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This post is a first step towards integrating the information transfer versions of the IS-LM model and the quantity theory. We'll begin with one of the basic equations from the information transfer framework:
$$ P = \frac{1}{\kappa}\frac{Q^d}{Q^s} $$
In the LM market, we have aggregate demand represented by $NGDP$ as a... |
Prologue: The big $O$ notation is a classic example of the power and ambiguity of some notations as part of language loved by human mind. No matter how much confusion it have caused, it remains the choice of notation to convey the ideas that we can easily identify and agree to efficiently.
I totally understand what big... |
Let $X \subset \mathbb R^n$, $f:X\to\mathbb R^m$, $x_0\in X$
Assumption: All partial derivatives of f at $x_0$ exist and are continuous
$\Rightarrow$ f is differentiable at $x_0$.
$\Rightarrow D_vf(x_0)=\nabla f(x_0)\cdot v$ (assuming $m=1$ for simplicity)
Which means that all directional derivatives of f at $x_0$ can ... |
The easiest way to find a differential equation that will provide wavefunctions as solutions is to start with a wavefunction and work backwards. We will consider a sine wave, take its first and second derivatives, and then examine the results. The amplitude of a sine wave can depend upon position, \(x\), in space,
\[ A... |
Edit: Edge cases suck; see comments. See also MWG Chapter 10 section C, D.
Suppose $(\vec x^*, \vec m^*)$ solves
$$\max \sum^I_{i=1} m_i + \phi_i(x_i)$$
but is not Pareto optimal.
$$\begin{align}\implies \exists \ (x_i', m_i') \quad \text{s.t.} \quad & u_i(x_i', m_i') \geq u_i(x_i^*, m_i^*) \quad \forall \ i = 1,\cdots... |
Could anyone recommend a method for the following least-squares problem:
find $R \in \mathbb{R}^{3 \times 3}$ that minimizes: $\sum\limits_{i=0}^N (Rx_i - b_i)^2 \rightarrow \min$, where $R$ is a unitary (rotation) matrix.
I could get an approximate solution by minimizing $\sum\limits_{i=0}^N (Ax_i - b_i)^2 \rightarrow... |
Decomposing the ELBO Rob Zinkov 2018-11-02
When performing Variational Inference, we are minimizing the KL divergence between some distribution we care about \(p(\v{z} \mid \v{x})\) and some distribution that is easier to work with \(q_\phi(\v{z} \mid \v{x})\).
\[ \begin{align} \phi^* &= \underset{\phi}{\mathrm{argmin}... |
Answering the question in the title, no, but during the course of writing the past few posts, I'd looked at the wikipedia article on general equilibrium. I saw this random bit about Sraffa:
Anglo-American economists became more interested in general equilibrium in the late 1920s and 1930s after Piero Sraffa's demonstra... |
I'm working on a qualifying exam question and I am stuck about how to even commence.
Let $M$ be a $3$ dimensional manifold. Suppose $\alpha$ is a $1$-form such that the $3$-form $\alpha \wedge d\alpha$ is nowhere zero. Show that there is a unique vector field $v$ such that $\alpha(v) = 1$ and $d\alpha(v,w) = 0$ for any... |
Prove that $$e^{\binom{n}{2}}>n!$$
$n \in \mathbb{Z_+}$
Sorry, couldn't attempt it.
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Prove that $$e^{\binom{n}{2}}>n!$$
$n \... |
Equivalence of Definitions of Integral Dependence Contents Theorem
For $x \in A$, the following are equivalent:
\((1):\quad\) \(\displaystyle \) \(\) \(\displaystyle \) $x$ is integral over $R$ \(\) \((2):\quad\) \(\displaystyle \) \(\) \(\displaystyle \) The $R$-module $R \left[{x}\right]$ is finitely generated \(\) \... |
Nodal solutions for an elliptic equation in an annulus without the signum condition
Bull. Korean Math. Soc. Published online August 20, 2019
Tianlan Chen, Yanqiong Lu, and Ruyun MaDepartment of Mathematics, Northwest Normal University
Abstract : This paper is concerned with the global behavior of components ofradial no... |
1. The problem statement, all variables and given/known data
A spherical capacitor consists of a spherical conducting shell charge [itex]-Q[/itex] concentric with a smaller conducting sphere of radius [itex]4.0[/itex] cm and charge [itex]Q[/itex]. The larger conducting shell has inner and outer radii of [itex]11.0[/ite... |
I can't seem to grasp the following:
Let $X_1 \sim \exp(\lambda_1), X_2 \sim \exp(\lambda_2)$ and independent.
