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For any graph with order $n \geq 3$, given that its size is
$$m \geq \frac{\left(n-1\right)(n-2)}{2} + 2,$$
show that the graph is Hamiltonian.
I know that if I can show that the degree sum of any two non-adjacent vertices is $\geq n$, then I'd be done.
Likewise, if I could show that the above somehow implied that the ... |
Here is something I've been wondering about recently.
Suppose you have an arbitrary ordered field $F$, and let $F(\sqrt{a})$ be a field extension with $a>0$ in $F$. Is there then some way to order $F(\sqrt{a})$ such that $F(\sqrt{a})$ is also an ordered field? Here $F(\sqrt{a})$ is the set of all $p+q\sqrt{a}$ for $p,q... |
Let $f$ is integrable function on $[0,1]$.
Define $g(x)=\int_x^b\frac{f(t)}{t}dt$ for $0<x\leq 1$ and $g(0)=0$.
How can I show that $g(x)$ is integrable?
|
I am looking for an analytic function that approximates the minimum function. i.e.,
$|f(x_1,x_2) - \min(x_1,x_2)| < \zeta$ for some $\zeta$ that may be related to $|x_1 - x_2|$. Or may be a series $f_1,f_2,....$, where $\lim_{n \to \infty} \zeta = 0$.
|
From a bank of exams:
Let $u(x,y) = f(r)$ be a smooth
function in the plane that depends
only on $r = \sqrt{x^2 + y^2}$.
Compute $\Delta u = u_{xx} + u_{yy}$
in terms of $f$ and its derivatives.
Wikipedia states that the Laplace operator in polar coordinates is $$\Delta f = \frac{1}{r}\frac{\partial f}{\parti... |
I am somewhat struggling to see the difference between a regular CW complex and a non-regular CW complex.
The difference is all the attaching maps are homeomorphisms - i.e. there are no identifications made on the boundary. So I guess if I produce a 1-sphere (circle) by a single zero cell and a single one cell, this is... |
Can someone give me an example illustrating physical significance of the matrix-vector multiplication?
Does multiplying a vector by matrix transforms it in some way?
Do left & right multiplication signify two different things?
Is matrix a scalar thing? (EDIT)
Thank you.
|
Given a list of $i$ probability distributions $f_j(x)$ and a list of $i$ probabilities $p_j$ and an interval I.
A probability distribution $f_z(x)$ is chosen from the list with probability p_z and a random number R from the interval I is chosen with this distribution.
Given $R$,$I$ and the two lists of distributions an... |
For $x, y \in \mathbb{R}$, define $x \sim y $ if $x-y \in \mathbb{Q}$. Is $\mathbb{R}/\!\!\sim$ Hausdorff?
|
If $X$ is a very nice topological space, for example a finite simplicial complex, then is it true that the cohomology with compact supports $H^1_c(X,\mathbf{Z})$ is torsion-free? I have seen an assertion in a paper that seems to be tantamount to this statement (unless I've made a slip and misread between the lines) but... |
Let $f(\bar x)$ be a multivariable polynomial with integer coefficients.
The zeros of that polynomial are in bijection with the homomorphisms $\mathbb Z[\bar x] \rightarrow \mathbb Z$ that factor through $\mathbb{Z}[\bar x]/(f)$.
As I understand it this viewpoint leads to the contrafunctor $\text{Spec}$ and schemes and... |
Show that $\mathbb{R}^2$ is not homeomorphic to $\mathbb{R}^2 \setminus \{(0,0)\} $.
|
So, I have this function:
$$ y_t=v_t+\rho v_{t-1}+\rho^2 v_{t-2}+\dots+\rho^{t-1}v_1+\rho^ty_0 $$
And I want to find the variance (and after that the covariance, but I should be able to do that..). I know that the variance is: $ Var[y_t]=\frac{var[v]}{1-\rho^2}=\frac{\sigma^2_v}{1-\rho^2} $
But somewhere I mess everyt... |
I want to find an approximation of the gradient $\nabla V(J)$ of the following function $V(J) = P(X\in T(J))$. Where $X$ is a multidimensional stochastic vector with a smooth continuous probability density and $T$ is a (convex) set that depends on some parameters $J=(J_1,...,J_n)$. $V(J)$ is considered to be many times... |
I'm a software engineer and while my math is ok it's not great.
