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8.1 - One Sample Proportion
One sample proportion tests and confidence intervals are covered in Section 6.1 of the Lock
5 textbook.
In the last lesson you were introduced to the general concept of the Central Limit Theorem. The Central Limit Theorem states that if the sample size is sufficiently large then the sampling... |
I've read the proof for why $\int_0^\infty P(X >x)dx=E[X]$ for nonnegative random variables (located here) and understand its mechanics, but I'm having trouble understanding the intuition behind this formula or why it should be the case at all. Does anyone have any insight on this? I bet I'm missing something obvious.
... |
It seems that merely loading the
graphdrawing library can mess up drawing a tree using the standard TikZ syntax. Is there a way to avoid this unwanted effect?
For example:
\documentclass[tikz,border=10pt]{standalone}\usetikzlibrary{arrows.meta}\tikzset{ my tree/.style={ ->, nodes={draw, circle, minimum size = .5cm}, >=... |
a) Correct. The new equilibrium position occurs at distance $x=mg/k$ below the initial position (where the collision occurred). Alternatively it is $X=(M+m)g/k$ below the top of the unloaded spring (with no cymbal attached).
b) The new angular frequency of oscillations can be written down without any calculation : $\om... |
If the question is why the "$4\pi$" in the Coulomb constant (k=$\frac{1}{4\pi\epsilon_{0}}$), then an equally valid question could be why the "4$\pi$" in the magnetic permeability of vacuum, $\mu_{0}=4\pi\times10^{-7}H/m$ ?
Perhaps a clue can be found in the Maxwell's equation for the speed of electromagnetic wave (lig... |
a) Correct. The new equilibrium position occurs at distance $x=mg/k$ below the initial position (where the collision occurred). Alternatively it is $X=(M+m)g/k$ below the top of the unloaded spring (with no cymbal attached).
b) The new angular frequency of oscillations can be written down without any calculation : $\om... |
a) Correct. The new equilibrium position occurs at distance $x=mg/k$ below the initial position (where the collision occurred). Alternatively it is $X=(M+m)g/k$ below the top of the unloaded spring (with no cymbal attached).
b) The new angular frequency of oscillations can be written down without any calculation : $\om... |
Standard deviation formula is used to find the values of a particular data that is dispersed. In simple words, the standard deviation is defined as the deviation of the values or data from an average mean. Lower standard deviation concludes that the values are very close to their average. Whereas higher values mean the... |
You know that you have $\ell_1=\ell_2=1$, and the $m_{\ell_1}=+1$ while $m_{\ell_2}=-1$. Hence you must have (up to a factor of $1/\sqrt{2}$):$$\vert\psi_\pm\rangle = \vert 1 1\rangle_1\vert 1,-1\rangle_2 \pm \vert 1,-1\rangle_1\vert 1 1\rangle_2$$Now for the spin part, you can conclude likewise that$$\vert\chi_\pm\ran... |
a) Correct. The new equilibrium position occurs at distance $x=mg/k$ below the initial position (where the collision occurred). Alternatively it is $X=(M+m)g/k$ below the top of the unloaded spring (with no cymbal attached).
b) The new angular frequency of oscillations can be written down without any calculation : $\om... |
A particle moves along the x-axis so that at time t its position is given by $x(t) = t^3-6t^2+9t+11$ during what time intervals is the particle moving to the left? so I know that we need the velocity for that and we can get that after taking the derivative but I don't know what to do after that the velocity would than ... |
Suppose $(f_n)_{n >0}$ is a sequence of bounded continuous functions that converges locally uniformly to $f$.Is the following statement true?
$$\lim_n \sup_{\gamma \in (0,2)}\int_0^\infty \frac{f_n(x+t)-f_n(x)}{t^\gamma}dt = \sup_{\gamma \in (0,2)}\int_0^\infty \frac{f(x+t)-f(x)}{t^\gamma}dt $$
Suppose $(f_n)_{n >0}$ i... |
I posted an algorithm yesterday, that purported to solve the co-NP Complete 'Boolean Tautology Problem' in polynomial time.
