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Let $X$ be a scheme and $x \in X$. Consider the functor
$\text{Qcoh}(X) \to \mathcal{O}_{X,x} \text{-Mod} , M \mapsto M_x.$
Does it have a right-inverse? I.e. is there, for every $\mathcal{O}_{X,x}$-module $N$ a (functorial) quasi-coherent $\mathcal{O}_X$-module $M$ such that there is a natural isomorphism $M_x \cong N... |
We use a simple argument to estimate the speed of traffic on a highway as a function of the density of cars. The idea is to simply calculate the maximum speed that traffic could go without supporting a growing traffic jam.
Follow @efavdb Follow us on twitter for new submission alerts! Jam dissipation argument
To estima... |
My book
My book,
Designing Data-Intensive Applications, was published by O’Reilly in March 2017.
Published by Martin Kleppmann on 26 Jan 2017.
This blog post uses MathJax to render mathematics. You need JavaScriptenabled for MathJax to work.
Many distributed storage systems (e.g. Cassandra, Riak, HDFS, MongoDB, Kafka, ... |
A First Look at Quantum Probability, Part 1
In this article and the next, I'd like to share some ideas from the world of quantum probability.* The word "quantum" is pretty loaded, but don't let that scare you. We'll take a
first—not second or third—look at the subject, and the only prerequisites will be linear algebra ... |
How do I generate $1000$ points $\left(x, y, z\right)$ and make sure they land on a sphere whose center is $\left(0, 0, 0\right)$ and its diameter is $20$ ?. Simply, how do I manipulate a point's coordinates so that the point lies on the sphere's "surface" ?.
Use the fact that if you cut a sphere of a given radius with... |
Let $\theta\gt 0$ and $X_1, ..., X_n$ be independently and identically distributed with probability densitiy function $f_\theta(x) = \frac{1}{2\theta} \chi_{x\in[-\theta,\theta]}$, where $\chi$ is the indicator function. What is the maximum likelihood estimator for $\theta$?
This came up while studying for an exam and ... |
To be a knot in the first place, it essentially needs a well-defined regular neighborhood, sort of as proof of its tameness. If you think of a knot as being in the one-skeleton of a triangulation of $\mathbb{R}^3$, then if you want a triangulation of the complement without too many more simplices, you can remove a regu... |
Intuitively, I would expect the Taylor expansion around $x_0$ of a polynomial in $(x-x_0)$ to be identical to the polynomial. However, I cannot seem to show that/whether this is the case:
For a finite power series $f(x) = \sum_{i=0}^{n} a_i (x-x_0)^i$ the $k$-th derivative is given by $$\frac{d^k f(x)}{dx^k} = \sum_{j=... |
@JosephWright Well, we still need table notes etc. But just being able to selectably switch off parts of the parsing one does not need... For example, if a user specifies format 2.4, does the parser even need to look for e syntax, or ()'s?
@daleif What I am doing to speed things up is to store the data in a dedicated f... |
What i am seeking is to explain why the relationship here is not V2/R2 instead it's given as (V1-V2)/R2
Because ohm's law is actually:
$$\Delta V=RI <=> Va-Vb=RI_{ab}$$
Where
is the voltage at one terminal of the resistor, and Va is the voltage at the other terminal. I just added the little index to the current so that... |
The orthogonal group, consisting of all proper and improper rotations, is generated by reflections. Every proper rotation is the composition of two reflections, a special case of the Cartan–Dieudonné theorem.
Yeah it does seem unreasonable to expect a finite presentation
Let (V, b) be an n-dimensional, non-degenerate s... |
Answer
$\theta = 30 ^{\circ}$
Work Step by Step
1. $x=1.73\approx \sqrt 3$ ; $y=1$ 2.$r=\sqrt {(1)^{2}+(\sqrt 3)^{2}} = \sqrt 4 = 2$ 3. $\sin\theta = \frac{y}{r}=\frac{1}{2}$ $\sin^{-1} 0.5=30^{\circ}$ $\theta = 30^{\circ}$
You can help us out by revising, improving and updating this answer.Update this answer
After you... |
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Research schools
Works by Sarig and Benovadia have built symbolic dynamics for arbitrary diffeomorphisms of compact manifolds. This shows thatthere can be at most countably many ergodi... |
I try to solve numerically the following PDE for $E(r, z)$ with a cylindrical symmetrie (i. e. $E(r, z) = E(-r, z)$).