Then $$ \mathbb{E}\left[X_1 | X_1 < X_2\right] = \frac{1}{\lambda_1 + \lambda_2} $$
Why? How do I get this result?
Also, is this somehow related to $ \mathbb{E}\left[\min(X_1,X_2)\right] = \frac{1}{\lambda_1 +... |
As motivation of the title, consider the shape of the function $e^{-x}\left(x+\lfloor x\rfloor^2\right)$ as plotted by WolframAlpha:
This exercise I believe that is very easy, let $\lfloor x\rfloor$ the floor function (... obviously we combine with this function when we want to define an integral of the kind hedgehog),... |
An \(n\)th order linear system of differential equations with constant coefficients is written as
\[ {\frac{{d{x_i}}}{{dt}} = {x’_i} } = {\sum\limits_{j = 1}^n {{a_{ij}}{x_j}\left( t \right)} + {f_i}\left( t \right),\;\;}\kern-0.3pt {i = 1,2, \ldots ,n,} \]
where \({x_1}\left( t \right),{x_2}\left( t \right), \ldots ,{... |
2019-09-12 12:25
Measurements of hadron production in $\pi^{+}$+C and $\pi^{+}$+Be interactions at 60 GeV/$c$ / Aduszkiewicz, A (NA61/SHINE Collaboration) Precise knowledge of hadron production rates in the generation of neutrino beams is necessary for accelerator-based neutrino experiments to achieve their physics goa... |
Say I want to find the n-th prime. Is there an algorithm to directly calculate it or must I do with sieving? I know always calculate the next prime with a sieve principle, but what if I want the n-th prime?
Duplicate:
Computer Science Stack Exchange is a question and answer site for students, researchers and practition... |
Let's put the succinct answer by @TheAlmightyBob into an abstract model:
We want to model the labor market.
Markets' structure assumptions: goods market and labor markets are perfectly competitive. All participants are "too small" economically, and they cannot affect equilibrium price through their quantities demanded/... |
I am having an issue classifying $\mathbb{Z}\times\mathbb{Z}/\langle(0,3)\rangle$ according to the fundamental theorem of finitely generated abelian group (i.e. finding what $\mathbb{Z}\times\mathbb{Z}/\langle(0,3)\rangle$ is isomorphic to). I think It should $\mathbb{Z}$, but I am not sure why. Thanks!
Well, it is not... |
I have the next system of ODEs: $$ \frac{1}{2}\sigma^2 p''_n(x)+x p'_n(x)+p_n(x)-\frac{p_n(x)-p_{n-1}(x)}{\Delta t}=0,$$ $$p_1(a)=p(b)=0;\quad p_0(x)=0.1,\quad n=1.\dots N, $$ which was derived from the elliptic pde by method of lines: $$\frac{\partial p}{\partial t}=p+x\frac{\partial p}{\partial x}+\frac{1}{2}\sigma^2... |
Berkey et al. (1998) describe a meta-analytic multivariate model for the analysis of multiple correlated outcomes. The use of the model is illustrated with results from 5 trials comparing surgical and non-surgical treatments for medium-severity periodontal disease. Reported outcomes include the change in probing depth ... |
I am working the following USNCO problem (#41 from 2002). Based on this question and answer Deriving a reduction potential from two other reduction potentials, it seems that $\Delta G$ must be calculated and then added. However, when I do this, I get an answer that is not one of the given choices.
