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If $A$ is a differential one form then $A\wedge A .. (more\text{ }than\text{ }2\text{ }times) = 0$ Then how does the $A\wedge A \wedge A$ make sense in the Chern-Simon's form, $Tr(A\wedge dA + \frac{2}{3} A \wedge A \wedge A)$ ?
I guess this anti-commutative nature of wedge product does not work for Lie algebra valued... |
I play a game known as Bejeweled (I'm sure some of you have heard of it) which has the following properties:
Given a planar graph with every vertex having degree 4, any path of 3 (or more) contiguous colors is considered "complete." Additionally, any two adjacent vertices may be "swapped" to produce said path. If su... |
Can anyone explain how to do these types of questions for me? I am having trouble wrapping my head around it. Thanks.
A spherical soap bubble is seen to undergo oscillations when slightly deformed. Assuming
that the frequency of these oscillations is a function of the surface tension S of the soap bubble,
the size of t... |
My friend is taking a course on probabilities and come across a problem that has a solution we both have trouble understanding:
A single printer prints, on average, 22 jobs an hour. Let's use a simplification where no job takes more than 2 minutes to complete. Using these assumptions, calculate the upper limit for the ... |
Say you have two groups $G = \langle g \rangle$ with order $n$ and $H = \langle h \rangle$ with order $m$. Then the product $G \times H$ is a cyclic group if and only if $\gcd(n,m)=1$.
I can't seem to figure out how to start proving this. I have tried with some examples, where I pick $(g,h)$ as a candidate generator of... |
Here is the question for my homework:
A mother wants to invest $\$7000.00$ for her son's future education. She invests a portion of the money in a bank certificate of deposit (CD account) which earns $4\%$ and the remainder in a savings bond that earns $7\%$. If the total interest earned after one year is $\$420.00$, h... |
Say I have $\sqrt{\frac{2}{9}}$. How would I convert this to a mixed radical where the radicand is a whole number?
I can convert the $\sqrt{8}$ to a mixed radical easily, $2\sqrt{2}$, but this fraction is tripping me up.
|
Let $n = p^k$ be a power of a prime. Let $G$ be a transitive permutation group on $n$ letters. Show that there exists a fixed-point free element of order $p$.
I can show that there must be a fixed point:
The transitivity of the group implies that there is only $1$ orbit. Burnside's lemma then implies that the average nu... |
My question:
A cashier has a total of $114$ bills, made up of tens and hundreds. The total value of the money is $\$6450.00$. How much of each kind does he have?
He has [BLANK] tens and [BLANK] hundreds.
I'm pretty sure there is an algebra equation for this. There is the hard way of doing it on paper (that takes long)... |
I have been tasked with creating a C++ program (with GDI+ for graphics) that takes a set of user defined points and creates polynomial curve through them. For extra credit, I have to support a parametric polynomial for any number of points. The thing is.. he didn't explain what a parametric polynomial is! So I need som... |
The essence of my question is, if I have a Hermitian matrix that is linearly dependent on a set of parameters and I have an estimate of its eigenvalues, is there a "simple" way to determine the values of the parameters? Ideally, I would also like to have some measure of the goodness of the fit and the degree of variat... |
I was reading through some notes on closure operations, and the example was given that for a poset $(S,\preceq)$, the operation on $(\mathcal{P}(S),\subseteq)$ given by $E\mapsto LU(E)$ is a closure operation. Here $LU(E)$ is the set of lower bounds of the upper bounds of $E$ for some $E\subseteq S$. I verified that in... |
According to Wikipedia,
A Sphenic number is a positive integer which >is the product of three distinct prime
numbers.
Anybody knows whether there is a list, say first 1000 sphenic numbers? It would be much helpful to know.
Thanks in advance
|
folks!
I have the following problem:
Suppose you have a coin that has chance p of landing heads. Suppose you flip the coin N times and let
X denote the number of "head runs" in N flips. A "head run" is defined as any sequence of heads.
For example the sequence HHTHHHHHTTTTHHTHT contains 4 head runs. I want to compute E... |
1.Find the number of ways in which a mixed double tennis game can be arranged between 10 players consisting of 6 men and 4 women.
My approach : Since,if every pair of selection of men and women gives rise to 4 matches so C(6,2) * C(4,2) * 4.