Link to the algorithm : polynomial time algorithm
In that post, I presented the algorithm's motivation, and implementation, but not proof of validity. Herein I present said proof :
Recap :
The alg... |
Imagine I want to compute this
$$D^{\dagger2}D_{\alpha}(\Phi^*\Phi)$$
where the $D$-s are super-covariant derivatives and $\Phi$ is a chiral superfield. Following the notation of this review http://arxiv.org/abs/hep-ph/9709356 on supersymmetry, the chiral covariant derivatives are (page 33)
$$D_{\alpha}=\frac{\partial}... |
a) Correct. The new equilibrium position occurs at distance $x=mg/k$ below the initial position (where the collision occurred). Alternatively it is $X=(M+m)g/k$ below the top of the unloaded spring (with no cymbal attached).
b) The new angular frequency of oscillations can be written down without any calculation : $\om... |
Lets refactor and reword these statements for ease of thought.
Let $A(n)$ be $Θ(g(n))$.
Let $B(n)$ be $O(g(n))$.
Note that $A$ implies $B$ because $A$ is stronger than $B$.
This means for $A$ to be fulfilled we have to fulfill the criteria of $B$ and more. Therefore $A$ being fulfilled implies $B$ must also be.
Written... |
I am currently reading Computability and Logic by Boolos Burgess Geoffrey for the proof on "undecidability of first order logic". however, I find the notations a bit confusing. Can anyone recommend any resource website link/ video lecture or a book perhaps which will help me understand the proof of undecidability of fi... |
Linear Classifiers are one of the most commonly used classifiers and Logistic Regression is one of the most commonly used linear classifiers. The concepts we are going to learn here will actually extend a lot of other classification methods beyond linear classifiers. We’re going to learn the fundamental concepts, but a... |
I'm trying to do a series of exercises from Spivak's Calculus, in chapter 8, Least Upper Bounds.
I'm trying to tackle these two exercises, $5.$ and $^*.6$
From $5.$ I have proven the first claim
$(a)$ Let $x-y>1$. Prove there is an integer $k$ such that $x<k<y$.
P Let $\ell$ be the greatest integer such that $\ell \leq... |
Let me give a more « conceptual» Galois answer. First , fix an integer
m and consider a field K of characteristic not dividing m, containing a primitive m-th root of unity. Let F/K be a finite Galois extension, and let $E = F (\sqrt[m]{\alpha})$, with $\alpha \in K*$ . By Kummer theory, E only depends on the class $[\a... |
Interesting idea to use a grid. I doubt it will work for this question, since writing things in that grid format in a sense splits into arithmetic progressions modulo $p$, and usually saying things about the primes in a progression is harder.
However, I cannot help but mention that using a grid like that was applied br... |
The quantum harmonic oscillator $H=\frac{p^2}{2m}+\frac{1}{2}m\omega^2 x^2$ has energies $E_n=\hbar\omega(n+1/2)$, so to achieve "classical" energies $n$ must be very large.
My question is: how does appear the classical behaviour of a point mass in this potential, as energy increases? Classically, a point mass has
exac... |
I am looking at this paper : http://arxiv.org/pdf/1411.3419v1.pdf But somehow I am not being able to fish out a method to calculate this quantity called the "block-sensitivity".
Can someone kindly provide some discussion/examples or such?
I am wondering if there is a way to talk of "block sensitivity" of any function o... |
Mount Everest is 8,848 metres (29,028 feet) above sea level and is the result of a continental plate smashing into another continental plate. Can a tectonic process build a mountain that's even higher? (Volcanoes excluded!)
Found a article that used a simple analytical modelling to determine how high a mountain can be.... |
March 17th, 2017, 06:26 AM
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Posts: 3
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Trying to derive a chem problem
I am trying to find a rate law for a chemical reaction through mechanisms.
I have the mechanisms set out below and I am left with the rate listed
1: 2A + 2B -> 2C (fast)
2: 2C + B -> D (slow)
3: D + ... |
I'm studying fluid mechanics in more depth during my Ph. D. and there is something related with the diffusive term that has been bothering me for a long time. Looking at the convection diffusion equation: $$ \frac{\partial v}{\partial t} + a\cdot\nabla v - \nabla(\nu \nabla v )=f, $$
and thinking in Fick's law, it's no... |
Adjoint space of a topological vector space $E$
The vector space $E^{*}$ consisting of continuous linear functions on $E$. If $E$ is a locally convex space, then the functionals $f\in E^{*}$ separate the points of $E$ (the Hahn–Banach theorem). If $E$ is a normed space, then $E^{*}$ is a Banach space with respect to th... |
R V Anavekar
Articles written in Bulletin of Materials Science
Volume 6 Issue 6 December 1984 pp 1009-1012
The d.c. electrical conductivity of Na
2O-ZnO-B 2O 3 glass system has been measured as a function of temperature in the range of 350–600°K. The conductivity data show that the activation energy of Na + ions is dep... |
Notes - Linear Equation in one variable
Category : 7th Class
LINEAR EQUATION IN ONE VARIABLE
FUNDAMENTALS
Symbols used to denote a constant are generally, 'c', 'k' etc...