From time to time I run into the need to solve a problem that is beyond my abilities.
They are generally of the rearrange this formula so x is the output type. And generally highly specific to whatever I'm working on.
I get some traction from feeding thing... |
If I have this equation:
$$\frac{\partial^2u}{\partial x^2}=\frac{\partial^2u}{\partial t^2}$$
And this general solution:
$$u(x,t)=\sum^\infty_{n=-\infty}\cos k_nx(C_n\cos k_nt+D_n\sin k_nt)$$
Would it then be wrong to write the above solution with only positive values of $n$? In my text book they often write the resul... |
the division in the casting out nines is not clear to me. In the given example he got a 8 and a 4, and later he got an 8 and a 3. Shouldn't it be an 8 and a 4 (or 3) in both?
|
Take the quotient space of the cube $I^3$ obtained by identifying each square face with opposite square via the right handed screw motion consisting of a translation by 1 unit perpendicular to the face, combined with a one-quarter twist of its face about it's center point.
I am trying to calculate the homology of this... |
How would I write the flow of the following graph as a linear combination of flows along s,t-paths and t,s-paths and cycles? The values of the edges in the graph represent the flow along that edge.
I'm not sure how to actually express flow in terms of a linear combination of a path/cycle. Would it be something like...... |
Let $A$ be a positive definite matrix. $B$ is said to be the $k$th root of $A$ if $B^k=A$.
My question is whether $B$ is unique.
In Matrix Analysis, Horn, 7.2.6, it is stated 'there exists a unique positive definite Hermitian matrix B such that $B^k=A$'. It seems that $B$ can be $B=U\Lambda^{1/k}U^T$ if $A=U\Lambda U^T... |
Here's a snippet from the working in a trigonometry textbook. I'm confused about the second line:
Am I correct in interpreting from this that: $1 - \sin^2 \theta \equiv (1 - \sin\theta)^2$ ?
Until now I had thought that $1 - \sin^2 \theta \equiv 1 - (\sin\theta)^2$
Which is correct?
Thanks!
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new here (apologies for the formatting). I want to express the relationship between
$$A \longrightarrow B$$
and
$$B \longrightarrow \neg A.$$
Clearly this is neither converse, inverse, nor contrapositive; does it have a name at all?
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There's a limit that I am unable to solve. I think it should be equal to $\infty$.
$$\lim_{n\to\infty}\left(1 + \frac{1}{2} + \frac{1}{3} + \cdots+ \frac{1}{n}\right)$$
|
What would be a common algorithm with an order of Θ(2^n)? When I say "order", I mean time complexity analysis. I was thinking exponential growth but are there any that are more computer science oriented?
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What are the conditions under which a distribution reduces down a dimension?
For example, suppose I have a 2D gaussian distribution for X and Y. Under what condition(s) on Y does the distribution "reduce" down to a 1D gaussian distribution for X?
I don't want to say more so as not to bias the answers.
|
Possible Duplicate:
How can I prove sup(A+B)=supA+supB if A+B={a+b}
How would I go about proving that the supremum of A + B (where A and B are each subsets if $\mathbb{R}$) is equal to the supremum of A plus the supremum of B?
I was thinking of using variables to represent the sup of A and the sup of B (say a & b), ... |
Let $\sigma$ be a permutation of $\mathbf Q.$ We call $\sigma$ bounded (the term might be somewhat misleading, but however it is used in a couple of papers) if there is a real number $M$ such that
$$
\mathrm{dist}(\sigma x,x) =|\sigma x-x| \le M
$$
for all $x \in \mathbf Q.$
Now can a bounded infinite cycle
$$
\pi=... |
I ran across this integration problem that has an interesting pattern.
$$\int_{0}^{(n-1)\pi}\frac{1}{\tan^{n}(x)+1}dx=\frac{(n-1)\pi}{2}$$
I evaluated increasing values of n up to n=10, and the result is always one half the upper limit of integration.