2.Find the number of ways in which a mixed double game can be arranged from am... |
I have used logic for specification of security policies in a security model. One of my reviewers asked a question that "why did you use logic and not algebra for this purpose, and what is your justification?".
The first answer that comes to my mind is that algebra is more suitable for using in modelling the behaviour ... |
How does one find the solution of
$$\dfrac{dy}{dx}\left( 1-\left( 1-t\right) x-x^{2}\right) -\left( 1+h\left( 1+t\right) +x\right) y=0\quad ?$$
where $h$ is an integer constant and $t$ is a real constant between $0$ and $1$.
$($ In Roger Apéry, Interpolations de Fractions Continues et Irrationalité de certaines Constan... |
Let $\mathcal{F}$ be an open cover of a metric space $(X,d)$. I have a question concerning some algebraic aspects of $\mathcal{F}$ and $X$.
First of all, is it always possible to consider $(X,d)$ a subspace of some bigger space $(X^{\prime},d)$, where $d$ is the inherited metric from $X^{\prime}$? If this is possible, ... |
I recently started with 2d transformations in my class. I was just working with a program when I realized the formula I am using rotates the object spirally inwards. I have no idea whats over about this.
I expected my figures to be rotated about a point but rather they all deform with every degree of rotation. I used ... |
In the $d$ variable polynomial ring $R=k[x_{1},\cdots,x_{d}]$ show that
$0, x_{1}R, (x_{1},x_{2})R, \cdots , (x_{1},x_{2},...,x_{d})R$ is a strictly increasing sequence of prime ideals and there is no longer such chain. how do I prove this claim?
Well, I am thinking that for this problem this result may be helpful: fo... |
I know how to count derivatives, but I actually don't understand what are those? What do they show?
Wikipedia explanation: Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity. I understand nothing what is written here?
Please, if you can, ... |
Let $S$ be a string of length $n$. Each character of $S$ has probability $p$ of being 'A' and probability $1-p=q$ of being 'B'. $R$ is the number of occurrences of the substring 'AB' in $S$. I'd like to determine $\mathbf{E}[R]$ and $\mathbf{var}[R]$ . I can determine the expectation via a recursive definition and tota... |
According to this article in Wikipedia: A billiard is a dynamical system in which a particle alternates between motion in a straight line and specular reflections from a boundary. When the particle hits the boundary it reflects from it without loss of speed. Billiard dynamical systems are Hamiltonian idealizations of t... |
Let $p(x)$ be a polynomial with integer coefficients, which is not constant. Then is this condition possible: $$p(x)=3^{x}$$ whenever $x \in \mathbb{N}$.
Motivation: https://mathoverflow.net/questions/34059/if-f-is-infinitely-differentiable-then-f-coincides-with-a-polynomial
|
The strength of glue is known to follow a normal distribution with a mean of $59$ and a standard deviation of $3.4$.
Find the mean strength needed such that the probability that the glue is weaker than $55$ is less than $5$%.
To solve this, I just guessed and checked in Excel:
=NORMDIST(55, 50.1, 3.4, 1)
=NORMDIST(5... |
As a part of my studies in ring theory, I've encountered the concept of an idempotent element, i.e., an element $e$ such that $e^2=e$.
Are there some interesting examples of rings with idempotent elements?
|
I'm learning category theory by self-study. I have a couple of texts, and they both talk about how we ought to try not to think so much about the equality between objects in categories. Rather, the important relation is isomorphism.
Okay, sure.
Then they go on to talk about "Cat", the category of (small) categories. O... |
Are there any good places for me to sell off my mathematics books online especially Springer and Dover books?
(I thought perhaps this was off topic, but then I thought everybody in math probably has the problem of having bought pricey books that they would prefer to get some money back for, at one point or another.)
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I have an image encoded in the form of a list of points, like so:
335.0 2743.0
335.0 2754.0
325.0 2754.0
304.0 2743.0
304.0 2733.0
283.0 2723.0
273.0 2702.0
273.0 2691.0
273.0 2681.0
273.0 2670.0
283.0 2670.0
294.0 2670.0
304.0 2670.0
325.0 2670.0
335.0 2681.0
346.0 2702.0
346.0 2712.0
356.0 2723.0
34... |
Suppose there are a finite number of disjoint unit-radii disks in the
plane, each spinning clockwise or counterclockwise at the same
angular velocity.
