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I'm not sure where I could pose a challenge to find best $f(n)$ so people will join in. $n\ge 5$ will never probably be proven optimal, but some lucky computations or out of the box analysis might give nice results.
(Given $n$ fixed digits and operations $(+,-,\times,\div)$, whats the highest $N\in\mathbb N$, such that... |
This question already has an answer here:
If $X= \newcommand{\W}{\operatorname{W}}\sqrt{A}^{\sqrt{A}^{\sqrt{A}^{\sqrt{A}^{\sqrt{A}^{\sqrt{A}^{\sqrt{A}^{\sqrt{A}^{.{^{.^{\dots}}}}}}}}}}} $ then what is the value of $X^2-e^{1/X}$ ?
Mathematics Stack Exchange is a question and answer site for people studying math at any l... |
The First Isomorphism Theorem, Intuitively
Welcome back to our little discussion on quotient groups! (If you're just now tuning in, be sure to check out "What's a Quotient Group, Really?" Part 1 and Part 2!) We're wrapping up this mini series by looking at a few examples. I'd like to take my time emphasizing intuition,... |
The Sierpinski Space and Its Special Property The Basic Idea
Last time we chatted about a pervasive theme in mathematics, namely that
objects are determined by their relationships with other objects, or more informally, you can learn a lot about an object by studying its interactions with other things. Today I'd to giv... |
Show/Hide Sub-topics (O Level) Volume (V) is defined as the amount of space occupied by a three-dimensional object as measured in cubic units. SI unit of volume is metres cube ($m^{3}$). It is a scalar quantity. Density ($\rho$) is defined as the mass (m) of a substance per unit volume. SI unit of density is kilograms ... |
Osaka Journal of Mathematics Osaka J. Math. Volume 42, Number 3 (2005), 633-651. Asymptotic behavior of least energy solutions to a four-dimensional biharmonic semilinear problem Abstract
In this paper, we study the following fourth order elliptic problem $(E_p)$: \begin{eqnarray*} (E_p) \left \{ \begin{array}{l} \Delt... |
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... |
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Please help me solve the following Integral :
I=∫cos(2x)cosxdx \large I = \int\dfrac{\sqrt{cos(2x)}}{cosx} dx I=∫cosxcos(2x)dx
NoteNoteNote : Anyone and everyone please post your solution , this question appeared in my class test.
Note by Rishu Jaar 1 year, 11 mo... |
@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... |
Find the centre of mass of an uniform cone of height $h$ and radius $R$. Let the density of the cone be $\rho$.
It is obvious from the diagram that the x and y components of the centre of mass of a cone is 0:
$$\begin{aligned} x_{CM} &= 0 \\ y_{CM} &= 0 \end{aligned}$$
Hence, we just need to find $z_{CM}$. We will need... |
Difference between revisions of "Ineffable"
m (→Ethereal cardinal: w)
m (as a weakening of subtle cardinals)
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Ineffable cardinals were introduced by Jensen and Kunen in <cite>... |
Conveners QCD & Heavy Ions Radja Boughezal (Argonne National Laboratory) Daniel Tapia Takaki (University of Kansas) Salvatore Rappoccio (The State University of New York SUNY (US)) Olga Evdokimov (University of Illinois at Chicago (US)) QCD & Heavy Ions Olga Evdokimov (University of Illinois at Chicago (US)) Salvatore ... |
In the last lesson, we saw that the derivative was the rate of change.
We saw multiple ways of calculating this rate of change.
Finally, we said that when we have a function $f(x)$, we can calculate the derivative with knowing the starting point and the change in our input, $x$:
$$ \frac{f(x_1 + \Delta x) - f(x_1)}{\De... |
Use Residue theorem to compute contour integral $$\int_C \frac{4e^z}{\sin z} dz$$
I need help figuring out singularities that are within the circle $|z|= 4$. I am stuck at that part. Thanks in advance.
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in re... |
Show that the following subests of $(\mathbb{R},\tau_e)$ are homeomorphic.
$(0,1)$ , $(0,+\infty)$, $(-\infty,+\infty)$.