$\frac{\partial E}{\partial z} = \frac{i}{2k} \Delta E + \mathcal{N}(E)$
Where $\Delta$ is the Laplace operator in transversal direction and $k$ a real number. I want to use the Crank-Nicolson scheme to... |
You may have heard the terms
resistivity and resistance as they relate to resistors. They sound alike but have slightly different meaning. Resistivity and resistance capture the idea that materials fight against the flow of current.
There are two more resistor words you should know about:
conductivity and conductance. ... |
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Higher harmonic flow coefficients of identified hadrons in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV
(Springer, 2016-09)
The elliptic, triangular, quadrangular and pentagonal anisotropic flow coefficients for $\pi^{\pm}$, $\mathrm{K}^{\pm}$ and p+$\overline{\mathrm{p}}$ in Pb-... |
Search
Now showing items 1-1 of 1
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 ... |
Tomorrow, for the final lecture of the
Mathematical Statistics course, I will try to illustrate – using Monte Carlo simulations – the difference between classical statistics, and the Bayesien approach.
The (simple) way I see it is the following,
for frequentists, a probability is a measure of the the frequency of repea... |
Next, we combine what we have learned about convection and diffusion and apply it to the Burger's Equation. This equation looks like —and is— the direct combination of both of the PDE's we had been working on earlier.$$ \frac{\partial u}{\partial t} + \frac{\partial u}{\partial x} = \nu \frac{\partial^2 u}{\partial x^2... |
I'm trying to prove the following:
If $(a_n)$ is a sequence of positive numbers such that $\sum_{n=1}^\infty a_n b_n<\infty$ for all sequences of positive numbers $(b_n)$ such that $\sum_{n=1}^\infty b_n^2<\infty$, then $\sum_{n=1}^\infty a_n^2 <\infty$.
The context here is functional analysis homework, in the subject ... |
MathView
MathView is a third-party view library, which might help you display math formula on Android apps easier. Two rendering engines available: MathJax and KaTeX. Support Android version 4.1 (Jelly Bean) and newer.
Setup
There are two ways you can add
MathView to your project in Android Studio:
From a remote Maven ... |
Convolutions from a DSP perspective
I'm a bit late to this but still would like to share my perspective and insights. My background is theoretical physics and digital signal processing. In particular I studied wavelets and convolutions are almost in my backbone ;)
The way people in the deep learning community talk abou... |
Imagine that you had access to one very long (or very many somewhat shorter) unbiased MD simulation(s). What would (or should) you do with the dataset; what quantities can be estimated?
First, we can estimate
equilibrium expectation values. Each trajectory is, by construction, a realization of a Markov chain whose stat... |
The numbers of periodic orbits hidden at fixed points of $n$-dimensional holomorphic mappings (II)
DOI: http://dx.doi.org/10.12775/TMNA.2009.006
Abstract
Let $\Delta ^{n}$ be the ball $|x|< 1$ in the complex vector space ${\mathbb C}
^{n}$, let $f\colon \Delta ^{n}\rightarrow {\mathbb C}^{n}$ be a holomorphic mapping a... |
In today’s post, we document our efforts at applying a gradient boosted trees model to forecast bike sharing demand — a problem posed in a recent Kaggle competition. For those not familiar, Kaggle is a site where one can compete with other data scientists on various data challenges. Top scorers often win prize money, b... |
I need to prove that Constant Absolute Risk Aversion (CARA) is equivalent to \begin{gather} \int u'(x)dF(x) = u'(c(F,u)) \end{gather}
where $u(x)$ is a Bernoulli utility function, $F$ is the distribution of the lottery and $c(F,u)$ is the certainty equivalent.
