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Although the title is about Lie algebras, the question body mentions Lie groups, and my answer will deal more with these. As mentioned in other answers, Lie groups show up frequently in geometry as groups of symmetries of geometric objects. For example, given a manifold $M$ we can sometimes find a Lie group $G$ that ac... |
The climate of Earth has been roughed up quite a bit last century. But it has no idea what it's got coming with this portal of yours. Earth turns into Venus.
Update: As R.M. pointed out, the amount of energy is not 'maybe a long term thing', it's the Major Issue. This has been fixed now. How much water are we talking?
... |
For the following exercises, draw a graph of the functions without using a calculator. Use the 9-step process for graphing from Class Notes and from the section 4.5 text.
The answers here are just the graph (step 9). Your solutions should have all steps with the information (intervals of incr/decr, local max/min, etc) ... |
This is the spin-off of the question I previously asked.
First, let me remind you some notation from that question:
$G_0$ - compact, simply connected Lie group giving rise (by complexification) to a semi-simple Lie Group $G$
$\mathfrak{g}$ - Lie algebra of $G$
$\delta=\frac{1}{2}\sum_{\alpha>0}\alpha$ (summation over a... |
Skills to Develop
Identify rational numbers and irrational numbers Classify different types of real numbers
be prepared!
Before you get started, take this readiness quiz.
Identify Rational Numbers and Irrational Numbers
Congratulations! You have completed the first six chapters of this book! It's time to take stock of ... |
[pstricks] [Fwd: Re: binom_distribution] John Campbell jcdotcalm at shaw.ca Mon Apr 17 17:45:54 CEST 2006 Thank you very much. I did not realize that there was a new version of
pst-func.tex. I will update; thanks again.
J. Campbell
----- Original Message -----
From: "Herbert Voss" <LaTeX at zedat.fu-berlin.de>
To: "Gra... |
The groups of monotonically increasing and monotonically decreasing functions have some special properties. A
monotonically increasing function is one that increases as \(x\) does for all real \(x\). A monotonically decreasing function, on the other hand, is one that decreases as \(x\) increases for all real \(x\). In ... |
Journal of Commutative Algebra J. Commut. Algebra Volume 9, Number 3 (2017), 387-412. Lattice-ordered abelian groups finitely generated as semirings Abstract
A lattice-ordered group (an $\ell $-group) $G(\oplus , \vee , \wedge )$ can naturally be viewed as a semiring $G(\vee ,\oplus )$. We give a full classification of... |
This is the question i would like to discuss, properly stated.
Given a model $M$ for a collection of set theory axioms (ZFC, for example), list all basic modal formulas $\phi$ such that $M\Vdash \phi$ and $\nVdash \phi$ (that is, $\phi$ is valid on the basic modal frame $M$, and $\phi$ is not a formula valid in the cla... |
Let $A$ be a commutative ring, $B$ (resp. $C$) be a commutative $A$-algebra endowed with a valuation $v$ (resp. $w$), not necessarily of rank 1. Assume that $v$ and $w$ induce equivalent valuations on $A$. How to construct a valuation $u$ on $B\otimes_A C$ extending $v$ and $w$?
Without loss of generality, we may assum... |
Preprints (rote Reihe) des Fachbereich Mathematik Refine Year of publication 1996 (2) (remove)
276
Let \(a_1,\dots,a_n\) be independent random points in \(\mathbb{R}^d\) spherically symmetrically but not necessarily identically distributed. Let \(X\) be the random polytope generated as the convex hull of \(a_1,\dots,a_... |
Answer
Percent of Total is 10%. Degrees of a Circle is $36^\circ$.
Work Step by Step
$percent = \frac{part}{whole}\times100$ $percent = \frac{546}{5460}\times100=\frac{1}{10}\times100=10$ A complete circle is $360^\circ$. Find 10% of $360^\circ$. $part = percent \times whole$ $0.10\times360=36$ |
Claim: No, there is no such $\mu$.
Proof: We give an infinite sequence of AVL trees of growing size whose weight-balance value tends to $0$, contradicting the claim.