e.g., 2x - 6; here, 2 is the coefficient of \['x';\,\,'x'\] is the variable and \[-6\]is the constant. Similarly in \[ay+b;\,\,a\] is the coefficient... |
The time delay between neutrinos and photons does
not tell us directly about the absolute mass of the neutrinos. The time delay between a neutrino of mass $m$ and a massless neutrino does:$$\Delta t = \frac{d}{v} - \frac{d}{c} \approx 0.5 \left(\frac{mc^2}{E}\right)^2 d,$$where $\Delta t$ is the time delay in seconds, ... |
How can I prove that $$\int_0^1(1+\epsilon^{-1}e^{-\beta x/p\epsilon})dx\leq C,$$ where $\epsilon$ is a small parameter. In the limit $\epsilon^{-1}$ is unbounded so how is this integral bounded?
Just calculate:
$$\int_0^1 \! (1 + \epsilon^{-1}e^{-\beta x/p\epsilon}) \, dx$$ $$ = 1 + \epsilon^{-1}\int_0^1 \! e^{-\frac{... |
Let $X_n(\Bbb{Z})$ be the simplicial complex whose vertex set is $\Bbb{Z}$ and such that the vertices $v_0,...,v_k$ span a $k$-simplex if and only if $|v_i-v_j| \le n$ for every $i,j$. Prove that $X_n(\Bbb{Z})$ is $n$-dimensional...
no kidding, my maths is foundations (basic logic but not pedantic), calc 1 which I'm pr... |
(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... |
Carbon-14 has a half-life of 5,730 years. That means that after 5,730 years, half of that sample decays. After another 5,730 years, a quarter of the original sample decays (and the cycle goes on and on, and one could use virtually any radioactive isotope). Why is this so? Logically, shouldn't it take 2,865 years for th... |
An object is dropped from a building of height $h\,\mathrm m$. The object falls half the total distance to the ground during the last $1.00\,\mathrm s$ of its fall. Find the height of the building. Take the downward direction to be negative and $9.80\,\frac{\mathrm m}{\mathrm s^2}$ to be the magnitude of the accelerati... |
Circular motion in special relativity is somewhat tricky: Note that for circular motion, the acceleration in the spaceship travelling in a circle is
not zero, so the spaceship is not in a single frame of inertia.
Here is an interesting thought: Distances
perpendicular to the direction of motion are not subject to contr... |
I am studying through the book Thermodynamics and Statistical Mechanics by Walter Greiner and I’ve got a couple of doubts when I was reading about the classical ensembles, specially the Canonical ensemble (chapter 7, pages 159-160, Springer, 2004).
In the case of the canonical ensemble it is considered that the system ... |
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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... |
Computing the normal from vertex positions is quite simple using the vector cross product.
The cross product of two vectors $u$ and $v$ (noted $u \times v$, or sometimes $u \wedge v$) is a vector perpendicular to $u$ and $v$, of length $||u \times v|| = ||u|| \cdot ||v|| sin(\theta)$, with $\theta$ the angle between $u... |
If I have the hamiltonian of the simple harmonic oscillator
$$H = \frac{p^2}{2m} + \frac{1}{2} m \omega ^2 x^2 $$
Then it's partition function is:
$$Z = \frac{k_b T}{\hbar \omega} $$
You can get the average energy using $$U = \frac{\partial \ln{Z}}{\partial \beta} $$
where $\beta = k_b T $. in 1D , $$ U = kb * T $$
My ... |
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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... |
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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 ... |
that the electron and the proton are a particle pair
This may appear inconsistent with current theory, as it is widely assumed that particle pairs created in a single event, must have opposite charge and equal mass (matter/antimatter). This assumption turns out to be wrong.
