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The ALICE Transition Radiation Detector: Construction, operation, and performance
(Elsevier, 2018-02)
The Transition Radiation Detector (TRD) was designed and built to enhance the capabilities of the ALICE detector at the Large Hadron Collider (LHC). While aimed at providing electron... |
Learning Objectives Find the macro equilibrium using algebra
In the income-expenditure model, the equilibrium occurs at the level of GDP where aggregate expenditures equal national income (or GDP). We can identify this equilibrium using algebra as well as graphically. Given algebraic equations for the aggregate expendi... |
Update: The MathJax Plugin for TiddlyWiki has a new home: https://github.com/guyru/tiddlywiki-mathjax Some time ago I came across MathJax, a nifty, Javascript based engine for displaying TeX and LaTeX equations. It works by “translating” the equation to MathML or HTML+CSS, so it works on all modern browsers. The result... |
I have the following problem : I'm calculating the sample covariance matrix in the frequency domain ( $y_{k}$ is the FFT of a time domain $k_{th}$ symbol vector signal , basically a simulated received signal) as follows:
$$\mathbf{R}=\frac{1}{N_{f}}\sum_{k=0}^{N_{f}-1}y_{k}y_{k}^{H}$$
Well , the next step on my algorit... |
(Sorry was asleep at that time but forgot to log out, hence the apparent lack of response)
Yes you can (since $k=\frac{2\pi}{\lambda}$). To convert from path difference to phase difference, divide by k, see this PSE for details http://physics.stackexchange.com/questions/75882/what-is-the-difference-between-phase-differ... |
I am stuck on finding the 'right' mediator in weak interactions. Consider the following reactions.
1:
$$\mu^+\rightarrow \bar{\nu}_\mu + e^+ +\nu_e$$
This is mediated by the vector boson $W^+$.
2:
$$\pi^-\rightarrow \bar{\nu}_\mu+\mu^-$$
This is mediated by the vector boson $W^-$.
3:
$$\nu_\mu +e^- \rightarrow \nu_\mu ... |
Happy Pi day to all non-American applied mathematicians and scientists (like me) who make approximations!
This is in fact TeX related as I have a question, or perhaps a puzzle. How would I make the equation
$\pi \approx \today$
give the output that makes sense, given the appropriate formatting of today's date. Furtherm... |
9.10. Predicting Pizza Prices - Linear Regression¶
Linear regression is probably one of the most widely used algorithms in data science, and many other sciences. One of the best things about linear regression is that it allows us to learn from things that we know or use observations and measurements of things we know t... |
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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 ... |
Proceedings of the Thirty-Second Conference on Learning Theory, PMLR 99:2173-2174, 2019.
Abstract
We study the linear contextual bandit problem with finite action sets. When the problem dimension is $d$, the time horizon is $T$, and there are $n \leq 2^{d/2}$ candidate actions per time period, we (1) show that the mini... |
The definition of a limit continues on in our learning limits and how they are applied. Specifically we are going to look at some proofs in this section. With a precise definition we can now prove many limit properties.
Definition of a Limit
The \(\delta\) value will always depend on the \(\epsilon\) value. That is imp... |
Proceedings of the Thirty-Second Conference on Learning Theory, PMLR 99:696-726, 2019.
Abstract
We propose the first contextual bandit algorithm that is parameter-free, efficient, and optimal in terms of dynamic regret. Specifically, our algorithm achieves $\mathcal{O}(\min\{\sqrt{KST}, K^{\frac{1}{3}}\Delta ^{\frac{1}... |
1 Fractional control actions 1.1 Time domain
In the following, we illustrate the effects of the basic fractional-order control actions in the time domain [1]. For this we consider the response of the system
where $K$ is the gain of the differentiator/integrator of order $\alpha$, such that $-1\leqslant \alpha \leqslant... |
Category:Convergence Let $T = \left({S, \tau}\right)$ be a topological space.
Let $\left \langle {x_n} \right \rangle_{n \in \N}$ be an infinite sequence in $S$.
