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Preprint 2013-20 Sergio Caucao, David Mora, Ricardo Oyarzúa: Analysis of a mixed-FEM for the pseudostress-velocity formulation of the Stokes problem with varying density Abstract:
We propose and analyse a mixed finite element method for the nonstandard pseudostress-velocity formulation of the Stokes problem with varyin... |
I want to obtain a good numerical approximation (up to 10 decimal place would be ok for me) to an integral:
$$ \int^{\infty}_{0} f(r)r^2dr $$
I am using the function $f(r)$, which is related to the function
$$g(r)=-\frac{\sqrt[3]{3} \sqrt[3]{e^{-2 r}}}{\pi ^{2/3}}-\frac{\sqrt[3]{2 \pi }}{5 \sqrt[3]{e^{-2 r}} \left(\fra... |
Difference between revisions of "Inertia"
(→Relationship between Inertia and Frequency)
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== Derivation ==
== Derivation ==
−
[[Image:Arc_circle.png|right|thumb|250px|Cross-section of a cylindrical body rotating about the axis of its centre of mass]]
+
[[Image:Arc_circle.png|right|thumb|250px|Cross-sectio... |
Archimedean Principle Contents Theorem
Let $x$ be a real number.
Then there exists a natural number greater than $x$. $\forall x \in \R: \exists n \in \N: n > x$
Let $x$ and $y$ be a natural numbers.
Then there exists a natural number $n$ such that: $n x \ge y$ Proof
Let $x \in \R$.
Let $S$ be the set of all natural nu... |
Your equations are flawed. Also there is no expectation if the process $\{r_s\}$ is deterministic.The correct reasoning is, assuming $\{r_s\}$ is stochastic:$$f(t,u)=-\frac{d}{du}\ln P(t,u)=-\frac{\frac{d}{du}P(t,u)}{P(t,u)}\\=-\frac{\frac{d}{du}E^Q_t[e^{-\int_t^u r_s ds}]}{P(t,u)}=\frac{E^Q_t[e^{-\int_t^u r_s ds} r_u]... |
Difference between revisions of "Inertia"
m
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[[Category:Fundamentals]]
[[Category:Fundamentals]]
+ Latest revision as of 00:31, 22 December 2018
In power systems engineering, "inertia" is a concept that typically refers to rotational inertia or rotational kinetic energy. For synchronous systems that ... |
In my textbook, it's stated that:
When $\epsilon < -1$, demand is elastic and raising price will result in smaller income, while lowering price will result in bigger income.
When $\epsilon = -1$, demand is neither elastic nor inelastic and change in price won't result in change in income.
When $\epsilon > -1$, demand i... |
It is the resultant polyhedron after having made a parallel cut to the basis of a pyramid. The mentioned cut will be named a minor base.
Lateral faces will have now the shape of isosceles trapeze.
The height will be the distance between basis.
The following figure is an example of a frustum of pyramid with pentagonal b... |
Onsager's regression hypothesis
“…the average regression of fluctuations will obey the same laws as the corresponding macroscopic irreversible process"
comes vividly to life when experimentalists observe the Brownian motion $q(t)$ of a damped oscillator (as nowadays they commonly do). Setting
$\qquad q(t)= x(t) \cos(\o... |
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... |
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... |
Alright, I have this group $\langle x_i, i\in\mathbb{Z}\mid x_i^2=x_{i-1}x_{i+1}\rangle$ and I'm trying to determine whether $x_ix_j=x_jx_i$ or not. I'm unsure there is enough information to decide this, to be honest.
Nah, I have a pretty garbage question. Let me spell it out.
I have a fiber bundle $p : E \to M$ where ... |
Prove that $tr\left(\gamma_\mu\gamma_\nu\gamma_\rho\gamma_\sigma\gamma_5\right)=0$ when the spacetime dimension is not 4.
