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Generally speaking, the answer to both questions is linked to some number becoming increasingly large so that, for atoms you have a large density of higher excited states (think to Rydberg atoms as an example) or for electromagnetic field one has such a large number of photons that a coherent state is a good descriptio... |
The Incredible Process of Packaging Potato Chips ...vertical form fill seal packaging machines grain packaging equipment sealing PRODUCTS Detail
we are a professional
The Incredible Process of Packaging Potato Chips ...vertical form fill seal packaging machines grain packaging equipment sealing machine vertical packing... |
The Annals of Probability Ann. Probab. Volume 21, Number 1 (1993), 248-289. The Continuum Random Tree III Abstract
Let $(\mathscr{R}(k), k \geq 1)$ be random trees with $k$ leaves, satisfying a consistency condition: Removing a random leaf from $\mathscr{R}(k)$ gives $\mathscr{R}(k - 1)$. Then under an extra condition,... |
$\def\abs#1{|#1|}\def\i{\mathbf {i}}\def\ket#1{|{#1}\rangle}\def\bra#1{\langle{#1}|}\def\braket#1#2{\langle{#1}|{#2}\rangle}\def\tr{\mathord{\mbox{tr}}}\mathbf{Exercise\ 7.7}$
Fast Fourier Transform Decomposition
a) For $k < l$, write the entries $F_{ij}^{(k)}$ of the $2^k\times 2^k$ matrix for the Fourier transform ${... |
Another day in latex wonderland … Today I was writing an equation in an
aligned environment using
sum and those fancy things. Unfortunately
aligned is a display math environment such that the limits of
sum are displayed above and below, which was really not suitable in my case. So how do I display inline-math style in ... |
Frequent Links Mountain range (options)
This article does not cite any references or sources. (November 2006) Mountain ranges are exotic options originally marketed by Société Générale in 1998. The options combine the characteristics of basket options and range options by basing the value of the option on several under... |
Search results for: A. Gomes −1of integrated luminosity at the centre-of-mass energies of 7, 8, and 13 TeV, respectively, the decay Λ b 0 → χ c 1 $$ {\Lambda}_{\mathrm{b}}^0\to {\upchi}_{\mathrm{c}1} $$ (3872)pK −with χ c1(3872) → J /ψ π +π −is observed for the first time. The significance of the observed...
Concurrenc... |
Suppose $A=6z\hat i+(2x+y)\hat j-x\hat k$ .Evaluate $$\iint A.dS$$ Over the entire surface S of the region bounded by the cylinder $x^2+z^2=9,x=0,y=0,z=0$ and $y=8$.
I split it into three surface 1.Upper circle part, $S_1$ 2.Lower circle part, $S_2$ 3.cylindrical part, $S_3$. I couldn't do surface integral for $S_3$.Si... |
High Speed AD Converter: AD 9467
The AD converter is the heart of every direct sampling receiver. Its properties are crucial for the overall receiver performance. This is because once the signal has been digitized, virtually any receiver performance can be obtained by digital signal processing in FPGA or software. Impo... |
Integration over manifolds is commonly defined with object called chains. What about if I want to integrate the exterior derivative of a $k-form$ over the n-sphere and use Stokes theorem:
\begin{eqnarray} \int_{\sigma} d\omega &=& \int_{\partial \sigma} \omega \end{eqnarray}
I found in several books that this integral ... |
If $f(x) = 0.5 e^{-|x|}$ for $-\infty < x < \infty$, how would you find the moment generating function for this? Also how would you find the distribution of $Y = |X|$?
Attempt:
$$E(e^{tX}) = \int_{-\infty}^\infty f(x) e^{tx} \; dx.$$
Mathematics Stack Exchange is a question and answer site for people studying math at a... |
1 ) When B travels towards A, wouldn't each twin observe the other's clock moving ["running", "ticking"] slower?
No, quite the opposite:
If two participants (such as A and B) were moving towards each other (at constant mutual speed, $v := c~\beta$, $\beta > 0$) and if one stated signal indications at constant frequency... |
Export 28 results:[ Author] Title Type Year
Filters: is First Letter Of Last Name [Clear All Filters] T
T
Deformation and strain storage mechanisms during high-temperature compression of a powder metallurgy nickel-base superalloy. Metallurgical and Materials Transactions A. 41:2002–2009.. 2010.