(i) If I take $\varphi:(\mathbb{R},\tau_e) \rightarrow (0,+\infty)$, $x \mapsto e^x$ this map is continuous, bijective, and the inverse is continuous and so is a homeomorphism.
(ii) $\varphi:(0,1) \r... |
I am trying to prove the need of a convexity adjustment to a forward rate by calculating the next expectation:
\begin{align*} P(t_0, T_s)E^{T_s}\big(L(T_s, T_s, T_e) \mid \mathcal{F}_{t_0}\big). \end{align*}
Where $E^{T_s}$ denotes the expectation under a T-measure with $P(t,T_s)$ as numéraire and $t_0< T_s < T_e $ and... |
Consider a non-negative continuous process $X = \left (X_t \right)_ {t\geq 0}$ satisfying $ \mathbb E \left \{ \bar X \right\}< \infty $ (where $ \bar X =\sup _{0\leq t \leq T} X_t $) and its Snell envelope
$$ \hat {X_\theta} = \underset {\tau \in \mathcal T _{\theta,T} } {\text{ess sup}} \ \mathbb E \left\{ X_\tau | \... |
Solve in integers: $x^3+x^2-16=2^y$.
my attempt:
of course $y\ge 0$, then $2^y\ge 1$, so $x\ge 1$.
for $y=0,1,2,3$ there is no good $x$.
so $y\ge 4$ and we have equation $x^2(x+1)=16(2^z+1)$, where $z=y-4\ge 0$.
what now?
Mathematics Stack Exchange is a question and answer site for people studying math at any level and... |
I am having trouble with figuring out what my initial conditions should be for a simple finite difference algorithm I wrote in Matlab.
Specifically, I'm trying to show that the regular 1-Dimensional wave eqt $$\frac{\partial u^2}{\partial t^2} = c^2\frac{\partial u^2}{\partial x^2}$$ Looks like diffusion with some drif... |
I try to show that $A_n \times \mathbb{Z} /2 \mathbb{Z} \ \ncong \ S_n$ for $n \geq 3$.
It is not hard to show the statement for $n=3$.
We have $$ A_3 \times \mathbb{Z} /2 \mathbb{Z} \ \cong \ \mathbb{Z} /3 \mathbb{Z} \times \mathbb{Z} /2 \mathbb{Z} \ \cong \ \mathbb{Z} /6 \mathbb{Z} $$ an abalian group, while $(123)(1... |
I understand that if the Hamiltonian does not depend on the time, the Schrödinger Equation becomes separable, so you get
$$ H \psi(x) = E \psi(x) $$
and
$$ \Psi(x,t) = \psi(x)\exp\left(-\frac{\imath E}{\hbar}t\right). $$
But $-\frac{\imath E}{\hbar}t$ is a purely imaginary number, so $$ \left|\exp\left(-\frac{\imath E}... |
The expectation clearly is proportional to the product of the squared scale factors $\sigma_{11}\sigma_{22}$. The constant of proportionality is obtained by standardizing the variables, which reduces $\Sigma$ to the correlation matrix with correlation $\rho = \sigma_{12}/\sqrt{\sigma_{11}\sigma_{22}}$.
Assuming bivaria... |
Please use this identifier to cite or link to this item:
http://buratest.brunel.ac.uk/handle/2438/570
Title: On the Gierer-Meinhardt System with Saturation Authors: Winter, M
Wei, J
Keywords: Saturation, Nonlocal Eigenvalue Problem,;Stability Issue Date: 2004 Publisher: World Scientific Citation: Comm Contemp Math 6 (2... |
Learning Objective
Convert from one unit to another unit of the same type.
In Section 2.2, we showed some examples of how to replace initial units with other units of the same type to get a numerical value that is easier to comprehend. In this section, we will formalize the process.