Why is this?. That is, how could we show it. I graphed it and as n ... |
In the Cartesian coordinate system, given 3 geometrical solid objects (interior plus boundary): spheres S1(x1,y1,z1, R1), S2(x2,y2,z2, R2) and a cube (which is orthogonal with coordinate system) at the center C (x3,y3,z3) with size L x L x L. The question is “Whether the 3 objects have any common volumetric intersect... |
Let $\{a_n\}$ be a sequence and $k$ a natural number so that:
$\{a_{nk}\}$ , $\{a_{nk+1}\},\ldots, \{a_{nk+(k-1)}\}$ - every sub-sequence converges to the same limit $L$.
I need to show that $\{a_n\}$ itself converges to $L$.
It is pretty obvious to me why, regarding the fact that from $N=k$, every $a_n$ belongs to one... |
Basically a beginner type of topology question here, but I am trying to understand something and am a bit stuck on a definition.
According to J.P. May, a fibration is a map $p : E \to B$ such that for all spaces $Y$, that embed into $E$ by some map $f$, and have a compatible homotopy onto $B$ by $h: Y \times I \to B$, ... |
How can I find all positive integers $x$ and $y$ such that $2x^2-1=y^{15}$?
PS. See here.
|
For complex manifolds , people usually write the first fundamental form as $ds^2=g_{a\bar{b}}dz^ad\bar{z}^b$ (at least physicists) with a bar over the second index of the metric, but don't usually write the bar over the second one-form $d\bar{z}^b$. I am not sure why this is done. As I see it, for the notation to be co... |
Given pdf of $I$ and $R$ (both $I$ and $R$ are independent RV's), how to find cdf of $W =I^2R$?
Where,
$$
\begin{align}
f_I(i)&=6i(1-i), &0 \leq i \leq 1 \\
f_R(r)&=2r, &0 \leq r\leq 1.
\end{align}
$$
|
It's well-known that
$$\max(a,b)=\frac{a+b+|a-b|}{2}.$$
Is there a (good) generalization to several variables? Of course $\max(a,b,c)=\max(a,\max(b,c))$ and so
$$\max(a,b,c)=\frac{a+\frac{b+c+|b-c|}{2}+|a-\frac{b+c+|b-c|}{2}|}{2}$$
$$=\frac{a+0.5b+0.5c+0.5\left|b-c|+|a-0.5b-0.5c-0.5|b-c|\right|}{2}$$
but I'd like a fo... |
This is a pretty trivial question. How do you rationalize a function with a denominator that contains a third degree root?
Edit: My expression is $\displaystyle{\frac{1}{\sqrt[3]{2}-1}}$.
|
Let $f:X\times Y\rightarrow Z$ be a mapping of topological spaces, the product given the product topology. Then for all $y_{0}\in Y$, the map $f(.,y_{0}):X\rightarrow Z$ is continuous. Any hints on how to show this?
Thanks.
|
There are two racers in a circular
racetrack of 1200 meters. When both
are moving in the same sense, the
first racer comes across the second one
every 200 seconds. But in different
sense, they come across each other
every 100 seconds. What speeds have
each one ?
I tried to figure it out but I have no idea how to do i... |
I'm new here and I'm hoping that maybe I could get some help with something my teacher told me. He said that it is possible to have a closed set nested within another closed set where the intersection between these two sets was empty. In fact, he said that it could be extended to a closed set within a closed set within... |
This is a pretty elementary concerning the terminology commonly used in Desargues' Theorem
from plane geometry (or really, projective geometry).
At least in some representative cases, I totally buy the terminology of two triangles being "perspective from a point," at least in the sense that if I visualize the triangle ... |
How can I increase/decrease (frequency/pitch) and phase using fft/ifft
I think I have the basic code but I’m not sure what to do next
PS: It's done in Octave/matlab code
Example I have a signal that repeats 1 time every second and I want to
have it repeat 3 times a second instead.
%Voiceprint raise lower freq phase co... |
I need an introduction to Floer theory that's suitable for perhaps a beginning math grad student or a 2nd year physics grad student. The wiki article is sufficiently over my head that it reads as "bar" "bar" "bar". Editor, please improve the tags.
The reason this comes up is that an answer to a problem on unitary matri... |
Given $y=\ln(2x-1)/\ln(x)$, prove $y$ is decreasing for $x>1$.