What I have tried:
We know that $\gamma_\alpha\gamma^\alpha=d\mathbb{1}$, so we can write:
$tr\left(\gamma_\mu\gamma_\nu\gamma_\rho\gamma_\sigma\gamma_5\right)=\frac{1}{d}tr\left(\gamma_\alpha\gamma... |
In the weak-field case,$$\mathrm{d}s^2 = -\left(1+2\frac{\Phi}{c^2}\right)c^2\mathrm{d}t^2 - \frac{4}{c}A_i\mathrm{d}t\mathrm{d}x^i + \left(1-2\frac{\Phi}{c^2}\right)\mathrm{d}S^2\text{,}$$where $\Phi$ is the Newtonian potential and $\mathrm{d}S^2 = \mathrm{d}x^2 + \mathrm{d}y^2 + \mathrm{d}z^2$ is the Euclidean metric... |
Compact Subspace of Linearly Ordered Space/Reverse Implication/Proof 1 Theorem
Let $\left({X, \preceq, \tau}\right)$ be a linearly ordered space.
Let the following hold: $(1): \quad$ For every non-empty $S \subseteq Y$, $S$ has a supremum and an infimum in $X$. $(2): \quad$ For every non-empty $S \subseteq Y$: $\sup S,... |
Definition:Boolean Algebra/Definition 3 Definition
A
Boolean algebra is an algebraic structure $\left({S, \vee, \wedge}\right)$ such that:
\((BA \ 0)\) $:$ $S$ is closed under both $\vee$ and $\wedge$ \((BA \ 1)\) $:$ Both $\vee$ and $\wedge$ are commutative \((BA \ 2)\) $:$ Both $\vee$ and $\wedge$ distribute over the... |
Rana Baydoun, Omar Samad, Maria Aoun, Bilal Nsouli and Ghassan Younes
Abstract
A new radiocarbon laboratory has been established recently at the Lebanese Atomic Energy Commission. This laboratory consists of benzene synthesis line and a low background liquid scintillation counter, Tri-Carb 3180 TR/SL for measurements w... |
The ring $R$ is commutative with unit. An ideal $I$ is called primary, if it stands the following:
If $ab \in I$ then $a \in I$ or $b^n \in I$, for a natural number $n$.
Show that if $I$ is a primitive ideal of $R$, then $Rad(I)$ is a prime ideal of it.
Could you give me a hint how we could show this?
EDIT:
That's what... |
I haven't done a surface integral in a while so I am asking to get this checked.
$\mathbf{F} = \langle x, y, z\rangle$ and the surface is $z = xy + 1$ where $0\leq x,y\leq 1$.
$\hat{\mathbf{n}} = \nabla f/ \lvert\nabla f\rvert = \frac{1}{\sqrt{3}}\langle 1, 1, 1\rangle$
$dS = \frac{\lvert\nabla f\rvert dxdy}{\frac{\par... |
(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... |
ISSN:
1937-1632
eISSN:
1937-1179
All Issues
Discrete & Continuous Dynamical Systems - S
June 2016 , Volume 9 , Issue 3
Issue in memory of Alfredo Lorenzi
Select all articles
Export/Reference:
Abstract:
In the study of mathematical models, which lead to Cauchy problems for differential equations of parabolic (resp. hype... |
I will present a very short proof of the Prime Number Theorem.
My question is, if the following proof is acceptable?
Let ф(np) be the Euler ф function (Euler totient function) for any primorial np with (1) $$np=\prod_{p=prime}^{p≤n} p$$ which is defined as (2) $$ф(np)=np*\prod_{p=prime}^{p≤n} (1-1/p)=np*\prod_{p=prime}... |
Problem.If $X$ and $Y$ measure the lifetimes of two components operating independently. Suppose each has density (in unit of 100 hours)
$$ f(x) = \begin{cases} \frac{1}{x^2}, & \text{if } x > 1 \\ 0, & \text{elsewhere}, \end{cases} $$
If $Z = \sqrt{XY}$ measures the quality of the system, show that $Z$ has density func... |
@Rubio The options are available to me and I've known about them the whole time but I have to admit that it feels a bit rude if I act like an attribution vigilante that goes around flagging everything and leaving comments. I don't know how the process behind the scenes works but what I have done up to this point is lea... |
Today we (Chamseddine-Connes-van Suijlekom) posted a preprint on grand unification in the spectral Pati–Salam model which I summarize here.