The problem is:
Use t... |
Your intuition is correct. The factor $A$ changes with temperature.
This article details how the value of $\ce{A}$ for an elementary, bimolecular reaction between $\ce{P}$ and $\ce{Q}$ can be derived to be:
$$A_{\ce{PQ}}=N_\ce{P}N_\ce{Q}d^2_{\ce{PQ}}\sqrt{\frac{8k_\mathrm{B}T}{\mu}}$$
The RHS is clearly a function of t... |
I'm trying to understand why is it possible to describe every diagonal line in the Ulam-Spiral with an quadratic polynomial $$2n\cdot(2n+b)+a = 4n^2 + 2nb +a$$ for $a, b \in \mathbb{N}$ and $n \in 0,1,\ldots$.
It seems to be true but why?
Wikipedia says: "The pattern also seems to appear even if the number at the cente... |
This problem arises from a Bayesian statistical modeling project. In order to compute with my model, I need to perform an integration in which part of the integrand is the "Pólya" or "Dirichlet-Multinomial" Distribution,
$$p(n\mid \alpha) = \frac{(N!) \Gamma(K\alpha)}{\Gamma(\alpha)^K \Gamma ( N + K\alpha)} \prod_{i=1}... |
Let $G$ be a context free grammar in Chomsky normal form (CNF) with language $L(G)\subseteq \Sigma^n$. In other words, all strings generate by $G$ have size $n$.
Say that a string $w\in L(G)$ has height $h$ if $w$ has a parse-tree of height at most $h$. Say that $G$ has height $h$ if each string $w\in L(G)$ has height ... |
It should be: "$f:R\to R'$ is a
ring homomorphism". Otherwise this is not true. Indeed, if $f$ is not a ring homomorphism then $f(ab)\neq f(a)f(b)$ for some $a,b\in R$. It is clear that $\varphi(ab)\neq\varphi(a)\varphi(b)$ as well where $a,b$ are now treated as polynomials of degree $0$. Note that for polynomial $r$ o... |
It is certainly not required but usually one writes a weighted sum of probability density functions where the sum of the weights equals 1. In your example the sum of the weights is $\sqrt{\pi}$. One can rewrite the pdf of $X$ as
$$f_X(x)={{2m^m x^{2m-1}}\over{\Gamma(m)}}\sum_{i=1}^n w_i h(t_i)$$
with $\sum_{i=1}^n w_i=... |
We are here with you hands in hands to facilitate your learning & don't appreciate the idea of copying or replicating solutions. Read More>>
MTH101 Calculus And Analytical Geometry GDB Solution & Discussion
For a functiona pointand a positive numberFind
Moreover find a number such that
Note:
Please follow the following... |
The bounty period lasts 7 days. Bounties must have a minimum duration of at least 1 day. After the bounty ends, there is a grace period of 24 hours to manually award the bounty. Simply click the bounty award icon next to each answer to permanently award your bounty to the answerer. (You cannot award a bounty to your ow... |
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... |
The intensity of light (as calculated from time average of the poynting vector) is given by $I = (1/2) \epsilon v E_0^2$. Here the intensity is dependent on the velocity of light in the medium. The refractive index also depends on the velocity of light. So is it safe to say that the intensity of light depends on the re... |
I will refer to Qiaochu's excellent answer here as proof that if we define
$$f(N):=\sum\limits_{n=0}^N n^2$$
then $f$ is a polynomial of degree $3$.
It is easy to calculate the first few values of this sum. Namely,
$\begin{align}f(0) &= 0 \\f(1) &= 1 \\f(2) &= 5 \\f(3) &= 14\end{align}$
I claim that these four points a... |
I have two arbitrary vectors $\vec{x}$ and $\vec{x}'$ given in spherical coordinates $(|\vec{x}|=x,\theta,\phi)$ (as convention I take the "physics notation" given on Wikipedia http://en.wikipedia.org/wiki/Spherical_coordinate_system). I now want to rotate the coordinate system so that it's $z$-direction points along $... |
Kay, David, Styles, Vanessa and Süli, Endre (2009)
Discontinuous Galerkin finite element approximation of the Cahn--Hilliard equation with convection. SIAM Journal on Numerical Analysis, 47 (4). pp. 2660-2685. ISSN 0036-1429 Abstract
The paper is concerned with the construction and convergence analysis of a discontinuo... |
I am solving old problems from various qualifiers from different universities to prepare myself for an upcoming test. I came across this and wanted to ask if anyone can confirm my answers?