Single-crystal solidific... |
Black ring
Roberto Emparan and Harvey Reall (2010), Scholarpedia, 5(9):8786. doi:10.4249/scholarpedia.8786 revision #135545 [link to/cite this article]
A
black ring is a black hole with an event horizon with topology \( S^1 \times S^p \ .\) Black rings can exist only inspacetimes with five or more dimensions. Exact bla... |
As a student of mathematics, I'm often interested in how fascinating math works its way into other subjects. In particular, I recently became curious about why computer scientists are talking about complicated categorical machinery, and this post is a quasi-answer to this question. As a disclaimer, I'm neither a comput... |
I am interested in the complexity of a problem involving spanning hyperforests (a union of hypertrees, which covers all of the vertices) of a $k$-hypergraph. I describe the relevant definitions for hypergraphs below, but the following is the problem on
SPANNING HYPERFOREST ROOT SET.For a directed hypergraph $D$ and an ... |
This is no longer really a hint: the induction step ended up messy enough that I went ahead and wrote it out, though the internal induction has only been indicated, not actually carried out properly. For the main induction step:
$$\begin{align*}\sum_{k\ge 0}2k\binom{n+1}{2k}&=\sum_{k\ge 0}2k\left(\binom{n}{2k}+\binom{n... |
Can somebody explain to me ( or give a proof ) why the field extension $\mathbb{R/Q}$, that is the field of real numbers as an extension of the field of rational numbers, is transcendental and not algebraic, which would mean that each element of $\mathbb R$ would be a root of some polynomial with rational coefficients ... |
If $\triangle$ is the diagonal of $X \times X$, show that its tangent space $T_{(x,x)}(\triangle)$ is the diagonal of $T_x(X) \times T_x(X).$
I don't have the slightest idea on how to do this.
By definition, the tangent space of $X$ at $x$ is the image of the map $d\phi_0: \mathbb{R}^k \rightarrow \mathbb{R}^N$, where ... |
Let's consider a call on min option on two underlying
arithmetic Browniation motions $V_t$ and $H_t$ (no drift). Let $P_t$ denotes the price process of the option, $r$ the riskfree rate, $\tau$ the time to maturity, then following the notation and the procedure in [Stulz, 1982] (eq (3) - (7) in particular), we obtain a... |
Calculates the p-value of the statistical test for the population mean.
Syntax TEST_MEAN( x, mean, Return_type, Alpha) x is the input data sample (one/two dimensional array of cells (e.g. rows or columns)) mean is the assumed population mean. If missing, the default value of zero is assumed. Return_type is a switch to ... |
$\def\abs#1{|#1|}\def\i{\mathbf {i}}\def\ket#1{|{#1}\rangle}\def\bra#1{\langle{#1}|}\def\braket#1#2{\langle{#1}|{#2}\rangle}\def\tr{\mathord{\mbox{tr}}}\mathbf{Exercise\ 4.20}$
Let $O_{\theta_1}$ be the single-qubit observable with $+1$-eigenvector
$\ket{v_1} = \cos\theta_1\ket{0} + \sin\theta_1\ket{1}$ and $-1$-eigenv... |
If the inradius=$2013$ of a right angled triangle with integer sides. Find the no. of possible right angled triangles that can be formed using the above information. I have tried $r(a+b+c)=ab$ and $a^2+b^2=c^2$ , but couldn't reach further. Thanks in anticipation
One thing we can get is
$CF=CD=b-r$ and $BE=BD=c-r$. So,... |
Saddle-node bifurcation
Yuri A. Kuznetsov (2006), Scholarpedia, 1(10):1859. doi:10.4249/scholarpedia.1859 revision #151865 [link to/cite this article]
A
saddle-node bifurcation is a collision and disappearance of two equilibria in dynamical systems. In systems generated by autonomous ODEs, this occurs when the critical... |
\({ \sqrt{5x^2+11}} = x + 5\)
How would I solve this equation algebraically? \(\large{ \sqrt{5x^2+11}} = x + 5\)
\(\begin{array}{|rcll|} \hline \sqrt{5x^2+11} &=& x + 5 \quad & | \quad \text{square both sides} \\ 5x^2+11 &=& (x + 5)^2 \\ 5x^2+11 &=& x^2+10x+25 \\ 4x^2-10x-14 &=& 0 \quad & | \quad : 2 \\ 2x^2-5x-7 &=& 0... |
Epidemics
Dr. Angela McLean accepted the invitation on 10 July 2007 (self-imposed deadline: 10 October 2007).