Let $C_h$ the complete tree of height $h$; it has $2^{h+1}-1$ nodes.
Let $S_h$ the
Fibonacci tree of height $h$; it has $F_{h+2} - 1$ nodes. [1,2,TAoCP 3]... |
We studied
differentials in Section 4.4, where Definition 18 states that if \(y=f(x)\) and \(f\) is differentiable, then \(dy=f'(x)dx\). One important use of this differential is in Integration by Substitution. Another important application is approximation. Let \(\Delta x = dx\) represent a change in \(x\). When \(dx\... |
Hey everyone do you sense anything different? Well the Project Euler counter breezed from 166 to 175 in these one or two days, and it's like I can reach 200 or 225 without much difficulty. The main reason is that a new difficulty rating is out (it may not be new for you if you visit the site frequently though), and we ... |
This question sparked from a long discussion in chat about the nature of $\ce{H2O2}$ and whether that molecule can be considered to rotate around the $\ce{O-O}$ axis (and hence display axial chirality) or not.
Considering two rather clear cases:
Ethane is considered to rotate freely around the $\ce{C-C}$ bond. The acti... |
We've all learned at school that the earth was a sphere. Actually, it is more nearly a slightly flattened sphere - an oblate ellipsoid of revolution, also called an oblate spheroid. This is an ellipse rotated about its shorter axis. What are the physical reasons for that phenomenon?
Normally in the absence of rotation,... |
Property AP: A discrete group $\Gamma$ has property AP (Approximation Property) if there exists a net $(\phi_i)_{i \in I}$ of finitely supported functions on $\Gamma$ such that $\phi_i \to 1 $ weak$^*$ in $B_2(\Gamma)$ i.e $w(\phi_i) \to w(1)$ for every $w \in Q(\Gamma)$.
A wanted to know, if anything is known in the l... |
Diffraction-limited system
The resolution of an optical imaging system – a microscope, telescope, or camera – can be limited by factors such as imperfections in the lenses or misalignment. However, there is a fundamental maximum to the resolution of any optical system which is due to diffraction. An optical system with... |
Linear Momentum
Linear momentum is the product of the mass and velocity of an object, it is conserved in elastic and inelastic collisions.
Learning Objectives
Calculate the momentum of two colliding objects
Key Takeaways Key Points Like velocity, linear momentum is a vector quantity, possessing a direction as well as a... |
I'm trying to convert some English statements to first order logic statements and I'm trying to use Prolog to verify the translations. My question is: how do I convert a first order logic statement (having $\forall$ and $\exists$ quantifiers) into Prolog rules?
For example, there's this English statement:
Every voter v... |
The Annals of Probability Ann. Probab. Volume 20, Number 2 (1992), 801-824. Limit Theorems for Random Walks Conditioned to Stay Positive Abstract
Let $\{S_n\}$ be a random walk on the integers with negative drift, and let $A_n = \{S_k \geq 0, 1 \leq k \leq n\}$ and $A = A_\infty$. Conditioning on $A$ is troublesome bec... |
In this note, we produce a proof of Taylor’s Theorem. As in many proofs of Taylor’s Theorem, we begin with a curious start and then follow our noses forward.
Is this a new proof? I think so. But I wouldn’t bet a lot of money on it. It’s certainly new to me.
Is this a groundbreaking proof? No, not at all. But it’s cute,... |
What works
If you nest the definition of the fixpoint on lists inside the definition of the fixpoint on trees, the result is well-typed. This is a general principle when you have nested recursion in an inductive type, i.e. when the recursion goes through a constructor like
list.
Fixpoint size (t : LTree) : nat :=
let s... |
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1. Steiner symmetry in the minimization of the first eigenvalue in problems involving the p-Laplacian
Proceedings of the American Mathematical Society, ISSN 0002-9939, 08... |
1) If $$z = \frac{ \left\{ \sqrt{3} \right\}^2 - 2 \left\{ \sqrt{2} \right\}^2 }{ \left\{ \sqrt{3} \right\} - 2 \left\{ \sqrt{2} \right\} }$$ find $\lfloor z \rfloor$.