We shall see that the difference in mass betw... |
We look here at the continuity of a sequence of functions that converges pointwise and give some
counterexamples of what happens versus uniform convergence. Recalling the definition of pointwise convergence
We consider here real functions defined on a closed interval \([a,b]\). A sequence of functions \((f_n)\) defined... |
"Abstract: We prove, once and for all, that people who don't use superspace are really out of it. This includes QCDers, who always either wave their hands or gamble with lettuce (Monte Zuma calculations). Besides, all nonsupersymmetric theories have divergences which lead to problems with things like renormalons, insta... |
Possible Duplicate: Showing that an inclusion is null homotopic
I asked this question here a while ago. Meanwhile I've come up with the following and was wondering if you could have a look and tell me if it's correct.
claim: $X$ homotopy equivalent to a point $\ast$ $\implies$ for all neighbourhoods $U$ of $\ast$ there... |
This is an old revision of the document!
If you need a pdf version of these notes you can get it here
The 2014 video was corrupted..again. I have made some changes on my computer and hopefully the problem will not happen again..
In a transformer two coils are coupled by an iron core so that the flux through the two coi... |
Suppose $W$ consists of all vectors $(x,y,z)$ such that $x + 2y - 3z = 0$. Which of the following is a basis for the orthogonal complement?
The answer is $(1,3,-2)$ but I don't understand that at all. How do I get to that answer?
Mathematics Stack Exchange is a question and answer site for people studying math at any l... |
Differential Equations
An equation involving derivatives of one or more dependent variables with respect to one or more independent variables is called a
. For example: differential equation
\begin{equation} \frac{d^{2}y}{dx^2} + xy \left( \frac{dy}{dx}\right)^2 = 0 \end{equation} \begin{equation} \frac{d^{4}x}{dt^4} +... |
The original renewal process has independent and identically disributed (i.i.d.) inter-renewal times $\{T_1, T_2, T_3, ...\}$. Thus, starting from time 0, renewals occur at times $\{T_1, T_1+T_2, T_1+T_2+T_3, ...\}$. Now fix a probability $p >0$. Independently place each renewal time to $P_1$ with prob $p$. So we get n... |
The most relative that I found on Google for
de morgan's 3 variable was: (ABC)' = A' + B' + C'.
I didn't find the answer for my question, therefore I'll ask here:
What is De-Morgan's theorem for
(A + B + C)'?
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professional... |
Weierstrass Substitution Proof Technique
The
Weierstrass Substitution is an application of Integration by Substitution. The substitution is: $u \leftrightarrow \tan \dfrac \theta 2$
for $-\pi < \theta < \pi$, $u \in \R$.
It yields:
\(\displaystyle \sin \theta\) \(=\) \(\displaystyle \frac {2 u} {1 + u^2}\) \(\displayst... |
Talk:Gamma-function $\Gamma$-function $ \newcommand{\abs}[1]{\left|#1\right|} \newcommand{\Re}{\mathop{\mathrm{Re}}} \newcommand{\Im}{\mathop{\mathrm{Im}}} $
A transcendental function $\Gamma(z)$ that extends the values of the factorial $z!$ to any complex number $z$. It was introduced in 1729 by L. Euler in a letter t... |
$$\frac {\Delta d_{t+1}}{d_t} = \frac {\frac {D_{t+1}}{Y_{t+1}}-\frac {D_{t}}{Y_{t}}}{\frac {D_{t}}{Y_{t}}} = \frac {D_{t+1}Y_{t}-D_{t}Y_{t+1}}{D_{t}Y_{t+1}}$$
$$=\frac {D_{t+1}Y_{t}}{{D_{t}Y_{t+1}}}-1 = \frac{Y_{t}}{Y_{t+1}}\cdot \left[{\frac {D_{t+1}}{D_{t}} -\frac {Y_{t+1}}{{Y_{t}}}}\right]$$
$$=\frac{Y_{t}}{Y_{t+1}... |
a) Correct. The new equilibrium position occurs at distance $x=mg/k$ below the initial position (where the collision occurred). Alternatively it is $X=(M+m)g/k$ below the top of the unloaded spring (with no cymbal attached).
b) The new angular frequency of oscillations can be written down without any calculation : $\om... |
What is the way to calculate the centroid of polygon? I have a concave polygon of 16 points, and I want know the centroid of that.
thanks
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up.Sign up to join ... |
Imagine we have a U-tube with constant diameter which is filled with water and oil in its equilibrium state (where water and oil are fully separated).
Then, we start inserting oil with constant speed at the end of the U-tube where the oil is.