This article will briefly cover: observed patterns of epidemics of infectious diseases and the underlying processes thought to generate those patterns.
Contents The SIR Model Control and Eradication Age Structu... |
I'm trying to make a "triplot" to illustrate Bayesian inference (so I'd like to have prior, likelihood and posterior in the same picture). For likelihood I'm using \begin{equation}\label{eq:lik}f(y|\tau) = \prod_{i=1}^{n}\frac{\tau}{\sqrt{2\pi}}\exp\left(-\frac{\tau(y_{i}-\mu)^{2}}{2}\right) = \frac{\tau}{\sqrt{2\pi}}\... |
Let $X_n(\Bbb{Z})$ be the simplicial complex whose vertex set is $\Bbb{Z}$ and such that the vertices $v_0,...,v_k$ span a $k$-simplex if and only if $|v_i-v_j| \le n$ for every $i,j$. Prove that $X_n(\Bbb{Z})$ is $n$-dimensional...
no kidding, my maths is foundations (basic logic but not pedantic), calc 1 which I'm pr... |
Let $X_n(\Bbb{Z})$ be the simplicial complex whose vertex set is $\Bbb{Z}$ and such that the vertices $v_0,...,v_k$ span a $k$-simplex if and only if $|v_i-v_j| \le n$ for every $i,j$. Prove that $X_n(\Bbb{Z})$ is $n$-dimensional...
no kidding, my maths is foundations (basic logic but not pedantic), calc 1 which I'm pr... |
I have a set of $n\times n$ matrices with entries on $\mathbb{F}_2$, given by $$\mathcal{A}=\left\{A\in\mathcal{M}_{n\times n}(\mathbb{F}_2):A= \left( \begin{array}{ccc} I_{k_1} & 0 & 0 \\ 0 & J & 0 \\ 0 & 0 & I_{k_3} \end{array} \right) \right\} $$ where $J=\left( \begin{array}{cccc} 0 & \ldots & 0 & 1 \\ 0 & \ldots &... |
My questions are about worldline path integrals from the book Gauge Fields and Strings of Polyakov.
On page 153, chapter 9, he says
>Let us begin with the following path integral
\begin{align} &\mathscr{H}(x,y)[h(\tau)]=\int_{x}^{y}\mathscr{D}x(\tau)\delta(\overset{\,\centerdot}{x}{}^{2}(\tau)\boldsymbol{-}h(\tau)) \no... |
Let $X_n(\Bbb{Z})$ be the simplicial complex whose vertex set is $\Bbb{Z}$ and such that the vertices $v_0,...,v_k$ span a $k$-simplex if and only if $|v_i-v_j| \le n$ for every $i,j$. Prove that $X_n(\Bbb{Z})$ is $n$-dimensional...
no kidding, my maths is foundations (basic logic but not pedantic), calc 1 which I'm pr... |
People are always fascinated by intelligent devices, and today they are software “chatbots”, which are becoming more and more human-like and automated. The combination of an immediate response and a permanent connection makes them an attractive way to expand or replace the web applications. The high-level diagram of an... |
You are absolutely right that the limit in which this approximation holds is
$$\beta(\epsilon - \mu) \gg 1 \,,$$
which is not trivially the 'high-temperature limit', and indeed
looks rather like the low temperature limit. However, it also looks like the limit of large negative $\mu$. If we want to know how temperature ... |
Some implementations of MFCC apply sinusoidal liftering as the final step in calculations of MFCC. It is claimed that speech recognition can be significantly improved. For instance, if $\text{MFCC}_i$ is a cepstral coefficient, and $w$ is a lifter, then $$\widehat{\text{MFCC}_i}=w_i\text{MFCC}_i$$
is a liftered cepstra... |
Well consider an orbit - I'm trying to calculate the exact time spent in the shadow of the body you orbit around. An explanation of "shadow" (sun is positioned to the far left):
For a circular orbit this is quite easy: One just calculates the orbit radius and solve it using a simple sine ($T$ is the orbital period):
$$... |
Digital barrier options pricing: an improved Monte Carlo algorithm 7.6k Downloads Citations Abstract
A new Monte Carlo method is presented to compute the prices of digital barrier options on stocks. The main idea of the new approach is to use an exceedance probability and uniformly distributed random numbers in order t... |
According to Ortin, Gravity & Strings (Chapter 2), we define
$$\dfrac{\delta S}{\delta \phi} \equiv \dfrac{\partial \mathcal{L}}{\partial \phi} - \partial_\mu \bigg(\dfrac{\partial \mathcal{L}}{\partial(\partial_\mu\phi)}\bigg)$$
Now, as you can easily see,
$$\delta S = \displaystyle\int d^4x \bigg(\dfrac{\partial \mat... |
It is possible to approximate a solution to this problem for most parametric trajectories. The idea is the following: if you zoom deep enough on a curve, you cannot tell the curve itself from its tangent at that point.