2) Find all $x$ for which $$\left| x - \left| x-1 \right| \right| = \lfloor x \rfloor.$$ Express your answer in interval notation.
3) Which positive rea... |
875 17 1. Homework Statement
Suppose that the number of asbestos particles in a sam-
ple of 1 squared centimeter of dust is a Poisson random variable
with a mean of 1000. What is the probability that 10 squared cen-
timeters of dust contains more than 10,000 particles?
2. Homework Equations
[tex] E(aX+b) = aE(X) + b[/t... |
What precisely is a scalar autonomous differential equation? I'm confused about what this precisely means, more so because we did not discuss this in any lectures nor is it, as far as I can tell, defined in the notes. I've tried looking it up as well, but I couldn't find anything, only specific examples. It occurs in t... |
I'm very confused about calculating solubility.
Everything is in temperature of $298\ \mathrm K$
From Atkins's book, exercise 16.83:
Based on solubility constant, calculate solubility of $\ce{Al(OH)3}$ in acid solution of $\mathrm{pH}=4.5$, $K_{\rm s}=1\cdot10^{-33}$.
Using stoichiometry and equilibrium constants I pro... |
Casel, Katrin; Fernau, Henning; Khosravian Ghadikolaei, Mehdi; Monnot, Jerome; Sikora, FlorianExtension of vertex cover and independent set in some classes of graphs and generalizations. International Conference on Algorithms and Complexity (CIAC) 2019
We study extension variants of the classical problems Vertex Cover ... |
Let $X_n$ be a sequence of independent random variables (but not necessarily identically distributed) taking values in $[-1,1]$ that have the following property:
1) The average $A_n := \frac{(X_1+ \ldots + X_n)}{n} $ converges in probability to $0$, i.e. for every $\epsilon >0 $, the probability that $|A_n| > \epsilon ... |
Answer
$$\frac{\cos\theta+1}{\tan^2\theta}=\frac{\cos\theta}{\sec\theta-1}$$ The equation has been verified to be an identity.
Work Step by Step
$$\frac{\cos\theta+1}{\tan^2\theta}=\frac{\cos\theta}{\sec\theta-1}$$ We would deal with the right side first, taking $\sec\theta=\frac{1}{\cos\theta}$ $$\frac{\cos\theta}{\se... |
We have not yet verified the power rule, $\ds{d\over dx}x^a=ax^{a-1}$, for non-integer $a$. There is a close relationship between $\ds x^2$ and $\ds x^{1/2}$—these functions are inverses of each other, each "undoing'' what the other has done. Not surprisingly, this means there is a relationship between their derivative... |
AP Statistics Curriculum 2007 Infer 2Means Dep From Socr
(→Paired vs. Independent Testing)
(→Paired vs. Independent Testing)
Line 154: Line 154:
: \(T_o = {\overline{x}-\overline{y} - \mu_o \over SE(\overline{x}+\overline{y})} \sim T(df=17)\)
: \(T_o = {\overline{x}-\overline{y} - \mu_o \over SE(\overline{x}+\overline{... |
Consider a standard setting for the development of the theory of distributions. Let $D(\Omega)$ be the space of test functions and $D'(\Omega)$ be the space of distributions ("generalized functions").
Can $\langle f,g\rangle$ be given a sensible definition for all $f,g\in D'(\Omega)$? Of course, $\langle f,\phi\rangle$... |
Elastic and inelastic 19.8 GeV/c proton-proton collisions in nuclear emulsion are examined using an external proton beam of the CERN Proton Synchrotron. Multiple scattering, blob density, range and angle measurements give the momentum spectra and angular distributions of secondary protons and pions. The partial cross-s... |
Question: Is there a condition on an object $x$ of an $(\infty,2)$-category $\mathcal C$ which is equivalent to $x = Z(pt_+)$ for a unique TFT $Z$ from the $(\infty,2)$-category of framed bordisms where we only allow $2$-cobordisms for which the incoming and outgoing boundary of every component is non-empty. Remark: if... |