My intuition says that if I take a control volume around the separation bound... |
In geometry, a tangent of a circle is a straight line that touches the circle at exactly one point, never entering the circle’s interior. It is a line through a pair of infinitely close points on the circle.
The tangent lines to circles form the subject of several theorems and play an important role in many geometrical... |
Yeah, this software cannot be too easy to install, my installer is very professional looking, currently not tied into that code, but directs the user how to search for their MikTeX and or install it and does a test LaTeX rendering
Some body like Zeta (on codereview) might be able to help a lot... I'm not sure if he doe... |
I've been reading about the equation, and all of the sources I found state that the equation preserves the trace, self-adjointness, and positivity of the density matrix.
The first two properties are easily verified, but I can't seem to figure out how to prove the positivity ($\langle\alpha|\rho|\alpha\rangle\geq0$) is ... |
While performing my excavation activities on no-answer questions, I found this very sensible one, to which, I guess, by now the OP has found an answer.
But I realized that I had various questions of my own regarding the issue of perfect separation in logistic regression, and a (quick) search in the literature, did not ... |
Reduced Mass
\[\mu\].
The educed for masses
\[m, \: M\]is labelled
\[\mu\]and satisfies
\[\frac{1}= \frac{1}{m} + \frac{1}{M} \rightarrow \mu = \frac{mM}{m+M}\]
The reduced mass is less that the total mass
\[M=m\]and in fact less than each individual mass.
Or ital equations and equations using Newton's Second Law of mo... |
Some NP-hard problems which are exponential on general graphs are subexponential on planar graphs because the treewidth is at most $4.9 \sqrt{|V(G)|}$ and they are exponential in the treewidth.
Basically I am interested if there are subexponential algorithms for PLANAR SAT which is NP-complete.
Let $\phi$ be a CNF form... |
When I click on the Wolfram output, I see $-\frac{2}{3} \sqrt{1 - \cos(3t)}$ only in the indefinite integral calculation: there are no bounds at all. (There are some specific, numerically computed definite integrals below the symbolic calculation, but this is not where $-\frac{2}{3} \sqrt{1 - \cos(3t)}$ is.)
This is im... |
Consider the Lagrangian density
\[ \mathcal{L} (\tilde{\phi},\phi) = \tilde{\phi}\left((\partial_t + D_A(r_A – \nabla^2)\right)\phi – u\tilde{\phi}(\tilde{\phi} – \phi)\phi + \tau \tilde{\phi}^2\phi^2. \]
Particle physicists of the 1970s would recognize this as the Lagrangian for a Reggeon field theory with triple- and... |
Intertemporal choice is the study of how people make choices about what and how much to do at various points in time, when choices at one time influence the possibilities available at other points in time. These choices are influenced by the relative value people assign to two or more payoffs at different points in tim... |
a) Correct. The new equilibrium position occurs at distance $x=mg/k$ below the initial position (where the collision occurred). Alternatively it is $X=(M+m)g/k$ below the top of the unloaded spring (with no cymbal attached).
b) The new angular frequency of oscillations can be written down without any calculation : $\om... |
Let $\Sigma = \{0, 1\}$ and $$L = \{ w \in \Sigma^* | w = \mathrm{odd}(w) · \mathrm{even}(w) \},$$ where $\mathrm{odd}(w) = w_1, w_3, w_5 \ldots{}$ and $\mathrm{even}(w) = w_2, w_4, w_6, \ldots{}$ are the words constructed from the characters in all the odd and even positions of the string. I.e. $w = 0110110110 \in L$,... |
This is related to my academic project
An extended finite state machine is a tuple $SM=(I,S,T)$ (simplified):
$I$ is the set of identifiers and it's divided into two sets Inputs and outputs, for simplification we will just consider boolean variables. Let $\sigma$ be the evaluation function $\sigma :I \to \{0,1\}$ which... |
EDIT AT 10/12/06:
ok, this is pretty much the best construction I can get, see if any one come up with better ideas.
Theorem. For each $n$ There is an $(5n+12)$-state NFA $M$ over alphabets $\Sigma$ with $|\Sigma|=5$ such that the shortest string not in $L(M)$ is of length $(2^n-1)(n+1)+1$.