By making this assumption, there is no need to precompute anything more than two vectors (three for c... |
When dividing by any quantity,or when canceling out two quantities in a ratio(for example, canceling $x$ and $x$ to find that $\frac xx=1$),you need to be aware of what assumptions you have to make sothat the division or canceling makes sense,and remember that those assumptions apply to any results you get.
For example... |
I want to use the integral test to show that $ \sum_{n=3}^{\infty} {1 \over {n\cdot \log{n} \cdot \log{\log {n}}}} $ diverges.
First, I let $ f(x) = {1 \over {x\cdot \log{x} \cdot \log{\log {x}}}} $
I have learned that in order to use the Integral test, $f(x)$ must be continuous, positive, and decreasing at the interva... |
September 17th, 2018, 08:12 AM
# 1
Member
Joined: Sep 2014
From: Sweden
Posts: 94
Thanks: 0
How many different 5-digit number combinations can be created?
How many
different 5-digit number combinations can be created using 5, 7ths and 3, 2s? 77777 | 5
222 | 3
So my first thought was to use this formula:
$\displaystyle ... |
I was wondering if it is important in Quantum Mechanics to deal with operators that have an orthonormal basis of eigenstates? Imagine that we would have an operator (finite-dimensional) acting on a spin system that has real eigenvalues, but its eigenvectors are not perpendicular to each other. Is there any reason why s... |
Help me, please.
Radicals: Simplify or Reduce
√3/8
Just to make sure.... Is this the expression in your question:
\(\sqrt\frac38\)
??
Okay....
\(\ \quad\sqrt{\frac38}\\ =\\ \quad\sqrt{\frac38\cdot\frac88}\\ =\\ \quad\sqrt{\frac{24}{8^2}}\\ =\\ \quad\frac{\sqrt{24}}{\sqrt{8^2}}\\ =\\ \quad\frac{\sqrt{24}}{8}\\ =\\ \quad... |
Here are a couple of "proofs" of Stirling's formula. They are quite elegant (in my opinion), but not rigorous. On could write down a real proof from these, but as they rely on some hidden machinery, the result would be quite heavy.
1) A probabilistic non-proof
We start from the expression $e^{-n} n^n/n!$, of which we w... |
EDIT: Reread it some hours later and found my error. I figured I was doing something wrong. I was applying operations out of order when calculating the conditional probability. It is 1/2 in each case. I'll leave the commentary untouched.
I think the answer is Yes, or at least I'm not entirely convinced the answer is no... |
In deriving the half-angle formulas, my textbook first says: "Let's take the following identities:"
$$\cos^2\left(\frac a2\right)+\sin^2\left(\frac a2\right)=1;$$
$$\cos^2\left(\frac a2\right)-\sin^2\left(\frac a2\right)=\cos(a);$$
These identities I know. But then the texbook says "through addition and subtraction, we... |
Update, trying to explain this in a better way:
I mean how to find the result without a calculator.
Base 2 Log 16 = 4: simple to figure out: 2 . 2 . 2 . 2
what about
Base 2 Log 18 = ??