The paper builds on two recent discoveries in the noncommutative geometry approach to particle physics: we showed how to obtain inner fluctuations of the metric without having to a... |
About the last question, the usual undecidability proof for universality could be adapted.
Recall that in this proof, one considers an instance $\langle \Sigma,\Delta,u,v\rangle$ of Post's correspondence problem, where $\Sigma$ and $\Delta$ are two disjoint alphabets, and $u$ and $v$ are two homomorphisms from $\Sigma^... |
I want to create a table of values, and the values are defined recursively as follows: $$ b_{t,m} = \begin{cases} b_{t+1,m} + b_{t+1,m-1}\delta^{t-T} & \text{ if } t \in \{2,\ldots,T-1\} \text{ and } m \in \{2,\ldots,T-t+1\} \\ % 1 & \text{ if } t\in \{2,\ldots,T\} \text{ and } m = 1 \\ % 0 & \text{ otherwise } \end{ca... |
Singer-Terhaar is part of CFA II and III curriculum. It estimates risk premium for some asset, traded at some local market, as weighted average of expected premiums for the case of (1) local market, completely integrated with global, and (2) local market completely isolated from global.
For integrated case, risk premiu... |
So I have this equation from cosmology giving $H_0 t$ as a function of $a$:
\begin{equation} \int_0^a \frac{da}{\left( \frac{\Omega_{\text{rad,0}}}{a^2} + \frac{\Omega_{\text{m,0}}}{a} +\Omega_{\Lambda\text{,0}} a^2\right)^{1/2}}=H_0 t \end{equation} I can plot it on a log-log scale like this:
ParametricPlot[{Log10[NIn... |
The spindle is the exterior surface of the volume that has the shape of a segment of a mandarine or orange, which is known as a wedge.
The time zones are (although the Earth is not exactly spherical) the most habitual example of this figure.
If we apply proportions according to the area of the sphere (with the degree o... |
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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 ... |
I'm still looking at how shocks behave in the ideal information transfer model, but I'd like to discuss non-ideal information transfer for a minute.
The information transfer model of supply $S$ and demand $D$ essentially has the 'invisible hand' operating as an entropic force -- I have some animations here (and here is... |
I previously worked out that ensembles of information equilibrium relationships have a formal resemblance to a single aggregate information equilibrium relationship involving the ensemble averages:
\frac{d \langle A \rangle}{dB} = \langle k \rangle \frac{\langle A \rangle}{B}
$$
I wanted to point out that this means en... |
Seeing that in the Chomsky Hierarchy Type 3 languages can be recognised by a DFA (which has no stacks), Type 2 by a DFA with one stack (i.e. a push-down automaton) and Type 0 by a DFA with two stacks (i.e. with one queue, i.e. with a tape, i.e. by a Turing Machine), how do Type 1 languages fit in...
Considering this ps... |
I came across John Duffield Quantum Computing SE via this hot question. I was curious to see an account with 1 reputation and a question with hundreds of upvotes.It turned out that the reason why he has so little reputation despite a massively popular question is that he was suspended.May I ...
@Nelimee Do we need to m... |
@Rubio The options are available to me and I've known about them the whole time but I have to admit that it feels a bit rude if I act like an attribution vigilante that goes around flagging everything and leaving comments. I don't know how the process behind the scenes works but what I have done up to this point is lea... |
Alright, I have this group $\langle x_i, i\in\mathbb{Z}\mid x_i^2=x_{i-1}x_{i+1}\rangle$ and I'm trying to determine whether $x_ix_j=x_jx_i$ or not. I'm unsure there is enough information to decide this, to be honest.
Nah, I have a pretty garbage question. Let me spell it out.