While this is obvious by couple computations, the usual differentiation method to show this is true is not getting me anywhere since finding the $y'=0$ point is rather nuisance with ln and what not.
We know the limit of this function is 1, and with first fe... |
Given two latitudes/longitudes (th1,ph1 and th2,ph2), I want to find a
simple formula for the locus of th3,ph3 that are equidistant from
th1,ph1 and th2,ph2.
Mathematica happily spits out an answer (giving ph3 as a function of th3), but it's unbelivably long (below). Is there a simpler form? I realize I could convert t... |
Can a partial order by symmetric in addition to being reflexive, antisymmetric, and transitive?
Also, can an equivalence relation be antisymmetric aside from being reflexive, symmetric, and transitive?
All of the definitions I see only state that a relation has to be those things in order for it to be considered a part... |
How can the following be proved by induction?
$$\sum\limits_{i=1}^{n} \frac{1}{n+i} = \sum\limits_{i=1}^{n} \left(\frac{1}{2i-1} - \frac{1}{2i}\right)$$
I am out of ideas after practicing for a while:
$$\frac{1}{n+1}+\frac{1}{n+2}+\dots+\frac{1}{2n}=\left(1-\frac{1}{2}\right)+\left(\frac{1}{3}-\frac{1}{4}\right)+\dot... |
How do I solve the following differential equation:
$$
f''(x)+\frac{(n-1)(f'(x))^2}{\sinh(x)}=0
$$
under the boundary conditions $f(1)=1$ and $\lim_{x\to\infty}f(x)=0$.
More generally, how to solve
$$
f''(x)+g(x)(f'(x))^2=0
$$
for some known function $g(x)$ for the same boundary conditions.
|
The product integral is the multiplicative version of standard integrals. Indefinite products are the discrete counterpart to this integral; they multiply iterations on a function $f(x)$ by each other.
Is there a simple relation between the two? If so, what is this relation?
Motivation
This may give an alternative (a... |
Most of the time, I solve a problem by doing the following steps:
1. Look for a related theorem.
2. Look for a related formula.
3. Find a similar problem or sub-problem.
4. Try to adapt the one that I had done.
5. Asking at Math.SE is an alternative solution that I've just found out.
When I read the article named "Eigh... |
I saw a greek letter in an infinite series, and found out it was Kappa. What does this do? It looks like a giant K.
http://www.wolframalpha.com/input/?i=find+continued+fraction+of+square+root
That's where i found it.
|
I'm looking for a proof of Liouville's Theorem for conformal mappings.
I can't find any proofs online in English (I'd settle for a German proof, though I'd take forever to read it. I cannot speak or read French or Russian however).
The local library contains none of the books mentioned on the wikipedia article nor the ... |
I need some help rearranging some orbital mechanics formulas.
All images have been borrowed from http://www.braeunig.us/space/orbmech.htm which has a through treatment of orbital equations, but provides no further insight on my question.
Given the following:
I have $r$, $\phi$ and $R_{a}$ or $R_{p}$ (only one will be... |
I'm new here and was hoping you guys could help me with a statistics problem that I don't quite understand. I'm not sure if it's proper etiquette to ask for help on a specific homework problem here, so I apologize if this question is out of line.
Here is the problem:
Suppose a variable of a population has mean 5 and s... |
let $f \in L^\infty$
and let $M(f)=sup\{\left|\int \phi f\right| : \phi \text{ simple, } ||\phi||_1 \le 1 \}$
i wish to show that $||f||_\infty=M(f)$
i was able to show $||f||_\infty \ge M(f)$ using Hölders inequality but I am having trouble showing $\le$. Any tips?
|
Given two sets of random numbers, is it possible to say that one set of random numbers has a greater degree of randomness when compared to the other?
Or one set of numbers is more random when compared to the other?
EDIT:
Consider this situation:
A hacker needs to know the target address where a heap/library/base of the... |
I'm not sure if this is a strong enough condition to imply compactness, since it seems that it must be "totally bounded" and complete. Complete means that X is closed. In R^n bounded and closed set imply compact, but not in general. Any thoughts would be appreaciated
|
When reading the book Measures, Integrals and Martingales written by R.L. Schilling, I saw a statement as below:
$$\mathcal{A} \times \mathcal{B}:= \{A \times B: A\in \mathcal{A}, B\in \mathcal{B}\}$$
where $\mathcal{A}$ and $\mathcal{B}$ are $\sigma$-algebras, is not $\sigma$-algebra in general.