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It ... |
The formula is $(A_r\land b)\cdot C_s=A_r\cdot (b\cdot C_s)$, where $0<r<s$. Hestenes suggests to expand $(A_rb)C_s=A_r(bC_s)$ and extract the $s-r-1$-vector part. But this method requires one to know the formula for the Clifford product of two arbitrary blades, and as far as I can see, the book only gives formulas for... |
Credit goes to Semiclassical for doing most of the work on this one. My answer is only different in that I don't directly appeal to the Poisson summation formula, but just plug the Fourier series into the integral directly; a tenable sum results. Consider the integral from Semiclassical,
$$I=\frac{1}{\sqrt{2\pi \sigma^... |
So let me whine for a bit about LaTeX. LaTeX is document-preparation software used a lot in the sciences - in the mathier sciences particularly. The basic idea is that you have a source file, you feed it into the LaTeX processor, and it spits up a PDF. The reason you'd do this is because LaTeX is really good at type-se... |
Yeah, this software cannot be too easy to install, my installer is very professional looking, currently not tied into that code, but directs the user how to search for their MikTeX and or install it and does a test LaTeX rendering
Some body like Zeta (on codereview) might be able to help a lot... I'm not sure if he doe... |
MathModePlugin
Add math formulas to TWiki topics using LaTeX markup language
Description
This plugin allows you to include mathematics in a TWiki page, with a format very similar to LaTeX. The external program
latex2html
is used to generate
gif
(or
png
) images from the math markup, and the image is then included in th... |
№ 8
All Issues
Ukr. Mat. Zh. - 2002νmber=3. - 54, № 8. - pp. 1031-1041
We consider periodic components of
A-diffeomorphisms on two-dimensional manifolds. We study properties of these components and give a topological description of their boundaries.
Ukr. Mat. Zh. - 2002νmber=3. - 54, № 8. - pp. 1042-1052
We consider a ... |
(I have already asked this at MathOverflow, but got no answers there.)
Background
In the untyped lambda calculus, a term may contain many redexes, and different choices about which one to reduce may produce wildly different results (e.g. $(\lambda x.y)((\lambda x.xx)\lambda x.xx)$ which in one step ($\beta$-)reduces ei... |
You are right. Even though the phase jumps at the zeros of the frequency response, such a phase response is usually still called "linear". For a frequency selective filter with frequency response zeros in the stopband, the phase always has discontinuities at the zeros. A purely linear phase response (without jumps) is ... |
It wouldn't.
It is a well-known fact from gravity, which also has a law $\nabla\cdot\vec F_g \propto \rho$ expressing a $1/r^2$ force, that the force of a
spherical shell of mass is zero inside that shell, but outside it is $-\hat r G M m / r^2$ as if all of that mass were at the shell's center.
The same mathematics wi... |
A straight rod is made of two parts, $[0,x_1]$ (green in the figure) with thermal diffusivity $\kappa_1$ and $[x_1,x_2]$ (blue) with thermal diffusivity $\kappa_2$. The rod is perfectly insulated. Zero $y$ and $z$ temperature gradients are assumed.
At $x=0$ temperature is maintained at constant $T_0$. At $x=x_2$ the ro... |
Existence and concentration of nodal solutions to a class of quasilinear problems
DOI: http://dx.doi.org/10.12775/TMNA.2007.012
Abstract
The existence and concentration behavior of nodal solutions are
established for the equation $-\varepsilon^{p} \Delta_{p}u + V(z)|u|^{p-2}u=f(u)$ in $\Omega$, where $\Omega$ is a doma... |
Prof. Stephen Playfer Position: Personal Chair Research Theme: Particle and Nuclear Physics Research Group: Particle Physics Experiment Institution: Edinburgh Email address: s.m.playfer@ed.ac.uk Telephone number: +44 (0)131 650 5275 Address: School of Physics and Astronomy, James Clerk Maxwell Building, Peter Guthrie T... |
ISSN:
1078-0947
eISSN:
1553-5231
All Issues
Discrete & Continuous Dynamical Systems - A
December 2015 , Volume 35 , Issue 12
Special issue on contemporary PDEs between theory and applications
Select all articles
Export/Reference:
Abstract:
This special issue of Discrete and Continuous Dynamical Systems is devoted to so... |
I am solving:
$(\sigma_A^2 - 2\rho\sigma_A\sigma_B +\sigma_B^2)x^2 +2(\rho\sigma_A\sigma_B - \sigma_B^2)x +\sigma_B^2 = 0$
I need to show that a real $x$ exists if and only if $\rho = \pm 1$
Using the quadratic formula I could only get as far as
$ x = \frac{-2(\rho\sigma_A\sigma_B - \sigma_B^2) \pm \sqrt{4\sigma_A^2\si... |
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In statistics and probability theory, the median is the numerical... |
№ 8
All Issues
Ukr. Mat. Zh. - 2005νmber=4. - 57, № 5. - pp. 3-11
Ukr. Mat. Zh. - 2005νmber=4. - 57, № 5. - pp. 582–600
We give a brief survey of results on functional analysis obtained at the Institute of Mathematics of the Ukrainian National Academy of Sciences from the day of its foundation.
