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The typical difference-in-differences estimator (as fixed effects) fits a model of the form $$ y_{it} = \alpha_i + \delta T_{it} + X_{it}'\beta + \epsilon_{it} $$
where $T$ is some treatment that happens to $i$ at time $t$.
The coefficient $\delta$ is identified from the jump between time periods when T goes from zero ... |
I think in common literature about statstics the authors are often very imprecise when it comes to residuals and errors. So far, I could not work that difference out completely and therefore have several questions.
Setting: Let us consider the simple linear regression model, $$ Y = \beta_0 + \beta_1 x + \epsilon,$$ or ... |
Mathematical operators, such as function names, should be set in roman type, not italics. Latex already has commands for some operators, including
\max,
\min, and
\log. How can I define additional such commands?
\DeclareMathOperator{\foo}{foo} and
\DeclareMathOperator*{\hocolim}{hocolim} for sub- and superscripts in th... |
Is there any formula for this series?
$$1 + \frac12 + \frac13 + \cdots + \frac 1 n .$$
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up.Sign up to join this community
There is no formula for the nth part... |
LaTeX supports many worldwide languages by means of some special packages. In this article is explained how to import and use those packages to create documents in
Italian.
Contents
Italian language has some accentuated words. For this reason the preamble of your document must be modified accordingly to support these c... |
I have the following question, I really appreciate if someone can help me to clarify ideas and I apologize if is a stupid question: This is from Conway's complex analysis book:
Let $f: G \to \bf{C}$ and $g: G\to \bf{C}$ be branches of $z^a$ and $z^b$ respectively. Show that $fg$ is a branch of $z^{a+b}$ and $f/g$ is a ... |
thinking about invariants of 2-knots ... is there an obvious map from $H_2(X)$ (or from part of it) into $\pi_1(X)$?
Where in the derived series of $\pi_1(X)$ would the image of $H_2(X)$ live?
Have you heard of things like Dwyer's filtration on $H_2$ and Stallings/Cochran-Harvey theorems about the lower central/derived... |
It's hard to say just from the sheet music; not having an actual keyboard here. The first line seems difficult, I would guess that second and third are playable. But you would have to ask somebody more experienced.
Having a few experienced users here, do you think that limsup could be an useful tag? I think there are a... |
Soil composition
by
V
olume and
M
ass, by phase:
a
ir,
w
ater,
v
oid (pores filled with water or air),
s
oil, and
t
otal.
Water content or moisture content is the quantity of water contained in a material, such as soil (called soil moisture), rock, ceramics, fruit, or wood. Water content is used in a wide range of scie... |
The (asymptotically) most efficient deterministic primality testing algorithm is due to Lenstra and Pomerance, running in time $\tilde{O}(\log^6 n)$. If you believe the Extended Riemann Hypothesis, then Miller's algorithm runs in time $\tilde{O}(\log^4 n)$. There are many other deterministic primality testing algorithm... |
This question was inspired by my attempt to understand the duration of a floating rate note, or FRN for short. Several answers, like this, say the duration of a FRN is just time to next coupon payment. But I'm still a bit confused even with the very definition of durations of FRNs.
In a continuous time model, let $\{P(... |
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Production of charged pions, kaons and protons at large transverse momenta in pp and Pb-Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV
(Elsevier, 2014-09)
Transverse momentum spectra of $\pi^{\pm}, K^{\pm}$ and $p(\bar{p})$ up to $p_T$ = 20 GeV/c at mid-rapidity, |y| $\le$ 0.8, in pp and ... |
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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 ... |
Consider the finite 1D wedge-shaped potential well given by
$$V(x)=V_0\left(\frac{|x|}{a}-1\right) \hspace{10pt}\mathrm{for}\hspace{3pt} |x|<a;\hspace{6pt}V(x)=0 \hspace{10pt}\mathrm{for}\hspace{3pt} |x|>a.$$
I'm trying to find the reflection and transmission coefficients for a stream of electrons coming from $x=-\inft... |
1,062 6
Quick question, what is the approach to this problem?