I started from the fact that CARA is defined as $-\frac{u''... |
There are several questions here so let me start by defining the different types of cells and standard reduction potentials.
Definition of Electrochemical (Galvanic) cell: A cell that converts chemical energy into electrical energy. In these cells a redox reaction creates electrons that can do work.
Definition of Elect... |
I would like to solve the following nonlinear PDE:
$$ \frac{\partial^2 \phi}{\partial x^2} - \frac{\partial^2 \phi}{\partial t^2} = \lambda |\phi|^2 \phi $$
I was trying:
NDSolve[{D[f[x, t], x, x] - D[f[x, t], t, t] == f[x, t]^3, f[x, 0] == Sin[2*Pi*x], f[0, t] == 0, f[1, t] == 0}, f, {x, 0, 1}, {t, 0, 1}]
but, I am co... |
I work on an inverse problem for my Ph.D. research, which for simplicity's sake we'll say is determining $\beta$ in
$L(\beta)u \equiv -\nabla\cdot(k_0e^\beta\nabla u) = f$
from some observations $u^o$; $k_0$ is a constant and $f$ is known. This is typically formulated as an optimization problem for extremizing
$J[u, \l... |
Neutrino Mass and Proton Lifetime in a Realistic Supersymmetric SO(10) Model Дата2015 Автор
Severson, Matthew Michael
Advisor
Mohapatra, Rabindra N
DRUM DOI MetadataПоказать полную информацию Аннотации
This work presents a complete analysis of fermion fitting and proton decay in a supersymmetric $SO(10)$ model previous... |
I'm having trouble finding the Lagrangian of:
$$L = \frac{\dot x^2}{y^2}+\frac{\dot y^2}{y^2}$$
So far, I've got the following: $$\frac{\partial L}{\partial \dot x} = \dot x \frac{2}{y^2}$$ $$\frac{\partial L}{\partial \dot y} = \dot y \frac{2}{y^2}$$ $$\frac{\partial L}{\partial x} = 0$$ $$\frac{\partial L}{\partial y... |
The Fundamental Group of the Circle, Part 2 EDIT 11/22/16: I encourage the reader to skip this post and proceed directly to Part 3. Part 2 merely contains the justification of a shortcut that we never actually use in the remainder of this series. In particular, we are certainly not proving 'well-definedness,' even thou... |
When you fit a generalized linear model (GLM) in R and call
confint on the model object, you get confidence intervals for the model coefficients. But you also get an interesting message:
Waiting for profiling to be done...
What's that all about? What exactly is being profiled? Put simply, it's telling you that it's cal... |
The Fundamental Group of the Circle, Part 3
Welcome back to our proof that the fundamental group of the circle is isomorphic to $\mathbb{Z}$. Today's post is part 3 of our outline:
Part 1: Set-up/observations
Part 2: Show $\Phi$ is well defined Part 3: Show $\Phi$ is a group homomorphism Part 4: Show $\Phi$ is surjecti... |
Academic Wednesday, October 24, 2018
Workshop | October 24 | 9 a.m.-3 p.m. | 24 University Hall
Seminar | October 24 | 12-1 p.m. | 106 Stanley Hall
Nicole Seiberlich, Case Western Reserve University
Magnetic Resonance Imaging of the heart is challenging due to cardiac and respiratory motion, and making quantitative mea... |
The Fundamental Group of the Circle, Part 4
Welcome back to our series on the fundamental group of the circle where we're following the outline below to prove that $\pi_1(S^1)\cong \mathbb{Z}$:
Part 1: Set-up/observations
Part 2: Show $\Phi$ is well defined Part 3: Show $\Phi$ is a group homomorphism Part 4: Show $\Phi... |
Difference between revisions of "Inaccessible"
(Created page with " Inaccessible cardinals are the traditional entry-point to the large cardinal hierarchy (although there are some weaker large cardinal notions, such as universe cardinals). ...")