My answers:
** I use $\succeq$ to denote "at least as good as".
(a) A certainty equivalence, in general, is the amount of money $c(... |
A blog of Python-related topics and code.
The following code attempts to pack a predefined number of smaller circles (of random radii between two given limits) into a larger one.
The Morse oscillator is a model for a vibrating diatomic molecule that improves on the simple harmonic oscillator model in that the vibration... |
In layman's terms:
First let's start with the Fourier series, a method that Fourier wrote for the first time in a paper about heat diffusion modelling. The idea is that any continuous function can be approximated by adding up lots of sine an cosine functions. The more terms you use, the more accurate will be the approx... |
I want to evaluate
$$\lim_{x\rightarrow0^+}\frac{\log{x}}{e^{1/x}}$$
I know that for $x\rightarrow0^+$, $\log{x}\rightarrow-\infty$ and $e^{1/x}\rightarrow+\infty$.
This leads to an indeterminate form $\left[\frac{\infty}{\infty}\right]$, so I'm not sure what to do in these situations. Perhaps change the variable, but ... |
First, a disclaimer: I'm not sure I see the statistical validity of combining both linear and logistic regression
with the same measurement vectors $x_n$. I am going to assume you know what you are doing :-) and address the optimization question only.
Some quick and dirty approaches:
My Matlab toolbox CVX 2.1 can handl... |
On the quality of semidefinite approximations of uncertain semidefiniteprograms affected by box uncertainty Aharon Ben-Tal and Arkadi Nemirovski Let P(z) = A_0 + z_1 A_1 + ... + z_L A_L be an affine mapping taking valuesin the space of m x m real symmetric matrices such that A_0 is positivesemidefinite. Consider the fo... |
Mohammadi, B., Alizadeh, E. (2019). Endpoints of generalized $\phi$-contractive multivalued mappings of integral type. Caspian Journal of Mathematical Sciences (CJMS), 8(2), 137-144. doi: 10.22080/cjms.2018.9207.1265
Babak Mohammadi; Esmaeil Alizadeh. "Endpoints of generalized $\phi$-contractive multivalued mappings of... |
The other contributor deleted his answer, maybe to let me extend my above comment, so here it is.
Let $T$ be a possibly nondeterministic transducer, and $L$ be a regular language. Modify $T$ into a transducer $T'$ that checks that its input is in $L$ (by, e.g., changing the state set into the Cartesian product of the s... |
You can usually view the cost function as the average squared error over some dataset with $N$ pairs of data, thus being defined as:
\begin{align}J &= \frac{1}{N} \sum_{i=1}^{N} \left(f(x_i,\beta) - y_i \right)^2\end{align}
We want the average error of our model (for all data we have) to decrease as we fine tune values... |
A blog of Python-related topics and code.
Two important parameters in plasma physics are the
electron Debye length, $\lambda_{\mathrm{D}e}$, a measure of the distance over which charge-screening effects occur and deviations from quasi-neutrality are observed, and the number of paricles in a "Debye cube" (of side length... |
CryptoDB Igor E. Shparlinski Affiliation: University of New South Wales Publications Year Venue Title
2005
EPRINT
Elliptic Curves with Low Embedding Degree
Motivated by the needs of the {\it pairing based cryptography\/}, Miyaji, Nakabayashi and Takano have suggested a construction of so-called MNT elliptic curves with... |
Continuing in this series (here, here and here), I found Cobb and Douglas's original paper from 1928 [pdf] where their least squares fit gives them the function:
P = 1.01 L^{3/4} C^{1/4}
$$
And they get a pretty good result:
Also, Noah Smith writes today:
Yes, in a Solow model you can tie capital K to observable things... |
We now summarize the postulates of Quantum Mechanics that have been introduced. The application of these postulates will be illustrated in subsequent chapters.