Ukr. Mat. Zh. - 2005νmbe... |
Let’s take an example base which can be said to be fully dissociated in water, e.g. $\ce{NaOH}$. You take $40~\mathrm{g}$ of the pure compound and dissolve it in $0.5~\mathrm{l}$ of water. The standard way to calculate the concentration of sodium ion is:
$$c = \frac nV = \frac m{MV} = \frac{40~\mathrm{g}}{40~\mathrm{g\... |
What are the minimum depth circuits possible for addition and multiplication of two n-bit numbers using just AND and XOR gates? I read somewhere that we can achieve constant depth for addition if we have an OR gate. Can I achieve that using XOR gates?
You can simulate an OR gate using a constant number of AND and XOR g... |
Well, now I have an answer. The sketch of proof is following.
Suppose we have confining theory with chiral fermions and gauge group $G_{\text{gauge}}$; it has global symmetry $G$, which has not gauge anomalies and chiral gauge anomalies $GG_{\text{gauge}}^{2}$, but has anomaly $G^{3}$, i.e., symmetric tensor
$$ d_{abc}... |
743 1
Hey all,
This might seem like a stupid question, and this might not be the correct forum, but hopefully someone can clarify it really easily.
I often have seen two definitions of an inner product on a vector space. Firstly, it can be defined as a bilinear map on a [itex] \mathbb F-[/itex]vector space V as [tex] \... |
Let $f: [0, \infty) \rightarrow \mathbb{R}$. Define the value of the left-hand limit of $f$ at $t>0$ to be $f(t^-) = \lim_{x \rightarrow t^-} f(x)$. Define the "left-hand limit function" of $f$ as $f^-: (0, \infty) \rightarrow \mathbb{R}, f^-(t) = f(t^-) = \lim_{x \rightarrow t^-} f(x)$. Prove that $f^-$ is left contin... |
$\qquad\qquad\qquad\qquad\qquad\qquad\qquad$
Is $~\pi^2\approx g~$ a coincidence ?
Some have answered
, others said yes , and no yet others considered $(!)$ as perfectly viable options. Personally, I cannot help but chuckle, as this question reminds me of both Newton’s famous disc, which can be said to be both white an... |
2018-09-11 04:29
Proprieties of FBK UFSDs after neutron and proton irradiation up to $6*10^{15}$ neq/cm$^2$ / Mazza, S.M. (UC, Santa Cruz, Inst. Part. Phys.) ; Estrada, E. (UC, Santa Cruz, Inst. Part. Phys.) ; Galloway, Z. (UC, Santa Cruz, Inst. Part. Phys.) ; Gee, C. (UC, Santa Cruz, Inst. Part. Phys.) ; Goto, A. (UC,... |
Method to calculate the pH of a solution with a strong monoacid
$$\begin{array}{|c|c|c|c|c|}\hline&\text{Before}&&\text{After}&\\\hline&\ce{AH}&\ce{H2O}&\ce{A-}&\ce{H3O+}\\\hline\text{Initial}&n0&\text{excess}&0&0\\\hline\text{Equilbrium}&\epsilon&\text{excess}&n0&n0\\\hline\end{array}$$
Then we have $\mathrm{pH}=-\log... |
Given a group $G$, with its binary ("product") and unary ("inverse") operations:$$\begin{equation}\begin{split}\circ&\colon G^2\to G\\\operatorname{inv}&\colon G\to G\end{split}\end{equation}\tag{1}$$you can consider the restrictions of them on $H^2$ and $H$ respectively, where $H\subset G$:$$\begin{equation}\begin{spl... |
first of all, I need to confess my ignorance with respect to any physics since I'm a mathematician. I'm interested in the physical intuition of the Langlands program, therefore I need to understand what physicists think about homological mirror symmetry which comes from S-duality. This question is related to my previou... |
In Zweibach's
A first course in string theory, he used the least action principle to get the equations of motion for strings, wehre the variation of action(which should be zero) is :$$\delta S = \int_{\tau_i}^{\tau_f} d\tau [\delta X^\mu \mathcal{P}^\sigma_\mu]^{\sigma_1}_0 - \int_{\tau_i}^{\tau_f} d\tau \int_0^{\sigma... |
The classical point vortex model corresponding to the 2D incompressible Euler equation in vorticity form is the system of $N$ ODES
$$\begin{cases} \dot{x}_i(t) = \sum_{1\leq i\neq j\leq N} a_j K(x_i(t),x_j(t)) \\ x_i(0) = x_i^0\end{cases}\tag{1}$$
where $K(x,y) := -\frac{1}{2\pi}(\frac{(x-y)_2}{|x-y|^2}, -\frac{(x-y)_1... |