I have a fiber bundle $p : E \to M$ where ... |
Erwin Kreyszig Section 2.8, Problem 1:
Define a functional on $C[a,b]$ by fixing $t_0\in[a,b]$ and setting:
$$f_1(x)=x(t_0)$$
Define a second functional on $l^2$ by choosing a fixed $a=(\alpha_j)\in l^2$ and setting $$f(x) = \sum_{j=1}^\infty \xi_j\alpha_j$$ where $x=(\xi_j)\in l^2$
Show these two functionals are linea... |
$f\left(\mathbf{x}\right):\mathbb{R}_+^n\rightarrow\mathbb{R}_+$ is a concave monotonically increasing function to be minimised over the feasible region $\sum_{i=1}^n x_i=1$ and $x_i\geq 0\quad\forall1\leq i\leq n$.
Given that the feasible region is a convex polytope, is it possible to say anything about the optimal $\... |
Logblog: Richard Zach's Logic Blog
You are looking at an archived page. The website has moved to richardzach.org.
Dana Scott's proof reminded commenter "fbou" of Kalmár's 1935 completeness proof. (Original paper in German on the Hungarian Kalmár site.) Mendelsohn's
Introduction to Mathematical Logic also uses this to p... |
I apologize if the dynamic equilibrium [1] posts are getting monotonous, but as the blog's primary purpose is as a "working paper" (one that is now apparently a few hundred pages long) I must continue!
The latest Case-Shiller price index data was released earlier today showing a continued rise in housing prices. In loo... |
(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... |
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... |
Suppose I made a tag and it is used by many people everyday, so will it increase my reputation? And also, suppose no one uses it even once for a long time, i.e. 6 months, then?
Maybe it could be called book-errata? I cannot give many examples of discussions from math.SE offhand but at least one example from here Find l... |
I came across John Duffield Quantum Computing SE via this hot question. I was curious to see an account with 1 reputation and a question with hundreds of upvotes.It turned out that the reason why he has so little reputation despite a massively popular question is that he was suspended.May I ...
@Nelimee Do we need to m... |
Suppose initially there are no fixed costs.
What does it mean to take an average?
Consider a cost function $C(y)$. What does it mean to take the “average” of this function? Mathematically, it is just $$A(y) = \frac{c(y)}{y}$$
Let’s suppose we are considering $C(y) = y^3$. Suppose we now consider $y = 5$. Then $$A(5) = ... |
I have simple code, which flags nodes with in region enclosed by cylinder. On implementing the code, the result is mild tilt of the cylinder observed case with $\theta=90^{\circ}$.
The algorithm for checking any point inside arbitrarily oriented cylinder is as follows. Let $\vec{r}$ be the vector joining center $\vec{c... |
I seek to prove the identity
$$\int_2^x\frac{dt}{\log^kt}=O\left(\frac{x}{\log^kx}\right)$$
I was given the following hint:
Split the integral into $\int_2^{f(x)}+\int_{f(x)}^x$ for a well-chosen function $f(x)$ with $2\le f(x)<x$ and estimate both parts from above.
but my proof was different. Can anyone (i) confirm if... |
Morris (2008) discusses various ways for computing a (standardized) effect size measure for pretest posttest control group designs, where the characteristic, response, or dependent variable assessed in the individual studies is a quantitative variable.
As described by Becker (1988), we can compute the standardized mean... |
Is there a bijection from a finite (closed) segment of the real line to $\mathbb{R}$? For example, is there a bijection from $[0,1]$ to $\Bbb{R}$?
If so, is there a straightforward example? If not, why?
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in r... |
For analytic $f$, how can I represent the expression $f(z)\cdot\exp\left({s\,\log(z)}\right)$, i.e. $f(z)\cdot z^s$ in the form
$$\sum_{n}^\infty\left(\sum_{k}^\infty a_k s^k\right)z^n,$$
at least as a formal power series, where the index runs over the number needed?