Postulate 1
The properties of a quantum mechanical system are determined by a wavefunction Ψ(r,t) that depends upon the spatial coordinates of the system and ti... |
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Production of light nuclei and anti-nuclei in $pp$ and Pb-Pb collisions at energies available at the CERN Large Hadron Collider
(American Physical Society, 2016-02)
The production of (anti-)deuteron and (anti-)$^{3}$He nuclei in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV has ... |
An RLC circuit is a simple electric circuit with a resistor, inductor and capacitor in it -- with resistance
R, inductance Land capacitance C, respectively. It's one of the simplest circuits that displays non-trivial behavior.
You can derive an equation for the behavior by using Kirchhoff's laws (conservation of the st... |
Knowing that at 25 °C the following galvanic cell: $$\ce{Pb~|~Pb(NO_3)_2~1M~||~PbS~saturated~|~Pb}$$ shows an $\mathrm{EMF} =0.413~\mathrm{V}$, find the $K_\mathrm{sp}$ of $\ce{PbS}$.
My Approach This is a concentration cell based on $\ce{Pb^2+}$. Since $\ce{Pb(NO3)2}$ dissociates completely, while $\ce{PbS}$ is a salt... |
I'll give this a shot, since I'm sufficiently disturbed by the advice given in some of the other answers.
Let $\vec{X},\vec{Y}$ be infinite bit sequences generated by two RNGs (not necessarily PRNGs which are deterministic once initial state is known),and we're considering the possibility of using the sequence $\vec{X}... |
An excess return is the payoff of a zero cost portfolio. For example: $R_i - R_f$ is an excess return. $c \left( R_i - R_f \right) $ is an excess return for any $c \in \mathbb{R}$,. More generally, $R_i - R_j$ is an excess return for any returns $R_i$ and $R_j$.
Excess returns are nice to work with because you cans sim... |
Your friend meant that all
complex numbers can be represented by such matrices.
$$a+bi = \begin{pmatrix} a & -b \\ b & a \end{pmatrix}$$
Adding complex numbers matches adding such matrices and multiplying complex numbers matches multiplying such matrices.
This means that the collection of matrices:
$$R = \left\{ \begin... |
Unicity of mermorphic functions concerning shared functions with their difference
Bull. Korean Math. Soc. Published online August 9, 2019
Bingmao Deng, Mingliang Fang, and Dan LiuInstitute of Applied Mathematics, South China Agricultural University
Abstract : In this paper, we investigate the uniqueness of meromorphic ... |
1) The region \(D\) bounded by \(y = x^3, \space y = x^3 + 1, \space x = 0,\) and \(x = 1\) as given in the following figure.
a. Classify this region as vertically simple (Type I) or horizontally simple (Type II).
Type: Type I but not Type II
b. Find the area of the region \(D\).
c. Find the average value of the functi... |
To use this tool, enter the required fields and click "Calculate"
This calculator uses the classical method of calculating gyroscopic stability, as described by Bob McCoy in his book Modern Exterior Ballistics. Because the classical method requires detailed bullet dimensions and aerodynamic coefficients, we apply the s... |
Definition:Euclidean Space Contents Definition
Let $S$ be one of the standard number fields $\Q$, $\R$, $\C$.
Let $S^n$ be a cartesian space for $n \in \N_{\ge 1}$.
Let $d: S^n \times S^n \to \R$ be the usual (Euclidean) metric on $S^n$.