This will give us $f(n) = \O... |
For a homework , I struggled to solve the following question but couldn't go further:
endowment of person 1 = (30,0)endowment of person 2 = (0,20)
utility functions are such that:\begin{eqnarray*} U (a_1,b_1) & = & \min(a_1,b_1) \\\\ U (a_2,b_2) & = & \min(4a_2,b_2).\end{eqnarray*}
What I am doing is setting a1 equal t... |
Help:Formatting
You can format your text using the formatting toolbar or wiki markup. Wiki markup can be thought of as a simplified version of html and it consists of normal characters like asterisks, single quotes or equation marks which have a special function in the wiki. For example, to format a word in
italic, you... |
Automatic Feature Extraction
Summary
"
Automatic Feature Extraction (AFE) is a technique by which approximate eigen-functions can be extracted from gram matrices constructed via kernel functions. These eigen-functions are features engineered by a particular kernel."" Some Mathematical Background¶ Definitions¶
Let X_k \... |
$$\newcommand{\holonomy}{[\mathcal{H\mathbb{O} \ell}]}$$
This answer is an expansion of Qmechanic's comment.
Holonomy
Holonomy can be imagined as the integral, or global version, of the Riemann Curvature Tensor. The Riemann Curvature tensor, indeed is
$$R_{\mu\nu\rho}^\sigma=\mbox{d}\holonomy$$
Where $\mathcal{\holonom... |
I have a circuit that consists of a voltage source in series with a resistor and a parallel of an inductor with a capacitor. I have to determine the resonance frequency of this circuit. I am very confused about this. First of all the impedance of the circuit is given by
$$Z=R+j(\frac{\omega L}{1-\omega^2 L C})$$
Now my... |
The Hubbard model is a model to describe electrons in a lattice. In general, the Hubbard model Hamiltonian $H$ contains two terms:
The kinetic term:$$T=-t\sum_{\langle ij\rangle\sigma} [c_{i\sigma}^\dagger c_{j\sigma} + h.c.] $$ The onsite Coulomb interaction term:
$$U=u\sum_{i=1}^N n_{i\uparrow}n_{i\downarrow}$$
So my... |
A particle moves along the x-axis so that at time t its position is given by $x(t) = t^3-6t^2+9t+11$ during what time intervals is the particle moving to the left? so I know that we need the velocity for that and we can get that after taking the derivative but I don't know what to do after that the velocity would than ... |
I have the following normal cone inclusion
$$-(A x + b) \in \mathcal{N}_\mathcal{C}(x) \qquad (1)$$
where $\mathcal{N}_\mathcal{C}$ denotes the normal cone to the convex set $\mathcal{C}$ at the point $x \in \mathcal{C}$. Matrix $A$ is non-symmetric.
Normally if $A$ would be symmetric, the convex optimization problem i... |
First of all, it is every integer (not every rational) that can be written as you have presented it as a sequence $a_n\in\{0,\ldots, p-1\}$. The number $1/p$ cannot be so represented.
To answer your cardinality question, there are at least two arguments that $\mathbb Z_p$ is uncountable, and thus that $\mathbb Q_p$ is ... |
It is relatively easy to derive the
potential energy stored into the magnetic field of an uniformly magnetized sphere of radius $R$ and total magnetic moment $\mu$ :\begin{equation}\tag{1}U_{\text{magn}} = \frac{\mu_0 \, \mu^2}{4 \pi R^3}.\end{equation}
The field is uniform inside the sphere, and dipolar on the exterio... |
$N_2,N_1$ are constant. $M_0$ is initial manifold, and evolving under volume preserving mean curvature flow. $A$ is the second fundamental form. $H$ is mean curvature. $h(t)$ is the average of mean curvature $$ h(t)=\frac{\int_{M_t} H d\mu}{\int_{M_t} d\mu} $$ And $$ H_T=\max_{t\in[0,T]} \max_{M_t}H $$ Then, how to get... |
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 ... |
6. Maclaurin and Taylor series – Edexcel Further Pure Mathematics 2 (FP2) What students need to learn: Third and higher order derivatives.
Derivation and use of Maclaurin series.
The derivation of the series expansion of \(e^x , \sin x, \cos x, ln (1 + x)\) and other simple functions may be required.
Derivation and use... |
Here $T$ is a sufficiently strong, effective theory of arithmetic,$\text{Pvbl}$ is the formalized provability predicate of $T$, and $\text{Con}(T)$ is the formalized statement of $T$'s consistency.
The case of #1, $T \vdash \text{Pvbl}(\text{Con}(T))$, is interesting.