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Inaccessible cardinals are the traditional entry-point t... |
We're very close now to building the final Navier-Stokes simulation that brought us here in the first place but before that, let's take a quick look at the Navier-Stokes equations for an incompresssible fluid, where $\vec{v}$ represents the velocity field:$$ \nabla \cdot \vec{v} = 0 $$$$ \frac{\partial \vec{v}}{\partia... |
This question already has an answer here:
A question in math mode 1 answer
I have written two equations for the report of my Master thesis:
$NLL_{k} = - \sum_{j=1}^n \ln(pdf(PD_{k}^{i},skill_{i}^{j}))$$person_{k}(interest) = \dfrac{1}{n} \sum_{p=1}^n \dfrac{person_{k}(task_{p})}{\alpha_{k}^{i}}$
In math mode everything... |
I'm really confused about the argument in Cardy's book for why there can't be long range order in 1D for discrete models. Let me just copy it out, and hopefully someone can explain it to me.
He takes an Ising-like system as an example. We start with the ground state with all spins up, and we want to see if this state i... |
Well, the title of the question pretty much says everything. To be more precise: I'd like to know (1) what font would be visually suitable to use with Linux Libertine and/or Linux Biolinum as the main text font (I haven't decided which of the two I'll use) and (2) how to enable it (as a math font) in XeTeX.
A good guid... |
The Fundamental Group of the Circle, Part 6
At last we come to the sixth and final post in our proof that the fundamental group of the circle is $\mathbb{Z}$. In the first five posts, we showed that the map $\Phi:\mathbb{Z}\to\pi_1(S^1)$ given by $n\mapsto[\omega_n]$ where $\omega_n:[0,1]\to S^1$ is the loop $s\mapsto ... |
It's called a Principal-Agent Conflict.The RIAA/MPAA act as agents on behalf of the people who actually produce content (and consequently end-consumer value).To maintain relevance to their principals', the RIAA/MPAA must signal value to them (i.e. claim loudly and repeatedly that they do something good for them [regard... |
I have following first order nonlinear ordinary differential and i was wondering if someone can suggest some method by which either i can get an exact solution or approaximate and converging perturbative solution.
$$\begin{align*} \dfrac{dx}{dt} &= 2(1-W^{-1}) x + \dfrac{2xy}{W} - 8x^{2}\\ \dfrac{dy}{dt} &= \gamma W (x... |
Difference between revisions of "Reflecting"
(→Reflection and correctness: I1)
(typo)
Line 25: Line 25:
Although it may be surprising, the existence of a correct cardinal is equiconsistent with ZFC. This can be seen by a simple compactness argument, using the fact that the theory ZFC+"$\kappa$ is correct" is finitely c... |
This will be the first of a series of short posts relating to subject matter discussed in the text, “An Introduction to Statistical Learning”. This is an interesting read, but it often skips over statement proofs — that’s where this series of posts comes in! Here, I consider the content of Section 5.1.2: This gives a l... |
Measuring Cloud Oktas From Outer Space
This article describes the approach undertaken by data scientists at Axibase to calculate cloud cover using satellite imagery from the Japanese Himawari 8 satellite.
Today, cloud cover is measured using automated weather stations, specifically ceilometers and sky imager instrument... |
Hallo,
I have a question on a paper of Azad and Kobayashi "Ricci-flat Kähler metrics on symmetric varieties". Here is the link: http://www.academia.edu/2579043/Ricci-flat_Kahler_metrics_on_symmetric_varieties
On the first, there is mentioned the main result: "Theorem (1.1): Let $G^{\mathbb{C}} / K^{\mathbb{C}}$ be a sy... |
Let $w=a_1a_2a_3...$ be an infinite word over a finite alphabet and $\epsilon>0$. Do there exist integers $n,k$ such that $\frac{d(a_1a_2...a_n,a_{k+1}a_{k+2}...a_{k+n})}{n}<\epsilon$ ? ($d(u,v)$ is the hamming distence)
OK, let's go over it slowly.