Then $\tuple {S^n, d}$ is a
Euclidean space. Special Cases
Let the Euclidean metri... |
I'm new to quantum computing, so while studying Grover's algorithm I (and, I think a lot of other people too) could not help but notice that exactly the same operator is applied $\sqrt{N}$ times:
$$U = [2 \left| \psi \right> \left<\psi \right| - I ]\mathcal{O} $$
Of course, it depends on the oracle $\mathcal{O}$ and, a... |
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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 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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hep-th
Change to browse by: Bookmark(what is this?) High Energy Physics - Theory Title: Rectangular superpolynomials for the figure-eight knot
(Submitted on 1 Sep 2016 (v1), last revised 10 Sep 2016 (this version, v2))
Abstract: We rewrite the recently proposed differential expansion formula for... |
I am by no means an expert on LLL, but I have worked with it before. Please correct me if this answer is in some way incorrect.
Define a basis $\beta = \{v_1,v_2,\ldots,v_n\}$ for $\mathbb{R}^n$. Then the lattice $L$ generated by $\beta$ is the set of
integer linear combinations of $\beta$:
$$L = \{ m_1v_1 + \cdots + m... |
We're coming up to the end of a forecast I made almost three years ago. The previous update is here and everything is at the aggregated forecast post. It's a forecast I made in comparison with a NY Fed DSGE model, and it appears to be coming down to a tie. However that's a win for the five parameter monetary informatio... |
C SHIVAKUMARA
Articles written in Bulletin of Materials Science
Volume 19 Issue 4 August 1996 pp 607-613
A series of oxides LnBaCuCoO
5 (Ln=Pr, Nd, Sm, Dy, Gd, Ho and Er) have been synthesized by ceramic method. The oxides crystallize in a tetragonal structure, isostructural to YBaCuCoO 5. All the oxides in the series ... |
ISSN:
1937-1632
eISSN:
1937-1179
All Issues
Discrete & Continuous Dynamical Systems - S
April 2013 , Volume 6 , Issue 2
Issue dedicated to Michel Frémond on the occasion of his 70th birthday
Select all articles
Export/Reference:
Abstract:
This special volume of Discrete and Continuous Dynamical Systems - Series S is de... |
I was studying special relativity and i found this derivation of the Lorentz transformations \begin{equation} \left( \begin{array}{cccc} x'^0 \\ x'^1 \\ x'^2\\ x'^3 \end{array} \right)= \left( \begin{array}{cccc} \gamma & -\gamma \beta & 0& 0 \\ -\gamma \beta &\gamma &0 & 0 \\ 0 & 0 & 1 & 0\\ 0 & 0 & 0 & 1 \end{array} ... |
Interested in the following function:$$ \Psi(s)=\sum_{n=2}^\infty \frac{1}{\pi(n)^s}, $$where $\pi(n)$ is the prime counting function.When $s=2$ the sum becomes the following:$$ \Psi(2)=\sum_{n=2}^\infty \frac{1}{\pi(n)^2}=1+\frac{1}{2^2}+\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{3^2}+\frac{1...
Consider a random binary str... |
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... |
This is a naive question, out of my expertise; apologies in advance.
Goldbach's Conjecture and many other unsolved questions in mathematics can be written as short formulas in predicate calculus. For example, Cook's paper "Can Computers Routinely Discover Mathematical Proofs?" formulates that conjecture as
$$\forall n ... |
So far in my education career I have only met differential equations as small parts of courses on other stuff. Solving special cases as part of calculus, solving simple systems as a part of linear algebra. This coming semester I'm going to have two courses devoted entirely to differential equations, so I thought I woul... |
The procedure below assumes that the original distribution $X$ (the "signal") is non-Gaussian, and $Y$ is Gaussian (normally distributed noise.)
General procedure
The procedure is as follows:
Find a function $F$ that applied to a collection of real numbers produces one value (say, 0) for normally distributed data and o... |
Bayes' Rule for Ducks
Sunday February 23, 2014
You look at a thing.
Is it a duck?
Re-phrase: What is the probability that it's a duck, if it looks like that?