This is the third issue in our ARMA Unplugged modeling series. In this issue, we introduce the common patterns often found in real time series data and discuss a few techniques to identify/model those patterns, paving the way for more elaborate discussion decomposition and seasonal adjustment methodologies in future is... |
Let $X_n(\Bbb{Z})$ be the simplicial complex whose vertex set is $\Bbb{Z}$ and such that the vertices $v_0,...,v_k$ span a $k$-simplex if and only if $|v_i-v_j| \le n$ for every $i,j$. Prove that $X_n(\Bbb{Z})$ is $n$-dimensional...
no kidding, my maths is foundations (basic logic but not pedantic), calc 1 which I'm pr... |
In this post the matroid theory connections are everywhere, but I won’t use any matroid language. Can you spot them all?
I’m going to discuss my favorite lecture from the course MAT377 – Introduction to Combinatorics, which I have taught at Princeton in the past three years (lecture notes can be found here). This parti... |
A famous theorem of Dirichlet says that infinitely many primes are of the form:$\alpha n+\beta$, but are there infinitely many of the form: $\alpha ^n+\beta$, where $\beta$ is even and $\alpha$ is prime to $\beta$? or of the form $\alpha!+\gamma$, where $\gamma$ is odd?
Out of mere curiosity has this question come, thu... |
I have an interval $[0, 1]$ and a probability density function $f(x)$ defined on that interval. I know $f$ at say 1000 unevenly spaced points along that interval, but I don't have an analytic formula for $f$. How can I calculate the median and the quartiles of $f$?
The median is the point where 50% of the population li... |
This is a basic electronics calculation, do it a hundred times before you move on.
It's Ohm's Law:
\$ V = I \times R \$
or, put differently:
\$ R = \dfrac{V}{I} \$
The voltage is the remainder after the 3.5V drop caused by the LED, so that's 8V - 3.5V = 4.5V. The current seems to be 800mA (though I see also 350mA here ... |
This is the second entry in our series of “Unplugged” tutorials, in which we delve into the details of each of the time series models with which you are already familiar, highlighting the underlying assumptions and driving home the intuitions behind them.
In financial time series and other fields, we often face a non-s... |
No, this is not a recap from the O.J. Simpson trial, but it is a question we face whenever we propose a model for our data: does the model fit and does it explain the data variation properly?
In a time series modeling process, we seek a quantitative measure of the discrepancy (or the goodness of fit) between the observ... |
What about this we have two people A and B both born in February. I will make four cases:
Case1:Both born in a year with February with 28 day. this year has the probability 3/4 Hence we have the set which present their birthday day $\{(1,1) , (1, 2) , \cdots (28 , 28)\}$ This set has $28 \cdot 28$ days and $28$ element... |
This is (again) more a comment than an answer - motivated by René's question for more conceptional background A couple of years ago I began to look at the full primefactorization of the cyclotomic polynomials $f_b(n) = b^n-1 $ by looking at $f(n)$ modulo the primes, creating a little "algebra" on it based on the theore... |
Look at the plot below. It generates noise according to the distribution you mentioned, and averages it (with different numbers of measurements). What is shown is the histogram of the obtained averaged noise values. As you can see, the more you average, the more the noise goes to the center. However, for $m \log m$ mea... |
RESULTS
Predicted PK
Peak 34.8 mcg/mL
Trough 17 mcg/mL
(goal 15-20 mcg/mL)
AUC:MIC 599 mcg*hr/mL Vancomycin Concentration Graph Over Time
PK Parameters
Apparent CrCl
75 mL/min
Vd 73.5 L (0.7 L/kg)
Kel 0.068 hr -1
T 1/ 2 10.2 hrs
This website is intended to be used in conjunction with reasonable clinical judgment. This ... |
I am aware of matched filter and its application. Now, wondering if there is any application of inverse matched filter? What I mean my inverse matched filter is that convolution of matched filter and the inverse matched filter would lead to close to delta function.