1. Use the inductive definition of an to prove that \((ab)^{n} = a^{n}b^{n}\) for all nonnegative integers \(n\).
2. Give an inductive definition of \(\bigcup\limits_{i=1}^{n}S_{i}\) and use it and the two set distributive law to prove the distributive law \(A \cap \bigcup\limits_{i=1}^{n}S_{i} = \bigcup\limits_{i=1}^{... |
Set in present day New York City, an unknown spacecraft of alien origin expelled millions of micro blackholes each with the mass of a grape in the earth atmosphere. I like to know what happens if these millions of micro blackholes were to fall on building structures such as skyscrapers, would it trigger an extinction l... |
11:00 AM to 12:30 PM
CSB 480
Cindy Xiong, Northwestern University
Your visual system can crunch vast arrays of numbers at a glance, providing the rest of your brain with critical values, statistics, and patterns needed to make decisions about your data. But that process can be derailed by biases at both the perceptual ... |
This is joint work with Thomas Hulse, Chan Ieong Kuan, and Alex Walker, and is a another sequel to our previous work. This is the third in a trio of papers, and completes an answer to a question posed by our advisor Jeff Hoffstein two years ago.
We have just uploaded a preprint to the arXiv giving conditions that guara... |
Solvers for ordinary differential equations (ODEs) belong to the best-studied algorithms of numerical mathematics. An ODE is an implicit statement about the relationship of a curve $x:\mathbb{R}_{\geq 0}\to\mathbb{R}^N$ to its derivative, in the form $x'(t) = f(x(t),t)$, where $x'$ is the derivative of curve, and $f$ i... |
[exer:4.2.1] A thermometer is moved from a room where the temperature is \(70^\circ\)F to a freezer where the temperature is \(12^\circ F\). After 30 seconds the thermometer reads \(40^\circ\)F. What does it read after 2 minutes?
[exer:4.2.2] A fluid initially at \(100^\circ\)C is placed outside on a day when the tempe... |
Some people make a habit of occasionally visiting Wikipedia’s front page and following hyperlinked phrases down a rabbit hole of articles. I do a similarly thing with Andries Brouwer’s tables of strongly regular graphs, which leads to a cascade of papers, checking BCN and computing stuff in Sage. How does that happen e... |
Trivial forgery: If you know the CRC polynomial, then you can add (‘xor’) any multiple of it to the message without changing the CRC.
Short answer.If the hardware can only evaluate CRCs with fixed polynomials determined by the hardware designer, it's of little use to you for making a MAC. If you can choose the polynomi... |
I am currently working on the following Problem:
Imagine you are given a $d$-ary tree $T_d$, which means an infinite tree with one vertex $x_0$ on top and in which each vertex has $d$ children.
Next, I'm assigning iid random variables $\omega_e$ to all edges $e$ in the graph. Here $\omega_e$ should follow an exponentia... |
EditI realized that the key piece of information that I need is question 1, and so I'd like to rephrase this post:
What are the possible eigenvalues of nonnegative integer matrices?
Any answer to this question would be appreciated and checkmarked.
Original Question:
My question is related to this question about integer... |
In the rectangular coordinate system, the definite integral provides a way to calculate the area under a curve. In particular, if we have a function \(y=f(x)\) defined from \(x=a\) to \(x=b\) where \(f(x)>0\) on this interval, the area between the curve and the x-axis is given by
\[A=\int ^b_af(x)dx. \nonumber\]
This f... |
I'll give you the numbers. I'm breaking this up into 3 different terms. There's atmospheric drag, what I'll call the "hover" term, and the gravitational potential climb. I will more or less assume a flight directly up. You're welcome to use whatever term for velocity you want, as none of them will be representative. I'... |
My machine learning textbook states the following when discussing second-order Taylor series approximations in the context of Gradient descent:
The (directional) second derivative tells us how well we can expect a gradient descent step to perform. We can make a second-order Taylor series approximation to the function $... |
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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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Journal of Cellular Physiology, ISSN 0021-9541, 05/2016, Volume 231, Issue 5, pp. 1163 - 1170
Unloading induces bone loss and causes disuse osteoporosis. However, the mec... |
Section 4.7 Fitting Exponential Models to Data
In the previous section, we saw number lines using logarithmic scales. It is also common to see two dimensional graphs with one or both axes using a logarithmic scale.
