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A contour plot of the effective potential
of a two-body system due to gravity and inertia at one point in time. The Hill spheres are the circular regions surrounding the two large masses.
An astronomical body's
Hill sphere is the region in which it dominates the attraction of satellites. The outer shell of that region ... |
We need to schedule tasks. Each task must be assigned to a single time slot. Not every time slot is allowed: each task has a set of time slots where it can be executed. An example small data set is:
In addition we have a maximum of tasks that can be assigned to a single time slot (i,e, a capacity). The goal is to minim... |
Let
$(\Omega,\mathcal{A},\operatorname{P})$ be a probability space $X=(X_t)_{t\ge 0}$ be a real-valued and continuous stochastic process on $(\Omega,\mathcal{A},\operatorname{P})$ $0\le a<b$
I want to show, that $$\Omega\to\mathbb{R}\;,\;\;\;\omega\mapsto\int_a^bX_t(\omega)\;dt$$ is $\mathcal{A}$-measurable.
Since $X$ ... |
Does the mass of matter falling into a black hole affect the size of an event horizon the moment it passes through it, or when it has been incorporated into the singularity?
Indeed, as commenters already suggested, for
test particles the question of when they cross horizon (and when they are 'incorporated into singular... |
There is an approximate $SU(3)_F$ flavour symmetry that exists at the quark level between $u$, $d$ and $s$ quarks. But we often talk about an approximate isospin $SU(2)$ between up and down quark only? Why?
Both SU(3) flavor and SU(2) isospin are approximate symmetries of the Standard Model at low energies. Consider ph... |
Consider the following MWE:
\documentclass{article}\usepackage{amsmath}\begin{document}\begin{equation*} t = \frac{\dfrac{T_1}{T_2}}{1+\dfrac{Q_1}{Q_2}}\end{equation*}\end{document}
For my taste, the vertical spacing above and below the fraction line is too small. I'm aware of the various questions that have been asked... |
From (1):
Let us say we have \(n\) binary variables \(x_i\) for all \(i=1,2,…,n\) i.e., \(x_i \in \{0,1\}\) for all \(i=1,2,…,n\). I need to write the following constraint: If \(x_i=1\) and \(x_{i+2}=1\), then \(x_{i+1}=1\). In other words, the variables \(x_i\) must be consecutives.
Basically we want to prevent the se... |
According to De Boor's algorithm, a B-Spline basis function can be evaluated using the formula:
$$ B_{i,0} = \left\{ \begin{array}{ll} 1 & \mbox{if } t_i \le x < t_{i+1} \\ 0 & \mbox{otherwise} \end{array} \right. $$
$$ B_{i,p} = \frac{x-t_i}{t_{i+p}-t_i}B_{i-1,p}(x) + \frac{t_{i+p+1} - x}{t_{i+p+1}-t_{i+1}}B_{i+1,p-1}... |
This question already has an answer here:
The equation given for plane sine wave (for instance used to "derive" the Schrödinger equation) is $$ \Psi(\mathbf r,t)=\Psi_0e^{i(\mathbf k \cdot \mathbf r-\omega t)} $$
I would have assumed that it would be equal to the REAL part of this complex number, i.e. a cosine (or a ph... |
8.1. Sequence Models¶
Imagine that you’re watching movies on Netflix. As a good Netflix user you decide to rate each of the movies religiously. After all, a good movie is a good movie, and you want to watch more of them, right? As it turns out, things are not quite so simple. People’s opinions on movies can change quit... |
I am trying to solve the cubic equation $x^3-15x-4=0$ using Cardano's formula. I already know that the solutions are $x=4$, $x= \sqrt{3}-2$ and $x= -\sqrt{3}-2$ and that using the formula in this problem requires finding the cube roots of $2+11i$ and $2-11i$, which are $2+i$ and $2-i$. But when I try to use the formula... |
I'm trying to evaluate $$\int_0^{\infty}\dfrac{e^{-x}}{1+x^2}dx$$ By making the substitution $x=\tan\theta$, $$\int_0^{\infty}\dfrac{e^{-x}}{1+x^2}dx=\int_0^{\frac \pi 2}\exp(-\tan\theta)d\theta$$ So it converges to something less than $\frac \pi 2$. Is there any way to find the exact value, using only elementary metho... |
Let $p$ be an odd prime. Prove that Legendre Symbol $\left(\frac{(p-1)!}p\right)=1$ if $p\equiv1\pmod4$, $-1$ if $p\equiv3\pmod4$.