$\forall U \in \tau: \alpha \in U \implies \left({\exists N \in \R_{>0}: \forall n \in \N: n > N \implies x_n \in U}\right)$ Subcategories
This category has t... |
Electrical resistivity and conductivity is an important property for materials. Different materials have different conductivity and resistivity. Electrical conductivity is based on electrical transport properties. These can be measured with multiple techniques by using a variety of instruments. If electricity easily fl... |
The Lagrangian formulation of mechanics will be useful later when we study the Feynman path integral. For our purposes now, the Lagrangian formulation is an important springboard from which to develop another useful formulation of classical mechanics known as the
Hamiltonian formulation. The Hamiltonian of a system is ... |
Mumford’s drawing has a clear emphasis on the vertical direction. The set of all vertical lines corresponds to taking the fibers of the natural ‘structural morphism’ : $\pi~:~\mathbf{spec}(\mathbb{Z}[t]) \rightarrow \mathbf{spec}(\mathbb{Z}) $ coming from the inclusion $\mathbb{Z} \subset \mathbb{Z}[t] $. That is, we c... |
Distributions Introduction
This section will begin to formalize the connection between random variables, probability density functions, and population parameters. We generally use language like the random variable $X$ follows a named distribution, which has a probability density function defined by, possibly many, para... |
Please assume that this graph is a highly magnified section of the derivative of some function, say $F(x)$. Let's denote the derivative by $f(x)$.Let's denote the width of a sample by $h$ where $$h\rightarrow0$$Now, for finding the area under the curve between the bounds $a ~\& ~b $ we can a...
@Ultradark You can try d... |
The question is long because of the demonstrations I give, but the problem is simple, so bear with me for a minute.
I am trying to derive the dispersion relation of a semi-infinite system using Euler-Lagrange equations, and I started with the simplest case of a semi-infinite string. However, the result, as I show below... |
Hi, Can someone provide me some self reading material for Condensed matter theory? I've done QFT previously for which I could happily read Peskin supplemented with David Tong. Can you please suggest some references along those lines? Thanks
@skullpatrol The second one was in my MSc and covered considerably less than my... |
The bounty period lasts 7 days. Bounties must have a minimum duration of at least 1 day. After the bounty ends, there is a grace period of 24 hours to manually award the bounty. Simply click the bounty award icon next to each answer to permanently award your bounty to the answerer. (You cannot award a bounty to your ow... |
Definition:Relation Induced by Partition Definition
Let $S$ be a set.
Let $\mathcal R \subseteq S \times S$ be the relation defined as:
$\forall \tuple {x, y} \in S \times S: \tuple {x, y} \in \mathcal R \iff \exists T \in \Bbb S: \set {x, y} \subseteq T$ Then $\mathcal R$ is the (equivalence) relation induced by (the ... |
Here is a way with aligned minipages:\documentclass[a4paper, 10pt, oneside]{memoir}% Page layout\setlrmarginsandblock{1.7cm}{8.5cm}{*}\setulmarginsandblock{1.7cm}{2.5cm}{*}\setmarginnotes{0.5cm}{\dimexpr(\stockwidth-\textwidth-4.4cm)}{1em}\checkandfixthelayout\chapterstyle{bianchi}\usepackage{titlesec}\usepackage{title... |
NTSGrad Spring 2018/Abstracts
This page contains the titles and abstracts for talks scheduled in the Spring 2018 semester. To go back to the main NTSGrad page, click here.
Contents Jan 23
Solly Parenti Rankin-Selberg L-functions
What do you get when you cross an Eisenstein series with a cuspform? An L-function! Since t... |
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Now showing items 1-10 of 27
Production of light nuclei and anti-nuclei in $pp$ and Pb-Pb collisions at energies available at the CERN Large Hadron Collider
(American Physical Society, 2016-02)
The production of (anti-)deuteron and (anti-)$^{3}$He nuclei in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV has ... |
Under the CEV model the stock price has the following dynamics:
$dS_t=\mu S_tdt+\sigma S_t^\gamma dW_t$, where $\sigma\geq0, $ $\gamma\geq0$.
According to Wikipedia, if $\gamma <1$ the volatility of the stock increases as the price falls.