The plane is filled with a thin fluid layer,
and the disks can be viewed as spinning fan blades
determining vectors of fluid motion tangent to the disks.
Is the resulti... |
I know that a function of bounded variation on a closed interval can be written as a difference of increasing functions. The same is true is the function is of bounded variation on all of R, but I can't come up with a proof.
Any hints?
|
A school play ran for two nights, with
audiences totaling 1390 adults and
students. They paid 4285 dollars for
admission. One adult ticket cost 4 dollars
and one student ticket cost 2.50 dollars. The
ratio of adults to students was 3:5
for the first night and 2:3 on the
second night. How many students
... |
I have the following situation: let $m,n$ be integers such that $m|n$ and let $\zeta_m$, $\zeta_n$ denote primitive $m$ and $n$th roots of unity. Then we have the inclusion of fields
$$\mathbb{Q}\subset \mathbb{Q}(\zeta_m) \subset \mathbb{Q}(\zeta_n)$$
Now suppose we also have primes (where $(p,n)=1$)
$$(p)\subset \m... |
So I have to find the maximum possible error $dR$ in calculating equivalent resistance for three resistors, $\displaystyle\frac{1}{R}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}$ if the maximum error in each is 0.5%; $R_1=25\ \Omega$, $R_2=45\ \Omega$, $R_3=50\ \Omega$.
Now, originally I did $dR_1=dR_2=dR_3=0.005$, and t... |
Let $G$ be a group of order $pqr$, where $p$, $q$ and $r$ be three distinct primes. By Cauchy's theorem there exist three elements, $a$, $b$ and $c$, whose orders are $p$, $q$ and $r$, respectively. If the subgroup generated by $a$ and $b$ is the whole group, then I wonder if it is possible that there exists a proper n... |
I was wondering if there is a nice way to see that $\mathbb{RP}^{3}$ is orientable without using tools of algebraic topology, like homology.
The only think I could think of was to argue that $\mathbb{RP}^{3}=\mathbb{R}^3 \cup \mathbb{RP}^{2}$ and perhaps you could argue that to get back to any starting position you ha... |
I thought I would post (as a puzzle) one of my favourite results in combinatorics. I actually use variants of this result in research quite often. It's not impossible that someone will post an unexpected proof that could be used in future research. But even if that does not occur, I hope it will be a fun exercise.
A... |
If $(r, \theta)$ are polar coordinates on $\mathbb{R}^2\setminus \{ (0,0)\}$, then how do I show/prove that
\begin{equation*}
d\theta =\dfrac{x dy - y dx}{x^2 + y^2}?
\end{equation*}
|
This is Exercise 3.20 from Apostol's book. Many of them seem tough and here is one of them which I am struggling with.
For $n \in \mathbb{N}$, prove that this identity is true: $$\Bigl\lfloor{\sqrt{n} + \sqrt{n+1}\Bigl\rfloor} = \Bigl\lfloor{\sqrt{4n+2}\Bigl\rfloor}$$
|
I have been reading about Riemann Zeta function and have been thinking about it for some time.
Has anything been published regarding upper bound for the real part of zeta function zeros as the imaginary part of the zeros tend to infinity?
Thanks
|
Given an affine variety, we can forget it into a variety. The other way round, given a variety $X$ we can look at
$$\mathrm{spec}(\mathcal O_X(X)$$
Is this necessarily an affine variety (a priori its just an affien scheme)?
If so, am I right that this implies that taking spec of the global functions is left adjoint to... |
If $M$ is a differentiable manifold, De Rham's theorem gives for each positive integer $k$ an isomorphism
$Rh^k : H^k_{DR}(M,\mathbb R) \to H^k_{singular}(M,\mathbb R)$. On the other hand, we have a canonical map $H^k_{sing}(M,\mathbb Z) \to H^k_{singular}(M,\mathbb R)$ . Allow me to denote (this is not standard) its ... |
Please list both the problem/area and justify why it is important philosophically. This question doesn't cover questions that are only important within the philosophy of mathematics itself.
|
This question is intended to complement What mathematical questions or areas have philosophical implications outside of mathematics?
|
Is it possible to make up a distinct number that is made up of four tuples. One of which indicates the direction of the arrangement of the other three.