Not sure where to begin but here are my initial thoughts.
Clearly, the only way $p$ can be an odd prime is if $p\equiv1$ or $3\pmod4$. Then I see that by Legendre Symbol properties:
$\left(... |
By denoting the source coordinates with prime, I get flux through a closed surface:
$$\Phi= \displaystyle\oint_{A} \mathbf{E}(x,y,z) \cdot \mathbf{\hat{n}}\ dA =q (x',y',z')$$
And now using the formal definition of divergence:
$$\displaystyle \nabla \cdot \mathbf{E}(x,y,z)=\dfrac{d\Phi}{dV} = \dfrac{d^3\ q (x',y',z')}{... |
You can directly imply a probability distribution from a volatility skew.Note that, for any terminal probability distribution $p(S)$ at tenor $T$, we have the model-free formula for the call price $C(K)$ as a function of strike $K$\begin{equation}C=e^{-rT} \int_0^\infty (S-K)^+ p(S) dS\end{equation}Therefore we can wri... |
Problem
The problem (from [1]) is to determine where to pump gasoline (and how much) during a trip, where prices between gas stations fluctuate.
We consider some different objectives:
Minimize Cost. This results in an LP model. Minimize Number of Stops. This makes the model a MIP. Minimize Number of Stopsfollowed by Mi... |
The follow link gives an overview of most CMOS gates. Note that "AND OR Inverted" (AOI) and "OR AND Inverted" (OAI) in the link. These circuits are typically a fraction of the size it would take to create the same circuit using their discrete components. For example, a OAI33 circuit (taken from a commercial foundries s... |
@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 ... |
Hi guys I'm currently trying to solve a mock exam for an exam in a few days and am a bit confused by the solutions they gave us for this exercise:
Exercise:
A solid is composed of N atoms which are each localized at points in a lattice. Excursions about the equilibrium position of each results in each atom behaving as ... |
One complete chapter of my thesis is devoted to explaining how the variational optical flow, disparity and level-set models can be solved. In this chapter I show, step by step, how these models can be solved using different kinds of solvers (Jacobi, Gauss Seidel, Alternating Line Relaxation and Additive Operator Splitt... |
Now that I am no longer on the tablet, I can try and make some quick posts, using latex.
The Gravielectric Field Analogue
The electric field is defined as
[math]\mathbf{E} = -\nabla \phi - \frac{\partial \mathbf{A}}{\partial t}[/math]
from the usual energy density equation for an electromagnetic field, the energy is ob... |
The category of simplicial presheaves on a small Grothendieck site $\mathcal{C}$ can be given a model structure by defining weak equivalences and cofibrations sectionwise. It's called the (global) injective model structure and has a mapping space functor $Hom$, given by $Hom(X, Y)_n = hom(X\times \Delta^n, Y)$.
Using t... |
Based on my recent study and motivated by a recent paper, I have a naive question.
Consider a 2d Hubbard model for electrons at half filling $H=\sum c_k^\dagger h_k c_k+U\sum n_{i\uparrow }n_{i\downarrow }$, assuming the following facts:
(1) the noninteracting part is a Chern insulator (CI)
(2) for large enough $U(>U_c... |
Determining the image of some singular function 39 Downloads Abstract
The problem is as follows: How to describe graphically the set
T(1)(Γ) where \(T(1)(z) = \int_\Gamma {\tfrac{{d\mu (\zeta )}}{{\zeta - z}}} \) and Γ = Γ θ is the Von Koch curve, θ ∈ (0, π/4)? In this paper we give some expression permitting us to com... |
Given SPD matrix $$A \in \mathbb{R}^{N \times N} $$ and positive diagonal matrix $$D \in \mathbb{R}^{N\times N}.$$ What is then spectrum of the product $$D^TAD.$$ Is there a closed-form relationship between spectra of $A, D$ and that of the product? Or at least can we find bounds of it?