I got to $$f(z)\cdot\exp\left({s\,\mathrm{log}(z)}\r... |
What will be the complexity of finding Gini Index of a sorted vector of $N$ values, which is defined as:
$Gini(\mathbf{x})=1-2\sum_{k=1}^N \frac{\mathbf{x}(k)}{\Vert\mathbf{x}\Vert_1}(\frac{N-k+.5}{N})$
Computational Science Stack Exchange is a question and answer site for scientists using computers to solve scientific... |
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Application of the preventive maintenance scheduling to increase the equipment reliability: Case study- bag filters in cement factory Extension of g... |
This is a continuation of a problem I asked over at physics exchange and math exchange. Basically I have two ODEs that I am solving in order to calculate the radial and tangential velocity of liquid dispensed on the center of a disk rotating at rate of $\omega$. $u_m$ is the average flow velocity in the $r$-direction, ... |
Alternating current From Academic Kids
An
alternating current ( AC) is an electrical current where the magnitude and direction of the current varies cyclically, as opposed to direct current, where the direction of the current stays constant. The usual waveform of an AC power circuit is a sine wave, as this results in t... |
I am studying Numerical Analysis with the book of Richard L.Burden. A question which I'm struggling with right now is following.
Transform the second-order initial-value problem
$y'' - 2y' + 2y = e^{2t}\sin t$ for $0 \leq t \leq 1, $ with $y(0) = -0.4, y'(0) = -0.6, h=0.1$
into a system of first order initial-value pro... |
This question already has an answer here:
Let $f_n$ be a uniformly bounded sequence of holomorphic functions on $D$. Suppose there exists a point $a\in D$, such that $\lim_{n\rightarrow\infty}f_n^{(k)}(a)=0$ for each $k$. Show that $f_n\rightarrow0$ uniformly on each compact subset of $D$.
Since $f_n$ is holomorphic an... |
Number problems involve finding two numbers that satisfy certain conditions.
If we label the numbers using the variables \(x\) and \(y,\) we can compose the objective function \(F\left( {x,y} \right)\) to be maximized or minimized.
The constraint specified in the problem allows to eliminate one of the variables.
When w... |
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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 ... |
One of the most important ways to get involved in complex variable analysis is through complex integration. When we talk about complex integration we refer to the line integral.
Line integral definition begins with γ a differentiable curve such that
$$ \begin{matrix}\gamma : [a,b] \mapsto \mathbb{C}\\ \;\;\;\;\; \;\;\;... |
Let's start with the experiment of throwing a six-sided dice and looking at what number turns out. We can represent its sample space by $$\Omega=\lbrace 1,2,3,4,5,6 \rbrace$$.
Let's consider two events: $$A =$$ "to extract an even number", $$B =$$ "to extract the number $$4$$ or higher". As we already know , the set of... |
$\newcommand{\Sym}[1]{\operatorname{Sym}{#1}}$
Let $V$ be a $n$-dim real vector space with dual space $V^*$. Let $\alpha$ be a covariant $k$-tensor, i.e., $\alpha \in T^k(V^*) \equiv (V^*)^{\otimes k}$. Then how would you show that the symmetrization $\Sym{\alpha}$ of $\alpha$ is the unique symmetric $k$-tensor such th... |
With the release of the Fed transcripts from the September 16th 2008 meeting, a narrative of the Fed worrying about commodities inflation distracted it from the worsening economic situation is forming. Here are e.g. Matthew Yglesias and David Glasner. In general this is part of a larger monetarist narrative that the Fe... |
It is well-known that the complement of $\{ ww \mid w\in \Sigma^*\}$ is context-free. But what about the complement of $\{ www \mid w\in \Sigma^*\}$?
Still CFL I believe, with an adaptation of the classical proof. Here's a sketch.