Keep in mind I am supposed to use the Fundamental Theorem of Line Integrals.
[tex]\int_{C} 2ydx + 2xdy [/tex]
Where C is the line segment from (0,0) to (4,4).
Unless I am missing something I need to make that into the form of [tex]\vec{F} \cdot \vec_d{R}[/te... |
Given a complex manifold $M$, its complexified tangent bundle is $TM \otimes \mathbb C$. It is quite confusing for me as to why we want to do this since at each point $TM$ can already be viewed as a complex vector space.
A complex manifold is given by two alternative definitions. First you have $M$ a "nice" topological... |
Let $a_0=1,a_n=\tan{a_{n-1}}$. Then is $\{a_n\}_{n=0}^\infty$ dense in $\Bbb{R}$? I've drawn a map of this dynamical system and it seems that the sequence is dense on $\Bbb{R}$.
Before I start, I want to point out that I do not answer the specific question. I believe that no one can with the current tools available in ... |
In canonical quantization, the particles arise as quantized excitations on the vacuum $|0\rangle$. For example, a one-particle state with four momentum $p=(E,\textbf{p})$ is given by $$|p\rangle\sim a^\dagger_{p}|0\rangle.$$ Is it possible to arrive at the particle picture in the path-integral formulation of quantum fi... |
Just curious. If the purpose of a proof is to inform and persuade, why don't Venn diagrams count? Is it just convention or is there a more, umm, formal reason haha. Thanks!
I don't know exactly what you have written, but I would venture to say that anything you "prove" with Venn diagrams probably has an extremely direc... |
Consider a small system in thermal contact with a large system which has coolness $\beta$. For simplicity, the small system has just one state per energy level. It could be a harmonic oscillator with a small quantum energy. The large system has a multiplicity $\Omega_0$ when the small system is in its ground state.
Whe... |
First consider a scheme $X$ with an open cover $\mathcal{U}=\{U_i\}$. An object with descent data on $\mathcal{U}$ is a collection $(\mathcal{E}_i,\phi_{ij})$ where $\mathcal{E}_i$ is a quasi-coherent sheaf on each $U_i$ and $\phi_{ij}$ is an isomorphism $pr_2^*\mathcal{E}_j\to pr_1^*\mathcal{E}_i$ in $Qcoh(U_{ij})$ wh... |
12 0
Hi,
I'm currently reading the book "Quantum Field Theory for Mathematicians" by Ticciati and in section 2.3 he mentions that the Lorentz action on the free scalar field creation operators [itex] \alpha(k)^\dagger [/itex] is given by
[tex] U(\Lambda)\alpha(k)^\dagger U(\Lambda)^\dagger = \alpha(\Lambda k)^\dagger .... |
Many thanks to Bart Andrews for this contribution!
Question
Consider a gas in contact with a solid surface. The molecules of the gas can adsorb to specific sites on the surface. These sites are sparsely enough distributed over the surface that they do not directly interact. In total, there are N adsorption sites, and e... |
It’s been a while since my last math post. It seems that my previous assertion correlating the quality of question with the period of final exams could not have been further from the truth. It now seems quite likely that the occurrence of a few “good” questions on Yahoo Answers in a short period of time a few weeks bac... |
@Secret et al hows this for a video game? OE Cake! fluid dynamics simulator! have been looking for something like this for yrs! just discovered it wanna try it out! anyone heard of it? anyone else wanna do some serious research on it? think it could be used to experiment with solitons=D
OE-Cake, OE-CAKE! or OE Cake is ... |
The theorem is: Let be f, g : X→Y two continuous maps between topogolical spaces and
H : X$\times$[0, 1] a homotopy such that H(x,0)=f(x) and H(x,1)=g(x).
Given $x_0\in X$ let be $y_0=f(x_0)$, $y_1=g(x_0)$ and $\tau(t)=H(x_0,t)$ a path in Y from $y_0$ and $y_1$.