Consider a simple example: how many ... |
The (spherical)
, or the rhumb line, is the curve of constant bearing on the sphere; that is, it is loxodrome the spherical curve that cuts the meridians of the sphere at a constant angle. A more picturesque way of putting it is that if one wants to travel from one point of a (spherical) globe to the antipodal point (s... |
Answer
.36 centimeters
Work Step by Step
We know that the height difference will be equal to 2 cm times $1-\frac{\rho_{oil}}{\rho_{water}}$. Thus, it follows: $h = 2 \times (1 - .82) = .36 \ cm$
You can help us out by revising, improving and updating this answer.Update this answer
After you claim an answer you’ll have
... |
The cone frustum is the figure resulting from having made a cut parallel to the basis of a cone.
To calculate the area of the mentioned figure we have to add up the areas of two bases and the area of the lateral face: $$$A_{total}=A_{basis}+A_{minor \ basis}+A_{lateral} \\ A_{lateral}=\pi (R+r)\cdot g$$$
In many exerci... |
Let's call the base of the first triangle $x$, the base of the second $\frac{8}{7}x$. The other side of the first and of the second will be $y$ and $z$. We'll have:
$$ \left\{\begin{matrix}x+2y=\frac{8}{7}x+2z\\ x\sqrt{y^2-\frac{x^2}{4}}=\frac{8}{7}x\sqrt{z^2-\frac{16x^2}{49}}\end{matrix}\right.\Rightarrow \left\{\begi... |
Given that $\sin\theta = \dfrac{1}{2}$ and that $\cos\theta = -\dfrac{\sqrt{3}}{2}$ and $0^\circ \leq \theta \leq 360^\circ$, find the value of $\theta$.
Since $\sin\theta > 0$ and $\cos\theta < 0$, you have correctly concluded that $\theta$ is a second-quadrant angle. You also took the inverse cosine of $-\dfrac{\sqrt... |
Is there either a closed-form expression or fast/elegant algorithm for computing the positive root of the polynomial $$f(x)=x^q + \beta x - \beta,$$ where $\beta>0$ and $q\geq2$? How about the $q\in\mathbb R$ case with $q\geq1$?
Note there is exactly one positive root of the function $f(x)$, since $f(0)=-\beta<0$, $\li... |
I am having the following equation:
\begin{equation} Q(\lambda,\hat{\lambda}) = -\frac{1}{2} P(O \mid \lambda ) \sum_s \sum_m \sum_t \gamma_m^{(s)} (t) \left( n \log(2 \pi ) + \log \left| C_m^{(s)} \right| + \left( \mathbf{o}_t - \hat{\mu}_m^{(s)} \right) ^T C_m^{(s)-1} \left(\mathbf{o}_t - \hat{\mu}_m^{(s)}\right) \ri... |
Here, we characterize the data compression benefits of projection onto a subset of the eigenvectors of our traffic system’s covariance matrix. We address this compression from two different perspectives: First, we consider the partial traces of the covariance matrix, and second we present visual comparisons of the actu... |
Using the relation $\phi - 1 = 1/\phi$, we find that
\begin{align*}&\int_{0}^{1} \frac{(1-x)(1-2x^{\phi})+\phi(x-x^{\phi})}{(1-x)^2}\cdot\left(\frac{1-x^{\phi}}{1-x}\right)^{1/\phi} \, \mathrm{d}x \\&= \int_{0}^{1} \left( 2 - \frac{\phi^2}{1-x^{\phi}} + \frac{\phi}{1-x} \right) \left(\frac{1-x^{\phi}}{1-x}\right)^{\phi... |
Difference between revisions of "Vopenka"
(→Generic: unless...)
(→Generic: stricter terminology, but is the rest of the information correct in the stricter language?)
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Definitions:
Definitions:
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* The '''
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* The '''''' states that for every proper class $\mathcal{C}$ of structures of the same type ... |
Physics can be a scary ordeal for some and a very interesting subject for the rest. There are many scholars who want a program or some tips about important topics that supports and helps them in studying physics. With a proper preparation strategy, idea about the important questions, derivations and formulas in physics... |
I recently came across this in a textbook (NCERT class 12 , chapter: wave optics , pg:367 , example 10.4(d)) of mine while studying the Young's double slit experiment. It says a condition for the formation of interference pattern is$$\frac{s}{S} < \frac{\lambda}{d}$$Where $s$ is the size of ...
The accepted answer is c... |
Circularity of Finite Groups without Fixed Points 46 Downloads Citations Abstract.