However, I cannot cons... |
I wanted to know if I did this problem right or not.
$A$ and $B$ are the following matrices:
$A=\begin{bmatrix}2&6\\1&-3\end{bmatrix},$
$B=\begin{bmatrix}3&2\\1&0\end{bmatrix}.$
Then
$$\frac{\langle A,B\rangle}{\|A\|\|B\|}
=\frac{\left\langle\begin{bmatrix}2&6\\1&-3\end{bmatrix}, \begin{bmatrix}3&2\\1&0\end{bmatrix}... |
I am reading a text and I have a somewhat "abstract" question regarding probability. It involves a technique I have never seen before. The text is: Mobile Communication Systems by Parsons, page 208-209. Another text which contains the same information but in a slightly different form is Microwave Mobile Communications ... |
This is a beginner question but bear with me, let's say i have thrown a dice 5 times, and every time the result was 1. The next time i throw it what are the chances/probabilities it will be 1 again? Is it still 1/6? If not how is this calculated?
What i am trying to understand is whether the past is relevant for the ne... |
For a constrained optimization problem, there can be different formulations.
For example, consider the problem with the following formulation:
$$\min_{x \in X \subseteq \mathbb{R}^n} \, f(x), $$
subject to $g(x) \leq 0, h(x)=0 $.
One can move part of those
(in)equality constraints into the
set $X$, or shrink $X$ by m... |
The Yule process is a pure birth process with parameter $\lambda_n = n\beta$. If $X(0) = 1$, then find the probability there are no births during the time interval $(5,8]$.
I was thinking of conditioning on $X(5)$ but I was unsure on how to proceed… Thanks for the help!
|
Please I need help with the evaluation of this integral. I've tried with both mathematica and maple, but to no avail. Here is the integral:
$$
e^{-r(T-t)}\int_{-\infty}^{\infty}\frac{(Se^{x})^{n}}{\sqrt{2\pi\sigma^{2}(T-t)}}\exp\left[-\frac{\left\{ x-\left(r-\frac{1}{2}\sigma^{2}\right)\left(T-t\right)\right\} ^{2}... |
Using polar coordinates, create a system with a fixed point at the origin, and with infinitely many periodic orbits which alternate between clockwise and counterclockwise flows.
|
So for my homework I've gotten an incorrect answer on this problem 3 times in a row. Here's an overview of my work
A large tank holds 250 liters of water with a salt concentration of 7 grams per liter. A brine solution containing 3 grams per liter is added to the tank at a rate of 9 liters per minute. The well-mixed ... |
Can you help me find the integral
$$
\int{\frac{1}{\sinh(x)}dx}?
$$
|
To put it more rigorously: Does there exist constants $0 < a < 1$ and $0 < b < 1$ such that for all real $\theta$ which are non-rational multiples of $\pi$ and all natural numbers $n$ it holds that $b a^n\leq \sin(\theta n) $. My reasoning is that because $\theta$ is restricted to be a non-rational multiple of $\pi$, w... |
I've scoured the internet and have found many proofs showing that in Euclidean geometry, the angle sum of a triangle is always 180 degrees. I've also found many proofs showing that in hyperbolic geometry, the angle sum of a triangle is always less than 180 degrees. For some reason I have been unable to find a proof tha... |
If we have a quad tree where each node must have 0 or 4 children, is there an expression that can me the maximum height of a quad tree with $n$ nodes?
|
What is the sum of the series $\displaystyle\sum_{k=1}^\infty{\frac{-1}{2^k-1}}$?
Also, more generally, can we find $\displaystyle\sum_{k=1}^\infty{\frac{-1}{c^k-1}}$ for some $c$?
|
For those who commented on my previous questions, sorry for the lack of information and explanation. Clearly I did not do a good job of explaining myself so I deleted the question and hope this one goes better.
EDIT: here is what I have so far, can anyone tell me if it is right/wrong? http://www.box.net/shared/static/... |
In a recent lecture a professor told a story about the integral below. Lobachevsky calculated this integral at first time incorrectly. Following the publication of the integral, Ostrogradsky sent a letter with correct answer to Lobachevsky.