Say, $9*4*7 = 252 \ . \ 252$ is distinct in the sense that you cannot get it as a multiplication of 3 distinct single digit numbers other than 9, 4, 7. Now, the problem... |
I have Line $A$ with points $(1,1)$ and $(8,8)$ and another Line $B$ with points $(2,2)$ and $(4,4)$. I would like to prove Line $B$ lies on Line $A$. How can I do this?
|
A quick question-Something that I learned that I forgot throughout the years.
If a question asked you for a multiple of 9 and 12, which would be less than 40, would "36" be an answer, as both 9 and 12 can multiply to get 36, yet it fits under the criteria for being under 40?
|
I've been doing some maths work using the rate of flow of liquids. I've used various models for the flow and various methods to integrate these models. The one thing that is confusing me is the difference between constants of proportionality, and constants of integration?
|
According to Wikipedia:
Let $G$ be a covering group of $H$. The
kernel $K$ of the covering homomorphism
is just the fiber over the identity in
$H$ and is a discrete normal subgroup of
$G$.
It is easy to show that the kernel is a normal subgroup, but why is it discrete?
I know this would be true if the identi... |
Let's say you have a set of numbers S and you want to obtain subsets of $S$, $s_1,s_2,\ldots, s_i$, where $i < N$.
Is there a particular operation that will group the numbers that are "close to each other"?
I will give an example to clarify the question:
Let's say you have a set $S$ which contains $\{1.4, 2, 2.5, 2.7, ... |
I am trying to understand, in as simple terms as possible:
How to define integration for non-orientable manifolds, and
why it is impossible to do so using only differential forms.
In particular, I've seen some discussion of using "densities" instead of $n$-forms for integration, but am not really clear on why densiti... |
Any curve can be considered to be made of sufficiently small straight lines. What is the name of the theorem which states this fact?
Thank you.
I asked the same question at Hacker News.
[Edit: in the Hacker News question, the OP included the following link, which I think clarifies his/her intent:
http://musr.physics.u... |
Allow me to preface this by saying this is not a homework problem. If I had had this thought four years ago when I was taking calculus, I probably could do it...
I'm trying to calculate the limit as $n \to \infty$ of $1-\left(\frac{n-1}{n}\right)^n$ -
- it's a constant I'm inclined to call "natural chance of success".... |
Hmmm... this question might be a bit low-brow. I'm no mathematician.
Let's say that I have an unordered sequence of fuzzy values $T = (t_1 \ldots t_n)$, $T \in (0,1]^n$. Each value is a positive indication towards some observation (hence, the values are not probabilities in that a value of 0.1 does not indicate a valu... |
Let $P$ be some partial order.
We say that $x$ and $y$ are compatible if $\exists r\in P (r\le x \wedge r\le y)$, we denote this by $x \perp y$. Otherwise, we say that $x$ and $y$ are incompatible.
An order $P$ is called separative if whenever $\neg (x \le y)$ then there exists some $r\le x$ which incompatible with $y$... |
Suppose we have an atom at every point with integer coordinates in $\mathbb{R}^d$. Take a ($d-1$)-dimensional hyperplane going through $\mathbf{0}$ and orthogonal to $(1,1,1,\ldots)$. What is the name of the lattice formed by atoms in that plane?
|
There's a theorem that every planar graph can be colored with $4$ colors in such a way that no $2$ adjacent vertices have the same color. Is the opposite true as well?
|
Suppose we have a linear ODE of the form $\dfrac{dy}{dt}= Ay$. We know that $y= e^{tA} y(0)$ is a solution to the ODE, where $e^{tA}$ represents the matrix exponential. Suppose we also knew that this is stable in the sense of Lyapunov (i.e for any $\varepsilon >0$, there exists a $\delta > 0$ such that if $\vert y(0... |
Hey, sorry for the non so mathematical question but that's the only place where I'd thought someone would answer this so here we go.