The alphabet will consist of 4 symbols: $x,u,b,c$.
The infinite word w... |
During logistic regression, in order to compute the optimal parameters in the model, we have to use an iterative numerical optimization approach (Newton method or Gradient descent method, instead of a simple analytical approach). Numerical optimization is a crucial mathematical concept in machine learning and function ... |
Let $(M,g)$ be a Riemannian manifold with Levi Civita connection $\nabla$. Then $\nabla$ satisfies a compatibility condition:
$(\nabla_ZX,Y)+(X,\nabla_ZY)=Z((X,Y))$ where $(\cdot,-)$ is a Hermitian pairing. In general, if we have a connection $\nabla$ on bundle $E$ (in our case $E=TM$) one can define the dual connectio... |
Fatou's Lemma The Basic Idea
Given a sequence of functions $\{f_n\}$ which converge pointwise to some limit function $f$, it is
not always true that $$\int \lim_{n\to\infty}f_n = \lim_{n\to\infty}\int f_n.$$ (Take this sequence for example.) Fatou's Lemma, the Monotone Convergence Theorem (MCT), and the Dominated Conve... |
The possibility of recursive self-improvement is often brought up as a reason to expect that an intelligence explosion is likely to result in a singleton - a single dominant agent controlling everything. Once a sufficiently general artificial intelligence can make improvements to itself, it begins to acquire a compound... |
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Note by Jessica Wang 3 years, 11 months ago
Easy Math Editor
This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thin... |
So, we know, that the atomic carbon in the electronic configuration $1s^22s^22p^2$ has the following terms
$${}^1S, {}^1D, {}^3P$$
My question is - how can I correctly specify these terms in the terms of coupled and uncoupled representations? My attempt
So, in the case of terms, we're only considering the orbital angul... |
The
IEEEtran class actually makes provisions for such constructions via the
IEEEeqnarraybox family of commands. The environment
IEEEeqnarrayboxm typesets its material in math mode. The syntax is
\begin{IEEEeqnarrayboxm}[initialcommands][pos][width]{format}
....
\end{IEEEeqnarrayboxm}
Making
[pos] equal to
[t] means tha... |
I am new to Latex and was trying to insert the below equation.
But I am not getting it right
below is my code
\begin{equation} S (ω)=1.466\, H_s^2 \, \frac{ω_0^5}{ω^6 } \, e^[-3^ { ω/(ω_0 )]^2}\end{equation}
TeX - LaTeX Stack Exchange is a question and answer site for users of TeX, LaTeX, ConTeXt, and related typesetti... |
Assume we have communication system between transmit and receive over wireless channel.
The Friis path loss model is given by the following equation
$$P_r = P_t G_t G_r (\frac{\lambda}{4\pi D})^2$$
Where $P_{r(t)}$ is the received (transmit) power, $G_{t(r)}$ is the gain of the antennas at transmitter (receive) and $\l... |
Notes - Linear Equation in one variable
Category : 7th Class
LINEAR EQUATION IN ONE VARIABLE
FUNDAMENTALS
Symbols used to denote a constant are generally, 'c', 'k' etc...
e.g., 2x - 6; here, 2 is the coefficient of \['x';\,\,'x'\] is the variable and \[-6\]is the constant. Similarly in \[ay+b;\,\,a\] is the coefficient... |
What is a Natural Transformation? Definition and Examples
I hope you have enjoyed our little series on basic category theory. (I know I have!) This week we'll close out by chatting about natural transformations which are, in short, a nice way of moving from one functor to another. If you're new to this mini-series, be ... |
Learning Outcomes Conduct and interpret hypothesis tests for two population proportions
When conducting a hypothesis test that compares two independent population proportions, the following characteristics should be present:
The two independent samples are simple random samples that are independent. The number of succe... |
Fit the Neyman-Scott cluster process with Cauchy kernel
Fits the Neyman-Scott Cluster point process with Cauchy kernel to a point pattern dataset by the Method of Minimum Contrast, using the pair correlation function.