Let Φ be a fixed point free group given by the presentation \(\langle A, B\,\vert\, A^\mu=1,\, B^\nu=A^t,\, BAB^{-1}=A^\rho\rangle\) where μ and ρ are relative prime numbers,
t = μ/ s and s = gcd(ρ − 1,μ), and ν is the order of ρ modulo ... |
I am trying to do Exercise 5.33 on page 64 of Fulton's book on algebraic curves.
5.33 Let $C$ be an irreducible cubic, $L$ a line such that $L\bullet C = P_1+ P_2 + P_3,$ $P_i$ distinct. Let $L_i$ be the tangent line to $C$ at $P_i:$ $L_i \bullet C = 2P_i + Q_i$ for some $Q_i.$ Show that $Q_1, Q_2, Q_3$ lie on a line. ... |
In randomized-controlled trials, interim analyses are often planned for possible early termination of the trial for claiming superiority or futility of a new therapy. Such formal interim analyses are performed, closely following the specifications in the study protocol to maintain the overall type I error rate at a nom... |
I'm studying from Reitz's
Foundations of Electromagnetic Theory and trying to understand how the results obtained under electrostatic conditions are affected when there is a current flowing through material.
I understand that it isn't true anymore that the electric field inside a conductor is zero if there is a current... |
I was helping my kid study for a precalculus examination and looking at her old tests from the year, and came across a question about vectors. Below is the typed up version of the question and her answer; an image from the actual test can be found at the end.
6.A vector with tail at the origin has a magnitude of $5$ an... |
I'm having trouble understanding the proof given in Morgan's
The Seiberg-Witten Equations that every 4-manifold $X$ admits a $Spin^c$ structure (Lemma 3.1.2). One can easily see from the exact sequence:\begin{equation*}H^1(X;Spin^c) \to H^1(X; SO(n)) \oplus H^1(X;\mathbb{Z}) \xrightarrow{c_1+w_2} H^2(X;\mathbb{Z}_2)\en... |
According to the kinetic theory of gas,
– Gases are composed of very small molecules and their number of molecules is very large.
– These molecules are elastic. – They are negligible size compare to their container. – Their thermal motions are random.
To begin, let’s visualize a rectangular box with length L, areas of ... |
A Gentle Introduction to AI A Gentle Introduction to AI Get a simple introduction to Artificial Intelligence is and why it should be important to you, with a specific focus on Machine Learning.
Join the DZone community and get the full member experience.Join For Free
Looking at the latest Google and Apple conventions, ... |
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<translate>
<translate>
−
=Siril processing tutorial=
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=Siril processing tutorial=
+
* [[Siril:Tutorial_import|Convert your images in the FITS format Siril uses (image import)]]
* [[Siril:Tutorial_import|Convert your images in... |
Search
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... |
I would like to solve the following exercise but there is something I am not clear about:
Let $A$ be the Banach algebra of $C^1([0,1])$ endowed with the norm $\|f\|=\|f\|_\infty + \|f'\|_\infty$. Show that the Gelfand representation is not surjective.
I believe the Gelfand representation is the map $f \mapsto \widehat{... |
On Constructing Functions, Part 1
Given a sequence of real-valued functions $\{f_n\}$, the phrase, "$f_n$ converges to a function $f$" can mean a few things:
$f_n$ converges uniformly $f_n$ converges pointwise $f_n$ converges almost everywhere (a.e.) $f_n$ converges in $L^1$ (set of Lebesgue integrable functions) and s... |
De Bruijn-Newman constant
For each real number [math]t[/math], define the entire function [math]H_t: {\mathbf C} \to {\mathbf C}[/math] by the formula
[math]\displaystyle H_t(z) := \int_0^\infty e^{tu^2} \Phi(u) \cos(zu)\ du[/math]
where [math]\Phi[/math] is the super-exponentially decaying function
[math]\displaystyle... |
On Constructing Functions, Part 2
This post is the second example in an ongoing list of various sequences of functions which converge to different things in different ways.