I'm doing a chemistry homework and I have to answer this very question:
If 50 grams of a particular mineral containing copper nitrate (II) gave, after appropriate treatment 1.6933 grams ... |
I'm having a little trouble with the following problem:
Calculate $F'(x)$:
$F(x)=\int_{1}^{x^{2}}(t-\sin^{2}t) dt$
It says we have to use substitution but I don't see why the answer can't just be:
$x-\sin^{2}x$
|
Ahem. I can only now laugh at how blind I am to not see such a simple answer, LMAO. Thanks to Isaac ♦, Paul VanKoughnett, and Bill Dubuque!
Case closed!
How would you factor $6x^2 + 18x - 60$ over a set of complex numbers?
When I did it myself, I had $6(x - 1.5 + 3.25i)(x - 1.5 - 3.25i)$ .
I am not 100% sure about ... |
I was wondering what are the general spaces that the concepts limsup and liminf can apply to?
Is complete lattice one of them? Also How about metric space?
What are limsup and liminf specified with respect to? A subset? A sequence/net/filter base?
How many kinds of definitions for limsup and liminf in these various cas... |
I was under the impression that all 2-forms are the wedge $(\wedge)$ of two 1-forms. Is it possible to have a 2-form that you can't write as $A\wedge B$ with $A,B$ 1-forms?
|
I'm studying for an exam an I came across a problem that I am having difficultly solving.
Let $\mathcal{F}$ is a family of analytic functions on the closed unit disc, $D$.
Suppose
$\int_{D} |f|^{2} dA \le 1$
for all $f \in \mathcal{F}$.
Can I conclude that $\mathcal{F}$ is locally bounded?
|
I'm a private tutor of High school & pre-engineering level mathematics. Obviously, only those people who have some trouble with maths take tuitions. Most of my students are actually good. I mean they are not dumb. Its just that they are "don't like", "hate", "scared of", "bored" (these are their own words) of mathemati... |
In a usual category $\mathcal{C}$ one can pull the colim out of the Hom like this:$\DeclareMathOperator{\Hom}{Hom}\DeclareMathOperator{\colim}{colim}\DeclareMathOperator{\hocolim}{hocolim}\DeclareMathOperator{\Ho}{Ho}\DeclareMathOperator{\holim}{holim}$ $$\Hom\nolimits_\mathcal{C}(\colim A_i,B)=\lim \Hom\nolimits_\math... |
i have arc A ,i know startangle,endangle,startPoint,Endpoint,centre,radius of arc and i have point B, i like to find point B lies or not in arc A , i need formula or algorithum for this
|
The card game Set lead to the following question. Lets call a subset $A$ of $(\mathbb{Z}/3)^n$ dependent, if there is $\{x,y,z\}\subset A$ with $x+y+z=0$. (So unlike the case of linear dependence we are not allowing any coefficients here).
Let $f(n)$ denote the maximal size of a independent subset of $(\mathbb{Z}/3)^n$... |
You play a game flipping a fair coin. You may stop after any trial, at which point you are paid in dollars
the percentage of heads flipped. So if on the first trial you flip a head, you should stop and earn \$100
because you have 100% heads. If you flip a tail then a head, you could either stop and earn \$50,
or co... |
Is there a reasonable statistic test one can do to standard random number generators (say, one of those that come built in in Python libs) which shows they are not really random?
(By reasonable I mean to exclude silly things like «generate a looong list and see that it is periodic»)
Later: Notice I am looking for a tes... |
I have been stumped for long by this exercise (3.12(d)) from Stokey and Lucas's Recursive Methods in Economic Dynamics. Would greatly appreciate any hints.
Let $\phi: X \to Y$ and $\psi: X \to Y$ be lower hemicontinuous correspondences (set-valued functions), and suppose that for all $x \in X$
$$\Gamma(x)=\{y \in Y: y... |
I've been trying to solve this problem from Elements of Applied
Bifurcation Theory, but even with the hints given I haven't found out
how to proceed yet. I would appreciate any further hints or insights
you could give me in order to make some progress.
It's exercise 2.6.(2):
The following system of partial differential... |
If I give you the following definition of the set $A$, how could you prove it is equal the set of the natural numbers without an explicit definiton for the latter?
The set $A$ is inductively defined as follows:
i) $0 \in A$; and
ii) $\forall n$, a natural number, if $n \in A$, then $n+1 \in A$.
I can easily prove that... |
Let $f$ be an analytic function on the open unit disk domain $D$. Suppose also that $f$ is bounded.