Usage
cauchy.estpcf(X, startpar=c(kappa=1,scale=1), lambda=NULL, q = 1/4, p = 2, rmin = NULL, rmax = N... |
Here, we review parameter regularization, which is a method for improving regression models through the penalization of non-zero parameter estimates. Why is this effective? Biasing parameters towards zero will (of course!) unfavorably bias a model, but it will also reduce its variance. At times the latter effect can wi... |
I understand that the ATM volatility of Swaption moves quite frequently and the SABR will need to be recalibrated. Which parameter should I recalibrate?
Is there any financial meanings why we only recalibrate on certain parameters?
Thanks.
Quantitative Finance Stack Exchange is a question and answer site for finance pr... |
The Most Obvious Secret in Mathematics
Yes, I agree. The title for this post is a little pretentious.
other mathematical secrets that are more obvious than this one, but hey, I got your attention, right? Good. Because I'd like to tell you about an overarching theme in mathematics - a mathematical mantra, if you will. A... |
Ancillary-file links:
Ancillary files (details): python3_src/KW_scaldims.py python3_src/LICENSE python3_src/README python3_src/TNR.py python3_src/cdf_ed_scaldimer.py python3_src/cdf_scaldimer.py python3_src/custom_parser.py python3_src/ed_scaldimer.py python3_src/initialtensors.py python3_src/modeldata.py python3_src/p... |
Considering a number expressed by four decimal digits $n=ABCD_d$ let $\sigma(n) = A+B+C+D$ the sums of its decimal digits.
Doubling the number is equivalent to summing it to itself: $2n = ABCD_d + ABCD_d$ so the result will be composed summing each digit and, if the result is more than 10, the second digit is the carry... |
I have two matrices $A, B$ coming from a finite element discretization of a system of partial differential equations. $A$ represents the system matrix and is symmetric and indefinite. $B$ is symmetric positive definite and is used as a preconditioner. Direct solver is used for computation of action of $B^{-1}$. The pre... |
Global bifurcation for discrete competitive systems in the plane
1.
University of Rhode Island, Kingston, RI 02881, United States, United States
$x_{n+1} = f_\alpha(x_n,y_n) $
$y_{n+1} = g_\alpha(x_n,y_n)$
where $\alpha$ is a parameter,
$f_\alpha$ and $g_\alpha$ are continuous real valued functions
on a rectangular dom... |
But if you don't want to have a Google account: Chrome is really good. Much faster than FF (I can't run FF on either of the laptops here) and more reliable (it restores your previous session if it crashes with 100% certainty).
And Chrome has a Personal Blocklist extension which does what you want.
: )
Of course you alr... |
This is the last exercise of a quite challenging exercises paper a friend who is taking calculus has which I'm trying to help. I already helped her doing the other bunch. But this got me. I will appreciate anyone help to see my work and to tell me if is right or If I need to correct something.
The exercise is:
If $f'(a... |
If we pretend our data is like a big pool of numbered balls, we draw one ball from the pool and copy the number to another ball that we set aside. Now, toss the ball back, mix, pick another ball and repeat. In this scheme you have a chance of drawing the same ball twice (or more). This probability is $ \frac{1}{N}^D $,... |
For a while now I have tried to come up with a macro, that can properly format inegrals (the way I like).Aswell as giving it a few options that can be chosen e.g.
\int and
\oint.So far there is a little problem arising in the code. It occurs when you choose the
\oint by adding a
* to the argument.It does come with rigt... |
I'm just trying to build the formula shown below in Latex. My approach would be the following:
prob[ \tilde{n}=n \mid \tilde{s}=s]However, the first two
n's are not displayed correctly. Does anyone know what is wrong about my approach? (absolute Latex beginner)
I'm just trying to build the formula shown below in Latex.... |
During my 4-week visit as an OpenMM Visiting Scholar, I implemented a constant pH algorithm for implicit solvent. A brief overview of the algorithm is given in this video:
Below, I describe the algorithm in much greater detail and also highlight key features of OpenMM that enabled me to quickly implement the algorithm.... |
@HarryGindi So the $n$-simplices of $N(D^{op})$ are $Hom_{sCat}(\mathfrak{C}[n],D^{op})$. Are you using the fact that the whole simplicial set is the mapping simplicial object between cosimplicial simplicial categories, and taking the constant cosimplicial simplicial category in the right coordinate?