E.g., one can see that if $D = \... |
Quantum Computation Preliminaries- Hilbert Spaces (Part 2)
Here is a LaTeX version of this tutorial, which will be easier to read.
Linear_Algebra.pdf
(186.05K)
Number of downloads: 46
In this tutorial, we continue introducing mathematical preliminaries necessary to discuss quantum computation. The goal of this tutorial... |
The halting problem states there is no algorithm that will determine if a given program halts. As a consequence, there should be programs about which we can not tell whether they terminate or not. What are the simplest (smallest) known examples of such programs?
A pretty simple example could be a program testing the Co... |
I came across the following (solved) problem in my textbook:
The Henry's law constant for $\ce{O2}$ dissolved in water is $\pu{4.34 \times 10^4 atm}$ at $\pu{25 ^\circ C}$. If the partial pressure of oxygen in air is $\pu{0.4 atm}$, calculate the concentration (in terms of molarity, $\pu M$) of dissolved oxygen in wate... |
1. One-Hot Encoding
As we mentioned before, we could use one-hot encoding for categorical data:
pandas.get_dummies or
sklearn.preprocessing.OneHotEncoder.
Here is an examples.
2. Structured Data
Structured means result can alter by changing the order, such as text, speech, image, links, etc.
2.1 Bag-of-Words (BoW) Repr... |
The question might at first sight sound like the answer is trivially "yes", so let me clarify the question a bit. Consider given a nonnegative Radon measure $\mu$ on $\mathbb{R}^n$. Let $\mathcal{D}(\mathbb{R}^n)$ denote the space of real test functions, that is, the space of infinitely differentiable functions with co... |
Dear Dean, Dear All,
This is hopefully the last (4th) edition of my answer. I spend few hours in calculations which could be dismissed would I think a bit before doing them. I believe that now I understand what happens and what most of you probably knew before.
First of all, there exists no canonical construction $K\ma... |
The equation of motion for the density matrix of a many body isolated quantum system is the von Neumann's equation: $\dot{\rho }(t)=i[\rho (t),H]$. How about the equation of motion for the reduced density matrix of one particle, is there a general procedure to obtain it?
There are a number of schemes that have been dev... |
The trivial answer is no, as promise problems cannot be (by definition) in NP, and thus cannot be NP complete. The basic complexity classes e.g. $P, NP$ refer only to decision problems.
However, if you want to relate your promise problem to the standard classes, you can say it is NP-hard in the sense that if it can be ... |
I am trying to prove that we cannot use the definition of the Riemann integral as
$$ \int_{a}^{b} f(x) dx = \lim_{n \rightarrow \infty} S_n $$ using the Dirichlet function. I don't know if my reasoning makes sense when I say we cannot use it as the definition because the values are not unique:
By the definition of the ... |
Given a Hamiltonian of the form
$$H=\sum_k \begin{pmatrix}a_k^\dagger & b_k^\dagger \end{pmatrix} \begin{pmatrix}\omega_0 & \Omega f_k \\ \Omega f_k^* & \omega_0\end{pmatrix} \begin{pmatrix}a_k \\ b_k\end{pmatrix}, $$
where $a_k$ and $b_k$ are bosonic annihilation operators, $\omega_0$ and $\Omega$ are real constants a... |
I have a problem with the transition from quantum relativistic wave equations (specifically Klein-Gordon equation) to QFT, since a lot of assumptions seem implicit. For example I have a problem with the time evolution operator, which is crucial on deriving the perturbative expansion $-$ the main tool in QFT I believe. ... |
We can assume WLOG that $\bar x=\bar p=0$ and $\hbar =1$. We don't assume that the wave-functions are normalised.