But why is this true? Shouldn't be the exponent negative in order to have an inve... |
We have the following definition about convergence in a normed space:
"Let $(x_n)_{n=1}^\infty$ be a sequence in a normed space $(X,\|\cdot\|)$. We say that $x_n\to x$ in $X$ if, $$d(x_n,x)\equiv \|x-x_n\|\to 0$$ as $n\to \infty.$"
My questions:
How is it that we read this statement, and consequently understand it? In ... |
In O'searcoid,
Metric Spaces, he provides the following example of a metric space:
Suppose C is a circle and, for each $a,b ∈ C$, define $d(a,b)$ to be the distance along the line segment from $a$ to $b$. Then $d$ is a metric on $C$.
I have decided to confirm that his example is, indeed, a metric (here might be a good ... |
One Mean
Consider a dataset about $N = 54$ cars sampled from the year $1993$. Of interest is the (unknown population) mean miles per gallon, $\mu$. We assume
The parameter $\sigma$ might be of interest to some, but not us now. By choosing this model we are implicitly assuming that $\mathbb{E}(Y) = \mu$, where $\mu$ is ... |
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Now showing items 1-10 of 26
Kaon femtoscopy in Pb-Pb collisions at $\sqrt{s_{\rm{NN}}}$ = 2.76 TeV
(Elsevier, 2017-12-21)
We present the results of three-dimensional femtoscopic analyses for charged and neutral kaons recorded by ALICE in Pb-Pb collisions at $\sqrt{s_{\rm{NN}}}$ = 2.76 TeV. Femtoscopy is used to... |
Please assume that this graph is a highly magnified section of the derivative of some function, say $F(x)$. Let's denote the derivative by $f(x)$.Let's denote the width of a sample by $h$ where $$h\rightarrow0$$Now, for finding the area under the curve between the bounds $a ~\& ~b $ we can a...
@Ultradark You can try d... |
I'm writing an exercise book, and in some exercises I'll have several numbered equations in an align environment, e.g.,
(1) x^2+x+1=0, (2) ax^3+2x=0, (3) x^5=2i,
(4) x^4=-i, (5) x-1/x=2, (6) cosh(x)=3.
(I'll want them to be aligned with respect to the number).
I'm using a macro
\newcommand*\ExoEq{\refstepcounter{ExoEq}... |
I need to give a lot of quite basic background to this question because I think (at least from conversing with fellow graduate students) that most mathematicians have not
really thought about fractions for a long time. I think that there is an interesting germ of an idea in here somewhere, but I cannot exactly pinpoint... |
The question
I consider the Laplacian $\Delta = \partial_1^2 + \partial_2^2 + \partial_3^2$ in $\mathbb{R}^3$. By the "standard" fundamental solution of the Laplacian, I mean the function
$$ \displaystyle E(x) = C|x|^{-1} $$
where $C$ is some normalization constant.