Then, $g_*=\varphi_{[\tau]}\circ f_*$
i.e. $\require{AMSc... |
I am struggeling to derive the squared-bias and variance based on an eigendecomposition for the OLS-procedure.
The model
Consider the univariate model $y_i = f(x_i) + \epsilon_i, \ i = 1, \dots, n$ with $E(\epsilon_i)=0$ and $Var(\epsilon_i)=\sigma^2$.
Let $S$ be a projection matrix (obtained by OLS) such that the fitt... |
In the paper http://www.sciencedirect.com/science/article/pii/S0045782509003521, an HDG element-local equation is described on page 584 equation (4), with one of the equations taking the following form
$$-(u_h,\nabla q)_K = -\left\langle\hat{u}_h \cdot n, q - \bar{q}\right\rangle_{\partial K}$$
Which is the variational... |
The
amsmath package provides a handful of options for displaying equations. You can choose the layout that better suits your document, even if the equations are really long, or if you have to include several equations in the same line.
Contents
The standard LaTeX tools for equations may lack some flexibility, causing o... |
Consider the wave equation:
$$ \square A(t,x^i) = S(t,x^i) , $$
where $\square = -\partial_\mu \partial^\mu = \partial_t ^2 - \nabla^2 $, $S(t,x^i)$ is the source term and $A(t,x^i)$ is the field of interest.
There are various ways to find the Green's function for the wave equation.
$$ \square G(t,x^i) = \delta^{(4)}(t... |
Linear code constructors that do not preserve the structural information¶
This file contains a variety of constructions which builds the generator matrixof special (or random) linear codes and wraps them in a
sage.coding.linear_code.LinearCode object. These constructions aretherefore not rich objects such as
sage.codin... |
principal or initial loan balance Interest rate Loan term Loan product, important parameter which fully specifies a loan Repayment rate (dollars per time) \(P = \frac{rB_0}{1- e^{-rt_\text{term}}}\) Fraction of initial payment to interest Total payment to interest Sum of all payments Overpay ratio
Because most loans ar... |
Given \(n\) circles with radius \(r_i\) and value \(v_i\) try to fill a rectangle of size \(W\times H\) with a subset of the circles (such that they don't overlap) and that maximizes the total value of the "payload".The data looks like:
The area was computed with the familiar formula: \(a_i = \pi r_i^2\). The mathemati... |
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... |
Notation. By $\mathbb{Z}_{(2)}$, I mean the localization of $\mathbb{Z}$ at the prime ideal $(2).$ So basically, this is obtained by adjoining a multiplicative inverse for every positive prime number distinct from $2$. Equivalently, we can think of $\mathbb{Z}_{(2)}$ as the set of rational numbers with odd denominator.... |
$0 \rightarrow \mathbb{Z} \stackrel{f}{\rightarrow} \mathbb{Z}^3 \stackrel{h}{\rightarrow} H_1(X) \rightarrow 0$
Where $f(1) = (1,0,2)$
Then $H_1(X) \cong \frac{\mathbb{Z}^3}{im(f)} \cong \frac{\mathbb{Z}^3}{\langle 1,0,2 \rangle}$
Is this all correct so far? The image of $1$ under $f$ is $(1,0,2)$, but i'm just confus... |
[I already posted this question on the math forum of stackexchange and I was advised that I should post this question here]
In Evans and Jovanovic (1989) you will find a model for entrepreneurs with credit constraints. The part that is important for my question follows. Here it is the production function and the income... |
I'm making a compound fraction for a review worksheet. I currently have this:
\begin{multicols}{2}\begin{enumerate}\itemSimplify\[\dfrac{\frac{3}{5} + \frac{5}{5x}}{1 - \frac{1}{10x}}\]
The problem is that the fractions 3/5 are extremely tiny. If I replace \dfrac with \frac, I see that they are exactly the same. I want... |
The theorem is called the noiseless coding theorem, and it is often proven in clunky ways in information theory books. The point of the theorem is to calculate the minimum number of bits per variable you need to encode the values of N identical random variables chosen from $1...K$ whose probabilities of having a value ... |
Does a bond paying floating coupon
LIBOR, still has the value at par when we use the
OIS as discount factor?It seems only when the Identity:$$B(t,T_2)(1+(T_2-T_1)F(t,T_1,T_2))=B(t,T_1)$$still holds, the proposition above will be true. Here $B(t,T)$ is the value of zero coupon bond, $F(t,T_1,T_2)$ is the
forward LIBOR.