Let$$\sigma_x\equiv \frac{\displaystyle\int_{\mathbb R} |x|\;|\psi(x)|^2\,\mathrm dx}{\displaystyle\int_{\mathbb R}|\psi(x)|^2\,\mathrm dx}$$and$$\sigma_p\equiv \frac{\displaystyle\int_{\mathbb R} |p|\;|\ti... |
I'm reading A First Course In Dynamics, chapter about Lipschitz continuity.
There is an example I can't understand.
The function $ f(x) = \sqrt x $ defines a contraction on $ [1, \infty) $. To prove this, we show that for $ x \geq 1 $ and $ t \geq 0 $ we have $ \sqrt {x + t} \leq \sqrt x + t/2$.
Why is this enough to p... |
Erdős’s Work on the Sum of Divisors Function and on Euler’s Function
Part of the Bolyai Society Mathematical Studies book series (BSMS, volume 25)
Chapter
Abstract
The following notation will be used throughout
r xis the rtimes iterated logarithm of x,
ψ is Euler’s constant, \(\alpha _0 = \log \Pi _p \;prime\;(1 - \fra... |
I have a PDE that I solve in
MATLAB over a 2D domain using the "recommended workflow", i.e. the functions
descg,
createpde and so on. The solver (
solvepde) works and return a solution which looks reasonable. So far so good.
Now I want to take the result and calculate various integrals on it over the whole domain. Main... |
17 2 Summary I am wondering at the striking similarity between the expressions for creation/annihilation operators in terms of position and momentum operators and the expressions for sine and cosine in terms of the exponential.
Hello everyone,
I have noticed a striking similarity between expressions for creation/annihi... |
This tutorial walks through an example of how to implement ADMM on a blockchain, and complements my Devcon3 talk. Github repository is here
Goal: Use a smart contract to coordinate decentralized optimization¶
This can model federated machine learning or federated optimization problems
We will use the Alternating Direct... |
Problem statement
Given \(n\) points with their distances \(d_{i,j}\), select \(k\) points such that the sum of the distances between the selected points is
maximized[1].
A simple MIQP (Mixed-Integer Quadratic Programming) model is:
Non-convex MIQP Model \[\begin{align} \max & \sum_{i \lt j} \color{darkblue} d_{i,j} \c... |
Content – Forms of energy
Electromagnetic energy is a form of energy that is reflected or emitted from objects in the form of electrical and magnetic waves. The energy carried by an electromagnetic wave is proportional to the frequency of the wave. The wavelength and frequency of the wave are connected via the speed of... |
Let's assume we have a normal distribution $X\sim \mathcal{N}(\mu,\sigma^2)$. In a normal distribution the quantile can be calculated as follows:
\begin{equation} \Phi_X ^{-1}(p)=\mu +\sigma {\sqrt {2}}\operatorname {erf} ^{-1}(2p-1) \end{equation}
If we want to calculate the value in the future of a stock we map it as... |
To clarify you must be talking about the optimal exercice boundary for the
American Put. Consider an American put with maturity $T$ and let $B(t)$ be the optimal exercise boundary as a function of time $t$.
Let $dt$ be a small time step. Let $S$ be the stock price at time $T-dt$ and assume that it is
optimal to early e... |
Science Advisor
Gold Member
2,224 1,256 Summary Wigner's friend seems to lead to certainty in two complimentary contexts Summary:Wigner's friend seems to lead to certainty in two complimentary contexts
This is probably pretty dumb, but I was just thinking about Wigner's friend and wondering about the two contexts invol... |
[−][src]Module curve25519_dalek:: backend:: vector only.
feature="simd_backend" and (target feature
avx2 or target feature
avx512ifma)
Vectorized implementations of field and point operations, using a modification of the 4-way parallel formulas of Hisil, Wong, Carter, and Dawson.
These notes explain the parallel formul... |
\(L\)-series for elliptic curves¶
AUTHORS:
Simon Spicer (2014-08-15) - Added LFunctionZeroSum class interface method Jeroen Demeyer (2013-10-17) - Compute L series with arbitrary precision instead of floats. William Stein et al. (2005 and later) class
sage.schemes.elliptic_curves.lseries_ell.