One common use of a logarithmic scale on the vertical axis is to graph quantities that are changing expon... |
Problem: To prove the $\textsf{NP-Completeness}$ of the problem of "Packing Squares (with different side length) into A Rectangle", $\textsf{3-Partition}$ is reduced to it, as shown in the following figure.
In the $\textsf{3-Partition}$ instance, there are $n$ elements $(a_1, \cdots, a_i, \cdots, a_n)$. The target sum ... |
My favourite one: $[0, 1]$ is compact, i.e. every open cover of $[0, 1]$ has a finite subcover.
Proof: Suppose for a contradiction that there is an open cover $\mathcal{U}$ which does not admit any finite subcover. Thus, either $\left[ 0, \frac{1}{2} \right]$ or $\left[ \frac{1}{2}, 1 \right]$ cannot be covered with a ... |
Definition:Continuous Mapping (Topology)/Point/Open Sets
Jump to navigation Jump to search
Definition
Let $T_1 = \left({S_1, \tau_1}\right)$ and $T_2 = \left({S_2, \tau_2}\right)$ be topological spaces.
Let $f: S_1 \to S_2$ be a mapping from $S_1$ to $S_2$.
Let $x \in S_1$.
For every neighborhood $N$ of $f \left({x}\ri... |
2019-09-04 12:06
Soft QCD and Central Exclusive Production at LHCb / Kucharczyk, Marcin (Polish Academy of Sciences (PL)) The LHCb detector, owing to its unique acceptance coverage $(2 < \eta < 5)$ and a precise track and vertex reconstruction, is a universal tool allowing the study of various aspects of electroweak an... |
There is also a really nice proof using what is called reductio ad absurdum (or infinite regress), which can also be framed as a simple contradiction using the minimality property of the natural numbers.
Suppose WLOG (without loss of generality) that $$\sqrt3=\frac{u}{v}$$ for $u,v\in\mathbb{N}$ relatively prime (any p... |
Tags: beer, homebrew, northernbrewer
I’ve been brewing my own beer for roughly a year. I have a lot of my own equipment, and I’m borrowing some from a friend while I acquire the rest. I just started my fifth batch tonight, a darkish ale with above average alcohol content called Winter Warmer.
I get my supplies from Nor... |
When modeling engineering systems, it can be difficult to identify the key parameters driving system behavior because they are often buried deep within the model. Analytical models can help because they describe systems using mathematical equations, showing exactly how different parameters affect system behavior.
In th... |
I remember arriving at the following equality: $$\lim_{n\to\infty}\sum_{k=n}^{\infty}\left(\frac{1}{n\left\lfloor\frac kn\right\rfloor}-\frac1k\right)=\gamma$$ where $\gamma$ denotes the Euler-Mascheroni constant. However, I cannot find back where I wrote its proof, and I am now having a hard time reconstructing it. I ... |
(sorry in advance for my english. Im not sure my terminology is correct)
I'm trying to solve a problem: Let $e_1$ , $e_2$ , $e_3$ be a base of $C^3$ (3-D vectors with complex elements). Let $A(g)e_i=e_{g(i)}$ be a representation of the symmetric group $S_3$ ($g\in S_3$). Also let $V=\{z_1,z_2,z_3\in C^3|z_1+z_2+z_3=0\}... |
Physicist and spy Klaus Fuchs has expressed the opinion that Born's rule (squared complex amplitudes are interpreted as probabilities or probability densities) could be derived from something deeper. I think that this wishful thinking is demonstrably impossible. Why? We just don't have any method or theorem in mathemat... |
DISCLAIMER: Very rough notes from class. Some additional side notes, but otherwise barely edited.