Consider $L = \{xyz : |x|=|y|=|z| \land (x \neq y \lor y \neq z)\}$, which is the complem... |
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Now showing items 1-2 of 2
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 ... |
Search
Now showing items 1-10 of 33
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... |
Let's imagine the following scenario:
algebraic multiplicity: $\lambda_{1} = \lambda_{2} = \lambda_3: 3$ geometric multiplicity: 1
the first column of the fundamental matrix can be found as follows using row expansion:
$\vec{y_{1}(t)} = e^{\lambda_{1}t}[I\vec{x_{1}}+ \frac{t^1}{1!}(A-\lambda_{1}I)\vec{x_{1}}+...+\frac{... |
So this is a little cheating, but you asked for an interesting order:
Classify all groups of order $24k+4$. ALL OF THEM.
I find it interesting that there is even an answer!
I'll let you assume someone else has already classified the groups of order $4$ and $n/4 = 6k+1$, though the latter can get pretty tricky [ no one ... |
Infeasible-start primal-dual methods and infeasibility detectors for nonlinear programming problems Yurii Nesterov, Yinyu Ye, and Michael ToddIn this paper we present several ``infeasible-start''path-following and potential-reduction primal-dualinterior-point methods for nonlinear conic problems.These methods try to fi... |
Let $A\in \mathbb{R}^{n\times n}$ symmetric and positive semidefinite, and $\omega\in \mathbb{R}\setminus\{0\}$. I am interested in solving the following linear system for a range of values of $\omega$:
$$((A-\omega^2 I)(A-\omega^2 I)+\omega^2 I)x = b.$$ It may be useful to note that the matrix factors as $$ (A-(\omega... |
Every functor $\mathbf{Set} \rightarrow \mathbf{Set}$ I can think of preserves monomorphisms (i.e. injective functions), including:
$\mathrm{Hom}(X,-)$, $X \times -$, $X \sqcup -$, and the constant functors.
The monads I can think of all have this property, too.
What are some natural examples that don't? |
A general class of counterexamples is given by Exercises II.3.9 and II.3.10 of [Conway]; see references below.
Exercise II.3.9. Let $A \in \mathscr B(\mathscr H)$ and $\mathscr N = \operatorname{graph}(A) \subseteq \mathscr H \oplus \mathscr H$, that is, $\mathscr N = \{h \oplus Ah \, : \, h\in\mathscr H\}$. Because $A... |
There is a classic problem:
Suppose that $X_1,\ldots,X_n$ form an i.i.d. sample from a uniform distribution on the interval $(0,\theta)$, where $\theta>0$ is unknown. I would like to find the MLE of $\theta$.
The pdf of each observation will have the form: $$ f(x\mid\theta) = \begin{cases} 1/\theta\quad&\text{for }\, 0... |
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Now showing items 1-1 of 1
Higher harmonic flow coefficients of identified hadrons in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV
(Springer, 2016-09)
The elliptic, triangular, quadrangular and pentagonal anisotropic flow coefficients for $\pi^{\pm}$, $\mathrm{K}^{\pm}$ and p+$\overline{\mathrm{p}}$ in Pb-... |
Here are some details that are in the spirit of Tarski's work:
Let $M$ be a system of magnitudes and select any element in the carrier set and call it $1$, so that the set $M$ is a pointed set and the object of study becomes $(M,1,+)$. We also have an injective morphism
$\tag 1 \iota: \mathbb N^> = \mathbb N \setminus ... |
I have
$$\begin{pmatrix} 0&B_3&-B_2 \\ -B_3&0&B_1 \\ B_2&-B_1&0 \end{pmatrix}\begin{pmatrix} \omega_1 \\ \omega_2 \\ \omega_3 \end{pmatrix}=\begin{pmatrix} \Delta_1 \\ \Delta_2 \\ \Delta_3 \end{pmatrix}$$
With $\Delta_1 B_1 + \Delta_2 B_2 + \Delta_3 B_3 = 0$. Because the constraint, the system has clearly solutions in ... |
2018-08-25 06:58
Recent developments of the CERN RD50 collaboration / Menichelli, David (U. Florence (main) ; INFN, Florence)/CERN RD50 The objective of the RD50 collaboration is to develop radiation hard semiconductor detectors for very high luminosity colliders, particularly to face the requirements of the possible u... |
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astro-ph.CO
Change to browse by: Bookmark(what is this?) Astrophysics > Astrophysics of Galaxies Title: The MASSIVE Survey - X. Misalignment between Kinematic and Photometric Axes and Intrinsic Shapes of Massive Early-Type Galaxies
(Submitted on 31 Jan 2018 (v1), last revised 21 Jun 2018 (this v... |
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Now showing items 11-20 of 24
Coherent $\rho^0$ photoproduction in ultra-peripheral Pb-Pb collisions at $\mathbf{\sqrt{\textit{s}_{\rm NN}}} = 2.76$ TeV
(Springer, 2015-09)
We report the first measurement at the LHC of coherent photoproduction of $\rho^0$ mesons in ultra-peripheral Pb-Pb collisions. The invarian... |
Morris (2008) discusses various ways for computing a (standardized) effect size measure for pretest posttest control group designs, where the characteristic, response, or dependent variable assessed in the individual studies is a quantitative variable.