... |
In thermodynamics,
chemical potential of a species is energy that can be absorbed or released due to a change of the particle number of the given species, e.g. in a chemical reaction or phase transition. The chemical potential of a species in a mixture is defined as the rate of change of free energy of a thermodynamic ... |
I have been given the following homework problem... struggling. Any help would be appreciated.
With the following functions state;
a) State if the function is monotone. 1
b) Decide if it is injective, surjective or bijective on the given domain.
c)Find the Supremum and Infimum (if they exist); in each case state whethe... |
Electronic Journal of Probability Electron. J. Probab. Volume 24 (2019), paper no. 23, 29 pp. The speed of critically biased random walk in a one-dimensional percolation model Abstract
We consider biased random walks in a one-dimensional percolation model. This model goes back to Axelson-Fisk and Häggström and exhibits... |
Jacob, KT and Matthews, T and Hajra, JP (1990)
Low oxygen potential boundary for the stability of $YBA_2Cu_3O_{7−\delta}$. In: Materials Science and Engineering B, 7 (1-2). pp. 25-29.
PDF
Low_Oxygen_Potential_Boundary_for_the_Stability_of_YBa2Ctl307__6.pdf
Restricted to Registered users only
Download (432kB) | Request ... |
Briefly,
Question: Is it "good enough" to use least prime factor in choosing a maximal set of coprime integers in an interval?
The post title comes from a 1993 paper of Erdos and Sarkozy. They define some functions and show their asymptotic growth without showing explicit bounds. To restate their theorem 7, given natur... |
I am dealing with the vector field:
$$v = \dfrac{\hat{\mathscr r} }{{\mathscr r}^2}$$
And I am studying its divergence. If we compute it we get:
$$\nabla\cdot\left(\dfrac{\hat{\mathscr r} }{{\mathscr r}^2}\right) = 0, \qquad {\mathscr r} \ne 0.$$
I understand we are dealing with a delta function, which explains why we ... |
The time series is governed by the equation $S(T)=S(0)e^{(\mu-\frac{\delta^2}{2})T+\delta(w(T)-w(0))}$, in which $w(t)$ is a standard Brownian motion. Now given the data $\{S(t)\}_{t=0}^{t=T}$， how to estimate $\delta$ and $\mu$?
By considering the log of the time series, i.e.
$$ \{\log{S(t)}\}_{t=0}^{t=T}$$
we have
$$... |
GloVe word vectors
GloVe stands for Global Vectors for word representation. Previously we were picking up context (c) and target(t) in the window randomly. GloVe makes this selection explicit.
$X_{ij}$ = NUmber of times $i$ appear in context of $j$.
Here $i$ and $j$ play the role of context (c) and target (t). The defi... |
John's answer is a good one, I just wanted to add some equations and addition thought. Let me start here:
Heating is really only significant when you get a shock wave i.e. above the speed of sound.