I would like to know if one can construct a fundament... |
For fixed $m = 0, 1, 2, ...$ $$f_m(k) = \prod_{j=1}^{m}(k+j).$$ Some examples of $f_m(k)$ are as following: $$f_0(k) = 1, \quad f_1(k) = (k+1), \quad f_2(k) = (k+1)(k+2).$$
The $s_m(n)$ is defined as following: $$s_m(n) = \sin\left(\frac{t}{2}\right)\sum_{k=0}^nf_m(k)\sin(k+0.5)t,\qquad t\in[0,\pi].$$
The $s_m(n)$ can ... |
There are many question about life and physics in higher dimensions. but is there any physical thing (i mean things like force, momentum, speed,...) that cannot exist in 2D world? could 2D world have life forms(not necessarily the life form we have) or there is something used by life that needs at least 3 spatial dimen... |
How to Implement the Fourier Transformation from Computed Solutions
We previously learned how to calculate the Fourier transform of a rectangular aperture in a Fraunhofer diffraction model in the COMSOL Multiphysics® software. In that example, the aperture was given as an analytical function. The procedure is a bit dif... |
I actually got this part and I got $16$ choose $2$, which would be $120$. The part I didn't get which wouldn't fit into the title was in how many of these solutions is $x_1 \geq 1$, $x_2 \geq 2$,and $x_3 \geq 3$? I'm not very good at combinatorics so I don't really know. I think the way to approach it would be saying h... |
Answer
\begin{equation} N_{m}=\frac{n-1}{2}+1=\frac{n-1+2}{2}=\frac{n+1}{2} \end{equation}
Work Step by Step
We suppose we have an odd number of items, like $15 .$ Our task is to find the position for the middle item. Here's how we can find the position for a 15 -element list: $15=14+1=2 \cdot 7+1=7+1+7$ Here we can se... |
Hi, Can someone provide me some self reading material for Condensed matter theory? I've done QFT previously for which I could happily read Peskin supplemented with David Tong. Can you please suggest some references along those lines? Thanks
@skullpatrol The second one was in my MSc and covered considerably less than my... |
Using the Product Rule to Simplify Square Roots
To simplify a square root, we rewrite it such that there are no perfect squares in the radicand. There are several properties of square roots that allow us to simplify complicated radical expressions. The first rule we will look at is the
product rule for simplifying squa... |
This task is more complex than the task to solve a quadratic equation, for example, and one must master a significant portion of a textbook – such as Georgi's textbook – and perhaps something beyond it to have everything he needs.
For the 8-dimensional representation of $SU(3)$, things simplify because it's the "adjoin... |
Let $T$ be a torus. We have a parameterization by $((c+a \cdot cos(v))cos(u),(c+a\cdot cos(v),a\cdot sin(v))$ for $u,v \in [0,2\pi)$. The first fundamental form is given by $E=(c+a\cdot cos(v))^{2}, F=0, G=a^2$
and the second fundamental form is given by $e=-(c+a\cdot cos(v))cos(v),f=0,g=-a$. Since gaussian curvature i... |
A
tetrahedral snake, sometimes called a Steinhaus snake, is a collection of tetrahedra, linked face to face.
Steinhaus showed in 1956 that the last tetrahedron in the snake can never be a translation of the first one. This is a consequence of the fact that the group generated by the four reflexions in the faces of a te... |
Dini Lipschitz functions for the Dunkl transform in the Space \(\mathrm {L}^{2}(\mathbb {R}^{d},w_{k}(x)dx)\) 799 Downloads Citations Abstract
Using a generalized spherical mean operator, we obtain an analog of Theorem 5.2 in Younis (J Math Sci 9(2),301–312 1986) for the Dunkl transform for functions satisfying the \(d... |
Lorenz equations part II: "randomly" rotated homoclinic orbits and chaotic trajectories
1.
Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260
$x' =s(y-x), \quad y'= Rx -y-xz, \quad z'= xy -qz,$
where $s$, $R$, and $q$ are positive parameters. We show by a purely analytic proof that for each non-n... |
Night Side Maneuvers
We can minimize
night light pollution (NLP) by turning the thinsat as we approach eclipse. The goal will be to perform one complete rotation of the thinsat per orbit, with it perpendicular to the sun on the day-side of the earth, but turning it by varying amounts on the night side.
Another advantag... |
For some strange reason, this:
\hat{\dot{\bm{\phi}}}
prints the dot and the hat slightly off the left of the phi letter. Any ideas if this can be fixed? thanks. Using bm package for bold symbols.
TeX - LaTeX Stack Exchange is a question and answer site for users of TeX, LaTeX, ConTeXt, and related typesetting systems. ... |
Current browse context:
hep-th
Change to browse by: Bookmark(what is this?) Mathematics > Differential Geometry Title: Spectral sections, twisted rho invariants and positive scalar curvature
(Submitted on 23 Sep 2013 (v1), last revised 25 Apr 2014 (this version, v3))
Abstract: We had previously defined the rho invarian... |
does this series converge/diverge conditionally or absolutly
$\sum_{n=2}^{\infty} (-1)^n \cdot \frac{\sqrt{n}}{(-1)^n + \sqrt{n}} \cdot \sin(\frac{1}{\sqrt{n}})$
i can use the facts that:
$\lim_{x\to0}\frac{\sin x}{x} =1 $;
$\sin(\frac{1}{\sqrt{n}})$ is monotone decreasing
my problem is the alternating $-1$'s in the de... |
Why does the heat capcity not jump at an energy threshold
To understand why heat capacity rises continuously and not step-wise consider a simple harmonic oscillator with eigenenergies $\epsilon_n = \hbar \omega \left(n + \frac 1 2\right)$. In the following $k_B = 1$ and $\beta = 1/T$.