Lseries_ell(
E)¶
An ellipt... |
Some mathematicians distinguish between theorems, lemmas, and corollaries.
Though they are all statements that require proofs, the difference between them is their intention.
Theorems are considered to be important. The appearance of the word theorem is the equivalent of drawing a circle around the subsequent statement... |
This is a followup to my previous question here.
Let $G = \operatorname{GL}_n(F)$ for $F$ a $p$-adic field. Let $Z$ be the center of $G$, and let $f: G \rightarrow \mathbb{C}$ be a function which is locally constant and compact modulo $Z$.
This means that there exists a compact set $\Omega \subseteq G$ such that $\{ g ... |
Consider the function $f: \mathbb R \rightarrow \mathbb R$ defined by
$$f(x)=\begin{cases}x & x\neq 1,2\\ 2 &x=1\\ 1 &x=2\end{cases}.$$
That is $f$ is the identity except it swaps $1$ and $2$. Then $f$ is Borel and bijective and maps countable dense sets to countable dense sets, since if $D \subset \mathbb R$ is a dens... |
I am trying to prove the Euclidean algorithm for ordinals. More specifically: For any ordinals $\alpha, \beta$ where $\beta >0$, there are unique $\gamma, \delta$ such that $\alpha = \beta\gamma+\delta$ and $\delta<\beta$.
For now, I have difficulties. For example, I am not sure what to do when, $\alpha$ is a limit ord... |
So my question is: is Pauli-repulsion a phenomenon that has also not
yet been explained in terms of any of the three other forces that we
know of?
$\def\ket#1{|#1\rangle} \let\up=\uparrow \let\dn=\downarrow \def\PD#1#2{{\partial#1\over\partial#2}}$There is no repulsion and no unexplained force. I would also add that PE... |
I am currently studying turing computability and related problems such as the halting problem with a background in formal languages.
I know that the class of recursive (decidable) languages is a closure under union, intersection and complement, and that recursively enumerable languages (semi-decidable) are a closure un... |
Type spaces of newforms¶
Let \(f\) be a new modular eigenform of level \(\Gamma_1(N)\), and \(p\) a prime dividing \(N\), with \(N = Mp^r\) (\(M\) coprime to \(p\)). Suppose the power of \(p\) dividing the conductor of the character of \(f\) is \(p^c\) (so \(c \le r\)).
Then there is an integer \(u\), which is \(\opera... |
I have only one return for calculating sharp ratio. As you know, we should calculate standard deviation of returns and standard deviation of one item is 0. Suppose that the single return is 0.1 and the risk less return is 0.2. How can I calculate sharp ratio for these two inputs?
closed as off-topic by Ric, LocalVolati... |
How many photons does a free electron (in sunlight say) interact with per second?
I did a rough calculation assuming the electron interacts with any photon that enters through an area the size of the Thomson cross-section, and that the light is monochromatic with angular frequency 2x10^14 Hz and electric field of 1000 ... |
UPDATE
This answer raised some controversy, which I believe comes from the fact I didn't properly define what I mean by energy. In this post, whenever I say energy I refer to
the canonical/Hilbert definition of the energy-momentum tensor, i.e., the functional derivative of the Lagrangian with respect to the metric. In ... |
Duality is a very pervasive and important concept in (modern) mathematics. See Encyclopedia of Mathematics for a list.
Two mathematical objects $A$ and $B$ form a dual pair if there is a mapping $\beta: A \times B \mapsto \mathbb{F}$ from their direct product $A \times B$ to a scalar field $\mathbb{F}$ that preserves s... |
Perimeter of a Regular Polygon Inscribed in a Circle Radius r
\[n\]sides is inscribed in a circle of radius
\[r\], with the vertices of the polygon touching the circle.