The question asks specifically about a $200^{\circ} C$ increase in temperature in the atmosphere. This qualifies as "signi... |
Notice:
If you happen to see a question you know the answer to, please do chime in and help your fellow community members. We encourage our fourm members to be more involved, jump in and help out your fellow researchers with their questions. GATK forum is a community forum and helping each other with using GATK tools a... |
A point charge \(Q\) is at the centre of a sphere of radius \(r\). Calculate the \(D\)-flux through the sphere. Easy. The magnitude of \(D\) at a distance \(a\) is \(Q/(4(\pi r^2)\) and the surface area of the sphere is 4\(\pi\)
r 2. Therefore the flux is just \(Q\). Notice that this is independent of \(r\); if you dou... |
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Below I show a neat application of perfect hashing, which is one of my favorite (cluster of) algorithms. Amazingly, we use it to obtain a purely information-theoretic (rather than algorithmic) statement.
Suppose we have a finite universe $U$ of size $n$ and a $k$-element subs... |
I study by myself with the QFT, in the page 197 of book of Lewis H. Ryder (2nd edition), The author wrote that he take the functional derivative of equation 6.69:
$$\frac {\delta\widehat{Z}[\phi]}{\delta\phi}$$
where $$\widehat {Z}[\phi]=\frac{{e}^{iS}}{\int{{e}^{iS}}{\cal D}\phi}\tag{6.69}$$
and
$$S=-\int{\left[\frac ... |
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The circle space of a spherical circle plane
(BELGIAN MATHEMATICAL SOC TRIOMPHE, 2014)
We show that the circle space of a spherical circle plane is a punctured projective 3-space. The main ingredient is a partial solution of the problem of Apollonius on common touching circles.
On kl... |
The Annals of Statistics Ann. Statist. Volume 24, Number 3 (1996), 1235-1249. On the existence of inferences which are consistent with a given model Abstract
4 If ${p_{\theta}$ is a $\sigma$-additive statistical model and $\pi$ a finitely additive prior, then any statistic
T is sufficient, with respect to a suitable in... |
There are many possible definitions; see e.g. Rutanen et al. [1].
Generally speaking, if you define your $O$ over domain $X$, you will need an order relation $\leq$ on $X$. The definition then reads:
$\qquad O(g) = \{ f : X \to \mathbb{R}_{\geq 0} \mid \exists\,x_0 \in X, c \in \mathbb{R}_{>0}.\ \forall\,x\in X.\\\qqua... |
The electric field and the magnetic field are not the same thing. An electric dipole with positive charge on one end and negative charge on the other is not the same thing as a magnetic dipole having a north and a south pole. More specifically: An object can have positive charge but it can’t have “northness”.
On the ot... |
If the external potential $V$ in the time-dependent Schroedinger equation doesn't depend on time, then we can separate the wavefunction as spatial part and time part.
$$ \Psi(x,t)=\psi(x) \theta(t) $$
$\psi(x)$ is the solution of well-known time-independent Schroedinger equation, and $\theta(t) = e^{-Et/\hbar}$. Then t... |
''Diamond Paradox'' by Diamond (1971)
This is a "less-known paradox," usually put as a counter to famous Bertrand paradox. It is a starting point in the literature on informational frictions in consumer markets, and the scientists in the field agree on its significance.