The partition function is given by... |
Notice that $A$ is upper triangular, so you can just set $L = {\rm I}_2$, $U = A$.
Without that, we can do some computation. I denote elements of $L$ as $l_{ij}$ and elements of $U$ as $u_{ij}$ (both for $i=1,2$ and $j=1,2$).
If the first row of $L$ is zero, then the first row of $A$ is zero. So, $l_{11} \ne 0$, i.e., ... |
Reynolds Number (Re) - Blayne Sarazin Contents Reynolds Number
The Reynolds number is a dimensionless quantity in fluid mechanics that is used to help predict flow patterns in different fluid flow situations. The Reynolds Number serves as a guide to the laminar-turbulent transition in a particular flow situation,
1 and... |
Maryam Aliakbarpour,Themis Gouleakis,John Peebles,Ronitt Rubinfeld,Anak Yodpinyanee;
Proceedings of the Thirty-Second Conference on Learning Theory, PMLR 99:34-82, 2019.
Abstract
In this work, we consider the sample complexity required for testing the monotonicity of distributions over partial orders. A distribution $p... |
Difference between revisions of "Probability Seminar"
(→Tuesday , May 7, Van Vleck 901, 2:25pm,, Duncan Dauvergne (Toronto))
(→Tuesday , May 7, Van Vleck 901, 2:25pm, Duncan Dauvergne (Toronto))
Line 121: Line 121:
</span></b>
</span></b>
</div>
</div>
+ + + Revision as of 09:45, 1 May 2019 Spring 2019 Thursdays in 901... |
I am reading this resource to learn statistical mechanics: http://blancopeck.net/Statistics.pdf
I am trying to learn about the partition function, which as I understand it, is equal to the number of legal configurations, in some of these randomized systems that we study to simulate molecular dynamics (hard disks, cloth... |
Kaushar Ali
Articles written in Journal of Earth System Science
Volume 119 Issue 6 December 2010 pp 753-762
Surface snow and lake water samples were collected at different locations around Indian station at Antarctica, Maitri, during December 2004-March 2005 and December 2006-March 2007.Samples were analyzed for major ... |
X-rays
In order to make metal radioactive one have to turn it into another element or isotope. This can be performed only with high-energy particles (including photons).
X-rays can be produces if an electron enters metal with very high speed in two ways:
deceleration radiation (Bremsstrahlung) an atom absorbs part of t... |
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Now showing items 1-10 of 18
J/Ψ production and nuclear effects in p-Pb collisions at √sNN=5.02 TeV
(Springer, 2014-02)
Inclusive J/ψ production has been studied with the ALICE detector in p-Pb collisions at the nucleon–nucleon center of mass energy √sNN = 5.02TeV at the CERN LHC. The measurement is performed in... |
D-Wave Systems Inc. builds annealing devices that exhibit quantum effects. These devices as well as other physical systems implement a programmable Ising model of the form.
\begin{equation}
H = \sum_i c_i Z_i+\sum_{ ij} c_{ij}Z_iZ_j \end{equation
Where zed is the familiar Pauli matrix.