From the centre of the circle lines are drawn to each vertex, and
\[n\]triangles are formed. The angle of each triangle at the centre of the circle is
... |
I want to show that the Haar functions in $L^2([0,1])$ forms an orthonormal basis:
Let $$f = 1_{[0, 1/2)} - 1_{[1/2,0)} \ \ \mbox{,} \ \ f_{j,k}(t) = 2^{j/2}f(2^jt - k).$$ Let $\mathscr{A} = \{(j.k) : j \geq 0, k = 0, 1, 2, ..., 2^j -1\}.$ I can prove that $\ A := \{1_{[0,1]}\} \cup \{f_{j,k}: (j,k) \in \mathscr{A}\}$ ... |
If a particle moves along a path $\gamma : I\subset \mathbb{R}\to \mathbb{R}^3$ then the work done by a force $\mathbf{F}$ is defined by
$$W = \int_{\gamma} \mathbf{F} = \int_{I}\mathbf{F}(\gamma(t))\cdot \gamma'(t) dt.$$
If $\mathbf{F}$ happens to be the total force, then we can use Newton's second law to prove that
$... |
Before I begin let me pause to observe that there is a slight
lie in the following words (and, more or less, in the entire undegraduate curriculum) that one discovers when one gets very mathematically involved; right now it's present in this Wikipedia article as "subtleties of the unbounded case"... our "Hermitian" ope... |
I have a question on the following exercise from S. Shreve: Stochastic Calculus for Finance, I:
Exercise 4.2. In Example 4.2.1, we computed the time-zero value of the American put with strike price $5$ to be $1.36$. Consider an agent who borrows $1.36$ at time zero and buys the put. Explain how this agent can generate ... |
Yes, one can define $BP\Delta_i^P$. Indeed, for any class $\mathcal{C}$ one can define $\mathsf{BP} \cdot \mathcal{C}$ as $L \in \mathsf{BP} \cdot \mathcal{C}$ iff there is a language $L' \in \mathcal{C}$ such that
$$ x \in L \Rightarrow (x,y) \in L' \text{ for at least 2/3 of the $y$ of length } \leq poly(x) $$
$$ x \... |
Is there an example of an eigenfunction of a linear time invariant (LTI) system that is
not a complex exponential? Justin Romberg's Eigenfunctions of LTI Systems says such eigenfuctions do exist, but I am not able to find one.
All eigenfunctions of an LTI system can be described in terms of complex exponentials, and co... |
The following exercises don't have answers in Practical Signal Processing by Mark Owen. What is the author looking for here? A mathematical proof?
2.1 A cosine wave of frequency f is sampled at $t = n\times 1 / f_{s}$ where $n$ is the sample number (an integer) and $f_{s}$ is the sample rate. Verify that $\cos2\pi ft =... |
Andrea Mori has given you a counterexample, so I'll try to comment on your attempted argument.
It looks like you have shown that if $P_1 \leq G_1$ and $P_2 \leq G_2$, then $P_1 \times P_2 \leq G_1 \times G_2$. Let's see what happens when we try to prove the converse.
Suppose $H \leq G_1 \times G_2$. We aim to find $P_1... |
I am totally confused between ODEs which I am familiar with, and differential algebraic equations (DAE) and Algebraic Differential Equations (ADE). Are they the same but just different names or what is the key difference between them (their nature and solution methods). Thanks and best regards
At least one difference i... |
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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 ... |
How to find all roots of an equation in Matlab? I tried and it gave me just one of the roots.
For example: my equation is $F(x)=0$ where
F(x) = (cos(7*x)).*exp(-2*x.^2).*(1-2*(x.^2))
Computational Science Stack Exchange is a question and answer site for scientists using computers to solve scientific problems. It only t... |
Fix $n\geq 2$ and let $S_n$ be the symmetric group on $n$ letters with identity $e$. We consider elements of $S_n$ to be bijections $[n]\to [n]$ as well as sequences (one line notation). For $1\leq i<n$, let $s_i$ be the transposition exchanging $i$ and $i+1$. Consider the following algorithm that successively construc... |
Introduction¶
Decision Trees are commonly described as being Classifiers(Regressors) that greedily search for the best division of the Input Space into exhaustive, mutually exclusive hyper-rectangles, returning as a prediction the most frequent class(mean value of the regressand) in the respective hyper-cube that a new... |
Consider the Born-Infeld Lagrangian, page 30 of Born-Infeld Action and Its Applications by Cong Wang.