Bayes' rule says that the probability of it being a duck, if it looks like that, is the same as the probability of any old thing being a duck, times the probabili... |
Inertia
In power systems engineering, "inertia" is a concept that typically refers to rotational inertia or rotational kinetic energy. For synchronous systems that run at some nominal frequency (i.e. 50Hz or 60Hz), inertia is the energy that is stored in the rotating masses of equipment electro-mechanically coupled to ... |
I think the Op's proof is correct assuming both functions are entire. However, even if $F(x)$ is entire, the fractional iterate is in general not entire. The Op's result does not hold if the fractional iterate is not entire
$$F^{o\frac{1}{n}}(x)\;\;\;\;h(x)=F^{o \frac{1}{2}}(x)\;\;\;\;h(h(x))=F(x)$$
If the half iterate... |
Suppose we have summary estimates (e.g., estimated average effects) obtained from two independent meta-analyses or two subgroups of studies within the same meta-analysis and we want to test whether the estimates are different from each other. A Wald-type test can be used for this purpose. Alternatively, one could run a... |
We consider the double semion model proposed in Levin and Wen's paper
In their paper, the double semion model is defined on a honeycomb lattice.
Now I am trying to study the same model on a square lattice.
Question 1: Is the following Hamiltonian correct?
$$H=-\sum_{\textrm{vertex}} \prod_{k \in \textrm{vertex}}\sigma_... |
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Production of Σ(1385)± and Ξ(1530)0 in proton–proton collisions at √s = 7 TeV
(Springer, 2015-01-10)
The production of the strange and double-strange baryon resonances ((1385)±, Ξ(1530)0) has been measured at mid-rapidity (|y|< 0.5) in proton–proton collisions at √s = 7 TeV with the ... |
Interested in the following function:$$ \Psi(s)=\sum_{n=2}^\infty \frac{1}{\pi(n)^s}, $$where $\pi(n)$ is the prime counting function.When $s=2$ the sum becomes the following:$$ \Psi(2)=\sum_{n=2}^\infty \frac{1}{\pi(n)^2}=1+\frac{1}{2^2}+\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{3^2}+\frac{1...
Consider a random binary str... |
Coefficients of Expansion
Almost all materials expand on heating—the most famous exception being water, which contracts as it is warmed from 0 degrees Celsius to 4 degrees. This is actually a good thing, because as freezing weather sets in, the coldest water, which is about to freeze, is less dense than slightly warmer... |
I'm trying to solve the Poisson equation with pure Neumann boundary conditions, $$ \nabla^2\phi = \rho \quad in \quad \Omega\\ \mathbf{\nabla}\phi \cdot \mathbf{n} = 0 \quad on \quad \partial \Omega $$ using a Fourier transform method I found in Numerical Recipes. The method uses a discrete cosine transform, if you don... |
When you have a sequence of the form $a_{n+1}=f(a_n)$ that apparently does not lead to a closed formula for $a_n$, then you have to study the function $f(x)$.
When you graph the curve $y=f(x)=\dfrac{10}x-3$ in blue and $y=x$ in red, you notice there are two intersection points.
These are called fixed points of $f$ sinc... |
Exercise: Let $(S,\mathcal{A},\mu)$ be a measurable space and let $A_1,A_2,\ldots\in \mathcal{A}$. Define $B\subseteq S$ as $B = \bigcap\limits_{k = 1}^\infty\bigcup\limits_{n = k}^\infty A_n$. Show that $B\in\mathcal{A}$ and show that if $\sum_{n = 1}^\infty\mu(A_n)<\infty$ we have that $\mu(B) = 0$. What I've tried: ... |
I saw some data from the Atlanta Fed [1] on wage growth that looked remarkably suitable for a dynamic information equilibrium model (also described in my recent paper). One of the interesting things here is that it is a dynamic equilibrium between wages ($W$) and the rate of change of wages ($dW/dt$) so that we have th... |
The use of bootstrapping in the meta-analytic context has been suggested by a number of authors (e.g., Adams, Gurevitch, & Rosenberg, 1997; van den Noortgate & Onghena, 2005; Switzer, Paese, & Drasgow, 1992; Turner et al., 2000). The example below shows how to conduct parametric and non-parametric bootstrapping using t... |
I have a specific problem I have been set, I'm asking here because I can't really find an answer anywhere else.