I guess I'm just v... |
Welcome back to our mini-series on quantum probability! Last time, we motivated the series by pondering over a thought from classical probability theory, namely that marginal probability doesn't have memory. That is, the process of summing over of a variable in a joint probability distribution causes information about ... |
I am trying to prove $$X_n \xrightarrow{d} X, Y_n \xrightarrow{d} a \implies Y_n X_n \xrightarrow{d} aX$$where $a$ is a constant.
What I tried: Let $g:\mathbb R\to \mathbb R$ an arbitrary uniformly continuous, bounded function. It suffices to show $\mathbb E[g(Y_n X_n)] \to \mathbb E[g(aX)]$. We have $$\left \lvert \in... |
A common task in applied statistics is the pairwise comparison of the responses of $N$ treatment groups in some statistical test — the goal being to decide which pairs exhibit differences that are statistically significant. Now, because there is one comparison being made for each pairing, a naive application of the Bon... |
There's a mistake in your proof, you do not have$F=\bigcup_{k=1}^mR_k$.The idea is however correct.
To see where it fails, try drawing it in 2 dimensions.F is then a rectangle, you've sliced each side into $m$ equal portions, in other word you made an $m$ by $m$ grid of smaller rectangles out of F. You then defined you... |
Automorphisms of the Complex Plane
Welcome back to our little series on automorphisms of four (though, for all practical purposes, it's really
three) different Riemann surfaces: the unit disc, the upper half plane, the complex plane, and the Riemann sphere. Last time, we proved that the automorphisms of the upper half ... |
As per the title, I was wondering if there was a $\operatorname{sinc}$ based interoplation formula for reconstructing a signal in the frequency domain which has been sampled with respect the bipolar coordinate system?
For instance, we all know the $\operatorname{sinc}$ based Whitakker-Shannon interpolation formula for ... |
As far as intuition goes, maybe this will help. For any two vectors $\bf a$ and $\bf b$, the dot product $\bf a \cdot \hat b$ is the component of $\bf a$ in the direction of $\bf b$. If you "remove" that component from $\bf a$ you would be left with the part of it which is perpendicular to $\bf b$:
$$\begin{align}{\bf ... |
Basically, you are right: the reason we do that is that we only care about the real part of the solution (for basic physics problems), and that gives it to us.
Now, you might ask why you can do this. One really important fact about the wave equation is that it is "linear". This means that you can add two solutions to e... |
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Now showing items 1-9 of 9
Production of $K*(892)^0$ and $\phi$(1020) in pp collisions at $\sqrt{s}$ =7 TeV
(Springer, 2012-10)
The production of K*(892)$^0$ and $\phi$(1020) in pp collisions at $\sqrt{s}$=7 TeV was measured by the ALICE experiment at the LHC. The yields and the transverse momentum spectra $d^2 ... |
Proof by contradiction.
Let us assume that $\{v_1, \dots, v_n\}$ are linearly independent, $\{v_1+w, \dots, v_n+w\}$ are linearly dependent and that $w \not\in \mathrm{span}\{v_1, \dots, v_n\}$. Because $\{v_1 + w, \dots, v_n + w\}$ are linearly dependent, we know that there are non-zero constants $\beta_1, \dots, \bet... |
In what circumstances should one consider using regularization methods (ridge, lasso or least angles regression) instead of OLS?
In case this helps steer the discussion, my main interest is improving predictive accuracy.
Cross Validated is a question and answer site for people interested in statistics, machine learning... |
In order to study the behavior of an RC circuit, I connected a resistor and a capacitor to an Arduino's I/O as shown:
The Arduino digital Output feeds the circuit with a square pulse of 2 sec duration.