Also in this series:
Example 1: converges almost everywhere but not in $L^1$
Example 3: converges in $L^1$ but not uniformly Example 4: $f_n$ are i... |
Next, we tackle the one-dimensional diffusion equation:$$ \frac{\partial u}{\partial t} = \nu \frac{\partial^2 u}{\partial x^2} $$
First obvious difference is that — unlike our previous two simple equations — this equation has a second-order derivative. Before continuing we must learn how to discretize it.
Any second o... |
Suppose we have largangian of QCD axion below PQ scale:
$$
L_{a} = \frac{1}{2}\partial_{\mu}a\partial^{\mu}a - C_{G}\frac{a}{f_{a}}G \wedge G + C_{\gamma}\frac{a}{f_{a}}F_{EM}\wedge F_{EM} + L_{SM}, $$
where $G$ denotes gluon field strength, $\wedge$ denotes contraction with Levi-Civita tensor, $L_{SM}$ is SM lagrangia... |
De Bruijn-Newman constant
For each real number [math]t[/math], define the entire function [math]H_t: {\mathbf C} \to {\mathbf C}[/math] by the formula
[math]\displaystyle H_t(z) := \int_0^\infty e^{tu^2} \Phi(u) \cos(zu)\ du[/math]
where [math]\Phi[/math] is the super-exponentially decaying function
[math]\displaystyle... |
On Constructing Functions, Part 4
This post is the fourth example in an ongoing list of various sequences of functions which converge to different things in different ways.
Also in this series:
Example 1: converges almost everywhere but not in $L^1$
Example 2: converges uniformly but not in $L^1$ Example 3: converges i... |
2019-07-18 17:03
Precision measurement of the $\Lambda_c^+$, $\Xi_c^+$ and $\Xi_c^0$ baryon lifetimes / LHCb Collaboration We report measurements of the lifetimes of the $\Lambda_c^+$, $\Xi_c^+$ and $\Xi_c^0$ charm baryons using proton-proton collision data at center-of-mass energies of 7 and 8 TeV, corresponding to an... |
Defining parameters
Level: \( N \) = \( 6 = 2 \cdot 3 \) Weight: \( k \) = \( 2 \) Character orbit: \([\chi]\) = 6.a (trivial) Character field: \(\Q\) Newforms: \( 0 \) Sturm bound: \(2\) Trace bound: \(0\) Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6))\).
Total New Old... |
If $X$ is a complex space, not necessarily a manifold nor even reduced,
any cover $\mathcal U=(U_i)_{i\in I}$ by open subsets $U$ which are Stein is acyclic for any coherent sheaf. Indeed any finite intersection $U=U_1\cap\dots\cap U_n $ of sets $U\in \mathcal U$ is Stein : this is trivial if you define "Stein" as holo... |
A vector field defines a situation where the magnitude and direction of vectors are a function of location only. We can best understand this on a rotating rigid body where the linear velocity of each particle $\boldsymbol{v}$ depends on its location $\boldsymbol{r}$.
$$ \boldsymbol{v} = \boldsymbol{\omega} \times \bold... |
On Constructing Functions, Part 5
This post is the fifth example in an ongoing list of various sequences of functions which converge to different things in different ways.