Consider the scenario where a company offers some service to its users. The company has an enterprise value which is a function of the number, $n$, of users it has, $f(n)$.
When people use the service provide... |
Since I apparently can't seem to sit down and write anything that isn't on a blog, I thought I'd create a few posts that I will edit in real time (feel free to comment) until I can copy and paste them into a document to put on the arXiv and/or submit to the economics e-journal (H/T to Todd Zorick for helping to motivat... |
Earlier this semester, we saw how to approximate a function \(f (x, y)\) by a linear function, that is, by its tangent plane. The tangent plane equation just happens to be the (\(1^{\text{st}}\)-degree Taylor Polynomial of \(f\) at \((x, y)\), as the tangent line equation was the (\(1^{\text{st}}\)-degree Taylor Polyno... |
Very well, this is really more of a mathematics than a physics post, but so what. Besides, equations of this nature do pop up in physics problems from time to time.
Question (variants of which often appear on Quora): How do you solve the equation, \(x^a=b^x\)?
Equations of the type
$$x^a=b^x$$
do not usually have solut... |
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... |
Nagoya Mathematical Journal Nagoya Math. J. Volume 194 (2009), 91-147. The absolute Galois group of the field of totally $S$-adic numbers Abstract
For a finite set $S$ of primes of a number field $K$ and for $\sigma_{1}, \dots, \sigma_{e} \in \operatorname{Gal}(K)$ we denote the field of totally $S$-adic numbers by $K_... |
The rates of diffusion of two gases $\ce{A}$ and $\ce{B}$ are in the ratio $1:4$. If the ratio of their masses present in the mixture is $2:3$, the ratio of their mole fraction is?
My tries:
$\frac{r_1}{r_2}=\frac{1}{4}=\sqrt{\frac{M_2}{M_1}}\to\frac{1}{16}=\frac{M_2}{M_1}$, $M_i$ is molar mass of $i$.
Also given $\fra... |
Third, since $\sf{L} \subseteq \sf{NC}^2$, is there an algorithm to convert any logspace algorithm into a parallel version?
It can be shown (Arora and Barak textbook) given a $t(n)$-time TM $M$, that an oblivious TM $M'$ (i.e. a TM whose head movement is independent of its input $x$) can construct a circuit $C_n$ to co... |
I've become confused about spherical coordinates when dealing with electric fields.
The way I always understood spherical coordinates is something like the below picture. To define a vector, you give it a distance outwards (r), and two angles to get a final position. Below, the $\theta$ and $\phi$ components are measur... |
For simplicity, in the following we set the electric charge $e=1$ and consider a lattice spinless free electron system in an external static magnetic field $\mathbf{B}=\nabla\times\mathbf{A}$ described by the Hamiltonian $H=\sum_{ij}t_{ij}c_i^\dagger c_j$, where $t_{ij}=\left | t_{ij} \right |e^{iA_{ij}}$ with the corr... |
CentralityBin () CentralityBin (const char *name, Float_t low, Float_t high) CentralityBin (const CentralityBin &other) virtual ~CentralityBin () CentralityBin & operator= (const CentralityBin &other) Bool_t IsAllBin () const Bool_t IsInclusiveBin () const const char * GetListName () const virtual void CreateOutputObje... |
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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 ... |
X-ray protein crystallography is a technique by which it is possible to determine the three dimensional positions of each atom in a protein. Now over 100 years old, x-ray crystallography was first used to determine the three dimensional structures of inorganic materials, then small organic molecules, and finally macrom... |
This is not really an answer to your question, essentially because there isn't (currently) a question in your post, but it is too long for a comment.
Your statement that
A co-ordinate transformation is linear map from a vector to itself with a change of basis.
is muddled and ultimately incorrect. Take some vector space... |
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