The approach I took program D-Wav... |
Abstract
We prove that almost any pair of real numbers $\alpha,\beta$, satisfies the following inhomogeneous uniform version of Littlewood’s conjecture: $$\begin{align}\label{C1abst}\tag{C1} \forall \gamma,\delta\in\mathbb{R},\quad \liminf_{|n|\to\infty} \left|n\right|\langle n\alpha-\gamma \rangle\langle n\beta-\delta... |
First of all it's good to graph the functions $(a)$ (red) and $(b)$ (blue):
The second step is to fund points of intersection, so we find all solutions of
$$\begin{cases}r=|4\cos(2\theta)|\\r=|4\sin(2\theta)|\\\end{cases}$$
We are taking absolute values because $r$ may be negative and this might complicate things. The ... |
I think there are two issues here. The first is that
LogicalExpand is for expanding
logical expressions, like so:
In[1]:= LogicalExpand[(a || b) && (b || c)]
Out[1]= (a || b) && (b || c)
Second, you can actually work directly with power series and expand them about $ \infty $, as follows:
In[2]:= series = Series[f[(a L... |
Strictly Monotone Mapping with Totally Ordered Domain is Injective Theorem
Let $\struct {S, \preceq_1}$ be a totally ordered set.
Let $\struct {T, \preceq_2}$ be an ordered set.
Let $\phi: \struct {S, \preceq_1} \to \struct {T, \preceq_2}$ be a strictly monotone mapping.
Then $\phi$ is injective. Proof
\(\displaystyle ... |
1Department of Mathematics, Yazd University, 89195-741, Yazd, Iran.
2Department of Mathematics, Yazd University, Yazd, Iran.
Receive Date: 04 October 2016,Revise Date: 18 September 2017,Accept Date: 19 September 2017
Abstract
The distinguishing number (resp. index) $D(G)$ ($D'(G)$) of a graph $G$ is the least integer $... |
In 1877, Richard Dedekind discovered one of the most famous pictures in mathematics : the black&white tessellation of the upper half-plane in hyperbolic triangles. Recall that the group $SL_2(\mathbb{Z}) $ of all invertible 2×2 integer matrices with determinant $1$ acts on the upper halfplane via
$\begin{bmatrix} a & b... |
Switched Three Phase Slot Antenna Drive Note, 2015 April 21: This will not work without modification. Different frequencies will scatter at different angles. With a signal bandwidth of 1 GHz, and a thinsat 20 cm wide, and a beam angle of 45°, there is a ±234 psec difference at the edges of the array, ±0.117 radians at ... |
Dr Eligio Lisi (INFN, Bari, Italy)
15/03/2015, 08:30
Theory
Ordinary
The status of known and unknown three-neutrino parameters will be briefly reviewed, providing an introduction to subsequent talks in the neutrino session.
Dr Barbara Caccianiga (INFN, Sezione di Milano)
15/03/2015, 08:55
Experiment
Ordinary
Borexino i... |
Forcing and construction schemes 19 Downloads Abstract
We investigate forcing and independence questions relating to construction schemes. We show that adding \(\kappa\geq\omega_{1} \) Cohen reals adds a capturing construction scheme. We study the weaker structure of
n-capturing construction schemes and show that it is... |
Find all the functions $f:\mathbb{R}→\mathbb{R}$ such that $f(mx+c)=mf(x)+c$, $m≠1$.
I know that $f(x)=x$ and $f(x)=c/(1-m)$ are two solutions. But to completely solve it I have no idea. Can we completely solve it using elementary mathematics (without assuming additional conditions) ?
Find all the functions $f:\mathbb{... |
Taken together, the product rule, quotient rule, and power rule are often called “laws of logs.” Sometimes we apply more than one rule in order to simplify an expression. For example:
We can use the power rule to expand logarithmic expressions involving negative and fractional exponents. Here is an alternate proof of t... |
Given an ensemble with many members, each member having a different phase space vector \(x\) corresponding to a different microstate, we need a way of describing how the phase space vectors of the members in the ensemble will be distributed in the phase space. That is, if we choose to observe one particular member in t... |
Part 6 in the quest for the hydrogen molecule
In this part I will present, as promised, a derivation of the famous Schrödinger equation.