What is the right answer?
$$I(a)=\int_{0}^{\infty}\frac{(e^x-e^{-x})x}{e^{2x}... |
imagine my function as a staircase with two steps. This function is to be fitted to some empirical data and I'm searching for an algorithm which minimizes the Root Mean Squared Error between this function and the data.
The decision variables are L1 and L2 (for the level of the steps on the y-axis) and C (for the cut-of... |
Let $X(t)$ be a pure death process starting from $X(0)=N$. Assume that the death parameters are $\mu_1, \mu_2,\dots,\mu_N$. Let $T$ be an independent exponentially distributed random variable with parameter $\theta$. Show that $Pr\{X(T)=0\} = \prod_{i=1}^{N} \frac{\mu_i}{\mu_i+\theta}$.
My thoughts are that I should co... |
So let's assume I have a point $P$ in $3D$ space $(x_0, y_0, z_0)$. And I have a circle $C$ that is centered at $(x_1, y_1, z_1)$ with a radius $r$. I need to find the distance from $P$ to the nearest point of $C$. I'm not totally sure how to define a circle in $3D$ space, so suggestions there would help too :D
I reall... |
Possible Duplicate:
Are Continuous Functions Always Differentiable?
If such a function exists, can anyone give an example of a function $f(x) : \mathbb{R} \longrightarrow \mathbb{R}$ that is continuous for all $x \in \mathbb{R}$ but differentiable nowhere?
|
How do you analyse for convergence/divergence on the circle of convergence of a particular power series?
|
I'm trying to find good books on the history of mathematics, dating as far back as possible.
There was a similar question here Good books on Philosophy of Mathematics, but mostly pertaining to Philosophy, and there were no good recommendations on books relating specifically to Math History.
|
I'm reading a rather old mechanics paper and the author uses the following to derive certain stresses.
Let x + iy = f(u + iv)
Then, J$e^{i\phi}$ = f'(u+iv)
J is the Jacobian, and $\phi$ is the angle between a tangent to the curve v = constant and the x axis
given f is a conformal mapping.
How can this be derived?
|
I wish to prove the following, but I'm not sure if the steps of my proof are correct. Here it goes:
Suppose A is an $m \times m$ matrix with $m$ pivot columns and that $v_1, \ldots, v_p$ is a
linearly independent set of vectors in $\mathbb{R}^m$.
Is $Av_1, \ldots, Av_p$ a linearly independent set of vectors?
Here's an ... |
The group of orientation preserving isometries of Cube is $S_4$. But if we allow orientation reversing isometries also, then the group will be of order 48. What is this group (Structure)? ( Part of answer can be $S_4\rtimes \mathbb{Z}_2$, because $S_4\triangleleft G$, $\mathbb{Z}_2\leq G$, which contains a reflection i... |
My ODEs textbook uses both graph and plot but I can't figure out how it chooses one over the other.
From the book:
Sketch the graph of the solution in the x1x2-plane for t ≥ 0.
[this one was referring to a continuous function]
Also from the book:
Plots of the solution and a tangent line approximation for the initi... |
I have taken two image from two different camera and lens from 3 fixed point which makes a 90 degree angle on a plane. the position of camera when taking photo is also changed but the 3 fixed points are in both images.
How can I find a relation to map points in these two images? I just want to map the points on the pla... |
How can I find the solution to the series $\sum_{n=1} ^\infty n^2(\cos(nx) + i \sin(nx))$
|
I make some videos of math courses on the internet and some of them are in English. I want to find some where to upload it. Who can help me with this issue? I only know about Youtube, but that is stopped by the Chinese Great Wall. Any other places? (for maths or science is best)
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If a ring $R$ satisfies the property $P$, but the matrix rings $M_n(R)$ do not satisfy $P$, then $P$ is not a Morita property; that is the definition.
But that is not fix this situation. I want to know the reason that Invariant Basis Number (IBN) is not a Morita property. (IBN means that $R^m=R^n$ implies $m=n$).
|
This was asked by my maths lecturer a couple of years ago and ive been wracking my brains ever since:
Find a number that, when multiplied by
99 will give the original number but
with a 1 at the beginning and a 1 at
the end.