Its idea is diametrically opposite to that of Ber... |
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Search for new resonances in $W\gamma$ and $Z\gamma$ Final States in $pp$ Collisions at $\sqrt{s}=8\,\mathrm{TeV}$ with the ATLAS Detector
(Elsevier, 2014-11-10)
This letter presents a search for new resonances decaying to final states with a vector boson produced in association with a... |
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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... |
Answer
30.4 meters per second
Work Step by Step
We first must find the value of $\mu$: $\mu = \sqrt{\frac{14}{18^2}}=.04$ Thus, we can find the new velocity. $ v = \sqrt{\frac{F}{\mu}}=\sqrt{\frac{40}{.0432}}=30.4 \ m/s$
You can help us out by revising, improving and updating this answer.Update this answer
After you cl... |
(a) If $AB=B$, then $B$ is the identity matrix. (b) If the coefficient matrix $A$ of the system $A\mathbf{x}=\mathbf{b}$ is invertible, then the system has infinitely many solutions. (c) If $A$ is invertible, then $ABA^{-1}=B$. (d) If $A$ is an idempotent nonsingular matrix, then $A$ must be the identity matrix. (e) If... |
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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 i... |
Basic LaTeX Equation Maker supports a subset of LaTeX commands, including the most commonly used commands. Common Commands
Whitespace \space Normal text \text { content } Bold text \textbf { content } Italic text \textit { content } Underline \underline { content } Superscripts base^{ super } Subscripts base_{ sub } Sq... |
Chemical Bonding and Molecular Structure Molecular Orbital Theory MOED (molecular orbital energy diagram) : (from O 2 molecule onwards) \sigma 1s < \sigma^{*}1s <\sigma2s < \sigma^{*}2s < \sigma2p_{z} < \pi2p_{x} = \pi2p_{y} < \pi^*2p_{x} < \sigma^* 2p_{z} MOED (From N 2 molecule onwards) \sigma 1s < \sigma^{*}1s <\sig... |
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Change to browse by: References & Citations Bookmark(what is this?) Computer Science > Social and Information Networks Title: Comparative Resilience Notions and Vertex Attack Tolerance of Scale-Free Networks
(Submitted on 1 Apr 2014)
Abstract: We are concerned with an appropriate mathemati... |
"La variante di Lüneburg" and China's rice productionIn 1993, Paolo Maurensig, an Italian writer from Gorizia, wrote a novel entitled "La variante di Lüneburg" (Adelphi, 1995, pp. 164, ISBN 88-459-0984-0). The novel is set in Nazi Germany during World War II and the main theme is the game of chess.
At the beginning of ... |
I am trying to derive Galerkin type weak formulation for the Stokes equations. I'm having a bit of a problem reconciling the notation in the integration by parts. I know that the answer I'm looking for is: $ \int_\Omega \Delta\mathbf{u}\cdot\mathbf{v}d\Omega = \int_\Gamma (\mathbf{n}\cdot\nabla\mathbf{u})\cdot\mathbf{v... |
To be frustratingly concise, they are the same quantity. In fact, that was the whole genius of Einstein to realize that the inertia of a particle (the "measurement of how much a particle accelerates given a force") is really a measure of its energy. Thus, the title of his $1905$ paper:
"Does the . inertia of a body dep... |
Lee and Bryk (1989) analyzed a set of data in illustrating the use of multilevel modeling. The data set includes mathematics scores for senior-year high school students from 160 schools. For each student, information on her/his social and economic status (SES) is also available. For each school, data are available on t... |
Surely yes, and in more generality, but can it be proved?
It seems that most, if not all, statements about quadratic forms representing primes fall back on algebraic number theory (i.e. splitting of primes in $\mathbb{Q}(\sqrt{7})$) for their proofs, and so are incompatible with the condition that $0 < y < x/10$.
Some ... |
By the electrostatic induction a total charge $-q$ will appear in the inner surface of $A$ (let's call it $S_{A, int}$) with a density $\sigma_{A,int}$, and a total charge $+q$ will appear on the outer surface $S_{A,ext}$ with a density $\sigma_{A,ext}$.
Let's call the electrostatic fields generated by the charge densi... |
Re: One form <-----> vector fieldThat makes sense, but doesn't that only work for a perfect differential df, whose coefficients are \frac{\partial f }{\partial x^i}? If df is not the differential of some function f, but instead a general 1-form, would you still writedf[V]= V[f]only this...
Re: One form <-----> vector f... |
What are the best current lower bounds for time and circuit depth for 3SAT?
As far as I know, the best known "model-independent" time lower bound for SAT is the following. Let $T$ and $S$ be the running time and space bound of any SAT algorithm. Then we must have $T \cdot S \geq n^{2 \cos(\pi/7) - o(1)}$ infinitely oft... |
Rayleigh-Bénard Convection A model of thermal convection Rayleigh-Bénard convection (RBC) is the buoyancy-driven flow of a fluid heated from below and cooled from above.