Since $f$ is bounded I believe that $f$ can be continuously extended to the closed unit disk.
I know that the zeros of $f$ in the open disk $D$ are isolated. Are the zeros of $f$ in the closed unit disk also necessari... |
So if you have a distribution fx(x) and you observed x=a, how do you calculate E{x | x=a} = integral (x*fx(x|x=a) from -inf to inf, or more specifically, fx(x|x=a)
I am having trouble when using Bayes or finding Fx(x|x=a) because I end up with P(x=a) which is just a constant. Is there a simple example somewhere? Searc... |
My first post here...not really a math expert, but certainly enjoy the challenge.
I working writing a random string generator and would like to know how to calculate how many possible combinations there are for a particular combination.
I am generating a string of 2numbers followed by 2 letters (lowercase) e.g. 12ab
I ... |
Can this expression be further simplified : $ \sum_{k=0}^{n-1} { n -1 \choose k } (-2)^{k} (2n - k)! $? This is the coefficient of $x^{2n}$ in the formal power series expansion of $(1-2x)^{n-1} \times \sum_{ k \geq 0} k! x^k$.
Motivation: I came across this when trying to solve a problem using inclusion-exclusion prin... |
I'm currently teaching myself calculus and I'm probably trying to run before I can walk, but I've been working on this problem..
I managed to find the correct result for:
$$\int_{0}^{\infty }(2e^{-3x}+4e^{-7x})^2dx$$
by expanding it to:
$$\int_{0}^{\infty}4e^{-6x}+16e^{-10x}+16e^{-14x}dx$$
and then working from there.
... |
Theorem 2 in a paper by Borodin, Okounkov, and Olshanski states that the discrete Bessel kernel $J(x,y,\theta)$ is given by
\begin{equation*}
\sqrt{\theta} \frac{J_x J_{y+1} - J_{x+1} J_y}{x-y}
\end{equation*}
where $J_x = J_x(2\sqrt{\theta})$ is the Bessel function of order $x$ and argument $2\sqrt{\theta}$.
Does an... |
Why does the following integral converge?
\begin{equation}
\int_{0\leq |x_1|\leq|x_2|\leq\dots\leq |x_n|\leq 1}\frac{(1-\sum_{i=1}^n\log |x_i|)^r}{|x_1x_2\dots x_n|^{1/2}}dx_1dx_2\dots dx_n
\end{equation}
Here, $r$ is any positive real number.
|
$
3= \sum_{n=1}^{t} \frac{1}{1.08^n}
$
I see that it is $3 = 1.08^{-t}(12.5 \times 1.08^t{-12.5})$ (from Wolfram Alpha, but I'm not sure how to get it. I tried solving as a geometric series, I had problems and didn't get the correct answer.
I see that $ t\approx3.56592$, which seems like it's correct, but I have no ide... |
I'd like to understand why $ \int{\rho}dV = \frac{1}{c} \int{j^0}dV = \frac{1}{c} \int{j^i}dS_i $ (the second equality), where
$j^i = \rho \frac{dx^i}{dt} $ is the current density 4-vector
$\mathbf{j} = \rho \mathbf{v}$ is the current density 3-vector
$ j^i = (c\rho, \mathbf{j}) $
$\rho$ is the charge density
$dS_i$ i... |
One way of looking at the Viète (Viete?) product
$${2\over\pi} = {\sqrt{2}\over 2}\times{\sqrt{2+\sqrt{2}}\over 2}\times{\sqrt{2+\sqrt{2+\sqrt{2}}}\over 2}\times\dots$$
is as the infinite product of a series of successive 'approximations' to 2, defined by $a_0 = \sqrt{2}$, $a_{i+1} = \sqrt{2+a_i}$ (or more accurately, ... |
and in the other way, orthogonal nullspace and range require symmetry?
Thanks,
R
|
It would seem that one way of proving this would be to show the existence of non-algebraic numbers. Is there a simpler way to show this?
|
I'm currently studying basic Combinatorics for a college course and my professor is awful (and that is being generous).
Therefore I'm looking for good resources to learn basic Combinatorics so that I can prepare for his exams and ace the course.
Thanks for any help
|
Suppose $f$ is an analytic function defined on the unit disk, $D$. I want to evaluate
$\int_{D} f(\omega) dA(\omega)$
using a change of variable. Suppose $\phi$ is a conformal map of the $D$ onto itself.