For example: 42546254 * 99 would equal
1425462541 (it doesn't, but it
illustrates wha... |
Good morning,
I would love your help with this:
Given a sequence {$ a_{n} $} with this initial data:
$a_{2k}= \frac{a_{2k-1}}{2}$
$a_{2k+1}= a_{2k}+\frac{1}{2}$
I need to find $\liminf a_{n}$ and $\limsup a_{n}$
Thank you
|
I think I understand these concepts ok:
chain rule
u-substitution
Riemann-Stieltjes integral
But there seems to be a layer that I miss: They all seem to be connected, alas I don't know how exactly. In a way you should be able to transform one into the other?!?
Could anyone please enlighten me? Thank you!
|
A famous problem:
A lady is in the center of the circular lake and a monster is on the boundary of the lake. The speed of the monster is $v_m$, and the speed of the swimming lady is $v_l$. The goal of the lady is to come to the ground without meeting the monster, and the goal of the monster is to meet the lady. Under... |
In How can you prove that a function has no closed form integral?, the accepted answer points to http://www.sci.ccny.cuny.edu/~ksda/PostedPapers/liouv06.pdf where one can find a corollary by Liouville providing sufficient and necessary conditions for the integral:
$$\int{f(t)e^{g(t)}\mathrm dt}$$
to be determinable (u... |
I was wondering what "anti-optimization" is about? Is it related to optimization? What topics does it cover?
All I can find out from Google is this paper. It looks like having some relation with probability and optimization?
Thanks and regards!
|
I have just begun to learn about the fundamental group.
An exercise asks me to prove that $$X=\{(x,y,z): z \ge 0\}-\{(x,y,z): y=0,0\leq z \leq 1\}$$ has trivial fundamental group.
What I know is:
1) the definition of the fundamental group.
2) X has trivial fundamental group iff any loop in X can be shrunk into a const... |
my definition of p-point in $\beta\mathbb{N}$ is: $\mathcal{U}$ is a p-point if and only if every $\{A_n:n\in\mathbb{N}\}\subset\mathcal{U}$ has a pseudo-intersection, i.e. a $B\in\mathcal{U}$ such that $B\backslash A_n$ is finite for every $n$.
In topology the definition is: the intersection of a countable family of n... |
In Feynman's 'Lectures on Physics', I read a chapter on probability which tells that P(Head) for a fair coin 'approaches' 0.5 as no. of trials that we take goes to infinity (well, I tossed the coin 50 times & got heads 17 times, instead of 25 :-) ...). Can someone elaborate?
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can somebody explain me this equality please
{ω : g(ω) ≤ r} =$\bigcup^\infty_{n=1}${ω : $f_{n}$(ω) ≤ r}
where $g=\sup_{n\geq 1} f_n$
this is to prove that the supremum of mesurable sequences is mesurable too but i can't understand where the equality came from.
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Does there exist a simple graph with five vertices of the following degrees?
(a) 3,3,3,3,2
I know that the answer is no, however I do not know how to explain this.
(b) 1,2,3,4,3
No, as the sum of the degrees of an undirected graph is even.
(c) 1,2,3,4,4
Again, I believe the answer is no however I don't know the rule to... |
I have wanted to make math videos, but was never sure how to go about it. (Please redirect to the correct forum if this is wrong). I noticed how the khan academy videos are made on a computer, I would like to do the same thing with a software like LyX. But how would I capture the screen, and the voice at the same time?... |
I've had a look for intuitive explanations of the variance of an RV (e.g. Intuitive explanation of variance and moment in Probability) but unfortunately for me, I still don't feel comfortable with the concept. Why would you opt to use variance over the standard deviation (which usefully is in the same units as the expe... |
From a bank of past master's exams:
Let $u(x,y)$ satisfy $$ -\left( \frac{\partial^2 u}{\partial x^2}+\frac{\partial^2 u}{\partial y^2}\right) = \lambda u $$ in a bounded region $\mathcal{D} \subset \mathbb{R}^2$ with smooth boundary $\mathcal B$. Assume $u=0$ on $\mathcal B$ (but $u \not \equiv 0$ on $\mathcal D$)... |
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