(one second HIGH, one second LOW)
for a charge time of 1 sec: $$V_c = E(1-e^{-\dfrac{t}{\tau}}) = E(1-e^{-\dfrac{1}{0.... |
The Hermite polynomial is the one that interpolates a set of points and the value of their derivatives in any points we want. That is, let's suppose that we have $$(x_k,f_k)$$ and $$(x_k,f'_k)$$.
Then we construct the same table as in Newton's method, placing $$x_k$$ in the first column and writing twice the same point... |
L^2 and intersection cohomologies for the reductive representation of the fundamental groups of quasiprojective manifolds with unipotent local monodromy
Xuanming Ye, Kang Zuo
Let X be a projective manifold, and D be a normal crossing divisor of X. By Jost-Zuo's theorem that if we have a reductive representation \rho of... |
Gauss Law
The Gauss law is a very convenient tool to find the electric field of a system of charges. It is especially useful when situations of symmetry can be easily exploited. The electric flux (\(d\phi \)) through a differential area is the dot product of the electric field and the area vector (this vector is normal... |
@JosephWright Well, we still need table notes etc. But just being able to selectably switch off parts of the parsing one does not need... For example, if a user specifies format 2.4, does the parser even need to look for e syntax, or ()'s?
@daleif What I am doing to speed things up is to store the data in a dedicated f... |
There are many categories of windows, e.g., rectangular, Gaussian, and triangular. What are their effects on STFT?
A widnow $w[n]$ truncates and weights the input signal $x[n]$ to prepare it for subsequent spectral analysis. A windows's effect on the input signal's true spectrum $X(e^{j\omega})$ is mathematically descr... |
Is there a simple description of a Chow ring of a blow-up of a point on a smooth projective variety? Or at least of successive blow-ups of $\mathbb{P}^n$?
Maybe something like $A(\tilde{X})=f^*(A(X))\oplus\mathbb{Z}(E)$, where $f\colon\tilde{X}\to{}X$ is a blow-up, E is an exceptional divisor, with multiplication given... |
Exercise:Suppose that $a_k \geq 0$ for $k$ large and that $\sum_{k = 1}^{\infty} \frac{a_k}{k}$ converges.
Prove that $$\lim_{j \to \infty}\sum_{k = 1}^{\infty} \frac{a_k}{j+k} = 0$$
Attempt in proof:
Suppose $a_k \geq 0$ for any large $k$ and that $\sum_{k = 1}^{\infty} \frac{a_k}{k}$ converges. . Then give $\epsilon ... |
I know the following generalization of Borwein - Preiss's Variational Principle(BPVP), known as Loewen-Wang's Variational principle (LWVP)
$\textbf{Loewen- Wang Variational Principle}$
Let $f:X\to \mathbb{\bar{R}}$ be proper, l.s.c and bounded below. Let $\epsilon >0$ and consider a point $\bar{x}$ such that ${f(\bar{x... |
How to solve this logarithmic equation? $8n^2 = 64n\log n$, ($\log n$ here is base 2) I have tried to convert it to $n-8\log n = 0$, but how to solve the latest?
This doesn't have any solutions using elementary functions. But, using the Lambert W function, we get: $$n = -\frac {8}{\ln 2} \operatorname{W} \left (-\frac ... |
This question already has an answer here:
What are common lower bounds for ${{2n} \choose {n}}$?
Edit: I made a mistake in my original question.
It doesn't change my question but there is no reason for me to include the mistake.
Mathematics Stack Exchange is a question and answer site for people studying math at any le... |
Defining parameters
Level: \( N \) = \( 12 = 2^{2} \cdot 3 \) Weight: \( k \) = \( 2 \) Character orbit: \([\chi]\) = 12.a (trivial) Character field: \(\Q\) Newforms: \( 0 \) Sturm bound: \(4\) Trace bound: \(0\) Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(12))\).
Total ... |
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