms called *cofibrations, fibrations,* and *weak equivalences.* These are closed under composition and satisfy certain axioms, such as lifting properties. Furthermore, according to Mark Hovey (but this apparently varies in the ... |
Why is Top a model category? |
Recall that a **model category** is a complete and cocomplete category with classes of morphisms called *cofibrations, fibrations,* and *weak equivalences.* These are closed under composition and satisfy certain axioms, such as lifting properties. Furthermore, according to Mark Hovey (but this apparently varies in the ... |
What you are asking for is a special case of the joint distribution of the maximum and sum of a sequence of random variables. The fact that the variables are stable simplifies this and allows us to compute the joint distribution in the limit as n goes to infinity. This limit can be described in terms of the joint distr... |
This is some sort of standard puzzle, which many do it using trial and error or brute-force method. The question goes like this, given the numbers, 11,13,31,33,42,44,46 what is choices of numbers (a number can be chosen more than once) so that sum adds up to 100.
Is there a formula like way or approach to this other... |
Are there any interesting examples of second order stationary process on ${\mathcal R}^2$ or ${\mathcal R}^3$ that are not isotropic? The book I am looking at has no examples. |
What you are asking for is a special case of the joint distribution of the maximum and sum of a sequence of random variables. The fact that the variables are stable simplifies this and allows us to compute the joint distribution in the limit as n goes to infinity. This limit can be described in terms of the joint distr... |
Could you prove or disprove the following statement?
> Let
> $f\colon[0,1]^2\rightarrow \mathbb R$
> be a continuous function. Then
> there are continuous functions
> $g,\ h\colon [0,1]\rightarrow \mathbb R$ and
> $\Phi\colon \mathbb R \to \mathbb R$
> such that $$ f(x,y) = \Phi(g(x) + h(y)).$$
(This ... |
The Green theorem has the form:
$$\oint P(x,y)dx = - \iint \frac{\partial P}{\partial x}dxdy , \oint Q(x,y)dy = \iint \frac{\partial Q}{\partial y}dxdy $$
The Cauchy-Riemann equations has the following form:
$$\frac{\partial P}{\partial x} = \frac{\partial Q}{\partial y}, \frac{\partial P}{\partial y} = - \frac{\pa... |
Is there any connection between Green theorem and Cauchy-Riemann equations? |
The Green theorem has the form:
$$\oint P(x,y)dx = - \iint \frac{\partial P}{\partial x}dxdy , \oint Q(x,y)dy = \iint \frac{\partial Q}{\partial y}dxdy $$
The Cauchy-Riemann equations has the following form:(Assuming $z = P(x,y) + iQ(x,y)$)
$$\frac{\partial P}{\partial x} = \frac{\partial Q}{\partial y}, \frac{\par... |
Green's Theorem has the form:
$$\oint P(x,y)dx = - \iint \frac{\partial P}{\partial x}dxdy , \oint Q(x,y)dy = \iint \frac{\partial Q}{\partial y}dxdy $$
The Cauchy-Riemann equations have the following form:(Assuming $z = P(x,y) + iQ(x,y)$)
$$\frac{\partial P}{\partial x} = \frac{\partial Q}{\partial y}, \frac{\part... |
Is there any connection between Green's Theorem and the Cauchy-Riemann equations? |
Recall that a **model category** is a complete and cocomplete category with classes of morphisms called *cofibrations, fibrations,* and *weak equivalences.* These are closed under composition and satisfy certain axioms, such as lifting properties. Furthermore, according to Mark Hovey (but this apparently varies in the ... |
In propositional logic, for example:
¬p v q
If p is true at the outset, does that mean it must be considered false when comparing with q in the disjunction?
P.S. I am unsure about tags for this question. |
Are standalone propositions affected by negation operators? |
In propositional logic, for example:
$$\neg p \vee q.$$
If $p$ is true at the outset, does that mean it must be considered false when comparing with q in the disjunction?
P.S. I am unsure about tags for this question. |
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