As I have shown in the last part, with our approach so far we are able to calculate important properties of physical systems already. Usually these properties are calculated from the ... |
"A good notation has a subtlety and suggestiveness which at times make it almost seem like a live teacher."— Bertrand Russell "We could, of course, use any notation we want; do not laugh at notations; invent them, they are powerful. In fact, mathematics is, to a large extent, invention of better notations."— Richard Fe... |
Mumford’s drawing has a clear emphasis on the vertical direction. The set of all vertical lines corresponds to taking the fibers of the natural ‘structural morphism’ : $\pi~:~\mathbf{spec}(\mathbb{Z}[t]) \rightarrow \mathbf{spec}(\mathbb{Z}) $ coming from the inclusion $\mathbb{Z} \subset \mathbb{Z}[t] $. That is, we c... |
A long while ago I promised to take you from the action by the modular group $\Gamma=PSL_2(\mathbb{Z})$ on the lattices at hyperdistance $n$ from the standard orthogonal laatice $L_1$ to the corresponding ‘monstrous’ Grothendieck dessin d’enfant.
Speaking of dessins d’enfant, let me point you to the latest intriguing p... |
One of the most intriguing consequences of Bell’s theorem is the idea that one can do
experimental metaphysics: to take some eminently metaphysical concepts such as determinism, causality, and free will, and extract from them actual experimental predictions, which can be tested in the laboratory. The results of said te... |
A
tetrahedral snake, sometimes called a Steinhaus snake, is a collection of tetrahedra, linked face to face.
Steinhaus showed in 1956 that the last tetrahedron in the snake can never be a translation of the first one. This is a consequence of the fact that the group generated by the four reflexions in the faces of a te... |
I was trying to evaluate this product$$ \sin (1^\circ) \sin (2^\circ) \sin (3^\circ) ... \sin (88^\circ) \sin (89^\circ) \sin (90^\circ) $$But I think it got weird results with this
Product[Sin[i], {i, pi/180, pi/2}]Can anyone suggest me something??
I was trying to evaluate this product$$ \sin (1^\circ) \sin (2^\circ) ... |
Area of Square Contents Theorem Integer Side Length
In the case where $L = 1$, the statement follows from the definition of area.
If $L \in \N, L > 1$, then we can divide the square into smaller squares, each of side length one.
Since there will be $L$ squares of side length one on each side, it follows that there will... |
I think you made a small typo. The sum in the denominator should be running from $1$ to $k-1$, not $k$. Edit: nevermind you fixed it :)
Fitting $k-1$ independent regressions, you get estimates for $\{\theta_j\}$ with $j=1, \ldots, k-1$. The $k-1$ models are parametrized as:$$P(Y=j|X^{(i)}) = \frac{\exp(\theta_j^TX^{(i)... |
Learning Objectives
To describe the relationship between solute concentration and the physical properties of a solution. To understand that the total number of nonvolatile solute particles determines the decrease in vapor pressure, increase in boiling point, and decrease in freezing point of a solution versus the pure ... |
A Matlab toolbox to analyze grain boundary inclination from SEM images¶
First of all, download the source code of the Matlab toolbox.
This toolbox helps to find the grain boundary inclination from two micrographs from serial polishing. At least three marks such as microindents are needed for registration of the images.... |
I'm probably missing something elementary here, but I guess the only way to be sure is to ask here.
Now, I have encountered a situation where given an nth-degree polynomial $p_n(z)$ with complex coefficients, and a positive real number $\rho$, I need to find the value(s) of $\theta$, $0\leq\theta<2\pi$, such that the v... |
I try to solve the following recursion for $n \in \mathbb{N}$.
$r_i = r_{i-1} - \frac{1}{2} \cdot \sqrt{1 - \frac{4\pi^2\cdot r_{i-1}^2}{n^2} \cdot \cos^2 \left(\frac{\pi}{n}\right)}$
$r_0 = \frac{n}{2\pi}$
I translated it into the following code for Mathematica:
RSolve[{g[x]==g[x-1]- 1/2 Sqrt[1 - 4 Pi^2 g[x-1]^2/n^2 (... |
Part 5 in the quest for the hydrogen molecule
Last time we investigated the energy states of a free particle. That is of course a bit of a boring example: the particle does not really have any behavior except that it flies in one direction or another. This time we will derive our first results on how quantum mechanics ... |
Just as we studied special types of sequences, we will look at special types of series. Recall that an
arithmetic sequence is a sequence in which the difference between any two consecutive terms is the common difference, [latex]d[/latex]. The sum of the terms of an arithmetic sequence is called an arithmetic series. We... |
Definition:Ordering/Definition 1 Definition
Let $S$ be a set.