These are notes for the UofT course PHY2403H, Quantum Field Theory, taught by Prof. Erich Poppitz.
Determinant of Lorentz transformations
We require that Lorentz transformations leave the dot product invariant, that is \( ... |
This question already has an answer here:
I am confused why we can introduce differentials into an integral when performing an integration by substitution.
Consider the integral $$\int \frac{1}{ x \sqrt{1-x} } dx.$$ We can perform the substitutions $$x=\sin^2u,$$ $$dx=2\sin u \cos{u} du ,$$ on the integral to give $$\i... |
There seems to be two different meanings of mathematical logic. One is "Classical Logic, Intuitionistic Logic, etc" and another "Set theory, Model Theory, Recursive Theory, etc (http://en.wikipedia.org/wiki/Mathematical_logic). Then, Theory is a somewhat mixture of one from the one class, and one from another class. Am... |
Xypic offers many placement and formatting options for labels, including rotation.
However, I can't get this last feature to work correctly.
I have two problems with this:
with some inclinations the label won't be correctly shifted sideway (see the downleft arrow below) with some inclinations the label won't be correct... |
Can a planet, star or otherwise have a magnetic field that is stronger or have more range than its gravity?
Let's look at the proper magnetic force (as opposed to the Lorentz force on a
moving, charged object described in @KenG's answer) on a specimen $S$ of magnetized material with mass $M_S$ as a way to try to compar... |
Here's a very simple method: Find the largest number below $2^n$ that is a safe prime. Use standard primality tests for $p$ and $q = (p - 1)/2$. For example, $2^{2048} - 1942289$ is the largest safe prime below $2^{2048}$.
But you didn't specify what you want this for. If you want to use this with Diffie–Hellman to res... |
Gold Member
525 92
It's been a long time since my last exam on QM, so now I'm struggling with some basic concept that clearly I didn't understand very well.
1) The Sch. Eq for a free particle is ##-\frac {\hbar}{2m} \frac {\partial ^2 \psi}{\partial x^2} = E \psi## and the solutions are plane waves of the form ##\psi(x... |
The answer is
no, of course.
Consider, for instance, the following languages:
$L_1 = \{ \langle M \rangle \# \langle M \rangle \mid \, \text{$M$ is a TM which does not halt on input $\langle M \rangle$} \}$ $L = \{ \langle M \rangle \# \langle M \rangle \mid \, \text{$M$ is a TM} \}$ $L_2 = L \cup \{ \langle M \rangle ... |
Assume that a matrix $\mathbf{R}$ of size $N\times N$ is given such that $r_{i,j} \ge r_{i,j+1}$ for any $i$ and $j$, where $r_{i,j}$ is the $i$th row and $j$th column element of $\mathbf{R}$.
I will solve the following problem: $$ \begin{array}{cl} \displaystyle \max_{K_i, i=1,\ldots,N} & \displaystyle f(K_1,\ldots,K_... |
We want to understand the integral
$\displaystyle \int_{-\infty}^\infty \frac{\mathrm{d}t}{(1 + t^2)^n}. \ \ \ \ \ (1)$
Although fattybake mentions the residue theorem, we won’t use that at all. Instead, we will be very clever.
We will do a technique that was once very common (up until the 1910s or so), but is much les... |
Let the binary relation computed by a nondeterministic transducer be the relation between input strings and the possible output strings the transducer can produce (and accept) for the given input string.
It is easy to see that the nondeterministic transducers using polynomial time can compute different binary relations... |
Answer
$29^\circ$
Work Step by Step
The measure of an inscribed angle of a circle is one-half the measure of its intercepted arc, thus $\angle B=\frac{1}{2}\overset{\frown}{AC}$.