As described by Becker (1988), we can compute the standardized mean... |
A very basic question. As title, what is the difference between "sort" and "universe" in type theory? Are they interchangable? Or are there only finite number of sorts, but infinite universes?
Sort is (typically, though see Pure Type Systems) a meta-level concept and universes are an internalization of a particular cas... |
I was inspired by Dietrich Vollrath's latest blog post to work out the generalization of the macro ensemble version of the information equilibrium condition [1] to more than one factor of production. However, as it was my lunch break, I didn't have time to LaTeX up all the steps so I'm just going to post the starting p... |
Nick Rowe has a post up where he blegs the impossible ... A 3D Edgeworth box does not exist (it is at a minimum 6D as I mention in a comment at the post) [1]. However, Nick does cite MINIMAC, a minimal macro model described by Paul Krugman here. It gives us a fun new example to apply the information equilibrium framewo... |
ISSN:
1937-1632
eISSN:
1937-1179
All Issues
Discrete & Continuous Dynamical Systems - S
June 2008 , Volume 1 , Issue 2
Guest Editors
Boris Belinskiy, Kunquan Lan, Xin Lu, Alain Miranville, and R. Shivaji
Select all articles
Export/Reference:
Abstract:
In this paper we describe a new implicit finite element scheme for t... |
In the canonical ensemble, the Helmholtz free energy \(A (N, V, T)\) is a natural function of \(N , V \) and \(T\). As usual, we perform a Legendre transformation to eliminate \(N\) in favor of \( \mu = \frac {\partial A}{\partial N} \):
\( \tilde{A}(\mu,V,T)\)
\( A(N(\mu),V,T) - N\left(\frac {\partial A}{\partial N}\r... |
Given the radius and $x,y$ coordinates of the center point of two circles how can I calculate their points of intersection if they have any?
This can be done without any trigonometry at all. Let the equations of the circles be$$(x-x_1)^2 + (y-y_1)^2 = r_1^2, \tag{1}$$$$(x-x_2)^2 + (y-y_2)^2 = r_2^2. \tag{2}$$By subtrac... |
Diamagnetism arises from closed atomic shells of electrons. When a B-field is applied, these electrons set up a screening current that opposes the applied field.
Start by thinking of electrons in a circular orbit of radius
ρ in the xy plane.
Recall
Flux
Force on an electron
Current due to
Z electrons in an atom
So
Magn... |
Skills to Develop
Graph exponential functions. Graph exponential functions using transformations.
As we discussed in the previous section, exponential functions are used for many real-world applications such as finance, forensics, computer science, and most of the life sciences. Working with an equation that describes ... |
Hi I'm learning about Lie Groups to understand gauge theory (in the principal bundle context) and I'm having trouble with some concepts. Now let $a$ and $g$ be elements of a Lie group $G$, the left translation $L_{a}: G \rightarrow G$ of $g$ by $a$ are defined by : $L_{a}g=ag$ which induces a map $L_{a*}: T_{g}G \right... |
Learning Objectives To understand the autoionization reaction of liquid water. To know the relationship among pH, pOH, and p K w.