This model of thermal convection is a paradigm for nonlinear and chaotic dynamics, pattern formation and fully developed
turbulence (Kadanoff 2001 [1]). ... |
I've a question about the effect of aliasing on the magnitude of autocorrelations. From a simulation in MATLAB, I don't see any effect of aliasing or any need to anti-alias filter when I take the magnitude of the autocorrelation. Which means I can undersample the data and then take the autocorrelation. There is a paper... |
A
Function assigns to each element of a set, exactly one element of a related set. Functions find their application in various fields like representation of the computational complexity of algorithms, counting objects, study of sequences and strings, to name a few. The third and final chapter of this part highlights th... |
L # 1
Show that
It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
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Last edited by krassi_holmz (2006-03-09 02:44:53)
IPBLE: Increasing Performance By Low... |
I am doing an Intermediate Microeconomics class... in a 2*2*2*2 economy, I know that MRS (marginal rate of substitution) is supposed to be equal to MRTS (marginal rate of technical substitution) in order for it to be a competitive equilibrium. Why is this? I understand that supply is supposed to be equal to demand... T... |
I've confused myself about a rather trivial point. I could write the Lagrangian of the Dirac equation as
$\cal L = {\rm i}/2 \left( \bar \psi \gamma^\nu \partial_\nu \psi + {\rm cc} \right)$
which, for all I can tell is the same as
${\rm i}/2 \left( \partial_\nu (\bar \psi \gamma^\nu \psi) \right) $
So, assuming the cu... |
Cone Angle
When a sample is inserted at the focus of a convergent beam (at the focal plane), then biconical transmittance should be calculated:
\[T_b=\frac{total \; flux\; in \;output \;beam}{total\; flux\; in\; input \;beam}\].
The biconical transmittance \(T_b\) can be calculated as follows:
\[ T_b=\frac{\int_{\varph... |
In the ACTIVE study, we have data on verbal ability at two times (hvltt and hvltt2). To investigate the relationship between them, we can generate a scatterplot using hvltt and hvltt2 as shown below. From the plot, it is easy to observe that those with a higher score on hvltt tend to have a higher score on hvltt2. Cert... |
Statistics Variance and Standard Deviation Standard deviation (σ) = \tt \sqrt{variance} For the Individual series, the standard deviation is \tt \sigma = \sqrt{\frac{\sum (x_i - M)^{2}}{n}} (general method) (Actual mean type) For the individual series, the standard deviation is \tt \sigma = \sqrt{\frac{\sum x_i^{2}}{n}... |
The wave is
$\bar{E} = E_{0} sin(\frac{2\pi z}{\lambda} + wt) \bar{i} + E_{0} cos(\frac{2 \pi z}{\lambda}+wt) \bar{j}$
Let's simplify with $z = 1$. Now the xy-axis is defined by parametrization $(sin(\frac{2\pi }{\lambda}+wt), cos(\frac{2\pi }{\lambda} + wt)$ where $t$ is time and $\lambda$ is wavelength. This parametr... |
In his celebrated paper "Conjugate Coding" (written around 1970), Stephen Wiesner proposed a scheme for quantum money that is unconditionally impossible to counterfeit, assuming that the issuing bank has access to a giant table of random numbers, and that banknotes can be brought back to the bank for verification. In W... |
Now that LIGO has finally measured gravitational waves using a huge laser interferometer, to me, the question remains, why was it possible? As it is explained in many news articles, gravitational waves are similar to water waves or electromagnetic waves, they just do not exist in a medium like water or space, but space... |
i am currently toying around with the behaviour of a classical relativistic point particle a bit. For a free one we get the action
\begin{align} S =\int_\tau - m\sqrt{- \dot X_\mu \dot X^\mu}. \end{align} This action is invariant to reparametrization of the worldline parameter $\tau$, which i can see mathematically, bu... |
The fact is that, in the general case $$\vec{E} = -\vec{\nabla}V - \frac{\partial\vec{A}}{\partial t};$$(signs depend on conventions used) where $\vec{A}$ is called
vector potential. You can consult for example Wikipedia.