In your question, you postulate the existence of two f... |
I have the calculation: $2^{31}\pmod {2925}$
It's for university and we should solve it like:
make prime partition $2^{31}$ mod all prime partitions Solve with Chinese Remainder Theorem.
I started with $2925 = 3 \cdot 3 \cdot 5 \cdot 5 \cdot 13$ , and found out that: $$2^{31} \equiv 2 \pmod{3}$$ $$2^{31} \equiv 3 \pmod... |
Since $\mathbb{F}_9$ is a field, its units $\mathbb{F}_{9}^* = (1,2,3,4,5,6,7,8)$ should form a multiplicative group. However in this group $3 \times 3 = 0 \notin \mathbb{F}_{9}^*$. I'm trying to understand how this is possible. Don't rush on me since I'm new to the literature.
$\Bbb F_9$ is a quotient ring of the poly... |
Let $p_n$ denote the $n^\text{th}$ prime. Find a lower bound for $\left|S\right|$ where
$$S = \left\{ q \in \mathbb{N} \mid q \text{ is prime and } p_n - n \leq q \leq p_n + n \right\}. $$
Any good bounds known? See this graph: http://oeis.org/A097935/graph
[Edit 1] Let
$$ a = n\left(\ln(n) + \frac{13}{500}\right), \ \... |
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Now showing items 1-10 of 20
Measurement of electrons from beauty hadron decays in pp collisions at root √s=7 TeV
(Elsevier, 2013-04-10)
The production cross section of electrons from semileptonic decays of beauty hadrons was measured at mid-rapidity (|y| < 0.8) in the transverse momentum range 1 < pT <8 GeV/c w... |
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Now showing items 1-9 of 9
Measurement of $J/\psi$ production as a function of event multiplicity in pp collisions at $\sqrt{s} = 13\,\mathrm{TeV}$ with ALICE
(Elsevier, 2017-11)
The availability at the LHC of the largest collision energy in pp collisions allows a significant advance in the measurement of $J/\ps... |
In the article Automata and semigroups recognizing infinite words an automaton is specified by $\mathcal A = (Q, A, E, I, F)$ where $I$ is a set of initial states and $F$ a set of final states, $Q$ its state set, $E \subseteq Q\times A \times Q$ the transitions and $A$ its alphabet. It is called
deterministic if for ev... |
The
weighted mean is similar to an arithmetic mean (the most common type of average), where instead of each of the data points contributing equally to the final average, some data points contribute more than others. The notion of weighted mean plays a role in descriptive statistics and also occurs in a more general for... |
Let there be two point charges, positive or negative, having velocities in directions perpendicular to each other. I need to evaluate the total interactive force on those (Lorentz force).
I do it by assuming magnetic force is an effect of special relativity on the electrostatic force. In doing so I am finding a value h... |
The first complex, from Weibel, is a projective resolution of the trivial $\mathfrak g$-module $k$ as a $\mathcal U(\mathfrak g)$-module; I am sure Weibel says so!
Your second complex is obtained from the first by applying the functor $\hom_{\mathcal U(\mathfrak g)}(\mathord-,k)$, where $k$ is the trivial $\mathfrak g$... |
Could 2 moons that orbit same terrestrial planet never see each other if they orbit the planet at same time?
Moons have different mass and gravity.
Worldbuilding Stack Exchange is a question and answer site for writers/artists using science, geography and culture to construct imaginary worlds and settings. It only take... |
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Production of charged pions, kaons and protons at large transverse momenta in pp and Pb-Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV
(Elsevier, 2014-09)
Transverse momentum spectra of $\pi^{\pm}, K^{\pm}$ and $p(\bar{p})$ up to $p_T$ = 20 GeV/c at mid-rapidity, |y| $\le$ 0.8, in pp and ... |
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