$L_{BI} = \sqrt{\det (1+ F)}$ where $F_{\mu \nu} = \partial_\mu A_\nu - \partial_\nu A_\mu$. I am trying to derive the EOM as done here. However I coudn't follow several steps. I am uncomfortable with the author treati... |
It is logical, once you consider the matrix notation that your formula will be translated into internally. In the matrix, the non-constant predictors will be translated into (one or more) columns, and the intercept will be translated into a column consisting entirely of ones.
For instance, in R you would write a very s... |
In the first of my links one sees the surjective isometry between real or complex $(1,3)$ signature Minkowski space and the real or complex (respectively) span of Pauli matrices to be given as, $V_\mu \mapsto V_{\alpha \dot{\alpha}} = V^\mu \sigma _{\mu \alpha \dot{\alpha}}$ using the standard Pauli matrices.
In refere... |
14 0 Homework Statement A yo-yo is placed on a conveyor belt accelerating ##a_C = 1 m/s^2## to the left. The end of the rope of the yo-yo is fixed to a wall on the right. The moment of inertia is ##I = 200 kg \cdot m^2##. Its mass is ##m = 100kg##. The radius of the outer circle is ##R = 2m## and the radius of the inne... |
An abelian group is the same thing as a module over the ring $\mathbb{Z}$ (think about it). The ring $\mathbb{Z}$ is a PID, thus submodules of free $\mathbb{Z}$-modules are free. Reformulated in the context of abelian groups, submodules of free abelian groups are free abelian. You can use this fact to show that every a... |
I have a book that says the Moon's orbit is [in this context assumed to be] circular. The Earth does no work on the moon. The gravitational force is perpendicular to the motion. Why is there no work done if support force is perpendicular to the motion?
As explained by SchrodingersCat, mathematically work is proportiona... |
Problem statement
Given \(n\) points with their distances \(d_{i,j}\), select \(k\) points such that the sum of the distances between the selected points is
maximized[1].
A simple MIQP (Mixed-Integer Quadratic Programming) model is:
Non-convex MIQP Model \[\begin{align} \max & \sum_{i \lt j} \color{darkblue} d_{i,j} \c... |
Wikipedia only lists two problems under "unsolved problems in computer science":
What are other major problems that should be added to this list?
Rules:
Only one problem per answer Provide a brief description and any relevant links
Theoretical Computer Science Stack Exchange is a question and answer site for theoretica... |
For a latin square (LS) of order $n$, we will define a
(or maybe cut general transversal, I don't know whether there is an entrenched name for this) as a collection of $n$ cells such that no two share the same row or column.
Call the number of different symbols of such a cut its
. Thus a $n$-cut, i.e. a cut of rank $n$... |
I didn't have time to write this before but I found an answer. Here is what I did:
Let $O$ be the original $PDA$. We will construct a new $PDA$, call it $M$ ($M$ stands for modified).
To find the complement of $O$, we can flip final states to be non-final states and vice-versa. It is the same procedure as for finite au... |
Loan balance vs time principal or loan balance at Interest rate Loan term Loan product, important parameter which fully specifies a loan Repayment rate (dollars per time) Fraction of loan term Fraction of payment to interest Fraction of initial payment to interest; like Total payment to interest Sum of all payments Ove... |
Apple’s recently introduced Mac Pro features a distinctive pattern of holes on the front grill. I’m not likely to own one anytime soon (prices for a well configured machine approach a new car), but that pattern is very appealing, and re-creating it is a fun exercise.
The best clue about the pattern comes from this page... |
(HP65) Factorial and Gamma Function
10-21-2017, 08:32 AM (This post was last modified: 10-26-2017 05:10 AM by Gamo.)