If $T$ is satisfied by the standard model of arithm... |
Covariance Matrix is a measure of how much two random variables gets change together. It is actually used for computing the covariance in between every column of data matrix.
The Covariance Matrix is also known as dispersion matrix and variance-covariance matrix. The covariance between two jointly distributed real-valu... |
As the previous answer states, your problem is NP-hard by reduction from Max-Cut. It actually also turns out to be Poly-APX-hard by reduction from Max Independent Set (which is Poly-APX-complete). The reduction is almost a strict reduction, where the optimal solution for the instance of $P$ has as its cost the negative... |
Subalgebras whose root system is not a subset of the root system of the original algebra are called special subalgebras. Therefore, the generators are not a subset of the original's group generators.
That is not quite right. A special subalgebra is one such that their step operators do not form a subset of the algebra ... |
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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 ... |
I can’t actually take much credit for this. I made the initial conjecture that sparked this theorem, but my friend John Bytheway was the first person to codify the actual theorem and prove it. My proof of it is pretty independent of his, but I probably wouldn’t have come up with it unless I already knew the theorem was... |
This is a question that it is not homework but I would like clear.
I have this Proximal interpretation, that is: the solution of the problem is a fixed point of the following mapping: $$ x^{\ast} \in \ \ \arg \min_{x \in X_{\text{adm}}} \{\ \frac{1}{2}||x-x^{\ast}||^{2} + \gamma \ \ f(x) \} \ , \ \gamma >0$$
with $$X_{... |
While I was studying the Euler-Lagrange equation, Hamilton's principle of least action and geodesics, I started to wonder how to find the equations of motion of a particle restricted to a particular surface (e.g. the sphere). I know that the Lagrangian is defined as $L=K-U$ where $K$ is the kinetic energy and $U$ is th... |
15 minute read
In this summary, I assume you are familiar with Markov Decision Processes. In a Markov Decision Process (MDP), an agent interacts with the environment, by taking actions that induce a change in the state of the environment.
MDP: The robot knows the position
of the fuze bottle.
Image courtesy of the Perso... |
One of my data anaylsis pet peeves is false precision. Just because it is possible calculate a quantity to three decimal places doesn’t mean all of those decimal places are meaningful. This post explores how much precision is justified in the context of two common sports statistics: batting average in Major League Base... |
Question is to check which of the following holds (only one option is correct) for a continuous bounded function $f:\mathbb{R}\rightarrow \mathbb{R}$.
$f$ has to be uniformly continuous. there exists a $x\in \mathbb{R}$ such that $f(x)=x$. $f$ can not be increasing. $\lim_{x\rightarrow \infty}f(x)$ exists.
What all i h... |
The supply elasticity at a point is the willingness to produce more or less after the price has changed (due to whatever reason?).
$$\mu_{Q,P}=\frac{\partial Q_S/Q_S}{\partial P/P}=\frac{\partial Q_S}{\partial P}\cdot\frac{P}{Q_S}$$
Where $Q_S$ is the quantity supply function, $P$ is the price. $\frac{P}{Q_S}$ is the c... |
Response Surfaces¶
Response surfaces are inexpensive surroagates for expensive computational models.
Polynomial Ridge Function¶ class
psdr.
PolynomialRidgeFunction(
basis, coef, U)¶
A polynomial ridge function
derivative_roots()¶
Compute the roots of the derivative of the polynomial
profile_grad(
X)¶
gradient of the pr... |
@egreg It does this "I just need to make use of the standard hyphenation function of LaTeX, except "behind the scenes", without actually typesetting anything." (if not typesetting includes typesetting in a hidden box) it doesn't address the use case that he said he wanted that for
@JosephWright ah yes, unlike the hyphe... |
I'm working on the mathematical theory of parabolic equations. The prototype of such equations is heat equation given as follows : Let $\Omega$ be a bounded region of the space and $T>0$ a fixed time. In $\Omega_T=(0,T)\times \Omega$ we consider the following equation $$u_t =\alpha\Delta u -a(x)u,$$ $$u(0,x)=f(x),$$ wh... |
Definition:T3 1/2 Space Definition
Let $T = \left({S, \tau}\right)$ be a topological space.
$\left({S, \tau}\right)$ is a $T_{3 \frac 1 2}$ space if and only if: For any closed set $F \subseteq S$ and any point $y \in S$ such that $y \notin F$, there exists an Urysohn function for $F$ and $\left\{{y}\right\}$. Variants... |
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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 in... |
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