Example 1: converges almost everywhere but not in $L^1$
Example 2: converges uniformly but not in $L^1$ Example 3: converges in $L^1$ but not unifor... |
At the one side, you can always calculate the percentages of the acid or it's ions in solution:$$\ce{\alpha(H_{n-m}A^{m-})} = \frac{x^{n-m} \prod_{j=1}^{m}k_{a,j}}{\sum_{i=0}^{n}x^{n-i} \prod_{j=1}^i k_{a,j}}$$with $x = [\ce{H+}]$, $n>0$ as the number of protons and $0 \le m \le n$ as the number of dissociated protons.... |
I met this question says how to price a vanilla call option $C(St,t,T,K) = \frac{1}{S_T}$which pays the inverse of a stock $V_{t} = \frac{1}{S_{t}}$ at maturity if the stock price follows a geometric Brownian motion $dS_{t}=\mu S_{t}dt+\sigma S_{t}dB_{s}$? I tried to use the risk-neutral measure approach, however, I ca... |
A photon is a tiny particle that comprises waves of electromagnetic radiation. As shown by Maxwell, photons are just electric fields traveling through space. Photons have no charge, no resting mass, and travel at the speed of light. Photons are emitted by the action of charged particles, although they can be emitted by... |
MathRevolution wrote:
[Math Revolution
GMAT math practice question]
If the \(2\) roots of the equation \(x^2+px+q=0\) are \(-3\) and \(2\), where \(p\) and \(q\) are constants, what is the value of \(p + q?\)
\(A. -5\)
\(B. -3\)
\(C. -1\)
\(D. 0\)
\(E. 1\)
\(? = p + q\)
\(\left\{ \matrix{
\, - 1 = - 3 + 2 = {\rm{sum}}\... |
Search
Now showing items 1-1 of 1
Anisotropic flow of inclusive and identified particles in Pb–Pb collisions at $\sqrt{{s}_{NN}}=$ 5.02 TeV with ALICE
(Elsevier, 2017-11)
Anisotropic flow measurements constrain the shear $(\eta/s)$ and bulk ($\zeta/s$) viscosity of the quark-gluon plasma created in heavy-ion collisions... |
I wanted to better understand dfa. I wanted to build upon a previous question:Creating a DFA that only accepts number of a's that are multiples of 3But I wanted to go a bit further. Is there any way we can have a DFA that accepts number of a's that are multiples of 3 but does NOT have the sub...
Let $X$ be a measurable... |
Motivated by the public's desire to learn as much as possible following the occurrence of damaging events, we have developed a methodology to spatially map the probability of earthquake occurrence in the next 24 hours. We start with the simple aftershock model of Reasenberg and Jones (1989, 1990, 1994):
\[\ {\lambda}(t... |
I'm currentely discussing pigeon hole principle (simple and generalised) in class. However, when solving problems, I get the idea, but I never know the proper way to write it, I always feel like I'm either writing too much or not enough. Here is an example of a very simple problem and 2 ways I wrote the proof and if yo... |
I took a shot in the dark and assumed that this is similar to solving $\int e^{x}\sin{x}\ dx$, but wolfram is giving me a different answer than what I got, and on top of that, I tried to differentiate my result and am not getting back what I started with. It's putting into question whether I was doing previous question... |
I'm currently analysing some spatial point patterns that come from some fluid dynamics simulations and I'm having some difficulty computing the structure factor, $S(\pmb{k})$, from
both the positions of the points and the radial distribution function, $g(\pmb{r})$. I have been following the structure factor Wikipedia p... |
Answer
The angles of the triangle are as follows: $A = 64.6^{\circ}, B = 74.8^{\circ},$ and $C = 40.6^{\circ}$ The lengths of the sides are as follows: $a = 8.92~in, b = 9.53~in,$ and $c = 6.43~in$
Work Step by Step
We can use the law of cosines to find $b$: $b^2 = a^2+c^2-2ac~cos~B$ $b = \sqrt{a^2+c^2-2ac~cos~B}$ $b =... |
We consider how the GDP or utility output of a city depends on the number of people living within it. From this, we derive some interesting consequences that can inform both government and individual attitudes towards newcomers.
Follow @efavdb Follow us on twitter for new submission alerts! The utility function and ben... |
Author Message Topic: small caps zedler Replies: 6 Views: 30036 Forum: MathTime Pro II Beta Posted: Sun Apr 23, 2006 11:37 pm Subject: Re: small caps But will this package now break Y&Y? There are issues of font naming and font encoding involved, which of course are handled differently by Y&Y vs.
You asked for a soluti... |
In Proposition 7.6 of his paper "Higher Direct Images of Dualizing Sheaves", Kollár shows that if $X,Y$ are smooth complex projective varieties and $f:X\rightarrow Y$ is a proper surjective morphism with connected fibers, then there is an isomorphism $R^df_{\ast}\omega_X \simeq \omega_Y$, where $d=\dim X-\dim Y$.
I was... |
There is a remark (Remark IV.4.3.2) in Shrawan Kumar's book* that says it is unknown to the author that the set of smooth points of an ind-variety is open.I was wondering if this has been answered ...