Post: #1
(HP65) Factorial and Gamma Function
Just noticed that HP 65 cannot calculate decimal Factorial and HP67 app for Android also cannot do it.
Here is a handy program using Stirling's approximation ... |
If you have 2 ions of equal but opposite charge, will the force between them be larger in a vacuum and smaller in water? Would this be because the relative permittivity of water is greater than 1 (around 80)? Also, what does this mean for the interaction energy? Would an interaction be larger in vacuum? I am trying to ... |
Use the definition of the derivative to find $f'(x)$ if $f(x) = \frac{3}{x^{0.5}+2} , x>0$
To begin with the definition is $$f'(x) = \lim_{h \rightarrow 0}\frac{f(x+h)-f(x)}{h}$$
Thus, this is what I have so far,
$$f'(x) = \lim_{h\rightarrow0} \frac{f(x+h)-f(x)}{h}= \lim_{h\rightarrow0} \frac{\frac{3}{(x+h)^{0.5}+2} - ... |
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02/2018
Phys. Rev. Lett. 120 (2018) 202007 A search for the narrow structure, $X(5568)$, reported by the D0 Collaboration in the decay sequence $X \to B^0_s \pi^\pm$,...
Physics - High En... |
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I've come across the polynomial algorithm that solves 2SAT. I've found it boggling that 2SAT is in P where all (or many others) of the SAT instances are NP-Complete. What makes this problem different? What makes it
so easy (NL-Complete - even easier than P)?
I've come across the polynomial algorithm that solves 2SAT. I... |
The problem (let me call it
$s$-$t$-prime-connectivity) is in P; more precisely, it is NL-complete.
NL-hardness is clear: we can reduce plain $s$-$t$-connectivity to $s$-$t$-prime-connectivity just by making sure that every vertex has a self-loop. Then, if there is any path from $s$ to $t$, there are paths of arbitrary... |
This is a paraphrasing of a statement from
Data Mining by Witten et al., 4th edition, on section 1.6.
Consider the set $S = \{1, \dots, 288\}$.
A
rule is defined as a one-element singleton set whose element is from $S$, e.g., $\{1\}$, $\{2\}$, etc.. The question: how many sets with no more than $14$ rules can be create... |
What is the computational complexity of multiplication in a Carnot group ?
A Carnot group is a real nilpotent Lie group $N$ whose Lie algebra $Lie(N)$ admits a direct sum decomposition Background:
$$Lie(N) = V_{1} + ... + V_{m}$$
such that $[V_{i}, V_{j}] \subset V_{i+j}$ if $i+j \leq m$, otherwise $[V_{i} , V_{j}] = 0... |
Difference between revisions of "Output Feedback"
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\end{aligned}
\end{aligned}
</amsmath></center>
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−
is said to be ''observable'' if we can determine the state of the system through measurements of the input <
+
is said to be ''o... |
What exactly would happen depends on a lot of factors. For instance, you cannot quite assume perfect spherical symmetry of the Earth, and how exactly this symmetry is broken changes the outcome. Also, if the black hole is as massive as the Earth (and thus 9 mm in size), half of the planet's material is suddenly attract... |
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Change to browse by: References & Citations Bookmark(what is this?) Astrophysics > Solar and Stellar Astrophysics Title: RW Dor: A G-type shallow contact binary with new orbital period investigation
(Submitted on 2 Apr 2018 (v1), last revised 26 Dec 2018 (this version, v2))
Abstract:... |
My desired placement would be or between the last two ticks or in place of the second last tick. For units, this function isn't existing yet, but at least it is possible to define the units separately as part of the
\usepgfplotslibrary{units}. Maybe in future this will be possible to define their placement.
For the tic... |
Michael's answer is fine, but here is a more in-depth analysis.
We want to look at the connected components of the graph whose vertices are the reals and where there is an arrow from $x$ to $y$ when $y = f^2(x) = x^2-2$.
It is clear that $f$ has to send connected components to connected components, so that given one co... |
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