An
ordering on $S$ is a relation $\mathcal R$ on $S$ such that:
\((1)\) $:$ $\mathcal R$ is reflexive \(\displaystyle \forall a \in S:\) \(\displaystyle a \mathop {\mathcal R} a \) \((2)\) $:$ $\mathcal R$ is transitive \(\displaystyle \forall a, b, c \in S:... |
I would like to use charter for text and formula symbols, excerpt for greek letters, these I'd like to do in palatino (
mathpazo). I've tried around a lot with
\DeclareSymbolFont,
\DeclareMathSymbol and so on. But to be honest, I'm not close to a solution.
A minimal (not working) code example follows:
\documentclass{ar... |
Problem Authoring Best Practices
Below is a summary of the stylistic guidelines for "cleaning" and uniformizing WeBWorK problems that were adopted during the WeBWorK Programming Workshop at MSRI on 20-24 May 2004. These guidelines apply to problems intended for the National Problem Library.
The items listed below cover... |
Bug introduced in 8 or earlier and persists through 11.0.1 or later
I am trying to plot the following single variable function:
$$\small\frac{180 \sqrt{\pi ^2-625 t} \left(\pi ^2 (36 t-25)-1500 t \left(45 t-\sqrt{900 t-\pi ^2}-15\right)\right)}{\pi ^4 \sqrt{2500 t-\pi ^2}}+\tan \left(2 \sqrt{\pi ^2-625 t}\right)$$
with... |
MAP (Maximum a posteriori) Inference is a form of Bayesian inference that deals with MAP queries. The goal of a MAP query is to find the most likely assignment for all of the non-evidence random variables given the evidence variables, this is also called the Most Probable Explanation (MPE). This is similar to Bayesian ... |
I am interested in deriving the convergence rate of the smallest eigenvalue of a sequence of random matrices with diverging dimension. More precisely, let $W_n(r)$ represent an $n$-dimensional standard brownian motion at time $r$, and define $\lambda_1(A)$ as the minimum eigenvalue of A. Then, I would like to know how ... |
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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 ... |
Maths loves symbols. Everyone loves emoji. It’s 2017 and time we brought the two together. To get you started, here are our
top ten emoji for use in mathematics! 10.
Don’t leave home without one: it’s the nifty
45° set square. What better reminder is there that $$\sin\left(\frac{\pi}{4}\right) = \frac{\sqrt{2}}{2}, \qq... |
Here we want to give an easy mathematical bootstrap argument why solutions to the time independent 1D Schrödinger equation (TISE) tend to be rather nice. First formally rewrite the differential form$$-\frac{\hbar^2}{2m} \psi^{\prime\prime}(x) + V(x) \psi(x) ~=~ E \psi(x) \tag{1}$$into the int...
[Some time travel comme... |
I use the notation introduced in the paper: The parameters of ElGamal are $(G, q, g)$ where $q$ is prime, $G$ is a cyclic group of order $q$ and $g$ is a generator. In the paper, the authors use "exponential ElGamal" such that they have an additive homomorphism, i.e., the message is represented as "exponent" of $g$, i.... |
I know, you think that
Multi Layer Perceptron seems to be very similar to the Perceptron. And yeah, it is but wait ! It’s not completely only that but lots of things are to be going under hood. To be frank, it is some what difficult to understand the underlying concepts in the Neural Networks at the beginning. But lear... |
Real Analysis Exchange Real Anal. Exchange Volume 34, Number 2 (2008), 501-520. Divergence in Measure of Rearranged Multiple Orthononal Fourier Series Abstract
Let $\{\varphi_n(x)$, $n=1,2,\dots\}$ be an arbitrary complete orthonormal system (ONS) on the interval $I:=[0,1)$ that consists of a.e. bounded functions. Then... |
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