Let $\mathbb{k}$ be an algebraically closed field and let $A$ be a $\mathbb{k}$-algebra which is a free module of rank ... |
Seminar
Parent Program: Location: MSRI: Baker Board Room
Thomas McConville, Preparation for “Circuits and Hurwitz action in finite root systems”
Joseph Doolittle, Nerves of Simplicial Complexes and Reconstruction
The standard nerve of a covering $U=\{U_1, \ldots U_j\}$ of some topological space $X$ is the simplicial co... |
Difference between revisions of "Vopenka"
(→Variants: gVP so?)
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==Variants==
==Variants==
−
(Information in this section from <cite>Bagaria2012:CnCardinals</cite>
+
(Information in this section from <cite>Bagaria2012:CnCardinals</cite><cite>BagariaGitmanSchindler2017:VopenkaPrinciple</cite>)
(Boldface)... |
Let us construct an axiom schema that declares that every set is definable from previous sets. For any formulas $\phi$, $\pi$, $\tau$, the following is instance of this axiom schema:
$$\forall x\forall y.\left( \begin{array} {rl} & \phi(\emptyset) \\ \land & \phi(\mathbb N) \\ \land & (\phi(x) \land \phi(y) \implies \p... |
I am currently reading through a proof of Proposition 6 in
Chernoff's theorem and discrete time approximations of Brownian motion on manifolds OG Smolyanov, H Weizsäcker, O Wittich - Potential Analysis
which is relating the geodesic distance in a Riemannian manifold $L$ to the geodesic distance in a Riemannian manifold... |
I currently try to design my first transistor circuit to switch an LED on and off. So I came up with this circuit diagram:
I have to use the following components:
What I need to figure out are the values of R1 and R2. So first I picked a desired current of 70mA from the 5V source to GND. According to the LED datasheet,... |
A topological space $X$ is said to be irreducible if for any decomposition of $X$ with $X=A \cup B$ where $A,B$ are closed subsets of $X$ we either have $X=A$ or $X=B.$
Theorem$:$
Let $X$ be a topological space such that any non-empty open subset of $X$ is dense in $X.$ Then show that $X$ is irreducible.
My attempt $:$... |
I was watching Geoff Hinton's lecture from May 2013 about the history of deep learning and his comments on the rectified linear units (ReLU's) made more sense that my previous reading on them had. Essentially he noted that these units were just a way of approximating the activity of a large number of sigmoid units with... |
Filtering time-series data can be a tricky business. Many times what seems to obvious to our eyes is difficult to mathematically put into practice. A recent technique I've been reading about is called "total variance minimization" filtering or another name would be "$ \ell_1 $ trend filtering." Another member of this f... |
Learning Objectives
Define density. Use density as a conversion factor.
Density (\(\rho\)) is a physical property found by dividing the mass of an object by its volume. Regardless of the sample size, density is always constant. For example, the density of a pure sample of tungsten is always 19.25 grams per cubic centim... |
Suppose $p$ is a prime number and $G$ is a finite group, such that $\Phi(G) = D_4 = \langle a \rangle_4 \rtimes \langle b \rangle_2$, where $\Phi$ denotes the Frattini subgroup. Is it always true, that $32$ divides $|G|$?
To solve that problem I tried to apply the method from the answer to the following question: A que... |
I would appreciate help with a valuation of a fixed income derivative, with an embedded exit option.
Summary:Goal is to provide valuation of a fixed schedule of quarterly cash flows with an option to exit at any quarter (3 years from today) for a lump sum exit payment (to dispose by refinancing). The lump sum payment i... |
Definition 1:Let $X$ be a countably infinite set and let $B$ be the set of one-to-one maps $\alpha: X\to X$ with the property that $X\setminus X\alpha$ is infinite. Then $B$ with composition is the Baer-Levi semigroup.