As you learned in Chapter 8 and Chapter 4, acids and bases can be defined in several different ways (Table 16.1.1 ). Recall that the Arrhenius definition of an acid is a substance that disso... |
Something has been buzzing me recently. It is well-known that $\textbf{PCP}[poly(n), 0] = \textbf{coRP}$, but does $\textbf{PCP}[poly(n), O(1)] = \textbf{coRP}$ ?
I have found a proof for this statement but something feels wrong about it. Here it goes :
Let $L \in \textbf{PCP}[poly(n), O(1)]$. There is a verifier $V$ f... |
I am having trouble solving this set of two coupled differential equations using NDSolve:
$$\left[\left\{-\frac{\mu _0 Q_e M_{\text{earth}} \text{vy}(t)}{4 \pi m_e \left(\left(5 R_{\text{earth}}-t \text{vx}(t)\right){}^2+t^2 \text{vy}(t)^2\right){}^4}=\text{vx}'(t),\frac{\mu _0 Q_e M_{\text{earth}} \text{vx}(t)}{4 \pi ... |
Here is an extended answer that concludes
Summary On entropic grounds, gravitational radiative decoherence is similarly irreversible to all other forms of radiative decoherence, and in consequence, Nature's quantum state-spaces are effectively low-dimension and non-flat.
Update B For further discussion and references, ... |
Associativity is About Composition
Complex multiplication can be visualized as rotating and scaling the complex plane. So, besides thinking of a complex number $z$ as a point, we can think of it as encoding a transformation composed of a rotation and scaling.
Recall associativity:$$ z \cdot (q \cdot c) = (z \cdot q) \c... |
In this section, we will investigate the shape of this room and its real-world applications, including how far apart two people in Statuary Hall can stand and still hear each other whisper.
For the exercises 1-4, write the equation of the ellipse in standard form. Then identify the center, vertices, and foci.
1) \(\dfr... |
The deeper problem with this supposition is that it assumes a conceptual identity between the notions of Hamiltonian and energy, and this is an identity that is not correct. That is, discernment needs to be applied to separate the two of these things.
Conceptually, energy is a physical quantity that is, in a sense, "na... |
The cone is the revolution volume resulting from rotating a rectangle triangle of hypotenuse $$g$$ (the generatrix), low leg $$r$$ (which is the radius) and leg $$h$$ (which is the height of the cone).
Also it is possible to interpret the cone as the pyramid inscribed into a prism of circular basis.
To calculate the ar... |
In Mas-Colell, Whinston, and Green's Microeconomics they define the
indirect utility function, $v(p,w)$ as
$$ v(p,w) := u(x^*) $$
Where $x^* \in x(p,w)$ solves the utility maximization problem.
They state a property of $v(p,w)$ is quasiconvexity, i.e. the set
$$ \{(p,w): v(p,w) \leq \bar{v} \} $$
is convex for any $\ba... |
In a two-good space, initially the consumer maximizes $U(x,z)\;\; s.t. \;\;p_xx+p_zz =I$ and we assume it obtains the solution $(x^*, z^*)$ as a function of prices and income.
In the constrained case, the consumer will either choose $(0, \tilde z)$ or $(x^*+\epsilon, z'$), for some $\epsilon >0 $ always exhausting its ... |
My chemistry textbook introduces the wave function as
$$\psi(x)= A \sin\left(\frac{2\pi x}{\lambda}\right)$$ Therefore, the Schrödinger Equation is:
$$\frac{d^2\psi(x)}{dx^2} = -~\left(\frac{2\pi}{\lambda}\right)^{2}\psi(x)$$
and by multiplying each side by $\frac{-h^2}{8\pi^2m}$ you get:
$$-~\frac{h^2}{8\pi^2m} \frac{... |
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