You can help us out by revising, improving and updating this answer.Update this answer
After you claim an answer you’ll have
24 hours to send... |
In physics, the wave function is a mathematical function $\psi: \mathbb{R}^3 \to \mathbb{C}$. In the discussion of
fermions and bosons we can talk about how the wave function behave under the interchange of two particles. There are two fundamental cases:
$$ \psi(x,y) = \pm \psi(y,x)$$
If there is a "+" we get bosons, i... |
I must say I find it odd (and a bit worrisome) that one can find textbooks whereby you learn the definition of a Banach algebra (and even a Banach *-algebra) without seeing examples that are not $C^*$-algebras. There is more to life than $B(H)$...
Anyway, some commutative examples which are naturally algebras of functi... |
According to WolframAlpha, $i^i=e^{-\pi/2}$ but I don't know how I can prove it.
Write $i=e^{\frac{\pi}{2}i}$, then $i^i=(e^{\frac{\pi}{2}i})^i = e^{-\frac{\pi}{2}} \in \mathbb{R}$. Be careful though, taking complex powers is more... complex... than it may appear on first sight $-$ see here for more info.
In particular... |
There is a certain pattern to learning mathematics that I got used to in primary and secondary school. It starts like this: first, there are only positive numbers. We have 3 apples, or 2 apples, or maybe 0 apples, and that’s that. Sometime after realizing that 100 apples is a lot of apples (I’m sure that’s how my 6 yea... |
Hi.
On Wednesday at 9:05 CET / 8:05 UCT you can participate in the GYM version of the finals of 2017-2018 Russian Olympiad in Informatics (ROI), Day 1. And on Thursday there will be day 2, same time.
5 hours, 4 problems, IOI-style scoring with subtasks. Statements will be available in three languages: English, Russian,... |
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Now showing items 1-5 of 5
Forward-backward multiplicity correlations in pp collisions at √s = 0.9, 2.76 and 7 TeV
(Springer, 2015-05-20)
The strength of forward-backward (FB) multiplicity correlations is measured by the ALICE detector in proton-proton (pp) collisions at s√ = 0.9, 2.76 and 7 TeV. The measurement... |
That was an excellent post and qualifies as a treasure to be found on this site!
wtf wrote:
When infinities arise in physics equations, it doesn't mean there's a physical infinity. It means that our physics has broken down. Our equations don't apply. I totally get that
. In fact even our friend Max gets that.http://blo... |
This is only a comment about classes of rings in which
no counter-examples can be found.
Since a one-dimensional GCD domain is a Bézout domain [1, Corollary 3.9], GCD domains will not provide any counter-example.
We will show that Dedekind domains will not provide any counter-example either. To do so, we will use the f... |
The usual simple algorithm for finding the median element in an array $A$ of $n$ numbers is:
Sample $n^{3/4}$ elements from $A$ with replacement into $B$ Sort $B$ and find the rank $|B|\pm \sqrt{n}$ elements $l$ and $r$ of $B$ Check that $l$ and $r$ are on opposite sides of the median of $A$ and that there are at most ... |
2019-09-04 12:06
Soft QCD and Central Exclusive Production at LHCb / Kucharczyk, Marcin (Polish Academy of Sciences (PL)) The LHCb detector, owing to its unique acceptance coverage $(2 < \eta < 5)$ and a precise track and vertex reconstruction, is a universal tool allowing the study of various aspects of electroweak an... |
Convert from Decimal Notation to Scientific Notation
Remember working with place value for whole numbers and decimals? Our number system is based on powers of 10. We use tens, hundreds, thousands, and so on. Our decimal numbers are also based on powers of tens—tenths, hundredths, thousandths, and so on.
Consider the nu... |
Rocky Mountain Journal of Mathematics Rocky Mountain J. Math. Volume 46, Number 2 (2016), 559-570. An application of Cohn's rule to convolutions of univalent harmonic mappings Abstract
Dorff et al.~\cite {do and no} proved that the harmonic convolutions of the standard right half-plane mapping $F_0=H_0+\overline {G}_0$... |
65 4 1. Homework Statement
This isn't exactly a problem but rather a problem in understanding the derivation of the phenomenon, or more precisely, one step in the derivation.