Does
$\int_{D} f(\omega) dA(\omega) = \int_{D} f(\phi(z)) |\phi^{'}(z)|^{2} dA(z) $?,
where $\phi^{'}$ is the d... |
To give you some background, I have a grasp on the basics of statistics and probability theory and even remember touching Bayes theorem at the university data mining course. But being a few years away from the university made my math got extremely rusty (so much for last-minute pre-exam cramming). While I remember vari... |
I've come across a paper that mentions the fact that matrices commute if and only if they share a common basis of eigenvectors. Where can I find a proof of this statement?
|
I'm trying to figure out how many ways are there to stack N cubes on top of each other.
Once you get a particular stack of 4 cubes let's say, the order of the cubes doesn't matter, just which sides are being shown does.
I'm generally finding 2 numbers:
1.) 6 * 24^(n-1)
and
2.) 3 * 24^(n-1)
Which is the correct answer,... |
This question is mainly to understand the meaning of my professor's correction to a proof of a theorem I gave during an oral examination.
The question was to show that $\text{diam}A = \text{diam}\bar{A}$ where $\text{diam}$ is the diameter of a subspace of a metric space and $\bar{A}$ is the closure of the subset $A$.
... |
If $\sum a_n$ and $\sum b_n$ both converge and one of them absolutely then the Cauchy product $\sum c_n$ converges to $\sum a_n \sum b_n$. ($c_n = \sum_{k = 0}^n a_k b_{n - k}$), by Mertens Theorem.
Now, if both converge conditionally then the product does not have to converge as $a_n = b_n = (-1)^n/n$ shows.
My questi... |
Suppose $f: \mathbb{R} \to \mathbb{R}$ is a continuous function which is 1-1, then does $f$ map Borel sets onto Borel sets?
|
I often find this at the bottom of pages.
Page generated in 0.00013899803161621
Sometimes, I come across
Page generated in 9.0122222900391E-5
What does that time mean?
I tried searching Wikipedia for E and maths but found the e mathematical constant. My guess is E stand for Exponential and -5 is the power it is rai... |
In a book about radar signal processing, they are estimating the squared distance between two objects as:
$$d^2 = \frac{(R_p-R_o)^2}{\sigma^2_R} + \frac{(\theta_p-\theta_o)^2}{\sigma^2_\theta}$$
where R is a radius, $\theta$ is an angle and $\sigma^2$ is the variance of the radius and angle respectivly. p is the predic... |
Edit: question simplified to remove confusion
Assuming a sorted list of items with indexes from 1 to N, and given only an index number i and the maximum index N, is there a simple function which will return the two possible indexes that would be reached next in a binary search of the list?
Example:
i = 6
N = 8
LeftSear... |
Let $\pi(x)$ denote the Prime Counting Function.
One observes that, $\pi(6) \mid 6$, $\pi(8) \mid 8$. Does $\pi(x) \mid x$ for only finitely many $x$, or is this fact true for infinitely many $x$.
|
Let us consider that there are G girl students and B boy students in a class, we need to arrange them in a single row, but arrangement of students should be in order to minimize the gender regularity*. Find the minimum gender regularity among all possible arrangements.
*The gender regularity of an arrangement is the ma... |
I'm trying to simplify the following booleans:
Y = ¬A¬B¬C¬D + ¬A¬B¬CD + ¬A¬BC¬D + ¬A¬BCD + A¬B¬C¬D + A¬BC¬D + ABC¬D
The solution is:
Y = ¬A¬B + ¬B¬D + AC¬D
My solution is:
Y = ¬A¬B (¬C¬D + ¬CD + C¬D + CD) + A¬B¬C¬D + A¬BC¬D + ABC¬D
= ¬A¬B (¬C (¬D + D) + C (¬D + D)) + A¬B¬C¬D + A¬BC¬D + ABC¬D
= ¬A¬B (¬C + C) + A¬B... |
I am trying to calculate the average distance between all vertices of a complete $k$-ary tree. A complete $k$-ary tree is a tree such that all vertices have $k$ children except for the leafs of the tree.
Suppose the tree has $r$ levels, where level 0 is the root. So the height of the tree is $r-1$. First i have to kno... |
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