Let us consider homogeneous Maxwell equations:
$$\begin{cases}\vec{\nabla}\cdot\vec{B} = 0,\\\vec{... |
In his celebrated paper "Conjugate Coding" (written around 1970), Stephen Wiesner proposed a scheme for quantum money that is unconditionally impossible to counterfeit, assuming that the issuing bank has access to a giant table of random numbers, and that banknotes can be brought back to the bank for verification. In W... |
(I am reposting here a question I asked on stack overflow, since it actually sits right in between programming
(modeling of 2D physics) and physics proper (kinematics). I think I have the physics part of my solution right, but would be grateful to anyone who could provide a second look).
Issue:
I am modeling a simple d... |
This answer focuses more on minimalizing the code, rather than finding the source of the problem, as the top-voted answer does. It is intended to be concise and hands-on, but digestible rather than exhaustive. Suggestions for improvement welcome!
Here are some strategies for reducing your code, which will help you get ... |
Electrostatic Potential and Capacitance Potential due to a Point Charge, Electric Dipole and system of charges The potential at a point due to an Electric dipole is \tt V=\frac{P\cos\theta}{4\pi \varepsilon_{0}r^{2}} For a point on the axial line is \tt V=\frac{P}{4\pi \varepsilon_{0}r^{2}} For a point on the equatoria... |
I'm trying to understand Milnor's proof of the existence of exotic 7-spheres.
Milnor finds his examples among $S^{3}$ bundles over $S^{4}$ (with structure group $SO(4)$ ). Such a bundle can be described as follows:
Given $M$, an $S^{3}$ bundle over $S^{4}$, if we restrict $M$ to the northern (or southern) hemisphere of... |
Ideal derivative filter
Let $f(x)$ be a signal bandlimited to frequencies $(-\pi,\, \pi)$. Given $f(x)$ as input, the same $f(x)$ is given as output by a system that has as its impulse response the sinc function:
$$\operatorname{sinc}(x) = \left\{\begin{array}{ll}1&\text{if }x = 0,\\\frac{\sin(\pi x)}{\pi x}&\text{othe... |
Evaluate: $$\int_C \frac{e^z+\sin{z}}{z}dz$$ where, $C$ is the circle $|z|=5$ traversed once in the counterclockwise direction.
I can't find an anti-derivative to this function, and I am not sure one exists. I was thinking about using several theorems but each come up short. For instance, I cannot use the
Closed Curve ... |
In his webpage, Fabrice Bellard mentions an exotic formula for $\pi$ as follows $$\pi = \frac{1}{740025}\left(\sum_{n = 1}^{\infty}\dfrac{3P(n)}{{\displaystyle \binom{7n}{2n}2^{n - 1}}} - 20379280\right)\tag{1}$$ where \begin{align} P(n) = &-885673181n^{5} + 3125347237n^{4} -2942969225n^{3}\notag\\ &+1031962795n^{2} - ... |
[I have no idea about the history --though I do have interest, and would like the OP to post whatever his research reveals-- but this is how I like to approach the transition pedagogically. Pardon the length; I'll attempt to edit things down later.]
We'll enter the discussion at the point where we agree that $\sin\thet... |
A year ago I asked [this] (Proving a few properties of Bertrand curves) same question (without the "why can't a curve be a Bertrand mate of itself" part) - see that post if you want to know the essential definitions - and gave a partial answer to the first question (I showed it was constant, but hand-waved away a sign ... |
This question already has an answer here:
In my quantum mechanics textbook it says that the relation between the basis $|x\rangle$ and $|p\rangle$ is given by:
$\langle p | x \rangle = \Large \frac{e^{-ip x/ \hbar}}{\sqrt{2\pi \hbar}} \, .$
However, i'm not sure how to go about proving this relation. My idea was that t... |
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