In the following we will consider the EPR pair of two spin ##1/2## particles, where the state can be written as
$$ \vert \psi\rangle =\frac{1}{\s... |
Equivalence of Definitions of Normal Extension Contents Theorem
Let $L / K$ be an algebraic field extension.
Let $L / K$ be a field extension.
Then $L / K$ is a
normal extension if and only if: for every irreducible polynomial $f \in K \left[{x}\right]$ with at least one root in $L$, $f$ splits completely in $L$.
Let $... |
Is there an algorithm for finding the shortest path in an undirected weighted graph?
All-Pairs-Shortest Path
Given a graph $G = (V, E)$ find the shortest path between
any two nodes $u,v \in V$. It can be solved by Floyd-Warshall's Algorithm in time $O(|V|^3).$ Many believe the APSP problem requires $\Omega(n^3)$ time, ... |
This question prompted a reformulation:
What is a really good example of a situation where keeping track of isomorphisms leads to tangible benefit?
I believe this to be a serious question because it actually is oftentimes a good idea casually to identify isomorphism classes. To bring up an intermediate-level example I'... |
In this question we are interested in the number of limit cycles which appear in the following perturbational system:
\begin{equation}\cases{ x'=y -x^{2}+\epsilon P(x,y) \\ y'=-x+\epsilon Q(x,y) } \end{equation} where $P$ and $Q$ are polynomials of degree n. The unperturbed system (i.e, $\epsilon=0$) is not a Hamiltoni... |
This is a post for my math 100 calculus class of fall 2013. In this post, I give the 4th week’s recitation worksheet (no solutions yet – I’m still writing them up). More pertinently, we will also go over the most recent quiz and common mistakes. Trig substitution, it turns out, is not so easy.
Before we hop into the de... |
[Click here for a PDF of this post with nicer formatting]
Many authors pull the definitions of the raising and lowering (or ladder) operators out of their butt with no attempt at motivation. This is pointed out nicely in [1] by Eli along with one justification based on factoring the Hamiltonian.
In [2] is a small excep... |
I have come across the following deceptively simple expression:
$$ H_n^s=\sum_{j=1}^n(-1)^{j-1}\left(\begin{array}{c}n\\j\end{array}\right)j^{-s} $$
We have (using eg mathematica, though probably not difficult to prove): $H_n^0=1$, $H_n^1=H_n$ (the harmonic numbers), expressions involving hypergeometric series with uni... |
A vector is a quantity consisting of a non-negative magnitude and a direction. We could represent a vector in two dimensions as \((m,\theta)\), where \(m\) is the magnitude and \(\theta\) is the direction, measured as an angle from some agreed upon direction. For example, we might think of the vector \( (5,45^\circ)\) ... |
The use of superscripts and subscripts is very common in mathematical expressions involving exponents, indexes, and in some special operators. This article explains how to write superscripts and subscripts in simple expressions, integrals, summations, et cetera.
Contents
Definite integrals are some of the most common m... |
Phosphoric acid has basicity of 3 i.e it can loose 3 $\ce{H+}$ while phosphorous acid has basicity of 2. Why is phosphorous acid more acidic than phosphoric acid? Acidity refers to the ability to liberate protons. Phosphoric acid liberates more protons than phosphorous acid (as the basicity of phosphoric acid is 3 and ... |
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Hello, I propose this problem to the Brilliant community. Hope you enjoy it! This problem was one of the questions in Olympiads.
What is the remainder obtained of the long division x81+x49+x25+x9+xx3−x\large \dfrac{x^{81}+x^{49}+x^{25}+x^{9}+x}{x^3-x}x3−xx81+x49+... |
We have seen how to create, or derive, a new function $f'(x)$ from a function $f(x)$, summarized in the paragraph containing equation 2.1.1. Now that we have the concept of limits, we can make this more precise.
Definition 2.4.1 The derivative of a function $f$, denoted $f'$, is $$f'(x)=\lim_{\Delta x\to 0} {f(x+\Delta... |
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