Definition 2:We call $S$ right simpleif $\mathcal R=S\times S$, and left simpleif $\mathcal L=S\times... |
What is a Category? Definition and Examples
As promised, here is the first in our triad of posts on basic category theory definitions: categories, functors, and natural transformations. If you're just now tuning in and are wondering
what is category theory, anyway? be sure to Category theory takes a bird's eye view of ... |
Show that $C_{c}^{\infty}(\Omega)$ is dense in $L^{\infty}(\Omega)$ with respect to the topology $\sigma(L^{\infty},L^{1})$, where $\Omega$ is an open subset of $\mathbb{R^n}$.
My try: Let $$\Omega_n=\{x \in \Omega: d(x,\partial \Omega) \gt \frac{2}{n},||x|| \lt n\}$$
For $u \in L^{\infty}(\Omega)$, define $\bar{u}$ by... |
Difference between revisions of "Rank into rank"
(→$C^{(n)}$ variants: I wrote what I could)
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(section from <cite>Bagaria2012:CnCardinals</cite>)
(section from <cite>Bagaria2012:CnCardinals</cite>)
−
Assumming $\mathrm{I3}(κ, δ)$, if $δ$ is a limit cardinal (instead of a ... |
Basically 2 strings, $a>b$, which go into the first box and do division to output $b,r$ such that $a = bq + r$ and $r<b$, then you have to check for $r=0$ which returns $b$ if we are done, otherwise inputs $r,q$ into the division box..
There was a guy at my university who was convinced he had proven the Collatz Conject... |
In signal processing, cross-correlation is a measure of similarity of two waveforms as a function of a time-lag applied to one of them. This is also known as a sliding dot product or sliding inner-product. It is commonly used for searching a long signal for a shorter, known feature. It has applications in pattern recog... |
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... |
If you know nothing about CMOS, you need ohms law, a data sheet, and some common sense.
If you know something about CMOS, then just the common sense will do.
Per the data sheet, the input leakage current for a 74HCT08 is \$1 \mathrm{\mu A}\$. Per ohms law, this means we need \$R < \mathrm{\frac{0.9V}{1\mu A} = 900k\Ome... |
When was the word "bias" coined to mean $\mathbb{E}[\hat{\theta}-\theta]$?
The reason why I'm thinking about this right now is because I seem to recall Jaynes, in his
Probability Theory text, criticizing the use of the word "bias" used to describe this formula, and suggesting an alternative.
From Jaynes'
Probability Th... |
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Anisotropic flow of inclusive and identified particles in Pb–Pb collisions at $\sqrt{{s}_{NN}}=$ 5.02 TeV with ALICE
(Elsevier, 2017-11)
Anisotropic flow measurements constrain the shear $(\eta/s)$ and bulk ($\zeta/s$) viscosity of the quark-gluon plasma created in heavy-ion collisions... |
We want to show that for $\succcurlyeq$ on $X$,
Def 1 $\iff$ Def 2
$\boxed \Longrightarrow$
Assume that $\succcurlyeq$ is continuous by
Def 1.
Let us say $x \succ y$. Denote our open-balls as $B(x, r)$, an open ball around $x$ of radius $r$. Suppose $\forall n, \ \exists \ x^n \in B(x, \frac{1}{n}), \ y^n \in B(y, \fra... |
[Top][All Lists] [Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index] need double save-excursion -- why?
From: Joe Corneli Subject: need double save-excursion -- why? Date: Thu, 25 Dec 2003 15:30:03 -0600 When I run the function below on a file containing things like this:
########################... |
First of all, $\sqrt{2}+\sqrt{3}$ most certainly
is a number. It is a real number, approximately equal to $3.14626$ Perhaps what you're asking is why the sum of two simple radicals isn't also a simple radical, when the sum of two integers is an integer, and the sum of two fractions is a fraction.
Roots of integers are ... |
Difference between revisions of "Superstrong"
(→Relation to other large cardinal notions: +1)
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* Every $C^{(n)}$-superstrong cardinal belongs to $C^{(n)}$.
* Every $C^{(n)}$-superstrong cardinal b... |
In signal processing, cross-correlation is a measure of similarity of two waveforms as a function of a time-lag applied to one of them. This is also known as a sliding dot product or sliding inner-product. It is commonly used for searching a long signal for a shorter, known feature. It has applications in pattern recog... |
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